plane thermoelastic waves in infinite half-space caused operational research in engineering sciences: theory and applications vol. 5, issue 2, 2022, pp. 176-189 issn: 2620-1607 eissn: 2620-1747 doi: https://doi.org/10.31181/oresta190822135u * corresponding author. anilutku@munzur.edu.tr (a. utku), semakayapinar@munzur.edu.tr (sema k.k) deep learning based a comprehensive analysis for waste prediction anıl utku1, sema kayapinar kaya2* 1 department of computer engineering, munzur university, tunceli, turkey 2* department of industrial engineering, munzur university, tunceli, turkey received: 14 may 2022 accepted: 27 july 2022 type of paper abstract: in its simplest definition, waste can be defined as any substance that is used, not needed and causes harm to the environment. waste management covers control activities such as prevention of the formation of waste, reuse, separation according to its characteristics and type, storage, transportation, recycling and disposal. the main purpose of waste management is to leave a livable world to future generations, to create a sustainable environment, to protect natural resources, to save energy and costs, to reduce the rate of pollution and the amount of hazardous waste. in today's world where urbanization and industrialization rates are increasing, waste management is gaining importance. the aim of this study is to utilize waste data from istanbul, turkey's largest and fastest growing city, to estimate waste amount using a constructed long short-term memory (lstm) based deep learning model. the developed lstm-based model has been compared in practice with k-nearest neighbors (knn), random forest (rf), support vector machine (svm), multi-layered perceptron (mlp) and gated recurrent unit (gru). as a result of the comparative and comprehensive analyzes, the experimental results showed that the developed lstmbased deep learning method is more successful in the waste prediction problem than the other compared models. key words: waste management, deep learning, machine learning, long short-term memory 1. introduction municipal solid waste (msw) is presently one of the most pressing concerns in urban planning. msw creation has accelerated as a consequence of global urbanization, population increase, and massive material consumption. along with processes such as urbanization and urban transformation, the amount of municipal rubbish generated is increasing. the volume of msw, one of the most significant byproducts of an civil lifestyle, is increasing even faster than the growth of urbanization as the globe rushes towards an urban future. today, msw generation has grown to deep learning based a comprehensive analysis for waste prediction 177 almost 3 billion residential per day, resulting in 1.2 kg of waste per person/day (1.3 billion tonnes). by 2025, this number is expected to rise to 4.3 billion urban communities, producing 1.42 kg/capita/day of municipal solid and around 2.2 billion tons per year (hoornweg & perinaz, 2012). due to the large quantity of generated waste, an increasing amount of msw can cause severe damage to the environment and population health (huang et al. 2020). msw management remains one of the best most tough problems for developing country governments to address to safeguard the environment and reduce public health risks. (younes et al. 2016; towa et al. 2020) and to maintain natural resources. to minimize the adverse effects of msw, an accurate prediction of future waste volumes is a crucial issue. efficient predicting of msw generation is vital to the implementation of an optimum msw management system as a primary tool for msw management. fu et al. (2015). waste quantity predictions serve as the foundation for waste management process adoption, development, and optimization (cubillos, 2020). incorrect prediction of waste amounts can adversely affect process costs and cause systems to be inefficient. another of the main challenges in using prediction models in waste management is the high variability and ambiguity of data wastage. the amount of waste produced can be affected by unpredictable factors such as people's behaviors, holidays, seasonal conditions. the volatile nature of waste data can cause problems in generating future forecasts. in addition, insufficient and incomplete data will reduce the accuracy of the predictions to be made. in recent years, significant studies on waste prediction using statistical modelling techniques, including machine learning (ml), have been presented (abbasi et al. 2013; abbasi & hanandeh, 2016; johnson et al. 2017; ghanbari et al. 2021). the application of deep learning models to prediction issues has risen to prominence as high-performance data processing and computer power have advanced. deep learning is a kind of ml that uses numerous layers of artificial neural networks to learn nonlinear interactions. it differs from typical ml approaches in that it allows for the learning of nonlinear relationships (le et al. 2019). due to the approaches' ability to understand common uncertainty and learn from long-term patterns, deep learning methods have proved to be a valuable technique for waste prediction and modelling. the deep learning (dl) has recently become popular in municipal waste generation (sakr et al. 2016; adedeji & wang, 2019; akanbi et al. 2020). in particular, lstm models have proved to be successful in waste prediction problem, the efficiency of the forecasts is strongly dependent on the volume of historical waste dataset utilized to train the methods (cubillos, 2020). in this study, a waste management model, which reduces cost and environmental damage, has been developed by using deep learning. waste prediction enables efficient management of waste storage, logistics and disposal processes. it directly affects the ecosystem from factors such as waste management, climate change and air pollution. therefore, it is very important to make accurate waste predictions. the growing quantity of solid waste generated by municipalities, as well as its disposal, has been one of turkey's substantial environmental issues, particularly in istanbul (turan et al. 2009). istanbul has a population of over 15 million people, or roughly 19% of turkey's overall population. istanbul generates an average of 18,000 tons of domestic waste every day. mw is collected regularly from different locations of the city by the istanbul environmental management industry and trade cooperation (istac) company. nearly 22,000 tons of mw have been compiled utku et al./oper. res. eng. sci. theor. appl. 5 (2) (2022) 176-189 178 annually with the most advanced technological tools and specific outfits. in this study, it is aimed to predict the amount of waste produced by using the waste data in istanbul, turkey's largest and most developed city. the dataset used consists of the daily waste amounts in istanbul, recorded for approximately 6 years between january 1, 2016 and october 31, 2021. the developed lstm-based model has been compared in practice with knn, rf, svm, mlp and gru. experimental results obtained according to mse (mean squared error), rmse (root mean squared error) and mae (mean absolute error) metrics for each model have been compared. to our knowledge, no other study has used a deep learning model for predicting istanbul's msw generation. the rest of the paper is presented as follows: the literature studies on waste prediction are covered in section 2, which presents state-of-the-art methods for predicting and forecasting municipal waste. data description and implementation of deep neural learning models are also presented in section 3. experimental results of the proposed lstm model development and a comparison of metrics for several ml techniques are given in section 4. lastly, the discussion and conclusion are presented in sections 5. 2. literature review a diverse variety of prediction studies on waste generation rates have been studied by many researchers. many different methods, such as traditional models, regression analysis, time series analysis, and artificial intelligence are some of the approaches utilized for waste prediction (lavee & khatib, 2010; abbasi et al. 2013). the capacity to efficiently learn both linear and non-linear connections among time series and good prediction ability are two of those approaches' key benefits over traditional time series methods. recently, ml algorithms have been employed successfully to predict waste generation (xu et al. 2021). to predict waste generation using svm combined with partial least square (abbasi et al. 2013), a gradient boosting model (johnson et al. 2017), two hybrid models based on decision trees and neural network was applied to predict canada wide municipal waste generation svm and rf (kumar et al. 2018), a hybrid model based on svm and recurrent neural network (meza et al. 2019), gaussian process regression (gpr) model tuned by bayesian optimization (ceylan, 2020), prediction model using four combination intelligent algorithms, namely svm, an integrated artificial neural network (ann), rf, and multivariate adaptive regression splines (mars) models (ghanbari et al. 2021), decision tree and rf approach (joshi et al., 2021). among numerous nonlinear methods, ann is one of the effective non-linear models to predict msw generation. ann could produce high-accuracy nonlinear estimation thanks to its intelligent learning method and hierarchical design. it has been successfully used in msw prediction (kannangara et al. 2018; coşkuner et al. 2021; abbasi et al. 2013; jahandideh et al. 2009; nguyen et al. 2021; wu et al. 2020). recently, the dl algorithms, a subset of ml algorithms, have recently shown huge success in a wide range of disciplines (lecun et al. 2015; kaya & yıldırım, 2020). deep learning allows models to construct hierarchical representations of incoming information with varying degrees of complexity. as a result, it can expose the complex structure of targeted information, enhancing pattern identification and deep learning based a comprehensive analysis for waste prediction 179 classification capabilities (lecun et al. 2015). one of the most important qualifications of deep learning architecture is that it can learn feature representations automatically, which saves time and effort. the rapid growth of deep learning can be attributed to improved chip processing capabilities, significant breakthroughs in ml algorithms, and the relatively low cost of computing hardware (coşkun et al. 2017). recently, dl approach has been widely used in waste generation at municipal level. sakr et al. (2016) presented a combined convolution neural network (cnn) and svm classification that categorized waste into 3 types: plastic, paper, and metal. they concluded that svm had an accuracy of classification of 94.8 percent, while cnn only had an accuracy of 83 percent. svm also demonstrated outstanding adaptability to various waste types. adedeji and wang (2019) suggested a new various waste classification system based on the 50-layer remaining net pre-train cnn model, which is a machine learning tool that is designed as an extractor, and svm, which classifies waste into different groups/types such as glass, metal, paper, and plastic, among others. akanbi et al. (2020) employed multi-layer deep learning architecture to create a computational tool for estimating the amount of construction materials and building demolition waste. cubillos (2020) implemented a multi-site lstmnn to anticipate garbage generation rates from residences. according to their results, lstm model can successfully developed the results by 85% on average when compared to classical ml methods such as arima. wang et al. (2021) proposed a cnn to categorize waste into nine different garbage categories such as kitchen, other, plastic, glass, paper or cardboard, metal, fabric, and other recyclable waste. furthermore, data exchange between garbage containers and the waste management point has been taken from the internet of things (iot) sensors embedded in garbage containers. 3. data analysis istanbul, which straddles the bosporus strait and is in both europe and asia, has a population of over 15 million people, comprising nearly 19% of the total population, istanbul is the most populated city in europe and the fifteenth most crowded metropolis on the globe. istanbul is the most populated city in europe, and the world’s fifteenth-largest city. it is located on the bosporus strait, between the black sea and the marmara sea, in turkey's northwest corner. istanbul, turkey is positioned at 41.015 latitude and 28.979 longitude. istanbul, turkey is in the urban place class of the turkey country, with gps coordinates of 41° 0' 54.493" n and 28° 58' 46.30" e. an average of 18,000 tons of household waste is generated daily in istanbul. approximately 5 thousand tons of household waste have been transported by district municipalities and 13 thousand tons by istanbul environmental management industry and trade cooperation (istaç) transport fleet to solid waste transfer stations located on istanbul asian side and european sides. istaç operates with a total of 8 thousand tons’ solid waste landfill on the european and asian sides of istanbul, given in fig. 1. utku et al./oper. res. eng. sci. theor. appl. 5 (2) (2022) 176-189 180 figure 1. istanbul waste network’s structure due to the population growth in istanbul, the amount of waste is constantly increasing due to the increase in residential areas. municipal waste collected from houses and workplaces is collected and separated by district municipalities. transfer stations have been put into operation due to the cost and time consuming of direct transportation of the waste collected by the district municipalities to the landfills. in this way, fuel savings are achieved by eliminating the commuting of small-capacity municipal waste collection vehicles to landfills over long distances, traffic density is reduced; and possible air pollution caused by exhaust emissions is prevented. then, the waste is brought to the sanitary landfills by transport trucks from the transfer stations. 3.1. dataset in this study, an original statistical dataset consisting of daily waste amounts produced in istanbul, recorded for approximately 6 years between jan. 1, 2016 and oct. 31, 2021, has been used. the dataset used consists of 2131 lines of waste data. the dataset contains the parameters of date and amount of waste produced. the first 10 rows of the dataset used are given in figure 1. fig. 2a shows the time distribution of the waste amounts in the dataset. figure 2. municipal waste amounts in the dataset deep learning based a comprehensive analysis for waste prediction 181 the distribution of the amount of waste produced over time is given in fig.2b. in addition, fig. 2c shows the average amount of municipal solid waste produced between 2016 and 2021. 3.1. developed deep learning based waste prediction model in this study, popular ml and deep learning models, that are widely used in the literature, such as knn, rf, svm, mlp, gru and lstm, are compared in practice. the dataset has been pre-processed before the models have been applied. possible blank or incorrect fields in the dataset have been checked. after the data pre-processing step, training, validation, and test datasets have been selected. 80% of the dataset is split into training and 20% testing. 10% of the training data has been split for validation. validation data has been used for the optimization of model parameters. for predictions to be made on time series data using machine learning and deep learning, it is necessary to structure the time series data as a supervised learning problem. for y to represent output and x to represent inputs, time series data needs to be converted to input-output prefixes y=f (x) using a function f. in supervised learning problems, it is expected to be possible to predict future data using past observation data. in supervised learning problems, it is to predict the value at time t by using the observation data at t-3, t-2 and t-1 time steps. in this study, using a 3dimensional sliding window structure, the observation data at t-3, t-2 and t-1 time steps are configured as inputs and the observation value at time t as an output. in this way, time series data is transformed into a supervised learning problem. it is aimed to select the most suitable model parameters using validation data. using the obtained parameters, the models have been created, and waste amounts have been predicted. the algorithm of the developed system is presented below: figure 3. the algorithm of the developed system utku et al./oper. res. eng. sci. theor. appl. 5 (2) (2022) 176-189 182 deep learning models are artificial neural network models with complex architectures that aim to learn complex functions in high dimensions by making nonlinear transformations from input data to output data. lstm is an advanced version of recurrent neural networks that stands out from other deep learning models. the main difference between rnn and lstm is the retention time of information. lstm is more advantageous than rnn because lstm can process information in memory longer than rnn. lstm cells retain cell states that have been read from and written to them. based on the input and cell state values, the 4 gates regulate read, write and output to cell state. the developed lstm based model is represented in fig. 4. figure 4. developed lstm-based deep learning model lstm stands out over other deep learning models because of its success in remembering long-term dependencies. in this study, the developed lstm-based deep learning model is compared with knn, rf, svr, mlp and gru in practice. the developed deep learning model takes daily waste data as input and produces the predicted amount of waste as output. the developed lstm based prediction model consists of an input layer, two lstm layers, a dense layer and an output layer. in this study, it is aimed to optimize the parameters of the developed model. the time series data converted into a supervised learning problem structure is presented as an input to the lstm. with parameter analysis studies, it is aimed to reach the highest prediction accuracy with parameters such as the number of layers, the number of neurons, the number of epochs and the batch size. adam has been used as the optimizer. deep learning based a comprehensive analysis for waste prediction 183 3.2. experimental results in this study, a dataset consisting of daily waste amounts produced in istanbul, recorded for approximately 6 years between january 1, 2016 and october 31, 2021, has been used. the dataset contains the parameters of date and amount of waste produced. the developed lstm-based deep learning model was compared against models such as knn, rf, svm, mlp, and gru. mse, rmse and mae values obtained for each model have been analyzed comparatively. the is represents the actual value of the waste amount at time t. the is the predicted waste amount at time t. the error value is calculated by . scale-dependent metrics are effective when comparing different methods on the same dataset. commonly used scale-dependent metrics are mae and mse metrics. the mae metric is the mean of the errors as seen in eq. (1). (1) mae is the difference between the predicted values and the actual values. it is the mean of the absolute value of each difference between the actual value and the predicted value for that sample across all samples of the dataset. mse metric has been calculated by mean of the squares of errors as seen in eq. (2), and the rmse has been calculated by the square root of the mean of the squares of error as seen in eq. (3). (2) (3) walk forward validation has been used in the applied models to eliminate the overfitting problem and improve the generated models' quality. all applied models have been run 10 times, and the average of the obtained results has been taken. the dataset used consists of 2131 lines of waste data. 80% of this data is split for training and 20% for testing. after the training/test split, 1704 lines of data have been used in the training and 427 rows of data have been used in the testing. table 1 and fig. 5 show the average mse, rmse and mae results obtained for each model. utku et al./oper. res. eng. sci. theor. appl. 5 (2) (2022) 176-189 184 table 1. experimental results for each model according to the mse, rmse and mae model mse rmse mae knn 1756420233222.19 1325300.05 978735.43 rf 1756605384968.68 1325369.90 978556.77 svm 1722543245603.30 1312456.95 972004.19 mlp 1700317575744.18 1303962.26 932025.24 gru 1672888061407.19 1293401.74 930672.17 lstm 1670468166123.95 1292465.92 930325.64 the experimental results show that the average mse values of knn, rf, svm, mlp, gru and lstm are 1756420233222.19, 1756605384968.68, 1722543245603.30, 1700317575744.18, 1672888061407.19, 1670468166123.95, respectively. the average rmse values of knn, rf, svm, mlp, gru and lstm are 1325300.05, 1325369.90, 1312456.95, 1303962.26, 1293401.74, 1292465.92, respectively. the average mae values of knn, rf, svm, mlp, gru and lstm are 978735.43, 978556.77, 972004.19, 932025.24, 930672.17, 930325.64, respectively. figure 5. comparative experimental results according to mse, rmse and mae experimental results showed that lstm is more successful in waste prediction than knn, rf, svm, mlp and gru. the lstm's superior performance over other models is due to its architecture, which incorporates unique units in addition to the regular units found in the gru. fig. 6 shows the prediction results of lstm on the test data. deep learning based a comprehensive analysis for waste prediction 185 figure 6. prediction results of lstm as seen in fig. 6, the data marked in blue shows the test data, and the data marked in red shows the prediction values. the test dataset consists of 427 rows of data, that is, the amount of waste produced for 427 days. on the real data, the developed lstm based prediction model shows a successful pattern. it is seen that svm is more successful in waste prediction than knn and rf. svm requires less computation than knn and is easier to interpret but can only describe a limited set of models. also, knn can find very complex patterns, but its output is more difficult to interpret. both algorithms work better on categorical data. knn is resistant to noisy training data and is effective in the case of a large number of training samples. rf works with a mixture of numerical and categorical features. rf is advantageous when features are of various scales. as a result, rf can utilize the data as is. svm maximizes the distance between different points and calculates the distance between points. in the classification problem, rf gives the probability of belonging to the class, while svm gives the points closest to the boundary between classes. since the features in the data are numerical, svm performed better than rf and knn. svm generally has higher prediction accuracy than mlp. svm is usually better at prediction as there are advanced computations such as translating n-dimensional space using kernel functions. neural network models require scaling of features. the numerical features in the dataset used in this study caused mlp to perform better than knn, rf and svm. as presented in fig. 2c, the average amount of waste between 2016-2021 is 17894680.5. in table 2, a comparative analysis of the mae values, which express the average error values obtained from the applied models, according to the average waste amount values is presented. utku et al./oper. res. eng. sci. theor. appl. 5 (2) (2022) 176-189 186 table 2. failure rates of applied models according to average waste amount and mae values model mae failure rates (%) knn 978735.43 5.46 rf 978556.77 5.46 svm 972004.19 5.43 mlp 932025.24 5.20 gru 930672.17 5.20 lstm 930325.64 5.19 table 1 shows the failure rates according to the average waste amount and mae values for the models applied. equation 4 has been used to calculate the failure rate. (4) as seen in table 1, the average waste amount and the failure value calculated according to the mae values of the models have been calculated as 5.46 % for knn, 5.46 % for rf, 5.43 % for svm, 5.20 % for mlp, 5.20 % for gru and 5.19 % for lstm. 4. conclusions the waste amount prediction problem is an important research area for waste management and recycling. excessive population growth, combined with technological improvements and industrialization, are placing increasing pressure on the environment all around the world. while the development of production and marketing activities required a more intensive use of natural resources, the wastes created as a result of this trend have reached levels that endanger the environment and human health. the goal of this research is to establish an lstm-based trash prediction model employing daily waste data. using data from istanbul's daily garbage, the constructed result was validated against knn, rf, mlp, and gru. the dataset used consists of the daily waste amounts produced in istanbul, recorded for approximately 6 years between january 1, 2016 and october 31, 2021. the experimental results show that lstm, gru and mlp models have very successful results. following these models, svm, rf and knn have been successful, respectively. the most successful results have been obtained with lstm, and the most unsuccessful results have been obtained with knn. the failure rate of lstm is 5.19% while the failure rate of knn is 5.46%. as a result of the comparative and comprehensive analyses, it has been seen that the lstm-based deep learning model is applicable to the waste prediction problem. in the literature, there are studies in which machine learning and deep learning methods are used in waste management. however, there is no successfully implemented study to predict the amount of waste produced. in this study, the waste data of istanbul, one of the largest industrial and tourist cities in the world, has been used for the first time in the literature. experimental results showed that the deep deep learning based a comprehensive analysis for waste prediction 187 learning-based prediction model can be successfully applied in industrial areas such as waste management. in future studies, more successful prediction results can be obtained by developing hybrid deep learning models. acknowledgement: we thank the editor and anonymous reviewers for their constructive comments, which helped us to improve the manuscript. references abbasi m, abduli m.a., omidvar b, baghvand a. 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(2016). landfill area estimation based on integrated waste disposal options and solid waste forecasting using modified anfis model. waste management, 55, 3–11. https://doi.org/10.1016/j.wasman.2015.10.020. © 2022 by the authors. submitted for possible open access publication under the terms and conditions of the creative commons attribution (cc by) license (http://creativecommons.org/licenses/by/4.0/). https://doi.org/10.1016/j.wasman.2008.06.004 https://doi.org/10.1016/j.wasman.2021.08.028 https://doi.org/10.1016/j.wasman.2020.04.015 https://doi.org/10.1016/j.wasman.2021.02.029 https://doi.org/10.1016/j.wasman.2015.10.020 plane thermoelastic waves in infinite half-space caused operational research in engineering sciences: theory and applications vol. 2, issue 1, 2019, pp. 27-36 issn: 2620-1607 eissn: 2620-1747 doi: https://doi.org/10.31181/oresta1901030k * corresponding author. evelin.krmac@fpp.uni-lj.si (e. krmac) bbn.djordjevic@gmail.com (b. djordjević) evaluation of the tcis influence on the capacity utilization using the topsis method: case studies of serbian and austrian railways evelin krmac, boban djordjević university of ljubljana, faculty of maritime studies and transport received: 05 february 2019 accepted: 12 march 2019 first online: 19 march 2019 original scientific paper abstract: increasing train traffic on the railway infrastructure implies the use of enlarged railway network capacity and the corresponding increase in intelligence i.e. “intelligentization” of the railway industries. the train control information system (tcis) as one of the most important railway systems with a significant impact on the overall railway performance in terms of its efficiency and influence upon the railway infrastructure capacity (ric). in this paper, the model for evaluation of the tcis influence upon the capacity utilization, based on the topsis method, is proposed as an alternative to the dea-based models. indeed, the main drawback of the dea-based models is that the dea evaluates alternatives from only one point of view and classifies them as efficient or inefficient while the topsis allows the benchmarking of the alternatives by detecting the best practices based on the ranking of the alternatives. for the purposes of this paper, the topsis based evaluation where years represent alternatives were tested through case studies of serbian and austrian railways for the period from 2006 to 2015. based on the obtained results it can be pointed out that the topsis method can be applied to evaluation and comparison of the influence of different tcis on the railway capacity (rc) utilization. key words: evaluation, train control information system, railway, capacity, multicriteria decision-making 1. introduction according to the european commission (2016) the railway is a “backbone of the eu transport system” and it is crucial when a rising demand for transport, traffic jams, fuel security, and decarbonisation are considered. nevertheless, many european rail markets are still facing stagnation and downturns (european commission, 2016), which suggests the possibility of an increase in the future rail traffic. many of the railways are already exploiting their maximum capacity, so they will have to implement certain solutions to meet the new demand. as stated in krmac and djordjević/oper. res. eng. sci. theor. appl. 2 (1) (2019) 27-36 28 (djordjević and krmac, 2018), the main challenge of many railways around the world is limited availability of capacity for all trains of their infrastructure related to topological configuration; although in some cases the capacity of infrastructure did not change despite doubling, tripling or quadrupling tracks. there are many different factors influencing the railway capacity (rc) utilization. some of the most important are timetable, signaling, nodal capacity constraints, rolling stock, infrastructure, external factors and governance. signaling, for example, is a kind of the traffic management system (tms), which is an important class of the train control information systems (tcis) that provides for safe running of trains on a given infrastructure. advanced signaling system such as the european railway traffic management system (ertms) can provide for not only a higher level of safety but also for reduction of headways and blocking time of infrastructure (melody, 2012) (krmac and djordjevic, 2017). regarding that the factors influencing efficiency of the railway capacity (rc) utilization are many and different as well as that signaling is one of the most important of them, in this paper the focus is on evaluation of the tcis influence using the topsis (technique for order of preference by similarity to ideal solution) method as an example of the mcdm (multi-criteria decision-making) techniques. the tciss were already considered in (djordjević and krmac, 2018), where the evaluation of the tcis impact on the railway utilization was performed using the dea method. in this paper, the topsis method is introduced as a new approach to evaluation and comparison of the tcis influence on the rc utilization. the application of the topsis method was performed on real data for serbian and on partially assumed data for austrian railways. the following section presents a survey of the previous papers considering analysis, measurement, evaluation and improvement of the railway capacity (rc) utilization, as well as the mcdm methods application in this field. in section 3 description of the topsis method with selection of criteria and alternatives is presented. results of the topsis method are presented in section 4. finally, in section 5 conclusions and proposals for future work are summed up. 2. literature review so far, the topic of railway capacity has been frequently discussed by researchers (bevrani, 2005). different methods for estimating the railway capacity utilization and different categorizations or classifications of these methods can be found in the referential literature (melody, 2012). recently, detailed classification of methods and approaches related to the estimation of the railway capacity utilization was presented in the referential literature by (djordjević and krmac, 2018). in their paper, methods and approaches are grouped as analytical, optimization, and simulation methods, as well as parametric ones. the factors and parameters which affect the railway capacity utilization are identified and reviewed. further, the literature review regarding the consideration of the tcis influence on the capacity consumption is also presented. moreover, (djordjević and krmac, 2018) also introduced a “new approach based on the dea method for evaluation of the tcis efficiency in improvement of the railway capacity utilization.” evaluation of the tcis influence on the capacity utilization using the topsis method: case studies of serbian and austrian railways 29 considering that the rc utilization is a multidisciplinary area, other mcdm methods for evaluation of the tcis impact on the railway capacity utilization, besides the dea method, can be applied. therefore, in this paper the introduction of the topsis method for that purpose is considered. in order to confirm the novelty of introduction of the topsis for evaluating the tcis efficiency influence on the rc utilization, the literature is reviewed regarding the application of the topsis in railway engineering. in the evaluation of high speed transport systems where high-speed rail and transrapid maglev are presented as alternatives, after determination of the importance of particular criteria using the entropy method, janic (2003) applied the topsis to the “selection of the preferable alternative (high-speed systems) under given circumstances.” the topsis method with the multilevel grey evaluation (mge) was employed by chen et al. (2014) to evaluate the overall performance of passenger transfer at large transport terminals in different alternatives through a case study on the beijing south railway station in china. zhao et al. (2018) used the topsis for the evaluation of china transportation networks. in combination with cargo rates, the topsis was used for three models of transportations i.e., railway, highway, and national road – to “synthesize the evaluation of indices and three networks” with the aim of ranking the city nodes according to their importance. the entropy-topsis method was formulated and used by huang et al. (2018) for the evaluation of operation performance of the urban rail transit system from different perspectives: operator’s, passenger’s, and government’s. the topsis method was also used for analysis of the swedish railway’s network vulnerability of multi-commodity networks with the aim to identify critical links in the network (whitman et al., 2017). bababeik et al. (2018) utilized the topsis for determination of links priorities or calculation of the links while resolving the problem of “optimal location and allocation of relief trains.” the fuzzy topsis with failure mode and effect analysis was proposed by jinbao and xing (2014) “for determination of the closeness coefficient of each failure mode of metro door fault criticality.” for measurement of a service quality of rail transit lines the fuzzy-topsis in combination with statistical analysis and trapezoidal fuzzy numbers has been adopted by (aydin, 2017). 3. methodology railway capacity and railway performance analyses often deal with multiple conflicting key indicators, what creates a high degree of complexity. the use of the mcdm can be a potential tool for solving such complexities. as an example of the mcdm methods a special dea model – i.e., a non-radial dea model has been applied krmac and djordjević/oper. res. eng. sci. theor. appl. 2 (1) (2019) 27-36 30 in (djordjević and krmac, 2018) as a tool for consideration of influence of the tcis efficiency on the railway capacity utilization. however, the authors pointed out that the dea evaluates alternatives from only one point of view and classifies them as efficient or inefficient. in order to overcome these disadvantages of the dea method, in this paper the topsis method, which enables minimization and maximization criteria simultaneously, as well as ranking of the evaluated alternatives, is proposed. based on the fact that the non-radial dea model implies some weaknesses and considers decision-making units (dmus) only from one point of view, in this paper the topsis method is introduced in order to improve the disadvantage of the dea method and consider the results of the dea method obtained in (djordjević and krmac, 2018). regarding their results of the sensitivity analysis, it can be said that the dea is not the most suitable benchmarking tool in the field of the evaluation of the tcis efficiency influence on the rc utilization. to overcome this weakness, a topsis could be applied as a mcdm method for benchmarking the alternatives by detecting the best practices based on the ranking of alternatives and on the evaluation of the tcis influence on improvement of the railway infrastructure capacity (ric). the introduction of the topsis method for evaluation of the tcis influence on the ric and ranking of alternatives was based on its benefit in terms of the simultaneous consideration of alternatives from different viewpoints i.e., both pessimistic and optimistic aspects while the dea ranking methods utilized input or output oriented aspects. 3.1 a description of the topsis method in this part of the paper, the topsis method proposed by hwang and yoon (1981) was employed as a decision-making tool to aid decision-makers (dms) in “trade-offing” all the alternatives. in the literature, this method has received much interest from researchers and practitioners that confirms a wide range of real-world applications across different fields and specific sub-areas (behzadian et al., 2012). this method is based on the assumption that the selected alternative is at the shortest possible distance from the ideal positive solution and ideal negative solution. as one of the best and most frequently used mcdm methods, it implies the overall assessment, comparison and ranking of alternatives. since the dea divides alternatives into efficient and inefficient with low total discrimination (djordjević and krmac, 2018), in this paper the aim of the topsis method is to find the best alternative i.e., to rank and solve the drawbacks of the dea method. consequently, the additional reason for selecting the topsis for evaluation of the tcis influence on improvement of the rc utilization and for ranking alternatives, is based on the content of the topsis i.e., decision-makers’ (dm) intention to rank alternatives with the best ranking score closer to the positive ideal and to have the greatest distance from the negative ideal solution, as well as the ability to consider alternatives from both pessimistic and optimistic viewpoints i.e., inputs and outputs like a cost and benefit criterion (jahantigh et al., 2013), (lotfi et al., 2011). the following steps of the topsis method, proposed by wang et al. (2014) and delgarm et al. (2016) were performed: evaluation of the tcis influence on the capacity utilization using the topsis method: case studies of serbian and austrian railways 31 step 1: forming decision matrix 𝑋 = [𝑥𝑖𝑗 ]𝑛×𝑚 𝑖 = 1,2, … , 𝑛; 𝑗 = 1,2, … . , 𝑚. within the decision matrix, the alternatives represent years for each case study (see tables 1 and 2). step 2: performing the normalization of decision matrix x in order to get normalized decision matrix 𝑅 = [𝑟𝑖𝑗 ]𝑛×𝑚 by vector normalization method that is presented as 𝑟𝑖𝑗 = 𝑥𝑖𝑗 √∑ 𝑥𝑖𝑗 2𝑛 𝑖=1⁄ (1) step 3: calculation of the weight normalized decision matrix as 𝑉 = [𝑣𝑖𝑗 ]𝑛×𝑚 = [𝑤𝑖 𝑟𝑖𝑗 ]𝑛×𝑚 , (2) where wi is a weight given to criteria from dm and sum of weights ∑ 𝑤𝑖 𝑛 𝑖=1 = 1. this method is appropriate for decision-making which is based on criteria of different importance. different weights were delegated to each criterion only for evaluation of the tcis influence in terms of the obtained ric. for each criterion weights were assigned for each case study i.e., length of railway network (c1) (w1= 0.15), number of trains (per day) (c2) (w2= 0.2), freight kilometers (c3) (w3= 0.2), passenger kilometers (c4) (w4=0.2), number of failures of whole system or its subsystem (c5) (w5=0.1), punctuality of the trains (c6) (w6=0.15). step 4: determination of positive ideal and negative ideal solutions is denoted as 𝐴+and 𝐴−, respectively. in case of the paper, 𝐴+and 𝐴− represent the best and the worst alternative, respectively, demonstrated as 𝐴+ = {(max 𝑖 𝑣𝑖𝑗 |𝑗𝜖𝐽+) , (min 𝑖 𝑣𝑖𝑗 |𝑗𝜖𝐽−) |𝑖 = 1, 2, … , 𝑛} = {𝑣1 +, … , 𝑣𝑚 + } (3) 𝐴− = {(min 𝑖 𝑣𝑖𝑗 |𝑗𝜖𝐽+) , (max 𝑖 𝑣𝑖𝑗 |𝑗𝜖𝐽−) |𝑖 = 1, 2, … , 𝑛} = {𝑣1 −, … , 𝑣𝑚 − }, (4) where𝐽+ = {𝑗1, 𝑗2, … , 𝑗𝑚1 }, 𝐽− = {𝑗𝑚1+1, 𝑗𝑚1 +2, … , 𝑗𝑚 } and 𝐽+ ∪ 𝐽− = {1, 2, … , 𝑚} are benefit and cost criteria, respectively. in this case of the topsis method application, the benefit criteria are represented by length of railway network (c1), number of trains (per day) (c2), freight kilometers (c3), passenger kilometers (c4), while the cost criteria include number of failures of whole system or its subsystem (c5), and punctuality of the trains (c6). step 5: calculation of the separation measure between each alternative by euclidean distance. the separation of each alternative from the positive ideal is given as 𝑆𝑖 + = √∑ (𝑣𝑖𝑗 − 𝑣𝑗 + ) 2𝑚 𝑗=1 , 𝑖 = 1,2, … . . , 𝑛., (5) while the separation from the negative ideal is given as 𝑆𝑖 − = √∑ (𝑣𝑖𝑗 − 𝑣𝑗 − ) 2𝑚 𝑗=1 , 𝑖 = 1,2, … . . , 𝑛. (6) krmac and djordjević/oper. res. eng. sci. theor. appl. 2 (1) (2019) 27-36 32 step 6: calculation of relative closeness 𝐴𝑖 to positive ideal solution 𝐴 + defined as 𝐴𝑖 = 𝑆𝑖 + (𝑆𝑖 + + 𝑆𝑖 −)⁄ , 0 ≤ 𝐴𝑖 ≤ 1, 𝑖 = 1, 2, … , 𝑛. (7) if 𝐴𝑖 = 1 is clear that alternative is the best, and 𝐴𝑖 = 0 than alternative is the worst. alternative is closer to the best as 𝐴𝑖 approaches 1. step 7: ranking the alternatives according to 𝐴𝑖, where a higher value of 𝐴𝑖 denotes a better solution in terms of the tcis influence on improvement of the ric. 3.2 application of the topsis method to evaluation of the tcis efficiency on the obtained ric 3.2.1 selection of criteria based on the factors that affect rc, reviewed by (djordjević and krmac, 2018), available data, and the fact that other indicators can also be used for rc description, adequate criteria for the evaluation of the tcis influence on the obtained ric were selected. the obtained railway capacity is presented based on the required capacity and spare capacity. spare capacity might absorb variations from day to day or a future traffic increase (nystrom, 2009). regarding that railway transportation can be viewed as a production process, the length of railway network (c1) and number of trains per day (c2) were selected as timetable indicators. the number of trains per day also represents one of the main indicators of the infrastructure capacity, which is related to the infrastructure availability (patra et al., 2010). as outputs of railway transportation as production process, the realized freight (tkm) kilometers (c3) and passenger kilometers (c4) (boysen, 2012) were included as criteria in the topsis method. on the liberalized railway markets higher values of c1 and c2 produce higher capacity. therefore, “capacity is the maximum amount that can be produced in relation to the limiting constraints from infrastructure, rolling stock or staff” (boysen, 2012). according to (djordjević and krmac, 2018) two more criteria were selected: criteria that is closely related to the functioning of the tcis – the number of failures of the whole system or its subsystem (c5), and criteria punctuality of the trains (c6), which is the result of system failures and is related to the infrastructure availability (patra et al., 2010). 3.2.2 selection of alternatives and case studies the second important stage of the topsis methodology is the selection of alternatives. at the beginning of the topsis method application and the analysis of the results of the model, the tcis used at serbian and austrian railways were considered as case studies. because the railways of serbia and austria are significantly different in terms of length of the network and volume of the transport, they were not compared. hence, in the study these case studies were evaluated separately while years as alternatives were jointly considered for each case study. so, the alternatives of the selected case studies represent years. for each serbian alternative real data were used. data for criteria such as number of trains (per day) and punctuality of the trains were collected from planned and realized timetables, data of the number of failures were collected from the serbian railways evidence, while realized freight and passenger kilometers and length of railway network data were extracted from serbian statistics (djordjević and krmac, 2018). evaluation of the tcis influence on the capacity utilization using the topsis method: case studies of serbian and austrian railways 33 real data for the austrian case, published by (obb, 2016), were used only for 2015 and were collected for length of railway network and number of trains (per day) while eurostat data for freight and passenger kilometers was used. however, because of missing data for number of failures and unavailability of data for other years, these data were assumed. the data for serbian case study are presented in table 1 while those for austrian case study in table 2. since the data for each case study were not collected from the same source, there is a doubt in terms of the data and results accuracy. table 1. data used for the topsis method – serbian case study alternatives/dmus serbian case c1 c2 c3 c4 c5 c6 2006 3819 1.510 684110 4232 55 40% 2007 3819 1.515 687002 4551 43 55% 2008 3819 1.502 583071 4339 38 60% 2009 3819 1.430 522033 2967 35 65% 2010 3819 1.431 521933 3522 39 60% 2011 3819 1.431 540911 3611 34 70% 2012 3819 1.430 539727 2769 23 80% 2013 3819 1.433 612495 3022 34 70% 2014 3819 1.420 452963 2988 27 80% 2015 3739 1.436 508678 3249 30 80% table 2. data used for the topsis method – austrian case study alternatives/dmus austrian case c1 c2 c3 c4 c5 c6 2006 9646* 6.327* 110778 8907 8 90%* 2007 9646* 6.329* 115526 9167 7 95%* 2008 9646* 6.345* 121579 10365 7 95%* 2009 9646* 6.332* 98887 10184 9 80%* 2010 9646* 6.340* 107670 10263 10 85%* 2011 9646* 6.340* 107587 10778 7 95%* 2012 9646* 6.339* 100452 11211 6 96%* 2013 9646* 6.330* 95449 11804 8 90%* 2014 9646* 6.335* 98281 11981 7 95%* 2015 9646 6.340 97642 12104 5 96.3% *denotes assumed data 4. results of the topsis method both the railway capacity (rc) analysis and the railway performance analysis often deal with multiple conflicting key performance indicators (kpis) (bevrani, 2015). these complexities can be a subject of the mcdm. as the main mcdm method krmac and djordjević/oper. res. eng. sci. theor. appl. 2 (1) (2019) 27-36 34 in our case, the topsis method, which enables minimization and maximization criteria simultaneously as well as ranking of evaluated alternatives, is proposed. therefore, the topsis method with both viewpoints i.e., pessimistic and optimistic is used in order to evaluate and rank alternatives. moreover, in this paper, the topsis is employed with the aim of checking the results of the non-radial dea model applied in (djordjević and krmac, 2018). the results of the topsis method are calculated using excel environment and are summarized in table 3. in terms of serbia, the best influence of the tcis on the obtained ric was in 2007, while in austria the best impact of the tcis on capacity was in 2008 (see table 3). from table 3 the rank for other alternatives/years in terms of the tcis influence on the obtained ric may be seen. table 3. results of the topsis method alternatives/dmus serbian case austrian case ci rank ci rank 2006 0.6223 3 0.4588 6 2007 0.6942 1 0.5981 2 2008 0.6233 2 0.6158 1 2009 0.3574 9 0.3441 10 2010 0.4335 5 0.3758 9 2011 0.4436 4 0.4892 4 2012 0.3904 7 0.4737 5 2013 0.4203 6 0.4401 7 2014 0.3388 10 0.4350 8 2015 0.3625 8 0.5215 3 however, considering the characteristics and the process, the results of the topsis method were different from expected in comparison with the results obtained by the non-radial dea model in (djordjević and krmac, 2018). for instance, for the serbian case study, alternative 2007 was ranked as 1 by the topsis and also had the best value of efficiency obtained by the non-radial dea model, while for 2012 with efficiency 1 the rank was 7. also for the austrian case study, the results of the topsis method were different from the results of the non-radial dea model. for example, alternative 2008 had a rank of 1 and had also obtained the best efficiency by the non-radial dea model. however, the year 2015 with a rank of 3 by the topsis had an efficiency score of 1 by the non-radial dea method. the reason for differences in the results should be found in the fact that the dea considered inputs for a given level of outputs while the topsis method differed thusly; seeking the best alternatives, closest to the ideal positive solution and furthest from the negative. another reason for differences in the results is the involvement of weights for each criterion, not only for variables in the goal function in the non-radial dea model. 5. conclusion increasing train traffic on the railway infrastructure, such as the state of railways in eu, implies the use of enlarged railway network capacity. to realize all necessary changes and increase speed, capacity and higher overall performance, the railway evaluation of the tcis influence on the capacity utilization using the topsis method: case studies of serbian and austrian railways 35 industries have to move towards so-called “intelligentization” creating “modern railway transport” (li et al., 2003). in terms of railway, according to fantechi et al. (2014), “one such example of complex systems refers to the tcis which is characterized by a large number of components of various kinds (mechanical, electrical, computer, etc.) that have different types of interactions (local, simultaneous, etc.) which are interconnected and operate in synergy with each other.” in order to evaluate the tcis efficiency influence on the ric, the non-radial dea model was introduced in (djordjević and krmac, 2018). however, based on the disadvantages of the dea method described above, in this paper the topsis method, which allows ranking of considered alternatives and enables their evaluation from pessimistic and optimistic point of view, was introduced. the evaluation where years represent alternatives was tested through case studies of serbian and austrian railways for the period from 2006 to 2015. while data for serbian railways were real, those for austrian railways were mainly assumed. based on the obtained results it can be pointed out that the topsis method can be applied to evaluation and comparison of the influence of different tciss on the rc utilization. as future work, the proposed method can be applied to a comprehensive and accurate set of real data, using different variables or criteria, along with the performance of validity check. the proposed method could also be applied on the micro level, i.e., the evaluation of the tcis influence on the capacity utilization for a particular line. likewise, it could also be applied to other concepts of capacity. references aydin, n. 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(2018). evaluation of consolidation center cargo capacity and locations for china railway express. transportation research part e, 117, 58-81. operational research in engineering sciences: theory and applications vol. 2, issue 2, 2019, pp. 12-23 issn: 2620-1607 eissn: 2620-1747 doi:_ https://doi.org/10.31181/oresta1902001k * corresponding author. e-mail addresses: nkomazec@gmail.com (komazec), ale_petrovic@live.com (petrović) application of the ahp-vikor hybrid model in media selection for informing about the endangered in situations of emergency nenad komazec, aleksandar petrović* university of defence, pavla jurišića 33, 11010 voždovac, belgrade, serbia, received: 17 april 2019 accepted: 12 july 2019 first online: 24 july 2019 research paper abstract: a distribution of information in situations of emergency represents a serious challenge for the expert services engaged in protection and rescue. the number of the people who need help in situations of emergency is rather large and the number of those who can really be helped depends on their availability to expert services. a large number of people, especially endangered groups, can be saved with the help of timely and qualitative information. in the conditions determined by a lack of time, the staff in charge of situations of emergency have to make a decision on informing the population about the incoming danger. in the paper, a hybrid model based on the analytic hierarchy process (ahp) and multi-criteria compromise ranking (vikor) is presented, as applied through the selection of the best medium for informing the population in situations of emergency. the ahp method is used to determine criteria weight coefficients, while the vikor method is applied in order to find the best media by means of making a selection amongst numerous concrete options – i.e. alternatives. key words: media, situations of emergency, ahp method, vikor method. 1. introduction situations of emergency represent the state of the high endangerment of a social community. the consequences of situations of emergency are manifold and have farreaching effects. considering the size of a danger from various natural disasters and other accidents, and different categories of the endangered population, timely warning and informing are of great significance. preventive acting through informing and alerting the population is the basis for reducing the consequences of situations of emergency. there are various population categories that need be informed about the incoming danger. the most endangered are persons with special needs, only to be followed by women and children, and, in the end, the persons who are able to save themselves on their own. mailto:ale_petrovic@live.com komazec and petrović/oper. res. eng. sci. theor. appl. 2 (2) (2019) 12-23 13 in a situation of emergency, the problem of the functionality of the media may occur due to their territorial prevalence and the signal reception (for the television and the radio) or equipment supply and functionality (the internet). informing by emergency sirens could be a solution in the areas with good coverage and a high population density. otherwise, the effect of emergency sirens can be very small. depending on the type of the situation of emergency, electricity supply can also be problematic (komazec et al. 2014). the manner in which people should be informed is mostly restricted by the effects of a situation of emergency and its diffusion, and very frequently, the availability of information to certain groups of people is the only criterion (акимов & порфирьев, 2004). however, by carrying out a thorough analysis of the relevant factors, conclusions can be drawn which refer to the selection of the optimal medium (or media) for the purpose of informing as many people as possible in order to select those media that meet the created needs. in this paper, the analytic hierarchy process (ahp) and the multi-criteria compromise ranking (vikor) methods are applied to problem solving. the contribution of the paper reflects in the enhancement of the evaluation and selection methodologies regarding the media for the purpose of informing the population in situations of emergency through a new approach to the treatment of imprecision due to the fact that the application of this model or similar models in situations of emergency has not been reviewed in the existing literature. 2. problem description the paper is focused on finding out the hybrid model which will enable the optimal selection of the media for informing the population in situations of emergency. the occurrence of the need for informing the population in the situations of natural disasters and technical-technological accidents depends on the level of the endangerment of the social community. the alert signal announcing a danger is activated by the authorities according to the law. the level of the danger, i.e. the endangerment, is the basis for the proclamation of a situation of emergency (karovic & komazec, 2009). a situation of emergency is proclaimed by the staff in charge of situations of emergency when risks and threats, or the resulting consequences are on such a scale and of such an intensity that they cannot be stopped or diminished by conducting the authorities’ regular activities, for which reason it is necessary that special measures, additional strengths and the means with an enhanced operation mode should be taken for the purpose of their mitigation and removal (zakon o smanjenju rizika od katastrofa i upravljanju vanrednim situacijama [law on disaster risk reduction and emergency management], 2018; pamucar et al. 2016). the proclamation of a situation of emergency follows immediately after becoming aware of the danger. this moment is a milestone in the protection and salvation of the endangered population, material goods and the environment. namely, as long as the staff in charge of situations of emergency are unaware of a danger, they cannot proclaim a situation of emergency, nor can they inform the endangered population about it; competent services (republic hydrometeorological service of serbia (rhms), republic geodetic authority (rga), etc.) are, however, responsible for informing the population. the competent services usually inform people through the media (the television and the radio) and via the internet (posting warnings on relevant websites). in that period of time, the staff in charge of situations of emergency collect pieces of application of the ahp-vikor hybrid model in media selection for informing about the endangered in situations of emergency 14 information and may perform such informing through local communities and responsible individuals. in some special situations, the electric-power industry, the water industry and the other business associations using hydro-accumulations and landfills are obliged to ensure that the population is timely informed about the incoming danger (zakon o smanjenju rizika od katastrofa i upravljanju vanrednim situacijama [law on disaster risk reduction and emergency management], 2018). the members of the staff in charge of situations of emergency may use local radio and television stations. the transmission of information to the endangered population carried out by the republic staff in charge of situations of emergency the law also envisages the obligation of mobile companies to transfer information to endangered people. all mass-media means are applicable when informing the population is concerned, even before situations of emergency occur (petrovic et al. 2017). a special problem is a situation of emergency when a danger to the population, material goods and the environment has arisen. the conditions of all the people inside the endangered territory are such that they all fear for themselves, for their families, and for their material possessions. there is a similar situation in business companies which, simultaneously having to protect their own assets, also need to engage the employees whose families are jeopardized at that moment as well. in the case of a concrete problem, persons with special needs, the elderly, women and children are considered as special and specific groups of people. in the case of a particular problem, the means of mass communications are restricted to a segment of the mass media (the television, the radio and the internet – especially social networks and mobile communications)1 (radojkovic & miletic, 2005). there is a possibility of using print media, but this way of communication is restricted by the type and level of the influence of the concrete danger. 2.1 informing in situations of emergency the practical usage of effective informing is the basis for effective management (moriarty et al. 2012). informing in situations of emergency (and alerting, too) is an activity of great significance with respect to decreasing human casualties and mitigating damage to material goods and the environment. namely, timely information provides a quick and right reaction of the endangered population to the danger. timelessness depends on the type of danger (dey, 2001). situations of emergency and other accidents which may occur suddenly and develop rapidly are more complex to announce. practically, their announcement is conducted after the moment of their occurrence. the possibility that the majority of the population will not receive information on time is most likely (komazec et al. 2018). the dangers that occur in a longer period of time and develop gradually are much easier to announce, along with the appearance of the first indicators. the staff in charge of situations of emergency and the authorities’ specialized institutions (rhms, rga, etc.) have the legal obligation to provide information in situations of emergency. this approach is essential for controlling the information flow, the types of information, and the process of receiving information to as many 1the presence of social media is generally implied, due to the fact that they include mobile companies and their ability to transfer information as well. komazec and petrović/oper. res. eng. sci. theor. appl. 2 (2) (2019) 12-23 15 people as possible. for the purpose of informing effectively and efficiently, the staff in charge of situations of emergency have several instruments at their disposal, namely: 1. the television and the radio; 2. the internet-social networks; 3. the early warning, informing and alerting system; 4. print media and 5. mobile telecommunications. the television and the radio belong to a group of highly widespread and available media. it is to be assumed that every single home has the ability to access them. the main issue in the usage of such media is the ability of the municipality staff in charge of situations of emergency to send information through the national television and radio network due to the fact that the national services are watched/listened to by a large number of individuals. also, there is a problem in local services in the territory of the municipality and their availability throughout that territory. the internet is also a widely applicable instrument for the transmission of information. there is a certain limitation when access to the internet is in question. it is possible to quickly transfer information to a large number of people throughout social networks, but the availability of those individuals to the staff in charge of situations of emergency may be an issue. a special problem implies those elderly ones who do not use the internet at all, or use it poorly. the early warning, informing and alerting system is directly available to the staff in charge of situations of emergency. the limitation lies in the operational correctness of the system, the territorial coverage and the ability of all endangered groups to understand the sent signals. print media belong in the group of slower and mass means of information transfer. the limitation of their application lies in the fact that, in a situation of emergency, the distribution of such media may be stopped. also, not every municipality owns its own print media, which may refer to the dependence on a publishing house, its distance and capacity. mobile telecommunications represent a powerful, widespread and easily accessible medium for information transfer. a large number of people in all endangered groups own a mobile telephone. the main issue is the development of a database of telephone numbers, especially of the numbers of the endangered groups of individuals responsible for them. 2.2. description of the media selection criteria in order to successfully apply the ahp and vikor methods to solving the research problem, it is necessary to identify the criteria common to all the listed and considered media of mass communications and among which a selection of the best media for informing the population in situations of emergency will be conducted. (nenadovic et al. 2016). taking this into account, the following criteria are identified: k1 – the frequency of informing – this criterion is expressed by the number of the repetitions of informing through the amount of time in order to achieve as good reception as possible by as many individuals as possible. k2 – territorial coverage – this criterion is expressed in percentages and represents the ability to receive information in real time throughout the territory of the municipality. application of the ahp-vikor hybrid model in media selection for informing about the endangered in situations of emergency 16 k3 –presence in a target group– this criterion is expressed in percentages and reflects the presence of a concrete medium in a concrete target group, or the other way round – it reflects the percentage of the target group ‘consuming’ a particular medium. k4 – the availability of the medium – this criterion represents the coverage of the republic of serbia’s territory (by broadcasting or by distribution)2 and it is described by linguistic descriptors given in table 1. table 1. the descriptive scale of the linguistic criteria linguistic descriptors very poor poor medium good excellent assigned numerical value 1 2 3 4 5 k5 – the medium access price – this criterion is expressed by cash units and accounts for the amount which is necessary to pay in order to make the content of a particular medium available.3 the characteristics of the listed criteria are presented in table 2. table 2. the criteria characteristics ben4. cost5 qualitative quantitative к1 + + к2 + + к3 + + к4 + + к5 + + 3. applied methods the hybrid model used for the selection of the best media for informing the population in situations of emergency consists of the ahp and vikor methods. the ahp method is used to determine the weight coefficients of the identified criteria, while the vikor method is used to find a compromise solution, specifically for the selection of the optimal informing medium. 2 when electronic media (the television and the radio) are concerned, it is significant whether they are the media with a national frequency or the media covering only a certain region in serbia, whereas when the press (newspapers) is concerned, it is essential whether they are the media distributed throughout the territory or the media distributed locally. 3 when speaking about electronic media, the total amount represents the sum of all expenses, such as purchasing a television set or a radio receiver, the costs of electricity, broadcasting costs, a special fee for using a public service, etc., whereas in the case of the press, it accounts for the amount which has to be paid for certain newspapers, magazines and so forth. for the internet and mobile commu nications, it is the price for those services. 4 the subset of the criteria with the benefit characteristics, which means that a higher value of the criterion is preferable, i.e. better. 5 the subset of the criteria with the cost characteristics, which means that a lower value of the criterion is preferable, i.e. better. komazec and petrović/oper. res. eng. sci. theor. appl. 2 (2) (2019) 12-23 17 3.1. ahp the ahp method developed by thomas saaty at the beginning of the 1970s is a tool used in decision analysis, created for the purpose of providing assistance to decisionmakers in resolving complex decision-making problems in which many decisionmakers participate, numerous criteria and in various time periods. this process is based on the balance concept used in order to determine the overall significance of the set of relative attributes, activities or criteria, and relates to the analyzed decisionmaking problem (cupic & suknovic, 2010). in the paper, this method is applied so as to determine the criteria weight coefficients regarding the selection of the media for informing the population in situations of emergency. saaty’s standard nine-level scale presented in table 3 is applied in order to carry out a pairwise comparison (saaty, 1980). saaty’s scale is applied by the decision-makers or the analysts performing comparisons in pairs on the basis of the semantic preferences from the left-hand column of saaty’s scale or by direct association. the numerical values stated in the columns 2 or 3 of table 3, which correspond to the semantic preferences in the lefthand column, are entered into the square comparison matrix, equation (1). table 3. saaty’s pairwise comparison scale 𝐶1 𝐶2 … 𝐶𝑛 a = 𝐶1 𝐶2 ⋮ 𝐶𝑛 [ 𝑎11 𝑎12 … 𝑎1𝑛 𝑎21 𝑎22 … 𝑎2𝑛 ⋮ ⋮ ⋱ ⋮ 𝑎𝑛1 𝑎𝑛2 … 𝑎𝑛𝑛 ] (1) since it is true that aij= 1/ aji and aii= 1 for every i,j = 1,2,...,n, the matrix a is positive, symmetrical and reciprocal. when applying saaty’s classical scale, the relations in a pairwise comparison are strictly defined (pamucar et al, 2016). 3.2. vikor the vikor method was developed by opricovic serafim (opricovic, 1998) based on the elements from compromise programming with the beginning at the “border” forms of lp-metrics. these metrics represent the distance between the ideal point f* and the point f(x) in the space of the criteria functions (petrovic et al. 2017). the first step in the vikor method is the initial decision matrix: 𝑋1 𝑋2 𝑋3 ⋯ 𝑋𝑛 𝑊1 𝑊2 𝑊3 ⋯ 𝑊𝑛 definition standard values reciprocal values equal importance 1 1 weak importance of one over another 3 1/3 essential or strong importance 5 1/5 demonstrated importance 7 1/7 absolute importance 9 1/9 intermediate values between the two adjacent judgments 2,4,6,8 1/2, 1/4, 1/6, 1/8 application of the ahp-vikor hybrid model in media selection for informing about the endangered in situations of emergency 18 d = 𝐴1 𝐴2 𝐴3 ⋮ 𝐴𝑚 [ 𝑋11 𝑋12 𝑋13 ⋯ 𝑋1𝑛 𝑋21 𝑋22 𝑋23 ⋯ 𝑋2𝑛 𝑋31 𝑋32 𝑋33 ⋯ 𝑋3𝑛 ⋯ ⋯ ⋯ ⋱ ⋮ 𝑋𝑚1 𝑋𝑚2 𝑋𝑚3 ⋯ 𝑋𝑚𝑛] (2) by the decision matrix, the m alternatives and the n criteria are defined. every criterion is associated with its weight coefficient 𝑤𝑖. the weight coefficients of the criterion should follow the next condition: ∑ 𝑤𝑖 𝑛 𝑖=1 =1 (3) after defining the decision matrix, the method is to be applied. the next step in the vikor method is the determination of 𝑥𝑖 ∗ and 𝑥𝑖 −, which is conducted by the following equations: 𝑥𝑖 ∗ = max (𝑥1, 𝑥2,…, 𝑥𝑛); i=1,2,…, n; (4) 𝑥𝑖 − = min (𝑥1, 𝑥2,…, 𝑥𝑛); i=1,2,…, n; (5) the next step in the vikor method is the determination of the pessimistic (𝑆𝑗 ) and the anticipated (𝑅𝑗 ) solutions. 𝑆𝑗 = ∑ 𝑤𝑖 𝑛 𝑖=1 (𝑥𝑖 ∗ − 𝑥𝑖𝑗) (𝑥𝑖 ∗ − 𝑥𝑖 −)⁄ ; 𝑗 = 1,2, … , 𝑚 (6) 𝑅𝑗 = max 𝑖 [𝑤𝑖 (𝑥𝑖 ∗𝑥𝑖𝑗 ) / (𝑥𝑖 ∗ − 𝑥𝑖 −); 𝑗 = 1,2, … , 𝑚 (7) after that, the next step is finding a compromise solution 𝑄𝑗 : 𝑄𝑗 = 𝜈 𝑆𝑗− 𝑆 ∗ 𝑆−− 𝑆∗ + (1–𝜈) 𝑅𝑗− 𝑅 ∗ 𝑅−− 𝑅∗ ; j=1, 2,…, m (8) where 𝑆∗= min 𝑆𝑗 (9) 𝑆−= max 𝑆𝑗 (10) 𝑅∗= min 𝑅𝑗 (11) 𝑅−= max 𝑅𝑗 (12) 𝜈 – the weight of the strategy satisfied according to the majority of the criteria, 𝜈 ∈ {0.25, 0.5, 0.75}. the last step in the vikor method is the ranking of alternatives. a set of alternatives can be ranked by the value of the function of the criteria assigned to each alternative 𝑄𝑗. the best alternative is the one that is the least distanced from the ideal value, i.e., the one that has the minimal 𝑄𝑗value, and vice versa. as relevant, the rank list is taken for the value 𝜈 = 0.5, but even though it is the first on the list, that action has to meet two more conditions (petrovic et al. 2017), namely: komazec and petrović/oper. res. eng. sci. theor. appl. 2 (2) (2019) 12-23 19 1) there has to be sufficient advantage (more than the “minimum sufficient advantage”) related to the 2nd, 3rd, and other alternatives), which is established by applying the following expression: q(𝑎‚) q(𝑎‚‚)≥ 𝐷𝑄 (13) where: dq = min(0.25, 1 𝑚−1 ) (14) where 𝑎‚ and 𝑎‚‚ represent the values of the 1st and the 2nd alternatives, respectively, by 𝑄𝑗(𝜈=0.5), and m represents the number of the alternatives. the minimum sufficient advantage is to be 0.25 in the cases when there is a small number of alternatives. 2) it has to have a sufficiently stable position, i.e. position no. 1, according to the rank list qsj, or according to qrj, or according to q for 𝜈 = 0.25 and 𝜈 = 0.75 where (petrovic et al. 2017): q𝑆𝑗 = 𝑆𝑗 − 𝑆 ∗ 𝑆−− 𝑆∗ ; j = 1, 2,…, m (15) q𝑅𝑗 = 𝑅𝑗− 𝑅 ∗ 𝑅−− 𝑅∗ ; j = 1, 2,…, m (16) 4. presentation of the application of the hybrid model as already stated, the hybrid model consists of the ahp and vikor methods. the weight coefficients of the criteria are calculated by applying the ahp method in the expert choice program package and the results of that process are shown in tables 4 and 5. table 4. the criterion pairwise comparison according to saaty’s scale k1 k2 k3 k4 k5 k1 1.0 3.0 1/2 9.0 2.0 k2 1.0 (4.0) 2.0 2.0 k3 1.0 5.0 3.0 k4 1.0 (3.0) k5 1.0 cr=0.03 table 5: the values of the criteria weight coefficients k1 .300 k2 .092 k3 .406 k4 .051 k5 .151 inconsistency = 0.03 with 0 missing judgments. application of the ahp-vikor hybrid model in media selection for informing about the endangered in situations of emergency 20 for the purpose of applying the vikor method, a total of 6 different alternatives were chosen (from a1 to a6 ), by which the initial decision matrix was defined, which is accounted for in table 6. the alternatives are as follows: alternative a1–local television and radio station; alternative a2–national television and radio station; alternative a3–early warning, informing and alerting system; alternative a4–internet–social networks; alternative a5–print media, and alternative a6–mobile communications. the details regarding the listed alternatives are not presented in the paper in order to avoid a decrease in their positions in the media space and favoring certain media, too. table 6. the initial decision matrix criterion k1 k26 k3 k4 k5 alternatives 0.300 0.092 0.406 0.051 0.151 a1 6007 50 45 5 6 a2 300 48 60 4 5 a3 600 5 35 3 0.3 a4 750 4 40 2 0.35 a5 480 22 10 4 2.4 a6 430 18 8 1 1.8 xi* 750 50 60 5 0.3 xi300 4 8 1 6 characteristic of criterion max max max max min by solving the equations from 4 to 12, the final solutions are obtained and they are presented in table 7. table 7. the final values of the alternatives alternatives qsj qrj qj (v=0.5) qj (v=0.25) qj (v=0.75) a1 0.463 0.252 0.357 0.305 0.410 a2 0.353 0.576 0.465 0.520 0.409 a3 0.040 0.156 0.098 0.127 0.069 a4 0.000 0.000 0.000 0.000 0.000 a5 0.938 0.936 0.937 0.936 0.937 a6 1.000 1.000 1.000 1.000 1.000 according to the results obtained, the final ranking of the alternatives is as follows: a4, a3, a1, a2, a5 and a6. 6 according to the last analysis of the media market in serbia, conducted by ipsos strategic marketing agency in 2015 (regulatory body for electronic media, 2015), the television is the leading medium, with a market share of 53%, the press accounts for 20%, and the radio accounts for 4% (the other media account for a market share of 23%). 7 the number of repetitions in one day (i.e. 24 hours). komazec and petrović/oper. res. eng. sci. theor. appl. 2 (2) (2019) 12-23 21 5. sensitivity analysis when applying methods of multi-criteria decision-making, it is crucial to examine the sensitivity of the mathematical model applied, so that decision-makers could have some kind of guarantee according to the rationality and quality of the obtained solution (pamucar et al. 2016). the analysis of the sensitivity of the results obtained by the hybrid model implies the examination of changes in the weights of criteria and on the consistency of the solution with respect to a change in the measurement scale (pamucar et al. 2017). when examining change in the weight of the criteria, a total of six scenarios were developed (table 8) (a – the equal importance of all the criteria, b – the absolute dominance of k1, c – the absolute dominance of k2, d – the absolute dominance of k3, e – the absolute dominance of k4, f – the absolute dominance of k5). within the framework of the independence analysis regarding change in the measurement scale, a total of two scenarios were developed (table 9). in the first scenario, the qualitative criterion (k4) was given by the two different scales (s1 and s2) connected by a positive affine transformation (y = 2x – 1). in the second scenario, the quantitative criterion (k5), which represents the media access cost, expressed in cash units is was given by the two different scales: (s1) in rsd (republic of serbia’s dinar) and (s2) in euros. table 8. the sensitivity analysis of change in the weights of the criteria scenario a b c d e f alternatives alternatives rank a1 4 4 3 5 3 2 a2 1 2 5 3 4 3 a3 5 6 2 4 1 6 a4 3 1 1 1 5 1 a5 6 3 6 6 6 4 a6 2 5 4 2 2 5 table 9. the independence analysis of change in the measurement scale scenario scenario 1 scenario 2 s1 s2 s1 s2 alternatives alternatives rank a1 5 5 5 5 a2 3 3 3 3 a3 2 2 2 2 a4 1 1 1 1 a5 5 5 5 5 a6 6 6 6 6 6. discussion and conclusion according to the results obtained by conducting a sensitivity analysis of the developed hybrid model for the purpose of the selection of the best medium for informing the population in situations of emergency and with respect to the research studies (pamucar et al. 2018), a conclusion can be drawn that the hybrid ahp-vikor application of the ahp-vikor hybrid model in media selection for informing about the endangered in situations of emergency 22 model is completely applicable in the cases of solving the treated problem and satisfies the set goal. the sensitivity analysis of change in the weights of the criteria shows that the hybrid model is sufficiently sensitive and that it keeps alternative priorities (in this particular case, alternative a4 is favored). furthermore, checking the consistency of the solution by changing the measurement scale shows that the model is stable and that it generates sustainable solutions. by an analysis of all of the results obtained, it is possible to conclude that the application of the ahp and vikor methods can significantly help decision-makers to come to the necessary solution. the proposed model examined in the paper represents an integration of the ahp and vikor methods, where the ahp method is used to determine the weight coefficients of criteria within the process of the selection of the best medium for informing the population in situations of emergency, whereas the vikor method is used to rank the obtained alternatives and find the optimal solution. the model has been verified through the media selection process inside the territory of a certain municipality by six different alternatives. the results obtained by the application of the model show that alternative no. 4 is the best solution in all the scenarios with different values of the criteria. in comparison with the hybrid model, alternative no. 4 has a priority engagement. taking into consideration the fact that situations of emergency are concerned in this case, it is not only enough to depend on one single medium, but the competent staff in charge of situations of emergency will engage all available media. this means that informing the population would certainly be performed through the television, the radio, print media, and mobile communications. the early warning, informing and alerting system would be used for signal transmission. the sensitivity analysis has shown the stability of the results obtained by the application of the model in all of the considered scenarios. the presented application of the hybrid model provides an unbiased aggregation of experts’ choices by taking into consideration all the inconsistency and subjectivism of group decision-making. apart from the expressed contribution, it is essential to emphasize the authors’ attempt to apply this model in situations of emergency, which are characterized by uncertainty and a lack of time as well, the large amount of information and crisis decision making. the development of such models contributes to the literature in which the theoretical and practical application of multi-criteria techniques is subjected to review. the suggested model enables the evaluation of alternatives despite the imprecision and lack of quantitative information in the decisionmaking process. by applying the developed approach, problems concerning multicriteria decision-making and the evaluation and selection of a medium for informing the population in situations of emergency can easily be dealt with. the model can be applied to making various decisions. it is also applicable in the process of decision-making within the staff in charge of situations of emergency in situations of emergency. the flexibility of the model is proven by the fact that its verification can be performed by applying any type of multi-criteria decision-making methods. further research studies regarding this paper should refer to the application of this and similar models in combination with other methods and the development of a new method, which would lead to the enrichment of this highly applicable scientific area. situations of emergency are the state of the endangerment of social stability with great implications for the life and health of people, the state of material goods and the environment. therefore, every contribution to the improvement of the decision–making system of the staff in charge of situations of emergency is also a contribution to prevention and reaction in case a danger occurs. komazec and petrović/oper. res. eng. sci. theor. appl. 2 (2) (2019) 12-23 23 references 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(2004). кризисы и риск: к вопросу взаимосвязи категорий [crises and risk: towards a question of linking categories]. проблемы анализа риска, 38-49. plane thermoelastic waves in infinite half-space caused operational research in engineering sciences: theory and applications vol. 2, issue 2, 2019, pp. 1-11 issn: 2620-1607 eissn: 2620-1747 doi:_ https://doi.org/10.31181/oresta1902014t * corresponding author. e-mail addresses: ilijat@uns.ac.rs (tanackov), zarko.jevtic93@gmail.com (jevtić), gordan@uns.ac.rs (stojić), feta.sinani@unite.edu.mk (sinani), pamela.ercegovac@uns.ac.rs (ercegovac) rare events queueing system – reqs ilija tanackov*1, žarko jevtić1, gordan stojić1, feta sinani2, pamela ercegovac1 1 faculty of technical sciences, university of novi sad, serbia 2 faculty of applied sciences, state university of tetovo, republic of north macedonia received: 14 april 2019 accepted: 07 july 2019 first online: 24 july 2019 original scientific paper abstract: the paper deals with the queueing system for customers with poisson’s arrival process with the intensity  and two service modes: in the regular service regime of the intensity control ,, customers are served with a probability of p1, and in the special service regime provided to special customers, they are served with the intensity . special customers access reqs with a complementary probability of (1−p)0. a special customer service is analogous to a rare event. the standard methodology has developed analytical patterns for stationary reqs with one service channel and an infinite number of positions in the queue. the analysis of the work of reqs indicates that, when favorable metering parameters =/>2 are concerned, the queueing system is resistant to collapse when an occurrence comes up. however, the regular time losses of regular customers in reqs are extremely high. for this reason, this is the first time that the system stabilization period is being promoted, representing the time interval for the completion of a special customer service before reqs. the analytical apparatus of the queueing system has shown an excellent adaptability to the heterogeneous demands for services  and special customers, with a low service intensity , where >. the system can be applied to checkpoint calculations, traffic cuts due to accidents, incidents in industrial systems, i.e. in the case of the occurrence of rare events happening due to anthropogenic and technical factors in the intervals ranging from 10-4 to 10-6. the model is not intended for natural hazards. key words: collapse, special service, critical probability, stabilization time 1. introduction the development of rare events theory began in the 1970s and was above all aimed at predicting natural hazards (earthquakes) (cornell, 1968). after the quickly tanackov et al./oper. res. eng. sci. theor. appl. 2 (2) (2019) 1-11 2 obtained results, the importance of the new theory and the application possibilities for the calculation of the hazards induced by anthropogenic factors (e.g. by terrorism) and industrial hazards increased. since then, rare events theory has become a research field intended to improve the reliability and security of the system (der kiureghian, & liu, 1986; yang et al., 2015). from the point of view of systems theory, rare events are characterized by a low frequency of the implementation of the usually uncovered range. the unpredictable and undesirable jargon recognizes rare events caused by the system’s current operating regimes as a “black swan” or a “gray swan”. the low frequency of rare events makes it impossible to form the necessary statistical set (large datasets) for the significant verification of the distribution of their occurrences. therefore, it is common to assign an exponential distribution to the distribution of rare events (zweimuller, 2018; garnier and moral, 2006; jacquemart & morio, 2016; ruijters et al., 2019). such an approach is theoretically justified because of the memoryless properties of the exponential distribution, which completely eliminates the functional relationships between consecutive rare events. due to the unpredictability and the low probability of their occurrence, the simulation of rare events is a specific analytical task (morio et al., 2014; au & patelli, 2016; agarwal & de marco, 2018). in order to investigate the extreme working conditions caused by the realization of rare events, there are standards in technical systems that, under a rare event, adopt a frequency within the interval ranging from 10−4 to 10−6 during the lifetime of the system, or as low as 10−8, during the one hour of the operation of the system (paté-cornell, 1994). in this paper, the single-channel reqs model analyzed is the markovian, which implies the exponential structure of each parameter. rare events are substituted with a customer with a specific request, who accesses reqs and who is likely to be a rare event (1−p). a special customer requires to be described by the crucial parameter – the time of the special customer service incomparably greater than the time of the regular customer service. basically, reqs is a heterogeneous system. the analytical apparatus of the queueing system in the stationary mode of operation shows an exceptional adaptability to the introduction of a special customer. thanks to analytical elasticity, the reqs limitation modes are easily calculated, and the regular capacity of the system and the special customer service regions prevent the system from collapsing. 2. the birth-death process in reqs. single-channel reqs allow us now to consider the birth-death process in a system with the homogeneous birth process of the intensity . let the dying process be heterogeneous, with the standard mortality intensity  of the probability of p1. the mandatory working condition is <, with the complementary probability of (1−p)0, which represents the special dying process occurring after the regular dying process. the intensity of the special dying process has the intensity of , where >. keeping this in mind, the mean death time represents a special case of the complementary probability of (1−p)0, which is incomparably longer than the regular one. the graph of the elementary states of this process is presented in figure 1. rare events queueing system – reqs 3 figure 1. the elementary states of the single-channel reqs the average dying time is equal to, as in equation (1):   )p()p()p(pdtte)p(dttep ttt − += − + − +=−+   −−  − 11111 00 (1) the implications of this process for queueing systems are considered under the conditions of the limited value of the probability of the distribution of customers p in the case when the p→1 system is reduced to the standards of the markovian system with one channel of services(i.e. in a system without customers with special requests), which is expressed by kendall’s notation m()/m()/1/0, equation (2):  111 1 =      − + → )p( lim p (2) in the case where p→0 (all customers are special customers), the average time of the service described in raikov’s theorems is obtained. the stability of the poisson stream creates the second boundary result, as in equation (3). in the boundary conditions of equation (3), the queueing system is again the standard markovian queueing system, which is expressed by kendall’s notation m()/m(−1+−1)/1/0, equation (3):  1111 0 +=      − + → )p( lim p (3) the boundary conditions determine the mean time of the services of the singlechannel queueing system in the regular operation mode 0p1, equation (4):  11111 + − + )p( (4) tanackov et al./oper. res. eng. sci. theor. appl. 2 (2) (2019) 1-11 4 3. single-channel reqs with an infinite queue if the system of the homogeneous birth and heterogeneous dying processes is projected with an infinite number of points in the queue, the reciprocal value obtained from equation (4) or equation (5) is the intensity of the customer services in the queue (figure 2): )p( q −+ = 1   (5) figure 2. the single-channel reqs with an infinite number in the queue this system’s solution starts from setting balanced equations in the stationary operation mode. the probability of the states x0, x1a, x1b, x1+i is indicated by the protocol: p(x0)=x0, p(x1a)=x1a, p(x1b)=x1b, and the probability of the state of the queue system for i(1, ) with p(x1+i)=x1+i , equation (6), reads as follows: abbab aa ba ba x )p( xxx)p(:x x )p( x))p(p(x:x xxp xxxpx:x 11111 11101 11 01100 1 10 1 10 0          − =−−+= −+ ++−+−+= + =++−= + (6) in the sequel, all the three probabilities from equation (6) are shown through the probability of the state x0, equation (7): ( ) 011110 2 1110 021011 01 11 11 0 1 1 1 10 111 1 x )p( xx )p( x x )p( x))p(p(x x )p( xx )p( x )p( x xx x )p( xp xxp x a bab a aa ba                             −+ = −+ =  −+ ++−+−+= − = − = − = = − + = + = ++ + (7) allow us now to proceed with solving the probability in the order of x1+i, equation (8): rare events queueing system – reqs 5 ( ) ( ) ( ) ;...x )p( x ;x )p( x x )p( xx )p( x:x x )p( xx )p( x )p( x )p( xx )p( x:x a 0 4 410 3 31 3121211121 0 2 21210 2 211111111 11 11 0 1 1 1 11 0                                        −+ =        −+ =  −+ +− −+ −+=         −+ = −+ = −+  −+ +− −+ −+= ++ +++++ ++ ++++ (8) furthermore, for the probability of all the states in the induction queue, a recurrent form is obtained for the purpose of conducting the probability analysis of the state in the queue of x1+i, equation (9): ( ) 01 1 x )p( x i i             −+ =+ (9) the normative condition is as follows, equation (10): ( ) ( ) 1 1 1 1 1 1 1 0 20 0 00 1 1110 =      −+ −+ + −+ − + −+ +=+++    =  = + i i i iba )p( )p(p x )p(p )p( x )p(p x xxxxxx         (10) since >>0p1, it follows that the input condition is required of the input intensity  and the basic intensity of the service >, the sum of equation (10) being the required geometric order only under the conditions of equation (11).      − − −+ −+ )p( )p( )p( min 1 11 1 (11) otherwise, if the condition of equation (11) is not met, the average time of the −1 special customer service is extremely long, and the number of the customers in the queue diverges, i.e. reqs enters into collapse. with the above-mentioned condition, the value of the geometric order of equation (10) is equal to that of equation (12), namely as follows: )p( )p( )p( )p( i i −−− −+ =−       −+ − =               −+   = 1 1 1 1 1 11 1         (12) from the normative condition expressed in equation (9), the geometric order of equation (12) gives the probability from x0, equation (13): tanackov et al./oper. res. eng. sci. theor. appl. 2 (2) (2019) 1-11 6 )p( )p()p( x −−− −+ + − ++ = 1 11 1 1 0           (13) and all the probabilities of the system from equations (7) and (9). the average number of the customers in the queue for the fulfilled condition of equation (11) in the system is equal to that of equation (14): ( ) ( ))p( )p( )p( )p( )p( ik i i q −−− −+ = −+ −       −+ =               −+ =  = 1 1 1 1 1 1 2 2 1          (14) the average time that the customers spend in the queue is as expressed in equation (15): ( ) ( ))p( )p(k t q q −−− −+ == 1 1 2    (15) 4. the limits of collapse and stabilization time tst in reqs as in most queueing systems, the basic relationship in equation (15) determines the operation of the system:    = (16) for the values of the probability of the findings of special customers “(1−p)” and the anticipated average time of special customers −1, the minimum intensity of the regular customer min in equation (17) can be calculated, which guarantees the sustainability of the system: )p( )p( min min minmin −−  − −  1 1       (17) on the contrary, if the conditions from equation (17) are not satisfied, reqs goes into collapse by diverging the number of the customers in the queue. if the condition for the operation of a single-channel system in equation (17) is not satisfied, the service intensity may increase (if there is a variable capacity or capacity reserves) or the service additional channels may be introduced into the system. for the maximum industrial probability of the occurrence of rare events of 10−4, i.e. p=0.9999, the boundary conditions of reqs are presented in figure 3. the collapse limits are as follows for the different values of : • =1.5=0.75, min0.00030, or for the relative relation of the intensity of the ordinary and special customer services/min=5000, reqs very quickly enters into collapse, and the number of the customers in the queue rapidly diverges. the occurrence of a rare event, i.e. a rare customer with special requests, quickly destabilizes reqs. rare events queueing system – reqs 7 • =2.0=0.50, min0.00020, or for the relative relation of the intensity of the ordinary and special customer services/min=10000, reqs relates well to the appearance of a rare customer. the system is hardly introduced into collapse, but such collapse is a consequence of a high burden placed on the regular customers forming a queue, its slow customer service in the queue, and the big losses of time on the part of the customers in the queue. • =3.0=0.33, min0.000150, or for the relative relation of the intensity of ordinary and special customer services /min=20000, reqs is hardly introduced into collapse, remains stable for a long time with the low accumulation of the customers in the queue. • =4.0=0.25, min0.000133, or for the relative relation of the intensity of ordinary and special customer services /min=30000, reqs behaves similarly to the previous case. figure 3. the average number of the customers in the queue for p=0.9999 and the different parameter values of  and  if reqs provides special customer service protocols, it does not have to be specifically tailored to rare events. reqs points out the optimization issue regarding the relationship boundary, namely as follows in equation (18): pmin −  1 1   (18) which theoretically results in a relative relation =2.0, i.e. =0.50. one-channel reqs can be optimized. if the inverse value of the parameter of the service −1 is accepted for the independent variable (i.e. how many times the intensity of the regular customer service  is greater than the intensity of incoming customers ), and if the product (min)−1 (i.e. the relative parameter of the engagement of the tanackov et al./oper. res. eng. sci. theor. appl. 2 (2) (2019) 1-11 8 regular and special customer service) is accepted for the dependent variable, then the function shown in figure 4 is obtained. figure 4. the boundary of the collapse of reqs for the maximum engagement of the service channel for p=0.9999, the maximum ratio −1=f(−1) is obtained for =2. in these circumstances, the maximum time of the special customer service (min)−1 is equivalent to the time required for the arrival of 5000 regular customers, i.e. the services of 2500 regular customers. for min=0.00020 as per equation (17), the system is on the edge of collapse. if the customer service time is reduced by 25%, i.e. if the intensity of special customer services increases to =0.00025 (which is an equivalent to the arrival time of 4000 regular customers, or the service of 2000 customers), the average number of the customers in the queue during the lifecycle of the system without special customers is kq=7.50. comparatively, for the queueing system without special customers m()/m()/1/, at a ratio =2, the average number of the customers in the system is kq=0.5, i.e. 15 times smaller than in reqs. it is possible to conclude that the relations =2.0 the reqs are resistant to collapse, but the average number of the customers in the queue during the lifecycle of the system, i.e. the resulting time losses due to the appearance of special customers with the probability of p=0.9999, is/are extremely high. if the intensity of the services increases to =3, with the same intensity of special customer services =0.00025, the average number of the customers in the queue is 1.527, and for =4 at =0.00025, the average number of the customers in the queue is 0.773. a standard example of the application of reqs is a survey of traffic accidents. the basis of the numerical example lies in the calculation of the road capacity (bogdanović et al., 2013) and the application of the queueing system in the calculation of the road capacity (tanackov et al., 2019). for the mean intensity of the traffic flow of the main roads in the peak period of =900 vehicle/h and the maximum throughput of the traffic lane of 2200 vehicle/h, a special customer rare events queueing system – reqs 9 service is analogous to the closing of the traffic lane in order to protect the injured, perform surveys and undertake the other operations necessary for the remediation of the accident. a special customer service (i.e. the service of such a customer as a participant in a traffic accident) lasts incomparably longer than the regular customer service. for the likelihood of the occurrence of regular customers from p=0.99995, i.e. the occurrence of an accident on every 20000 vehicles, reqs collapses if the closing time of the traffic lane (the special customer service) is greater than (min)−1 13.13h. however, in the conditions of urban peak periods with twice the intensity of =1800 vehicle/h, the collapse limit is the closing of the traffic lane of (min)−1 2.02h, i.e. for a traffic flow twice as intense, under the same conditions of the regular customer service, the time to collapse is 6.5 times lesser. except for the collapse limit of reqs, another important parameter not evaluated in the literature until now is the stabilization time of reqs, which is marked with the tag tst. the users of reqs subjectively and usually negatively react to a loss of the service quality over time tst. during special customer services, there is an intensive accumulation of regular customers equal to the product of the input stream and the average time of a special customer service, i.e. −1. at the end of the accumulation of regular customers, the regular operation of the system begins with the intensity  to service to accumulated clusters −1 and new regular customers, who arrive with the intensity . therefore, the difference expressed in equation (19) must be greater than , i.e. the regular regime of reqs: )( tt)( stst    − − −− − − 1 1 (19) for the average time, the special customer services (closing the traffic lane) from −1=2h in the first numerical example (=900 vehicle/h) of the system stabilization time are equal to tst=1.285 h, whereas in the second (=1800 vehicle/h) tst=8.997h9h. the vehicle total cumulative time losses in the second numerical case (for the system stabilization period tst9h) are equal to 84000 vehicleh, or 3500 vehicledays. in the first numerical example, the time losses are about 7.5 times smaller. for a well-designed intensity, reqs resistance to collapse is certain. however, the appearance of the first “strike” of rare events and the stabilization period tst are a risky reqs time interval. if another special customer appears in the stabilization period, the risks of the collapse of reqs are incomparably larger. if tcr is indicated as the critical time elapsed since the beginning of the stabilization period tcr(0, tst), the critical probability pcr of the occurrence of special-customer rare events in the period passed since the beginning of the stabilization is equal to that of equation (20). although this probability is lesser than the probability of the appearance of the first special customer, it should not be neglected. )p(dte)p(p st crst t tt t cr −−=  − − 11  (20) tanackov et al./oper. res. eng. sci. theor. appl. 2 (2) (2019) 1-11 10 in addition to the specified case in road traffic, reqs can analogously be applied to the disruptions of the schedule of railways caused by accidents, in river traffic in the case of the malfunctioning of ship locks, in the case of the suspension of air traffic due to bad weather conditions, etc. reqs can also be applied in indirect cases, without the arrival of special customers. for example, in all systems that serve customers through the application of information systems, a “failure” of the information system can be considered as a phenomenon of a rare event with the probability of (1−p), and the system “rebooting” time can be considered as the intensity of special customer services. the principle to be followed refers to the classification of the system states that can be either stable (the regular mode), or metastable, or unstable. the arrival of customers with special requests always introduces the queueing system into a metastable state, and the appearance of customers with special requests at a critical time tcr(0, tst) introduces the system into an unstable state. 5. conclusion reqs modeling and analyzing indicate that the resistance of the system to the occurrence of rare events (special customers) is based on the capacity of the regular operation mode. if the intensity of the services  in the conditions of the usual occurrences of rare events from 10−4 to 10−6, and when a special customer service lasts incomparably longer than a regular customer service, namely several thousand times (up to 10,000 times) as long, for the relative relationships of 2, the boundary collapse of reqs are “so far”. the quantity of services can be maintained even in the conditions of disorder. this fact is encouraging for reqs managers. however, for regular users of reqs, the collapse limit, i.e. the system’s capacity, is not the primary parameter. in the implementation of rare events, reqs regularly operates in the destabilization mode. the new parameter of queueing theory, the stabilization time of the tst system, is the key parameter of the quality of the service that special customers (rare events) degrade primarily through regular customers’ intensive cumulative time losses. therefore, the reqs modes can be justified in exceptional, imperative, and most often unwelcome cases. references agarwal, a., de marco, s., gobet, e., liu, g. (2018). study of new rare event simulation schemes and their application to extreme scenario generation. mathematics and computers in simulation, 143, 89–98. bogdanović, v., ruskić, n., kuzović, m., han, l. (2013). toward a capacity analysis procedure for nonstandard two-way stop-controlled intersections, transportation research record, 2395, 132−138. cornell, c. a. (1968). engineering seismic risk analysis. bulletin of the seismological society of america, 58, 1583–1606. der kiureghian, a, liu, p. l. (1986). structural reliability under incomplete probability information. journal of engineering mechanics, 112, 85–104. rare events queueing system – reqs 11 garnier, j., moral, p. d. (2006). simulations of rare events in fiber optics by interacting particle systems, optics communinacions, 267, 205–214. jacquemart, d., morio, j. (2016). tuning of adaptive interacting particle system for rare event probability estimation. simulation modelling practice and theory, 66, 36−49. morio, j., balesdent, m., jacquemart, d., vergé, c. (2014). a survey of rare event simulation methods for static input–output models. simulation modelling practice and theory, 49, 287–304. paté-cornell, m. e. (1994). quantitative safety goals for risk management of industrial facilities. structural safety. 13, 145–157. r. zweimuller, hitting-time limits for some exceptional rare events of ergodic maps, stochastic processes and their applications (2018), https://doi.org/10.1016/j.spa.2018.05.011. ruijters, e., reijsbergen, d., de boer, p. t., stoelinga, m. (2019). rare event simulation for dynamic fault trees. reliability engineering and system safety, 186, 220–231. siu-kui au, s. k., patelli, e. (2016). rare event simulation in finite-infinite dimensional space. reliability engineering and system safety, 148, 67–77. tanackov, i., dragić, d., sremac, s., bogdanović, v., matić, b., milojević, m. (2019). new analytic solutions of queueing system for shared-short lanes at unsignalized intersections, symmetry, 11, 55. yang, m., khana, f., lye, l., amyotte, p. (2015). risk assessment of rare events. process safety and environmental protection 98, 102–108. https://www.scopus.com/authid/detail.uri?authorid=12244394600&amp;eid=2-s2.0-85061100669 https://www.scopus.com/authid/detail.uri?authorid=57205681772&amp;eid=2-s2.0-85061100669 https://www.scopus.com/authid/detail.uri?authorid=35590854300&amp;eid=2-s2.0-85061100669 https://www.scopus.com/authid/detail.uri?authorid=38960992400&amp;eid=2-s2.0-85061100669 https://www.scopus.com/authid/detail.uri?authorid=55251506800&amp;eid=2-s2.0-85061100669 https://www.scopus.com/authid/detail.uri?authorid=56224488200&amp;eid=2-s2.0-85061100669 operational research in engineering sciences: theory and applications vol. 5, issue 1, 2022, pp. 121-138 issn: 2620-1607 eissn: 2620-1747 doi: https://doi.org/10.31181/oresta250322151a * corresponding author. ahmed.shamah@bhit.bu.edu.eg (a. el-araby), ibrahim.sabry@bhit.bu.edu.eg (i. sabry), ahmed.el-assal@bhit.bu.edu.eg (a. el-assal) a comparative study of using mcdm methods integrated with entropy weight method for evaluating facility location problem ahmed el-araby*, ibrahim sabry, ahmed el-assal department of mechanical engineering, benha university, benha, egypt received: 26 november 2021 accepted: 14 february 2022 first online: 25 march 2022 research paper abstract: the location selection of facilities became a major interest for the organizations to establish their planned business for a long period of time. the choice of the best location among a set of candidate locations is a complex process. although the multiple criteria decision making (mcdm) methods are applicable for location selection problems, different solutions can be obtained using different mcdm methods. thus, a comparative study between four different mcdm methods was applied within numerical example to show the deviations in ranking of the alternatives that occurs when different methods are used. the weights of attributes are assigned using objective method namely entropy weight method. the rank disagreements are expressed using spearman`s correlation coefficients. keywords: multiple-criteria decision making (mcdm); facility location problem (flp); comparative study; rank disagreement. 1. introduction locating a facility is a common problem generally called facility location problem (flp). the study of facilities location was mainly as a result of weber`s book “theory of the locations of the industries” as weber and friedrich (1929) stated how to determine the location of a single warehouse to minimize the distance function. the location theory gained the researchers` interest as hakimi (1964) mentioned how to find the optimum location of a switching center in a communication network and the best location for police station in a highway system. facility location models can vary according to their objective function, number and sizes of the facilities and several other decisions (farahani, 2009). traditionally, the objective of flp could be minimizing either the costs of transportation or the distance from the demand areas. the flp was analysed by a lot of researchers (toregas et al., 1971; voogd, 1983; francis et al., 1992; marianov et al., mailto:ahmed.shamah@bhit.bu.edu.eg mailto:ibrahim.sabry@bhit.bu.edu.eg mailto:ahmed.el-assal@bhit.bu.edu.eg a. el-araby et al./oper. res. eng. sci. theor. appl. 5(1) (2022) 121-138 122 2002; drezner & hamacher, 2004) and throughout the analyzation, it was developed to be a mcdm problem where several criteria are taken into account. this type of problems is called multiple criteria facility location problem where it is required to assign suitable location for a facility relative to a set of criteria. these criteria could be transportation costs, the land costs, safety and security, etc. several alternatives are evaluated, data are collected and decisions are made relative to the defined set of criteria. the decision maker (dm) is responsible for making the right decision through various mcdm methods. the main steps in mcdm may be illustrated as follows: (1) establishing the criteria relating to a set of goals. (2) generation of the alternatives. (3) measuring the performance of the alternatives. (4) applying a mcdm technique. (5) ranking of the alternatives. (6) accepting the solution obtained from the mcdm technique(s). steps (1) and (6) are mainly dependent on the decision makers while the other steps are likely an engineering tasks. a lot of potential is exerted in generating and evaluating the alternatives (steps (2) and (3)), and it can be even more harder to evaluate the alternative in some cases such as in the dynamic environment where the performance can be changed as a function of time. the generation of alternatives is a complicated process where there is no exact method or mathematical model to help in such process. nothing can replace the human creativity in generating the alternatives. for step (4), the decision maker must show his preference in applying a certain technique for obtaining the weights of criteria and the ranking of alternatives. many mcdm approaches are available nowadays, most of them are following the same steps of making a decision. the only doubt is that each mcdm techniques produces a diverse ranking from the other techniques (voogd, 1983). the differences in the mathematical models of mcdm methods leads to inconsistency of ranking. afterwards, leads to several possible solutions. several mcdm methods can be applied to flps such as technique for order of preference by similarity to ideal solution (topsis) method, grey relational analysis (gra) method, weighted sum method (wsm), analytical hierarchical process (ahp) (alosta et al. 2021), evaluation based on distance from average solution (edas) method and combined compromise solution (cocoso) method. the pre-mentioned methods require a method for assigning the weights for criteria except for ahp as criteria weights are calculated using pairwise comparisons between the criteria. most of mcdm methods requires a technique for assigning the weights of criteria as each criterion must have its importance compared to other criteria. the assigned weights can be calculated through subjective or objective methods. in subjective methods, the weights are determined through the experience of judgements while the objective methods depend on mathematical computations that neglects the decision maker preference towards some criteria. one of the most common objective weighting methods is entropy weight method (ewm). the ewm is used widely by decision makers for determining criteria weights. however, it sometimes fails to express the importance of certain criterion within a set of decision criteria. a comparative study of using mcdm methods integrated with entropy weight method for evaluating facility location problem 123 in this research, the classical methods namely topsis and gra are compared with some newly developed methods namely edas and cocoso for evaluating the facility location problem. the focus will be on the deviation of ranking for the four different methods and whether they will agree the best and worst alternative or not. the procedures of each method will be illustrated and the methods will be compared through a numerical example concerning a facility location problem. 2. literature review in this section, the past studies that evaluated flps using mcdm is presented while there is a lot of focus on the studies that used more than one mcdm method for the evaluation of location problems as decision makers seek for optimal and consistent solutions. however, no solution will be considered to be the optimum one in the existence of conflicting criteria (shokri et al., 2013). some studies used only one method to evaluate location problems as athawale et al. (2012) applied promethee ii method for flp under linguistic expressions. the method was proved to be effective tool for location selection problems. żak and węgliński (2014) applied electre iii/iv method for location selection of logistics center in poland. stević et al. (2015) applied ahp method for location selection of logistics center with three candidate locations. many studies headed for using more than one mcdm method to ensure the consistency of results as chakraborty et al. (2013) applied four mcdm methods for location selection of distribution centers, the four methods are gra, multi-objective optimization on the basis of ratio analysis (moora), operational competitive rating analysis (ocra) and electre ii. the four methods agreed the best location while there was a deviation in ranking for the remaining locations. they concluded that the deviation that occurred in ranking of the locations within each method is due to the difference in the mathematical model of each method. niyazi and tavakkoli (2014) used three mcdm methods for the same problem, the methods are topsis, additive ratio assessment (aras) and complex proportional assessment (copras). the three methods produced different ranking even for the best location. parhizgarsharif et al. (2019) ranked forty locations in a construction site to choose the top twenty locations for establishing twenty facilities within them. the criteria weights were determined using best-worst method (bwm), gra and vikor methods were used for ranking the sites. they concluded that gra method is reliable and its ranking can be considered as a final solution for their case study. mihajlović et al. (2019) applied two mcdm methods for location selection of logistics center in serbia. they used ahp and hybrid ahp-waspas methods, ahp method for criteria weights, moreover, the ranking of alternatives and waspas for ranking of alternatives using weights from ahp method. the two methods agreed the choice of best and worst alternative, furthermore, the ranking was almost identical. adalı and tuş (2021) ranked four candidate hospital site locations by topsis, edas and combinative distance-based assessment (codas) methods. the three methods produced the same ranking and the authors pointed out to the simplicity of both topsis and edas methods. chen et al. (2018) used edas and modified waspas methods for a teahouse location selection in lithuania. the results showed that using a. el-araby et al./oper. res. eng. sci. theor. appl. 5(1) (2022) 121-138 124 random weighting techniques leads to inconsistent ranking of applied mcdm methods. the integration of fuzzy theory with mcdm methods was mostly used to overcome the problem of dealing with linguistic variables in most of mcdm methods. as a result, chauhan and singh (2016) applied fuzzy ahp and fuzzy topsis to determine a location for throwing away the healthcare waste. suman et al. (2021) compared between ahp and fuzzy ahp methods for location selection of furniture industry in bangladesh. the two methods agreed the ranking of alternatives. however, there was a variation in the priority of weights developed by the two methods. kieu et al. (2021) used hybrid spherical fuzzy ahp and cocoso method for location selection of distribution center in vietnam. they proved the stability of cocoso method as the ranking was consistent regardless the value of parameter 𝜆. 3. methodology in this study, the ewm is used to determine the criteria weights and the final ranking of alternatives will be done using topsis, gra, edas and cocoso methods. topsis and gra methods are well known to most of decision makers. however, the recently developed methods namely edas and cocoso require further analysis and preview. the beginning of the solution of any of the proposed methods must be the construction of the decision making matrix which represent the performance evaluation of alternatives with respect to criteria chosen by the decision makers. 𝐷 = [ 𝑥11 𝑥12 … 𝑥1𝑗 𝑥1𝑛 𝑥21 𝑥22 … 𝑥2𝑗 𝑥2𝑛 ⋮ ⋮ ⋮ ⋮ ⋮ 𝑥𝑖1 𝑥𝑖2 … 𝑥𝑖𝑗 𝑥𝑖𝑛 ⋮ ⋮ ⋮ ⋮ ⋮ 𝑥𝑚1 𝑥𝑚2 … 𝑥𝑚𝑗 𝑥𝑚𝑛] 𝑚×𝑛 the rows stand for alternatives and the columns stand for criteria, 𝑖 = 1, 2, … , 𝑚 and 𝑗 = 1, 2, … , 𝑛. 3.1 entropy weight method the entropy concept was developed by shannon (1948) in theory of the communication to deal with uncertain information and missing data. however, the entropy concept was used to describe the irreversible motion that occurs in thermodynamics science. later, entropy concept was found to be effective dealing with decision making problems (zeleny, 2012). the method depends on the numerical data collected by decision makers to determine the relative importance of each criterion. in other words, the shannon`s entropy was extended to entropy weight method which is an objective method for determining the weights of criteria. the steps of entropy weight method can be illustrated as follows: (1) the normalization of numerical data using weitendorf`s linear normalization (aytekin, 2021), �̅�𝑖𝑗 = 𝑥𝑖𝑗 − min 𝑖 𝑥𝑖𝑗 max 𝑖 𝑥𝑖𝑗 − min 𝑖 𝑥𝑖𝑗 (1) a comparative study of using mcdm methods integrated with entropy weight method for evaluating facility location problem 125 �̅�𝑖𝑗 = max 𝑖 𝑥𝑖𝑗 − 𝑥𝑖𝑗 max 𝑖 𝑥𝑖𝑗 − min 𝑖 𝑥𝑖𝑗 (2) eq. (1) for benefit criterion and eq. (2) for cost criterion. (2) calculate the intensity of the attributes using, 𝑦𝑖𝑗 = �̅�𝑖𝑗 ∑ �̅�𝑖𝑗 𝑚 𝑖=1 (3) (3) calculate the entropy measure using, 𝐸𝑗 = − 1 ln(𝑚) × ∑ 𝑦𝑖𝑗 ∙ 𝑙𝑛(𝑦𝑖𝑗) 𝑚 𝑖=1 ; {𝑖𝑓 (𝑦𝑖𝑗 = 0) → (𝑦𝑖𝑗 ∙ 𝑙𝑛(𝑦𝑖𝑗)) = 0} (4) (4) determine the weight of each criterion using, 𝑤𝑗 = 1 − 𝐸𝑗 ∑ (1 − 𝐸𝑗) 𝑛 𝑗=1 (5) 3.2 topsis method the classical topsis procedures was developed by hwang and yoon (1981) in their book “multiple-attribute decision making” that was considered to be one of the most efficient mcdm methods. the basic algorithm of topsis method is that the most preferred alternative having the minimum distance from the positive ideal solution (pis) and the maximum distance from the negative ideal solution (nis). the steps of classical topsis method can be illustrated as follows: (1) normalize the numerical data using vector normalization represented by the formula, 𝑟𝑖𝑗 = 𝑥𝑖𝑗 √∑ 𝑥𝑖𝑗 2 𝑚 𝑖=1 ⁄ (6) where 𝑖 = 1, 2, … , 𝑚 and 𝑗 = 1, 2, … , 𝑛 from the decision matrix [d]. (2) calculate the weighted normalized matrix using, 𝑣𝑖𝑗 = 𝑤𝑗𝑟𝑖𝑗 (7) where 𝑖 = 1, 2, … , 𝑚 , 𝑗 = 1, 2, … , 𝑛 and 𝑤𝑖 is weight of each criterion as ∑ 𝑤𝑗 = 1 𝑛 𝑗=1 . (3) determine the pis and the nis for each alternative using, a. el-araby et al./oper. res. eng. sci. theor. appl. 5(1) (2022) 121-138 126 𝑃𝐼𝑆 = {𝑣1 +, … , 𝑣𝑛 +} = {(max 𝑖 𝑣𝑖𝑗| 𝑗 ∈ 𝐼 ′) , (min 𝑖 𝑣𝑖𝑗| 𝑗 ∈ 𝐼 ′′)} (8) 𝑁𝐼𝑆 = {𝑣1 −, … , 𝑣𝑛 −} = {(min 𝑖 𝑣𝑖𝑗| 𝑗 ∈ 𝐼 ′) , (max 𝑖 𝑣𝑖𝑗| 𝑗 ∈ 𝐼 ′′)} (9) where 𝐼′ represents benefit criteria and 𝐼′′ represents cost criteria. (4) calculate the distances from the pis and nis for each alternative dependent on the euclidean distance. the distance from the pis is calculated as, 𝐷𝑖 + = √∑(𝑣𝑖𝑗 − 𝑣𝑗 +)2 𝑛 𝑗=1 (10) and similarly the distance from the nis is calculated as, 𝐷𝑖 − = √∑(𝑣𝑖𝑗 − 𝑣𝑗 −)2 𝑛 𝑗=1 (11) (5) calculation of the closeness coefficient for each alternative using, 𝐶𝐶𝑖 = 𝐷𝑖 − 𝐷𝑖 + + 𝐷𝑖 − (12) (6) ranking of the alternatives on basis of the closeness coefficient values. the higher the value of the closeness coefficient the more preferred the alternative. 3.3 gra method grey relational analysis (gra) is derived from the grey theory that was developed by ju-long (1982). the grey theory proved to be efficient dealing with incomplete information. the word “grey” refers to the mixture of black and white, the colour black for unavailable information and white for the available information. kuo et al. (2008) tested gra method as a decision making method by comparing it with three different methods. they proved that gra method is applicable as mcdm method for real-world problems. the steps of the gra method can be illustrated as follows: (1) the normalization of the decision making matrix using weitendorf`s linear normalization represented by equations (1) and (2). (2) compute the deviation from reference sequences matrix using, ∆𝑖𝑗= |𝑥0𝑗 − 𝑥𝑖𝑗| (13) where 𝑥0𝑗 = 𝑀𝑎𝑥{𝑥𝑖𝑗, 𝑗 = 1, 2, … , 𝑛} (3) calculation of the grey relational coefficients. a comparative study of using mcdm methods integrated with entropy weight method for evaluating facility location problem 127 𝛾(𝑥0𝑗, 𝑥𝑖𝑗) = ∆𝑚𝑖𝑛 + 𝜉∆𝑚𝑎𝑥 ∆𝑖𝑗 + 𝜉∆𝑚𝑎𝑥 (14) where, the distinguishing coefficient 𝜉 ∈ [0,1], ∆𝑚𝑖𝑛= 𝑀𝑖𝑛{∆𝑖𝑗, 𝑖 = 1, 2, … , 𝑚 ; 𝑗 = 1, 2, … , 𝑛}, ∆𝑚𝑎𝑥= 𝑀𝑎𝑥{∆𝑖𝑗, 𝑖 = 1, 2, … , 𝑚 ; 𝑗 = 1, 2, … , 𝑛}. (4) calculation of the grey relational grade (grg) for each alternative. γ(𝑋0, 𝑋𝑖) = ∑ 𝑤𝑖 𝑛 𝑗=1 𝛾(𝑥0𝑗, 𝑥𝑖𝑗) (15) 𝑤𝑗 is weight of each criterion as ∑ 𝑤𝑗 = 1 𝑛 𝑗=1 . (5) ranking of the alternatives on basis of grg values. the best alternative has the highest value of grg. 3.4 edas method the edas method developed by keshavarz et al. (2015), is claimed to be useful dealing with conflicting set of criteria in decision making problems. in edas method the evaluation is based only on one measure which is the distance from the average solution in positive and negative directions. the steps of edas method can be illustrated as below: (1) the average solution (av) according to a set of criteria is calculated using, 𝐴𝑉̅̅ ̅̅𝑗 = ∑ 𝑥𝑖𝑗 𝑛 𝑖=1 𝑛 (16) (2) the positive and negative distances from the average solution matrices are calculated using, if 𝑖 ∈ 𝐼′ then use equations, 𝑃𝐷𝐴𝑖𝑗 = max (0, (𝑥𝑖𝑗 − 𝐴𝑉̅̅ ̅̅𝑗)) 𝐴𝑉̅̅ ̅̅𝑗 (17) 𝑁𝐷𝐴𝑖𝑗 = max (0, (𝐴𝑉̅̅ ̅̅𝑗 − 𝑥𝑖𝑗)) 𝐴𝑉̅̅ ̅̅𝑗 (18) if 𝑖 ∈ 𝐼′′ then use equations, a. el-araby et al./oper. res. eng. sci. theor. appl. 5(1) (2022) 121-138 128 𝑃𝐷𝐴𝑖𝑗 = max (0, (𝐴𝑉̅̅ ̅̅𝑗 − 𝑥𝑖𝑗)) 𝐴𝑉̅̅ ̅̅𝑗 (19) 𝑁𝐷𝐴𝑖𝑗 = max (0, (𝑥𝑖𝑗 − 𝐴𝑉̅̅ ̅̅𝑗)) 𝐴𝑉̅̅ ̅̅𝑗 (20) (3) calculation of the weighted sum of 𝑃𝐷𝐴 and 𝑁𝐷𝐴 for each alternative using, 𝑆𝑃𝑖 = ∑ 𝑤𝑗𝑃𝐷𝐴𝑖𝑗 𝑛 𝑗=1 (21) 𝑆𝑁𝑖 = ∑ 𝑤𝑗𝑁𝐷𝐴𝑖𝑗 𝑛 𝑗=1 (22) (4) normalization of 𝑆𝑃 and 𝑆𝑁 values for each alternative using, 𝑁𝑆𝑃𝑖 = 𝑆𝑃𝑖 max 𝑖 𝑆𝑃𝑖 (23) 𝑁𝑆𝑁𝑖 = 1 − 𝑆𝑁𝑖 max 𝑖 𝑆𝑁𝑖 (24) (5) calculate the appraisal score for each alternative using, 𝐴𝑆𝑖 = 1 2 (𝑁𝑆𝑃𝑖 + 𝑁𝑆𝑁𝑖) (25) where 0 ≤ 𝐴𝑆𝑖 ≤ 1 (6) ranking the alternative based on the values of 𝐴𝑆𝑖 where the best alternative has the highest value of average score. 3.5 cocoso method this method was developed recently by yazdani et al. (2019) which is based on two common approaches namely weighted sum model (wsm) and exponentially weighted product model. this method develops three different appraisal scores to evaluate the alternatives. thus, a final coefficient combining these scores is calculated to obtain more robust results. the steps of the cocoso method is shown as follows: (1) the normalization of the decision making matrix using equations (1) and (2). (2) the calculation of the comparability sequences using, 𝑆𝑖 = ∑ 𝑤𝑖�̅�𝑖𝑗 𝑛 𝑗=1 (26) a comparative study of using mcdm methods integrated with entropy weight method for evaluating facility location problem 129 𝑃𝑖 = ∑(�̅�𝑖𝑗) 𝑤𝑗 𝑛 𝑗=1 (27) 𝑆𝑖 is the sum of the weighted comparability sequences and 𝑃𝑖 is the sum of the power weighted comparability sequences. (3) three appraisal scores are calculated using, 𝑘𝑖𝑎 = 𝑆𝑖 + 𝑃𝑖 ∑ (𝑆𝑖 + 𝑃𝑖) 𝑚 𝑖=1 (28) 𝑘𝑖𝑏 = 𝑆𝑖 min 𝑖 𝑆𝑖 + 𝑃𝑖 min 𝑖 𝑃𝑖 (29) 𝑘𝑖𝑐 = 𝜆𝑆𝑖 + (1 − 𝜆)𝑃𝑖 𝜆 max 𝑖 𝑆𝑖 + (1 − 𝜆) max 𝑖 𝑃𝑖 , 𝜆 ∈ [0,1] (30) (4) final ranking of the alternatives based on the values of coefficient 𝑘𝑖 as the higher the value the more preferred the alternative. 𝑘𝑖 = (𝑘𝑖𝑎𝑘𝑖𝑏𝑘𝑖𝑐) 1 3⁄ + 1 3 (𝑘𝑖𝑎 + 𝑘𝑖𝑏 + 𝑘𝑖𝑐) (31) 4. numerical example in this section, the location problem presented by żak and węgliński (2014) is adopted. the aim of the problem is to select the most suitable region for placing logistics center (lc) in poland. ten different locations are nominated for placing the lc on their region, each location covers an area of 12 – 44 thousands 𝑘𝑚2 and has a specific characteristic than the others. the performance of nominated locations is measured relative to nine criteria represented by c1, c2, …., c9 are considered to meet the stakeholders` interest and requirements. the set of criteria considered in this example are, condition of transportation infrastructure (c1); economic development (c2); investment cost (c3); level of transportation and logistics competitiveness (c4); investment attraction (c5); transportation and logistics attraction (c6); social attraction (c7); environmental affability (c8); safety and security (c9). the attentive reader can refer to żak and węgliński (2014) for more details about the case study. the performance of alternatives within the set of criteria is shown in table (1). the outranking electre iii/iv method was used to solve this problem. however, the proposed mcdm methods (section 3) are used in this study which gives a clear ranking of the alternatives. a. el-araby et al./oper. res. eng. sci. theor. appl. 5(1) (2022) 121-138 130 table 1. the performance of the alternatives respect to criteria criterion c1 c2 c3 c4 c5 c6 c7 c8 c9 preference max max min min max max max max max a1 90.3 11350 392 9 1110 9709 4.5 7.5 7.5 a2 132.2 11558 421 12 1019 13379 7.17 6.5 4.5 a3 98 9416 395 6 1176 6991 4.33 6.5 8 a4 101.3 13275 443 9 312 11904 4.17 6.5 6 a5 138.5 11939 402 6 606 7958 7 8 7.5 a6 146.8 20049 424 18 284 15669 4 6.5 3.75 a7 133.1 9396 393 7 900 10425 7 6 7.5 a8 121.7 12989 395 10 2789 13275 8 7.5 5.25 a9 222.7 13822 406 12 1733 14382 4.17 4 3.75 a10 146.9 10131 397 13 2355 11653 7 4.5 4.75 5. results and analysis in this section, the weights of each criterion are computed, the results of the four methods will be discussed and presented within tables. a comparative analysis between the four methods including spearman`s rank correlation analysis will be discussed. 5.1 ew method the weight of each criterion is calculated as shown in table (2). the weights of criterion c2 and c7 are the highest among the set of criteria which is realistic as the economic development (c2) and the social attractiveness (c7) are important factors for the success of the logistics center. the level of transportation and logistics competitiveness (c4) has the least value of weight which is confusing as the transportation is one of the most factors affecting the logistics centers. however, the weights obtained by the entropy method is satisfying for an objective weighting method. table 2. the entropy weights of each criterion criteria c1 c2 c3 c4 c5 c6 c7 c8 c9 𝑬𝒋 0.851 0.799 0.934 0.935 0.833 0.903 0.794 0.918 0.841 𝒘𝒋 0.125 0.168 0.055 0.054 0.141 0.081 0.173 0.069 0.133 5.2 topsis method the ranking of each alternative on basis of the closeness coefficient values is shown in table (3). the ranked one alternative (a8) has the shortest distance from the ideal solution and the longest distance from the worst solution. thus, it has the highest value of closeness coefficient. a comparative study of using mcdm methods integrated with entropy weight method for evaluating facility location problem 131 table 3. the final ranking of topsis method alternative 𝑫𝒊 + 𝑫𝒊 − 𝑪𝑪𝒊 rank a1 0.08149 0.04220 0.34117 9 a2 0.07506 0.04434 0.37136 6 a3 0.08488 0.04538 0.34837 8 a4 0.09632 0.03011 0.23820 10 a5 0.08081 0.04898 0.37739 5 a6 0.09445 0.05166 0.35360 7 a7 0.07892 0.04857 0.38097 4 a8 0.04640 0.08992 0.65963 1 a9 0.06414 0.06401 0.49948 3 a10 0.05745 0.07238 0.55746 2 5.3 gra method the results of gra method are presented in table (4). the value of the distinguishing coefficient (𝜉) was set initially at 0.5 as per past researches (tosun, 2006; kuo et al., 2008; abhang et al., 2021). the ranked one alternative (a8) has the highest value of grg. in other words, a8 has the most similarity to reference sequence that makes it the best possible choice among the set of alternatives. table 4. the final ranking of gra method alternative grg rank a1 0.51695 8 a2 0.49420 9 a3 0.52507 7 a4 0.43080 10 a5 0.58826 2 a6 0.53862 4 a7 0.55923 3 a8 0.68309 1 a9 0.53136 5 a10 0.52805 6 the value of distinguishing coefficient is analyzed to study its effect on the results of gra method for this example. the distinguishing coefficient was set at 0.25, 0.5, 0.75 and 1 respectively. the results are shown in fig (1). it is important to mention that the ranking of the of alternatives a8, a5, a9 and a4 are always ranked 1, 2, 7 and 10 respectively regardless the value of the distinguishing coefficient. a. el-araby et al./oper. res. eng. sci. theor. appl. 5(1) (2022) 121-138 132 figure 1. the ranking of gra method for different values of distinguishing coefficient 5.4 edas method the results of edas method are presented in table (5). the best alternative (a8) has the highest positive distance from average solution and the shortest negative distance from average solution (after normalization using eq. 24, the value of 𝑁𝑆𝑁𝑖 increases as the value of 𝑆𝑁𝑖 decreases). as a result, the appraisal score of alternative (a8) is the highest among the set of alternatives. it is valuable to note the gap in the appraisal score between a8 (rank one) and a10 (rank two). table 5. the final ranking of edas method alternative 𝑵𝑺𝑷𝒊 𝑵𝑺𝑵𝒊 𝑨𝑺𝒊 rank a1 0.20661 0.53047 0.36854 7 a2 0.20521 0.68894 0.44708 6 a3 0.26318 0.38895 0.32606 8 a4 0.09187 0.25713 0.17450 10 a5 0.43053 0.59305 0.51179 4 a6 0.52181 0 0.26090 9 a7 0.33481 0.64312 0.48896 5 a8 1 0.90288 0.95714 1 a9 0.64331 0.48344 0.56338 3 a10 0.64531 0.64019 0.64275 2 5.5 cocoso method the coefficient (𝜆) in eq. 30 is usually given the value of 0.5 by the decision makers. hence, the results of this method when 𝜆 = 0.5 are presented in table (6). a comparative study of using mcdm methods integrated with entropy weight method for evaluating facility location problem 133 table 6. the final ranking of cocoso method alternative 𝑲𝒊𝒂 𝑲𝒊𝒃 𝑲𝒊𝒄 𝑲𝒊 rank a1 0.09961 2.9070 0.82907 1.9001 6 a2 0.11205 3.2108 0.93264 2.1134 4 a3 0.09051 2.6170 0.75332 1.7166 8 a4 0.08936 2.3526 0.74374 1.6006 9 a5 0.11451 3.5790 0.95307 2.2798 2 a6 0.06815 2.3060 0.56724 1.4272 10 a7 0.10513 3.3134 0.87505 2.1042 5 a8 0.12015 4.0929 1 2.5270 1 a9 0.08841 2.8061 0.73584 1.7774 7 a10 0.11208 3.3375 0.93282 2.1648 3 the values for coefficient (𝜆) must be checked to measure the effect of (𝜆) on the ranking of the alternatives. the test values are 0.25, 0.5, 0.75, 1 respectively. the results of the analysis are shown in figure (2). the only change occurred due to the variation of (𝜆) is the ranking of alternatives a1 and a2 as they switched the ranks when the value of (𝜆) equal to one. the remaining alternatives had the same ranking regardless the value of (𝜆) coefficient. figure 2 the ranking of cocoso method for different values of (𝜆) coefficient. 5.6 comparative analysis the final ranking of topsis, gra, edas, cocoso and reference method is shown in table (7). the results show that there is an agreement on the rank one alternative (a8). a disagreement occurred between the methods for the second choice alternative as edas and topsis methods stand for a10 while gra and cocoso methods stand for a5. a. el-araby et al./oper. res. eng. sci. theor. appl. 5(1) (2022) 121-138 134 table 7. the comparative ranking between the four methods and reference method. alternative topsis gra edas cocoso reference method a1 9 8 7 6 7 a2 6 9 6 4 6 a3 8 7 8 8 10 a4 10 10 10 9 9 a5 5 2 4 2 3 a6 7 4 9 10 4 a7 4 3 5 5 4 a8 1 1 1 1 1 a9 3 5 3 7 1 a10 2 6 2 3 7 figure 3. graphical representation of the ranking order for each method a spearman`s rank correlation coefficient (𝑟𝑆) is calculated to express the deviation between the rankings of different methods in numerical numbers. the value of (𝑟𝑆) always lies between +1 and -1 where the value of (+1) indicates a perfect coincidence between the two methods and the value of (-1) indicated that there is no coincidence between the two methods. the closer the value of (𝑟𝑆) to zero, the weaker the association of the ranking between the two methods. the value of spearman`s rank correlation coefficient can be calculated using, 𝑟𝑆 = 1 − 6 ∑ 𝑑𝑖 2 𝑚 × (𝑚2 − 1) (32) where 𝑑𝑖 is the difference in ranking of the alternative by the two methods and 𝑚 is the number of alternatives. table 8. rank correlation coefficients between the four mcdm methods mcdm method gra edas cocoso topsis 0.69697 0.93939 0.69697 gra 0.61212 0.49090 edas 0.8303 a comparative study of using mcdm methods integrated with entropy weight method for evaluating facility location problem 135 as shown in table (8), there is almost a perfect match between topsis and edas methods as the two methods are similar to each other in the concept of solution while the smallest value of (𝑟𝑆) was between gra and cocoso methods. in general, the gra method has a moderate correlation coefficient when compared to the other three methods 6. conclusions in this study, four mcdm methods namely topsis, gra, edas and cocoso were compared to show the deviation in the ranking of alternatives that occurs when using different mcdm methods. the four methods were applied to solve flp regarding lc location selection and the weights of the criteria were assigned using ewm. the subsequent observations are: 1. the weights obtained by ewm is unreasonable regarding two criteria namely level of transportation and logistics competitiveness (c4) and transportation and logistics attraction (c6) as the transportation criterion is one the most important criterion for lc location selection problem. the decision maker`s preference must be present for such cases when the objective methods fail to express the importance of a certain criterion. however, the two criteria namely economic development (c2) and social attraction (c7) has reasonable weights. 2. although the presence of two conflicting criteria namely investment cost (c3) and investment attraction (c5), the four different mcdm methods proved to be efficient dealing with such case. the alternative (a8) was selected as the best alternative by the four methods while the ranking of the other alternatives has some deviations from a method to others. 3. topsis and edas methods has a very strong relation on basis of the spearman`s correlation value. 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(2014). the selection of the logistics center location based on mcdm/a methodology. transportation research procedia, 3, 555-564. https://doi.org/10.1016/j.trpro.2014.10.034 © 2022 by the authors. submitted for possible open access publication under the terms and conditions of the creative commons attribution (cc by) license (http://creativecommons.org/licenses/by/4.0/). https://doi.org/10.1108/md-05-2017-0458 https://doi.org/10.1109/tac.1963.1105511 https://doi.org/10.1016/j.trpro.2014.10.034 plane thermoelastic waves in infinite half-space caused operational research in engineering sciences: theory and applications vol. 5, issue 1, 2022, pp. 56-68 issn: 2620-1607 eissn: 2620-1747 doi: https://doi.org/10.31181/oresta190222076h * corresponding author. hendi_herlambang@yahoo.com (h. herlambang), zulfa.fitri@mercubuana.ac.id (z. f. ikatrinasari), k.kosasih@mercubuana.ac.id (k. kosasih) single-digit time: toward a quick change-over process with the smed method using the vision system hendi herlambang *, zulfa fitri ikatrinasari, kosasih kosasih industrial engineering department, university mercu buana, jakarta, indonesia received: 21 august 2021 accepted: 29 october 2021 first online: 19 february 2022 research paper abstract: increasing the speed of the product change-over process is critical by implementing the single minute exchange of dies (smed) effectively. the smallest activity variation between operators, activity speed, and process accuracy are identified research targets. this research was developed in the electronic component industry, where the define-measure-analyze-improve-control (dmaic) and hierarchy task analysis (hta) methods can describe the most crucial and key activities. therefore, it takes accuracy and reliability between operators to carry out this activity. this paper presents the acceleration of the product change-over process by developing an automated non-contact inspection method in the assembly area using a vision system. the results of the study illustrate that the change-over process can be carried out in single-digit minutes (7 minutes), or reduced by 81%, and the speed of changeover activities between operators is the same. key words: smed, vision system, automation, inspection, capability process, electronics component. 1. introduction image processing techniques used for robot guidance and automatic inspection are called vision systems widely used in the industrial field (semeniuta et al., 2018). the assembly inspection process is a crucial procedure to perform measurements and detect errors. the dimensional inspection assembly unit is still done manually using a caliper and micrometer that takes a long time, physical contact, and potential difference in measurement between operators (frustaci et al., 2020). connolly stated vision system is mighty, compact, and easy to operate even though it is not a programmer, and this is very interesting for the industry (connolly, 2003). machine vision has been successfully applied to electronic component companies so that the single-digit time: toward a quick change-over process with the smed method using the vision system 57 level of automation can be increased (hendi herlambang et al., 2021). therefore, the vision system is an image processing technique that is easy to use in industry, fast, without physical contact, can avoid measurement errors, and can increase the level of automation. every organization looking to speed up the transition from one product to another focuses on low cost, speed of delivery, and superior quality. single minute exchange of dies (smed) is a lean manufacturing tool that can shorten change-over activities by converting internal time to external time, then streamlining both (shingo, 1985). research conducted by michels concluded that smed can speed up the change-over process so that direct labor is reduced as a finding (michels, 2007). research conducted by demeter found that inventory can be reduced by applying the smed method effectively (demeter & matyusz, 2011). several studies have revealed that the combination of equipment repair and development with the 5s program is the goal so that smed can be implemented effectively (cakmakci, 2009). there have been several investigations found that the application of smed can reduce changeover activity by 41% in the press line (hendi herlambang, 2020b), 30% in the pharmaceutical industry (karam et al., 2018), 42.3% in the injection molding industry (bhade & hegde, 2020), and 43% in the cork industry (sousa et al., 2018). to reduce change-over activity significantly, several tools were used to conduct testing by researchers, rapid entire body assessment (reba) analysis (brito et al., 2017), time study method (simões, 2010), visual stream mapping (azizi, 2015), and the geometrically based methodology (nakeenopakun & aue-u-lan, 2019). therefore, the acceleration of the transition process from one product to another can be done by choosing the right equipment and technology according to the company's needs. based on the description above, there has been little discussion about accelerating the change-over process with the objective of single-digit minutes in the electronic component industry. therefore, researchers are interested in implementing a system vision to accelerate change-over activities in electronic component companies using the smed method. at the internal process, the streamline stage is inserted technology elements to achieve the speed of change-over activity in single-digit units of minutes. this study’s results can provide an overview of the change-over process that can be automated using vision systems quickly. 2. materials and methods the study stages of completion use the define-measure-analyze-improve-control method used by researchers to produce reliable smed application research (shingo, 1985)(roth & franchetti, 2010) (h herlambang, 2020b). 2.1. define this research was conducted in electronic component companies in indonesia, with connector output. electrical connectors are electrical appliances that connect between electrical circuits, most connectors can be removed or reattached, but some can be permanent. h. herlambang et al./oper. res. eng. sci. theor. appl. 5(1) (2022) 56-68 58 figure 1. connector part connectors make electronic products easier to assemble and manufacture and make it easier to repair electrical circuits and allow flexibility in design and modification. connectors are widely used in electrical circuits for communications, computers, industrial machinery, and electronic equipment used by everyone, as seen in figure 1. most connectors consist of two main parts, namely housing and terminals. housing is a cage or structure used to hold the terminals, stabilize the connection, and protect the contact from short circuits and various hazards caused by the environment. housing usually consists of several types of printed plastic but can be made of all kinds of insulator materials, as seen in figure 2, the flow process of connector made. figure 2. the process flow of making electronic connectors production data for one year has been collected to find out productivity indicators. it was found that the 5th process in the change-over activity is the most crucial activity carried out during the change of product type one to another, as seen in figure 2. this activity is carried out repeatedly by the operator manual, and there is physical contact on the product with an average time of 30 minutes. this is in line with herlambang et al., which states that the product detection system through physical contact can have a large measurement deviation between operators and takes a long time (hendi herlambang et al., 2021). 2.2. measure at this stage, secondary data collection from each operator is carried out during the change-over process. data is processed by using minitab software to find out the ability of the process. the data found that the process capability is still not satisfied with a cp value of 0.84 and a cpk value of 0.76, as seen in figure 3. it is also strengthened that in the capability histogram chart, two hills indicate there are two different populations between operators that perform the change-over process. initial data analysis is also carried out to determine the direction of continous improvement in the future as input to top management. four blocks of technology single-digit time: toward a quick change-over process with the smed method using the vision system 59 and control diagrams are used to visualize current conditions by calculating the value of z shift and z lt at this time. it was found that the current state of technology factors still need to be improved for the capability of the process to increase, as seen in figure 4. figure 3. capability process change-over activity 4.5 technology control 1.5 z shift z st poor go od poor go od a b c d ( zst = 2.92 ; z shift = 1.5 ) figure 4. four blok diagram assembly process activity 2.3. analyze at the analysis stage, the authors conducted a more in-depth examination by taking videos to determine the real activities carried out for each operator. to obtain consistency of the observed subjects’ natural movements can be recorded using video (asan & montague, 2014). this can help the author analyze the operator’s movement and then decomposition each activity in detail to see the potential occurrence of errors. analytical techniques are used to determine human error potential at each work level using hierarchy task analysis (hta) (shorrock & kirwan, 2002). as seen in figure 5, the activity of the change-over process of the replacement checker. hta for checker change process has been done decomposition and followed by identifying errors in each activity caused by errors sourced in people and on the h. herlambang et al./oper. res. eng. sci. theor. appl. 5(1) (2022) 56-68 60 information system. as seen in figure 5, sub-tasks given different colors are the most crucial activities with the most potential for errors. task 2.4 and 3.4: insert parts one by one. insert small box sticks one by one into the block stick, according to the product to be produced. this process is done manually, and the number of box sticks should not be more or less. the following errors have been identified in this activity : 1. box sticks amount more or less if done with a decreased concentration level. the operator must calculate the number of box sticks manually and align with the product set up, which will significantly help part installation errors. 2. the box stick is jammed because it is rusty. to prevent this from happening, the operator must perform cleaning and lubrication on the box sticks and stick blocks. task 4.1: manual positioning product with the checker. alignment process by aligning the product with box sticks, with the aim of optimal checker detection process. task 4.2: check the straightness visually. inspection using eye visualization is the most important. if task 4.1 and 4.2 are not appropriately done, then : 1. detection of less than maximum wasted products, but products that do not fit the requirements will still be wasted to the scrap box. 2. the machine’s ability will go down because often the machine trouble caused by the alignment is not good. 1. open machine cover 1.1. open the tools box 1.2. take a screwdriver to open the machi ne cover 1.3. open the cover with a s crewdriver 2.1. take heksago nal wrench set 2.2. open b lock set 1.4. secure the laying of the machine cover 1.5. return the screwdriver to its place 2. open part 1 st checker 2.3. clean up 2.4. ins ert part 1 by 1 2.5. close block set 3.1. take heksago nal wrench set 3.2. open b lock set 3. open part 2 nd checker 3.3. clean up 3.4. ins ert part 1 by 1 3.5. close block set 4.1. manual pos itioning product with checker 4.2. check the straightness visually 4. allignmnet setting 0. checker change-over tasks plan 0 : do 1, 2, 3, and 4 in order plan 1 : do 1.1 th en 1.5 in order plan 2 : do 2.1 th en 2.5 in order plan 3 : do 3.1 th en 3.5 in order plan 4 : do 4.1 th en 4.2 in order, repeat until 4.2 really s traight figure 5. hierarchy task analysis change-over activity single-digit time: toward a quick change-over process with the smed method using the vision system 61 this checker change activity is an activity that authors say requires a high level of concentration and work experience. to prove this hypothesis, the authors conducted tests on two operator populations. the first operator with a working period of more than two years, and the second is with an operational period of fewer than two years, with a hypothesis: ho: there is no difference in the speed of change-over activity above 2 years and below 2 years. h1: there is a difference in the speed of change-over activity above 2 years and below 2 years. it was found that the ho hypothesis was rejected, and the h1 hypothesis was accepted, with a p-value< 0.05 as seen in figure 6, for easier visualization of speed differences between operators, display the plot box diagram for total time change over, as seen in figure 7, and the detail as seen in figure 8. figure 6. compare means test figure 7. box plot operator capability h. herlambang et al./oper. res. eng. sci. theor. appl. 5(1) (2022) 56-68 62 figure 8. detail time checker change-over activity after a more in-depth data check of each operator’s activities, it was found that there were significant differences with some operators. as seen in figure 6, the average operator speed of group 1 (above 2 years) when doing the change-over activity is 29.7 minutes, and the 2nd group is 37 minutes. then the standard deviation value of the 1st operator group is better than the 2nd operator group. so from the analysis of this data, the speed of the 1st group operator and the 2nd group operator is better than group 1 is caused by more extended group 1 operator experience. although there are already guidelines for the change-over process, skills must be continuously trained so that the operator’s ability continues to improve. 2.4. improve internal activities by streamlining change-over activities choose the vision system’s application to eliminate the risk of errors, maintain quality factors, and speed up the change-over process. the vision system consists of an object detection module with the sensor head (camera), sensor amplifier, programmable logic controller (plc), and power supply. as seen in figure 9 is the configuration system applied to this research. figure 9. configuration system vision system (keyence, 2019) single-digit time: toward a quick change-over process with the smed method using the vision system 63 lighting techniques and lights are already integrated with the camera making it easier for researchers to conduct experiments quickly. the camera is mounted at a distance of 220 mm from the object to be detected. the detected object’s size is 25 mm, and the system will be mounted on the machine at a speed set by the pneumatic system. the camera acquisition configuration system uses a camera integrated with a led light with a size of 0.5 megapixels. objects detected by the vision system are the structure’s quality (incomplete part) and the quality of dimensions (following the requirements standards). experiments for image capture are carried out several times to measure the process’s stability, as seen in figure 11. the detection step with the vision sensor includes; step 1. the setting of image optimization set the image optimization for clearly imaging the target. adjust the image for defining the differences in the high and low-qualitytarget. set the trigger option, adjust the brightness, and imaging focus, as seen in figure 10, an external trigger time chart is selected. (1) start imaging by inputting the trigger at an arbitrary timing. when the trigger delay interval is set, the imaging start time will be delayed in the specified period. (2) performs internal processing after imaging. (3) outputs the status result. figure 10. external trigger selected time chart step 2. registration of master image, image the high-quality target, and register the master image to serve as the reference of judgment. step3. tool settings, set the tool to judge a target, set the tool onto the master image, and set the threshold for judgment. step 4. output assignment, assign the function to output to each output line. the quality of image processing will be better if the field of view (fov) size is 18 mm x 25 mm with vision sensor distance to objects as far as 50 mm, and field of view (fov) size of 157 mm x 210 mm with vision sensor distance with objects as far as 500 mm. not only does the quality of the structure have to be detected by the system, but the quality of the dimensions is also absolutely detected, with the allowed tolerance being below 0.1 mm. h. herlambang et al./oper. res. eng. sci. theor. appl. 5(1) (2022) 56-68 64 figure 11. experiment illustration 2.5. control external activities (activities performed while the machine is still running) and convert internal to external processes have been implemented by the company. eliminating unwritten activities in the order in which the change-over process is intended to make the process run effectively and efficiently (oakland, 2008)(hendi herlambang, 2020a). all change-over activities are documented on the computer by creating graphic visualizations for easy translation by operators. 3. result and discussion the experiment has been completed with each product damage results can be well detected by vision sensors. then the author checks the accuracy of output data from the vision sensor by using the statistic test with gage study, as seen in figure 12. figure 12. gage study vision system single-digit time: toward a quick change-over process with the smed method using the vision system 65 as seen in figure 12, data stability testing on dimensional measurement is excellent, with a cg value of 2.34 and a cgk value of 2.26. furthermore, this is strengthened by repeatability and repeatability-bias values with 8.56% and 8.86% values, respectively. the structure’s quality is collected from the findings of the findings that have occurred and done grouping each product defect’s quality. as seen in figure 13, the output of the vision system can capture well the standard product (a), defects in the product structure in the housing (b), and defects in the product structure on the pin (c). figure 13. output vision sensor the total time required to change one type of product to another is 6 minutes. so that change-over checker activity can be reduced significantly with detection level also increased to non-contact detection. thus, the hta table activities, as seen in figure 5, ranging from the 1st activity to the 4th activity, can be eliminated, with minimal risk of failure. after the experiment is complete, the authors validate each operator’s measurement results using a new method of system vision. this is done to find out the shift in z value from technology and control factors. from the results of data processing, it is seen that there is an increase in the level of quality in the quadrant of technological factors as seen in figure 14. 4.5 technology control 1.5 z shift z st poor go od poor go od a b c d ( zst = 2.92 ; z shift = 1.5 ) ( zst = 5.04 ; z shift = 1.5 ) figure 14. four blocks quadrant after evaluation using the vision system h. herlambang et al./oper. res. eng. sci. theor. appl. 5(1) (2022) 56-68 66 3. conclusion the purpose of this study was to determine the effect of adding elements of technology (vision system) to the speed of the change-over process carried out by operators with different working periods. the findings of this study make several contributions to the current literature. first, the use of a vision system in electronic companies can speed up the change-over process within 7 minutes, previously it was 37 minutes, as seen in figure 15. this achievement succeeded in achieving the singledigit minute target. second, the use of the vision system can be done easily for operators with different working periods. third, the variation in the speed of both change-over activities is small, so it can be said that the speed of the change-over process is the same for both. the change over process activity has been explained using the hierarchy task analysis (hta) method. fourth, four main manual activities can be eliminated after implementation with the vision system, so that measurement errors and measurement bias can be avoided. this research is limited by the size of the target object. one source of weakness in this study that can affect the length of change-over activity is the size of the product detected. thus, further research is required for a vision system that can be used for common product sizes but has an optimal field of view (fov) value. figure 15. result chart after improvement implementation acknowledgment: the authors would like to express deepest gratitude and appreciation to all parties who have helped during this research, including the editors and reviewers. references asan, o., & montague, e. 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(2018). applying smed methodology in cork stoppers production. procedia manufacturing, 17, 611–622. https://doi.org/10.1016/j.promfg.2018.10.103 © 2022 by the authors. submitted for possible open access publication under the terms and conditions of the creative commons attribution (cc by) license (http://creativecommons.org/licenses/by/4.0/). https://doi.org/10.1016/j.procir.2017.12.209 https://doi.org/10.1016/s0003-6870(02)00010-8 https://doi.org/10.3182/20100908-3-pt-3007.00065 https://doi.org/10.1016/j.promfg.2018.10.103 plane thermoelastic waves in infinite half-space caused operational research in engineering sciences: theory and applications vol. 5, issue 1, 2022, pp. 169-184 issn: 2620-1607 eissn: 2620-1747 doi: https://doi.org/10.31181/oresta250322166r * corresponding author. daniel.rossit@uns.edu.ar (d. rossit), ftohme@criba.edu.ar (f. tohmé), rodrigointrocaso@gmail.com (r. introcaso), jearodriguez.98@gmail.com (j. rodriguez) mathematical modelling of non-permutation flow shop processes with lot streaming in the smart manufacturing era daniel alejandro rossit 1,2*, fernando tohmé 2,3, ,rodrigo introcaso 1, jeanette rodríguez 1 1 engineering department, universidad nacional del sur, bahía blanca, argentina 2 inmabb, conicet, bahía blanca, argentina 3 economics department, universidad nacional del sur, bahía blanca, argentina received: 26 october 2021 accepted: 21 march 2022 first online: 25 march 2022 research paper abstract: industry 4.0 is leveraging the production capabilities of the industry. the deep digitalization that industry 4.0 promotes enables to extend control skills to an exhaustive detail in the shop floors. then, new planning strategies can be designed and implemented. we present mathematical models to represent non-permutation flow shop processes, incorporating industry 4.0 features and customer-focused attention. basically, we study the impact of lot streaming on the ensuing optimization problems, since the work-in-process inventory control is considerably enhanced by industry 4.0 technologies. thus, is possible to take advantage of subdividing the production lots into smaller sublots, as lot streaming proposes. to test this hypothesis we use a novel approach to non-permutation flow shop problems which requires a lot streaming strategy, incorporating total tardiness as objective function. our analysis indicates that lot streaming improves results increasingly with the number of machines. we also find that the improvement is less steep with more sublots, increasing the computational cost of solutions. this indicates that it is highly relevant to fine tune the maximum number of sublots to avoid extra costs. key words: scheduling, mathematical modelling, non-permutation flow shop, lot streaming, industry 4.0, total tardiness. 1. introduction manufacturing systems have changed substantially in the last decade by the increasing digitalization of productive processes (xu et al. 2018). this increases the accessibility, through the so-called cyber-physical systems (cps), to information that mailto:ftohme@criba.edu.ar mailto:rodrigointrocaso@gmail.com mailto:jearodriguez.98@gmail.com rossit et al./oper. res. eng. sci. theor. appl. 5(1) (2022) 169-184 170 before remained confined inside the production machinery (lee et al. 2015). with more access to information, often acquired in real time, it becomes possible to address more precisely decision problems that formerly could be only solved approximately (dolgui et al. 2019). thus, production planning processes can now be solved in a more efficient and integral way. scheduling is one of the stages that will be more affected by the new technologies, since it is the last phase before starting the physical production (ivanov et al. 2016; bicakci & kara 2019). decision-making in scheduling involves solving np hard problems, being thus at least as hard as any problem in which checking a solution requires polynomial time (garey et al. 1976, stanković et al. 2020). in this article we will focus on scheduling for non-permutation flow shop problems. flow shop processes represent systems in which all the production orders are processed in the same sequence. that is, given a class j of n jobs (with j=1,2,…,n) and a set m of m machines (such tha i =1, 2, …, m), the operations on each job j follows the same sequence 1, 2, ..., m on machines. that is, the first operation on j will be carried out on machine 1, the second on machine 2, and so on until the last operation is carried out by m (pinedo 2012). this is the production configuration applied by more than one quarter of the industries of the world (pan et al. 2011). flow shop problems have been widely studied in the literature, but largely focusing on permutation sequences (liao et al. 2006; rossit et al. 2018). in those cases, a single ordering of the jobs is imposed over all the machines, i.e. on each machine i all the n jobs will be processed in the same order. for instance, given 4 jobs such that the processing sequence on the first machine is 2, 1, 3, 4, in the next machines the sequence will be the same (2,1, 3, 4). this condition does not respond to a production process rationale, since in general the machines can process the jobs in different sequences. the main reason for solving the problem restricted to permutation sequences is that the number of possible solutions is n!, while if this restriction is lifted, the number of possible cases raises to n!m (potts et al. 1991). the general case, without the permutation constraint is that of non-permutation scheduling flow shop problems (npfs). note that the solutions to permutation scheduling problems constitute particular instances of npfs solutions. the recent improvements in capacities for decision-making in production environments, makes the latter more treatable. nevertheless, to avoid the combinatorial explosion of seeking npfs solutions, some strategies to reduce the search space are still needed. our approach is to incorporate a technique that contributes to facilitate production activities, namely lot streaming (trietsch & baker 1993). in this treatment, the number of items to be produced by each job is partitioned such that each part is processed independently. adding the lot streaming condition to flow shop problems has led to improved performances in the production processes (sarin & jaiprakash 2007; cetinkaya & duman 2021). lot streaming does not require neither extra layouts nor new technologies (d'amico et al. 2021), but demand more attention at the shop floor, since orders are now divided in several suborders. this division increases the demands on the information and control systems that have to keep track of more entities (pan et al. 2011; ferraro et al. 2019). it becomes thus interesting to analyze how this strategy may impact in the context of the new production environments where the information and control systems have been considerably enhanced. the implementation of lot streaming in non-permutation problems has not been widely mathematical modelling of non-permutation flow shop processes with lot streaming in the smart manufacturing era 171 analyzed, particularly when the focus is the quality of customer service. we analyze this problem in systems in which the compliance with the delivery date agreed on with the customer is the measure of the performance of the system. the goal of this paper is to present new ways of addressing the problems of scheduling in the industry 4.0 by focusing on the new challenges that the new paradigm poses for production planning processes. more specifically, this paper presents a novel milp model for npfs problems, where total tardiness is the objective function optimized by allowing lot streaming. this paper contributes to the literature on npfs by presenting a concrete contribution, namely the introduction of new mathematical formulations and the ensuing results. the rest of the paper is organized as follows. section 2 introduces industry 4.0 and decision making processes in that paradigm, and presents a brief npfs literature review. then, in section 3, we develop new mathematical formulations, detailing their underlying assumptions. section 4 presents and discusses the experimental design and the main results of our investigation. 2. industry 4.0 concepts and literature review in this section we review the relevant notions of industry 4.0 needed for our analysis as well as the literature on lot streaming in non-permutation flow shop processes. both issues become relevant in the last decade thanks to the technological advances that gave rise to the current fourth industrial revolution. 2.1. industry 4.0 concepts the main drivers of this revolution have been the internet of things (iot) and cyber-physical systems, which allow the connection among all the components in the shop floor, leading to the full digitalization of production. in this way, all the information generated in the production process becomes available to the different business functions of the firms (xu et al. 2018; dolgui et al. 2019). figure 1 illustrates how different levels of decision-making, associated to the classical control of production structure isa-95, are integrated by cps. the five levels of isa-95 start at level 0, where the physical process of production is carried out (raw materials are transformed into end products). next, level 1 is in charge of controlling the production tools, recording data as processing speed, temperatures of the tools and pieces, vibrations, etc. level 2 incorporates control systems like plc and scada, which can correct deviations in the production flow. at level 3 are the manufacturing execution systems, in charge of production planning and quality control. at this level is where scheduling problems are solved and the compliance with the plan is monitored. finally, the level 4, of business logistics systems, takes care of the strategic decisions of the firm. cps relate these systems by sharing their information among them, allowing its analysis in real time improving the global efficiency of decision-making (lee et al. 2015; grassi et al. 2020). this richness of information and the availability of powerful computing equipment at level 3 allow handling hard problems like npfs. rossit et al./oper. res. eng. sci. theor. appl. 5(1) (2022) 169-184 172 figure 1. isa-95 levels associated to cps. 2.2. flow shop literature review and research gap the literature on flow shop problems has a long history, starting with johnson’s first paper on the subject in 1954 (johnson, 1954). while the largest part of that literature is centered on pfs, the branch devoted to npfs is rich enough. a foundational result on these problems was published by conway et al. (1967), which shows that when makespan is the objective function, permutation solutions are enough to yield the optimal schedule for up to 3 machines. in a much simpler way, this result had been stated already in (johnson, 1954). this means that npfs genuine solutions make sense for makespan maximization with more than 3 machines. potts et al. (1991) studied instances in which npfs solutions improve the makespan over pfs ones in 1 2 m . rebaine (2005) analyzed the ratio of the makespans of npfs and pfs solutions in the presence of delays in the operations, showing that even with 2 machines pfs solutions cannot ensure the optimal result. rossit et al. (2018b) studied the critical paths of npfs and pfs solutions for 2 jobs and m machines, while in (rossit et al. 2021a) analyzed the processing times that allow pfs solutions to be better than npfs ones, in the same case of 2 jobs and m machines. besides these theoretical contributions there are many empirical studies that show that under different settings npfs solutions improve on those of pfs (tandon et al. 1991; strusevich & zwaneveld 1994; koulamas 1998; jain & meeran 2002; nagarajan & sviridenko 2009; rudek 2011; rossi & lanzetta 2014; benavides & ritt 2016; benavides & ritt 2018). mathematical modelling of non-permutation flow shop processes with lot streaming in the smart manufacturing era 173 as shown in table 1, in most of these works the objective function is makespan. only a few ones consider alternative goals, as for instance those related to delivery dates (for a more exhaustive list, see rossit et al. 2018a). liao et al. (2006) present a key result analyzing several single-objective functions and comparing the pfs and npfs solutions: they show that npfs solutions improve upon pfs ones, even for delivery date-related objective functions. ying et al. (2010) ran a similar analysis and found that in the cases of delivery date functions, npfs solutions improve over pfs ones even more than in the case of completion time-related functions. this is consistent with the findings of liao & huang (2010), who show that for total tardiness, npfs solutions are indeed better than pfs solutions. table 1. main works related to non-permutation flow shop scheduling. for further details see rossit et al. 2018a. reference npfs lot streaming objective function solution approach potts et al. (1991) ✓ ✓ makespan exact tandon et al. (1991) ✓ x makespan heuristic strusevich & zwaneveld (1994) ✓ x makespan exact koulamas (1998) ✓ x makespan heuristic jain & meeran (2002) ✓ x makespan meta-heuristic rebaine (2005) ✓ ✓ makespan exact liao et al. (2006) ✓ x total tardiness (among others) meta-heuristic nagarajan & sviridenko (2009) ✓ x makespan exact liao & huang (2010) ✓ x total tardiness (among others) meta-heuristic rudek (2011) ✓ x makespan exact ziaee (2013) ✓ x total weighted tardiness heuristic rossi & lanzetta (2014) ✓ x makespan meta-heuristic rossit et al. (2016) ✓ ✓ makespan exact benavides & ritt (2016) ✓ x makespan heuristic rossit et al. (2018b) ✓ x makespan exact benavides & ritt (2018) ✓ x makespan heuristic rossit et al. (2021a) ✓ x makespan exact rossit et al. (2021b) ✓ x total tardiness meta-heuristic current study ✓ ✓ total tardiness exact ziaee (2013) addressed npfs with setup times depending on the schedule, under the goal of minimizing the total weighted tardiness, by applying a two-stage method. the first stage yields a permutation solution while in the second stage a non-permutation local search improves it. rossit et al. (2021b) studied npfs problems in industry 4.0 environments with missing operations, optimizing total tardiness, showing that npfs solutions improved over pfs ones in average, in 98% of the cases. this indicates that npfs solutions are relevant in digital manufacturing environments. interestingly enough, there are no contributions analyzing npfs problems with lot streaming and delivery date-related objective functions. as far as rossit et al./oper. res. eng. sci. theor. appl. 5(1) (2022) 169-184 174 we know rossit et al. (2016) is the only one that applies lot streaming strategies to find non-permutation schedules, but with makespan as objective function. we intend, thus, to extend that line of analysis, studying the same problem but under objective functions appropriate for production systems focused on the customer, as for instance seeking the minimization of total tardiness. these features are highlighted in the last row of table 1, indicating that the current one is the only study incorporating npfs and lot streaming as well as total tardiness as objective function. 3. mathematical models in this section we discuss the mathematical formulation of our problem. since it involves industry 4.0 and client-oriented production system (wang et al. 2017; el hamdi et al. 2019; perez et al. 2022) some of the classical assumptions in the analysis of scheduling problems must be replaced. for instance, production orders are no longer make-to-stock but make-to-order, and thus, will not be released in bulk but according to demand. then, the release date becomes a relevant feature of jobs. other assumptions about this scheduling problem are: • preemption is not allowed • each machine can process only one job (or sublot) at a time • each job (or sublot) can be processed by only one machine at a time • processing times are standard and deterministic we follow here the notion of graham et al. (1979), in which j j j f r t corresponds to npfs without lot streaming, while ,j j j f r lot streaming t denotes the problem with lot streaming. 3.1. npfs without lot streaming sets j: jobs, indexed by {j} m: machines, indexed by {i} parameters processing time of unit of job j at the machine i release date of job j due date of job j lot size of items produced by job j setup time for processing job j at machine i. mathematical modelling of non-permutation flow shop processes with lot streaming in the smart manufacturing era 175 a positive large number variables completion time of job j at machine i. tardiness of job j. binary, 1 if job j’ is processed before job j at machine i, 0 otherwise. 1 min n j j z t = = (1) ( 1) , , 1 ij i j ij j ij ij c c p u st tr j i −  +  + +   (2) ( )' '1 , , 'ij ij ij j ij j jic c p u st x i j j +  + − −    (3) ' ' 1, ' j ji jj i x x j j+ =  (4) , 1, ij j ij j ij c r p u st i j +  + =  (5)  ( )max 0, , j j i m jt d c j== −  (6)  , 0; 0,1j ij ijt c x  (7) expressions (1)-(7) characterize the problem. (1) indicates the objective function, the minimization of total tardiness (which is computed according to equation (6)). inequality (2) represents the precedence restriction: a job cannot be processed by machine i until the processing has finished in machine i – 1. inequality (3) indicates that a job j can be processed by machine i after job j’ has released i, if and only if j’ precedes j in the sequence. equation (4) is the logic constraint according to which if job j’ precedes job j on machine i, the opposite cannot be the case. inequality (5) represents a capacity constraint on the first machine, according to which no job cannot start its processing before a request has been received in the form of a due release date, and the completion time depends on all the activities involved in its processing. equation (6) determines the tardiness of each job with respect to its due date, considering only positive values of tardiness. finally, (7) are the feasibility conditions on the variables. 3.2. npfs with lot streaming we have to introduce the expressions that correspond to the incorporation of lot streaming strategies. we keep expressions (1), (4) (6) and (7) of the previous rossit et al./oper. res. eng. sci. theor. appl. 5(1) (2022) 169-184 176 subsection, while (2), (3) and (5) have to be adapted to consider sublots. some additional constraints are also needed. sets f: sublots, indexed by {f} parameters transfer time of a sublot of job j from machine i to machine i + 1. setup time for processing a sublot of job j at machine i. variables completion time of sublot f of job j at machine i. sublot size of sublot f of job j. 1 , f fj j f s u j = =  (8) , , fj fj s y f j   (9) ( 1) ( 1)( 1) ( 1) , , 1 i f j i f j ij f j ij ij c c p s st tr j i = − = =  +  + +   (10) ( ) ( ) ( ) ( )'1 ' 1 1 , , 'ij ij j jii f j i f f j f jc c p s st x i j j= = = +  + − −    (11) ( ) ( )1 ' , , , 2,...., 1 ij fj ij fji f j i f f j c c p s stm y i j f f = =  +  +   = − (12) ( ) ( )1 , , , 2,... 1ifj ij fj fj ij iji f jc c p s y stm tr f j i m− +  +  +  = − (13) ( ) ( )1 1 , 1, j ij iji f j f j c r p s st i j = =  +  + =  (14) expression (8) indicates that all the units of job j must be included in a sublot f of j. since sublots are not fixed (i.e. the size of the sublots is determined by the optimization process), inequality (9) detects the non-empty sublots which require setups and displacement times. equation (10) is a precedence inequality analogous to (2): the first sublot of a product cannot be processed by machine i until it has been finished at machine i – 1. (11) captures the same constraint as (3), namely that job j can be processed after j’ has released machine i, if and only if j’ precedes j in the sequence. this is done considering the first and last sublots of j and j’, 1f = and f f= , respectively. inequality (12) orders the sublots of the same job to be processed sequentially at a given machine. in turn, equation (13) indicates that a sublot cannot be processed simultaneously by two different machines. constraint (14) replaces (5) ensuring that the first sublot of a job will not be processed until its release date has been received. mathematical modelling of non-permutation flow shop processes with lot streaming in the smart manufacturing era 177 4. experiments and results we present here the experiment design and the results obtained by using exact methods (cplex). these experiments are in order to compare the models with and without lot streaming, analyzing the impact of using lot streaming strategies. 4.1. experimental design we aimed to detect whether including lot streaming strategies improve results in industry 4.0 environments. in order to do that, we tested problems of different sizes (in jobs and machines) and different numbers of sublots. the number of jobs chosen was 4, 6, 8 and 10, as well as 3, 5 and 10 machines. we covered all the possible combinations yielding 12 different problems. in turn, for the problems with lot streaming we considered different numbers of sublots. to incorporate a larger number of sublots implies to extend the range of f, increasing the number of instances of expressions (8) – (14), with the consequence of enlarging the computation cost of analyzing the problems. for f we chose 2, 3, 4 and 5, meaning that we had to solve 48 problems. for the parameters defined in subsections 3.1 and 3.2 we selected the following values: uniform distribution [1;5] (it corresponds to processing each unit of uj). uniform distribution [1;50] uniform distribution [1;22] uniform distribution [10;25] uniform distribution [1;4] uniform distribution [1;10] for we used the following rule: 1 m j j ij i d r p = = + . five data sets are generated for all the combinations of machines, jobs and sublots. each data set corresponds to a well-defined problem where each parameter takes a value drawn from one of the probabilistic distributions presented above. then, each problem is solved deterministically by cplex12.10, with a time limit of 3.600 seconds. the experiments are performed on an intel core i5-7200u pc with 8gb of ram. 4.2. results our analysis starts by considering the results on the impact of using lot streaming to solve an npfs problem with total tardiness as objective function. table 2 shows the value of the objective function with plain npfs solutions and the improvement resulting from using lot streaming strategies. the improvements are expressed as percentages. rossit et al./oper. res. eng. sci. theor. appl. 5(1) (2022) 169-184 178 table 2. improvement in the value of the objective function, with respect to the different number of sublots allowed. results correspond to the average of all the runs. n m npfs npfs-lot streaming 2 f 3f 4f 5f 4 3 521 60.7% 61.4% 61.4% 61.4% 5 768 27.1% 35.4% 37.0% 37.2% 10 1241 90.7% 95.2% 98.5% 100.0% 6 3 1149 39.1% 42.1% 42.2% 42.2% 5 1504 18.9% 23.5% 24.3% 24.5% 10 2219 73.3% 83.5% 85.4% 86.0% 8 3 2058 30.0% 30.2% 30.2% 30.2% 5 2523 12.3% 15.9% 16.0% 16.0% 10 3513 60.9% 69.9% 72.0% 10 3 3136 24.0% 5 3721 10 4796 table 2 shows clearly that lot streaming has a considerable impact in improving the objective function. in many cases those improvements are over 50%, and for some case, like the case of 4 jobs and 10 machines, the result is 100% better when 5 sublots are allowed for each job. this means that no product was delivered at a late date, complying with the agreed on delivery dates while without lot streaming total tardiness was 1241. also in the cases where the improvement is not that large, it is over 10%, meaning that the whole system performance can be enhanced without requesting new machines or doubling resources, just exploiting production planning strategies. these enhancements are related to the number of sublots: the more the lot is split in sublots, the larger the resulting improvement. this can be observed by comparing at table 2, at the same row, moving to the right. nevertheless, this improvement is not monotonic, since it reaches a maximum. the largest variations from a number of sublots to the next one obtain at the transition from no lot streaming to allowing 2 sublots. the improvement from further increases in the number of sublots is less pronounced. on the downside, notice that incorporating lot streaming strongly increases the computational cost of finding exact solutions. this can be seen in table 2 by the use of “-” in the cases in which no satisfactory solution is found after an hour of running the solver. we mean by “satisfactory” here a solution that yields a better result with the incorporation of more sublots. so, for instance, if with 2 sublots total tardiness is 1136, when we increase the division to up to 3 sublots, the result will be less than 1136 (since the case of up to 3 sublots includes the case of 2). mathematical modelling of non-permutation flow shop processes with lot streaming in the smart manufacturing era 179 figure 2. lot streaming objective function improvement with respect to different numbers of sublots on the other hand, the impact of lot streaming varies with the size of the problem. figure 2 depicts the results for problems with 4 jobs and 3 and 10 machines, (dotted lines) and 6 jobs with 3 and 10 machines (solid lines). we can see that keeping the number of jobs fixed, lot streaming yields better results with more machines. in turn, if we fix the number of machines, a larger number of jobs worsen the objective function. finally, all the curves have the same shape, with decreasing marginal increases as a function of the number of allowed sublots. that is, there seems to be a saturation number of sublots, after which the objective function no longer improves. we can analyze this more clearly seeing table 3. table 3. number of sublots used in final solutions. (the values are presented in average). n m f_allowed f_used 4 3 2 1.8 3 2.05 4 2.05 5 2.05 5 2 1.95 3 2.65 4 3.1 5 3.25 10 2 2 3 2.9 4 3.25 5 3.25 6 3 2 1.93 3 2.03 4 2.1 5 2.1 5 2 1.97 3 2.6 rossit et al./oper. res. eng. sci. theor. appl. 5(1) (2022) 169-184 180 4 2.73 5 2.93 10 2 2 3 2.97 4 3.53 5 3.71 8 3 2 1.6 3 1.65 4 1.75 5 1.75 5 2 1.93 3 2.58 4 2.75 5 2.75 10 2 2 3 2.78 4 3.53 5 10 3 2 1.5 table 3 shows that, even if a number of sublots are allowed, the optimal value of the objective function can be reached using fewer sublots. as shown by table 2, we can see that allowing more sublots may improve the results in certain cases, but with an increasing computational cost. it is, thus, highly relevant to determine the useful maximal number of sublots that may allow to benefit from adding lot streaming to the search of solutions to npfs. table 4. average cpu time for solving each problem to optimality. n m npfs npfs-lt 2 f 3 f 4 f 5 f 4 3 <sec <sec <sec <sec <sec 5 <sec <sec 1,0 1,0 2,0 10 <sec <sec 2,0 2,0 2,0 6 3 <sec <sec <sec <sec 1,0 5 <sec <sec 1,0 2,0 2,0 10 <sec 1,0 2,0 3,0 3,0 8 3 <sec <sec <sec 1,0 2,0 5 1,0 1,0 2,0 10,0 191,0 10 1,0 1,0 3,0 11,0 429,0 10 3 2,0 1,0 4,0 4,0 >3600 5 2,0 >3600 >3600 >3600 >3600 10 3,0 >3600 >3600 >3600 >3600 for a deeper analysis we examine the computational behavior of the problem according to the features of the problem (number of machines, jobs and allowed sublots). the results are shown in table 4. it can be seen that for any problem size, lot streaming has a direct impact on the computational effort, increasing the time demanded to solve the problem. this effect is proportional to the maximum number of sublots allowed. the larger the number of allowed sublots, the larger the cpu time required by the solver to yield the optimal solution. mathematical modelling of non-permutation flow shop processes with lot streaming in the smart manufacturing era 181 4.3. discussion of results and future developments let us consider the cases in which allowing more sublots per job is associated to a reduction in the value of the objective function (table 2), for instance, in the case of 4 jobs and 10 machines. in this case if we consider the information provided by table 3, the average number of sublots does not change (it remains fixed at 3.25) when the maximum allowed number of sublots increases from 4 to 5 sublots. on the other hand, the objective function corresponding to these problems (table 2) yields a lower value in the case of 5 allowed sublots than in the case of 4 sublots. this means that when the maximum number of sublots remains fixed at 4, some jobs are divided into 4 sublots (the average is over 3), but when 5 sublots are allowed the average is the same. this can be explained by the fact that when 5 sublots are allowed, some jobs that were split into 4 sublots in the case of a maximum of 4 sublots can now be divided into 5 sublots while some other jobs are split into 3 sublots. the composition of sublots must change, because the value of the objective function changes. this prevents us from considering that the solution structure will remain the same for both maximum numbers of sublots. 5. conclusions in this article we analyze the introduction of lot streaming to find optimal schedules in industry 4.0 environments focused on the requests of customers. we seek non-permutation solutions appropriate to flow shop problems. we found that incorporating lot streaming strategies improves results, reducing the total tardiness of delivery. we detected that subdividing the number of items in more sublots has cumulative beneficial effects up to a point. afterwards, adding more sublots does not improve further the results. on the other hand, the computational cost of lot streaming is considerably larger than those of finding solutions without lot streaming. the main conclusion it that while some jobs can be divided into several sublots, others are more resistant to be split. if the jobs can be classified by their features (number of units, accumulated processing times, due dates, etc.), the optimizing process can be fine-tuned to allow more sublots only for the types of jobs that require them while keeping as low as possible the number of sublots of the other types. this will reduce the number of variables, and consequently the computational burden of the optimization process. but classifying jobs requires further research since the analyses presented here do not provide enough information on the best way of doing it. this opens up the possibility of focusing the computational effort (in terms of variables and number of sublots) on those jobs. but detecting them may require a further and deeper analysis. a promising future line of research involves the possibility of running first a parametric analysis of the different types of instances to identify which jobs require this special attention. it would be interesting to design modelling tools able to take advantage of 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and applications vol. 5, issue 1, 2022, pp. 41-55 issn: 2620-1607 eissn: 2620-1747 doi: https://doi.org/10.31181/oresta190222061s * corresponding author. hareshshrm@gmail.com (h.k. sharma), singh.aartij@gmail.com (a. singh), y.dixy12@gmail.com (d. yadav), kar_s_k@gmail.com (s. kar) criteria selection and decision making of hotels using dominance based rough set theory haresh kumar sharma 1*, aarti singh 2, dixy yadav1, samarjit kar3 1 department of mathematics, shree guru gobind singh tricentenary university, gurugram, india 2 department of management, fore school of management, new delhi, india 3 department of mathematics, national institute of technology durgapur, west bengal, india received: 16 june 2021 accepted: 24 december 2021 first online: 19 february 2022 research article abstract: accommodation is one of the necessities of tourists and travel agencies' significant responsibilities. with the growing competition and profit-making various tour organising companies have started providing attractive accommodation options to the travellers to win their choices. present research performs a case study on accommodation providing hotels through designing a strategy to enhance their profit earrings by welcoming more and more tourists. the methodology comprises rough set theory (rst) using the dominance based rough set theory (drst) on the collected data of selected variables such as location, facility, value for money, etc., of hotels. correspondingly, if and then decision rule has been used to classify these variables. the statistical methods regression analysis has also been used to define each variable's relationship and influence on concerned authorities' decision-making. the results show that hotels and tourists can benefit from the proposed strategy and help in decision making by understanding tourist behaviour, increasing profit, improving services, and quality of hotels. keywords: hotel criteria, dominance-based rough set theory, regression analysis, decision making. 1. introduction the indian tourism industry has been growing rapidly in the past decades. the tourism places attract tourists from all over the world, which makes indian tourism a direct contributor to the economy. according to the indian ministry of tourism annual report, the tourism industry contributed 6.23% to national gross domestic product (gdp) in the year 2018-2019, where the tourism industry growth rate is sharma et al./oper. res. eng. sci. theor. appl. 5(1) (2022) 41-55 42 increased from 3.0 to 14.12% percent from the year 2014 to 2019 respectively. this growth rate supports the rise in competition in hotels which are one of the main contributors to the tourism industry. the tourism industry became another crucial source of foreign exchange and new job creation by providing 8.78% of jobs in india. the global trends show that the indian tourism sector is one of the fast-growing industries which will proliferate in future (sharma and kalotra, 2016). in 2019, travel & tourism competitiveness index (2019) had confirmed that india secures at 34th place in the travel and tourism business. in contrast, in terms of costeffectiveness and business environment, it lies at 13 and 39 positions in worldwide competitiveness. there has been a progressive growth of tourism and hospitality management worldwide in the past decade (mohajerani and miremadi, 2012). as well as growing competition in the tourism business, management systems are trying to create equilibrium between the ethics of the business world and customer accommodation without compromising the quality of services to the customers in the hotels business (sohrabi et al., 2012). in other words, priority must be given to customer satisfaction. with increased competition in the hotel and tourism industry, the hotel management system must find the opportunity and threats of the quality of service they provided to their customers (chu and choi, 2000). the hotel business can proliferate only when the hotel offers high-quality services to their customers, which promotes longterm relationships among customers and the hotel management system (martin, 1986; croby et al., 1990). further, consider the creating steadiness of actual customer state of mind with customer ratings, i.e., establishing the linkage among actual customer ratings given by the customers to hotels management system with genuine customer sentiments (geetha et al., 2017). as tourism is considered an essential business activity for the hotel and tourism industry thus hotel management and tour agencies should introduce new advancements initiatives like adequate and flexible customer services for promoting business and attracting more customers (hsieh and lin, 2010). it shows that customer satisfaction is a vital measurement and essential to hotels. thus to maintain customer services and to satisfy customers, hotel management and tourism agencies have to keep their adequate flexibility in their services and also introduce promotional activities which can attract maximum customers (sohrabi et al., 2012). in literature, many studies have been conducted to analyse to explore the quality of hotels by using various research methodologies like factor analysis, descriptive statistics, and regression techniques ( ren et al., 2016; xu and li 2016; lahap et al., 2016; li et al.,2017; lai and hitchcock, 2017; patiar et al., 2017 ). hua and yang (2017) applied econometric models to identify factors of crime on the overall hotel performance of houston hotels. alptekin and büyüközkan (2011) identify influencing factors for the hotel industry by using exploratory factor analysis mixed with fuzzy logic. the regression model has been developed to analyse the effect of localised competition on the hotel industry by considering demographic variables, prize and population density as independent variables (joel and mezias, 1992). in the literature, there are several studies of rough set theory and its application in diverse domains. stević et al. (2017) formulated a multicriteria decision model with eight criteria and eight alternatives for an internal transport logistics of a paper criteria selection and decision making of hotels using dominance based rough set theory 43 manufacturing company. they used the simple additive weighting (saw) method and rough numbers, which is used for ranking the potential solutions and selecting the most suitable one. roy et al. (2019) has proposed an integrated uneven number based copras model to evaluate the ranking of delhi hotels. sharma et al. (2019) has offered a rough set based double exponential smoothing model for forecasting air passengers data. žižović & pamucar (2019) has suggested level based weight assessment (lbwa) based multicriteria decision-making model for the investigation of criteria weightage. popov (2020) applied johnson–kendall–roberts (jkr) theory to find the relation between smooth and rough elastic bodies. božanić et al. (2020) used a rough interval-based level based weight assessment and multi attributive ideal-real comparative analysis method (lbea-ir-mairca) model to determine constructive elements of new weapons. pamucar et al. (2022) has utilised full consistency method (fucom) and multi-attributive ideal-real comparative analysis (mairca) methods as integrated rough group analysis for and prioritisation of railway infrastructure project evaluation. sharma et al. (2021) hybrid rough set model-based analysis has been performed to forecast the sugarcane yield of india. kazemitash et al. (2021) has used the data of biofuel company's supplier selection for the information system performance calculation by the integration of rough set theory through the best-worst method (bwm). the authors have also employed the rough bwm to determine the weight values of the criteria. hu et al. (2021) proposed the weighted neighbourhood rough set (wnrs) and accordingly introduced a unique attribute reduction technique. subsequently, yu et al. (2021) demonstrated that the concept refinement in topology is too abstract to elucidate the variability of the rough set model along with the variation in granules. here, the authors proposed two novel granule cover refinements, including point-set topology and rough set theory. ye et al. (2021) also introduced a novel decision-making method based on a fuzzy rough set. they applied the technique in a real-world scenario to illustrate the feasibility of the proposed method. after that, kusunoki et al. (2021) considered two parametric dominance-based rough set approaches (drsa) and offered variable precision drsa (vp-drsa) and variable consistency drsa (vc-drsa). following this, błaszczyński et al. (2021) examined a new data set for auto loan applications using a technique not yet explored for financial fraud prediction, namely the dominance-based rough set balanced rule ensemble (drsa-bre). pawlak (1982) established an effective method known as rough set theory for extracting the facts from the information system. however, the traditional rough set methodology is not adequate to study the relationship among preference order arising from attributes like debt ratio (blaszczynski et al. 2007), service strategies, product quality, and business indicators (couto and gaiado, 2015). therefore, this study proposes applying the dominance-based rough set theory (drst) to solve preference-ordered situations. according to greco et al. (2000), drst approach has been anticipated to solve the preference-ordered situations in data mining. it is a powerful tool for attribute reduction in the qualitative-based data set. the dominance based rough set theory has been successfully employed in a variety of areas. chakhar and saad (2012) proposed a drst approach to study groups in the multicriteria class study. the dominance-based rough set methodology has been used to develop the model for limiting the speed of vehicles in speed-controlling zones (augeri et al., 2015). chakhar et al. (2016) suggested that drst has been used to derive rules in multicriteria group decision-making based on several case studies. sawicki and zak (2014) have reported that drst based analysis is done on sharma et al./oper. res. eng. sci. theor. appl. 5(1) (2022) 41-55 44 transportation problems by producing decision rules depending on customer view and expectations. moreover, it has also been used in different uncertain multicriteria decision-making applications (kazemitash et al., 2021; pamučar and janković, 2020; pamučar et al., 2018; đalić et al. 2020). the study has been organised as follows. the basic concepts and some related properties of drst are discussed in section' dominance based rst'. a case study of hotel data and analysis of hotel data using drst for multicriteria decision model is presented in case study section. the comparison purpose statistical analysis of hotel data is discussed in regression analyses section. finally, the result and discussion, conclusion, and future scope of our study are stated in section result and discussion, and conclusion'. 2. dominance based rough set theory (drst) drst extends the classical rough set theory (crst) introduced by pawlak in 1982. the multicriteria decision representation used in this research applies the concept of drst. thus, the rst methodology is an efficient mathematical mechanism to dealing with uncertainty and vagueness. however, classical rough set theory (crst) is restricted to sort problems where the preferences-orders in the set of attributes (criteria) are considered. these are the inconsistencies generated due to the violation of the dominance principle that eventually cannot be handled by the model. hence in case of such inconsistencies, some methodological changes to crst are required. greco et al. (2000) have proposed an expansion of the rst depending on the dominance concept that would allow it to handle the inconsistency. this idea relies on replacing the indiscernibility relation for a dominance relation in the rough approximation theory of the decision category. 2.1. information system sample the information concerning the objects is often structured in the form of an information table whose different rows mention distinct actions (objects) and whose columns mention the other criteria or attributes considered. formally, an information table is structured in a 4-tuple information system , where is a non-empty finite set of objects (universe) and is a non-empty finite set of attributes or criteria such that for every is the domain of the attributes or criteria q. and is the information function determined such that for every attributes q . the set q is often separated into a set c ≠ of condition attributes, and a set d ≠ of decision attributes such that and . in such a situation, s is called an information table. 2.2. rst with dominance relation if the scale of the condition attribute is arranged in increasing or decreasing preference, then it is called criterion. alternatively, it is known as regular condition attributes. drst exponents suppose that the preference increases with the value of for every criterion we also suppose that the set of decision attribute criteria selection and decision making of hotels using dominance based rough set theory 45 (perhaps a singleton {d}) create a parting of universe u into a set of decision classes, let {1,….,n} be a finite set of classes of universe u such that every belongs to one and only one class . we assume that classes are preference-ordered, i.e., for all , such that the objects from are more preferred to the objects from . suppose p ⊆ c is a subset of condition attributes. the dominance relation allied with p is described for every pair of objects x and y so; the letter " " should be changed with " " for criteria according to the decreasing preference. we associate pair of a sets with every object : (i) p-dominating set } having objects that dominate x and (ii) p-dominated set } having objects dominated by x. these pair of sets are familiar with approximate decision classes. the p-lower approximation of (upward union), ( ), is constituted of total objects x from such that all members y, contain at least the similar assessment on all of the examined criteria from , also member of a class or better. in another way, if any object y has at least as good an analysis based on the criteria from as object x member of , then indeed, y is a member of a class or preferable class. the p-upper approximation of (upward union), which involves all objects with a p-dominating set, is allocated to a class at least as good as . similarly, the p-lower and p-upper approximation with respect to respectively represented as and , are defined as: , (1) . (2) 2.3. accuracy of approximation and quality of classification for all and each, we described the accuracy of the approximation of and , respectively, as follow: , (3) the coefficient (4) is known as the quality of approximation of partition cl using attribute set . 2.4. decision rules on the foundation of the approximations found by the use of the dominance relation, it is viable to set off a generalised explanation of the preferential knowledge contained in the information table, such description of the preferential knowledge we can write in the form of “if ..., then..." decision rules. the algorithms for induction related to regulations are acquired by using 4emka2 software (poznan university of technology, poland, laboratory of intelligent decision support system 2006). all the decision rules can be considered in the following three ways: sharma et al./oper. res. eng. sci. theor. appl. 5(1) (2022) 41-55 46 1. -decision rules which are having the following form: if and and ……. , then , these decision rules are assisted by the member of the universe that belongs to the p-lower approximation . 2. -decision rules which have the following form: if and and ……. , then , these decision rules are assisted by a member of the universe that belongs to the p-lower approximation of . 3. -decision rules which have the following form: if and and ……. , and and ….. , then , these decision rules assisted by a member of the universe that belongs to the boundary region of the union of classes and , where ,( ) , and . 3. case study the hospitality industry is one of the major contributors of growth among the allservice sector industries in india. since, india is a country of diversity with its rich culture and heritage, hence the tourism contributes a significant source of foreign exchange. as, tourism is the integral part which has a considerable effect on the hotel industry. this indicates that the digital advancement in tourism sector also affect hospitality industry. the digital enhancement in tourism of india through digital tools used for planning, booking, and experiencing a journey have significant effect over hospitality industry. the empirical study focuses on the indian hospitality industry includes data collected from various online platforms in the hotels. since customer satisfaction harms the hotel industry, the possibility of getting a hotel that satisfies customers' needs is maximised by selecting specific attributes which are related to the hotel industry. the following study scrutinises the influence of overall rating (o) on location (lo), hospitality (ht), facilities (ft), sanitation and cleanliness (sc), the value of money (v), food quality (fd), and price (pr) using both indian and international tourists' hotel data. criteria descriptions are listed in table 1. the study's objectivity has been kept in mind, and all variables are used according to data availability. online reviews play an essential role in the hotel selection process as websites provide customer reviews based on their personal experiences with provided hotel services. these websites give the travelers an overall idea to select the best hotel which satisfies their needs based on others' experiences. sometimes decision-making becomes difficult as there are different reviews based on one's perspective. the data related to the hospitality industry are extracted from tourism websites. the presented approach assists the hotel selection process based on the influence of overall rating on location, hospitality, facilities provided, sanitation and criteria selection and decision making of hotels using dominance based rough set theory 47 cleanliness, the value of money, food, and price. the proposed study is used to select the best hotel based on existing data. table 1. criteria description criteria description location (lo) the geographical location of the hotel has been considered according to the convenience of tourists. hospitality (ht) it includes a friendly and generous welcome and entertainment for tourists. facilities (ft) it includes a travel desk, eating place, parking, pieces of equipment, or services provided to tourists for their stay. sanitation and cleanliness (sc) sanitation and cleanliness include the sanitary condition of a hotel. value for money (v) a beneficial combination of sustainability, cost, and quality to meet tourist requirements. food quality (fd) the acceptable standard quality of food served. price (pr) convenient fare according to traveler and hotel management overall rating (o) it includes the net classification of hotels based on the different quality scale. the objective of this case study is to extract the decision rules to show the hotel features and classify the different characteristics of the tourist industry. it has been found that the rough set theory is the most suitable approach for criteria selection in decision-making problems. for this study, data has been collected from the best tourism website (https://www.makemytrip.com), and it will help the tourism management for analysis of significant criteria of the hotel industry. the model must provide relevant information to hotel management for improvement of their service quality. 4. drst analysis based on several studies such as (geetha et al., 2017; li et al. (2017) of hotel tourism, and expert interviews of hotel managers and their management teams, tourism and travelling management of india has conclusively given higher priority to the eight essential criteria/attributes given in section 3 of 609 best indian hotels. because according to experts, these selected eights criteria are preferred mainly by the maximum tourists while making their hotel selection decision. in eight attributes, seven attributes are called condition criteria, and another one is decision criteria were investigated for analysis. in this study, we have applied the drst technique for rule generation. drst toolkit 4emka2 software from poland, laboratory of intelligent decision support system 2006, is used for constructing the decision rules. https://www.makemytrip.com/ sharma et al./oper. res. eng. sci. theor. appl. 5(1) (2022) 41-55 48 4.1. accuracy approximation and quality of classification table 2, provides approximation accuracy for all decision classes, as approximation sets (specifically lower and upper approximation) and accuracy of approximation has been already explained in section 2.2 and 2.3. the selected criteria can be adequate to approximate the classification if the classification quality and accuracy of the approximation. the class "at most medium" means class related to "overall hotel rating will be medium and lower values". the decision class "at most good" contains the two classes, which are "good" and "medium". further, the decision class" at least good" represents the class "overall hotel rating will be good or excellent". finally, the decision class "at least excellent" consists of only one class, i.e. overall rating of the hotel be will be excellent. table 2. accuracy of approximation at most medium at most good at least good at least excellent lower approximation 10 17 99 20 upper approximation 510 589 599 592 boundary 510 572 500 572 accuracy of approximation 0.636 0.0290 0.17 0.0340 quality of classification 0.049 table 3. certain decision rules of hotel data set decision rules support if (food ≥ excellent) & (hospitality ≥ excellent) then (overall rating≥ good) 61 if (food ≥ excellent) & (facilities ≥ medium) then (overall rating ≥ good) 83 if (food ≥ excellent) & (sanitation and cleanliness≥ excellent) then (overall rating ≥ good) 89 if (food ≥ excellent) & (price ≥ medium) & (value for money ≥ excellent) then (overall rating ≥ excellent) 18 if (food ≥ excellent) & (price ≥ high) then (overall rating ≥ excellent) 6 if (food ≤ poor) & (price ≤ low) & (location ≤ bad) then (overall rating ≤ good) 11 if (hospitality ≤ poor) & (facilities ≤ medium) then (overall rating ≤ good) 6 if (sanitation and cleanliness ≤ poor) then (overall rating ≤ good) 5 if (food ≤ poor) & (price ≤ low) & (facilities ≤ good) & location ≤good) then (overall rating ≤ medium) 5 if (value for money ≤ poor) & (facilities ≤ good) then (overall rating ≤ medium) 6 if (location ≤ bad) & (sanitation and cleanliness ≤ good) then (overall rating ≤ medium) 3 as clarified in the section as mentioned above 2.4, the decision rules were formed by analysing the training data of dominance-based rough set theory. these rules were applied to relationships among conditions and decision attributes. criteria selection and decision making of hotels using dominance based rough set theory 49 furthermore, 11 certain decision rules were obtained from the information system. total 5 decision rules are found to be more accurate since support is greater than 10. based on these decisions rule, we can analyse which criteria are significant for hotel management. the estimated results of reduced rules are presented in table 3. table 3 shows the 11 minimum cover rules generated from the hotel data set. the minimal cover certain decision rules can be written in the form of if-then statement. here is some example to illustrate if-then rules: if food is excellent and hospitality is excellent, then the decision criteria overall rating will be perfect. from table 3, it is clear that if the hotel's food is excellent and cleanliness is excellent, then the overall rating will be excellent with maximum support of 89 (cf. rule 3). it means that food and cleanliness are essential factors for travellers. if the hotel's food is excellent and facilities are medium, and above medium then the overall rating will be excellent with support of 83 (cf. rule 2). if food quality is excellent and hospitality is best then the overall rating will be excellent with support of 61 (cf. rule 1). these decision rules indicate that food, cleanliness, hospitality, and facilities are essential attributes for travelers. therefore, it can be suggested that most tourists select their hotel based on food, cleanliness, hospitality, and facilities. the different stages of analysis are depicted in figure 2. 5. regression analysis by analysing the literature review (sheather, s., 2009; ren et al., 2016; patiar et al., 2017; hua and yan., 2017), the regression model is obtained by using the following framework: overall rating (o) = α+α1 lo+α2 ht+α3 ft+α4 sc-α5 vα6 fd+α7 pr+ ε (5) where ε is the error, α, α1, …, α7 are the coefficients of considered variables (lo, ht, …, pr), o is the overall rating; lo is the location of the hotel, ht is the hospitality, ft is the facilities provided by the hotel, sc is the sanitation and cleanliness, v is the value of money, fd is food quality, and pr is for the price of the hotel's room. the estimated regression results are described in table 3. the acquired result indicates that the hotel's location, hospitality, sanitation and cleanliness, and performance and effectiveness of money charges, i.e. the value of money, has a significant positive effect on overall ratings of the hotel. whereas, facilities provided, i.e. physical characteristics associated with a hotel-like travel desk, eating place, parking, etc., food quality and hotel price don't seem to have a significant effect on the overall ratings of the hotel. moreover, the fstatistics results confirmed that the regression model is essential for criterion for hotel selection process since the p-value is 2.2e-16 ≈0.000, which is significant. estimating sturdiness of the model by using r2, which is 0.8459, i.e. all variables have an approximate 84.59% effect on overall ratings of the hotel for criterion for the hotel selection process, which is considerably good. therefore, the considered regression model is relevant for the empirical study. also, from figure1, it is clear that the relationship between overall rating with location, hospitality, facilities, sanitation, and cleanliness, the value of money, food, and the price is linear. the linear line indicates is that the best-fitted model with the curve for the multivariate analysis. our data are independent and follow gaussian sharma et al./oper. res. eng. sci. theor. appl. 5(1) (2022) 41-55 50 distribution, then the model is accepted within the robustness test. figure 1, shows a normal probability plot to decide whether it is reasonable to consider. the accuracy measure derived using regression analysis of hotel data set is sampled from a population, follows a normal distribution. the regression equation for the variables is: overall rating = 0.538+0.1854 location+0.6706 hospitality+0.3821 facalities+0.2193sanitation and cleanliness-0.01933 value of money-0.1549 food+0.000005004 price+ ε (6) table 4. regression analysis results residual standard error: 0.1673 on 601 degree of freedom multiple r-squared: 0.8477, pvalue < 2.2e-16 figure 1. normal probability plot of statistical analysis variables coefficients standard error tvalue pr(>│t│) constant 5.388e-01 7.654e-02 7.039 5.29e-12 *** location 1.854e-01 1.922e-02 9.646 <2e-12*** hospitality 6.706e-01 1.995e-02 33.619 <2e-16*** facilities 3.821e-03 2.380e-03 1.606 0.1088 sanitation and cleanliness 2.193e-01 2.071e-02 10.589 <2e-16*** value of money -1.933e-01 1.954e-02 -9.938 <2e-16*** food -1.549e-01 1.439e-02 -1.076 0.2822 price 5.004e-06 2.784e-06 1.797 0.0728 adjusted r2 0.8459 f-statistics 477.8 criteria selection and decision making of hotels using dominance based rough set theory 51 figure 2. stages for air transport passengers forecasting 6. results, discussion and conclusion this research focuses on hotel selection and estimation through a hybrid method of dominance rough set theory and regression analysis. this estimated model has been analysed under uncertainty in which drst is employed in acquiring the information related to significant attributes of the hotel business. furthermore, a case study on real-life data of indian hotels has been performed using the drst approach on the selected attributes. the foremost suggestion resulting from this study are (i) food, facilities, cleanliness, and hospitality are the most significant attributes for any hotel selection as uncovered in decision rule and the expert's opinion based on customer prioritization and feedback. (ii) hotel management has been turn-up with a clear picture of the hotel's criteria to improve performance according to the current business market. this facilitates the hotel management system to make appropriate decisions regarding the quality and services up-gradation of the hotel. (iii) it can be said that the drst is a knowledge-based decision-making system that can evaluate the effective and appropriate attributes by the comparison of collected data with secondary data obtained from tourism websites. hence, this research leads to a robust hybrid method, 'drst-regression', which confirms the accuracy and firmness of the decision making outcomes. it is a unique approach contributed by this study because it gives rise to the most precise and reliable outcomes without any statistical assumptions. comparatively, drstregression is more preferable to the statistical method due to its dynamic and advanced approach. therefore, this study resulted in an empirical model that can be preferred over the statistical model because it divulges the consequential decision sharma et al./oper. res. eng. sci. theor. appl. 5(1) (2022) 41-55 52 rules are easy to understand as compared to statistical methods without any distributional assumption. the main limitations of the drst are that the approximation sets (upper/lower) depend only on the choice of attributes, which may be regarded as disadvantage, since there may not be enough flexibility for some applications. in future, similar case studies can be considered and analysed using rough sets and different machine learning algorithms, including decision tree, random forest, support vector machine and elastic net. references alptekin, g. i., & büyüközkan, g. 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this supports to lift the consumption rate. along with stock-level, one can notice that sales of the goods are inversely proportional to the selling price. more will be priceless will be the demand. shah et al./oper. res. eng. sci. theor. appl. 5(2) 2022 85-98 86 many inventory models were developed under constant manufacturing rate. but, in reality the order may change according to the situation and demand. moreover, to grab the attention, the company develops a certain strategy to conceive consumer’s attention. the model deals with a two-level credit system to enhance the sale by permitting them to pay the bill under a certain allowable period. this paper introduces a perishable inventory model, assuming demand rate to be a function of stock and selling price with overtime production. the paper provides managerial insights corresponding to sensitivity analysis. the purpose is to evaluate optimum profit value. countless scholars functioned for the overtime manufacture rate under constant consumption rate. thus, for the first time, the study talks the overtime manufacture model for unpreserved goods, taking into consideration the simultaneous outcome of trade credit policy and preservation investments on a company’s revenue function. the paper is designed as: section 2 contains literature review. required notations and assumptions are introduced in section 3. section 4 discussed inventory model. computational algorithm is defined in section 5. a numerical example with sensitivity analysis is included in section 6. finally, section 7 provides a conclusion along with future scope. 2. literature review demand function plays a vital role in making tactics for inventory models. it fluctuates with respect to different parameters like time, quality, promotional offers etc. large displays in shops tend to grab consumer’s attention. moreover, the consumption level is directly proportional to the product’s selling price. setting higher power reduces demand rate. dey et al. (2018) investigated rebate, stock-level and price dependent demand. they analysis a comparison between static and dynamic rebate. chang (2013) revisit burwell contribution and put a note for quantity and freight discounts where demand is price-sensitive. ouyng et al. (2008) developed a non-instantaneous deteriorating problem under stock-dependent demand, considering all unit quantity discount. jaggi et al. (2017) established perishable products ordering policy under selling price dependent consumption rate. li et al. (2019) proposed a replenishment policy for perishable goods. mishra et al. (2018) presented an inventory model under credit periods considering preservation investment and pricing policy. liu et al. (2015) considered a time-dependent assessing policy where the goods decay with period. seifert et al. (2013) had reviewed trade credit literature. yang et al. (2015) examined a deteriorating system seeing conservation strategy and credit plan. halim et al. (2021) established an overtime strategy for the inventory problems dealing with decay products. khan et al. (2020) deals with time-sensitive stock cost and advanced payment policy under advertisement scenario. lee and dye (2021) developed a simple algorithm to solve replenishment schedules and preservation technology costs for decay products assuming stock-sensitive demand rate. tsao et al. (2021) proposed a network design problem assuming credit policy and freshness-keeping strategy. the model evaluated the total cost function by continuous approximation. dye and hseih (2012) formulated a worsening stock problem with salvation strategies and partial backordering. mishra et al. (2017) suggested a model for partly and totally tolerable a deteriorating inventory model under overtime production and credit policy for stockand price sensitive demand function 87 backordering under demand as a function of store level. geetha and udayamkumar (2015) formulated a credit model for dynamic demand. nowadays, many business enterprises focus on various promotional strategies to increase their sales. in inventory models, promotional policy is the basic requirement in business scenarios to compete with others. in the trade credit scheme, the seller offers some delay period to the retailer at the same time the retailer also permits the consumer to pay the bill within some permissible time interval to stimulate consumer’s need and demand. during the permissible credit period, retailers can earn interest from the sold products and gather revenue. a high interest is charged, if the amount is not settled at the end of the cycle period. credit period strategy makes financial sense and allows retailers to settle the account at the last moment of the allowable time. the approach is used to promote the products. chung et al. (2014) introduced an article, to minimize total price under permissible credit periods for decay items. soni et al. (2013) developed a stock-sensitive demand function under replenishment and credit policies when stock is limited. shaikh et al. (2020) studied an epq model for credit policy and permissible shortages. the model calculated optimization problems using the gradient method. pervin et al. (2020) formulated a production model considering safeguarding assets to overcome the decay rate for storage-and cost-related claims. the model evaluated the total profit function for optimal preservation investment and cycle length. rapolu and kandpal (2020) designed an inventory model for decay products having three-parameter weibull distribution. a simple algorithm is generated to evaluate optimal decision variables. the model is developed incorporating advertisement policy and joint assessing policy to increase profit level. mahata and de (2016) proposed an ordering strategy model for cost sensitive consumption rate. 3. notations and assumptions the article uses the following assumptions and notations given in table 1: table 1. notations np c per unit normal production cost (in $) op c overtime making charge per piece (in $) d c worsening rate per piece (in $) p vending worth per piece (in $) a set up fee per demand (in $) h stock charge per element per year (in $)  preservation investment rate per cycle  constant deterioration rate, 0 1   scale demand, 0   stock-dependent parameter, 0,    r(p, i( t )) stock and price sensitive demand q order quantity p t production period (in years) t rotation period (in years) shah et al./oper. res. eng. sci. theor. appl. 5(2) 2022 85-98 88 ( )i t inventory at a time t during the interval [0, ]t e i interest made per year (in $/ year) c i interest paid per year (in $/year) m time given by trader to vendor(in years) n time given by vendor to customer (in years) tp total profit per unit time (in $/year) • the system is generated for a single product. • the demand rate is a function of products price and stock available and is specified through 0 0 0r(p,i( t )) ( i( t )) p , , , ,         − = +     . • the model is formulated for the overtime production rate. the expression is  o rp ( t ) p ( i(t) r(p,i(t))) = + − + , where 0rp , and 0 1    . • the article does not permit refunding, replacement, or reworking of imperfect products. • the deterioration rate is a constant function. • to overawed destruction rate, the system includes salvation investment. 4. mathematical model here, the model is developed for dynamic production rate, taking into account the rate to be dependent on demand and stock level i.e.,  o rp ( t ) p ( i(t) r(p,i(t))) = + − + for rp to be continuous and ( i(t) r(p, i(t)) − + is overtime manufacturing rate. the demand rate is a non-linear function of product vending worth and storage level. i.e., r(p,i( t )) ( i( t )) p    − = + for 0 0,   . in the beginning, the storage amount is supposed to be zero. the manufacture takes place during period 0t = and continuous up to time p t t= , where the stock reaches its saturation point. hence, the manufacturing rate terminates at the time p t t= , that becomes zero at the end of cycle period i.e. t due to the simultaneous effect of demand and deterioration. the inventory during the period interval [ ,t] p t and [ ,t] p t is taken as ( )1i t and ( )2i t respectively. the mathematical expression for the different inventory are as follows: ( ) ( )( ) ( ) ( ) ( )( )1 1 o di t m i t p t r p,r t dt   + − = − (1) ( ) ( )( ) ( ) ( )( )2 2 di t m i t r p,r t dt   + − = − (2) a deteriorating inventory model under overtime production and credit policy for stockand price sensitive demand function 89 with boundary conditions ( )1 0i t = at 0t = and ( )2 0i t = at t t= . at time pt t= the inventory level preserves the continuity i.e. ( ) ( )1 2p pi t i t= . using boundary conditions, the solution of equation (1) and (2) are mentioned as follows: ( ) ( ) ( )1 1 1 r bt p p i t e b    − − + − = − (3) ( ) ( )( )2 1 a t tp i t e f   − −− = − (4) using the continuity at p t t= , the cycle time is defined as: ( )( )( )1 11 p p at r t a p p ef p t log f b fp e        −− − −−   + − −   = +        (5) where ( )( ) ( )( ) ( )1 1 1f m p ,b m p .        − −= − + = − + − − the order quantity is ( )( ) ( )( )1 2 0 p p t t t q i t p dt i t p dt       − − = + + +  (6) moreover, the holding cost for the entire cycle period is given by ( ) ( )1 2 0 p p t t t hc h i t dt i t dt   = +     (7) the production cost, preservation investment cost and ordering cost are as shown: ( ) ( )( )( )1 1 0 pt np r p op pc c p t c i t i t p dt      −  = + − + +    (8) ( ) ( )1 2 0 p p t t t pic i t dt i t dt   = +     (9) oc a= (10) the cost related to deteriorated items over the entire cycle period is evaluated as ( ) ( )1 2 0 p p t t d t dc c i t dt i t dt    = +     (11) the sales revenue for the proposed inventory model is shah et al./oper. res. eng. sci. theor. appl. 5(2) 2022 85-98 90 ( )( ) ( )( )1 2 0 p p t t t sr p i t p dt i t p dt       − −   = + + +     (12) the two cases take place under a two-level credit period system i.e., case 1 and case 2. case 1: m n here, we have three different possibilities defined as (1.1) 0 p m n t t    , (1.2) 0 p t m n t    , and (1.3) 0 p t t m n    . first, let’s discuss each subcase. sub-case 1.1. 0 p m n t t    with  0,m , retailers earned some interest over the revenue function defined as ( )( )11 1 0 m e ie pi i t p tdt    −   = +     here, the retailer will finance all the costs between  m ,t . hence, the interest charged is calculated as ( ) ( ) ( )11 1 2 p p t t np op c op c m t ic c c i i t dt c i i t dt     = + +            hence, the entire revenue function is ( )11 11 11 1 tp sr oc pc hc dc pic ie ic t = − − − − − + − (13) sub-case 1.2. 0 p t m n t    in this case, the interest is earned for the time interval  0,m , and the interest is charged for the interval  m ,t . the expression for interest made and interest paid are ( )( ) ( )( )12 1 2 0 p p t m e e t ie pi i t p tdt pi i t p tdt       − −     = + + +            ( )12 2 t np c m ic c i i t dt   =      here, the total profit function in this case is ( )12 12 12 1 tp sr oc pc hc dc pic ie ic t = − − − − − + − (14) a deteriorating inventory model under overtime production and credit policy for stockand price sensitive demand function 91 subcase 1.3. 0 p t t m n    one can observe that in this case m t implies that the products are vended formerly the permitted credit period. so, the total interest paid is nil. i.e., 13 0ic .= the interest rate is ( )( ) ( )( )13 1 2 0 p p t t m e t t ie pi i t p tdt i t p tdt t qdt       − −    = + + + +        the entire revenue function is ( )13 13 13 1 tp sr oc pc hc dc pic ie ic t = − − − − − + − (15) case 2: n m here, we have only one case to discuss .i.e., 0 p n t m t    the retailer must have to pay the charge to the products that are not sold after credit period. therefore, the interest charge is ( )2 2 t op c m ic c i i t dt=  here, the interest earned during interval  0,m is ( )( ) ( )( )2 1 2 0 p p t m e t ie pi i t p tdt i t p tdt       − −    = + + +       the entire revenue function is ( )2 2 2 1 tp sr oc pc hc dc pic ie ic t = − − − − − + − (16) here, the problem is 11 12 13 2 0 0 0 0 p p p p tp , if m n t t tp , if t m n t maximize tp tp , if t t m n tp , if n t m t          =           (17) the ultimate aim is to evaluate the entire revenue function related to is to calculate the production period, vending worth, conservation investment cost. shah et al./oper. res. eng. sci. theor. appl. 5(2) 2022 85-98 92 5. computational algorithm: the ambition is to exploit profit level. to solve problem, model uses a classical optimization algorithm. the algorithm is defined as follows: step 1. initially, consign some values to different variables. step 2. calculate the derivative of equation (17), of all profit functions that vary according to the credit policies with respect to vending worth, preservation technology investment, and production period. that stands, 0, 0, 0 p tp tp tp t p    = = =    (18) equation (18) yields the value of decision variables that are being used in equation (17) to calculate the extreme revenue price. 6. numerical example and sensitivity analysis example 1: consider  =5000,  =0.2,  =0.03,  =0.2, h =$1.5/unit/year, a =$200/order, 100 r p = , dc =$20/unit, npc =$20/unit, opc =$6.5/unit, 15. = , e i =0.10, c i =0.15, 07k .= , m = 0.0822, n= 0.164. using these numerical values, the decision variables are p = $82.77/unit,  = 0.307, p t =0.226 years, t = 3.221 years, and tp = $299.82/ year. figure 1 represents the convex nature of profit function with respect to decision variables selling price, preservation investment cost and production time. next, we compare two level trade credit cases in table 2, for given inventory system. chart amid  and p chart amid p t and p chart amid p t and  figure 1. concavity of objective function a deteriorating inventory model under overtime production and credit policy for stockand price sensitive demand function 93 table 2. shows the possible cases, when the relation between credit period varies. the sensitivity analysis is performed for case 1. a sensitivity of inventory parameters is performed by varying a particular inventory parameter by 10%,10%,20%, -20%, keeping other variables constant. figure 2. change in selling price related to inventory parameters. the purpose in figure 2 is to exploit the entire revenue function. by an upsurge in deterioration charge, the vending worth increases. moreover, higher deterioration cost reduces the damage rate which in turn decreases preservation cost. the increase in d c will have a negative impact on profit function. p (selling price)  (preservation investment cost) p t (production time) t (cycle time) tp (total profit) 1 0    p case . m n t t 82.77 0.307 0.226 3.221 299.82 2 0    p case . t m n t 81.01 0.264 0.195 2.725 293.03 3 0    p case . t t m n 57.57 0.030 0.186 1.495 378.75 4 0    p case . n t m t 78.15 0.237 0.237 3.104 307.27 shah et al./oper. res. eng. sci. theor. appl. 5(2) 2022 85-98 94 figure 3. change in preservation cost related to inventory parameters. it is depicted from the figure 3 that a large ordering cost, especially when the manufacturing rate is high, will have a negative effect. the company may introduce some inventory policy to overcome the loss that occurs due to high setup cost. the model uses a credit policy where the delay in payment is permissible up to a certain time. commonly, the demand for perishable products declines thru period. to avoid a loss that occurs due to damage and spoilage, preservation cost is one of the crucial strategies. an increase in preservation investment cost results in a decrease in profit level. the increase is not advisable. figure 4. change in production time related to inventory parameters. a deteriorating inventory model under overtime production and credit policy for stockand price sensitive demand function 95 from figure 4 it is advised that the company may boost the sale by introducing overtime production techniques. the firm will not face shortages and the products are available whenever needed. figure 5. change in cycle time related to inventory parameters. figure 6. change in total profit related to inventory parameters. figure 5 and figure 6 suggest that the system is temperately delicate to k and r p . the increase in the cost function is not advisable as it tends to decrease the profit level. the entire revenue function is exceedingly delicate toward the scale demand i.e.,  as large volumes provide choices and quality to the customers. it is observed shah et al./oper. res. eng. sci. theor. appl. 5(2) 2022 85-98 96 that with an increase in credit periods, cycle time increases. the stock sensitive demand helps manufacturers to fluctuate profit amounts and reflects product requirements in the market as well. an increase in deterioration rate tends to reduce cycle time, which ensure that one should order less in case to avoid damage rate. to cure the damage, the company requires more money for preservation technology. the total profit decreases. 7. conclusion in this paper, the model evaluates overall profit revenue considering the overtime production rate for perishable products. the demand rate is a function of vending worth and stock and selling price taking conservation technology assets to decrease the degree of decline. the model also provides some managerial insights related to key parameters and the problem is solved using classical optimization methods. the goal is to exploit the entire revenue function associated with vending worth, preservation technology investment and production period. to compete with the modern world, the model takes into account credit periods. the revenue parameter is exceedingly sensitive to scale demand. the preservation technology investment will have a positive impact on the deterioration rate and is negatively related to profit function. the overtime production helps to fulfill the demand on time. most of the researchers who study overtime production model consider demand rate to be a constant function but in reality it depends on certain factors such as price, time and stock. this work addresses the different research questions. what is the effect of deterioration on retailer’s profit? because of the overtime production process, the company needs to invest more during production time to neglect the situation of stock out. trade credit policy is being used along with the preservation investment to maximize the profit value. the model can apply to the problems, dealing with perishable products under permissible overtime production, credit periods and preservation investment to control decay rate. the model has some limitations as the problem is solved for constant rate of deterioration due to the complexity of the problem whereas deterioration rate changes 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(2015). optimal dynamic trade credit and preservation technology allocation for a deteriorating inventory model. computers & industrial engineering, 87, 356-369.ticle. journal of scientific communications, 163, 51–59. https://doi.org/10.1016/j.cie.2015.05.027 © 2022 by the authors. submitted for possible open access publication under the terms and conditions of the creative commons attribution (cc by) license (http://creativecommons.org/licenses/by/4.0/). https://doi.org/10.1080/10170660809509073 https://doi.org/10.1016/j.ejor.2013.03.016 https://doi.org/10.1016/j.ijpe.2013.07.006 https://doi.org/10.1016/j.cie.2015.05.027 plane thermoelastic waves in infinite half-space caused operational research in engineering sciences: theory and applications vol. 5, issue 2, 2022, pp. 99-116 issn: 2620-1607 eissn: 2620-1747 doi: https://doi.org/10.31181/oresta040722060b * corresponding author. ibrahim.badi@hotmail.com (i. badi), mljtech@gmail.com (l. j. muhammad), abubakar.mansir@auk.edu.ng (m. abubakar), mahmut.bakir@samsun.edu.tr (m. bakır) measuring sustainability performance indicators using fucom-marcos methods ibrahim badi 1*, l. j. muhammad 2, mansir abubakar 3 and mahmut bakır4 1 libyan academy, department of mechanical engineering, misurata libya 2 mathematics and computer science department, federal university of kashere, gombenigeria 3 department of mathematical sciences, al-qalam university, katsina state nigeria 4 department of aviation management, samsun university, samsun turkey received: 31 march 2022; accepted: 18 june 2022; first online: 04 july 2022. original scientific paper abstract: due to rising environmental concerns, green innovation has become a familiar and appealing topic worldwide in recent years. in addition, population growth, globalization, urbanization, and industrialization have given rise to many problems, such as damage to the environment, the economy, and the living conditions of society. this paper aims to evaluate and prioritize aspects of green innovation, taking into account sustainability performance indicators. fucom-marcos hybrid methods were used. the experimental results of the proposed method showed that management technological innovation (c1) is the most influential part for adopting green practices in the textile industry in nigeria. the study also showed that greening the supplier (c6) and product technology innovation (c5) are the second and third most important aspects of green innovation. furthermore, it analyzed the sustainability performance indicators using the marcos method. the findings reveal that social performance (spi-3) was the most sustainable and vital indicator in terms of green innovation practices in the textile sector in nigeria. sensitivity analysis was also conducted using five other methods, and the results obtained showed stability in the order of the indicators. key words: mcdm, marcos, fucom, green innovation, performance indicators 1. introduction environmental degradation is caused by changing interplay of technology, institutional, and socio-economic ventures (shujah-ur-rahman et al., 2019). environmental degradation has been stimulated by several elements, including badi et al./oper. res. eng. sci. theor. appl. 5(2) 2022 99-116 100 transportation, rising energy, a sudden increase in agriculture, urbanization, population, and economic expansion. this has raised several environmental concerns in environmental conservation. many countries are changing their business consumption and production models and emerging alleviation measures while generating an economic chamber that incorporates all environmental conservation measures. green innovation entails all kinds of innovations that industries and businesses participate in the formation of processes, services, or products that minimize declination impact and environmental harm and improve the use of typical resources (singh et al., 2020). green innovation magnifies an important capacity by directing the proper use of natural resources to better environmental conservation. moreover, the formation and integration of changes in production and product processes provide sustainable developments (glavič et al., 2021). with the increasing economic activities and the increasing climatic change, manufacturing in the industries is indicating a big interest in tenable manufacturing. this has followed the implementation of several collective social responsibility initiatives. however, implementations of the initiatives in certain areas have been drawn back by growing consumption in other regions. efficacity that has been attained in other areas has been outrun by scale effects. governments give clear program indicators regarding their long-term and short-term climate change goals and the expense of climate program dimensions that can be maintained low. improving effectiveness in resource and energy use and engaging in an extensive variety of innovations to better environmental performance will aid in forming new jobs and industries in the future. the ongoing economic crisis and agreements to confront climate change should be perceived as a chance to change to a greener economy (united nations, 2020). manufacturing must be reorganized, and standing inventions technologies be extra innovatively enforced to conceive green growth. brief relief packages set out in the present can excite investments in technologies and in fractures that aid innovation and empower changes in the ways we form and make use of products and services in the coming time. industries have customary evaluated pollution anxiety at the core of discharge. they have minimized the number of materials and energy used in the production process as a cleaner production method (chen & wang, 2017). in many manufacturing industries, they have focused on technological improvements and progression. however, several green innovations that are nontechnological that as developing discrete environmental segmentation or forming multi-stakeholder or inter-sectoral study networks, have instigated technological advancements. others have started to examine systemic innovations that are transforming consumer demand satisfaction. many manufacturing industries are contemplating the impacts of product lifecycle on the environment by blending environmental schemes and activities into their control systems (zhang & zhu, 2019). some founders have planned on developing a closed-loop production system that does away with end product disposal by retrieving wastes and changing them into something different for production. green innovation participates in making this a reality in industry practices. once more incorporated practices such as closed-loop production are implemented, it can lead to great environmental upgrades by integrating of variety of measuring sustainability performance indicators using fucom-marcos methods 101 innovation strategies with mechanisms and non-technological and technological changes. with the high prices and shortage of materials, steel and iron industries have made consequential advancements in improving environmental conduct through several energy-saving alterations and redesigns of different production processes (wong et al., 2020). refreshed means of working inside the industry have resulted in a variety of these technological developments in products and processes potential. a good example is the collective working between steelmakers and vehicle designers which resulted in improved high-strength steel to produce lighter and more ecofriendly automobiles. the electronic industry has concentrated on its energy consumption products. this is from the heightening consumer demands for electronic products, which is making them look for bigger productive means to get rid of their products into the environment. this makes many industries major in technological improvement inform of process redesign or product modification concerning environmental friendliness. the transport and automotive industry has also implemented various strategies to mitigate carbon (iv) oxide discharge and other environmental influence remarkably those related to fossil-fuel combustion. in the advancing economies, there is increasing demand for mobility leading to industries majoring in improving the energy effectiveness of automobiles and other means of transit. green innovation in automobile manufacturing has been achieved greatly by technological improvements. this is in areas such as maximization of the painting process, applying energy-saving tires, advanced power control systems, and improving fuelinjection technologies. government statutes and levels have participated in mitigating environmental damages to a vast extent although it is not the most valuable method to minimize emissions (owen et al., 2018). it also does not give sufficient encouragement to innovate exceeding end-stage solutions. conceiving the possibility of green innovations will demand actions to provide that complete rotation of innovations sufficient with strategies spanning from the endowment in study to advocate in profitable breakthrough technologies. green innovation can guide notable economic chances. however, industries and business investors need plain and reliable pricing to enhance a greener future investment. green innovations can help the environment and manufacturers. additionally, green innovation represents proactive and costeffective techniques that help companies to establish a sustainable competitive edge (lin et al., 2015). solutions and advancements to preventing industrial pollution will alleviate industrial pollution and damage to the environment. however, the process of implementing green innovation in industries and businesses has some drawbacks (peng et al., 2021). the barriers and drawbacks and barriers range from problems with financial challenges and poor team collaboration. oftentimes, industries face inadequate internal mechanisms to discharge viable initiatives. the problems are based on a low capital allotment for the policies of green innovation. managers disregard the necessity of minimizing exposure to energy price weightlessness and the environmental influence of their inward processes. this is a result of taking expenses connected with the same decisions extreme. poor participation and difference in priorities and opinions of teams make badi et al./oper. res. eng. sci. theor. appl. 5(2) 2022 99-116 102 engagement and implementation of green innovations hard. the project management team comes into action too late to make notable influence or change. today, businesses value sustainability policies as a means to achieve sustainable development (asadi et al., 2020). in this context, elkinton (1998) developed a model that includes economic, environmental, and social sustainability (i.e., triple bottom line) performance indicators to ensure environmental sustainability. accordingly, economic, environmental, and social dimensions must be prioritized and balanced for an industry’s sustainable development. moreover, economic, environmental, and social concerns have heightened the significance of green innovation practices (wang & yang, 2021). the academic literature has also flourished in this area. however, the literature on green innovation frequently focuses on western and developed countries (cainelli et al., 2012; del río et al., 2016). therefore, this issue should be highlighted, as the literature on green innovation and sustainable performance practices for developing countries is surprisingly insufficient (ullah et al., 2022). as such, the current research uses sustainability performance indicators (spis) suggested by wang & yang (2021) to evaluate the green innovation practices in nigeria. six aspects (criteria) of green innovation are used. the balanced score card (bsc) structure developed by kaplan and norton (1992) is frequently used for sustainable performance evaluation (aly & mansour, 2017; houck et al., 2012). however, this approach is inadequate as it cannot consolidate multiple performance factors. since sustainable performance evaluation incorporates multiple criteria, this issue can be regarded as an mcdm (multi-criteria decision making) problem (lu et al., 2018). as such, the aspects of green innovation are evaluated using the full consistency method (fucom) method. the ranking of the three spis is obtained using the measurement of alternatives and ranking according to compromise solution (marcos) method using the weights of the aspects of green innovation obtained from the fucom analysis. in the following respects, this work adds to the existing body of knowledge. firstly, sustainable production is essential in the textile industry, which consumes large quantities of water, chemical loads, and energy from the cultivation of raw materials through the creation of completed items, as in other industries (gbolarumi et al., 2021). therefore, the textile industry is under significant pressure to address sustainability issues (acar et al., 2015). based on the importance of sustainability performance evaluation in the textile industry, this study advances the understanding of the literature on green innovation through empirical analysis. second, to the authors' knowledge, this study is the first effort to highlight aspects of green innovation and spis in the textile industry in nigeria. therefore, this study is expected to provide important insights into green innovation to managers in the textile industry. this work adds to the literature by presenting for the first time the mathematically sound, integrated fucom-marcos technique to the area of sustainable performance assessment. the remainder of the paper is structured as follows: section 2 provides the research methodology that includes the fucom and marcos methods. in section 3, a case study of a real-world application is presented through a two-stage sensitivity analysis. finally, section 4 concludes with a summary and suggestions for further study. measuring sustainability performance indicators using fucom-marcos methods 103 2. research methodology mcdm is a technique utilized by researchers when making decisions involving the prioritization, ranking, or selection of preferences (muhammad et al., 2021). its goal is not to indicate the best conclusion but to help decision-makers in identifying nominated alternatives or a sole alternative that satisfies their needs and is in their favor. the mcdm system incorporates the behavior of preferences across many quantitative, qualitative, or conflicting criteria and consequences in a statement needing agreement. various disciplines, such as information systems, economics, computer science, and behavioral decision theory, are leveraged for this purpose. diverse mcdm techniques have been created, encouraged, and provided in a variety of necessity-driven contexts (badi & ballem, 2018). for example, popović (2021) employed the cocoso method in solving the personnel selection problem. similarly, popović et al. (2021) adopted the swara methodology and examined the criteria affecting the recruitment and selection of staff. özdağoğlu et al. (2021) proposed a comprehensive solution to the motorcycle selection problem consisting of mopa, copras, moosra, wpm, saw, and rov methods. mcdm techniques include, but are not limited to, analytical hierarchy process, simple additive weighting, data envelopment analysis, and analytical network process (alosta et al., 2021). despite numerous studies implementing the methods, mcdm continues to be a rapidly expanding issue in a number of departments. nevertheless, each method has a similar capacity to make decisions in the face of distrust, and each has its own advantages. in this research, a two-stage mcdm approach was used. during the first stage, the fucom method is utilized to calculate the weights of the criteria, and in the second stage, the marcos method is used to appraise the spis. the methodology can be divided into several steps as follows: identify the significance and scope of the research define the criteria that can be used in the study through previous studies contacting experts to clearly define the idea of the model and the purpose of the study, as well as completing the form calculating the weights of criteria using the fucom approach obtaining the ranking of choices using the marcos approach sensitivity analysis by using other methods of solution figure 1 also depicts the four-step flowchart of the research. badi et al./oper. res. eng. sci. theor. appl. 5(2) 2022 99-116 104 stage 1. preliminary inq uiry stage 2. determining criteria weight stage 3. evaluation of alternatives stage 4. sensitivity analysis recogniz e need for research and identify the scope create a set of criteria form a group of experts conduct pairw ise comparisons determine criteria w eights using the fucom method rank spis using the ma rcos method choose the o ptimal spi change criteria weights conduct a co mparative analysis figure 1. flowchart of the proposed methodology 2.1 fucom method pamučar et al. (2018) have created fucom, one of the most recent mcdm models. this method uses the approach of pairwise comparison (božanic et al., 2019). it requires fewer pairwise comparisons than alternatives such as the best worst method (bwm) and the analytical hierarchy process (ahp). in addition, it is capable of validating findings by describing the deviation from maximum consistency (dmc) of comparison and identifying transitivity in paired comparisons of criteria. it has been used in many applications in different areas of research (fazlollahtabar et al., 2019). in order to demonstrate the procedures of the method, we assume a number (n) of criteria that will be used to evaluate the decision (pamucar et al., 2022). the decision-maker must determine the importance of each of these criteria by assigning a weight to them. in pairwise comparison models, the effect of each criterion (i) on the other criterion (j) is determined. the fucom method can be illustrated by the following steps (badi & kridish, 2020): algorithm: fucom input: expert pairwise comparison of criteria output: optimal values of the weight coefficients of criteria/sub-criteria step 1: expert ranking of criteria/sub-criteria. step 2: determining the vectors of the comparative significance of evaluation criteria. measuring sustainability performance indicators using fucom-marcos methods 105 step 3: establishing the constraints of a model for nonlinear optimization. constraint 1: the percentage of weight coefficients for criteria represents the relative relevance of the given criteria. constraint 2: the amount of weights must meet the mathematical requirement of transitivity. step 4: creating a model for determining the final weights of assessment criteria. step 5: computing the final weights of criteria and sub-criteria for appraisal. 3.2 marcos method the marcos method involves calculating two reference alternatives, the ideal and the anti-ideal, and then determining the relative position of each alternative with respect to these two references (stević et al., 2020). the position of this alternative within these two solutions is known as the usefulness function. after calculating these positions, one can find the best solution, which is the closest to the ideal and the furthest from the anti-ideal solution. following are the steps necessary to describe this method (badi & pamucar, 2020): step 1: establish an initial decision matrix. step 2: this stage involves the calculation of ideal and anti-ideal solutions for each alternative and the creation of an extended matrix utilizing these solutions. in this step, each of the alternatives is evaluated for each of the criteria, and the optimal and anti-optimal solutions of this alternative are calculated for these criteria. this step is performed according to the following equations: (1) (2) where b denotes the criterion that should be maximized and c denotes the criteria that should be minimized. step 3. the standardization of the initial extended matrix. using the following equations, normalization is accomplished: (3) (4) where the values and constitute the values of the initial decision matrix. step 4. the process of determining a weighted decision matrix. the weighting procedure is based on multiplying the normalized decision matrix values with the associated criteria weights. step 5. computation of the usefulness degree for each alternatives ki. using the following formulae, we can calculate the usefulness degree:: (5) (6) badi et al./oper. res. eng. sci. theor. appl. 5(2) 2022 99-116 106 where si (i=1,2,..,m) is derived from the summation of the values of the weighted decision matrix. (7) step 6. the formulation of the usefulness function of the alternatives f(ki). using the following equation, the function of usefulness is obtained as the final step. (8) where f( ) is the usefulness function based on the anti-ideal solution; on the contrary, f( ) implies the usefulness function for the ideal solution. both usefulness functions can be calculated with the help of the following equations, respectively. (9) (10) step 7. sorting the alternatives. at the end of the computation procedures, alternatives are ranked based on their usefulness functions. the most optimal solution must have the highest score for the usefulness function. 3. case study extensive research highlights the growing concern about environmental issues in nigeria. the textile industry is a major cause of pollution and the emission of harmful contaminants into the environment and is the second-largest source of industrial pollution in lagos after the chemical and pharmaceutical industries. this pollution comes from the discharge of large quantities of toxins in high doses from the textile industry into the environment. the amount of toxic water with chemicals discharged amounts to more than 100 liters for every kilogram of textile product produced. these large quantities of water cause many textile manufacturers to discharge their effluents into nearby water bodies rather than into the sewage system. this has disastrous consequences for both aquatic life and the ability to supply fresh water. therefore, given the importance of this industry in the country, it is essential that decision-makers give importance to ideas and policies that protect the environment (durotoye et al., 2018). this research, therefore, aims to assess aspects of green innovation. the list of criteria in table 1 will be used. table 1. the criteria list criteria no. evaluation criteria c1 technological innovation c2 competitive advantage c3 process innovation c4 managerial innovation c5 product innovation c6 greening the supplier measuring sustainability performance indicators using fucom-marcos methods 107 all of these criteria are profit-oriented. a total of four experts were involved in the evaluation process, during which the purpose of the research was explained to them, and the methodology to be used was clarified. notable is the fact that four of the experts work in a field related to the industry sector, and two of them also hold academic positions. therefore, experts have sufficient knowledge and experience regarding the subject and field of research. purposive sampling was adopted in selecting experts, as experts need expertise in green innovation and the textile industry. as suggested by gupta and dhingra (2021), criteria weights were derived from a consensus-based group discussion to minimize the subjectivity of experts. the model will be described in the phases below: first step: after discussion, the criteria were ranked in terms of importance in the following order: c1> c6> c5> c3 >c2>c4 second step: the experts conducted a pairwise assessment of the criteria at this stage. all comparisons were made with criterion c1, which was defined as the most important criterion, and the scale [1,9] was used. table 2 depicts the result of the comparison obtained. table 2. prioritization of criteria criteria c1 c6 c5 c3 c2 c4 ( )j kc  1.0 2.0 3.0 4.0 4.0 5.0 next, on the basis of the acquired criteria priorities, comparative criteria priorities must then be determined: , , , third step: in this procedure, the following two requirements are met by the final weight coefficients: that the values of these coefficients satisfy the condition in the second step, and these coefficient values can be written as follows: , , , , that these values satisfy the mathematical transit condition, and it can be written as follows: , , , consequently, the model for finding the weights of the criteria may be expressed as follows: badi et al./oper. res. eng. sci. theor. appl. 5(2) 2022 99-116 108 min  the final results of the weight coefficients and the cfd of the outcomes are acquired by solving this model. figure 2 depicts the value of the criteria according to the first scores. using the microsoft excel solver tool, the model is solved. based on the observed data, it can be inferred that c1 is the most essential criterion, followed by c6. c4 is, however, the least important criterion. figure 2. the value of decision criteria after determining the criterion weights, the next step is to use the marcos method to rank the sustainability performance indicators. based on the steps that have been explained in the second part of this research, the decision matrix obtained from the experts is prepared, as shown in table (3). the sustainability performance indicators are spi 1 (economic performance), spi 2 (environmental performance), and spi 3 (social performance). table 3. the initial decision matrix weights of criteria 0.395 0.197 0.132 0.099 0.099 0.079 spi # c1 c2 c3 c4 c5 c6 spi 1 57 55 45 52 62 50 spi 2 52 58 47 55 57 51 spi 3 60 57 53 51 62 51 max 60 58 53 55 62 51 measuring sustainability performance indicators using fucom-marcos methods 109 a simple linear normalization is now used in order to obtain uninformed data. since all the criteria used in the case of the study are profit criteria, the maximization function has been used. applying equation (3), the normalized decision matrix is displayed in table 4. table 4. the normalized decision matrix spi # c1 c2 c3 c4 c5 c6 spi 1 0.950 0.948 0.849 0.945 1.000 0.980 spi 2 0.867 1.000 0.887 1.000 0.919 1.000 spi 3 1.000 0.983 1.000 0.927 1.000 1.000 the next step is to use the coefficient weights previously found to obtain aggregated values. then, the ideal solutions (i.e., the maximum values of a criterion) and the anti-ideal solutions (i.e., the minimum values of a criterion) are computed. the degree of usefulness is then calculated, and the findings are depicted in table 5. table 5. the weighted decision matrix and the negative-ideal solution spi # c1 c2 c3 c4 c5 c6 sum spi 1 0.375 0.187 0.112 0.093 0.099 0.077 0.943 spi 2 0.342 0.197 0.117 0.099 0.091 0.079 0.925 spi 3 0.395 0.194 0.132 0.092 0.099 0.079 0.989 ideal 0.395 0.187 0.132 0.092 0.099 0.079 0.983 anti-ideal 0.342 0.197 0.112 0.099 0.091 0.077 0.918 then, using equation 10, the usefulness function of each alternative is obtained by taking into account the usefulness function of the ideal and anti-ideal solutions. thus, the ultimate ranking for the alternatives is identified in table 6. it shows that the spi 3 indicator is the most important sustainability performance indicator. table 6. the relative assessment matrix and alternative performance spi # f(ki) rank spi-1 1.028 0.960 0.661 2 spi-2 1.007 0.941 0.648 3 spi-3 1.078 1.007 0.694 1 in order to measure the stability of the solution obtained, five other solution methods were used: codas (keshavarz ghorabaee et al., 2016), edas (ghorabaee et al., 2015), mabac (pamučar & ćirović, 2015), saw (goodridge, 2016), and waspas (mardani et al., 2017). figure 3 shows the results obtained. the results show the stability of the solution, except for indicators spi-1 and spi-2, which swap their order in the mabac method. badi et al./oper. res. eng. sci. theor. appl. 5(2) 2022 99-116 110 figure 3. results comparison in addition to the comparative analysis, a further analysis was performed on the input parameters to validate the results. using the equation (11) based on the most important criterion c1, simulated weights were calculated for 20 different scenarios (set1-set20) (simić et al., 2020; torkayesh et al., 2021). (1 ) (1 ) n n n w w w w = − −    (11) in this formula, nw  represents the altered weights of the criteria, whereas nw  represents the decreased weight of the most significant criterion. w represents the initial weight of each criterion, whereas nw represents the original weight of the most important criterion. for c1, the most important criterion, the rate of reduction was decreased by 5% in each scenario, and the application was finalized through 20 scenarios. figure 4 displays simulated weights for criteria. figure 4. criteria weights under 20 scenarios measuring sustainability performance indicators using fucom-marcos methods 111 scenario-based rankings relying on simulated criteria weights are portrayed in figure 5. consequently, the ranking is sensitive to changes in the weighting of criteria. however, we can conclude that there is no dramatic change in scenariobased rankings. although spi-1 and spi-2 share second and third ranks in various scenarios, spi-3 is the most optimal solution in all cases. overall, comparative analysis and sensitivity analysis based on simulated weights achieved a high level of consistency, thus yielding stability of the calculation. figure 5. scenario-based rankings through 20 scenarios 4. conclusion green innovation has turned out to be a common and ordinally topic of interest all over the globe due to the increasing environmental concerns. however, growing industrialization, urbanization, globalization, and population have brought about various issues such as living conditions of social problems, economic problems, and damage to the environment. through air pollution, industrialization has impacted air pollution through smoke and emissions caused by burning fossil fuels. the discharge contains carbon oxide that is a pollutant to the air. water pollution stands as the second problem caused by industrialization. this is especially in areas where industries are established next to water bodies. the toxins from the water bodies contaminate the water bodies in a gaseous, liquid, and solid state. this normally happens if the industries direct their discharge to the water sources or contamination from landfills. soil is also contaminated by industrial activities. lead is a commonly known soil contaminant, although other hazardous and heavy metals can leach into the soil and destroy plants. increased population, urbanization, industrialization, and others have resulted in dramatic environmental destruction. forests are destroyed to acquire timber and give space for roads and industrial space. using mcdm models, the study attempted to evaluate and prioritize green innovation aspects in light of sustainability performance metrics. the use of the fucom-marcos method indicates that green managerial innovations are the utmost instrumental innovation bearing for industries’ adoption in their manufacturing. the badi et al./oper. res. eng. sci. theor. appl. 5(2) 2022 99-116 112 methodology has a tactical necessity in naturalizing green practices in manufacturing. decision-makers can use this model to examine the green innovation exercises which will be of benefit in promoting social, economic, and environmental performance. although this paper attempts to add to the literature, it makes important suggestions for future research. as this study was limited to the textile industry in nigeria, the results may not be generalizable. therefore, future studies with similar analyses on leading textile exporters such as china, india, and turkey can yield more generalizable results (world trade organization, 2021). thus, the sustainable performance evaluation of the textile industry can better highlight the current global situation. moreover, relying on aspects of green innovation, researchers can adapt this framework to other industries in nigeria or any country. although six green innovation aspects and three spis were employed in this study, future research may apply more comprehensive frameworks. finally, this study adopted an approach including fucom as a subjective weighting method and the marcos method as a ranking method. however, the mcdm literature has grown dramatically in the last few years. in this context, numerous new mcdm methods have been proposed for handling weighting and sorting problems (ecer & pamucar, 2022). in terms of the weighting procedure, objective weighting methods such as lopcow (ecer & pamucar, 2022) and merec (keshavarz-ghorabaee et al., 2021) and subjective weighting methods such as vimm (zakeri et al., 2021) and lbwa (žižović & pamučar, 2019) have emerged. similarly, recent methods such as rafsi (žižović et al., 2020), raderia (jakovljevic et al., 2021), lmaw (pamučar et al., 2021), cocoso (yazdani et al., 2019) and trust (torkayesh & deveci, 2021) have been proposed for ranking problems. the popular mcdm methods in the literature can be applied to the research problem of this study, and future research can evaluate the efficacy of the 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(2020). eliminating rank reversal problem using a new multi-attribute model the rafsi method. mathematics, 8(6), 1–16. https://doi.org/10.3390/math8061015 © 2022 by the authors. submitted for possible open access publication under the terms and conditions of the creative commons attribution (cc by) license (http://creativecommons.org/licenses/by/4.0/). plane thermoelastic waves in infinite half-space caused operational research in engineering sciences: theory and applications vol. 2, issue 2, 2019, pp. 40-54 issn: 2620-1607 eissn: 2620-1747 doi:_ https://doi.org/10.31181/oresta190261p * corresponding author adispuska@yahoo.com (a. puška), ilija.stojanovic@teol.net (i. stojanović), a.maksimovic22@gmail.com (a. maksimović) evaluation of sustainable rural tourism potential in brcko district of bosnia and herzegovina using multi-criteria analysis adis puška*, ilija stojanović, aleksandar maksimović institute for scientific research and development brcko district of bosnia and herzegovina received: 02 june 2019 accepted: 03 august 2019 first online: 18 august 2019 original scientific paper abstract. for investment decisions to be made in tourism sector, it is necessary to determine tourism potential on the first place. tourism potential is the ability of a particular location to attract and host tourists. tourism development should be based on strengthening sustainability, and thus tourism will provide good effects. since rural settlements have experienced recession in the past few decades, these areas need to be revitalized. this can be achieved through development of rural tourism. sustainability of rural tourism potential in brcko district of bosnia and herzegovina is in focus of this study. based on sustainability criteria, we assessed the rural potential in brcko district of bosnia and herzegovina for certain rural settlements. assessment of the sustainability of rural tourism potential in brcko district of bosnia and herzegovina was carried out with expert evaluation and used methods of fucom, aras and critic, and a decision model will be created for this purpose. the findings from this study will provide guidelines for improvement of rural tourism in brcko district of bosnia and herzegovina through examination of good and bad sides of the examined rural settlements. the model with certain corrections can also be used in determining sustainable tourism potential in other branches of tourism. key words: rural tourism, sustainable tourism, tourism potential, multi-criteria analysis, brcko district bosnia and herzegovina 1. introduction tourism represents an economic branch which provides a basis for economic growth and development of the world economy. in some regions tourism contributes to the increase of employment and improvement of economy (ullah, et al, 2010). tourism development should be based on the principles of sustainability (weaver, evaluation of sustainable rural tourism potential in brcko district of bosnia and herzegovina using multi-criteria analysis 41 2014). sustainability in tourism includes three basic criteria: economic, environmental and social. the assessment of these criteria is a requirement to improve tourism. in particular, this is significant in rural areas. tourism in rural areas is accepted as a tool for development of these areas (rozman, et al, 2009). rural tourism represents a form of tourism in rural areas, all in a natural environment where tourist are being offered various offers and activities (jesus & franco, 2016), all of it in an attempt to further develop that rural community and develop the living standard of that population. the main importance of rural tourism is to attract tourists on the basis of a rural tourist offer so that the population’s income and living standard could increase, whilst using the already existing resources. rural tourism attracts tourists that are searching for emotional experiences. the starting point of rural tourism has to be intercultural interaction and a way to bring the rural way of life to the tourists. thus tourist won't just be passive consumers and the rural population won't be just powerless people who have had tourism imposed on them, instead, a social capital in tourism will develop (steel, 2012). the criteria of rural tourism potential can be different. therefore, it is necessary to apply the principle of a complete evaluation of sustainable tourism potential. this evaluation is performed using the method of multi-criteria analysis. the aim of this paper is to research sustainable rural tourism potential in brcko district of bosnia and herzegovina (hereinafter: brcko district). this research was done using the decision model. in cooperation with the government of brcko district, three experts were engaged in evaluating sustainable rural tourism potential. based on evaluation from the experts, good and bad side alternatives will be considered. the significance of this paper is to present the new model of research on sustainable rural tourism potential. in this study is presented the new research methodology using multicriterion analysis methods. based on this, the following research objectives are set: 1. create the model of sustainable rural tourism potential 2. test the model on the example of the rural settlements of the brcko district. this paper will first present methods of multi-criteria analysis and it will explain the model and research methodology. then, the results of the research will be presented that will be a basis for sensitivity analysis to examine these results. finally, we will provide the conclusion from the study. 2. multi-criteria analysis methods the decision model used in this study is based on the application of the following multi-criteria analysis models: fucom, critic and aras methods. the advantage of this model is that it takes advantage of these methods. the advantages of the fucom method are that it uses a simple algorithm, allows to obtain optimal values of weight coefficients with the ability to confirm the consistency of results, uses a simple mathematical apparatus that favors certain criteria, reduces subjective influence and inconsistency of experts' preferences, gets the same results as the bwm and ahp methods but with by performing a n-1 criterion comparison alone (pamučar et al, 2018). the critic method allows the criteria to be weighted in an objective manner puška et al./oper. res. eng. sci. theor. appl. 2 (2) (2019) 40-54 42 without subjective evaluations. criterion weighting using the critic method is performed using statistical parameters standard deviation and correlation coefficient. the aras method allows you to determine the ranking of the utility function. this allows the ratio of the optimal alternative to be used in seeking to rank alternatives and to find ways to improve the alternative projects that were the subject of observation (zavadskas and turskis 2010). based on these advantages, the model formation was performed. these methods will be explained below. 2.1. fucom method the fucom (full consistency method) method was developed by pamučar, et al. (2018) for determining the weights of criteria. the fucom provides a possibility to validate the model by calculating the error size for obtained weight vectors, by determining the degree of consistency (mujkanović, et al, 2019). the fucom method uses the following steps (zavadskas, et al., 2018): step 1. in the first step, the criteria from the predefined set of the evaluation criteria c = {c1,c2, … , cn} are ranked. the ranking is performed according to the significance of the criteria, from the most significant to the less significant. cj(1) > cj(2) > … > cj(k) (1) if there is a judgment of the existence of two or more criteria with the same significance, the sign of equality is placed instead of “>” between these criteria in the expression (1) step 2. comparison of the ranked criteria is carried out and the comparative priority (φk/(k+1), k = 1,2,3,…,n , where k represents the rank of the criteria) of the evaluation criteria is determined. φ = (φ1/2, φ2/3, …, φk/(k+1)) (2) step 3. the final values of the weight coefficients of the evaluation criteria (w1, w2, … wn)t are calculated. the final values of the weight coefficients should satisfy the following 2 conditions: a) the ratio of the weight coefficients is equal to the comparative priority among the observed criteria (φk/(k+1)) defined in step 2, i.e. the following condition is met: (3) b) in addition to the condition (2), the final values of the weight coefficients should satisfy the condition of mathematical transitivity, i.e. . since and ⊗ is obtained. thus, another condition, that the final values of the weight coefficients of the evaluation criteria need to meet, is obtained, namely: (4) evaluation of sustainable rural tourism potential in brcko district of bosnia and herzegovina using multi-criteria analysis 43 based on the defined settings, the final model for determining the final values of the weight coefficients of the evaluation criteria can be defined. min χ, s.t. (5) . 2.2. critic method the critic method is used in order to determine weight values of objective criteria which include intensity and contrast of the conflict inherent in the structure of decision problem. it belongs to a class of correlation method and is based on analytical testing decision matrix in order to determine information contained in the criteria by which to evaluate the variants. in order to determine the contrast criteria, a standard deviation of normalized criterion is used, as well as value variants, by columns and the correlation coefficients of all pairs of the columns. the critic method steps are (puška, et al., 2018a): step 1. there is a complex linear normalization. thus, the initial matrix is converted into a matrix with the generic elements xij. step 2. each vector has a standard deviation σj, which represents a measure of deviation values of variants for a given criterion of some average values. standard deviation is, in fact, the size which is still used in this method. step 3. then, a symmetrical matrix of dimension m x m with elements rjk is constructed, which represents the coefficients of linear correlation vector xj and xk. the greater the discrepancy between the criterion (value) for (criteria) variants j and k, the lower the coefficient value rjk is. the spearman correlation coefficient can be used instead of pearson correlation coefficient. (6) step 4. the previous term is a measure of conflict criterion j in relation to the other criteria in the crucial situation (milicevic & zupac, 2011). the subsequent evaluation of the amount of information cj which is contained or given in the criteria j, therefore it is determined by the combination of the above size and σj rjk as follows: (7) puška et al./oper. res. eng. sci. theor. appl. 2 (2) (2019) 40-54 44 step 5. the objective criteria weights are obtained by normalizing the size cj. 2.3. aras method the additive ratio assessment (aras) method is developed by zavadskas and turskis (2010). the process of solving decision making problems using the aras method, similarly to the other methods of mcdm, starts with forming the decision matrix and determining weights of criteria. after these initial steps, the remaining part of solving mcdm problem using the aras method can be precisely expressed using the following steps (karabasević, et al., 2015): step 1. determine the optimal performance rating for each criterion. in this step the decision maker sets the optimal performance rating for each criterion. if the decision maker does not have a preference, the optimal performance ratings are calculated as: (8) where x0j denotes the optimal performance rating of j-th criterion, ωmax denotes the benefit criteria, i.e. the higher the values are, the better it is; and ω min denotes the set of cost criteria, i.e. the lower the values are, the better it is. step 2. calculate the normalized decision matrix. (9) where rij denotes the normalized performance rating of i-th alternative in relation to the j-th criterion, i = 0,1,...,m. step 3. calculate the weighted normalized decision matrix. vij = wj rij, (10) where vij denotes the weighted normalized performance rating of i-th alternative in relation to the j-th criterion, i = 0,1,...,m. step 4. calculate the overall performance rating, for each alternative. (11) where si denotes the overall performance rating of i-th alternative, i = 0,1,...,m. step 5. calculate the degree of utility for each alternative. when evaluating alternatives, it is not only important to determine the best ranked alternative. it is also important to determine relative performances of considered alternatives, in relation to the optimal alternative. (12) evaluation of sustainable rural tourism potential in brcko district of bosnia and herzegovina using multi-criteria analysis 45 where qi denotes the degree of utility of i-th alternative, and s0 is the overall performance index of optimal alternative, i = 1,2,...,m. step 6. rank alternatives and/or select the most efficient one. the considered alternatives are ranked by ascending qi , i.e. the alternative with the largest value of qi is the best placed. 3. model and methodology evaluation of sustainable rural tourism potential requires assessment of alternatives by criteria of sustainability: environmental (c1), social (c2) and economic (c3) criteria. these criteria are the main criteria of the model. to see a sustainable rural tourism potential, each of these criteria is further developed into a sub-criterion. identifying these sub-criteria was based on the following paper: do & chen, (2013), zhou (2014), zhou, et al. (2015), mikulić, et al. (2016), topolansky barbe, et al. (2016), peng & tzeng (2019) and yan et al. (2017) the model for sustainable rural tourism potential is presented in figure 1. this model is formed to assess current sustainable tourist potential in the rural area of brcko district. four rural settlements make up a sample of four alternatives: gornji zovik (a1), brezovo polje (a2), maoča (a3) and bijela (a4). to evaluate these alternatives we used expert evaluations. the experts were appointed in cooperation with the government of brcko district in the following way. first, we set the list of potential experts which was a basis for selection of experts. in order to conduct the study, three experts were appointed who visited selected areas. furthermore, all the materials that the government of the brcko district has about these areas are presented and used by the experts. based on this, the experts carried out an assessment of the sustainable rural tourism potential of the brcko district. figure 1. model of sustainable rural tourism potential puška et al./oper. res. eng. sci. theor. appl. 2 (2) (2019) 40-54 46 the methodology of the study is presented in table 1. based on this methodology one can see how it will be used to particular methods of multi-criteria analysis. • the fucom method will determine the weights of the main criteria; • the critic method will determine by the weight of sub criteria; • the aras method will rank the alternatives. table 1. methodology of the research research phase the decision to study sustainable rural tourism potential. selection of criteria based on paper review. determining four rural settlements in cooperation with the government of brcko district. determining experts in tourism in cooperation with the government of brcko district. determining criteria and alternatives expert evaluation of the weight main criteria using the fucom method. evaluation of sustainable rural tourism potential rural settlements of brcko district application of the critic method for determining the weight of the sub criteria ranking alternatives use of the aras method for ranking sustainable rural tourism potential of brcko district. performing sensitivity analysis of the results. four rural settlements in brcko district area have been used in this study. each of selected rural settlements will be presented below. gornji zovik is located in the southeastern part of brcko district. this rural settlement has a variety of natural resources that are intact, preserved and pure, with a large number of potable water sources and uncultivated caves. above this settlement is the hill granaš which provides the possibility of applying mountain tourism. in the area of this settlement there are small gardens, decorated orchards and meadows. nearby is the site of the svatovsko cemetery with twenty-nine tombstones. in this settlement the sport-cultural and spiritual event called zovik summer has been organized. this area also has a large number of old houses dominated by begova house. brezovo polje is located on the banks of the sava river. in this settlement is located the aziza mosque, which has been placed under the protection of the state. from the old buildings there is nakic's tower, which was a strategically military place. the resort is famous for its fishing activities and fishing tradition and is known for its gastronomic offer based on fish. it has swimming pools and swimming beaches. nearby forests are full of wild game and birds, of which the well-known eagles are the counts that were here before extinction. every year, a seven-day event is organized under the name brezovo polje summer of culture. maoča is located below the slopes of majevica mountain. through the settlement flow two rivers along which there are plenty of picnics locations and pine forests. along the river is the nožin-agina mosque that has been rearranged to be the museum. this area has rich evergreen and deciduous forests giving clean air. above evaluation of sustainable rural tourism potential in brcko district of bosnia and herzegovina using multi-criteria analysis 47 maoča, there is a locality of dovište, where they used to learn prayers for rain during the dry days. residents of this settlement care about customs and traditions. at the end of this village there are rocks with caves, and the area above maoča is attractive for development of mountain tourism. every year, the traditional manifestation trešnjarevo is held, when a wine picking has been organized. bijela is located on the tinja river, which is rich with fish. the local streams that contain two ancient watermills are poured into this river. the famous monument of beg's tower is known, which is currently being reconstructed and preserved. above bijela are the wooded slopes of majevica. there is the katina cave, and on the other side are the dark caves that are unclean. above the hamlet of kalajdžija is the hill kukavičluk, which springs from the fields of the ivory coast. the terrain above bijela is attractive for development of mountain tourism. 4. results for this paper, the fucom method for determining the weighting of the criteria was applied. step 1. the criteria were ranged from the defined set of criteria, which is shown in the table 1. ranking of the criteria according to its significance was carried out by three experts. table 2. rank of criteria expert rank e1 e2 e3 c2>c3>c1 c2>c1=c3 c2>c1>c3 step 2. comparison of the ranked criteria was done and comparative significance of the evaluation criteria was determined. expert evaluation of comparative significance is shown in table 3. table 3. comparative significance of criteria expert rank e1 c2 1 c3 2 c1 2.3 e2 c2 1 c1 2.7 c3 2.7 e3 c2 1 c1 2 c3 2.5 step 3. following the steps the fucom method and using the lingo 17 software, the results for the main criteria were obtained. the results are presented in table 4. the results have shown that the experts favored the social criterion in relation to the other two sustainability criteria. at least importance is given to economic criterion. puška et al./oper. res. eng. sci. theor. appl. 2 (2) (2019) 40-54 48 table 4. weight coefficients of criteria expert w1 w2 w3 dfc (x) e1 0.225 0.517 0.258 0.000 e2 0.213 0.574 0.213 0.000 e3 0.263 0.526 0.211 0.000 average 0.234 0.539 0.227 after having determined the weights of the main criteria, the alternatives were evaluated according to the sub-criteria. the results of evaluation of the alternative are presented in table 5. the experts evaluated alternatives ranging from 1 to 7. the score 1 represents the lowest rating, while 7 represents the highest rating. table 5. expert evaluation of the alternative dm1 c11 c12 c13 c14 c21 c22 c23 c24 c31 c32 c33 c34 a1 5 6 5 4 2 2 3 2 4 5 4 7 a2 4 5 6 3 3 3 3 2 5 5 6 7 a3 4 5 5 5 3 2 3 2 5 4 3 5 a4 5 4 6 5 4 3 3 4 5 5 6 7 dm2 c11 c12 c13 c14 c21 c22 c23 c24 c31 c32 c33 c34 a1 5 5 6 5 2 2 3 5 3 4 5 4 a2 5 4 5 4 3 3 3 5 4 5 5 6 a3 4 3 4 4 4 4 5 3 5 6 4 5 a4 5 5 5 4 3 3 4 4 4 4 5 6 dm3 c11 c12 c13 c14 c21 c22 c23 c24 c31 c32 c33 c34 a1 5 5 6 5 3 3 4 6 4 4 6 4 a2 4 4 5 4 4 4 4 6 5 5 6 6 a3 4 4 5 4 5 4 5 4 5 5 5 4 a4 5 4 5 4 4 4 4 5 5 4 6 6 after evaluating the alternatives by sub-criteria it is necessary to match the evaluation of the experts, since group decision-making was used where there were three tourism experts. this will be done by the applied aggregate geometric mean on an initial matrix of decision-making. the initial decision matrix is presented in table 6. this matrix was used to determine the weight sub-criteria with the critic method, and was used for ranking the alternate with the aras method. table 6. initial decision matrix c11 c12 c13 c14 c21 c22 c23 c24 c31 c32 c33 c34 a1 5.00 5.31 5.65 4.64 2.29 2.29 3.30 3.91 3.63 4.31 4.93 4.82 a2 4.31 4.31 5.31 3.63 3.30 3.30 3.30 3.91 4.64 5.00 5.65 6.32 a3 4.00 3.91 4.64 4.31 3.91 3.17 4.22 2.88 5.00 4.93 3.91 4.64 a4 5.00 4.31 5.31 4.31 3.63 3.30 3.63 4.31 4.64 4.31 5.65 6.32 before alternating ranking was performed, it was necessary to determine the weight of the sub-criteria using the critic method. all weight sub-criteria were calculated for the main criteria using the steps critic method. first, normalization of the initial decision matrix was performed. second, standard deviation values and evaluation of sustainable rural tourism potential in brcko district of bosnia and herzegovina using multi-criteria analysis 49 correlation coefficients were calculated. third, the values )1( jk r− were calculated and these values were compiled. fourth, these values were multiplied with the standard deviation. fifth, normalization of weight sub-criteria was performed. finally, weights of sub-criteria were multiplied by the weights of the main criteria and the final weight was formed. table 7. steps of critic method c11 c12 c13 c14 c21 c22 c23 c24 c31 c32 c33 c34 normalized decision matrix 1.00 1.00 1.00 1.00 0.59 0.69 0.78 0.91 0.73 0.86 0.87 0.76 0.86 0.81 0.94 0.78 0.84 1.00 0.78 0.91 0.93 1.00 1.00 1.00 0.80 0.74 0.82 0.93 1.00 0.96 1.00 0.67 1.00 0.99 0.69 0.73 1.00 0.81 0.94 0.93 0.93 1.00 0.86 1.00 0.93 0.86 1.00 1.00 j  0.10 0.11 0.07 0.09 0.18 0.15 0.10 0.14 0.12 0.08 0.15 0.15 jk r 1.00 0.72 0.83 0.50 1.00 0.89 0.75 -0.39 1.00 0.65 -0.21 0.24 0.72 1.00 0.86 0.51 0.89 1.00 0.37 -0.05 0.65 1.00 -0.29 0.00 0.83 0.86 1.00 0.15 0.75 0.37 1.00 -0.78 -0.21 -0.29 1.00 0.90 0.50 0.51 0.15 1.00 -0.39 -0.05 -0.78 1.00 0.24 0.00 0.90 1.00 )1( jk r− 0.00 0.28 0.17 0.50 0.00 0.11 0.25 1.39 0.00 0.35 1.21 0.76 0.28 0.00 0.14 0.49 0.11 0.00 0.63 1.05 0.35 0.00 1.29 1.00 0.17 0.14 0.00 0.85 0.25 0.63 0.00 1.78 1.21 1.29 0.00 0.10 0.50 0.49 0.85 0.00 1.39 1.05 1.78 0.00 0.76 1.00 0.10 0.00  = − m k jk r 1 )1( 0.95 0.91 1.16 1.83 1.75 1.79 2.65 4.22 2.31 2.64 2.60 1.86  = − m k jkj r 1 )1( 0.10 0.10 0.09 0.17 0.32 0.26 0.27 0.60 0.27 0.20 0.38 0.27 j w 0.21 0.23 0.19 0.37 0.22 0.18 0.19 0.41 0.24 0.18 0.34 0.24 final j w 0.049 0.053 0.045 0.087 0.118 0.098 0.101 0.222 0.055 0.041 0.077 0.055 after calculating the weights for sub-criteria, ranking of the alternatives was performed using the aras method. first, normalization of the initial decision matrix was performed (table 8). second, the decision-making matrix was made more difficult and s0 values were determined (table 9). the third ranking was formed (table 10). table 8. normalized decision matrix c11 c12 c13 c14 c21 c22 c23 c24 c31 c32 c33 c34 a1 0.273 0.298 0.270 0.275 0.174 0.190 0.228 0.261 0.203 0.232 0.245 0.218 a2 0.235 0.241 0.254 0.215 0.251 0.274 0.228 0.261 0.259 0.270 0.280 0.286 a3 0.218 0.219 0.222 0.255 0.298 0.263 0.292 0.192 0.279 0.266 0.194 0.210 a4 0.273 0.241 0.254 0.255 0.277 0.274 0.251 0.287 0.259 0.232 0.280 0.286 s0 0.273 0.298 0.270 0.275 0.298 0.274 0.292 0.287 0.279 0.270 0.280 0.286 w 0.049 0.053 0.045 0.087 0.118 0.098 0.101 0.222 0.055 0.041 0.077 0.055 puška et al./oper. res. eng. sci. theor. appl. 2 (2) (2019) 40-54 50 table 9. weighted normalized matrix c11 c12 c13 c14 c21 c22 c23 c24 c31 c32 c33 c34 a1 0.014 0.016 0.012 0.024 0.021 0.019 0.023 0.058 0.011 0.009 0.019 0.012 a2 0.012 0.013 0.011 0.019 0.030 0.027 0.023 0.058 0.014 0.011 0.021 0.016 a3 0.011 0.012 0.010 0.022 0.035 0.026 0.029 0.043 0.015 0.011 0.015 0.012 a4 0.014 0.013 0.011 0.022 0.033 0.027 0.025 0.064 0.014 0.009 0.021 0.016 s0 0.014 0.016 0.012 0.024 0.035 0.027 0.029 0.064 0.015 0.011 0.021 0.016 the results of the aras method have shown that the best alternative is a4 which is the rural settlement of bijela, while the worst ranked rural settlement is a1 which is gornji zovik. table 10. results and ranking alternatives si ki rank a1 0.237 0.834 4 a2 0.254 0.896 2 a3 0.240 0.846 3 a4 0.269 0.949 1 s0 0.284 1.000 table 10 shows the summary results of the research conducted, which were obtained on the basis of a compromise of all criteria and sub-criteria used in the study. in order to gain a better understanding of the results, an alternative ranking will be made by major criteria. these results are shown in table 11. the results of the analysis by the main criteria show the following. when looking at environmental resources, alternative a1 shows the best results, while alternative a2 shows the worst results. this shows that the best environmental resources are in rural settlement gornji zovik. the reason for this is the fact that it is located on the slopes of majevica and that there are many natural beauties in the area that are not contaminated. however, it can be seen from the results that other rural settlements have good results with this criterion, so it can be concluded that all have good ecological resources, since the results are close to 1. looking at social resources, one can see that a4 has the best results, while a1 has the worst results. thus, rural settlement bijela has the best social resources over other rural settlements observed. it can be observed that no rural settlement has a value of 1 that is best in all subcriteria within social resources. considering only economic resources, the best alternative is a2, while the worst alternative is a4. these results show that rural settlement brezovo polje invests most in tourism compared to other rural settlements. table 11. results of partial analysis according to the main criteria ecological resources social resources economic resources si ki rank si ki rank si ki rank a1 0.279 1.000 1 0.223 0.774 4 0.226 0.809 4 a2 0.233 0.835 4 0.255 0.886 2 0.275 0.983 1 a3 0.233 0.836 3 0.247 0.857 3 0.232 0.829 3 a4 0.256 0.917 2 0.276 0.958 1 0.268 0.959 2 s0 0.279 1,000 0.288 1.000 0.279 1.000 evaluation of sustainable rural tourism potential in brcko district of bosnia and herzegovina using multi-criteria analysis 51 the following conclusions are drawn from the results obtained. alternative a1 gornji zovik must work on social and economic resources. more investment in tourism is needed to create a better environment in this area for the population to remain in the countryside and to engage in tourism. thus, with the strengthening of economic infrastructure, social resources will also improve. alternative a2 brezovo polje must work on ecological resources. it must use the location of the sava river flowing past this village to make up for the lack of mountains, hills and pastures located near to other rural settlements in the brcko district. alternative a3 maoča must empower the most of all resources and, above all, economic resources, because these resources have the worst results of all. alternative a4 must work on environmental and economic resources. this research has shown that in rural settlements, there are certain potentials that need to be upgraded. the brcko district government should pay greater attention to rural tourism and invest more in tourism in order to exploit the tourism potential available in these areas. 5. sensitivity analysis in the framework of the sensitivity analysis, a change in the weights of the criteria is made, and the effect on the result of the analysis is examined (puška, et al., 2018b). the main objective of the sensitivity analysis is not to consider the impact of different criteria on changing the value of alternatives, but also to consider the impact of these changes on the overall rating of alternatives (maksimović, & puška, 2015). table 12. sensitivity analysis scenarios c11 c12 c13 c14 c21 c22 c23 c24 c31 c32 c33 c34 scenario 1 0.45 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 scenario 2 0.05 0.45 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 scenario 3 0.05 0.05 0.45 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 scenario 4 0.05 0.05 0.05 0.45 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 scenario 5 0.05 0.05 0.05 0.05 0.45 0.05 0.05 0.05 0.05 0.05 0.05 0.05 scenario 6 0.05 0.05 0.05 0.05 0.05 0.45 0.05 0.05 0.05 0.05 0.05 0.05 scenario 7 0.05 0.05 0.05 0.05 0.05 0.05 0.45 0.05 0.05 0.05 0.05 0.05 scenario 8 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.45 0.05 0.05 0.05 0.05 scenario 9 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.45 0.05 0.05 0.05 scenario 10 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.45 0.05 0.05 scenario 11 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.45 0.05 scenario 12 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.45 in this study, the total weight was evaluated so that a sub-criterion will be taken and given greater importance in relation to other sub-criterion and it will be assigned a weight of 0.45 while the other criterion will assign the importance of 0.05. in this way, it will be examined how each criterion has an influence on ranking the alternatives, taking into account other criterion. thus, 12 different scenarios were obtained in the sensitivity analysis. the weights of each scenario are shown in table 12. in the first scenario, criterion c11 gained a weight of 0.45, while the other puška et al./oper. res. eng. sci. theor. appl. 2 (2) (2019) 40-54 52 criteria gained a weight of 0.05. in the second scenario, criterion c12 gained a weight of 0.45, while other criteria gained a weight of 0.05. in the 12th scenario, criterion c34 gained a weight of 0.45, while other criteria gained a weight of 0.05. the sensitivity analysis results are shown in figure 2. the results of the sensitivity analysis show that in most scenarios, the best results were obtained by a4 alternative bijela. other alternatives have the best results in one scenario. alternative a1 performed best in scenario 2 in which is ranked at the first place. this shows that alternative a1 has the best performance under c12 resource quality criteria, and when this criterion is given with highest priority, alternative a1 is the best. however, in five scenarios, alternative a1 shows the worst results (scenarios 5,6,7,9 and 10). alternative a2 shows the best results for scenario 10. this indicates that the alternative has the best results for criteria c32 existence of domestic products. however, in scenario 4, alternative a2 shows the worst results. alternative a3 shows the best results in scenario 7, while worst case results in scenarios 1, 2, 3, 8, 11 and 12. alternative a4 has the best results in scenarios 1, 3, 4, 5, 6, 8, 9, 11 and 12. however, the alternative a4 did not take the last place in either scenario. it had the worst results in scenario 10 in which is ranked at the third place. the results of the sensitivity analysis show that the a4 alternative is least sensitive to the application of different scenarios, while other alternative indicators are more sensitive for different scenarios. this points out that the alternative a4 bijela has the best indicators of sustainable rural tourism potential in brcko district. figure 2. sensitivity analysis 6. conclusion this paper reviews sustainability of rural tourism potential of brcko district. for this purpose, expert decision-making was used by different methods of multi-criteria analysis. a unique decision-making model and an innovative methodology for this research were formed. the fucom method was used to calculate the weights of the main criteria, the critic was calculated by the weight of the sub-criteria, and the evaluation of sustainable rural tourism potential in brcko district of bosnia and herzegovina using multi-criteria analysis 53 aras method was used to rank alternatives. three experts were engaged to evaluate the four alternatives. the results of this analysis have shown that the best-ranked is the rural settlement of bijela. sensitivity analysis has confirmed these results. the advantage of the model is in the following. weight for the main criteria was subjectively determined using the advantages of the fucom method. the experts compared three criteria, and had to compare 2 pairs. the alternatives were evaluated for sub-criteria. the experts did not have to determine the weight of the sub-criteria, but it is rather determined by using the critic method. in this way the questionnaire completed by the experts was reduced, their task was simplified and the ranking was accelerated using the aras method. the questionnaire consisted of two parts. the part one was intended for the subjective determination of the weights of the main criteria (table with one row and three columns); the second section was for evaluating alternatives by sub criteria (table with twelve rows and four columns). in this way, the experts filled only 13 columns. the model used in this way reduced the number of lines in the questionnaire and facilitated the work of experts. the model used took full advantage of the methods used and showed very good flexibility. thus, the set goals of the research were achieved. the flipchart of this study is that only four alternatives have been taken. in future research it is necessary to increase the number of settlements that determine sustainability of tourism potential of brcko district. this would give the overall rating of rural tourism potential. in addition, the lack of this study is that no linguistic values are used that are closer to 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(2015). resource-based destination competitiveness evaluation using a hybrid analytic hierarchy process (ahp): the case study of west virginia. tourism management perspectives, 15, 72-80. plane thermoelastic waves in infinite half-space caused operational research in engineering sciences: theory and applications vol. 5, issue 1, 2022, pp. 139-151 issn: 2620-1607 eissn: 2620-1747 doi: https://doi.org/10.31181/oresta070422211v * corresponding author. nikolvojin@gmail.com (n. vojinović), zeljko.stevic@sf.ues.rs.ba (ž. stević), ilijat@uns.ac.rs (i. tanackov) a novel imf swara-fdwga-pestel analysis for assessment of healthcare system nikolina vojinović 1*, željko stević 2, ilija tanackov 3 1 university of kragujevac, faculty of law, kragujevac, serbia 2 university of east sarajevo, faculty of transport and traffic engineering doboj, bosnia and herzegovina 3 university of novi sad, faculty of technical sciences, serbia received: 16 january 2022 accepted: 04 april 2022 first online: 07 april 2022 research paper abstract: decision-making represents a very popular field with many developed approaches. however, still exists the need for the creation of novel integrated models such as well is the case in this paper. the novel integrated improved fuzzy stepwise weight assessment ratio analysis (imf swara) method, fuzzy dombi weighted geometric averaging (fdwga) operator and pestel (p-political, e-economic, ssocial, t-technological, e-environmental, l-legal) model has been developed. five decision-makers (dms) have evaluated six main elements of the pestel analysis and 30 elements more (five for each group). in total, we have created 35 models based on the developed model. results of pestel analysis based on imf swara method and fdwga shows that legal and economic factors represent the most significant parameters, while last placed belong environmental group. also, the usefulness of the developed integrated model has been demonstrated. key words: imf swara, fuzzy dombi operator, pestel, decision-making, fdwga operator 1. introduction consideration of the problem of decision-making in the presence of a number of influential factors has become an extremely important area. methods, techniques, approaches that belong to the field of multicriteria decision making (mcdm) (alosta et al. 2021; yildirim et al. 2022; pamučar and savin, 2020) become very popular and applicable in all fields of both science and profession (mahmutagić et al. 2021; karagoz et al. 2021; stanujkić et al. 2021; švadlenka et al. 2020; shekhovtsov et al. 2021; özdağoğlu et al. 2021). they have practically become an indispensable tool for vojinović et al./oper. res. eng. sci. theor. appl. 5(1) (2022) 139-151 140 efficient management of any system, thanks to their very flexible performance if we add to that the possibility of making decisions in different conditions of uncertainty (ali et. al. 2021; mishra et al. 2021; bausys et al. 2021; stanujkić et al. 2021) then it is clear why this is one of the most developed areas of operational research in the last 10-15 years. in addition to a large number of newly developed mcdm methods, the development of different aggregators is being pursued in parallel (yang et al. 2020; vojinović et al. 2021; debnath, 2021) which contribute to decision-making in more precise way. another very flexible feature of mcdm methods is the easy way to integrate with other approaches (blagojević et al. 2020; ali et al. 2021; khan, 2018; wang et. al. 2020another very flexible feature of mcdm methods is the easy way to integrate with other approaches in order to overcome potential difficulties and make more precise decisions. the aim of this paper is to create an original integrated imf swara-fdwgapestel model in order to enable accurate quantification of pestel analysis. in this way, soft analysis becomes precise with clear quantified values that make decisionmaking easier. the imf swara method was developed last year and has been successfully applied in several studies so far. stević et. al. (2022) have created an objective critique of the application of the fuzzy swara method by proving the applicability and advantages of the imf swara methodseven different studies have been investigated to prove the validity of the imf swara method. damjanović et. al. (2022) have created the original dea (data envelopment analysis) – imf swara – marcos (measurement of alternatives and ranking according to compromise solution) model for determination level of traffic safety in montenegro in interval of 23 years. imf swara was applied in all six scenarios for determining the weighting coefficients of the criteria. zolfani et al. (2021) have applied an integrated mcdm model in which they used imf swara method for computing criteria weights for the evaluation of logistics villages in turkey. vojinović and stević, (2021) have just applied the combination of imf swara and pestel for health system analysis. they defined six main elements of pestel analysis and five sub-criteria for each of the main groups. vojinović et al. (2021) have also applied the imf swara method to determine the importance of criteria in the evaluation of companies engaged in the transport of dangerous goods. part of the criteria has been referred to the legal aspect, which is extremely important for the proper functioning of this area. when it comes to dombi operator, a number of approaches have been developed including various fuzzy forms: picture fuzzy dombi (jana et al. 2019), spherical fuzzy dombi (ashraf et al. 2020), pythagorean fuzzy dombi (khan et al. 2019), intuitionistic fuzzy dombi (seikh and mandal, 2021) etc. the combination of pestel analysis and mcdm methodology is rare. (tsangas et al. 2019) have combined swot (strengths, weakness, opportunities, threats) with pestel and ahp (analytic hierarchy process) for assessment hydrocarbons sector in cyprus. throughout the rest of the paper, the algorithms of the applied methodology are presented, the pestel analysis is set, and the results are presented, along with the presentation of the calculation of individual steps. a discussion of the results and concluding remarks were presented. a novel imf swara-fdwga-pestel analysis for assessment of healthcare system 141 2. methods 2.1. imf swara method imf swara method has been represented first time by vrtagić et al. (2021). algorithm of imf swara method can be represented through the next steps: step 1: arrangement of criteria in descending order based on their expected significance. step 2: starting from the previously determined rank, the relatively smaller significance of the criterion (criterion cj) was determined in relation j to the previous one (cj−1), and this was repeated for each subsequent criterion. tfn scale for assessment of criteria using imf swara is shown in table 1. table 1. linguistics and the tfn scale for application of imf swara method linguistic variable abbreviation tfn scale absolutely less significant als (1,1,1) dominantly less significant dls (0.5,0.667,1) much less significant mls (0.4,0.5,0.667) really less significant rls (0.333,0.4,0.5) less significant ls (0.286,0.333,0.4) moderately less significant mdls (0.25,0.286,0.333) weakly less significant wls (0.222,0.25,0.286) equally significant es (0,0,0) step 3: calculation the fuzzy coefficient j (1): 1 1 1 j j j j  =  =   (1) step 4: calculation the weights j (2): 1 1 1 1 j j j j j −  =  =    (2) step 5: calculation of the fuzzy weight coefficients (3): 1 j j m j j w = =  (3) where wj is the fuzzy relative weight of the criteria j, and m denotes the total number of criteria. vojinović et al./oper. res. eng. sci. theor. appl. 5(1) (2022) 139-151 142 2.2. fuzzy dombi operator fdwga is represented by equations (4) and (5) based on changing and modification of the previously developed approach rndwga (sremac et al. 2018), which implies the application of fuzzy instead rough numbers. ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 1 1/ 1 1 1/ 1 1 1/ 1 1 1 1 1 1 1 , , n l j j ln j j l j j n m j j mn j j m j j n u j j un j j u j j l j f w f l m u m j j j ij f w f u ij f w f fdwga       = = = = = =    −   +           −   +           −   +            =       =    =  =        =    (4) where wj denotes weights of s decision makers participating in the research, while p≥0 is non-negative number, l j  low value of tfn, m j  middle value of tfn and u j  upper values of tfn. ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 1 1 1 , , l jl j n l j j m jl m u m j j j j n m j j u ju j n u j j f f f f = = =     =          =  =        =        (5) 3. pestel analysis in this study has been reproduced pestel (political, economic, socio-cultural, technological, environmental and legal factors) analysis from the paper (vojinović and stević, 2021). pestel analysis of the healthcare system of the local community a novel imf swara-fdwga-pestel analysis for assessment of healthcare system 143 of pale with reference to the emergency situation caused by the covid-19 pandemic consist of 30 parameters and has been shown as follow. performing such analysis is very important because according to đukić, (2020) pandemic impact of coronavirus (covid-19) on human health can shutter international investment and the business environment. in addition to the economic crisis, a pandemic has influence on crisis of health systems, which requires huge economic investments (đukić et al. 2021). – 1 2 3 , 4 political factors p p political instability p corruption and political influence in the healthcare system p organization insurance and comprehensiveness of health care p social and healthcare polic − − − − 5 y of the executive p healthcare quality and safety policy− ( ) – 1 2 3 4 5 economic factors e e healthcare financing system e population living standard e investing in healthcare improvement e economic crises national and international e healthcare service prices − − − − − – 1 , 2 3 4 5 social factors s s education healthcare habits and lifestyle of the population s age of the population s demographic changes and migrations s social health care s public opinion and the media in he − − − − − alth promotion ( ) – 1 2 , , 3 technological factors t t application of technology in the diagnosis and treatment of diseases t negative impact of technology on health mobile telephony internet social networks t development and − − − 4 5 application of new medicines and methods in the treatment of diseases t automation of records of healthcare users and diseases t electronic communication in accessing health care and providing inform − − ation about health hazards and measures taken – 1 2 3 , 4 environmental factors en en healthy environment en competitiveness of the public and private health sector en education training and expertise of healthcare professionals en population awareness of − − − − 5 the importance of health and self care en population healthcare and health improvement projects − − vojinović et al./oper. res. eng. sci. theor. appl. 5(1) (2022) 139-151 144 – 1 2 3 4 legal factors l l legal and institutional framework of health care l healthcare quality control l legal protection of users of healthcare services l implementation and application of international l − − − − 5 egal norms l the role and activity of national and international regulatory bodies− 4. application of novel imf swara-fdwga-pestel model in this part of the paper has been demonstrated the application of a novel imf swara-fdwga-pestel model based on the preferences of five decision-makers (dms). as the first we have created five various imf swara models for the main factors of the pestel analysis. after that has been formed five similar models for each main parameter, so in total have been created 35 imf swara models. imf swara models with all elements calculated using equations (1) – (3) for five dms for the main parameters of the pestel analysis have shown in tables 2, 3, 4, 5, and 6. table 2. imf swara of the main factors of pestel analysis (dm1) dm1 j j jl jw c2 e (1,1,1) (1,1,1) (0.234,0.243,0.255) c3 d (0,0,0) (1,1,1) (1,1,1) (0.234,0.243,0.255) c1 po (0.222,0.25,0.286) (1.222,1.25,1.286) (0.778,0.8,0.818) (0.182,0.194,0.208) c6 pr (0.286,0.333,0.4) (1.286,1.333,1.4) (0.556,0.6,0.636) (0.13,0.146,0.162) c5 o (0.333,0.4,0.5) (1.333,1.4,1.5) (0.37,0.429,0.477) (0.087,0.104,0.122) c4 t (0.4,0.5,0.667) (1.4,1.5,1.667) (0.222,0.286,0.341) (0.052,0.069,0.087) sum (3.926,4.114,4.273) table 3. imf swara of the main factors of pestel analysis (dm2) dm2 j j jl jw c6 pr (1,1,1) (1,1,1) (0.233,0.242,0.254) c4 t (0,0,0) (1,1,1) (1,1,1) (0.233,0.242,0.254) c2 e (0.222,0.25,0.286) (1.222,1.25,1.286) (0.778,0.8,0.818) (0.181,0.194,0.207) c1 po (0.25,0.286,0.333) (1.25,1.286,1.333) (0.583,0.622,0.655) (0.136,0.151,0.166) c3 d (0.333,0.4,0.5) (1.333,1.4,1.5) (0.389,0.444,0.491) (0.091,0.108,0.124) c5 o (0.5,0.667,1) (1.5,1.667,2) (0.194,0.267,0.327) (0.045,0.065,0.083) (3.944,4.133,4.291) a novel imf swara-fdwga-pestel analysis for assessment of healthcare system 145 table 4. imf swara of the main factors of pestel analysis (dm3) dm3 j j jl jw c6 pr (1,1,1) (1,1,1) (0.251,0.265,0.284) c1 po (0.222,0.25,0.286) (1.222,1.25,1.286) (0.778,0.8,0.818) (0.196,0.212,0.233) c2 e (0,0,0) (1,1,1) (0.778,0.8,0.818) (0.196,0.212,0.233) c3 d (0.333,0.4,0.5) (1.333,1.4,1.5) (0.519,0.571,0.614) (0.13,0.152,0.174) c5 o (0.5,0.667,1) (1.5,1.667,2) (0.259,0.343,0.409) (0.065,0.091,0.116) c4 t (0.286,0.333,0.4) (1.286,1.333,1.4) (0.185,0.257,0.318) (0.047,0.068,0.09) (3.519,3.771,3.977) table 5. imf swara of the main factors of pestel analysis (dm4) dm4 j j jl jw c3 d (0,0,0) (1,1,1) (1,1,1) (0.23,0.238,0.248) c6 pr (0,0,0) (1,1,1) (1,1,1) (0.23,0.238,0.248) c4 t (0.222,0.25,0.286) (1.222,1.25,1.286) (0.778,0.8,0.818) (0.179,0.19,0.203) c5 o (0.286,0.333,0.4) (1.286,1.333,1.4) (0.556,0.6,0.636) (0.128,0.143,0.158) c2 e (0.25,0.286,0.333) (1.25,1.286,1.333) (0.417,0.467,0.509) (0.096,0.111,0.126) c1 po (0.333,0.4,0.5) (1.333,1.4,1.5) (0.278,0.333,0.382) (0.064,0.079,0.095) (4.028,4.2,4.345) table 6. imf swara of the main factors of pestel analysis (dm5) dm5 j j jl jw c1 po (0,0,0) (1,1,1) (1,1,1) (0.236,0.243,0.251) c2 e (0,0,0) (1,1,1) (1,1,1) (0.236,0.243,0.251) c6 pr (0.222,0.25,0.286) (1.222,1.25,1.286) (0.778,0.8,0.818) (0.184,0.194,0.205) c4 t (0.25,0.286,0.333) (1.25,1.286,1.333) (0.583,0.622,0.655) (0.138,0.151,0.164) c5 o (0.286,0.333,0.4) (1.286,1.333,1.4) (0.417,0.467,0.509) (0.098,0.113,0.128) c3 d (1,1,1) (2,2,2) (0.208,0.233,0.255) (0.049,0.057,0.064) (3.986,4.122,4.236) the next step represents the application of fdwga operator using equations (4) and (5) in order to aggregate previously obtained criteria weights by imf swara method. it is important to note that the weight wj of each dms is equal i.e 0.200. example of the application of fdwga operstor for the first pestel main parameter is as follows. vojinović et al./oper. res. eng. sci. theor. appl. 5(1) (2022) 139-151 146 ( ) ( ) ( ) ( ) ( ) 1 1/ 1 0.814 0.132 1 0.224 1 0.167 1 0.241 1 0.079 1 0.290 1 0.2 0.2 0.2 0.2 0.21 0.224 0.167 0.241 0.079 0.290 1 , , n l j j ln j j l j j l j f w f l m u j j j fdwga   = =  = = − − − − −           +  +  +  +  +            −             +           =  =    = ( ) ( ) ( ) ( ) 1 1/ 1 1 0.879 0.151 1 0.221 1 0.172 1 0.241 1 0.090 1 0.276 1 0.2 0.2 0.2 0.2 0.21 0.221 0.172 0.241 0.090 0.276 1 1 n m j j mn j j m j j n u j j j j m ij f w f u ij w   = = =  = = − − − − −           +  +  +  +  +            −             +         +     =  = ( ) ( ) 1/ 1 0.953 0.169 1 0.218 1 0.174 1 0.244 1 0.100 1 0.263 1 0.2 0.2 0.2 0.2 0.21 0.218 0.174 0.244 0.100 0.263 un j u j f f   = = = − − − − −           +  +  +  +  +            −                                       in the same way have been obtained the other main parameters of the pestel analysis and consequently all subparameters. after applying imf swara – fdwga – pestel model fuzzy weights for the main parameters is shown in figure 1. a novel imf swara-fdwga-pestel analysis for assessment of healthcare system 147 figure 1. weights of the main parameters of pestel analysis figure 1 shows fuzzy weights of the main parameters of pestel analysis. red color denotes low value of tfn, blue middle and green upper value of tfn. the most important parameter is the legal group with value of: ( ) ( )1 6, 0.194, 0.207, 0.20.085, 0.102, 0. 1 221 8w w= = the results obtained according to previously described steps of imf swara – fdwga – pestel model that denotes fuzzy values of subelements have been shown in table 7. table 7. overall results of importance of pestel analysis for each group after application of imf swara – fdwga model wj tfn wj tfn wj tfn w11 (0.085,0.102,0.118) w21 (0.215,0.227,0.239) w31 (0.23,0.245,0.261) w12 (0.203,0.217,0.232) w22 (0.184,0.207,0.226) w32 (0.15,0.171,0.192) w13 (0.181,0.201,0.221) w23 (0.192,0.207,0.222) w33 (0.089,0.108,0.126) w14 (0.162,0.185,0.205) w24 (0.092,0.11,0.127) w34 (0.275,0.285,0.297) w15 (0.195,0.21,0.226) w25 (0.16,0.178,0.195) w35 (0.134,0.153,0.172) wj tfn wj tfn wj tfn w41 (0.273,0.282,0.294) w51 (0.193,0.206,0.22) w61 (0.245,0.253,0.264) w42 (0.089,0.115,0.138) w52 (0.087,0.101,0.113) w62 (0.259,0.266,0.276) w43 (0.204,0.219,0.234) w53 (0.263,0.269,0.278) w63 (0.206,0.218,0.232) w44 (0.117,0.138,0.156) w54 (0.212,0.225,0.238) w64 (0.114,0.134,0.152) w45 (0.138,0.158,0.177) w55 (0.122,0.141,0.158) w65 (0.09,0.109,0.126) vojinović et al./oper. res. eng. sci. theor. appl. 5(1) (2022) 139-151 148 final results have been obtained multiplication of values represented in figure 1 (the main parameters of pestel analysis) and values of subcriteria represented in table 7. these final results have been shown in table 8. table 8. final results of importance of pestel analysis after application of imf swara – fdwga model wj tfn wj tfn wj tfn w11 (0.011,0.015,0.02) w21 (0.036,0.042,0.048) w31 (0.024,0.029,0.035) w12 (0.027,0.033,0.039) w22 (0.031,0.038,0.045) w32 (0.016,0.02,0.026) w13 (0.024,0.03,0.037) w23 (0.033,0.038,0.045) w33 (0.009,0.013,0.017) w14 (0.021,0.028,0.035) w24 (0.015,0.02,0.025) w34 (0.029,0.034,0.04) w15 (0.026,0.032,0.038) w25 (0.027,0.033,0.039) w35 (0.014,0.018,0.023) wj tfn wj tfn wj tfn w41 (0.024,0.031,0.039) w51 (0.014,0.02,0.026) w61 (0.048,0.053,0.059) w42 (0.008,0.013,0.018) w52 (0.006,0.01,0.013) w62 (0.05,0.055,0.061) w43 (0.018,0.024,0.031) w53 (0.02,0.026,0.032) w63 (0.04,0.045,0.051) w44 (0.01,0.015,0.021) w54 (0.016,0.022,0.028) w64 (0.022,0.028,0.034) w45 (0.012,0.018,0.024) w55 (0.009,0.014,0.018) w65 (0.017,0.023,0.028) according to calculated results shown in table 8, it can be concluded that legal (w62, w61, and w63) and economic factors (w21, w23, and w22) are the most significant within the pestel analysis with values of (0.05,0.055,0.061), (0.048,0.053,0.059), (0.04,0.045,0.051), (0.036,0.042,0.048), (0.033,0.038,0.045), and (0.033,0.038,0.045), respectively. least significant factors are , w33, w42, and w52 with values (0.009,0.013,0.017), (0.008,0.013,0.018), and (0.006,0.01,0.013) respectively. conclusion quality and adequate functioning of healthcare systems are not only medical question, because depends on economic factors, environment, legal factors, political events, organization of the healthcare system, and others. for that reason we have implemented a novel integrated imf swara-fdwga-pestel model in this important field to can observe the real and current state of healthcare system taking into account political, economic, socio-cultural, technological, environmental, and legal factors. strengths of the developed integrated model can be manifested through the possibility of its application in any area which considers various parameters and various solutions. results of pestel analysis based on imf swara method and fdwga shows that legal and economic factors represent the most significant parameters, while last placed belong environmental group. the contribution of the performed study can be observed from the following aspects: quantification of the pestel analysis, it is possible to find out how important and influential these factors 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(2021). evaluating logistics villages in turkey using hybrid improved fuzzy swara (imf swara) and fuzzy mabac techniques. technological and economic development of economy, 27(6), 15821612. https://doi.org/10.3846/tede.2021.16004 © 2022 by the authors. submitted for possible open access publication under the terms and conditions of the creative commons attribution (cc by) license (http://creativecommons.org/licenses/by/4.0/). https://doi.org/10.1109/access.2020.3039010 https://doi.org/10.3390/en12050791 https://doi.org/10.22190/teme210911046v https://doi.org/10.1155/2021/5141611 https://doi.org/10.3390/axioms10020092 https://doi.org/10.1016/j.scs.2019.101861 https://doi.org/10.2991/ijcis.d.200803.001 https://doi.org/10.31181/dmame181221001y https://doi.org/10.3846/tede.2021.16004 operational research in engineering sciences: theory and applications vol. 4, issue 2, 2021, pp. 140-150 issn: 2620-1607 eissn: 2620-1747 doi: https://doi.org/10.31181/oresta20402140z * corresponding author. sa.hashemkhani@gmail.com (s.hashemkhani zolfani), ebaditorkayesh@sabanciuniv.edu (a. ebadi torkayesh.), ramin.bazrafshan88@gmail.com (r. bazrafshan) vision-based weighting system (viwes) in prospective madm sarfaraz hashemkhani zolfani 1, ali ebadi torkayesh 2, ramin bazrafshan 3* 1 school of engineering, catholic university of the north, coquimbo, chile 2 faculty of engineering and natural sciences, sabanci university, istanbul, turkey 3 department of industrial engineering and management systems, amirkabir university of technology (tehran polytechnic), tehran, iran received: 14 june 2021 accepted: 06 july 2021 first online: 08 july 2021 original scientific paper abstract: policy-making is an undeniable decision-making process in every company where different kinds of decisions are taken based on different goals and preferences in each vision. “prospective multiple attribute decision making (pmadm)” is one of the well-known decision-making frameworks that have been used as a flexible decisionmaking tool for developing policies and making future decisions over different periods. this study presents a multi attribute problem with three different visions where a decision-making process is required for each vision in order to prioritize the potential set of alternatives. evaluation based on the distance from the average solution (edas) is used as a madm model to show the applicability and feasibility of the pmadm framework. a vision-based weighting system (viwes) prepares a new opportunity to take proper decisions in different visions and time requirements. this research is analyzed three-time vision (current, 2025, and 2030) and showed by changing the time, the rank of the alternatives also is changed. in numerical example is indicated in the current vision, alternative 5 gets rank one and alternative six get rank 2, for 2025 vision, the rank one and two don’t change, and in vision 2030, the rank of one does not change, but the rank of second change from alternative 6 to 3. key words: prospective multiple attribute decision making (pmadm), vision-based weighting system (viwes), evaluation based on the distance from the average solution (edas), policy-making, weighting system 1. introduction multiple attribute decision making (madm) models are considered reliable decision-making models that can help decision-makers and policymakers address vision-based weighting system (viwes) in prospective madm 141 complex evaluation problems such as supplier selection problems. logistics provide problem, waste management, location selection problem considering multiple attributes (ignatius et al. 2016; yazdani et al. 2017; ebadi torkayesh et al. 2019; hashemkhani zolfani et al. 2020). madm models such as bwm (fazlollahtabar et al. 2021; pamučar and savin, 2020), swara (radović and stević, 2018), ahp (alosta et al. 2021), fucom (durmić et al. 2020) are applied to determine the importance of decision criteria, while models such as edas (stević et al 2016), cocoso (biswas et al. 2019), codas (badi et al. 2018), topsis, marcos (đalić et al. 2021) are applied to evaluate alternatives of a multi attribute problem (mardani et al. 2016; kumar et al. 2017). madm models are able to address a complex problem with n criteria and m alternatives for a specific time. however, the decision-making process can be due to several changes in weight of criteria and then an evaluation framework, considering a decision maker’s or a company’s visions and goals for different periods. therefore, the decision-making process and obtained results from traditional madm models may not be reliable in the following years. so, nonexistent a madm model which considers the future makes more sense than previously. prospective madm (pmadm) is a new framework that can be used to process different companies' visions. the madm models make decisions in a steady and stable state (fix situation), but pmadm expands this decision environment and considers the time that hasn’t happened. the pmadm uses two items for studying the future, limiters and boosters. these items in the different situations given different values to alternatives in evaluation. companies can facilitate their policy-making process using pmadm, where several visions can be defined based on companies' goals. by this method, managers can survey and evaluate their future outcomes and modify their decisions and plan. there are many madm methods like promethee (brans 1982) and vikor (opricovic, 1988), and topsis (hwang and yoon in 1981), but they don’t consider the future, and this shortage of them causes managers less willing to use them. in contrast, these methods could help them make better policy decisions. for developing and make more efficient methods, this idea formed in our minds that using the pmadm framework can promote their performance and activities. the pmadm approach considers future vision and changes the value of criteria. this conversion affects the rank of alternatives. the researchers who study in the madm context usually consider the current time in their studies considering the future in decision making expressed by the pmadm method. but, researchers don’t use this method in their studies. this paper considers the future in decision-making by the use of the pmadm method. in this paper, we develop a pmadm framework and define three visions for a numerical decision-making example where weights of criteria are different in each vision based on goals and preferences and possible events that may happen in the future. for the evaluation part, the edas model, as a reliable and frequently used tool, is applied to prioritize the alternatives for each vision. 2. literature review as said before, most of the time, managers concentrate on future actions and goals and make plans to reach them. due to a lot of factors, managers are confused hashemkhani zolfani et al. /oper. res. eng. sci. theor. appl. 4 (2) (2021) 140-150 142 about set or ranking company priorities. therefore head manager or an administrator needs to see the future more clearly and make an appropriate decision. to determine the direction and guide policymakers or officers to make a better decision. this section first reviewed the pmadm model and its uses in various contexts and then described a madm model. because according to the subject of the article and for futuristic decisions, researchers want to use the pmadm framework for a madm model. hashemkhani zolfani et al. (2016) developed a new framework for madm problem, called prospective madm, which not only facilitate the decision-making process at the moment but also enables decision-makers to consider future visions and extend the decision making process using different sets of inputs based on possible events or goals that are planned for each vision. later, zolfani et al. (2018) studied the prospective madm framework for sustainability assessment problems, focusing on a multi-aspect set of criteria that can be used for multi-attribute problems. they consider futures sustainability an umbrella for sustainability, which consists of the future economy, environment, and social position. as to the importance of development in sustainability, they introduced a trend for exergy, which consists of energy, environment, and sustainable development. in this trend, energy is presented as a core item. zolfani and masaeli (2020) presented a comprehensive framework for the prospective madm approach and its application for the health device industry of iran, considering several visions during sanctions. by the pmadm, they achieved their goal to increase the medical device market share ten times more like a sustainable market for the country. in this research, max capacity, ideal directed scenario, and supportive backup criteria are used in the pmadm framework. hashemkhani zolfani et al. (2020) used a text-mining tool, latent semantic analysis, as a criteria selection and weighting system in prospective madm. they use this for machine tool selection and introduce five criteria as (1) cost and serviceability; (2) technical features and safety; (3) size and precision; (4) flexibility; and (5) productivity. after calculating and ranking them, they report that cost and serviceability have the highest priority among these criteria. after explaining the uses of pmadm in various contexts, it talks about a madm method and its uses in articles or case studies. evaluation based on the distance from the average solution (edas) is one of the recently developed madm models that is used to prioritize a set of alternatives concerning multiple factors (keshavarz ghorabee et al. 2015). kahraman et al. (2017) proposed a new extension of the edas model under fuzzy set theory to evaluate the waste disposal location selection process. in this research, they determined three alternatives and three criteria. the criteria uses are water pollution (w), distance to residential areas (d), and slope (s). for solving, they decided to use the interval-valued intuitionistic fuzzy edas (ivif edas) method. in the ivif method, membership and non-membership function and unknown degree (hesitancy degree) are calculated. ecer (2018) integrated ahp and edas models under fuzzy set theory to address third-party logistics (3pls) provider selection problems. first, fuzzy ahp was used to determine the importance of decision criteria, and then fuzzy edas was used to prioritize alternatives. he determined that cost, quality, and professionalism are the most critical factors for 3pls provider selection. vision-based weighting system (viwes) in prospective madm 143 li et al. (2019) developed another extension of the edas method using a neutrosophic set to consider the uncertainty that may happen in the decision-making process. they proposed a convex weighted average operator of multivalued neutrosophic numbers (mvnns) to calculate the average solution of criteria. torkayesh et al. (2020) proposed an integrated madm model using the shanon entropy and edas methods. the proposed decision-making model has applied a neighborhood selection problem for a new international student who wants to be located in istanbul, turkey. the usability and capacity of five renewable resources: solar pv, solar thermal, wind power, geothermal, and biomass concerning economic, technical, social, and environmental aspects are measured. by edas method are ranked these resources and showed wind power is the most suitable energy for their case study. behzad et al. (2020) used a hybrid decision-making model by using bwm and edas models to make an evaluation framework in order to assess waste management status in nordic countries. they use seven criteria as waste generation, composting waste, recycling waste, landfilling waste, recycling rate, waste to the energy rate, and greenhouse gas emissions from waste. comparing these criteria concludes that sweden has the best waste management profile. 2.1. main contribution in this article, researchers are trying to develop a decision-making policy to consider the future in decision-making furthermore to the current time. in most conventional decision-making methods, only the present time is considered. this paper attribute to this issue attempt to introduce a vision-based weighting system that facilitates the decision processes. this system is a combination of the pmadm framework with the madm method. the viwes helps administers or managers decide by considering time vision. finding or verdict in current time is different from the future because the weight of criteria to time vision changes. for example, suppose someone has a plan for reaching a specific goal in two years and wants to determine his alternative priorities; if he doesn’t consider the future vision, he may gain the wrong rank of alternatives and doesn’t reach his aim. in the numerical example section, this rank changing by time vision changing is shown by an example. 3. methodology this section describes the edas model that can be applied for pmadm problems that consider different types of weighting visions based on events that may happen in the future and affect the decision-making process. one of the reasons which opt edas method is it needs fewer computations concerning most of the other multiattribute decision-making methods. at the same time, it can produce the same ranking of alternatives (kahraman et al. (2017)). 3.1. evaluation based on the distance from the average solution (edas) keshavarz ghorabaee et al. 2017 proposed a new brand multiple attribute decision making (madm) method, called edas, to address multi-attribute problems such as supply chain management, transportation problem, waste management, etc. by measuring the distance from ideal and nadir solutions, is determined the best hashemkhani zolfani et al. /oper. res. eng. sci. theor. appl. 4 (2) (2021) 140-150 144 alternative. after calculating these distances, the one that has a lower distance from the ideal solution and a higher distance from the nadir solution is our perfect answer. the edas method calculating these distances from the average solution (av). this method defines the positive distance from average (pda) and negative distance from average (nda) and specified the best alternative after comparing these distances. for more detail of this method in continuing to explain the steps of this. the steps of the edas method are explained below. step 1. in this step, the decision-maker constructs the initial decision matrix. 11 12 1 21 22 2 * 1 2 ... ... . . . . . . . . . . . . ... m m ij n m n n nm x x x x x x x x x x x          = =             (1) step 2. the average solution for each criterion is calculated based on equations. 1* j m av av =   (2) 1av n ij i j x n ==  (3) step3. positive distance from average (pda) and negative distance from average (nda) are calculated. * ij n m pda pda =   (4) * nda= ij n m nda   (5) if j th criterion is beneficial, max(0, ( )) pda , ij j ij j x av av − = (6) max(0, ( )) nda , j ij ij j av x av − = (7) if j th criterion is non-beneficial, max(0, ( )) pda , j ij ij j av x av − = (8) max(0, ( )) nda , ij j ij j x av av − = (9) step 4. we calculate the weighted sum of pda and nda for all alternatives which are denoted as sp and sn. vision-based weighting system (viwes) in prospective madm 145 1 * ; m i j ij j sp w pda = =  (10) 1 * ; m i j ij j sn w nda = =  (11) step 5. we normalize the obtained values in step 4. these values are then added and construct a new vector, called nsp (normalized weighted sum of pda) and nsn (normalized weighted sum of nda). ; max ( ) i i i i sp nsp sp = (12) nsn 1 ; max ( ) i i i i sn sn = − (13) step 6. finally, appraisal score (as) for each alternative is calculated. 1 ( ), 2 i i i as nsp nsn= + (14) 4. numerical example in this part, define a numerical example in order to show the applicability and feasibility of the edas based pmadm framework. a multiple attribute problem is considered in the numerical example, which includes five decision criteria and six alternatives that should be evaluated accordingly. weight of decision criteria is proposed for three different visions as current vision, vision 2025, and vision 2030. the importance of decision criteria varies in each vision due to the possible changes that may happen and affect the decision-making process. for each set of weights, the edas model is used to solve the decision-making problem and identify the ranking order of alternatives for each time vision. in table 1, the initial decision matrix including scores of alternatives concerning each criterion is reported. the weight of criteria for each time vision is also reported in table 1. table 1. initial decision matrix criteria c1 c2 c3 c4 c5 max/min max min max max max weights current vision 0.2 0.25 0.2 0.15 0.2 vision 2025 0.22 0.21 0.18 0.2 0.19 vision 2030 0.25 0.18 0.18 0.24 0.15 a1 7 6 8 6 7 a2 6 7 8 7 8 a3 8 6 7 6 7 a4 7 7 7 7 8 a5 8 7 8 7 7 a6 6 5 8 6 7 hashemkhani zolfani et al. /oper. res. eng. sci. theor. appl. 4 (2) (2021) 140-150 146 in the next step, the edas model is used based on the steps explained in the previous section to solve the decision-making process. for this purpose, the sp, sn, nsp, nsn, as, and the final ranking of each alternative for each set of weights for each time vision is calculated. in table 2, the results for edas parameters and the corresponding ranking order of each alternative are reported. alternatives a5 and a6 are selected as the most preferred alternatives with respect to the current vision. in table 3, the results of the edas model for vision 2025 are reported. as same as the current vision, alternatives a5 and a6 are selected as the most preferred alternatives. for vision 2030, the results of the edas model are reported in table 4. alternatives a5 and a3 are selected as the most preferred alternatives. table 2. edas values for current vision sp sn nsp nsn as ranking a1 0.022 0.021 0.356 0.781 0.569 3 a2 0.038 0.094 0.626 0.000 0.313 5 a3 0.042 0.064 0.680 0.318 0.499 4 a4 0.030 0.083 0.485 0.118 0.302 6 a5 0.049 0.009 0.796 0.904 0.850 1 a6 0.061 0.049 1.000 0.479 0.739 2 table 3. edas values for vision 2025 sp sn nsp nsn as ranking a1 0.019 0.024 0.346 0.723 0.534 3 a2 0.040 0.087 0.741 0.000 0.370 6 a3 0.042 0.062 0.777 0.287 0.532 4 a4 0.033 0.071 0.598 0.182 0.390 5 a5 0.055 0.009 1.000 0.900 0.950 1 a6 0.052 0.055 0.952 0.360 0.656 2 table 4. edas values for vision 2030 sp sn nsp nsn as ranking a1 0.017 0.025 0.279 0.696 0.487 4 a2 0.040 0.083 0.644 0.000 0.322 6 a3 0.045 0.060 0.729 0.279 0.504 2 a4 0.032 0.063 0.518 0.241 0.380 5 a5 0.062 0.007 1.000 0.918 0.959 1 a6 0.046 0.061 0.737 0.266 0.502 3 figure 1 shows the ranking order of each alternative with respect to each time vision defined in this study. alternative a5 is selected as the top alternatives in all visions. although alternative a6 is selected as the second important alternative, it is ranked as the third one in vision 2030. the ranking order of other alternatives is also slightly changed concerning each time vision. vision-based weighting system (viwes) in prospective madm 147 figure 1. ranking order of alternatives in different time visions the main idea for this part is to show that essence could be changed in the current vision to future vision in a particular case. this numerical example is showing this issue of what a proper decision when considering the future is. this example shows in vision 2030, our alternative could be changed, and to reach the company's aim, this issue should be considered. the priorities in time vision could be changed. this issue helps decision-makers to set their decision by this long-term vision. 5. managerial tips managers usually write the company’s goals and attempt to reach them. for reaching goals and make a decision, a suitable plan should be set. this plan is consists of a set of alternatives and criteria, and managers should rank these alternatives and consider them according to priorities. since in the real situation, various criteria involve in decision making, managers should use multiple criteria decision making for finding the best alternative. as previously mentioned, the future vision is one of the crucial issues managers should consider in their decision-making. if a multi-criteria decision-making method exists that considers the future vision, it helps stakeholders take a proper decision in the current time. the current decision that considers the future facilitates the way for achieving the company’s goals. 6. conclusions decisions need to be taken according to the current needs and strategic plans and situations. when a policymaker wants to decide by classic madm form of study, everything must be considered fix in an acceptable primary evaluation. pmadm outline changes the previous games as a game-changer. new items have been developing the class madm structure since 2016 by introducing pmadm. in this study, a new flexible weighting system, as vision-based weighting system (viwes), hashemkhani zolfani et al. /oper. res. eng. sci. theor. appl. 4 (2) (2021) 140-150 148 presented shows how a decision can be made now but with proper preparation for all possible changes in the decisions. moreover, it can enhance this ability to show when we need to consider all the new changes in the priorities and alternatives due to the importance of the criteria in different periods and future visions. it is illustrated in the numerical example to see how the importance of alternatives can vary due to different criteria’s expectations. as a suggestion for future studies, something can be mentioned as to how policymakers and decision-makers can make a flexible vision-based decision making when alternatives can be different when they agree to change according to the essential needs and rules. when decision alternatives want to be adopted by necessary changes, a dynamic situation will happen in the classic way of decision making, and that would be a new challenge in the field of mcdm and prospective madm. this research is used the pmadm structure for considering the future in the edas madm model. comparing table 1 to 4 found that in the current vision, alternative 5 gets rank one and alternative six get rank 2, for 2025 vision, the rank one and two don’t change, and in vision 2030, the rank of 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(http://creativecommons.org/licenses/by/4.0/). vision-based weighting system (viwes) in prospective madm sarfaraz hashemkhani zolfani 1, ali ebadi torkayesh 2, ramin bazrafshan 3* 1. introduction 2. literature review 2.1. main contribution 3. methodology 3.1. evaluation based on the distance from the average solution (edas) 4. numerical example 5. managerial tips 6. conclusions reference plane thermoelastic waves in infinite half-space caused operational research in engineering sciences: theory and applications vol. 5, issue 2, 2022, pp. 17-27 issn: 2620-1607 eissn: 2620-1747 doi: https://doi.org/10.31181/oresta240622030s *corresponding author: indra.setiawan.2022@gmail.com (i. setiawan), hibarkah@gmail.com (h. kurnia), setiawan.fafa2@gmail.com (s. setiawan), hardi.purba@mercubuana.ac.id (h.h.purba), hadeita@yahoo.com (h. hernadewita) reduce transportation costs using the milk-run system and dynamo stages in the vehicle manufacturing industry indra setiawan 1*, hibarkah kurnia 2, setiawan setiawan 3, humiras hardi purba 3, hernadewita hernadewita 3 1 department of production and manufacture engineering, astra polytechnic, indonesia 2 department of industrial engineering, university pelita bangsa, indonesia 3 department of industrial engineering, university mercu buana, indonesia received: 05 january 2022 accepted: 28 may 2022 first online: 24 june 2022 research paper abstract: the vehicle manufacturing industry is one of the automotive industries in indonesia that produces four-wheeled vehicles with the main product being cars. the vehicle manufacturing industry has several sub-companies including vehicle manufacturers (vm) and vehicle sales (vs). the vm industry is experiencing problems with rising transportation operating costs. the same thing is also experienced by the corporate company such as vs. in 2020, transportation operational costs incurred by the company exceed the target, which can cause losses for the company. the purpose of this study is to find the cause of the problem and improve the transportation operational costs that continue to increase so that the company gets a reduction in transportation costs. the implementation of the improvement concept is carried out using the dynamo++ stages starting from pre-study until the implementation of improvements. through improvements to the milk-run system, it was found that vehicle manufacturers and vehicle sales benefited from a reduction in transportation costs of 77,861 usd or a decrease of 79.3%. keywords: covid-19, dynamo++, milk-run, transportation cost, vehicle industry 1. introduction the design of the safeguarding framework, realizing different supply chain capabilities is very helpful in identifying a good and efficient logistics system (muhammad et al., 2022). the development of industry in the world is increasing rapidly so increasing competitiveness is a priority for all industrial sectors in the world market (baalsrud hauge et al., 2021). this is important because the industrial sector is a driver of economic development (pattanaik, 2021). the existence of the setiawan et al./oper. res. eng. sci. theor. appl. 5(2) 2022 17-27 18 industrial sector can make a significant contribution and escalation of employment, and foreign exchange, and can make a major contribution to world economic development (bocewicz et al., 2019). in 2020, it was a very difficult year for the after-sales business of four-wheeled vehicles with the vehicle manufacturing (vm) brand due to the covid-19 pandemic situation. starting in may 2020 the company experienced a decline in sales. based on the medium-term plan from the vehicle manufacturing corporation (vmc), this condition will continue in fy21, but in fy22-fy25 a significant increase in sales is expected. based on initial observations, vm sales during 2020 showed that the decline in sales directly affected the decrease in purchases to suppliers, which caused the company to receive many complaints and requests from suppliers, including increasing transportation costs or implementing minimum order quantities, reducing loading and unloading queue times for spare parts center and delivery request 1 time/month. opportunities for rising transportation costs from suppliers, the company has set transportation for the export of service parts as the company's target. in the future, the company plans to estimate sales versus operating profit, which can be seen in figure 1. 90,1 97,9 66,2 69,7 103,9 143,6 188,9 235,4 27,7 38,6 25,1 31% 39% 38% 0% 5% 10% 15% 20% 25% 30% 35% 40% 0 50 100 150 200 250 fy18 fy19 fy20 fy21 fy22 fy23 fy24 fy25 sales operating profit sales vs op ratio figure 1. comparison of sales and operating profit figure 1 shows that fy20 experienced a decline in profits due to the covid-19 pandemic and government regulations regarding mobility restrictions so that transportation costs increased 5 to 10 times. indirectly, this condition causes losses to the company such as the high operating costs of the company. industrial growth in this globalization era requires companies to implement various kinds of improvements to save operational costs and must be able to improve performance and competitiveness to excel in competition in the global market (klenk & galka, 2019; suratno & ichtiarto, 2021). this will certainly trigger competition among industry players and have an impact on the supplier industry. in line with that, it is necessary to increase the efficiency and effectiveness of each industry player (kluska & pawlewski, 2018; yuik & puvanasvaran, 2020). various kinds of improvement strategies, use of resources, and all existing facilities must be used effectively and efficiently and must be implemented sustainably. through these improvements, industrial players can carry out their production activities with mid term plan reduce transportation costs using the milk-run system and dynamo stages in the vehicle manufacturing industry 19 increased productivity and efficient costs from time to time (mirzaei et al., 2021). the use of the supply chain operation references (scor) method shows that asset, agility, and cost are variables that must be improved in the logistics process to improve transportation schedules (shobur et al., 2021). one of the industrial sectors that continues to grow and provides the largest contribution to the world economy is the vm industry (mácsay & bányai, 2017; bajic et al., 2020). the vm industry is one of the automotive industries in indonesia that produces four-wheeled vehicles with the main product being cars. the vm industry has several sub-companies including vehicle manufacturers and vehicle sales. the vm industry is experiencing problems with rising transportation operating costs. the same thing is also experienced by corporate chains such as vehicle sales (vs). in 2020, transportation operational costs incurred by the company exceeded the target, causing losses for the company. factors that play a role in maintaining company productivity so that an industrial company can continue to compete in the market are minimizing operating costs. based on the problems shown in figure 1, several other studies have also made improvements to the milk-run system (urru et al., 2018). based on research (ranjbaran et al., 2020; adriano et al., 2020) milk-run can increase company productivity by reducing costs. according to tellini et al. (2019) and biswas & das (2020), the milk-run system can overcome loading and unloading times, so that an effective and efficient operational time is obtained. milk-run is also able to improve transportation efficiency (mei et al., 2017; mao et al., 2020). research by purba et al. (2019) applies the milk-run system to the supply chain. the difference is that this study uses a dynamo++ level approach in carrying out the repair stages, this is done so that corrective actions are more focused and conceptualized from the start of prestudy-measurement-analysis-implementation. the new approach in this research is the transportation system using the milkrun method with a corrective action flow using the dynamo++ stages. the difference with other studies related to articles related to transportation operations is that in applying the milk-run method by calculating the actual delivery time and distance from the transportation capital alone (bocewicz et al., 2019; klenk & galka, 2019), it does not calculate the reduction in transportation costs obtained after applying the milk-run method combined with the dynamo++ stages. the originality of this study provides added value related to the application of the milk-run system in reducing transportation costs in four-wheeled automotive companies and will analyze cost efficiency in the vehicle sales chain. the purpose of this study is to find out the causes and at the same time improve the transportation operational costs which have been increasing so far so that the company gets a reduction in transportation costs. 2. research method this research is included in the type of applied research and the research focus is cost efficiency in the vm industry. problem improvement analysis was carried out through focus group discussions (fgd) with experts (setiawan et al., 2021; kurnia et al., 2021). in this section, we will describe the research steps with a milk-run system using the dynamo++ stages which include pre-study, measurement, analysis, and implementation (herlambang et al., 2021; hendra et al., 2021) in the electronics setiawan et al./oper. res. eng. sci. theor. appl. 5(2) 2022 17-27 20 manufacturing industry. through this stage, it is hoped that the research will be systematic, orderly, and easy to understand in terms of the process and the results of its improvement. the research method used in this research is the milk-run method combined with the dynamo++ stages of improvement, this combination of methods is a new thing in its application to the car industry. the combination of these methods is expected to make it easier for other researchers to improve transportation costs to reduce logistics costs in the supply chain management of the automotive industry. the research steps can be seen in figure 2. figure 2. research framework 3. result and discussion 3.1. data analysis in this section, the data analysis used uses the dynamo++ stage. at the end of the chapter, there is a discussion on the comparison of the results with previous studies. data analysis in this study is as follows: 3.1.1 pre-study this section identifies the pre-repair process flow, where vm and vs receive parts from multiple suppliers who ship them directly to the company. the description of the process flow can be seen in figure 3. figure 3. direct transportation by suppliers pre-study implementation analysis measurement identification of transportation cost in the logistic transportation cost measurement analysis of the dominant problem of the 4m+1e factor through fgd implementation of improvement proposals with milk-run system and sop reduce transportation costs using the milk-run system and dynamo stages in the vehicle manufacturing industry 21 meanwhile, the type of transportation that is currently being carried out is divided into several parts, including logistics partners, companies, rental companies, and others which can be seen in figure 4. figure 4 shows that vm and vs mostly use truck logistics partners in making deliveries from suppliers or to distributors. the process of loading trucks from various suppliers is 65%, and there are major problems or an increase in transportation costs that is not proportional to the speed of receiving goods. figure 4. transportation type figure 5 shows that the most pareto loss of waiting time is 73%. this problem occurs because a lot of time is wasted entering the vm and vs areas. loss of time is caused by a lot of trucks queuing outside the factory because the factory is full of parking and loading capacity. so all suppliers complain and increase their transportation costs. this results in very high transport costs for vm and vs. the dominant problem from the pareto diagram can be seen in figure 5. figure 5. pareto diagram of increasing transportation cost setiawan et al./oper. res. eng. sci. theor. appl. 5(2) 2022 17-27 22 3.1.2. measurement vm and vs have spare parts suppliers from several suppliers who are still in the same area. this has the aim that the delivery of spare parts does not take too long to arrive at the location. the location of suppliers and the number of suppliers in the vehicle industry production chain can be seen in figure 6. figure 6. suppliers location based on highly fluctuating after-sales orders, the company manages milk-run flexibility by changing milk run route cycles daily. based on the milk-run cycle ratio shows that from july 2019 to june 2020, the costs incurred by vm and vs are different each month. the average reached 8000 usd and the total results for 1 year from the two companies can be seen in table 1. table 1. total transportation cost before improvement item amount (usd) vm cost 98,137 vs cost 106,965 total 205,102 table 1 shows that the amount of expenditure for vs is greater because of the large number of transportation activities that enter the company. 3.1.3. analysis this section analyzes the causes of the problem in the loss of waiting time. the factors causing the problem are known based on 5m through fishbone diagram which aims to find the main cause of the disappearance of the waiting time problem. analysis of the causes of the problem was carried out with experts through fgds (kurnia et al., 2022). the fishbone diagram of the fgd results can be seen in figure 7. 3.1.4. implementation vm after sales (as) has to manage milk-run operations that are not just for vms and vss. therefore there will be a new operation in the as vm which requires an additional 1 manpower to control the milk-run system. milk-run operations must operate at least 1 cycle/day to cover truck investment costs. the cost of using milk run can be seen in table 2. cibitung (mm2100) 5 supplier cikarang (giic+ejip) 4 supplier west karawang (kiic) 5 supplier east karawang (kim+ sci) 4 supplier purwakarta (kbi) 3 supplier reduce transportation costs using the milk-run system and dynamo stages in the vehicle manufacturing industry 23 figure 7. fishbone diagram of increased transportation cost table 2. cost of using milk-run item amount (usd) milk-run cost (186 days) 24,000 man power cost 10,828 base pallet 7,586 total 42,414 table 2 shows the investment costs in implementing the milk run system. investments are earmarked for the cost of procuring a special workforce in controlling this system and the cost of making standard pallets in the operation of loading and unloading materials from trucks. this section describes the post-repair process flow, where vm and vs receive parts from multiple suppliers who ship them in parallel to the company. that means the milk truck will pick up parts from suppliers a, b, c, and d and then return to vm and vs. the description of the flow of the new transportation process can be seen in figure 8. figure 8. milk-run transportation by suppliers setiawan et al./oper. res. eng. sci. theor. appl. 5(2) 2022 17-27 24 transportation costs after using the milk-run system between vm and vs have decreased. milk run is a shared project between vm and vs, therefore vm should negotiate with vs about compensation amount as a basis for increasing outsourcing costs. the results of the negotiation of the amount of compensation issued can be seen in table 3. table 3. total transportation cost after improvement c o m p a n y before improvement after improvemen t cost down (direct delivery) (use milkrun system) vm 98,137 20,276 77,861 vs 106,965 22,137 84,828 grand total 162,689 table 3 shows that the vm experienced a decrease in costs or profits after using a milk-run system of 77,861 usd. if the system is consistent up to fy25, it will benefit the company. the following predictions of cost usage until fy25 can be seen in figure 9. 2.638 2.770 4.130 5.708 7.508 9.357 1.670 1.782 2.463 3.240 4.038 2.000 4.000 6.000 8.000 10.000 fy20 fy21 fy22 fy23 fy24 fy25 non milkrun milkrun actual transport cost transport cost (after milkrun) figure 9. milk-run cost reductions (million idr) figure 9 shows that if the company consistently implements the milk-run system, it is predicted that in fy25, it will get a cost savings of 43% or only incur transportation costs of 4,038 usd. 3.2. discussion the findings of this study are very good and not too difficult to implemented. the implementation of improvements by applying the milk-run system is very effective in the vehicle industry. the results showed a decrease in transportation costs after the milk run application. this is in line with purba et al. (2019) research that an effective transportation system can reduce transportation operational costs. even the results of his research suggest focusing more on co2 efficiency. the system built in this research has added 1 new worker as a system control operator. this research is in reduce transportation costs using the milk-run system and dynamo stages in the vehicle manufacturing industry 25 line with klenk & galka (2019) that the model built provides optimization on the scheduling of transportation activities so that costs can be reduced. this research contributes directly to the reduction of transportation costs by optimizing the efficient and effective scheduling of the milk-run method. the benefit obtained after using the milk-run system but not is the reduction in the cost of purchasing spare parts which means that the price of mitsubishi parts is more competitive than other brands. this can support the government to reduce co2 emissions in the logistics chain. 3.3 research implications this research is limited to transportation carried out by vm logistics that implements a milk-run system. this research implication to provides benefits for companies related to the reduction of transportation costs. for similar companies, this research can provide input for manufacturing practitioners in saving transportation costs for competing in the global market. the milk-run system can also reduce labor impact on labor cost savings. this study also uses a gradual combination of the dynamo++ approach which will assist other studies in determining the decision of the main causal factors in the problem of transportation costs. while the milk-run system is very helpful for other researchers in reducing transportation costs by arranging transportation scheduling so that it is efficient and effective in carrying out supply chain management logistics work. 4. conclusion in this study, the biggest cause of the problem was found, namely too long delivery times from several vm suppliers. loss of time is due to the number of trucks queuing outside the factory because the factory is full of parking lots and loading capacity so all suppliers complain and increase transportation costs. implemented a milk-run system, which means deliveries can be controlled in truck mode. this system works to pick up and deliver to customers which are controlled by the workforce. as a result, transportation operational costs can be reduced by 77,861 usd or a decrease of 79.3%. therefore, the vm greatly benefits from implementing this milk-run system. based on the problem of lost waiting time, and the amount of wasted time and processes in the logistics system in the vm company, it is recommended for further research to use the lean manufacturing method, so that this waste can be reduced gradually and efficiently. references adriano, d. d., montez, c., novaes, a. g. n., & wangham, m. 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(2020). development of lean manufacturing implementation framework in machinery and equipment smes. international journal of industrial engineering and management, 11(3), 157–169. https://doi.org/10.24867/ijiem-2020-3-261 © 2022 by the authors. submitted for possible open access publication under the terms and conditions of the creative commons attribution (cc by) license (http://creativecommons.org/licenses/by/4.0/). plane thermoelastic waves in infinite half-space caused operational research in engineering sciences: theory and applications vol. 5, issue 2, 2022, pp. 190-205 issn: 2620-1607 eissn: 2620-1747 doi: https://doi.org/10.31181/oresta010422181b * corresponding author. amrita.bhattacharya@dnshm.ac.in (a. bhattacharya), dutta.avijan@nitdgp.ac.in (a. dutta) samarjit.kar@maths.nitdgp.ac.in (s. kar), does demographics influence the risk behaviour of urban investors? a machine learning model based approach amrita bhattacharya 1, avijan dutta 1, samarjit kar 2* 1 department of management studies, national institute of technology, west bengal, india 2 department of mathematics, national institute of technology, west bengal, india received: 21 october 2021 accepted: 11 january 2022 first online: 01 april 2022 original scientific paper abstract. the purpose of this paper is to examine the influence of demographic attributes on investment decision-making. we consider six demographic attributes such as gender, age, education, profession, income and number of dependents for analysing their influence on the investment decision making of the urban investors of the asansol-durgapur industrial belt, west bengal, india and intend to forecast the risk tolerance behaviour. around 2000 respondents took part in our study. the primary data were analysed using logistic regression and subsequently, we used the linear discriminant analysis method for validation purposes. we notice that gender and profession are the two demographic factors that have the most significant impact on the financial risk tolerance (frt) of the retail investors, whereas income and number of dependents have negligible impact. keywords: retail urban investors; financial risk tolerance (frt); investor behaviour; demographic factors; logistic regression; linear discriminant analysis 1. introduction one of the evident characteristics of the financial market is volatility which necessitates the importance of assessment of risk vis-à-vis any investment decision to formulate a portfolio for an investor (gupta et al., 2019a; biswas et al., 2019; karmakar et al., 2018). as a result, it is quite imperative to study the pattern of stock price movements, returns, dividends, the performance of the constituting organizations and the influence of the macroeconomic variables, for example, bond rates, interest rates, policy decisions, and global market scenario. a plethora of research has been conducted to describe and predict stock market changes. does demographics influence the risk behaviour of urban investors? a machine learning model based approach 191 however, conventional models work on the efficient market hypothesis (emh) which assumes that the markets are efficient and stable and investors are rational in decision-making. investment options depend on the fundamental intention to maximize the return on investment while minimizing the risk (toma, 2015). however, the ability to withstand a risk level varies from investor to investor according to their behavioural nature (gupta et al., 2019b) which contradicts the assumption of emh that all investors are similarly rational. in this context, a strand of literature related to the behavioural influence of investors on investment decision-making has emerged in the last two decades. this section of growing literature, popularly known as ‘behavioural finance’ (bf) has been a subject matter of research for policymakers and strategists in recent time s. the fundamental aim of bf related work is to find out the underlying intention and behavioural pattern and psychological aspects such as cognition, personality, and emotions of the investors during pre-investment, investment and post-investment phases and their reaction to available information (madition, et al., 2007). bf supplements the historical data based prediction of stock price movements for deriving a robust model to mitigate the disposition bias (takeda et al., 2013; jonsson et al., 2017). bf has its genesis in the seminal work of tversky and kahneman (1974) who propounded that investors do not behave rationally always and hence, it is important to estimate the perceived risk. over the years since the work of tversky and kahneman (1974), several researchers contributed significantly to developing the gamut of bf (bayer, bernheim & scholz, 2009; junkus & berry, 2010; weber, weber & nosic, 2013). however, demographic factors like gender, race, age, social status, peer group influence, and culture play a significant role in shaping out the psychological bias for the common investors apart from their economic considerations. therefore, only analysis of the market fluctuations subject to the influence of the company performance, and macroeconomic impact and prediction of future stock prices may not provide the true picture to analyse the investment decision-making process. for understanding the rationale behind the formation of a portfolio, these demographic factors also need to be given due considerations. the level of risk tolerance of a particular investor largely affects the timing to enter the market, selection of stock type, stock holding period, the decision to sell, composition of the portfolio and many other issues. for these reasons, the field of bf has been allured a substantial number of contributions from several researchers (for instance, barber and odean, 2013; lin, 2011). in a recent paper, alwahaibi (2019) has comprehensively pointed out the relevance of bf as below: “investment decisions are usually being complicated by emotional process, mental mistakes and individual personality traits…….. the objective of having an understanding and at the same time predicting the behaviour of an economy is intimately linked to understanding individual attitudes towards risk…… behavioural finance happens to be a contemporary field that tends to merge the theory of behavioural cognitive psychology with conventional economics and finance with a view to giving reasons on why individuals made financial decisions that are irrational.” bhattacharya et al./oper. res. eng. sci. theor. appl. 5 (2) (2022) 190-205 192 with this pretext, the present study attempts to discern the impact of the demographic factors on the urban retail investors’ behaviours while they make investment decisions, particularly focusing on risk factors. since every human being is treated as a bundle of emotions that defines a unique character, behavioural finance studies are always paid off. in addition, as we consider demographic factors as influencing variables here, location plays an important role. here, we focus on urban retail investors residing in the three major cities of west bengal, namely kolkata, asansol and durgapur. if we look at the cities of choice, it is evident that predominantly, income is assumed to be the most important factor. however, does that mean another influence of demographic factors is insignificant? in this paper, we aim to find the answer to this question. within our search, we found that the studies on risk behaviours of urban retail investors are rare in nature. therefore, this paper might be of importance to the research fraternity and policy-makers. the rest of the paper is organized as follows. in section 2, we present the demographic variables used in this study. section 3 briefly describes the methodology, while in section 4 summarizes the results. section 5 discusses some of the implications of this study. finally, section 6 concludes this paper while highlighting some of the future scopes. 2. related work the extant literature shows the relevance and significance of considering demographic factors in explaining and predicting the behaviours of the investors in formulating investment decisions and selection of portfolios and their reaction to the fluctuations in the market conditions. way back, chen & volpe (1998) advocated that age, gender and experience significantly influence the risk-taking behaviours of the investors. following this work, schooley & worden (1999) noted that the level of education has a positive correlation with the risk taking ability of the investors. mutswenje (2009) observed an interrelation between the constructs of bf theory and the behaviour of the average investors. shleifer et al. (2010) argued that demographic and socio-economic factors significantly influence the investment decision-making process. dash (2010) contemplated on the financial planning of the investors and mentioned that age and gender differences the investors in terms of their financial goals and lead to different choices in forming their portfolio at varying risk levels. lutfi (2011) made an attempt to examine the causal relationship among the demographic factors such as gender, age, marital status, education, income, and the number of a family with the risk taking behaviour and investment pattern of the investors and found significant interrelation. geetha and ramesh (2012) further contributed by considering the dependent variables like period of investment, source of information, frequency of investment and degree of analysis in the indian context and observed that demographic factors influence investment decisions. in tune with this work, kannadhasan (2015) further extended by considering factor such as occupation. heena (2015) aimed to ascertain the relationship between demographic features and personality elements and risk behaviour of the investors and observed a significant impact of income. chavali and mohan raj (2016) endeavoured to address the gap between an individual’s perceived and actually obtained return vis-à-vis risk tolerance level and presented a notable finding that most often, individual investor overestimates their risk tolerance level under the desire of social recognition. alquraan et al. (2016) conducted a study at saudi stock market by considering behavioural finance attributes like loss averse, perception of risk and overconfidence does demographics influence the risk behaviour of urban investors? a machine learning model based approach 193 in addition to demographic factors to examine their impact on investment decisions. the authors noted the significant impact of behavioural finance attributes and education on the investment pattern. lan et al. (2018) carried out a large scale study on over 9000 equity investors in china to investigate and predict the investment decision behaviour on the basis of demographic attributes and observed that demographics is closely associated with investment behaviour. alwahaibi (2019) attempted to classify the investors on the basis of the influences of several demographic variables on risk taking abilities of the investors and investment patterns. some other studies in this regard were made by isidore & christie (2018), dangi & kohli (2018), and raut & das (2015) to investigate the impact of behavioural biases; gautam & matta (2016) to examine the effect of attitudinal factors on the investment decision-making and paramashivaiah, puttaswamy & ramya (2014) to introspect into the investment behaviour of the women investors. more recently, ezekiel and oshoke (2020) studied the influence of demographic factors on investment behaviour of individual investors residing in edo state of nigeria using the maximum likelihood method of estimation to estimate four multinomial logit equations and showed that educational level, occupation and marital status are the main demographic determinants of individual investor’s behaviour. the regression results obtained by nosita et al (2020) indicated gender and age to be statistically insignificant but marital status, income, and education to be significantly important in determining risk tolerance of about 850 indonesian individual investors. in the most recent indian context, chaudhary et al (2021) analysed about 500 responses received from the residents of haryana state in india using multinominal regression and found that gender, residence, and work situation positively affected the investment behaviour of respondents. in another work, chakkaravarthy et al (2021) used regression analysis to study the financial risk profile of investors living in chennai city of india and found that the socio demo factors like age, income, occupation have a significant influence on the risk taking capacity of the investors whereas gender does not have any significant relation with the investor’s risk profile. in this paper, we consider six demographic attributes such as gender, age, education, profession, income and number of dependents for analysing their influence on the investment decision making of the investors of urban kolkata and the asansol-durgapur industrial belt, west bengal, india and intend to forecast the risk tolerance behaviour. to the best of our knowledge there is no report in the literature which has conducted a study on the investor behaviour of this location making our work as the first attempt to understand and forecast investor behaviour of this locality. table 1 summarises the demographic factors considered by us. table 1. demographic factors and related hypotheses used in this study. demographic variable relevance references hypothesis income (x1) the level of income decides the affordability and a general notion is that once the basic needs are met, people tend to invest dohmen, falk, huffman, sunde, schupp, and wagner (2011); kumar & goyal (2016) higher income investor has more frt than lower (h1) bhattacharya et al./oper. res. eng. sci. theor. appl. 5 (2) (2022) 190-205 194 gender (x2) it is evident from the literature that there are emotional differences among male and female investors because of the influence of gender. females are susceptible to herding than male while later is more confident than the former. jianakoplos & bernasek (2006); sapienza, zingales & maestripieri (2009); lin (2011); barber & odean (2013); kumar & goyal (2016) male has more frt than female (h2) age (x3) the priorities of life and investment goals get changed with age. it is seen that young aged people are more risk taker and get influenced by peers while the middle and upper middle-aged investors are more stable and take strategic decisions at an affordable risk level prosad et al. (2015); tekçe et al. (2016) an investor with more education have higher frt (h3) education (x4) an educated investor is more analytic and informed while they are assessing different investment options and calculative in risk taking. deaves et al. (2010); goo et al. (2010); ates et al. (2016); pašalić et al. (2020) the younger investor has higher frt than older (h4) profession (x5) profession often determines the level of income. a salaried person depends on a fixed income and most often prefers to invest in a structured way. it is seen from the literature that optimistic results, overconfidence and the disposition effect rise with the better profession grable & lytton (1999); prosad et al. (2015) salaried individuals have higher frt than others (h5) number of dependents (x6) higher the number of dependents, higher is the burden of running the family and lower is the tendency in the investment and risk taking abilities. moreover, the nature of the financial goals also changes with the number of dependents. holt & laury (2002); hallahan, faff and mckenzy (2003) an increase in the number of dependents decreases frt(h6) 3. research methodology the objective of this paper is to apply statistical methods to the data collected from the respondents living in kolkata, durgapur and asansolcities in order to develop a simplified model for the prediction of their risk behaviour based on their demographic data. with the six above-mentioned demographic factors as independent variables, the dependent variable that we want to predict from this study is the risk response, i.e., how likely an investor will make an investment through risky instruments, namely mutual funds, shares, stocks, etc. cook and does demographics influence the risk behaviour of urban investors? a machine learning model based approach 195 whittle (2015), defined an individual’s risk profile as the extent to which an individual prefers certain rewards compared to uncertain yet larger rewards. in general, the individual who favours a low probability outcome is a risk taker and an individual who does not favour a high probability outcome is a risk averse. in our work, data were collected from 2000 respondents using a structured questionnaire during the period of september to december 2017 from retail investors residing in kolkata covering diverse demographic factors. the questionnaire was prepared to keep in mind the typical questionnaires used by financial advisors of investment agencies to ensure the appropriateness of the survey. the raw data collected were then subjected to multi-logistic regression analysis to develop a model to forecast the probability of the response based on six independent demographic variables as above. age, income and number of dependents were measured on ratio scales whereas gender, education and profession were measured on a nominal scale. the detailed codes used to categorise the responses received against each of the independent variables are listed in table 2. table 2. list of independent variables and their response codes used in the study variable coding income (x1) in inr > 20,000 = 0; 20,000-50,000=1; 50000-120,000; > 120,000 gender (x2) male = 1; female = 0 age (x3) 20 – 40 = 2; 40 60 = 1; above 60 = 0 number of dependents (x4) 0 5 (absolute number) education (x5) under graduate = 0; graduate = 1; post graduate = 2; above = 3 profession (x6) salaried = 0; self-employed = 1 frt of an individual investor was the only dependent variable in the analysis and was classified into two categories: risk-takers were coded as 1 and risk-averse were coded as 0. respondents were requested to choose the responses that best described their financial investments through risky instruments (such as shares, stocks and mutual funds) in the percentage of their total savings in order to classify them into appropriate. respondents with more than 30% of total investment in shares, stocks and mutual funds were categorised as risk takers whereas those with less than 30% investment in shares, stocks and mutual funds were categorised as non-risk takers. in this paper, we use a widely used machine learning framework such as logistics regression for the following reasons: i) logistic regression does not assume a linear relationship between the dependent (risk) and independent variables (demographic factors). the dependent variable must be dichotomous (2 categories) and the independent variables need not be interval, nor normally distributed, nor linearly related, nor of equal variance within each group. bhattacharya et al./oper. res. eng. sci. theor. appl. 5 (2) (2022) 190-205 196 ii) the categories (groups) of the demographic factors must be mutually exclusive and exhaustive; a case can only be in one group and every case must be a member of one of the groups. iii) logistic regression determines the impact of multiple independent variables presented simultaneously to predict the membership of one or two dependent variable categories. for analysis purposes, we use spss (version 20) and python tools in this paper. 4. findings and discussion in order to examine whether the data is normally distributed and since the data under consideration was relatively large (2000 samples), we perform the kolmogorov-smirnov test using spss the results of which are presented in table 3. table 3. results of kolmogorov-smirnov test demographic factors in co m e g e n d e r a g e d e p e n d e n ts e d u ca tio n p ro fe ssio n normal parameters mean 1.95 1.37 2.13 2.10 2.05 1.86 standard deviation .893 .483 .694 1.197 .874 .873 most extreme differences absolute .234 .407 .260 .183 .226 .255 positive .234 .407 .260 .183 .226 .255 negative -.159 -.275 -.241 -.166 -.175 -.162 kolmogorov smirmov (z) 10.454 18.221 11.624 8.205 10.129 11.425 asymp. sig. (2 tailed) .000 .000 .000 .000 .000 .000 in general, if the significance value is less than .05 at 5% confidence level, then the data is said to be normally distributed. table 3 shows that the significance is .000 for all demographic variables, which confirms the normality test. logistic regression is used to test the role of demographic factors as a differentiating factor as this can handle both continuous and categorical variables. the overall model was statistically significant at 5% level. table 4 compares the observed and predicted category of individuals, the degree of their prediction accuracy and the success of the classification of the sample. the performance of the model was assessed by cross-tabulating the observed response categories with the predicted response categories which are shown in the classification table 4. here, whenever the predicted probability was greater than the cutoff value of 0.5, the predicted response category was treated as 1. it can be seen in table 4 that the model correctly classified 68.20% of non risk takers and 87.70% of those who are risk taker with an overall prediction of 81.20%. does demographics influence the risk behaviour of urban investors? a machine learning model based approach 197 table 4. classification table predictor (spss) observed predicted non-risk taker risk taker correct percentage (%) non-risk taker 456 213 68.2 risk taker 164 1167 87.7 overall percentage 81.2 table 5 shows the logistic regression coefficientswald tests, odds ratio (exp (b)) for each predictor used in the frt model. table 5 has several important elements. the significance of each predictor is explained by wald statistics which has a chisquare distribution. wald can be explained through the significance level. if the significance is more than .05 then the hypothesis is rejected. however, in our case, all the variables have a significance level 0, which indicates that all the hypotheses are accepted and that the logistic regression is statistically significant. this means that all the six demographic factors (income, gender, age, dependent, education, and profession) are significant and influences the frt of the retail investor. the high values of exp (b) associated with gender and profession (12.290 and 11.079, respectively) in table 5 indicate the strong dependence of the investors frt on these two demographic factors. on the other hand, very small values of exp (b) associated with income and number of dependents indicate negligible dependence of the investors’ frt on these two demographic factors. table 5. logistic regression parameters of the model for frt b se wald df sig. exp (b) income (x1) -3.248 0.263 152.882 1 .000 0.039 gender (x2) 2.509 0.293 73.569 1 .000 12.293 age (x3) 1.996 0.195 104.757 1 .000 7.357 dependents (x4) -0.953 0.175 29.680 1 .000 0.386 education (x5) 1.760 0.301 34.283 1 .000 5.810 profession (x6) 2.405 0.214 34.283 1 .000 11.079 constant -5.788 0.367 248.428 1 .000 0.003 to test the goodness of fit, hosmer lemeshow test was conducted as this provides useful information about the model. the significance level for chi-square was found to be .000, which indicates acceptance of the null hypothesis which states that there is not much difference between the predicted and the observed values. this result shows that the model is fit with chi-square value at 172.875 of this model at 0.01 significance level. this indicates that the logistic regression is meaningful, in accordance with the dependent variable related to each specified independent variable. logistic regression classifier (lrc) and linear discriminant analysis (lda) are used on the dataset for the purpose of prediction. some of the important associated hyperparameters for the classifier are reported in table 6. each of these hyperparameters is tuned using the class randomizedsearchcv, provided in the scikit-learn library of python. bhattacharya et al./oper. res. eng. sci. theor. appl. 5 (2) (2022) 190-205 198 table 6. hyperparameters of lrc and lda lrc lda hyperparameter value hyperparameter value 𝑡𝑜𝑙 0.0001 𝑠𝑜𝑙𝑣𝑒𝑟 ‘svd’ 𝑠𝑜𝑙𝑣𝑒𝑟 saga 𝑠𝑡𝑜𝑟𝑒_𝑐𝑜𝑣𝑎𝑟𝑖𝑎𝑛𝑐𝑒 true 𝑚𝑎𝑥_𝑖𝑡𝑒𝑟 300 − − − − 𝑓𝑖𝑡_𝑖𝑛𝑡𝑒𝑟𝑐𝑒𝑝𝑡 true − − − − for the prediction purpose, the dataset is divided into 70:30 percentage ratio to determine the training and testing dataset. subsequently, lrc and lda are trained on the training dataset and their predictive capability are measured considering the testing dataset in terms of five performance metrics, accuracy, precision, recall, f1score and receiver operating characteristic (roc) score. the accuracy, precision, recall, f1-score and roc score for lrc are calculated as 0.80, 0.76, 0.77, 0.77 and 0.77, respectively. whereas, for lda, the corresponding values of accuracy, precision, recall, f1-score and roc score are determined as 0.79, 0.76, 0.76, 0.76 and 0.76. accordingly, we observe that lrc outperforms lda with respect to each of these five performance metrics. furthermore, we provide the roc curve and the confusion matrix for both lrc and lda in fig 1 and fig 2 respectively. here, it is to be mentioned that for our dataset, we have conducted experimental trials on our dataset using various classifiers and eventually observed that lda and ldc generate better roc scores. hence, for the comparison purpose of our results, we have selected these two classifiers for our dataset in this study. furthermore, it is also observed that the dataset which we have considered consists of only 2000 instances (samples) which are relatively small to train the machine learning estimators. this essentially becomes the limitation of our study. the findings above are largely in accordance with previous literature. for example, one of the key findings of this study is that salaried men have a much higher level of frt than un-salaried women. this finding is similar to the findings of croson & gneezy (2009), grable & lytton (1999), and grable (2000) who also suggested that men are more risk takers than women. another important finding of this study is that the profession of the investor (whether self-employed or salaried) has a strong influence on the frt which is also in good agreement with other studies (shtudiner, 2019). also, the finding that the level of frt decreases with an increase in age in this study is consistent with the study of kannadhasan (2015). does demographics influence the risk behaviour of urban investors? a machine learning model based approach 199 (a) (b) figure 1. roc curve of (a) lrc and (b) lda (a) (b) figure 2. confusion matrix of (a) lrc and (b) lda it is generally believed that investors having higher income can afford to take a higher level of risk than their lower income counterparts but our study did not support this strongly. the reason for this is not well understood but could be associated with a number of other factors such as increased level of responsibilities, bhattacharya et al./oper. res. eng. sci. theor. appl. 5 (2) (2022) 190-205 200 dependants, etc. we also did not see much dependence of the frt on the number of dependents in the family and the reason for this could be in the perception of the dependents in the minds of the investor. if the dependents are perceived by an investor as family members irrespective of whether they are also earners, this could easily mislead the data implication. 5. research implications the findings of this study can be useful to the financial investment agencies/advisors in identifying their potential clients living in the cities of kolkata, asansol and durgapur who are likely to make investments through risky instruments such as stocks, shares, etc. based on demographic factors such as gender, profession, age and education. however, for better accuracy of prediction, the study would require the inclusion of more demographic details such as information on the number of earners in the family, ethnic origin, marital status, etc. 6. conclusion and future scope in this article, we have made an attempt to investigate the influence of six independent demographic factors which may influence the financial decision of the individual retail investors residing in the three major cities of the indian state of west bengal. the study specifically focuses to forecast the probability of investment (through risky instruments such as stocks, shares and mutual funds) of a retail investor based on his/her demographic information such as income, gender, age, number of dependents, education and profession for retail investors residing in the cities of kolkata, asansol and durgapur. we use the multi-logistic regression analysis to determine the influence of these factors which revealed that gender and profession are the two demographic factors that have the most significant impact on the frt of the retail investors whereas income and number of dependents have negligible impact. also, our multi-logistic regression analysis predicted the number of investors with high frt (risk takers) with up to 81.2 % accuracy. the study does suffer from certain limitations. from the perspective of data collection, some investors may refuse to answer certain questions which can cause difficulty in classification and in turn introduce some biases in the data. another problem regarding demographic variables is the fact that certain groups are overall more risk seeking or risk averse, but this does not necessarily mean that the questioned individual always acts in coherence with this group. men for example are considered more risk tolerant than women, but there are definitely other women as well who are more risk tolerant than the average man. so the problems of certain exceptions always pertain. according to jianakoplos&bernasek (2006), there is even a difference between actual risk tolerance and stated risk tolerance as they found that many men verbally claiming to be more risk tolerant were actually non risk taker when measured by their actual investments. market volatility and political instability may also have a strong impact on the financial risk decision of an informed retail investor and thus is a limitation of the current research. it is worth noting that demographics alone may not be sufficient to classify retail investors into different categories since the socio-economic and attitudinal factors does demographics influence the risk behaviour of urban investors? a machine learning model based approach 201 may also influence the financial risk decision of an investor (grable &joo, 2004). financial education of the investor is another parameter that may be included in future studies. more sampling from a larger number of respondents with information on additional demographic factors such as marital status, number of earners in the family, financial education, ethnicity, family background, personality, etc., would establish a more generalised model for predicting the retail investors' risk category. such studies may be extended to retail investors 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(2013). who takes risks when and why: determinants of changes in investor risk taking. review of finance, 17(3), 847-883. doi: https://doi.org/10.1093/rof/rfs024 © 2022 by the authors. submitted for possible open access publication under the terms and conditions of the creative commons attribution (cc by) license (http://creativecommons.org/licenses/by/4.0/). https://doi.org/10.1126/science.185.4157.1124 https://doi.org/10.1002/9781119769262.ch17 https://doi.org/10.1093/rof/rfs024 plane thermoelastic waves in infinite half-space caused operational research in engineering sciences: theory and applications vol. 2, issue 1, 2019, pp. 15-26 issn: 2620-1607 eissn: 2620-1747 doi: https://doi.org/10.31181/oresta1901001s * corresponding author. savkovic.t@uns.ac.rs (t. savković), mmilica@uns.ac.rs (m. miličić), pitka@uns.ac.rs (p. pitka), milenkovic@uns.ac.rs (i. milenković), dejan.koleska@scania.ba (d. koleška) evaluation of the eco-driving training of professional truck drivers tatjana savković a*, milica miličić a, pavle pitka a, ivana milenković a, dejan koleška b a faculty of technical sciences, trg dositeja obradovića 6, novi sad b scania bh d.o.o., sarajevo, bosnia & herzegovina received: 23 november 2018 accepted: 16 february 2019 first online: 04 march 2019 original scientific paper abstract. the paper presents the evaluation of the eco-driving program impact (classroom with on-road instructions) on truck drivers’ operation parameters. a total of 8 professional truck drivers were tested in the real driving conditions. evaluation of the training impact on the drivers’ behavior was done in three periods: intervention period (p1), one month after training (p2) and four months after training (p3). data was collected with the assistance of the scania fleet management systemtm. fuel economy and co2 emission, idling time and coasting were significantly improved in the periods p2 and p3 compared to period p1 while speeding significantly increased. statistically, the use of the brake did not significantly change in the first and fourth month after the completed training in comparison to the intervention period. the drivers’ adoption of the eco-driving tips showed that statistically significant differences in fuel consumption and brake usage were obtained. this study shows that the use of the eco-driving techniques has got a potential for significant short-term reduction of fuel consumption and co2 emission in road transport; hence in the future the research studies will deal with the effects of training and potential downtrend in the long run (> 6 months). also, future research projects should analyze the impact of the drivers’ socio-economic characteristics on the application of the eco-driving instructions. key words: eco-driving, truck drivers, effect evaluation, operation parameters 1. introduction road transport produces over 80% of emissions of harmful substances within the european union transport sector. the road transport (passenger and freight) will especially continue to dominate in the total fuel consumption, with the demand for energy in the road transport considered to be reaching 80% of total demand in the transport sector by the year of 2050 (kojima & ryan, 2010). given these facts, the savković et al. /oper. res. eng. sci. theor. appl. 2 (1) (2019) 15-26 16 fuel economy and, subsequently, greenhouse gas emissions in this section are of the highest priorities of all the countries. the manner in which the vehicle is operated has an important impact on fuel consumption so that the driver training leads to reduction of fuel consumption (barkenbus, 2010; ecmt, 2005) and, subsequently, emission reduction. eco-driving involves a series of simple rules for maximizing fuel economy of the existing cars while minimizing co2 emission. it is a modified way of driving that is the most suitable for modern engine technology. studies (decicco & ross, 1996; el-shawarby, kyoungho, & hesham, 2005) confirm a technical aspect of the eco-driving program, namely, its operations affecting fuel consumption upmost in driving (for example, in acceleration, deceleration, maintaining constant speed and idle vehicle operation). eco-driving in europe, in accordance with the programs and studies (cieca, 2007; zarkadoula, 2007) includes the following technical regulations which are of relevance for inducing changes in the driving behavior: maintaining a steady driving speed, turning off engine at the traffic lights (while parked, when loading and unloading, etc.), an appropriate level of transmission in comparison to the type of transmission and an efficient use of brakes. apart from the technical recommendations, eco-driving tips also require practical advices that refer more to the restraining of driving habits and drivers’ behaviors which are in accordance with the driving patterns. studies (wilbers, 1999; fujikawa & taniguchi, 2002; ukita & shirota, 2003; matsuki, 2006; barth & boriboonsomsin, 2009; iee, 2008) have prompted eco-driving tips which included: improvement of vehicle maintenance and that of aerodynamics, prediction of traffic conditions, avoidance of excessive vehicle weight, choice of appropriate fuel or motor oil, control of unnecessary use of equipment in the vehicle and the use of on-board computer and navigation systems (for example, simulators, driving systems, cruise control, gps, engine speedometer, etc.) numerous studies have proved a feasible fuel economy of between 5% and 10%, and even in some cases, over 20% (fiat, 2010; wilbers, 1999; onoda, 2009). reduced fuel consumption also affects reduction of co2 emission ranging from 525% (barkenbus, 2010; mensing, bideaux, trigui, & tattegrain, 2013; onoda, 2009). the eco-driving benefits are not only limited to the reduction of co2 emission, and to fuel economy but are far more extensive as indicated in the given studies (cieca, 2007; intelligent energy europe, n.d.; lauper, moser, fisher, matthies, & kaufmannhayoz, 2015): • noise reduction, • advancement of traffic safety, • minimizing of drivers' stress (that occurs when overtaking and speeding), • improvement of driving comfort, • positive influence on vehicle parts wear and tear or maintenance (for example, brakes, pneumatics), and, • improvement of travel time. in this study, the evaluation of the eco-driving training efficiency was done (classroom with on-road instruction training) through operation parameters (fuel consumption, co2 emission, idling time, braking events, speeding, coasting) of 8 evaluation of the eco-driving training of professional truck drivers 17 professional truck drivers over a short-term period, and in the first month after the p2 training and the fourth month after the p3 training in comparison to the p1 training period. besides, there is an approach which analyzes the differences in the adopted instructions among the drivers trained for eco-driving. 2. methodology 2.1 participants the drivers received in-vehicle feedback (advices) and classroom training. they all volunteered to participate in the research and they did not have previous experience with the eco-driving. the drivers’ average age was 32 years with sd=3.46 and their average driving experience was 7 years (sd=2.42). 2.2 testing vehicle when testing the drivers and measuring the operation parameters, the scania model s500a4*2latm tractor truck composition was used, with the semitrailer schmitztm that was fully loaded in order to create more realistic driving conditions. 2.3 testing route the length of the tested route is 26,2 km in the urban and rural area of derventa (fig. 1). both driving tests (before and after the training) were completed on the same route in order to avoid deviations in fuel consumption because of different distances whereas the parameters that affect fuel consumption remained identical (pressure in the pneumatics, load, etc.). in relation to the decline characteristics of the observed route, 8 sections with different lengths were formed. the biggest incline of 4.38% along the testing route was recorded in the section 4, 2.1 km long, whereas the biggest decline of 2.80% was recorded in the section 5 which is 0.5 km long (fig. 2). these characteristics of the slope provide an opportunity for the drivers to apply the advices they received during the training on uphill-downhill driving and thus reduce fuel consumption. figure 1 testing route savković et al. /oper. res. eng. sci. theor. appl. 2 (1) (2019) 15-26 18 figure 2 slope characteristics on testing route 2.4 measurement results results of the measured parameters show their monthly average values. results comparison of the tested driving parameters (fuel consumption and other parameters) intervention period (p1), one month after training (p2) and four months after training (p3) are presented in table 1. 2.5 chronological phases phase 1: intervention period: march 1 to 31 march, 2018: eco-driving training was conducted for all the drivers and in-vehicle advices were given to the drivers. phase 2: off period: april 1 to 31 july, 2018: no in-vehicle advices, no eco-driving training – the driving after eco-driving interventions. evaluation of the eco-driving training of professional truck drivers 19 table 1 training diagnostic data (intervention period, one month after training and four months after training) training data periods driver d1 d2 d3 d4 d5 d6 d7 d8 avg. d is ta n c e (k m *1 0 3 ) p1 22.97 24.61 21.68 22.55 22.49 23.28 22.21 26.26 23.26 p2 35.13 37.96 31.09 33.72 30.89 35.99 32.77 38.42 34.50 p3 72.92 82.25 72.20 75.27 63.04 77.15 73.89 81.86 74.82 avg.p2/p1 (%) 52.95 54.25 43.46 49.52 56.49 54.57 47.51 46.31 50.63 avg.p3/p1 (%) >100 >100 >100 >100 >100 >100 >100 >100 >100 f u e l c o n su m p ti o n (l / 1 0 0 k m ) p1 26.3 29 26.1 26.1 26.5 26.2 24.6 27.2 26.50 p2 23.9 26.6 25.8 25.0 24.8 24.7 22.8 26.6 25.03 p3 24.2 26.5 25.4 23.2 24.2 25.1 23.7 26.1 24.80 avg.p2/p1 (%) 9.12 -8.27 -1.15 -4.21 -6.41 -5.72 -7.32 -2.21 -3.27 avg.p3/p1 (%) -7.98 -8.62 -2.68 -11.11 -8.68 -4.19 -3.66 -4.04 -6.37 c o 2 e m is si o n (k g / k m ) p1 0.28 0.44 0.32 0.33 0.31 0.32 0.33 0.41 0.34 p2 0.22 0.25 0.21 0.22 0.18 0.23 0.19 0.22 0.22 p3 0.11 0.13 0.13 0.12 0.11 0.13 0.12 0.13 0.12 avg.p2/p1 (%) -21.42 -43.18 -34.38 -33.33 -41.94 -28.13 -42.42 -46.34 -36.39 avg.p3/p1 (%) -60.71 -70.45 -59.38 -63.63 -64.51 -59.38 -63.63 -68.29 -63.75 id li n g t im e (m in / 1 0 3 k m ) p1 41.40 41.89 41.71 46.70 45.54 38.48 34.80 46.91 42.27 p2 21.95 25.08 42.88 26.90 20.49 18.71 22.03 27.10 25.48 p3 14.84 12.86 11.74 21.18 13.75 19.27 12.20 18.53 15.63 avg.p2/p1 (%) -46.99 -40.11 2.82 -42.39 -55.00 -51.39 -36.70 -42.24 -39.71 avg.p3/p1 (%) -64.17 -69.30 -71.85 -54.64 -69.80 -49.92 -64.92 -60.50 -63.03 b ra k e a p p li c a ti o n s (# / 1 0 0 k m ) p1 25.8 24.4 32.9 23.9 30.9 25.2 24.9 20.4 26.05 p2 23.1 24.9 41.1 25.8 26.7 27.0 20.3 21.8 26.34 p3 23.1 31.3 42.8 27.3 29.9 30.6 19.8 19.5 28.04 avg.p2/p1 (%) -10.46 2.05 24.92 7.95 -13.59 7.14 -18.47 6.86 0.80 avg.p3/p1 (%) -10.46 28.27 30.09 14.22 -3.24 21.43 -20.48 -4.41 6.93 s p e e d in g (% o f e n g in e ru n n in g ti m e ) p1 11.5 1.4 2.1 20.6 0.4 11.5 0.8 0.8 6.14 p2 40.9 1.5 27.1 35.3 9.9 31.1 23.9 38.5 26.03 p3 38.7 5.4 14.6 40.0 8.7 37.1 28.6 40.1 26.65 avg.p2/p1 (%) >100 7.14 >100 71.35 >100 >100 >100 >100 >100 avg.p3/p1 (%) >100 >100 >100 >100 >100 >100 >100 >100 >100 c o a st in g ( % o f d is ta n c e d ri v e n ) p1 15 16 11 19 13 17 16 17 15.50 p2 17 18 12 20 14 19 17 18 16.88 p3 18 18 19 18 16 19 18 19 18.13 avg.p2/p1 (%) 13.33 12.5 9.09 5.26 7.69 11.76 6.25 5.88 8.97 avg.p3/p1 (%) 20.00 12.5 72.72 -5.26 23.07 11.71 12.5 11.76 19.88 2.6 training this study combined classroom training with on-road instructions by the instructor. the typical eco-driving training course consists of a test drive before the classroom training where the drivers learn the eco-driving principles. after the classroom training, the second test drive is conducted during which the instructor is advising the drivers. after the second test, the results are analyzed and compared. characteristics of the training are as follows: they are relatively expensive; a small number of people can be trained simultaneously because of the limited capacity, and the training has a great impact on the change of the driving behavior over a short period of time (basarić, et al., 2017; barać, zovak, & periša, 2013; husnjak, forenbacher, & bucak, 2015). a short resume of the training can be found below. all the participants completed the test drive held by the instructor in derventa, before completing the classroom training on 13th march 2018 (driver 1 – driver 4) savković et al. /oper. res. eng. sci. theor. appl. 2 (1) (2019) 15-26 20 and 14th march 2018 (driver 5 – driver 8) between 9 a.m. and 11:30 a.m. which served as the base point in comparison to the test drive after the training. after that, a 90-minute-long classroom training session (from 12 a.m. to 13:30 p.m.), was held for the same group of drivers during the above periods of time. the purpose of this classroom training is to encourage the drivers to apply techniques of eco-driving after their training (for example, smooth acceleration and deceleration, turning off the engine when the vehicle is idle, predicting traffic conditions, maintaining constant speed, using engine braking, etc.). after the classroom training, the second test drive was conducted from 14 p.m. to 16:30 p.m. combining the techniques learnt from the classroom training with instructions from the instructor during the same drive. in order to assess the effects of the training, the results obtained after the second drive were discussed with the drivers. 2.7 data collection data were collected with the assistance of the scania fleet management systemtm. the scania communicator c300tm is connected to the vehicle via can bus, and via gsm network on the scania server. all the data related to the work of vehicles and drivers can be found by logging on to the portal. 3. results and discussion the focus of this research study was to determine the impact of eco-driving training on drivers’ behavior. a special attention was given to the analyses of the vehicle operation indicators, i.e. how the driver operates the vehicle during the training period (p1), in the first month after the training (p2) and in the fourth month after the training (p3). table 1 and figs. 3-4 compare the average measuring driving quality indicators (fuel consumption, co2 emission, idling time, brake usage, coasting, and speeding) between the intervention period (p1), one month after training (p2) and four months after training (p3). the values are calculated as averages for all eight drivers. although there was a significant increase in speeding (>100%) in the first month after the training (p2) in comparison to the intervention period (p1), until an increase in braking (1,1%), there was still a small reduction in fuel consumption by 3.27% and co2 emission by significant 36.39%. there was also an increase in coasting by 8,97% in p2 period, i.e. the drivers used more the vehicle’s motion without pressing the accelerator, and a reduction of idling by 39.71%, i.e. the drivers were often turning off the idle vehicle. this shows how idling has a significant impact on fuel consumption and, consequently, co2 emission. accordingly, beusen et al., (2009) established that 1.5% reduction of engine idling reduces an average fuel consumption by 5%, four months after completing the eco-driving course. the findings show that idling fuel cost per truck per year with six hours of idling per day is $4,134 (omnitracks, n.d.). in addition, the literature indicates a significant impact of coasting on fuel consumption which was also established in this study. if the vehicle is moving on the straight road, coasting could reduce fuel consumption by 7,9% (shakouri, ordys, darnell, & kavanagh, 2013) whereas the coasting downhill could reduce fuel consumption by 5% (koch-groeber, n.d.). evaluation of the eco-driving training of professional truck drivers 21 0 20 40 60 fc [l/100 km] co2 [kg/km] idling [min/1000 km] brake application [#/100 km] speeding [% of ert] coasting[% of dd] march(p1) april(p2) [% of ert] % of engine running time [% of dd] % of distance driven figure 3 radar chart with average results of eco-driving training period p1 and period p2 0 20 40 60 fc [l/100 km] co2 [kg/km] idling [min/1000 km] brake application [#/100 km] speeding [% of ert] coasting[% of dd] march(p1) july(p3) [% of ert] % of engine running time [% of dd] % of distance driven figure 4 radar chart with average results of eco-driving training period p1 and period p3 there was a reduction in fuel consumption and co2 emission in period (p3) compared to intervention period (p1) by 6.37% and 63.75%, respectively, whereas the other observed parameters had the same tendency as in comparison to period p2 but significantly distinctive in p3 period. accordingly, there was an increase in speeding by >100%, braking increased by 6.93% vehicle's engine running when the vehicle is not in motion decreased by 63.03%, and coasting increased by 19.88%. this case also shows that the increased vehicle motion without braking and when coasting, turning off the vehicle while idle, have a positive impact on fuel consumption and co2 emission. savković et al. /oper. res. eng. sci. theor. appl. 2 (1) (2019) 15-26 22 the collected data were statistically analyzed in order to assess the effectiveness of the eco-driving training program in a short term period. the statistical evaluation of the driving parameters was conducted in the statistical program minitab 17 using anova one-way (at 5% significance level) and kruskal-wallis test if there was no data correspondence with normal distribution. these tests were used to determine whether there was a statistically significant difference in the mentioned parameters by periods. congruency with the normal distribution was tested using anderson-darling test, which showed that the fuel consumption and co2 emission values were susceptible to normal distribution unlike the values of idling time, brake applications, speeding and coasting. in 5 parameters (fuel consumption, co2 emission, idling, speeding and coasting) there is a statistically significant difference in values depending on the observation period (table 2). in fuel consumption, co2 emission, idling time and coasting there was a significant improvement after the intervention period, while the speeding significantly increased in the periods after the training, which is negative. table 2 summary statistics of variables by periods variable fuel consumption co2 emission idling time brake application speeding coasting ad test 0.481 0.071 0.011 0.023 0.010 0.007 p-value 0.025 0.000 0.000 0.851 0.009 0.050 note: ad test anderson-darling test the tukey comparison results are also used to formally test whether the difference between a pair of groups (p1-p2; p1-p3; p2-p3) is statistically significant in fuel consumption (fc) and co2 emission. the figures that include the tukey simultaneous confidence intervals (fig. 5, 6) show that the confidence interval for the difference between the means of four pairs these two parameters (p1 fc p3 fc; p1 co2 – p2 co2; p1 co2 – p3 co2; p2 co2 – p3 co2) does not include zero which indicates that the difference is significant, i.e. the values of co2 emission were significantly improved in p2 and p3 periods compared to p1 period as well as period p3 compared to p1 period in terms of fuel consumption. the pairs p1 p2 and p3 p2 in fuel consumption have zero in the confidence interval which means that there is no statistically significant difference in fuel consumption between the periods p1 and p2 as well as p2 and p3. to determine the difference between the pairs (levels), for parameters: idling time, speeding and coasting, the mann-whitney test was used. it helped establish the differences between all the pairs of the idling time parameter (p1-p2; p1-p3; p2-p3) with their p-values<0.05 as: 0.00009; 0.0009 and 0.0028, respectively. this indicates that the values of the vehicle's engine running, when the vehicle is not in motion, significantly improved in the first and the fourth month after the completed training. in addition, a significant improvement of the motion of the vehicle that is speeding without accelerating was confirmed in the period p3 compared to period p1 (p=0.0209). the differences were not detected in the pairs: p2-speeding and p3speeding (p=0.7929); p1-coasting and p2-coasting (p=0.2076); p2-coasting and p3coasting (p=0.3446), which indicates that there is no statistically significant difference in their medians (table 3). evaluation of the eco-driving training of professional truck drivers 23 table 3 mann-whitney test and tukey comparison results variable fuel consumption co2 emission idling time speeding coasting test tukey comparison (interval) mann-whitney test (p-value) p1-p2 (-3.03489, 0.0848897) (-0.170315, 0.0846847) 0.00009 0.0101 0.2076 p1-p3 (-3.25989, 0.140110) (-0.262815, 0.177185) 0.0009 0.0101 0.0209 p2-p3 (-1.78489, 1.33489) (-0.135315, 0.0496847) 0.0028 0.7929 0.3446 figure 5 tukey pairwise comparison of fuel consumption figure 6 tukey pairwise comparison of co2 emission there is also an approach to the statistical analysis which serves to determine whether there is a difference in the adopted eco-driving instructions among the drivers. when analyzing the normality of the data set, the same p-values for the anderson-darling test and the eco-driving training analysis by periods, have been obtained. accordingly, to check on whether there was a statistically significant savković et al. /oper. res. eng. sci. theor. appl. 2 (1) (2019) 15-26 24 difference in the mentioned parameters among the drivers, appropriate statistical tests have been applied in the analyses, namely, anova one-way (at 5% significance level) and kruskal-wallis test subject to data compatibility with normal distribution. in fuel consumption and brake usage there is a statistically significant difference in values among the drivers with p<0.05 (table 4). in the other analyzed parameters no statistically significant difference has been found. even though the drivers are of the same age and driving experience without major deviations, this points to the fact that the socio-economic characteristics of the drivers can be a significant factor for the way the eco-driving instructions are adopted and applied. table 4 summary statistics of variables by drivers variable fuel consumption co2 emission idling time brake application speeding coasting ad test 0.481 0.071 0.011 0.023 0.010 0.007 p-value 0.019 0.992 0.971 0.012 0.155 0.127 note: ad test anderson-darling test economic benefit of eco-driving fuel consumption economy estimate enables calculation of the eco-driving economic benefits. if each truck spent around 32,000 liters of fuel annually, with the average fuel consumption savings of 3.27%, it could save 1,046.4 liters of fuel per truck per year. if an average cost of one liter of fuel was 1.18eur, the annual savings per truck would be 1,235eur. economic gains could be even greater if we took into account a higher fuel consumption economy of 6.37% the drivers achieved 4 months after the training, on average. these savings are in accordance with the previous research results (barać, zovak, & periša, 2013). they determined that the implementation of the eco-driving training could save around 1,505eur per one commercial vehicle per year. 4. conclusion in this paper, the effects of the eco-driving program on the drivers’ vehicle operation have been shown in a short-term period. moreover, the effects of the driver eco-driving training were analyzed in the training period (p1) and in the first month (p2) and the fourth month (p3) after completing the training in relation to fuel consumption, co2 emission, idling time, brake usage, speeding and coasting. the obtained results are in accordance with the literature by showing how, with the implementation of the eco-driving, a reduction in fuel consumption and co2 emission in a short term period is attained. the results of the present study point to a statistically significant reduction in fuel consumption and co2 emission in the periods p2 and p3 compared to p1 period mostly due to a decrease of idling time parameter and increase of coasting parameter although there has been a significant increase of speeding, as proven statistically. this indicates that the targeted education about the change of drivers’ behavior can be effective. future research studies will focus on the effects of eco-driving in a long term period (> 6 months) and determine if the effects will downtrend over time. the facts obtained in this research show that the drivers’ socio-economic characteristics had an impact on the ecoevaluation of the 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(2007). training bus drivers to promote smart driving: a note on a greek eco-driving pilot program. transportation research part d: transport and environment, 12, 449-451. http://www.together-eu.org/docs/102/together_eco-driving_5_handout_15.pdf https://www.hs-heilbronn.de/5023311/coasting-on-highways.pdf https://www.hs-heilbronn.de/5023311/coasting-on-highways.pdf https://www.iea.org/publications/freepublications/publication/transport_energy_efficiency.pdf https://www.iea.org/publications/freepublications/publication/transport_energy_efficiency.pdf https://www.omnitracs.com/blog/truck-idling-fuel-consumption-burning-your-bottom-line-yes-and%20it-doesnt-have https://www.omnitracs.com/blog/truck-idling-fuel-consumption-burning-your-bottom-line-yes-and%20it-doesnt-have http://dx.doi.org/10.1155/2013/391650 operational research in engineering sciences: theory and applications vol. 4, issue 3, 2021, pp. 107-121 issn: 2620-1607 eissn: 2620-1747 *corresponding author biranchi.adhikari@gmail.com (b. n. adhikari), mail2ajaybehera@yahoo.co.in (a. k. behera), rnmahapatra@nitm.ac.in (r. n. mahapatra), harishdas@nitm.ac.in (h. c. das) cell phone related violations and motorcycle accidents: a bayesian approach biranchi adhikari 1, ajay behera 2*, rabindra mahapatra 1, harish das1 1 department of mechanical engineering, national institute of technology, meghalaya, india 2 department of mechanical engineering, iter, siksha o anusandhan, deemed to be university, bhubaneswar, india received: 29 june 2021 accepted: 27 august 2021 first online: 09 december 2021 research paper abstract: the effects of cell phone use on motorcycle riders’ behaviour are studied in smart city, bhubaneswar, capital of state odisha, india. most of motorcycle riders confess using cell phone devices while driving. moreover, relationship between near miss and accidents has been found with the use of cell phone, reflecting a risk factor for motorcycle riders.“ this study examines the relationship between such type of behaviours, comprising calling and manipulating the screen, and the frequency of near miss and actual accidents among motorcycle riders. we conducted a web based survey measuring cell phone-specific violations, human errors, near miss and accident to motorcycle riders (n=289; age range; 18-60).we hypothesized that the relationship between cell phone use and near miss would be explained by an increase in the number of human errors committed, thus increasing the likelihood of being involved in near miss. moreover, we hypothesized that near miss will predict actual accidents. outcomes of path analysis showed that cell phone-specific violations predicted accidents throughout their consecutive effects on human errors and near miss only in the subsample of men. these findings offer an explanation of how cell phone use contributes to increase the likelihood of getting involved in near miss and actual accidents. the current study builds a path model explaining how cell phone-specific violations lead to more near miss among motorcycle riders. key words: cell phone-specific violations; human errors; near miss; accidents; motorcycle riders safety doi: https://doi.org/10.31181/oresta091221107a mailto:biranchi.adhikari@gmail.com mailto:mail2ajaybehera@yahoo.co.in adhikari et al./oper. res. eng. sci. theor. appl. 4 (3) (2021) 107-121 108 1. introduction motorcycles are a popular means of transport worldwide, although they can serve different purposes in different world regions. in high-income countries, they are often used for leisure or recreation, whereas they are commonly used for transporting people and goods in lowand middle-income countries (organization for economic cooperation and development/international transport forum, 2015). most motorcycles in high-income countries are high-powered (over 250 cc), representing over 50% of the motorcycles fleet in north american and european countries compared to 5% in southeast asia (who, 2017). within southeast asia, the proportion of motorcycle fatalities is much higher in vietnam, malaysia, cambodia, and thailand, at 58, 58, 70, and 73%, respectively (abdul manan et al., 2013; ngo et al., 2012; who, 2015). since 2010, the proportion of motorcycle fatalities has remained stable in most world regions (who, 2015), suggesting that motorcycle accidents continue to be a global safety issue. among a number of factors contributing to motorcycle accidents, risk-taking behaviours have been found to be an important contributor (lin & kraus, 2009). thus, there has been a growing body of literature investigating risky riding behaviours of motorcycle riders in high-income countries (moskal et al., 2012; stephens et al., 2017) as well as in lowand middleincome countries (roehler et al., 2015; tongklao et al., 2016; vu & shimizu, 2007).” for example, in a study in hanoi, vietnam, vu & shimizu, (2007) found that habits and intentions were strong predictors of risk-taking behaviours such as speeding, running red lights, and reckless overtaking. a study in malaysia reported a high prevalence of street racing under the influence of alcohol and stunt riding (wong, 2011). in indonesia, susilo et al. (2015) found that young adults and students were more likely to violate traffic regulations while examining a range of traffic violations among motorcycle riders though cell phone use while driving a car has been a subject of much research (backer-grndahl & sagberg, 2011; beck & watters, 2016; harrison, 2011; ismeik et al., 2015; mcevoy et al., 2005; zhou et al,. 2012), mobile phone use while riding a motorcycle has only been investigated in recent research. it was observed that the prevalence of cell phone use while riding in 3 mexican cities was 0.64% (perez-nunez et al., 2013) compared to 8.66% in hanoi, vietnam (truong et al.,2016). self-reported prevalence of cell phone use while riding, at any time rather than a specific time of observation, was much higher. about 40% of high school students in vientiane, laos (phommachanh et al., 2017), and nearly 81% of university students in hanoi and ho chi minh city reported using a mobile phone while riding a motorcycle (truong et al., 2017). effects of gender, risk perceptions, and social networks on cell phone use while riding have also been highlighted (de gruyter et al., 2017; truong et al., 2017,long et al.,2019). cell phone use while riding can also be affected by situational factors. (truong et al.,2016).” the high prevalence of cellphone use while motorcycle riders reported in previous research conveys a clear message about the generalized presence of such practices.” 2. literature review a number of studies have further explored associations between risk-taking behaviours and crash involvement given their importance to the identification of cell phone related violations and motorcycle accidents: a bayesian approach 109 interventions and priorities. using french crash data, moskal et al. (2012) found that bike riders who were males, did not wear a helmet, or exceeded the alcohol concentration limit had a higher risk of being involved in a crash.” in a survey of motorcycle riders in new south wales, australia, stephens et al. (2017) showed that riders performing stunt behaviours and speed violations were more likely to be involved in a accident and close-accident, respectively. “according to a study of schoolchildren in india, tailgating and aggressive attitudes toward other motorcycle riders were associated with accident involvement” (rathinam et al., 2007). “it was found in taipei, taiwan, that female motorcycle riders or riders with a higher tendency to engage in risky riding behaviours were more likely to be involved in a accident (chang & yeh,2007). a recent study in france suggested that female riders were less likely to be involved in injured accidents and particularly fatal accidents, however (coquelet et al., 2018). in a study of fatal motorcycle accidents in cambodia, roehler et al. (2015) identified that speeding and drink riding were major contributing factors to motorcycle fatalities. a study of risky behaviours among students in thailand reported that not wearing a helmet, speeding, and riding under the influence of alcohol were associated with motorcycle injuries (tongklao et al., 2016).” though the associations between a range of risk-taking behaviours and motorcycle accident involvement have been extensively investigated, little is understood about accident involvement among motorcycle riders who use a cell phone while riding. this understanding is particularly important in regions such as southeast asia where motorcycling is the dominant transport mode coupled with high prevalence of cell phone use while riding” (phommachanh et al., 2017; truong et al., 2017). “to address the research gap, this article investigates crash involvement and severity among motorcycle riders with risky riding behaviours, particularly cell phone use while riding. data from a survey of university students’ risky riding behaviours in vietnam are utilized for the investigation because vietnam has bikedominated traffic (ntsc 2015; who, 2015) and young adults are more likely to engage in risky riding behaviours (chang & yeh, 2007; truong et al.,2016).traditionally, traffic accidents have been associated with human, road, environmental and vehicle factors (bucsuházy et al., 2020). human behaviour has been reported as the main contributing factor in 95% of bike accidents (petridou & moustaki, 2000; sheykhfard et al., 2020).” in vietnam, motorcycles contribute to around 95% of over 43 million registered vehicles and the vast majority of motorcycle are powered with an engine of less than 150 cc (ntsc, 2015; who,2017). motorcycle riding is particularly important for mobility of young adults; most young adults aged 21–30 years old (58–77%) possess a motorcycle (tran, 2013) and many students (40%) use one for travel to university (ohmori et al., 2011). in 2014, vietnam had over 25,000 reported traffic accidents and about 9,000 fatalities (ntsc, 2015). motorcycle riders were involved in more than 70% of traffic accidents (hung et al., 2008; truong et al., 2016) and contributed to about 58% of traffic fatalities (ngo et al., 2012). traffic regulations in vietnam specify penalties for risky riding behaviours such as not wearing a helmet, speeding, drink riding, running red lights, and using a cell phone or portable music device while riding. however, though helmet use has been well reported (hung et al., 2008;marco et al.,2019), little information is available about the compliance levels for other risktaking behaviours.” https://www.tandfonline.com/doi/full/10.1080/17457300.2021.1942922 https://www.tandfonline.com/doi/full/10.1080/17457300.2021.1942922 https://www.tandfonline.com/doi/full/10.1080/17457300.2021.1942922 adhikari et al./oper. res. eng. sci. theor. appl. 4 (3) (2021) 107-121 110 according to the previous definitions, cellphone behaviors on the motorcycles can be considered violations given that, even if not all the countries’ road rules officially ban them, they are deliberate deviations of the safe practice. all in all, even though the body of research on motorcycle riders’ cellphone use is growing, there is need for more research on motorcycle riders to further untangle how–and to what extent – this type of violations affects human error because use of motorcycles (two wheelers) is very high in bhubaneswar.” based on the previously reported findings and the stated need for more research, we establish a hypothesized path model in which cellphone -specific violations will be positively associated with human errors (hypothesis 1) and near miss (hypothesis 2).” we also hypothesize that errors will be positively associated with near near miss (hypothesis 3).to address this research gap, we hypothesized that close accidents will predict actual accidents (hypothesis 4). in a nutshell, we have hypothesized a model (see figure 1) in which cellphonespecific violations and human errors predict near miss. in turn, near miss were hypothesized to predict actual accidents. thus, we have posed that cellphone specific violations and human errors will indirectly increase the likelihood of actual accidents by raising the likelihood of occurrence of near miss. therefore, we hypothesize that near miss will mediate the effect of cellphone-specific violations and human errors on actual accidents (hypothesis 5). moreover, we have also proposed that cellphonespecific violations will enhance the probability of committing human errors, and this at the same time will increase the likelihood of being involved in near miss.” in addition, since we have also posed that accidents will be predicted by near miss, we hypothesize a serial mediation model in which human errors will mediate the effect of cellphone-specific violations on near miss, and these will act as a mediator between human errors and the occurrence of accidents (hypothesis 6). “ figure 1 displays the hypothesized path model. hypothesis 5 encompasses all the paths between cell phone-specific violations and accidents (i.e., those of h1, h2, h3, and h4), whereas hypothesis 6 includes those between human errors and accidents (i.e., those of h3 and h4).” figure 1. conceptual model of the study (hypothesized path model) cell phone related violations and motorcycle accidents: a bayesian approach 111 3. methodology data were collected from october15, 2019 to december 30, 2019 through a selfreported online questionnaire at bhubaneswar, capital of odisha, india. to reach a wide variety of participants with different demographics characteristics and from different locations in bhubaneswar, the questionnaire was disseminated through the web. we found the motorcycle riders associations’ websites and social media groups. social media groups with fewer than 500 participants were discarded. we contacted in total 40 groups and 25 websites. to reach the selected targets two methods were used: (a) firstly, the link to the questionnaire was directly posted on groups’ walls or on websites bulletin boards if available; (b) secondly, an email was written to the website administrators, kindly asking to advertise the questionnaire directly on their website, through their social media channels or inside their newsletter.” 3.1 descriptive statistics a total of 462 participants responded the questionnaire. after considering only those participants that had filled out the items for age, sex, and acknowledged to use the motorcycle at least once a week, the remaining sample comprised 289 (62.5%) participants. from these, 175 (60.5%) were male, 114 (39.4%) were female. the age of the participants ranged from age 18 to 60 years. the mean for female was 36.08 (sd = 14.42), the mean for male was 44.20 (sd 13.83), whereas the general mean value was 41.56 (sd= 14.42).” among these participants, 31 (10.7%) of them used the motorcycle once a week, 31 (10.7%) used it twice, other 34 (11.6%) participants using motorcycles three times a week, 30 (10.3%) did so four times, 42 (14.5%) of them used motorcycles five times a week, and the remaining 121 (41.8%) participants used the motorcycles six or more times per week. moreover, regarding the frequency of use in comparison with other means of transportation, 48.2% of the participants reported to use the motorcycles as a primary mode of transportation.” 3.1.1. cell phone specific violations.“ to measure cell phone -specific violations, we used a 5-item self-reported scale based on chataway et al.(2014) scale on distracted used motorcycles. we asked participants to state the perceived frequency with which they undertook behaviours, such as checking the phone while using motorcycles or texting messages.” the frequency was expressed by using a 5-point likert-type scale (ranging from 1= never to 5=always; assuming that “always” entails “as long as there is the possibility to do so” and not “continuously and all the time”). “table 1 shows the item and subscale structure of the questionnaire, as well as some descriptive and reliability values. adhikari et al./oper. res. eng. sci. theor. appl. 4 (3) (2021) 107-121 112 “table 1. “descriptive statistics of the unsafe motorcycle rider behaviours.” subscales m sd med α “cell phone-specific violations” 0.880 “use a cell phone to look for information or itineraries on the internet.” 1.52 0.87 1 “use a cell phone to send text messages.” 1.43 0.82 1 “use a cell phone to read text messages.” 1.62 0.86 1 “use the cell phone to respond a call.” 1.95 0.98 2 “use the cell phone to call someone.” 1.78 0.96 1 “human errors” 0.672 “abruptly brake in order to avoid/dodge a vehicle.” 2.59 0.92 3 “abruptly swerve to avoid a bus or truck that turns right.” 1.72 0.85 2 “be grazed or hit by a cycle.” 1.08 0.34 1 “almost hit a pedestrian while you were turning right.” 1.52 0.75 1 “not sight a vehicle merging from a next street.” 1.94 0.74 2 “realize late that you have neglected a traffic red light.” 1.34 0.62 1 “doubt about who has preference in a roundabout.” 1.34 0.68 1 3.1.2. human errors. to measure errors, we administered a 7-item scale based on those featured in the driver behavior questionnaire (dbq) (sakashita et al., 2014) and the adolescent motorcycling behavior questionnaire (ambq) (de waard et al., 2014), adapting the former ones to the context of cycling. this scale had been previously used by puchades et al.(2018). the items asked participants to state the frequency with which they undertook such behaviors by using a 5-point likert-type scale (ranging from 1= never to 5=always). table 1 shows the seven items and subscale structure of the questionnaire, as well as some descriptive and reliability values. 3.1.3. near miss and accidents. to obtain a measure of near miss and accidents, we used two items. regarding the item measuring near miss: ‘in this past year, have you been about to get involved in an accident (either with other road users or a single accident) while you were using your motorcycle?’ (0=no, it never happened to me, 1=once, 2=twice, 3= three times, 4=four or more). the item measuring accidents was ‘in your whole life, have you ever had an accident (either with other road users or a single crash) while you were driving your motorcycle?’ (1=no, it never happened to me, 2=yes, but i did not get hurt, 3=yes, i got injured and i went to emergency services to get checked, 4=yes, i got injured and after being checked i got hospitalized). to finally obtain three cell phone related violations and motorcycle accidents: a bayesian approach 113 categories, the last two replies were merged into one category that represented accidents involving injuries. 4. statistical analysis spss version 23 and analysis of a moment structures(amos) were used for statistical analysis. different stages were adopted for analysis of the data. first, correlation coefficients among the key variables were calculated. the magnitude of effect sizes of correlation coefficients was evaluated according to cohen’s (1988) guidelines for interpreting the magnitude of correlation coefficients.” specifically, correlation coefficients of .10 are “small,” correlation coefficients of .30 are “medium,” and correlation coefficients of .50 are “large” in terms of magnitude of effect sizes. “second, we employed path analysis to test mediations, as well as direct effects, because it allowed us to estimate a model that constrains several direct effects to zero (e.g., an eventual direct effect of cell phone -specific violations on accidents, thereby, letting us test our hypotheses without the need of testing a saturated model (hayes, 2013).”provided that two endogenous variables of our model (i.e., near miss and accidents) are ordinal, we applied bayesian estimation, amos’ approach to addressing ordered-categorical data in sem models (byrne, 2010; skrondal & rabehesketh, 2005).” 5. results the participants that had not been involved in any motorcycle accident were 112 (38.7%), whereas 106 (36.6%) suffered at least one accident but did not get injured, and 81 (28.0%) of them had been involved in a motorcycle accident in which they got injured.” the number of participants that had not suffered a near miss was 103 (35.3%), and 72 (24.9%) of them had indeed been involved in one. “of those that had been involved in more than one close accidents, 44 (15.2%) participants had suffered two, 28 (9.6%) three, and 42 (14.5%) of them suffered four or more.” ten (3.4%) cases had at least one missing value, and 12 (4.0%) values were missing among all the variables measured. since the percentage of missing values is not higher of 5%, it can be considered as irrelevant (schafer, 1999). table 1 displays the subscale items of the unsafe motorcycle rider behaviors questionnaire along with their mean and standard deviation values.” as it can be seen, the cellphone -specific violation and human error reported as most frequent were “use the cellphone to respond a call” and “abruptly break in order to avoid/dodge a vehicle,” respectively. computation of cronbach alpha has been done for all items by using the reliability command of spss software and its value are reflected in table-1. 5.1. unsafe motorcycle riding behaviours effect on near miss and accidents table 2 displays the spearman bivariate correlations between the key variables studied as well as the descriptive statistics. we employed spearman’s rho due after the shapiro–wilk test results suggested the non-normal distribution (i.e., p < .001) of all the variables in the model.” human errors correlated with cellphone-specific violations (p < 0.01) and with near miss (p < 0.01). this allows us to continue to test the hypothesized model. adhikari et al./oper. res. eng. sci. theor. appl. 4 (3) (2021) 107-121 114 table 2. descriptive statistics and variable intercorrelations factors m sd range 1 2 3 4 1. human errors 1.64 0.42 1–5 – 0.19** 0.31** 0.00 2. cellphonespecific violations 1.63 0.75 1–5 0.05 0 3. near miss 1.33 1.38 – 24** 4. accidents 0.81 0.76 – “note:*correlations are significant at p < 0.05 (2-tailed), **correlations are significant at p < 0.01 (2-tailed).” figure 2. path model with bayesian estimates regarding the hypothesised model, figure 2 shows the bayesian estimates for each path. cell phone -specific violations predicted human errors (hypothesis 1) but not near miss (hypothesis 2), whereas human errors did predict near miss (hypothesis 3). in turn, near miss predicted actual accidents (hypothesis 4). mediation analysis showed that close accidents were mediating the effect of human errors on accidents (bayesian estimate = 0.085, 95% confidence interval [ci] [0.043, 0.134]; hypothesis 5). furthermore, cell phone-specific violations predicted accidents throughout its consecutive effects on human errors and near miss (bayesian estimate=0.013, 95% ci [0.003, 0.026]; hypothesis 6).” we performed a gender comparison of the path model and found differences between males and females. the subsamples of male and female participants were of 175 and 114 participants, respectively. whereas the path estimates found in the general sample were confirmed for the subsample of male participants, we found that in the female subsample, cell phone-specific violations did not predict human errors (bayesian estimate=.043, 95% ci [0.055, 0.144]), and near miss did not predict accidents (bayesian estimate=.100, 95% ci [0.013, 0.213]). moreover, we also found that the estimate of the path between human errors and near miss is lower for females bayesian estimate=.672, 95% ci [0.181, 1.155]) than for males (bayesian estimate= 1.583, 95% ci [1.051, 2.112]). we give possible explanations for this in the discussion.” cell phone related violations and motorcycle accidents: a bayesian approach 115 6. discussion the objectives of the current study were to examine the impact of cellphonespecific violations and human errors on the likelihood of near miss as well as the indirect effect of such behaviors on actual accidents among motorcycle riders. moreover, it also aimed to unveil any gender differences in the relationships between the unsafe behaviors”(i.e., cellphone-specific violations and human errors) and the hazardous outcomes (i.e., close accidents and accidents).” “it is important to note that, differently from previous studies, our findings focused on cellphone -specific violations as a distinct type of violation, whereas other research had differentiated between more common and exceptional violations (e.g., feenstra et al., 2011). the rationale for this was that, as previously explained, such type of violations was thought to increase error occurrence by its effect on visual detection and perception. in addition, we wanted to examine whether such behaviors were indeed predicting human errors and near miss or, due to eventual compensatory behaviors (goldenbeld et al., 2012) they were not associated.” path analyses confirmed all the hypotheses except for hypothesis 2, that is, cellphone-specific violations did not directly predict near miss. nevertheless, it did predict human errors (hypothesis 1) in the general sample, thus bringing about the point that cellphone-specific violations may indeed involve more unsafe behaviors dependent on information processing, instead of leading to more compensatory behaviors. nevertheless, there is still the need to explore whether this relationship between cellphone-specific violations and errors is also due to a confounding variable such as motorcycle rider’s safety concerns. this way, motorcycle riders less concerned about safety could be committing more human errors and using more frequently the cellphone while motorcycle riding. errors predicted near miss, and these, accidents. our data only partially supported hypothesis 5 because there was no direct effect from cellphone -specific violations on near miss, impeding an indirect effect of the former on accidents unless considering the role of human errors.” moreover, the results confirm a mediation effect proposed in hypothesis 6, which explains the effect of cellphone-specific violations on accidents throughout human errors and near miss. these findings differ from those of feenstra et al. (2011) according to which human errors and violations (common and exceptional) were directly predicting near miss. in our study, only human errors predicted near miss frequency. moreover, they found exceptional violations to predict accident severity and human errors to predict accident frequency, whereas we did not find significant correlations between any unsafe motorcycle riding behaviors (i.e., human errors and cellphone -specific violations) and accidents. twisk et al. (2015) found errors, but not violations themselves, to predict accidents, thus concurring with our findings. nevertheless, it is worth noting main differences between these previous studies and our research. we conducted the study among adults and not adolescents, thus, age differences could be explaining some of the differences in findings.” moreover, we have found gender differences in the effects of cellphone-specific violations on errors and that of near miss on accidents. that is, the results found in the general sample were confirmed for men, whereas cellphone-specific violations did not predict human errors and neither near miss did predict accidents in the female subsample.” cellphone-specific violations not predicting human errors in the female subsample could be due to gender differences in perception and attention.“we adhikari et al./oper. res. eng. sci. theor. appl. 4 (3) (2021) 107-121 116 offer two possible sets of explanations next: one theoretical and another one concerning statistical artefact. on the one hand, previous research in psychology of individual differences has found that women are quicker in identifying and discriminating objects visually, have a wider peripheral vision, and are more likely to estimate situations as risky (ellis et al., 2008). moreover, feenstra et al. (2011) found that boys tended to engage in riskier behaviors, thus suggesting that women might adopt a less risky approach to motorcycle riding and, therefore, might undertake compensatory behaviors while committing cellphone-specific violations. this could diminish the effect of using cellphone while motorcycle riding on the human errors committed. a possible explanation for the fact that near miss did not predict accidents in the female subsample can be found in the smaller prediction of near miss by human errors. this can be interpreted as near miss being more dependent on variables other than human error in women. thus, the frequency of hazardous outcomes such as near miss, and accidents by extension, is not related to human error, perhaps due to women’s eventual less risky approach to motorcycle riding derived from their higher likelihood of estimating a situation as risky in comparison to men (ellis et al., 2008).” it is important to note that, differently from previous studies, our findings focused on cell phone-specific violations as a distinct type of violation, whereas other research had differentiated between more common and exceptional violations (e.g., feenstra et al., 2011). the rationale for this was that, as previously explained, such type of violations was thought to increase error occurrence by its effect on visual detection and perception. in addition, we wanted to examine whether such behaviours were indeed predicting errors and near miss or, due to eventual compensatory behaviours (goldenbeld et al., 2012) they were not associated.” fewer risk-taking behaviors could be reducing the motorcycle riders’ own influence on their accident frequency, leaving it up to other road users’ behaviors, and therefore conditioning the occurrence of near miss and accidents to eventual and more random encounters with other distracted or irresponsible road users. on the other hand, a possible explanation to the lack of association in the female subsample could be due to a lack of statistical power provided a not big enough subsample size. even though there is no single answer about whether a sample is large enough to conduct sem, a common rule of thumb is that there should be 20 observations per parameter that needs to be estimated in the model (kline, 2016). therefore, with 12 parameters to be estimated in our model, both subsample sizes are too small to obtain adequate statistical power. thus, not finding an association between cellphone -specific violations and human errors, and near miss and accidents could be due to the relatively small subsample size. thus, more research with bigger samples is needed to clarify whether these differences exist or are due to statistical artefact.” 7. limitations there are some limitations to this study. on the one hand, we used a self-reported questionnaire to measure unsafe motorcycle rider behaviors and safety outcomes (i.e., near miss and accidents). this entails two limitations: (1) memories of accidents and near miss (e.g., chapman & underwood, 2000), as well as those of unsafe behaviors that do not depend on conscious control (i.e., errors), may not be accurate cell phone related violations and motorcycle accidents: a bayesian approach 117 according to previous findings (bradburn et al., 1987; twisk et al., 2015).” previous research suggests that an estimated 80% of the near miss may be forgotten after 2 weeks of the event (chapman & underwood, 2000). “moreover, (2) common method variance (cmv), which refers to the amount of variance attributable to the use of the same method to measure related variables (podsakoff et al.,2003), constitutes a limitation to our study given that we measured all the variables using self-reported questionnaires. on the other hand, online surveys advertised on websites might involve self-selection bias and, therefore, the resulting sample might not be representative of the whole population of motorcycle rider. 8. conclusion this research has numerous societal and practical implications from which we have concluded regarding future research needs. cellphone -specific violations is introduced in the model and conceptualized them as a type of violation that is affecting the occurrence of unsafe behaviors relying on human errors in men, but not in women. “furthermore, for men, we have found them to anticipate near miss and accidents through an indirect effect. this entails that cellphone-specific violations might have an effect on other unsafe behaviors and, therefore, offers a broader understanding of how such behaviors end up leading to eventual accidents. that nevertheless, there might be some confounding variables that could explain the effect of cellphone-specific violations on human errors such as motorcycle rider’s safety concerns.” our findings suggest that cellphone -specific violations appear to contribute to the frequency of errors while motorcycle riding among men. furthermore, both human errors and cellphone-specific violations predict accidents throughout an indirect effect on near miss. finally, these findings contribute to examine possible gender factors that can moderate the relationship between unsafe motorcycle riding behaviours and accident risk.” in conclusion, this study has highlighted a number of relationship between near miss and accidents by motorcycle riders, in particular the use of cell phones while riding. the findings suggest a number of key challenges for road safety in bhubaneswar, india, not least the relatively high rate of accident involvement associated with cell phone use while riding a motorcycle. addressing these challenges is an important task given the dominance of motorcycle use in bhubaneswar, india and their increasing numbers each year. the findings of this study provide solid evidence on safety issues of cell phone use while riding a motorcycle, which should be utilized in educational programs and publicity campaigns. given the relatively high near miss and accidents associated with this behaviour, stronger police enforcement efforts should also be prioritized. despite some limitations, the study still provides a significant contribution to understanding cell phone related specific violations in developing countries by helping decision-makers to define safety strategies to minimize motorcycle riders’ near miss and accidents. in further stages of this research, a survey could be conducted to validate its findings. using mixed-methods analysis is also recommended for comparing various results and providing valuable lessons on developing a more sophisticated framework. apart from various factors, some adhikari et al./oper. res. eng. sci. theor. appl. 4 (3) (2021) 107-121 118 prominent factors like individual and environmental factors may be considered for future research. references backer-grøndahl, a., & sagberg, f. 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(2012). mobile phone use while driving: predicting drivers’ answering intentions and compensatory decisions. safety science, 50(1), 138-149. © 2021 by the authors. submitted for possible open access publication under the terms and conditions of the creative commons attribution (cc by) license (http://creativecommons.org/licenses/by/4.0/). cell phone related violations and motorcycle accidents: a bayesian approach biranchi adhikari 1, ajay behera 2*, rabindra mahapatra 1, harish das1 1. introduction 2. literature review 3. methodology 3.1 descriptive statistics 3.1.1. cell phone specific violations.“ 3.1.2. human errors. 3.1.3. near miss and accidents. 4. statistical analysis 5. results 5.1. unsafe motorcycle riding behaviours effect on near miss and accidents 6. discussion 7. limitations 8. conclusion references plane thermoelastic waves in infinite half-space caused operational research in engineering sciences: theory and applications vol. 5, issue 1, 2022, pp. 1-19 issn: 2620-1607 eissn: 2620-1747 doi: https://doi.org/10.31181/oresta290122001e * corresponding author. mohkholy5@hotmail.com demographic and institutional determinants affecting manpower’s development at the government sector (a comparative study) mohamed a. elkhouli 1,2 1 sadat academy for management science, department of mathematics and statistic, cairo, egypt 2 american university in emirates, college of business administration, dubai, uae received: 07 october 2021 accepted: 24 december 2021 first online: 29 january 2022 research paper abstract: this study aimed to apply the measurement of the impact of determinants of the change management process (cmp) on the competitive performance (cp) of the employees at the government sector in a practical environment by comparison between the employees’ expectation at the government of ras al-khaimah compared to the expectation of employees at ajman government. thus, the emirate of ajman within the uae was selected to apply the same scale of measuring which has same conditions of the work of the government sector and similar geographical aspects like the emirate of rak. the results have shown a significant impact of the role of direct determinants which were assumed by the current study in the influence of improving the competitiveness of the employees during the implementation to any change management process planned at the level of government sectors. there were five key determinants respectively in terms of impact strength, and those determinants were creation and innovation, institutional values, quality and excellence systems, administrative and legal aspects and finally, the role of leadership. key words: demographic, government sector, competitive performance, cmp. 1. introduction the determinants of change management have a significant role in developing the competitive performance of the manpower within the organizations. both of management commitment and quantitative evaluation are considered important factors to resist potential change to reinforce employees' performance (rees et al., 2007). there is a positive relationship between leadership style, human resource practices, and involvement in cultural traits of organization in the achievement of change management. application of the change process may improve decision areas such as benchmarking, executing best practices, adopting quality practices, and human resource policies (oon & ahmad, 2014). the association of change elkhouli/oper. res. eng. sci. theor. appl. 5(1) (2022) 1-19 2 management professionals (acmp) defines change management as the practice of applying a structured approach to transition an organization from a current state to a future state to achieve expected benefits. change management is considered a process used for managing the transition of the organizational culture of change to the employees' side in any organization based on critical factors like the incentives and motivation systems in order to guarantee that each change within the organization produces the planned outcomes (shah, 2016). generally, the report of global competitiveness in 2018 has ranked the governments according to 12 pillars that were weighted equally. these pillars including the following: institutions, infrastructure, information, and communication technology (ict) adoption, macroeconomic stability, health, skills, product market, labor market, financial system, market size, business dynamism, and innovation capability. although the vital impact of the change process on the competitive performance inside the institutions has targeted by some literature, its competitive environment facing new challenges unfolds over time and requires more to examine (finger et al., 2014). concerning the concept of competitiveness is defined as the ability to provide any organization more effectively and efficiently than the relevant counterparts or competitors in the same field and at the industry level. the competitiveness was defined as the ability of the organizations to achieve sustained success compared to its competitors (enright et al., 1996). the competitive performance means the best performance that an organization pursues in order to be more productive than its rivals or competitors. in order to earn and maintain its leading advantage among other organizations, it must be able to remark a higher comparative or differential value than its counterparts in the same field of the comparison at the national or international level. the concept of competitiveness is a distinctive position of the organization where its competition will be at its greatest possible level compared to the other organizations (schwab, 2017). it was noted a seldom found of academic endeavors that be related to any paper or research clearly can shed the light on examining the possible drivers of change management affecting the performance of the government sector in the arabic countries and uae specially. it also did not address which one of these drivers has the most impact on the performance of government sector employees. yet, it is noted that the link between direct and indirect drivers of change management doesn't sufficiently examine to determine it affecting the perceptions and convictions of the employees inside this sector, so the impact of these drivers was assessed from the perspective of the employees as they are considered the focus of any meaningful change of institutional development. thus, this study pursued seriously to create more meaningful value to decision makers and programs planners regarding the role of these determinates of change management in the government sector in order to reinforce the possibilities and enablers for optimizing the competitive performance of the employees in an optimal manner. the employees are considered as one of the stakeholder's categories inside each organization that they have needs and contribute to the effectiveness and the efficiency of the organization's performance to be more valuable at the highest level of the competitiveness desired by the decision-makers. indeed, any organization needs a new level of competitive performance, and thus it will require a change process within the workplace to improve the performance of employees until they reach the desired competitive performance that led to increased competition and the demographic and institutional determinants affecting manpower’s development at the government sector 3 demands on institutions to continuously, in particular, this insight is still suffering from lack of interest in the mena region in both of private and public sectors alike. consequently, this paper aimed at applying the measurement of the impact of determinants of the change management process (cmp) on the competitive performance (cp) of the employees at the government sector in a practical environment by comparison between the employees’ expectation at the government of ras al-khaimah compared to the expectation of employees at ajman government. thus, the emirate of ajman within the uae was selected to apply the same scale of measuring which has same conditions of the work of the government sector and similar geographical aspects like the emirate of rak. the main objective of this study to reach a confirmation or disprove about the most decisive determinants targeted in the statistical analysis of this study. and the extent of the effectiveness the experimental group of the employees at the government sector of the ras al khaimah. briefly, this study will consist of eight sections in terms of section 1 explains introduction about the importance of examining the change management determinants within the organizations to increase the competitive performance of the employees, then section 2 presents an overview about the case study groups including the key characteristics and features, then section 3 will touch a base regarding some literature review shed the light on the importance of addressing this topic by the current study, while section 4 has focused on showing how using case study for practical implication at the government sector to realize the target determinants of change management affecting on the competitive performance of employees, then section 5 shares the main results and findings which has reached by this comparative study based on both control and experimental groups, then section 6 provides in-depth managerial implications regarding this study, then section 7 discovers the most important conclusions and limitations facing the researcher, then finally section 8 discloses the figures and tables are relevance to main results. 2. case study groups overview this study will pursue to test if there are close results about the perspectives of the employees at the government sector about the impact of direct determinants of the cmp on their performance for both of the control group, which representing the ajman government employees of and the experimental group, which representing the rak government employees. the future scope of using the finding and conclusions of this study about the potential key beneficiaries could be summarized by listing the prospective recipients for the research, as follows: decision-makers at the government sectors in the uae and arab countries institutional excellence programs adopted by the governments government sector employees professional development programs within government entities. private sector institutions have productive partnerships. civil society organizations for competitiveness and global leadership. international organizations interested in human, sustainable development. committees of innovation and creativity. elkhouli/oper. res. eng. sci. theor. appl. 5(1) (2022) 1-19 4 community, partners, and clients for the government sector. experts and planners interested in the development of the public sector. professional organizations accredited to international standards 3. literature review the literature review does not ensure coherent recommendations for adopting determinants or drivers regarding cm; obviously, the most specific area of cm in the united arab emirates (uae) that has an impact on the employees' performance has not been studied yet. as well as, less specific literature was addressed by the cm in arab countries in general. consequently, few articles and studies were discussed the consequences and drivers of change management that may be effective to affect such as the following: one of studies has been demonstrated that using both of the management commitment and quantitative evaluation methods are important factors to resist possible change by employees (rees et al., 2007). a study investigated the relationship between some factors in the change management process such as leadership, human resource and organization's culture from one side and the operational excellence of the organization from the other side (fok-yew & ahmad, 2014). another study has shown a challenge regarding the lack of research previous studies about the change management inside the uae and examining the implications for government and business, and decision makers (baddah, 2016). there is another study that it has also referred that process re-engineering programs in the business have an impact on corporate change strategy, and the organizational change process has not received adequate attention inside many business institutions (sikdar, 2014). there is one of the studies that urges the role of cmp to adopt the organizational strategy developed where this kind of strategy has supported many organizations to become successful example as in the uae, and contribute in creating the positive impact on overall organizational performance as well (al-khouri, 2012). on top of that, one study has revealed that change is a vital issue in all types of organizations, and improving the performance of business is the focus of change. it has emphasized on the need to examine the similarities and differences among the determinants of cm (bashir and soomro, 2012). leadership is considered the main champion in causing change and the top of key determinants to each organization, as the leader is willing to take the risk and establish an environment conducive to the change in a competitive world. leadership is an important driver of the change that can take place and build the momentum required to improve the performance of the employees (ragaa, 2005). leaders need to be trained and educated to limit the resistance to change within the organizations (bateh et al., 2013). effective work environment provides the basis for cmp that includes the development of the knowledge sharing culture among the employees as well as the development of their performance and skills that needed to enable effective knowledge management for the ideal competitiveness (damodaran and olphert, 2000). the use of a continuous improvement system in the development of institutions, the government organizations in particular, directly depends on applying the quality and excellence systems (qes) as one of the success factors to support cm culture towards the planned outcomes (trkman, 2010). the innovation the demographic and institutional determinants affecting manpower’s development at the government sector 5 and creation (ic) can put a different climate of competitiveness among the employees that could be contributed to enhance the performance (al adwani, 2001). change is necessary for organizations that are seeking to raise low performance by improving their motivations and incentives (mi) systems over all units and employees. thus, the organizations will be able to stay competitive and gain more market share but are usually faced with obstacles and problems that apply these systems unfairly or inequitable (al hawi, 2014). teamwork have been widely acknowledged as a critical success factor (csf) in cmp for each organization adopted the change for the development of institutional performance (apostolou et al., 2011). it has noted that cmp should be reactive through responding to the new changes by reinforcing the institutional values (iv) imposed on the employees to accept and support the culture of the organization. thus, the officials should be proactive to deal with all challenges including the resistance of employees in order to achieve the target objectives (sacheva, 2009). this era has new institutions adopted the change processes through continuous trials to reinforce their internal operations, including administrative and legal aspects (ala) that has a critical effect on the performance of individuals or institutions for the competition according to industry criteria (stamatis, 2015). one of the studies have shown that over 33% of employees have failed to meet their stated objectives were considered poorly performing due insufficient resources or not availability of resources to achieve the desired change appropriately (sayers and al-hajj, 2014). one of the studies has shown that training and organizational learning should be so important for ensuring the effectiveness of cmp within modern enterprises, and to quantify the importance of this factor for the improvement the performance of employees and for the institutional development as well (stamatis, 2015). not only is cmp a popular culture within the institutional performance methodology, but also it has not yet been properly theoretically or practically grounded over the government institutions in developing countries according to established standards and bases to support the institutional development systems optimally (trkman, 2010). as it has noted the effects of change management on the performance of firms where there is a relationship between management change and organizational effectiveness. management of change connects to people’s encounter and the organizational process, and it has been referred that the change is inevitable and managers all over the world are adapting to changing market conditions and at the same time facing the need for creating a proactive rather than a reactive managerial system (daniel, 2020). in addition, another recent study has noted that leadership plays an important role in accepting changes and challenges so that company can attain predetermined goals or objectives in a more effective manner, especially in unpredicted global pandemics situations. it has highlighted the importance of effective leadership and people management in the transformation of an organization and the workforce as the source of competitive advantages and as a contributor to achieving a high level of performance and purposes even in the worst pandemic situations. this study has concluded that leadership is an important resource of the business organization, in the implementation of changes forces by the external environment. to meet the aspirations of the organization, resilient leadership (junnaid et al., 2011). elkhouli/oper. res. eng. sci. theor. appl. 5(1) (2022) 1-19 6 4. case study for practical implication the case study was applied on the finance department as a one of the government entities in the emirate of ajman. the selection process to this entity was based on a set of certain factors in favor of the application at this department in ajman. firstly, it has the same nature of work and the conditions of regulations that the entities are witnessing at the government sector of rak. this entity is a listed in the government of ajman, which the classification of all entities of ajman are based on that have effective partnership relationship with the rak government. as well as the research sample of employees was considered in order to match the criteria of the randomly selection by the survey to ensure the effective comparison between both two groups of study whether experimental or control alike. thereby, this institution meets all the basic and formal requirements requested by the current study conditions. the statistical analysis based on the survey has been done without the participation of this entity at the scope of this analysis. thus, the same questionnaire of survey was conducted only at finance department of ajman to determine if this selected entity is convenient for the case study. the survey aimed to apply on all level management at this entity where employees were selected randomly to involve in this questionnaire. the random sample was 30 employees for control group (ajman government employees) while the random sample was 100 employees for experimental group (rak government employees) whose were selected randomly to involve in this questionnaire during a specific time and a certain period, which began from mid of november to the end of december 2020. as this questionnaire was distributed and collected to covers the sample size required for the purpose of statistically acceptable analysis so that it was not allowed to be less than 30 units for the purpose of statistical analysis to both control and experimental groups in separately, especially the normality distribution condition. table 1 shows the overview of all background characteristics of the target group for case study employees involved in evaluating of the decisive factors or determinants affecting the performance of employees at the government sector. table 1. the background characteristics for the respondents’ sample of case study employees “control group targeted to compare with the experimental group” basic variables freq. % gender males 21 70% females 9 30% age from 189 70% from 31-45 21 30% nationality national 11 37% expatriate 19 63% education bachelor level 17 57% higher studies level 13 43% no. of experience from 5-10 years 10 33% more than 10 years 20 67% level of expertise local expertise 14 47% regional expertise 16 53% monthly income more than 15000 aed 18 60% from 15000-8000 aed 12 40% source: spss outputs. the demographic and institutional determinants affecting manpower’s development at the government sector 7 the results of table 1 revealed the main features of the control group in the case study that the percentage of male employees was the highest by 70%, while female employees by %. and the percentage of expatriate employees was the highest (63%) and nationals (37%). in general, the results try to reflect the demographic characteristics of the survey sample in the case study targeted. to acquire more confidence regarding sustainability to the reliability of the questionnaire tool used in the case study which is the same used in the main survey. the reliability of this tool was again calculated based on the size of the target group in the survey of case study. the value of the reliability of questionnaire has amounted for (0.985) using the α-cronbach method and the results of this analysis can discover in the appendix no.7 at the end of the current study. this value of this coefficient has asserted on the power of stability of this tool to measure what the purpose of this study in which there was more reliable about the potential results from this survey. figure 1. the total percentage to the impact of direct determinants of cmp affecting the competitive performance cp for both of control and experimental groups the figure 1 shows that there was not huge difference between the evaluations of employees to the impact of direct determinants of cmp in both of two groups whether experimental or control in which the delta of means derived by the assessments of both groups at only zero value clearly. there is only one way to compare the averages of evaluations for both control and empirical groups on the expected impact of direct determinants of change management process on the competitive performance of employees at the government sector by examining if there is a significant difference between those averages for each one of direct determinants separately. the figure 2 shows the evaluations about impact of the target direct determinants of cmp have large similarities in connection with the point of views to both of two groups based on the percentages of impact for each factor separately. this could lead to the conclusion the case study is typical direction to confirm on the results of main sample or survey. accordingly, the next figure shows the comparison of the percentages of the evaluations of the employees for the impact of the direct determinants (10 drivers of cmp) on their expected performance. elkhouli/oper. res. eng. sci. theor. appl. 5(1) (2022) 1-19 8 figure 2. the relative importance of direct determinants of cmp affecting the competitive performance cp according to the comparison between control and experimental groups the figure 2 shows that the percentages of employees' evaluations for the impact of direct determinants of cmp reflect somewhat how the extent of congruence in these evaluations between two samples whether experimental or control. from the previous figure, these percentages have shown that the highest percentage for the expected impact of direct determinants of cmp affecting the performance of employees was for training, learning organizational, teamwork culture, and leadership, respectively, in terms of the power of impact to improve the competitive performance of employees within the government sector, according to the perspectives to both of the control group represented for the case study and the experimental group which is relevant to the main survey application alike. the table 2 shows the % of change rate in the means values of evaluations for the impact of these direct determinants through the evaluations of the experimental group sample and then after re-applied process again based on the control sample evaluations. both samples have homogeneous evaluation of answers about the impact of those direct determinants in terms of there were three determinants had highest ranked and two had lowest ranked are identic over the assessment scale, and there is no noticeable change rate in the averages of evaluations regarding the total score of the impact over the change from group to other. the demographic and institutional determinants affecting manpower’s development at the government sector 9 table 2. comparison the change % of experimental group to control group in decisive factors d e ci si v e f a ct o rs e x p e ri m e n ta l g ro u p c o n tr o l g ro u p % o f c h a n g e r a te e v a lu a ti o n c h a n g e leadership 12.2 12.1 1% ▲ work environment 11.8 11.6 2% ▲ quality and excellence systems 11.6 11.2 3% ▲ creation and innovation 10.8 11.1 -3% ▼ motivations and incentives 11.5 10.7 7% ▲ teamwork culture 12.7 13.1 -3% ▼ institutional values 11.5 11.8 -3% ▼ administrative and legal aspects 11.7 12.1 -4% ▼ availability of resources 11.6 12.0 -3% ▼ training and learning organizational 12.5 13.0 -4% ▼ total score 117.8 117.8 0% ⬌ in general, the results in above confirms the same conclusion of the experimental group applied to the cmp including the direct determinants targeted by the main survey, compared to the control group results to which this system was not applied. thus, this indicates at the same time to the importance of those determinants in particular when adopting any change process aimed at developing of staff performance within the government sector of the united arab emirates, especially as the scope of application of the survey tool was different in the application of the control group which is representative of the case study compared to the experimental group, which represents the main scope of the current study, and both groups approximately reached for close averages in the assessment scores according to the use of the same tool in order to determine the impact of those factors or determinants of change. 4.1 case study explanation one of the main motivations that led the researcher to re-examine the determinants of the change management process based on the case study approach is to check to which extent of the positive impact of both direct and indirect determinants of change management in a new scope away from the main scope of this study. as well as to eliminate the bias factor resulting from the interest of implementation the change management systems within the government of ras al khaimah, and to ensure the ability of those determinants of the study target to bring about the desired change which aimed at developing the competitive performance of government employees optimally. elkhouli/oper. res. eng. sci. theor. appl. 5(1) (2022) 1-19 10 further, the application to case study will consider the potential influence of the researcher caused to the initiative to select rak as a practical field to test the hypotheses of study compared to another location. as the same time, the case study has to consider both of the time for implementation and reducing the volume of complexity during the analysis derived that leads to efficient findings to be easy to interpret in comparison with the main survey. this section supports the basics of upcoming parts that contribute to study the differences between the averages’ evaluation of case study group as a control group to study the impact of planned factors or determinants which were considered at the beginning of the study by determining how those averages differ statistically with the averages’ evaluation of main sample of survey as an experimental group. besides the criteria for selection the organization to apply this survey as a case study were determined without the researcher could influence the activities planned to implement this approach. this initiative has a set of key points that make it useful to select any organization for the implementation purpose to this tool as control group involved in the case study effectively as follows: the minimum size acceptable of control group to study the impact of direct determinants of change affecting a group of employees should be employees in only one institution. the researcher should be able to apply this method using the tool of scale based on his professional expertise in the research and development field as a project manager to ensure the controlling and implementation of the required activities and tasks in line with the measurement process planned. consider the general direction and the flexibility of the organization selected for the case study before the implementation to prevent any external impact impeding the achievement of the goal of the application or effect on the employees participated to accept a unified specific orientation. the need to increase the employees' awareness before the application of case study approach about the importance and purpose of this survey and what are the expected benefits at the short and long term for their performance alike. the researcher should thereby change his approach in light of the differences resulting from any feedback of case study to identify and note the requirement specifications to develop the hypotheses of the study in favor of the competitive performance desired of the employees at the government sector. the organization during selection should pursue to save more support and transparency for the researcher without any visible monetary return or any expected resistance at the implementation of case study according to the target scope by the survey. develop the tool of measurement was generated by the objective of case study in order to increase accuracy and calculability of timeline allowed to achieve along with administrative conditions of the alternative location to apply the case study. the organization selected as a case study have to adhere in the application of transparency during the selection for staff involved in the survey in order to ensure effective channels to adjust and prioritize tasks for the continuous improvement purpose. the demographic and institutional determinants affecting manpower’s development at the government sector 11 to recognize the scope of the change management process towards developing the competitiveness of employees based on the direct determinants at each organization that has the ability to apply this system, there is a need to illustrate listing of factors incurred through the implementation of this system within the government sectors. therefore, the organization targeted in the case study should take over these factors that: measure the impact for change management process needs the sufficient allocation of required resources such as a lot of time/efforts/ staff. ensure the direct determinants of cmp should be measured and quantified according to the same tool used before in the main survey. ensure that there is no any direction affecting on the answers of employees regarding each question. determine a specific time to distribute and collect the sample size required so that it was not allowed to be less than units for the purpose of statistical analysis, especially the normality distribution condition. conduct the comparisons between both of the experimental and control group that are suitable to test the statistically differences in appropriate manner to check validity of the positive impact for the direct determinants of cmp. 4.2 methodology of case study the forthright objective from the use of case study survey was determining the extent of effectivity of the direct determinants in the change management process as decisive drivers affecting on the competitive performance on the employees at the government sector in a different location far way about the main scope of the current study. the survey of case study was done using the same questionnaire distributed to the participants in the main survey. as such, two surveys were used by this study, to examine and test the importance of the direct determinants of cmp, the first survey at the beginning to apply on the target employees as an experimental group, while the second survey at the late phase of this study through the case study as a control group. therefore, the comparison was conducted between both of these groups to determine statistically differences of the averages’ evaluation of the employees about the impact of the direct determinants, thus the valued importance of these drivers could be determined in affecting on the performance of employees. on this way, throughout the effective implementation of case study based on the comparison with the results of main survey at the same time, the officials and planners at the government sector can notice the importance of the most important determinants of change management process which will be able to develop the performance of employees. thus, this could enable them to generate more appropriate plans, activities, and policies supporting the directions regarding these factors optimally. to ensure the effective participation of the target employees during the survey as a case study, and to avoid ambiguities could be raised when filling out the questionnaire used, the objective of this survey was provided to all employees elkhouli/oper. res. eng. sci. theor. appl. 5(1) (2022) 1-19 12 randomly by e-mail to interact and to increase their awareness before the time determined to conduct the survey in an adequate period of actual implementation. all questions formulated in the first survey based on a 5-point likert scale were the same questions in the second questionnaire used for the case study without any change in the formulation or measurement. thus, it was expected that this will generate significant differences in the responses of the employees between the first and second round of using the same survey twice in two different geographic areas so that government sector entities were targeted. so, there is no any difference of scales that could break inconsistency of the measurement tool used, in addition to the content of the questionnaire for both groups are completely similar while the size of both samples was differ according to the type of each group. the survey of this case study was conducted by a research fellow to avoid the factor of biased and affecting the employees participated or their directions as well. whereas the researcher was just a supervisor on the data collection process in order to ensure the right procedures in place to facilitate the data entry phase. then spss program was used to code and analyze the data collected by the sample of case study and then was combined with the data of main survey considering the unique code which was allocated to each sample for the purpose of statistical methods that will be used. 4.3 data analysis of a case study the data analysis in this phase has focused on the processing of data derived from the employees electronically in line with the nature of statistical tests targeted to be applied to test the differences statistically between the two groups whether experimental and control in connection with the impact of direct determinants of cmp. as a result, all questions were coded to analyze the data which were ranged from negative evaluation of the impact of factor (= 1 or "strongly disagree") to totally important impact of factor (= 5 or "strongly agree"). all analyses were related to the calculation of the frequencies of responses and the averages of values to each factor or determinant targeted by the scale. t-test for independent samples was used to examine the significant differences between the two groups which were drawn from two different populations or locations, and this will be by determining the differences in the averages of employees' evaluations in both groups with regard to each direct determinant. furthermore, multiple regression analysis was used only according to the survey data of the case study in order to identify the most important determinants within the change management process affecting on improving the performance of employees. then the results derived from this analysis should be compared with the results of the main survey which are subject to the researcher's experience, to strongly emphasize on the role of those determinants derived from regression analysis based on the same results of both groups, and the importance of targeting them urgently in any system of change management at the level of government institutions to serve decision-making within this sector specifically. the demographic and institutional determinants affecting manpower’s development at the government sector 13 5. results and findings in this part, the study pursues seriously to compare the impact of direct determinants on the experimental group that could be exposed to the interest by the change management culture with another group that did not receive this interest to prove definitely the importance of these determinants in influencing on the competitive performance of employees within the government sector. hence, t-test of independent samples was precisely used to examine the existence of statistically significant differences in determining the values of arithmetic averages or not and that may reflect the positive impact of direct determinants of change management process between both of control and experimental groups. the result of this testing will be fruitful ideally in favor of the decisionmaking at the government sector of rak in particular. so, the hypothesis testing of t-test of independent samples was formulated to investigate the source of difference in the evaluation process by the target employees either by case study or by main survey according to the kind of group, as follows: there are no significant differences in the evaluation process for the impact of direct determinant of cmp according to the type of group of employees (control / experimental). consequently, two sub-hypotheses were derived from the main hypothesis testing inabove for the data analysis purpose, and then were also formulated as follows: null hypothesis h0: (µ1 the mean of control group = µ2 the mean of experimental group) alternative hypothesis ha: (µ1 the mean of control group = µ2 the mean of experimental group) the use of this test resulted in the data analysis outputs as in table3. the results of table 3 have shown that there was no any statistically significant difference at a level less than 0.05 between the averages evaluations of two groups of employees according to the type of group (control/ experimental) about measuring the expected impact of each one of the direct determinants of the change management process affecting the overall performance of employees at the government sector. further there was no statistically significant difference in the total scores of scales as a whole between both of groups as well. this result clearly indicates the convergence of the point of views between the employees in both groups about the percentage of the impact of each one of the direct determinants separately within any change process targeted on enhancing their performance and leading them to the desired competitiveness over the level of government organizations. at the same time, it has emphasized the importance of the findings concluded of this study using the experimental group in the main survey. this will greatly enhance the confidence in the results of this research by the decision makers, officials, planners and those interested in issues of excellence and institutional development and human resources development both within the government sector in ras al khaimah in particular or at the level of the united arab emirates in general. elkhouli/oper. res. eng. sci. theor. appl. 5(1) (2022) 1-19 14 table 3. t-test of independent samples to examine relative differences in the impact level of the direct determinants of cmp on the competitiveness performance according to case study group determinants case study group n mean sd t. test sig. leadership control 30 12.1 2.9 -0.259 0.796 experimental 100 12.2 2.2 work environment control 30 11.6 2.7 -0.451 0.653 experimental 100 11.8 2.3 quality and excellence systems control 30 11.2 2.8 -0.706 0.481 experimental 100 11.6 2.4 creation and innovation control 30 11.1 2.8 0.635 0.527 experimental 100 10.8 2.5 motivations and incentives control 30 10.7 2.0 -1.512 0.133 experimental 100 11.5 2.7 teamwork culture control 30 13.1 2.3 1.165 0.246 experimental 100 12.7 1.8 institutional values control 30 11.8 2.9 0.653 0.515 experimental 100 11.5 2.2 administrative and legal aspects control 30 12.1 2.8 0.882 0.379 experimental 100 11.7 2.2 availability of resources control 30 12.0 3.1 0.900 0.370 experimental 100 11.6 2.1 training and learning organizational control 30 13.0 2.5 1.175 0.242 experimental 100 12.5 2.1 total score control 30 118.8 24.4 0.267 0.790 experimental 100 117.8 15.9 (*) significant at the level less than 0.05. source: outputs of spss program. for further in-depth analysis, the most important determinants of change management will be identified from the viewpoints of the sample of control group which represents the case study, in which these determinants have a significant role in predicting the level of improvement of the employees' performance. so, this will be clearly compared with the results of the experimental group involved in the main survey. therefore, multi regression analysis was used by the "stepwise" method to determine which the most important determinants of the change management process have the highest significant role in predicting the expect performance of the government employees for developing the competitiveness level. besides, this method will derive a multi regression model that includes a set of independent variables which have the highest impact in predicting the value of the dependent variable (overall performance level of the employees), while some independent variables will be removed from this proposed model which have either multicollinearity or less impact on the dependent variable targeted by this model. as the findings of this analysis will show in table 4. the demographic and institutional determinants affecting manpower’s development at the government sector 15 table 4. the coefficients of regression model equation using stepwise method for examining the impact of the most important determinants in predicting the level of competitiveness performance of the case study employees variables b std. error beta t sig. the fit of proposed model r2 = 0.988, f = 791.951* (constant) 13.501 .140 96.101 .000* institutional values 3.719 .072 .447 51.4 .000* administrative and legal aspects 2.655 .020 .299 132.139 .000* creation and innovation 4.371 .037 .495 116.638 .000* quality and excellence systems 2.9 .038 .337 78.0 .000* leadership 1.101 .080 .132 13.790 .000* (*) significant at the level less than 0.05. source: outputs of spss program. the results of multi-regression method in table 4 indicate that the value of r2 amounted for 98% and was statistically significant at a level less than 0.05. this value of r2 means that this proposed model has the ability to interpret about 98% of the total variance in the expected performance of employees and predict it very well for the next years. moreover, the results show the significantly of regression model using the anova variance test where the value of f 791.951 is statistically significant at a level less than 0.05, which indicates the significance of the proposed model of regression to study the relationship of the explanatory variables and the response variable in order to predict the expect performance of employees. thence, the equation of multi regression model can be formulated as follows: the expected performance of employees: 13.501+(3.719*iv)+(2.655*ala)+(4.371*ci)+(2.930*qes)+(1.101*lshp) regression analysis showed that there was a consensus among the employees in both control and experimental groups about only five key direct determinants without the rest variables or determinants that have the ability to influence and predict the level of competitive performance of employees within the government sector institutions. those five key determinants were creation and innovation, institutional values, quality and excellence systems, administrative and legal aspects and leadership respectively, in terms of their power of impact in predicting the value of the dependent variable. this conclusion will strongly confirm to the decision makers on the role that these determinants in particular can play in any process of change at the level of government institutions aimed at working to develop the performance of employees and their capacity building in order to push them to the competitiveness required to be achieved at the level of the state. especially in light of the uae leads in advanced ranks at the international level in the reports of global competitiveness in all fields, chiefly the key indicators supporting the development of human capital. 6. managerial implications in a nutshell, the main findings of the case study can be summarized in the following key points: elkhouli/oper. res. eng. sci. theor. appl. 5(1) (2022) 1-19 16 there were no statistically significant differences in the averages of the evaluations of employees about the impact of direct determinants of the change management process on their performance according to the type of group that was belonged them, whether control group of the case study or experimental group of the main survey. there was a very noticeable convergence of the perspectives of employees at both of control and experimental groups in identifying the most important direct determinants of the change management process, which has the ability to predict the value of competitive performance of government employees in terms of both groups have agreed on the importance of only five direct determinants in influencing and predicting the expected performance of the government employees. there was a difference between the control and experimental groups about the expected impact of each one of the direct determinants targeted by the study that should be included in any desired change process, based on the calculations of regression coefficients in the two multi-regression models within the study, the first model reflects the expectations of the experimental group or the main survey while the second survey reflecting the expectations of employees in the control group or case study. there were slightly differences between control and experimental groups about the employees' expectations with regard to the value of impact of each one of the direct determinants within the change management process in predicting the expected competitive performance of employees. as a result, the following table will show the impact of those direct determinants in order by the values of regression analysis coefficients based on the data extracted to each group either a case study or main survey. table 5. power of impact of the direct determinants of cmp for both control and experimental groups in order by the values of multi-regression analysis coefficients experimental group the power control group the power administrative and legal aspects creation and innovation work environment institutional values motivations and incentives quality and excellence systems quality and excellence systems administrative and legal aspects training and learning organizational leadership availability of resources leadership institutional values creation and innovation source: the researcher the table 5 shows the power of influence in predicting the expected performance of employees according to both case study approach and main survey. the determinant of creation and innovation has the highest value of impact in predicting by the dependent variable from the perspective of control group while the administrative and legal aspects was the highest impact value from the perspective of experimental group. both of groups share in the same determinants which were only five as key drivers affecting the predicted improving in the performance of the demographic and institutional determinants affecting manpower’s development at the government sector 17 employees, but the experimental group has exceeded the control group in monitoring the effect of 4 additional determinants has significant role on the performance of the government sector employees. 7. limitations and conclusions the case study has a certain set of limitations that could be affected to generalize its applicability on at a wider level away from the primary objective behind its use for the comparison purpose with the results of the basic survey. the sample size of this case study should be greater than units or employee to considerate the condition of normality distribution of the data as a key assumption to use specific statistical tests without other that will be suitable for the analysis purpose and comparisons. the researcher was aware of the minimum limit acceptable to collect data from participants and randomly selection process should include all the employees at the whole organization during the selection based on the records of employees at the target entity of case study in order to represent a systematic random sample that be appropriate to test the interventions and assumptions of this study. the case study only dealt with the culture of change management process; then its role based on some determinants whether demographic or institutional which only determined in the literature review and how it aimed to bringing out the radical change in the performance of employees towards the competitiveness desired. thus, the findings could be limited to examine these determinants on the competitive performance of employees at the organizational structures within the government sector only. thus, monitoring the gap between experimental and control group shows which one of these determinants will have high importance and more priority in developing the performance of government employees. this in turn, it was limited to show a distinct area of improvement within only the organizations of the government sector regarding the optimal using of human resources management by the officials and planners to achieve the global objectives planned. concerning to the statistical evaluation, the approach based on testing the impact of the same considered determinants to both two groups either experimental group of the rak government employees or control group of the ajman government employees. further to aforementioned previously, the factors affecting change management culture needs many future studies to make a stronger case and help decrease the failure rates of the organizations during managing change processes targeted. in short, there is a significant impact of the role of direct determinants which were assumed by the current study in the influence of improving the competitiveness of the employees during the implementation to any change management process planned at the level of 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(2010). the critical success factors of business process management. international journal of information management, 30(2), 125-134. https://doi.org/10.1016/j.ijinfomgt.2009.07.003 © 2022 by the authors. submitted for possible open access publication under the terms and conditions of the creative commons attribution (cc by) license (http://creativecommons.org/licenses/by/4.0/). https://doi.org/10.1080/09585190601068268 https://doi.org/10.1108/bpmj-02-2013-0020 https://doi.org/10.1016/j.ijinfomgt.2009.07.003 plane thermoelastic waves in infinite half-space caused operational research in engineering sciences: theory and applications vol. 2, issue 1, 2019, pp. 37-50 issn: 2620-1607 eissn: 2620-1747 doi: https://doi.org/10.31181/oresta1901015e * corresponding author. zivko.erceg@sf.ues.rs.ba (ž. erceg), fatima_m95@hotmail.com (f. mularifović) integrated mcdm model for processes optimization in the supply chain management in the wood company živko erceg*, fatima mularifović university of east sarajevo, faculty of transport and traffic engineering doboj received: 28 january 2019 accepted: 14 march 2019 first online: 19 march 2019 original scientific paper abstract. supply chain management (scm) is a global strategy in nowadays business environment. it is a useful tool for managing a number of processes and activities on a daily basis in order to achieve a competitive advantage. also, in order to achieve adequate bases for successful functioning, it is necessary to know their abilities and weaknesses; this knowledge, yet, requires decomposition of the overall system. in this paper the decomposition in a wood company and its supplier selection in the subsystem of procurement is performed. for determining criteria weights the full consistency method (fucom) is applied while the ranking of suppliers is performed using the weighted aggregated sum product assessment (waspas) method. the obtained results are checked through the sensitivity analysis that is formed with modeling of criteria weights. in the sensitivity analysis it was found that the changes in the significance of the criteria could influence the decision-making and ranking of suppliers. key words: fucom, waspas, scm, evaluation of suppliers, decomposition 1. introduction a system approach to management is the base of every company's success because optimization is directly related to cost reduction across the supply chain. the supply chain management, as a new field of research for economists, provides a lot of examples where it is almost impossible to reach precise evaluation of the variables affecting the decision-making (kozarević and puška, 2018). modern production is increasingly complex with regard to the participation of technology or production processes or operations. in complex process manufacturing, logistics is particularly important because it combines all the processes from the procurement of materials to the distribution of finished or semi-finished products. for the production process to be efficient, it is necessary to optimize the procurement erceg and mularifović/oper. res. eng. sci. theor. appl. 2 (1) (2019) 37-50 38 subsystem. in doing so, great coordination is needed of the preparation, storage, and, especially, production system. in this paper, the decomposition of logistics systems was first performed, i.e. the division of the same into procurement of materials, drying of boards, production, packaging, and distribution. in the part of the materials’ procurement, the supplier was evaluated according to the seven criteria, ranking from the best to the worst. the fucom methods for determining weight coefficients and the waspas methods for ranking suppliers were used. the selection of suppliers is the first step in the process of product realization, starting from the procurement of materials to the delivery of the product (stević et al. 2017b; puška et al. 2017). the aim of the paper is to integrate all the processes of the logistics system, starting from the procurement. i.e. selection of the best supplier, via the production processes to the distribution. in addition, the goal of the paper is to create an adequate basis for future actions that involve the segmentation of the key performance indicators based on the performed logistic system decomposition, and their measurement and monitoring. the research was carried out in the wood design company "wood design" ltd. in bosnia and herzegovina. by using the fucom method for determining criteria weights and the waspas method for ranking alternatives we obtain that supplier 1 represents the best solution. after the introductory considerations, the second part presents the algorithm of the used methods. in the third part of the paper, a case study was presented with a detailed explanation of the calculation. the fourth part presents the sensitivity analysis and the discussion of the obtained results, while in the fifth section the final considerations are presented. 2. methods by applying multi-criteria decision-making methods, it is possible to make valid decisions in different areas. some of these decisions are: selection of adequate strategies, rationalization of logistics processes, and the decision-making that has an impact on the operations of companies or their subsystems, as evidenced by the next research (stević et al. 2015; stević et al. 2016; ranjan et al. 2016; jusoh et al. 2018) 2.1 full consistency method (fucom) the fucom method represents a new method for determining criteria weights developed by pamučar et al. (2018). so far it is applied in few studies: (prentkovskis et al. 2018; nunić, 2018; pamučar et al. 2018; zavadskas et al. 2018; fazlolahtabar et al. 2019). it consists of the following three steps: step 1 in this step, the criteria from the predefined set of the evaluation criteria are ranked. the ranking is performed according to the significance of the criteria, i.e. starting from the criterion which is expected to have the highest weight coefficient to the criterion of the least significance: (1)  1 2, ,..., nc c c c= (1) (2) ( ) ... j j j k c c c   integrated mcdm model for processes optimization in supply chain management in wood company 39 step 2 in this step, comparison of the ranked criteria is carried out and comparative priority , , with k representing the rank of the criteria) of the evaluation criteria, is determined. (2) step 3 in this step, the final values of the weight coefficients of evaluation criteria are calculated. the final values of the weight coefficients should satisfy the following two conditions: (a) the ratio of the weight coefficients is equal to the comparative priority among observed criteria defined in step 2, i.e. the following condition is met: (3) (b) in addition to condition (2), the final values of the weight coefficients should satisfy the condition of mathematical transitivity, i.e. t . then and are obtained. thus, another condition that the final values of the weight coefficients of the evaluation criteria should meet is obtained, namely: (4) based on the defined settings, the final model for determining the final values of the weight coefficients of the evaluation criteria can be defined. (5) / ( 1) 1 ( ) k k k k c c  + + = 1, 2,...,k n= ( )1/ 2 2/3 / ( 1), ,..., k k   + = ( )1 2, ,..., t n w w w / ( 1) ( ) k k  + /( 1) 1 k k k k w w  + + = / ( 1) ( 1) / ( 2) / ( 2) k k k k k k    + + + +  = / ( 1) 1 k k k k w w  + + = 1 ( 1) / ( 2) 2 k k k k w w  + + + + = 1 1 2 2 k k k k k k w w w w w w + + + +  = / ( 1) ( 1)/ ( 2) 2 k k k k k k w w   + + + + =  ( ) / ( 1) ( 1) ( ) / ( 1) ( 1)/ ( 2) ( 2) 1 min . . , , 1, 0, j k k k j k j k k k k k j k n j j j s t w j w w j w w j w j       + + + + + + = − =  −  =  =     erceg and mularifović/oper. res. eng. sci. theor. appl. 2 (1) (2019) 37-50 40 by solving model (5), we obtain the final values of evaluation criteria and the degree of consistency (χ) of the results obtained. 2.2 waspas method the weighted aggregate sum product assessment method (waspas) (zavadskas et al. 2012) is one of the best known and often applied multiple criteria decisionmaking methods for evaluating a number of alternatives in terms of a number given criteria. in general, suppose that a given mcdm problem is defined on m alternatives and n decision criteria. next, suppose that wj denotes the relative significance of the criterion and xij is the performance value of alternative i when it is evaluated in terms of criterion j. waspas methods consist of the following steps: step 1 formatting of initial decision matrix (x). the first step is to evaluate m alternatives by n criteria. alternatives are shown to the vectors: where xij is value of i-th alternatives according to j-th criterion (6) step 2 in this step it is necessary to normalize the initial matrix using the following equations: (7) for (8) for step 3 weighing of the normalized matrix is done in such a way that the previous (normalized) matrix is multiplied by the weight coefficients: (9) (10) step 4 summarizing all obtained values of the alternatives (summation in rows): ( )1 2, ,..., t n w w w ( )1 2, ,...,i i i ina x x x= ( )1, 2, 3,..., ; 1, 2, 3,..., .i m j n= = 1 1 11 1 1 ... ... n n m m mn c c a x x x a x x     =       max ij ij i ij x n x = 1, 2 ,..., . n c c c b min i ij ij ij x n x = 1, 2 ,..., . n c c c b n ij m n v v   =   , 1, 2,..., , ij j ij v w n i m j=  = integrated mcdm model for processes optimization in supply chain management in wood company 41 (11) (12) step 5 determination of the weighted product model by using the following equations: (13) (14) step 6 determination of the relative values of alternative ai: (15) (16) coefficient λ can be crisp value; it can be any value from 0, 0.1, 0.2, … , 1.0. step 7 ranking of alternatives. the highest value of the alternative is the best ranked while the smallest value reflects the worst alternative. 3. case study 3.1 decomposition of the logistic systems the decomposition of the logistics of the system implies the division of the system into several smaller subsystems. concretely, in this case, the decomposition was performed on the following subsystems: procurement, boards’ drying, production, packaging and, finally, distribution of finished or semi-finished products. the process of the boards drying and its length depend on the type of wood, its moisture and dimensions. this process lasts from 15 to 100 days. when the drying process is completed, the acclimatization process of the board is performed where the board equals the outside temperature with the temperature in the chamber as well as moisture. this process takes 48 hours. when it is all over, the board is fully ready for use and technical processing. after that, the boards must be properly stored. the production at the company "wood design" ltd. usora is performed in 6 stages in order to reach the desired product. the phases are: 1. cutting the boards, 2. machining of the board on a four-sided machine, 3. pairing the board, 4. pressing and gluing, 5. cutting to a certain length, and, 1 i ij m q q   =   1 n ij ijj q v = = 1 i ij m p p   =   1 ( ) n wj ij ijj p v = = 1 i ij m a a   =   (1 ) ij i i a q p =  + −  erceg and mularifović/oper. res. eng. sci. theor. appl. 2 (1) (2019) 37-50 42 6. sanding the boards on both sides. after finishing the sanding of the boards, the next and final operation before delivery is the packaging of the boards. in this company, the finished packages are wrapped with stretch foil. the boards are packed in the pallets which are 66 cm wide while their length depends on the required package of the customer. 25 panels are placed in one pallet. when packing furniture boards, 10 boards are placed in one pallet, and each plate is wrapped in nylon, unlike the plates. the other principle of packaging is the same. as for the deadline for delivering of ready-made boards, it is usually two weeks after the date of the received order, or one week if the order is urgent. of course, the semi-finished products can be ordered earlier if the customer is not a priority. 3.2 supplier selection in the wood company the criteria for the evaluation of the supplier are shown below: c1 quality of material, c2 price of materials, c3 product certification, c4 delivery time, c5 reputation, c6 additional discount on quantity, c7 warranty period, c8 reliability, c9 payment method. these criteria have been used in the following studies (puška et al. 2018; stević et al. 2017b; stojić et al. 2018). the research was carried out at the company "wood design" ltd., and accordingly, a supplier evaluation table was given with six suppliers taken into consideration. it should be noted that the criteria c1, c3, c5, c6, and c8 qualitative indicators are evaluated according to the linguistic scale in (stević et al. 2017): 1 – excellent, 3 – very good, 5 – good, 7 – medium, 9 – poor, in the case that the criterion should be minimized. in the case where the criteria should be maximized, the evaluation is entered in reverse order. the c2, c4, c7 and c9 quantitative indicators are shown as the cash units for the price of the material, that is, during the delivery days, the warranty period and the method of payment. table 1. initial mcdm matrix c1 c2 c3 c4 c5 c6 c7 d1 9 1200 9 5 7 5 7 d2 7 1000 7 3 5 7 3 d3 9 1250 9 7 15 3 9 d4 9 1150 7 5 7 5 5 d5 5 750 9 5 3 9 3 d6 9 1200 9 5 15 7 1 according to criteria c5 and c6, all suppliers have an equal estimate of 5 of 9. in the next step, these criteria are eliminated because they have no influence on making the final decision. also, it is important to note that the suppliers are evaluated according to the criterion “payment method” on the basis of the following facts: 1 advance 30% before delivery; 3 cash (payment upon download); 5 delay up to 7 days after delivery; 7 delay up to 15 days after delivery; 9 delay up to 30 days after delivery. 3.2.1 determining criteria weights using the fucom method step 1 ranking the criteria: integrated mcdm model for processes optimization in supply chain management in wood company 43 1 2 4 7 6 5 3 c c c c c c c      step 2 comparison of the ranked criteria is carried out and the comparative priority of the evaluation criteria is determined. comparative priority of the evaluation criteria is obtained by equation (3). assessment of the criteria is shown in table 2. table 2. ranking and assessment of the criteria criteria c1 c2 c4 c7 c6 c5 c3 𝜔𝑗(𝑘) 1 2 2.3 2.7 3 3.8 4 on the basis of the obtained significance of the criteria (table 2) it is necessary to calculate comparative priority of the criteria: 1 2/ 2 / 1 2 c c  = = , 2 4/ 2.3 / 2 1.15 c c  = = , 4 7/ 2.7 / 2.3 1.17 c c  = = 7 6/ 3 / 2.7 1.11 c c  = = , 6 5/ 3.8 / 3 1.27 c c  = = , 5 3/ 4 / 3.8 1.05 c c  = = step 3 the final values of the weight coefficients should meet the following two conditions: a) the final values of the weight coefficients should meet condition (3), i.e. that 1 2 2 w w = , 2 4 1.15 w w = , 4 7 1.17 w w = , 7 6 1.11 w w = , 6 5 1.27 w w = and 5 3 1.05 w w = . b) in addition to condition (3), the final values of the weight coefficients should meet the condition of mathematical transitivity, i.e. that 1 4 2 1.15 2.3 w w =  = , 2 7 1.15 1.17 1.35 w w =  = , 4 6 1.17 1.11 1.30 w w =  = , 7 5 1.11 1.27 1.41 w w =  = and 6 3 1.27 1.05 1.33 w w =  = . by applying expression (5), the final model for determining the weight coefficients can be defined as: 7 6 51 2 4 2 4 7 6 5 3 7 61 2 4 4 7 6 5 3 7 1 min 2 , 1.15 , 1.17 , 1.11 , 1.27 , 1.05 , . . 2.3 , 1.35 , 1.3 , 1.41 , 1.33 , 1, 0, j j j w w ww w w w w w w w w w ww w w s t w w w w w w w j             =  −  −  −  −  −  −     −  −  −  −  −     =      by solving this model, the final values of the weight coefficients are: erceg and mularifović/oper. res. eng. sci. theor. appl. 2 (1) (2019) 37-50 44 quality of material 1 0.317w = , price of material 2 0.159w = , product certification 3 0.080w = , delivery time 4 0.138w = , warranty period 5 0.083w = , reliability 6 0.106w = , payment method 7 0.118w = and dfc of results 0.001 = are obtained. after obtaining the results we can conclude that the first criterion quality of material is the most important one with value 0.317. 3.2.2 supplier evaluation and selection using the waspas method in table 3 the multi-criteria decision-making model is shown as consisting of seven criteria and six alternatives, i.e. suppliers. this represents the first step of the waspas method. table 3. initial decision-making matrix extended with criteria orientation c1 c2 c3 c4 c5 c6 c7 s1 9 1200 9 5 7 5 7 s2 7 1000 7 3 5 7 3 s3 9 1250 9 7 15 3 9 s4 9 1150 7 5 7 5 5 s5 5 750 9 5 3 9 3 s6 9 1200 9 5 15 7 1 max min max min max max max 9 750 9 3 15 9 9 step 2 normalization of initial matrix (table 4) using the following equations: max ij ij i ij x n x = for criteria c1, c3, c5, c6 and c7, i.e. min i ij ij ij x n x = for criteria c2 andc4. table 4. process of calculation for normalization of initial matrix c1 c2 c3 c4 c5 c6 c7 s1 9/9 750/1200 9/9 3/5 7/15 5/9 7/9 s2 7/9 750/1000 7/9 3/3 5/15 7/9 3/9 s3 9/9 750/1250 9/9 3/7 15/15 3/9 9/9 s4 9/9 750/1150 7/9 3/5 7/15 5/9 5/9 s5 5/9 750/750 9/9 3/5 3/15 9/9 3/9 s6 9/9 750/1200 9/9 3/5 15/15 7/9 1/9 results obtained using normalization process are shown in table 5. integrated mcdm model for processes optimization in supply chain management in wood company 45 table 5. normalized matrix c1 c2 c3 c4 c5 c6 c7 s1 1 0.625 1 0.6 0.467 0.556 0.778 s2 0.778 0.75 0.778 1 0.333 0.778 0.333 s3 1 0.6 1 0.429 1 0.333 1 s4 1 0.652 0.778 0.6 0.467 0.556 0.556 s5 0.556 1 1 0.6 0.2 1 0.333 s6 1 0.625 1 0.6 1 0.778 0.111 step 3 multiplication of the previously obtained matrix with criteria weights. using the following equation: , 1, 2,..., , ij j ij v w n i m j=  = in table 6 the normalized matrix with criteria weights is shown. table 6. normalized matrix with criteria weights c1 c2 c3 c4 c5 c6 c7 s1 1 0.625 1 0.6 0.467 0.556 0.778 s2 0.778 0.75 0.778 1 0.333 0.778 0.333 s3 1 0.6 1 0.429 1 0.333 1 s4 1 0.652 0.778 0.6 0.467 0.556 0.556 s5 0.556 1 1 0.6 0.2 1 0.333 s6 1 0.625 1 0.6 1 0.778 0.111 w 0.317 0.159 0.080 0.138 0.083 0.106 0.118 example of calculation: 11 12 0.317 1.000 0.317 0.159 0.625 0.099 v v =  = =  = weighted normalized matrix is shown in table 7. table 7. weighted normalized matrix c1 c2 c3 c4 c5 c6 c7 s1 0.317 0.099 0.080 0.083 0.039 0.059 0.092 s2 0.247 0.119 0.062 0.138 0.028 0.082 0.039 s3 0.317 0.095 0.080 0.059 0.083 0.035 0.018 s4 0.317 0.104 0.062 0.083 0.039 0.059 0.066 s5 0.176 0.159 0.080 0.083 0.017 0.106 0.039 s6 0.317 0.099 0.080 0.083 0.083 0.082 0.013 step 4 summarizing of all values per alternatives (summarizing per rows, table 8) 1 n ij ijj q v = = example: erceg and mularifović/oper. res. eng. sci. theor. appl. 2 (1) (2019) 37-50 46 1 0.317 0.099 0.080 0.083 0.039 0.059 0.092 0.769q = + + + + + + = table 8. calculation of qi c1 c2 c3 c4 c5 c6 c7 qi s1 0.317 0.099 0.080 0.083 0.039 0.059 0.092 0.769 s2 0.247 0.119 0.062 0.138 0.028 0.082 0.039 0.715 s3 0.317 0.095 0.080 0.059 0.083 0.035 0.018 0.687 s4 0.317 0.104 0.062 0.083 0.039 0.059 0.066 0.730 s5 0.176 0.159 0.080 0.083 0.017 0.106 0.039 0.660 s6 0.317 0.099 0.080 0.083 0.083 0.082 0.013 0.757 step 5: determining of the weighted product model using the following equation (table 9): 1 ( ) n wj ij ijj p v = = , example: 0.317 0.159 0.080 0.138 0.083 1 0.106 0.118 (1.000) (0.625) (1.000) (0.600) (0.467) (0.056) (0.778) 0.741 p =       = table 9. weighted product model c1 c2 c3 c4 c5 c6 c7 pi s1 1 0.625 1 0.6 0.467 0.556 0.778 0.741 s2 0.778 0.75 0.778 1 0.333 0.778 0.333 0.675 s3 1 0.6 1 0.429 1 0.333 1 0.730 s4 1 0.652 0.778 0.6 0.467 0.556 0.556 0.703 s5 0.556 1 1 0.6 0.2 1 0.333 0.594 s6 1 0.625 1 0.6 1 0.778 0.111 0.655 w 0.317 0.159 0.080 0.138 0.083 0.106 0.118 step 6 determining of relative values alternatives 𝐴𝑖. we have taken value 𝜆=0.5. 1 0.5 0.769 (1 0.5) 0.741 0.755a =  + −  = step 7 ranking of the alternatives (table 10). alternative with the biggest value represents the best ranked while the smallest value denotes the worst alternative. table 10. ranking of alternatives qi pi ai supplier 1 0.769 0.741 0.755 supplier 2 0.715 0.675 0.695 supplier 3 0.687 0.730 0.709 supplier 4 0.730 0.703 0.717 supplier 5 0.660 0.594 0.627 supplier 6 0.757 0.655 0.706 1 4 3 6 2 5 s s s s s s     integrated mcdm model for processes optimization in supply chain management in wood company 47 using the fucom method for determining criteria weights and the waspas method for ranking alternatives we obtain that supplier 1 represents the best solution. 4. sensitivity analysis and discussion sensitivity analysis is a component part of experimental simulation and can have influence on formulation model. usually it is used for investigating behavior of the model. in this case, the sensitivity analysis is performed forming scenarios with changes of criteria weights (fig. 1). figure 1. formed scenarios in sensitivity analysis in set 1, weights of first two criteria 𝑤1 and 𝑤2 are decreased by 10%, while𝑤3, 𝑤4, 𝑤5, 𝑤6 and 𝑤7 are increased for 4%. in this set, with the decreasing significance of criteria quality and price as well as the increasing other criteria, the third supplier is getting higher values and represents the best solution. in the second place is the first supplier, in third supplier 6, fourth supplier 4, fifth supplier 2 and in the last place is supplier 5. in set 2, weights of the last three criteria 𝑤5, 𝑤6 and 𝑤7 are increased for 4%, while 𝑤1, 𝑤2, 𝑤3 and 𝑤4 are decreased per 3%. with the increasing significance of the criteria warranty period, reliability and payment method, and with the decreasing significance of the other criteria, supplier 3 has higher values and represents the best solution. in this set, supplier 1 is in the second place, supplier 4 in the third, supplier 2 in the fifth place and supplier 5 in the last place. in set 3, weight coefficients 𝑤1, 𝑤3, 𝑤5 and 𝑤7 are decreased per 6%, while other three 𝑤2, 𝑤4 and 𝑤6 are increased per 8%. in set 4, the first weight coefficient 𝑤1 is decreased per 24%, while other 𝑤2, 𝑤3, 𝑤4, 𝑤5, 𝑤6 and 𝑤7 are increased per 4%. in this set with the decreasing significance of the criterion quality of material and the increasing of the other criteria, supplier 3 gets higher values and 0 1 2 3 4 5 6 7 supplier 1 supplier 2 supplier 3 supplier 4 supplier 5 supplier 6 set 1 set 2 set 3 set 4 set 5 set 6 set 7 set 8 erceg and mularifović/oper. res. eng. sci. theor. appl. 2 (1) (2019) 37-50 48 represents the best alternative. in set 5, the first five weight coefficients 𝑤1, 𝑤2, 𝑤3, 𝑤4 and 𝑤5 are increased per 4%, while 𝑤6 and 𝑤7 are decreased per 10%. with increasing criteria quality, price, product certification, delivery time and warranty period, supplier 3 obtains the highest value. in set 6, only the last weight coefficient 𝑤7 is increased per 30%, while other 𝑤1, 𝑤2, 𝑤3, 𝑤4, 𝑤5 and 𝑤6 are decreased per 5%. with the increasing of significance of the criterion payment method and the other six criteria decreasing, supplier 3 is the best solution. in set7, the first and last weight coefficients, i.e. 𝑤1 and 𝑤7 are increased per 15%, while 𝑤2, 𝑤3, 𝑤4, 𝑤5 and 𝑤6 are decreased per 6%. the first ranked alternative in this set is also supplier 3. in the last set8, weight coefficients 𝑤3 and 𝑤5 are increased per 20%, while the other five criteria, i.e., 𝑤1, 𝑤2, 𝑤4, 𝑤6 and 𝑤7 are decreased per 8%. supplier 3 is the first ranked alternative. figure 2. ranking of suppliers in various scenarios with decreasing of the significance of criteria quality of material, product certification and warranty period, and, on other hand, with increasing the other criteria, the best solution is supplier 2. of the eight sets made, the best solution for them was supplier 3 in six sets as can be seen in fig. 2. 5. conclusion for each company, the main goal is to do successful business and achieve a competitive position in a very demanding market. in order to achieve long-term sustainability of the company in the business world, one needs to take into account all the business processes of one company. each manufacturer should respond to the customers’ requests to meet their needs. yet, in order to meet these requirements, each manufacturer must dispose of his product at the required place, at the required integrated mcdm model for processes optimization in supply chain management in wood company 49 time and in the required quantity. fulfilling these requirements and achieving a successful business both require the constant disposal of required quantities and types of products. in this paper, the decomposition of the logistic systems was carried out on the procurement of materials, drying of the boards, production, packaging, and distribution. the aim of the procurement is the quality and timely realization of material goods flows (stojić et al., 2018, stević et al., 2017a, stević et al., 2019), and in this regard, most attention was devoted to the development of a model for evaluating suppliers. in this section, the fucom-waspas model was used to rank suppliers. we realized that supplier 1 was the most suitable for further cooperation. after procurement of the material, the drying process of the board lasts from 15 to 100 days depending on the type and characteristics of the wood; in addition, this is very important for the process of production itself because artificial drying under controlled conditions provides material that is suitable for further processing. the production process takes place in six stages. all the phases are interconnected and each phase needs to be thoroughly done if the final product is to be of high quality. after the production process, the process of packaging follows. in the end, the distribution process in which the finished product is placed at the disposal of the customer is completed, that is, it follows the transport to the country from which the order came. since this company produces boards or semi-finished products, its final product is completed in cooperation with other companies. in addition, during the analysis and discussion of the solutions achieved, by changing the weight coefficients and by increasing or decreasing the value of certain criteria, the rank of the supplier also changed. it could be concluded that the changing of weight coefficients affected the final result. after setting eight set with changing of weight coefficients, supplier 3 had highest ranking results. through this research, an adequate basis for future actions is created, which implies the separation of key performance indicators based on the executed decomposition of logistics systems, and their measurement and monitoring. references fazlollahtabar, h., smailbašić, a., stević, ž., (2019). fucom method in group decisionmaking: selection of forkliftin a warehouse, decision making: applications in management and engineering, vol. 2(1), 49-65 jusoh, a., mardani, a., omar, r., štreimikienė, d., khalifah, z., &sharifara, a. 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(2016). performance evaluation of indian railway zones using dematel and vikor methods. benchmarking: an international journal, 23(1), 78-95. stević, ž. (2017). modeling performance of logistics subsystems using fuzzy approach. the international journal of transport & logistics, 17(42), 30-39. stević, ž., pamučar, d., kazimieras zavadskas, e., ćirović, g., & prentkovskis, o. (2017a). the selection of wagons for the internal transport of a logistics company: a novel approach based on rough bwm and rough saw methods. symmetry, 9(11), 264. stević, ž., pamučar, d., vasiljević, m., stojić, g., & korica, s. (2017b). novel integrated multi-criteria model for supplier selection: case study construction company. symmetry, 9(11), 279. stević, ž., tanackov, i., vasiljević, m., &vesković, s. (2016, september). evaluation in logistics using combined ahp and edas method. in proceedings of the xliii international symposium on operational research, belgrade, serbia (pp. 20-23). stević, ž., vasiljević, m., puška, a., tanackov, i., junevičius, r., &vesković, s. (2019). evaluation of suppliers under uncertainty: a multiphase approach based on fuzzy ahp and fuzzy edas. transport, 34(1), 52-66. stević, ž., vesković, s., vasiljević, m., &tepić, g. (2015, may). the selection of the logistics center location using ahp method. in 2nd logistics international conference (pp. 86-91). stojić, g., stević, ž., antuchevičienė, j., pamučar, d., &vasiljević, m. (2018). a novel rough waspas approach for supplier selection in a company manufacturing pvc carpentry products. information, 9(5), 121. zavadskas, e. k., nunić, z., stjepanović, ž., & prentkovskis, o. (2018). a novel rough range of value method (r-rov) for selecting automatically guided vehicles (agvs). studies in informatics and control, 27(4), 385-394. zavadskas, e. k., turskis, z., antucheviciene, j., & zakarevicius, a. (2012). optimization of weighted aggregated sum product assessment. elektronikairelektrotechnika, (6 (122)), 3-7. operational research in engineering sciences: theory and applications vol. 4, issue 3, 2021, pp. 122-141 issn: 2620-1607 eissn: 2620-1747 doi: https://doi.org/10.31181/oresta111221122m * corresponding author. 9285poojameena@gmail.com (p. meena), anil.sharma.maths@gmail.com (a. k. sharma), ganeshmandha1988@gmail.com (g. kumar) control of non-instantaneous degrading inventory under trade credit and partial backlogging pooja meena 1, anil kumar sharma 2, ganesh kumar 1* 1 department of mathematics, university of rajasthan, jaipur-302004, india 2 department of mathematics, raj rishi govt. college, alwar, india received: 12 june 2021 accepted: 08 november 2021 first online: 11 december 2021 original scientific paper abstract: inventory management is an extremely difficult task. it has become usual practice for a provider during the last few decades to provide a retailer with a credit term. in this article, a non-instantly degradable product inventory system is built with a price-sensitive demand and a weibull credit term allocation reduction rate. some backlogged deficiencies are permitted. the aim is to maximize the total profit by taking three cases into account. numerical examples, graphical representations and sensitivity analysis demonstrate the application of the approach developed in this study. key words: inventory control, weibull deterioration, price-sensitive demand, trade credit, non-instantaneous deterioration. 1. introduction everyday life is a prevalent phenomenon in the deterioration of commodities. some examples of these things are vegetables, fruits, dairy products, drugs and blood bank. therefore, the tendency of the object to deteriorate is important to take into account. in the real world, most products have a shelf life that allows them to maintain their quality or their original condition for a period of time. during that period of time, there was no deterioration in the situation. examples of such foods include vegetables and fruits as well as meat, fish, and seafood. this is referred to as "non-instantaneous deterioration" in the scientific literature. first and foremost, ghare and schrader (1963) took an important stride in this approach. giri et al. (2003) have presented a mathematical methodology for weibull decreasing items. ghosh and chaudhury (2004), as well as roy and chaudhuri (2009), proposed inventory systems for perishable commodities that are in low supply. das et al. (2010) created a model for control of non-instantaneous degrading inventory under trade credit and partial backlogging 123 an item with variable quality that takes into account random machine failure. an inventory model for small lots was developed by das et al. (2011), with regular and overtime works being combined to produce the production rates. kawale and bansode (2012) developed an inventory system for perishable items under the influence of time dependent holding cost using weibull rate of deterioration. barik et al. (2013) created a mathematical approach for deteriorating items under the influence of inflation. confident weights of experts were used by das et al. (2014) as part of an algorithmic method for magdm problems. in this topic, for m secondary warehouses (sws) and one primary warehouse, das et al. (2015) created a multi-item multi-warehouse inventory model for degrading goods. mahata et al. (2018) and muriana (2020) also offered several models. ghosh et al. (2021) studied an eoq model with full backorder for perishable commodities with varied advance and delayed payment conditions. non-instantaneous models were investigated by ouyang et al. (2006) and wu et al. (2009). soni (2013) used trade credit to overcome the problem of non-instantaneously decaying inventories (table 1). table 1. literature summary authors price dependent demand deterio ration trade credit constant holding cost noninstantaneous giri et al. (2003) no yes no no no ghosh and chaudhury (2004) no yes no yes no roy and chaudhuri (2009) no yes no yes no jain and kumar (2010) no yes no yes no geetha and udayakumar (2016) yes yes no yes yes mahata et al. (2018) no yes yes yes no singh et al. (2020) no yes yes yes no halim et al. (2021) yes yes no yes no present paper yes yes yes yes yes geetha and udayakumar (2016) employed advertisement dependent demand, shaikh and cárdenas-barrón (2020), and udayakumar et al. (2020) developed alternative inventory models for non-instantaneous falling commodities. models in this direction have also been presented by ahmad and benkherouf (2018) and tripathi and pandey (2020). ouyang et al. (2006) introduced a price-dependent inventory system. goyal and chang (2009) used stock-based demand to construct inventory policy. amutha and chandrasekaran (2013) created an inventory system for perishable items that incorporates the weibull rate of deterioration and pricebased demand. avinadav et al. (2013), guchhai et al. (2013), avinadav et al. (20 14), feng et al. (2017), and cheng et al. (2020) followed the work. halim et al. (2021) devised a strategy for resolving an inventory problem involving decaying products. sana et al. (2008) developed an inventory model with advertising cost and selling price dependent demand using trade credit. sarkar (2012) also provided an inventory system for deteriorated commodities purchased on trade credit. by assuming twolevel trade credits, shah et al. (2015) pioneered a novel methodology. several academics, including aggarwal and jaggi (2017), goyal (2017), and shah et al. (2017), created several approaches to address inventory problems while taking trade credit into account. tripathi and chaudhary (2017) and singh et al. (2020) employed the meena et al./oper. res. eng. sci. theor. appl. 4 (3) (2021) 122-141 124 weibull deterioration rate to develop distinct inventory models for perishable products with trade credits. tripathi et al. (2018) suggested mathematical systems with various trade credits. sundararajan et al. investigated the impact of trade credit under inflation on an eoq model (2020). jain and kumar (2010) created a strategy for perishable items with weibull deterioration rates and scarcity. sarkar and sarkar (2013) improved a partial backlog solution approach for time-dependent perishable commodities. mishra (2016) and gupta et al. (2018) employed partial backlogging to generate multiple systems for weibull degrading goods. jamal et al. (2017), san-josé et al. (2018), akbar et al. (2019), rastogi and singh (2019), and san-josé et al. (2020) all made major contributions in this area. although several researchers have developed inventory models that take the weibull deterioration rate into account in their work, practitioners have paid less attention to the inclusion of non-instantaneous deterioration. novelties of present study are as follows: • we focused our efforts on constructing a mathematical system for noninstantaneous weibull declining products under trade credit. • demand is thought to be price related. • shortages are considered partially backlogged are tolerated. • impact of different input variables is studied. • concavity of profit functions is shown by graphs. the structure of the paper is in the following format: segment 2 of this article describes several notations and assumptions. segment 3 discusses the model formulation. segment 4 contains the solution technique. segment 6 demonstrates concavity of profit functions. segment 7 discusses sensitivity analysis. segment 8 contains the conclusion. 2. notations and assumptions to create the mathematical model, some notations and assumptions are used. 2.1 notations k the ordering cost /order q the retailer’s order quantity ( )d p the demand rate m the time in which the item does not decay m permissible delay period c purchasing price /unit p selling price /unit h unit holding price s unit shortage cost/order l c lost sale cost/ unit control of non-instantaneous degrading inventory under trade credit and partial backlogging 125 p i rate of interest payable/dollar/unit time e i rate of interest earned/dollar/unit time  the time at which the inventory level becomes zero t replenishment period ( )t deterioration rate 1 ( )i t inventory level in period 0 t m  2 ( )i t inventory level in period m t   3 ( )i t inventory level in period t t   ( )z  total profit  optimal value 2.2 assumptions • the replenishment rate is assumed to be limitless. • the time stamp begins at zero. • shortages that are partially backlogged are allowed. the pace of backlogging is determined by the time required for subsequent replenishing. as a result, during the stock-out period, it is denoted as ( ) ( ) t t b t e − − = , where 0 1  . • articles within the cycle period cannot be replaced or repaired in any way. • the demand d depends on selling price p and ( ) µd p p −= , 0, 0   . • after the interval [0, ]m the goods begin to deteriorate with the weibull deterioration rate, ( ) 1; 0, 0t t    −=   . • for a specified term the supplier gives commercial credit to the retailer. 3. mathematical formulation during the period  0, m , there is no deterioration. the inventory level in the period  , m  is consumed by both demand and deterioration. in the period  , t , shortages occur which are partially backlogged. the change of inventory level ( )i t in different time durations given by meena et al./oper. res. eng. sci. theor. appl. 4 (3) (2021) 122-141 126 ( )1 0, µ di t p t m dt  − = −   (1) ( ) ( ) 2 1 2 , µ di t p t i t m dt     − − = − −  (2) ( ) ( )3 , t tµ di t p e t t dt    − −− = −   (3) the solution of equations (1), (2), and (3) with boundary conditions ( ) ( ) ( )1 2 30 , 0i q i i = = = , are ( ) 1 ( )i t p t q   − = − + . (4) ( ) ( ) ( ) ( )1 12 1 µ i t p t t t t          − + +  = − + − − −  +  . (5) ( ) ( ) ( )3 1 2 µ i t p t t t      −   = − − + +    . (6) using boundary conditions, ( ) ( ) ( )1 2 3,i m i m i t e= = − we get ( ) ( )1 1 1 µ q p m m m          − + +  = + − − −  +  . (7) ( ) ( )1 2 µ e p t t t      −   = − − + +    (8) the total annual profit/cycle is obtained by including the following: 1. ordering cost (o) = k . 2. inventory holding cost (h) ( ) ( ) 1 2 0 m m h i t dt i t dt  = +  ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 1 6 4 6 41 2 1 1 5 2 2 2 2 2 3 1 1 1 1 2 1 µ x x mx x x m m x x x m h m m p x x mm m m p                       + + + + + +   − −  − + −      + = − − − − −      −   + − − +  +     where control of non-instantaneous degrading inventory under trade credit and partial backlogging 127 2 1 (3 2 ) y x p b b= + + , 2 (1 ) b x zx b az= + + , 3 2 ( 1) y x p b= + , 4 ( 2)x zax b= + , 5 ( 1) y x p b= + , 6 ( 1)x ax b= + . 3. purchase cost (p) ( )c q e= − ( ) ( )1 1 21 1 2 2 µ c t m m m t t p             + +   = − − − + − + −   +    . 4. sales revenue ® ( ) ( ) ( )  0 t t t p d p dt d p e dt    − − = +  ( ) 1 t µ p e p      − − − = −    . 5. shortage cost (s) ( )3 t s i t dt  = − ( ) ( ) 2 2 2 3 6 µ s t t p    = − − + . 6. lost sale cost (l) ( ) ( )( )1 t t t l c d p e dt   − − = − ( )( )1tl c e t p        − − = − + − . 7. interest payable (i) when 0 m m  ( ) ( ) 1 1 2 m p m m ip ci i t dt i t dt  = +  ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 1 6 4 6 41 2 1 1 5 2 2 2 2 3 1 1 1 1 2 2 2 2 1 µ x x mx x x m m x x x b cip m m x x m m m m m p m                       + + + + + +     − −  − + −     +  = − − − −     + − −      + − +   −  +    . (ii) when m m   meena et al./oper. res. eng. sci. theor. appl. 4 (3) (2021) 122-141 128 ( ) 2 1p m ip ci i t dt  =  ( ) ( ) ( ) ( ) ( ) ( ) 1 6 4 6 41 2 1 1 5 2 2 2 2 3 1 1 x x mx x x m m x x x cip b m m x x            + + + +  − − − − −    =   +  + − + −     . (iii) when m t   , 3 0ip = . 8. interest earned (i) when 0 m m  ( ) 21 0 2 m e eµ p ie pi td p dt i m p  = = . (ii) when m m   ( ) 22 0 2 m e eµ p ie pi td p dt i m p  = = . (iii) when m t   ( ) ( ) ( ) 3 0 0 e ie pi td p dt m d p dt   = + −  2 µ p ie m p    = −    . the total profit/unit time ( )z  is written as ( ) ( ) ( ) ( ) 1 2 3 ; 0 ; ; z m m z z m m z m t           =      ( ) 1 11 r ie o p h s l ip z t  + − − − − − − = 1 x t = . (9) where ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 2 1 1 1 2 1 2 6 4 6 41 2 1 1 5 2 2 2 2 3 1 1 2 1 1 2 2 2 1 t µ µ µ µ p e p x iem k p p c t m m m t t p x x mx x x m m m x x x p h m m x x m m m p                                         − − + + + + + +     −  = − + −               − − − − + − + −    +     − − − + − − + − − − − − + − − + ( )1 1 1 m   + +                            −       +       control of non-instantaneous degrading inventory under trade credit and partial backlogging 129 ( ) ( ) ( )( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 2 1 6 4 6 41 2 1 1 5 2 2 2 2 3 1 1 1 2 2 3 1 6 1 2 2 2 2 1 tl µ µ cs t t e t p p x x mx x x m m x x x b cip m m x x m m m m m m p                                 − − + + + + + +     − − − + − − + −                  − −  − + −     +  − − − − −      + − −    + −  +   −  +                               ( ) 2 22 r ie o p h s l ip z t  + − − − − − − = 2 x t = . (10) where ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 2 2 1 1 2 1 6 4 6 41 2 1 1 5 2 2 2 2 2 1 1 1 2 1 1 2 2 1 2 t µ µ µ µ p e p x iem p p m m m c k p t t t x x mx x x m m x x x m h m m p x x m m p                                     − − + + + + + +     − = − +             − − −  +   − −     + − + −        − − − + − + − − − − − − + − ( ) ( ) ( ) ( ) ( )( ) 1 1 2 1 2 2 3 6 1 µ tl m m s t t p c e t p                 + + − −                         −   − +   +         − − − +      − − + −    meena et al./oper. res. eng. sci. theor. appl. 4 (3) (2021) 122-141 130 ( ) ( ) ( ) ( ) ( ) ( ) 1 6 4 6 41 2 1 1 5 2 2 2 2 3 1 1 x x mx x x m m x x x cip b m m x x            + + + +   − − − − −      −    +  + − + −       ( ) 3 33 r ie o p h s l ip z t  + − − − − − − = 3 x t = . (11) where ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 3 1 1 2 1 6 4 6 41 2 1 1 5 2 2 2 2 2 3 1 1 2 1 1 2 2 1 2 t µ µ µ µ p e p x ie m p p m m m c k p t t t x x mx x x m m x x x m h m m p x x m                                 − − + + + + + +     −   = − + −               − − −  +   − −     + − + −        − − − + − + − − − − − − + ( ) ( ) ( ) ( ) ( )( ) 1 1 2 1 2 2 3 6 1 µ tl m m m p s t t p c e t p                      + + − −                         −   − − +   +         − − − +      − − + −    4. solution procedure the aim of this article is to maximize total profit. the following condition must be fulfilled by ( )iz  for maximization: ( ) 0 i dz d   = , 1, 2, 3i = (12) control of non-instantaneous degrading inventory under trade credit and partial backlogging 131 solving the equation (12) for , we get optimal value *  of , for which ( ) * 2 | 0 ; 1, 2, 3 i d z i d     =  = 5. numerical examples example 5.1 when 0 m m  10000, 10, 20, 100, 0.08, 0.05, 0.125, 2, 6000, 0.9, 0.20, 0.25, 1, .7, 60, 70 e p l k h c p m m µ i i t s c     = = = = = = = = = = = = = = = = putting these values in equation (9), we obtain the optimal solutions * 1 0.6924 = * 1 2371z = * 1 67.1094q = example 5.2 when m m   10000, 10, 20, 100, 0.05, 0.07, 0.125, 2, 6000, 0.9, 0.20, 0.25, 1, .7, 60, 70 e p l k h c p m m µ i i t s c     = = = = = = = = = = = = = = = = putting these values in equation (10), we obtain the optimal solutions * 2 0.6930 = * 2 2363.2z = * 2 67.1989q = example 5.3 when m t   10000, 10, 20, 100, 0.05, 0.9, 0.125, 2, 6000, 0.9, 0.20, 0.25, 1, .7, 60, 70 e p l k h c p m m µ i i t s c     = = = = = = = = = = = = = = = = putting these values in equation (11), we obtain the optimal solutions * 3 0.7335 = * 3 1530z = * 3 71.2940q = meena et al./oper. res. eng. sci. theor. appl. 4 (3) (2021) 122-141 132 to solve the above examples, matlab software is used. 6. concavity of profit functions figures 1, 2, and 3 depict the concavity of the profit functions, and this finding corresponds to the theoretical idea of a profit functions with concavity. figure 1. concavity of profit function 1 ( )z  figure 2. concavity of profit function 2 ( )z  control of non-instantaneous degrading inventory under trade credit and partial backlogging 133 figure 3. concavity of profit function 3 ( )z  7. sensitivity analysis and observations for sensitivity analysis, we have used the preceding cases. the impacts of parameter modifications on optimal values of *, *z  and *q in this segment have been studied. the results are summarized in tables 2, 3 and 4. observations and managerial implications from table 2, table 3 and table 4, we observe that • as we increase the parameter h by 10% and 20% we observe that the total profit * z remains almost constant and the optimal values of *  and *q decrease. we can therefore suggest to the firm that they are free to accept any type of lot as long as the profit remains constant in accordance with the above parameters. • increasing the value of k by 10% and 20% increases the value of * z very rapidly but the optimal values of *  and *q decreases. in order to increase profits, a company will increase the value of k parameter. • enlarge of c by 10% and 20% results increase in * z and decrease in *q while it drops the value of *  very sharply. in order to increase profits, a company will increase the value of c parameter. • when p increases by 10% and 20%, it makes a decrease in * z and an increase in *  but it causes the value of total inventory *q to drop very rapidly. in order to increase profits, a company will decrease the value of p parameter. meena et al./oper. res. eng. sci. theor. appl. 4 (3) (2021) 122-141 134 • when we increase the parameters s and l c by 10% and 20% we see that the optimal values of *  and *q show the same behavior (they increase) while the total profit remains unchanged. we can therefore suggest to the firm that they are free to accept any type of lot as long as the profit remains constant in accordance with the above parameters. figures 4, 5, and 6 demonstrate the effect of various factors on profit functions. table 2. change in * , * 1 q and * 1 z with respect to parameters parameters %change in parameters * * 1 q * 1 z h -20 0.7013 68.0065 2323.9 -10 0.6968 67.5528 2347.6 +10 0.6881 66.6765 2394.1 +20 0.6837 66.2338 2416.9 k -20 0.6924 67.1094 371.041 -10 0.6924 67.1094 1371.0 +10 0.6924 67.1094 3371.0 +20 0.6924 67.1094 4371.0 c -20 0.7415 72.0749 2168.0 -10 0.7169 69.5820 2274.3 +10 0.6680 64.6568 2458.4 +20 0.6437 62.2236 2536.6 p -20 0.6668 78.8904 2922.2 -10 0.6801 72.4239 2624.5 +10 0.7037 62.6383 2151.2 +20 0.7142 58.8202 1957.5 s -20 0.6739 65.2490 2322.3 -10 0.6834 66.2037 2347.3 +10 0.7010 67.9762 2393.6 +20 0.7092 68.8038 2415.0 l c -20 0.6749 65.3494 2327.7 -10 0.6839 66.2539 2350.0 +10 0.7004 67.9157 2391.1 +20 0.7080 68.6826 2410.1 control of non-instantaneous degrading inventory under trade credit and partial backlogging 135 figure 4. changes in * 1 z with respect to parameters table 3. change in * , * 2 q and * 2 z with respect to parameters parameters %change in parameters * * 2 q * 2 z h -20 0.7018 68.0864 2316.0 -10 0.6974 67.6425 2339.8 +10 0.6886 66.7557 2386.4 +20 0.6843 66.3228 2409.2 k -20 0.6930 67.1989 363.2157 -10 0.6930 67.1989 1363.2 +10 0.6930 67.1989 3363.2 +20 0.6930 67.1989 4363.2 c -20 0.7420 72.1570 2161.0 -10 0.7175 69.6729 2266.8 +10 0.6686 64.7449 2450.3 +20 0.6444 62.3204 2528.2 p -20 0.6674 78.9980 2913.5 -10 0.6807 72.5215 2616.3 +10 0.7043 62.7211 2143.7 +20 0.7148 58.8972 1950.3 s -20 0.6745 65.3374 2314.6 -10 0.6840 66.2926 2339.6 +10 0.7016 68.0662 2385.7 +20 0.7097 68.8842 2407.0 l c -20 0.6755 65.4379 2320.0 -10 0.6845 66.3430 2342.2 +10 0.7010 68.0056 2383.2 +20 0.7086 68.7730 2402.1 meena et al./oper. res. eng. sci. theor. appl. 4 (3) (2021) 122-141 136 figure 5. changes in * 2 z with respect to parameters table 4. change in * , * 3 q and * 3 z with respect to parameters parameters %change in parameters * * 3 q * 3 z h -20 0.7418 72.1367 1477.1 -10 0.7376 71.7101 1503.7 +10 0.7294 70.8782 1556.0 +20 0.7253 70.4626 1581.7 k -20 0.7335 71.2940 -470.0094 -10 0.7335 71.2940 529.9906 +10 0.7335 71.2940 2530.0 +20 0.7335 71.2940 3530.0 c -20 0.7741 75.4279 1322.1 -10 0.7538 73.3572 1429.7 +10 0.7132 69.2379 1623.0 +20 0.6930 67.1989 1708.8 p -20 0.7092 84.1433 2092.8 -10 0.7220 77.1037 1789.2 +10 0.7440 66.4120 1304.7 +20 0.7536 62.2385 1105.9 s -20 0.7188 69.8044 1492.7 -10 0.7263 70.5639 1511.8 +10 0.7403 71.9843 1547.3 +20 0.7469 72.6551 1563.8 l c -20 0.7200 69.9259 1497.3 -10 0.7269 70.6247 1514.1 +10 0.7398 71.9335 1545.2 +20 0.7457 72.5331 1559.7 control of non-instantaneous degrading inventory under trade credit and partial backlogging 137 figure 6. changes in * 3 z with respect to parameters 8. conclusion and future scope in present article weibull rate of deterioration is influenced by trade credit and demand depends on selling price. the model is assessed with the variable time and optimized. stagnant shortages are acceptable with backlogged allowances. numerical examples and sensitivity analysis illustrate the constructed model. our findings demonstrate: • increasing holding cost increases the overall profit. • the optimal overall profit grows as the shortage costs increase. the supplied model can be used to keep inventory of things that do not perish quickly, such as electronic products, and fashion items. in retail trading, the approach is useful for optimizing unit time profit when partial backlogging occurs. future work in this area will examine freight charges and other factors. this is also applicable when all the parameters are clear and precise, but if there is any uncertainty in the future, we can use fuzzy mathematics to deal 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deteriorating items with price-sensitive demand”, international journal of systems science, 40(12):1273–1281. © 2021 by the authors. submitted for possible open access publication under the terms and conditions of the creative commons attribution (cc by) license (http://creativecommons.org/licenses/by/4.0/). control of non-instantaneous degrading inventory under trade credit and partial backlogging pooja meena 1, anil kumar sharma 2, ganesh kumar 1* 1. introduction 2. notations and assumptions 2.1 notations 2.2 assumptions 3. mathematical formulation 4. solution procedure 5. numerical examples 6. concavity of profit functions 7. sensitivity analysis and observations 8. conclusion and future scope references plane thermoelastic waves in infinite half-space caused operational research in engineering sciences: theory and applications vol. 5, issue 2, 2022, pp. 1-16 issn: 2620-1607 eissn: 2620-1747 doi: https://doi.org/10.31181/oresta180222031d * corresponding author. sdiyaley@gmail.com (s. diyaley), s_chakraborty00yahoo.in (s. chakraborty) metaheuristics-based nesting of parts in sheet metal cutting operation sunny diyaley 1*, shankar chakraborty 2 1*department of mechanical engineering, sikkim manipal institute of technology, sikkim manipal university, majitar, east sikkim, india 2department of production engineering, jadavpur university, kolkata, india received: 07 september 2021 accepted: 22 december 2021 first online: 18 february 2022 research paper abstract: nesting of regular and irregular shaped parts in a sheet metal having constrained boundary so as to maximize effective utilization of material with minimum wastage imposes a challenging task to the metal cutting industries. to resolve the problem, this paper presents the applications of six popular metaheuristics, i.e. artificial bee colony, ant colony optimization, particle swarm optimization, firefly algorithm, differential evolution and teaching-learning-based optimization (tlbo) algorithm with an objective to maximize effective utilization ratio during metal cutting operation. for all the metaheuristics, the considered parts are optimally allocated in the given sheet metal based on bottom left fill algorithm to minimize the corresponding nested height. it is observed that tlbo algorithm supersedes the others with respect to effective utilization ratio, nested height and computational effort. a comparative analysis using values of t-statistic also proves the uniqueness of this algorithm over the others in efficiently solving the nesting problems for regular and irregular shaped parts during sheet metal cutting operation. key words: sheet metal, nesting, cutting, metaheuristic, effective utilization ratio. 1. introduction sheet metal cutting operation results in generation of huge volume of waste material in the form of scrap while positioning various part configurations in the sheet. the sheet metal industries mainly focus on determining the optimal layouts of parts having dissimilar shapes within the available sheet boundary so as to maximize utilization of materials. maximum utilization of sheet metal can effectively reduce scrap while considerably decreasing the expenses during sheet metal cutting operation. these scraps are sometimes hazardous, causing injuries or environmental menaces. in order to reduce wastage of material and efficiently utilize the sheet diyaley and chakraborty/oper. res. eng. sci. theor. appl. 5(2) 2022 1-16 2 metal, an effective nesting strategy is essential for arranging different parts in the sheet before cutting them. nesting is a classical approach to attain an optimal layout of parts in non-overlapping configuration in a given sheet with same thickness and material so that minimal wastage can be guaranteed. nesting can be classified as onedimensional, two-dimensional and three-dimensional. in two-dimensional nesting, two-dimensional parts are positioned in the sheet metal assuming its width to be fixed with an aim of minimizing nested height of the parts (joshi et al., 2012). minimization of nested height of the parts ultimately results in reduction of the collective area involved in the entire nesting process. nesting is widely applied in various manufacturing industries, like shipbuilding, clothing, furniture etc. (ramesh & baskar, 2015). in earlier days, experienced workers of the concerned manufacturing industries were responsible to decide the optimal layouts, but in most of the cases, they were unsuccessful to arrive at the satisfactory solutions as the manual nesting process is tedious and time consuming (kumar & singh, 2008). the nesting problem is often characterized by the inherent complexity associated with the shapes and sizes of the parts, computational intricacy and non-overlapping configurations. presently, there are scarcities of efficient nesting algorithms in the manufacturing industries for locating complex parts which hinder in achieving the maximum productivity during sheet metal cutting operation. nesting algorithms, like rectangular enclosure method, bottom left fill (blf) algorithm and numerous heuristic techniques have commonly been applied to determine effective nesting patterns, but only few of them have been capable of providing satisfactory solutions (ramesh & baskar, 2015). several nesting software are also available in the market, but in most of the cases, they do not provide optimal layouts which may lead to unwanted wastage of materials. mathematical programming techniques have been a popular choice among the researchers while exploring the solutions for nesting problems for regular and irregular shaped objects. however, those techniques are also not suitable for nesting of complex shaped parts. in order to solve complicated nesting problems, many metaheuristic algorithms, like tabu search (ts) (dechampai et al., 2021), genetic algorithm (ga) (huang et al., 2020), simulated annealing (sa) (rausch et al., 2021) etc. have been adopted. even though these techniques can determine effective layouts, they are quite similar to manual methods with respect to computational time (ramesh & baskar, 2015). therefore, the above-identified drawbacks of the earlier adopted techniques have led to the development and implementation of improved mathematical tools to effectively determine the optimal layouts of parts in the sheet metals before the actual cutting operation. in this paper, an attempt is put forward to compare the applicability and optimization performance of six popular metaheuristics, i.e. artificial bee colony (abc), ant colony optimization (aco), particle swarm optimization (pso), firefly algorithm (fa), differential evolution (de) and teaching-learning-based optimization (tlbo) algorithm while solving two-dimensional nesting problems for regular and irregular shaped objects during sheet metal cutting operation. the optimization performance of these metaheuristics is validated with respect to nested height, effective utilization ratio (eur) of the sheet metal and computational time. the paired t-tests are also performed to identify the uniqueness of the adopted algorithms. the organization of this paper is as follows: section 1 describes the nesting process and its importance in sheet metal cutting industries; section 2 presents a metaheuristics-based nesting of parts in sheet metal cutting operation 3 review of the existing literature; and section 3 provides the problem statement along with the mathematical details of blf and metaheuristic algorithms. section 4 deals with the applications of the considered metaheuristics to solve the nesting problems for regular and irregular shaped parts. finally, conclusions are drawn in section 5. 2. literature review in metal cutting industries, nesting of regular and irregular shaped objects in sheets to minimize the trimming loss is a challenging issue. in this direction, several metaheuristic-based algorithms have been proposed by the past researchers along with the deployment of suitable placement strategies to identify the optimal nesting patterns for having maximum utilization of the material. table 1 provides a list of the nesting problems considered, and placement strategies and optimization tools adopted by the past researchers to resolve this issue. table 1. list of the nesting problems, placement strategies and optimization tools name of author(s) problem placement strategy optimization tool(s) cheng et al. (2021) 2d cutting stock problem in construction industry blf auto-tuning symbiotic organisms search algorithm daoden (2020) 2d irregularly shaped stock cutting problem no-fit polygon shuffled leaping algorithm daoden and thaiupathump (2017) 2d rectangular packing problem blf shuffled leaping algorithm dechanmpai et al. (2021) 2d irregularly shaped stock cutting problem blf ts dogde et al. (2021) 2d cutting stock problem blf dna-sticker algorithm erozan and çalışkan (2019) 2d orthogonal packing problem blf ga firat and alpashan (2020) 2d rectangular packing problem blf, no-fit polygon sa hopper and turton (2001) 2d rectangular packing problem blf ga, sa, naive evolution, local search heuristic huang and wang (2020) 2d rectangular packing problem rectangular layout strategy ga labaadi et al. (2020) 2d bin packing problem blf crow search algorithm li et al. (2021) 2d rectangular packing problem blf hybrid adaptive ga qin et al. (2021) 2d nesting problem of irregular shaped parts no-fit polygon, central expansion strategy ga, sa ramesh and bhaskar et al. (2015) 2d cutting stock problem ga diyaley and chakraborty/oper. res. eng. sci. theor. appl. 5(2) 2022 1-16 4 table 1. contd. name of author(s) problem placement strategy optimization tool(s) rao et al. (2021) irregular shaped parts packing problem no-fit polygon hybrid beam search, ts rausch et al. (2021) 2d irregularly shaped stock cutting problem blf sa reddy (2016) 2d regular and irregular shaped cutting problem blf ga sakaguchi et al. (2020) 2d nesting and scheduling of sheet metal parts environment-adaptive ga sherif et al. (2014) nesting and cutting sequence optimization in laser cutting process blf sa struckmeier and león (2019) 2d nesting problem in flatbed laser-cutting machine blf two variants of an evolutionary algorithm valvo (2017) 2d nesting problem of irregular rectangular pieces blf, no-fit polygon evolutionary computation, ga, evolution strategy, sa, estimation of distribution, de, pso virik and singh (2018) 2d nesting of non-guillotine irregular rectangular pieces blf cuckoo search algorithm, bat algorithm wang et al. (2021) 2d bin packing problem blf ga from the review of the above-cited literature, it can be clearly revealed that nesting of regular/irregular shaped parts in sheet metals is a complex problem and various metaheuristic algorithms, like ga, sa, de, aco and other hybrid techniques have already been considered for obtaining effective solutions for varying nesting problems. among the placement strategies, blf algorithm has been the most popular choice. it is also observed that no single algorithm can provide effective nesting solution within reasonable computational time. to the best of the authors’ knowledge, no research work has been conducted to contrast the optimization performance of the adopted algorithms in a single decision making framework. hence, this paper attempts to solve two-dimensional nesting problems for regular and irregular shaped objects in standard sheet metals with the generation of optimal patterns using six well-accepted metaheuristic algorithms, i.e. abc, aco, pso, fa, de and tlbo while employing blf algorithm as the placement strategy to ensure effective and closer packing of the parts. the eur values are computed for the optimal layouts of the regular and irregular shaped parts generated using all the considered algorithms, and are compared with that of randomly allocated parts (rap) in the sheet. the autocad software is utilized here to position the twodimensional parts in the sheet metal and develop the optimal layouts as identified by different metaheuristic algorithms. the uniqueness of these six algorithms is validated using paired t-tests. metaheuristics-based nesting of parts in sheet metal cutting operation 5 3. methods and problem statement 3.1. problem statement this paper aims to solve two-dimensional nesting problems for regular and irregular shaped objects to be cut from sheet metals of fixed dimensions to achieve higher productivity along with maximum material utilization. in order to resolve these problems, six metaheuristic algorithms are applied to obtain the optimal patterns of the parts to be positioned in the sheet metals of fixed width. the optimal pattern should have the minimum nested height of the parts. the minimum nested height would also provide minimum collective area in nesting while increasing the eur value. the eur value is the parameter for evaluating the nesting efficiency of the considered algorithms. the placement of regular and irregular shaped objects in the sheet metal to develop the optimal pattern is accomplished using blf algorithm subject to three restrictions, i.e. a) no parts are placed outside the boundary of the sheet metal, b) none of the parts should overlap each other and (c) height of the parts placed in the sheet is minimum. thus, the nesting problem can be formulated as below: minimize l (1) subject to xi≤ l−li, i = 1,…,n (2) yi≤ w−wi, i = 1,…,n (3) )1()()( ,,,,,,,, kjikjiijkjiijkji amyyxx −+−+−  (4)  =  jim k kjia , 1 ,, 1,ai,j,k {0,1}, xi, yj ≥ 0 where n is the total number of parts to be nested, m is a large positive number and ai,j,k is a binary variable associated with each part. the value of ai,j,k = 1 signifies that jth part is separated from ith part by the line defined by kth edge of the sheet metal; otherwise, it takes a value of 0. on the other hand, xi and yi respectively represent x and y coordinates of the bottom left corner of ith part, li and wi are respectively the length and width of ith part, and l and w are respectively the height of the nested parts and width of the sheet metal. the objective function of eq. (1), which needs to be minimized, signifies attainment of the minimum height of nested parts. equations (2) and (3) are the constraints assuring placement of the parts strictly inside the sheet metal. equation (4) prevents overlapping of the parts and the expression kjiijkjiijkji yyxx ,,,,,, )()((  =−+− ) denotes equation of the line including kth term of mi,j edges of the sheet metal. 3.2. blf algorithm the positioning-based heuristics, like bottom-left (bl) and blf algorithms are the common techniques to pack rectangles in the sheet metal. the blf algorithm is one of the improved versions of bl algorithm, which consists of placing parts into its lowest possible position (hopper & turton, 2001). in bl algorithm, the objects are shifted from the extreme top right corner towards the bottom left position diyaley and chakraborty/oper. res. eng. sci. theor. appl. 5(2) 2022 1-16 6 alternately. the inability of this algorithm to fill up the available spaces obtained from the prior arrangement of the parts is its major drawback, while blf algorithm is capable of filling up those spaces effectively. the strategy applied in blf algorithm consists of placing the parts from the extreme bottom left position resulting in closer packing of objects as compared to bl algorithm. the placement strategy of blf algorithm helps to minimize the nested height while placing the parts one by one, selecting the left-most feasible position in the sheet metal. hence, compared to bl algorithm, blf algorithm results in denser packing patterns. moreover, the application of blf algorithm as a placement strategy largely reduces the run times of the applied metaheuristics while generating high speed feasible solutions. this algorithm is simple to implement as compared to other nesting algorithms that generate good solutions. however, its time complexity is a serious problem. the steps involved in blf algorithm are as follows (xie et al., 2007): step 1: select the parts with similar width. step 2: place larger parts in the bottom left corner. step 3: for every nested part, allocate the remaining parts on its top. step 4: minimize the rectangular enclosure by shifting the parts towards the bottomleft corner of the sheet metal. step 5: repeat the above steps until the column is completely filled up by the parts. step 6: the column is remounted. step7: all the possible arrangements of the parts are attempted through re-nesting. step 8: again fill up the column with the parts. step 9: nest the unprocessed parts following step (1). step 10: nest the subsequent columns until the entire process is completed. 3.3. metaheuristic algorithms since the last two decades, a wide variety of metaheuristic algorithms, like ga, aco, pso, de, abc, fa, sa, ts and tlbo has been emerged out, and they have been gaining increasing popularity in solving complex optimization problems. these metaheuristic algorithms are more adaptive and intelligent as compared to heuristic techniques which are dependent on their computational ability based on trial and error method (yang, 2014). the term ‘meta’ in metaheuristic denotes ‘higher level’ and these algorithms can achieve better results than simple heuristics. all the metaheuristic algorithms consist of attributes of randomization and local search approach. the randomization feature of these algorithms assists in searching out solutions from local to global scale. hence, these algorithms are highly capable of arriving at the global optimal solutions. any metaheuristic algorithm has two main components, i.e. intensification and diversification. in intensification, exploitation of information is carried out assuming that the current good solution can be found out in a particular region. diversification creates varying solutions in order to explore the search space on a global scale (talbi, 2009). metaheuristic algorithms, like aco, abc, pso, fa, de and tlbo are categorized as population-based search techniques as they employ a set of strings or multiple particles to ensure global optimality. on the other hand, single solution-based approaches, like sa, guided local search etc. are metaheuristics-based nesting of parts in sheet metal cutting operation 7 those techniques which determine the global optimal solution based on improving a single candidate solution (manda et al., 2012).the metaheuristic algorithms employ the following procedural steps to arrive at the optimal solutions (khajehzadeh et al., 2011): step 1: in the search domain, set the population with random values. step 2: for each individual of the population, compute its fitness value. step 3: operators, like crossover, mutation etc. are applied to generate new populations through reproduction of the preferred individuals. step 4: go to step (2), until the criterion for termination is reached. 4. metaheuristic-based nesting of parts this paper applies six metaheuristic algorithms to solve two-dimensional nesting problems to determine effective nesting patterns for regular and irregular shaped parts during sheet metal cutting operations. in order to validate the nesting performance of the considered algorithms, two different problems for nesting of two-dimensional regular and irregular parts are considered here. in the first problem, an attempt is put forward to search out the optimal nesting pattern for 22 two-dimensional regular shaped parts in a sheet metal with dimension 100×120 mm. on the other hand, in the second problem, 22 irregular shaped parts are effectively nested in a sheet metal of 300×400 mm dimension. the configurations of the twodimensional regular shaped parts to be nested are shown in figure 1. these are the most commonly utilized shapes (although their dimensions may vary) for sheet metal cutting/punching operations. the optimal patterns of the parts obtained from simulation of the six metaheuristic algorithms are positioned in the sheet metal based on blf algorithm. while placing those parts, the nesting height should be minimized and width of the sheet is kept fixed with an objective of minimizing the collective area involved in the nesting process. the performance of arranging parts in the sheet metal is expressed with respect to eur value, which can be defined as the ratio of the sum of areas of the parts placed in the sheet metal to the total area of the sheet metal. it can be denoted as: s n i i a a =1 = (eur) ration utilizatio effective (5) where ai is the area of ith object to be nested and as is the total area of the sheet metal. for implementation of the considered metaheuristic algorithms, the corresponding computer codes are developed in matlab 2013a in 4.00 gb ram, 2.9 ghz processor and 32-bit operating platform. to validate the optimization performance of these metaheuristics, the derived solutions are compared with the rap in the sheet metal. the following values are set based on trial and error method for various algorithm-specific parameters to derive the optimal solutions (experiments performed by the past researchers also help in adjusting their values): diyaley and chakraborty/oper. res. eng. sci. theor. appl. 5(2) 2022 1-16 8 abc algorithm: number of iterations = 1000, swarm size = 300, number of onlooker bees employed = 50% of swarm size, number of cycles = 500, number of scouts per cycle = 1, limit = 50 and number of employed bees = 50% of swarm size. aco algorithm: number of iterations = 1000, sample size = 40, intensification factor = 0.5 and deviation distance ratio = 1. pso algorithm: number of iterations = 1000, population size = 300, inertia weight factor = 0.65, and acceleration coefficients = 1.65 and 1.75 fa: number of iterations = 1000, number of fireflies = 300, light absorption coefficient = 1, initial randomness = 0.91, randomness factor = 0.92 and randomness reduction = 0.75. de algorithm: number of iterations = 1000, population size = 300, lower bound of scaling factor = 0.2, upper bound of scaling factor = 0.8 and crossover probability = 0.9. tlbo algorithm: number of iterations = 1000 and population size = 300. 4.1. regular shaped parts figure 1. regular shaped parts in this problem, two-dimensional regular shaped parts, as shown in figure 1, are taken into consideration for searching out the optimal nesting pattern while subsequently placing them in a sheet metal having fixed dimension of 100×120 mm. now, the optimal patterns for these regular shaped parts are determined using all the metaheuristic algorithms, as presented in figure 2. the blf algorithm is applied here as the placement strategy to position these objects in the sheet metal. this placement strategy ensures better packing of parts so that the collective area involved in the nesting process is minimized. in figure 2, the positions of the regular shaped objects using rap are also portrayed which do not consider application of any algorithm for their allocations. it can be observed that the minimum nested height of 73.7 mm is obtained in tlbo algorithm, whereas, the maximum nested height of 85.13 mm is attained in rap. the abc, pso, fa and de algorithms provide those heights as 78.2, 77.65, 79.83, and 77.04 mm respectively. the aco algorithm with a nested height of 80 mm performs worst in comparison to other metaheuristic algorithms. thus, there are 6.10, 8.55, 5.36, 8.32, 4.53 and 15.51% reductions in the nested height in tlbo algorithm as compared to abc, aco, pso, fa, de and rap techniques respectively. the computed eur values and computational times required to develop the corresponding nesting patterns by these algorithms are metaheuristics-based nesting of parts in sheet metal cutting operation 9 provided in table 2. it is interesting to note that among all the algorithms under consideration, the calculated eur value based on tlbo algorithm is the maximum along with the lowest computational time. thus, it can be propounded that tlbo algorithm excels over the others with respect to height of the nested parts, eur value and computational time involved. the values of the nested height while placing the regular shaped objects in the given sheet metal obtained using the metaheuristic algorithms and rap are compared in figure 3. it reveals that tlbo algorithm outperforms the other techniques with respect to minimum nested height. 4.2. irregular shaped parts this problem consists of finding out the optimal nesting pattern for twodimensional irregular shaped parts in a sheet metal having fixed dimension of 300×400 mm. the optimal patterns derived by the six metaheuristics are exhibited in figure 4. the calculated values of eur and computational times for these algorithms are compared in table 3. it can be observed that the most effective nesting pattern is provided by tlbo algorithm with minimum height of the nested parts as 224.53 mm while arranging them in the given sheet metal. the pso algorithm provides the maximum nested height of 258.57 mm, while de, fa, abc and aco algorithms perform moderately. these nested heights for different layouts as obtained by the considered algorithms are shown in figure 5. from figures 4 and 5, it can be revealed that tlbo algorithm achieves 10.61, 7.65, 12.93, 1.53, 3.70 and 13.78% reductions in the nested height against abc, aco, pso, fa, de and rap techniques respectively. among the considered metaheuristics, it can be noticed that pso algorithm performs worst with respect to the nested height of the irregular shaped parts and eur value. for both the nesting problems, abc algorithm consumes maximum computational time to derive the optimal layouts of parts as compared to other algorithms. as mentioned earlier, this paper emphasizes on solving two-dimensional nesting problems to identify the optimal patterns for regular and irregular shaped objects during sheet metal cutting operation using six popular metaheuristic algorithms. those effective nesting patterns would assist in minimizing the scrap while reducing trimming losses to minimize the overall production cost in sheet metal industries. the convergence diagrams of the nested heights for 1000 iterations for all the six metaheuristics considering packing of regular and irregular shaped objects are depicted in figure 6. for both the problems, it is observed that tlbo algorithm excels over the others with respect to minimum nested height and computational time. it takes only 15-20 iterations in reaching at the minimum nested height, whereas, the other algorithms consume few more iterations to derive the optimal solutions. the tlbo algorithm is an efficient, simple and competent technique to achieve the global optimal solutions with less computational effort, having minimum algorithm-specific parameters, i.e. population size and number of iterations. the other adopted algorithms need more computational memory and have numerous algorithmic parameters, which if not tuned correctly, may result in local optimal solution with high computational effort. in order to confirm uniqueness of tlbo algorithm over the other metaheuristics, two-tailed paired t-tests are performed for both the packing problems with the following null hypothesis and alternative hypothesis: h0(null hypothesis): population means for two algorithms are equal (µ1 = µ2). hα(alternate hypothesis): population means for two algorithms are unequal (µ1 ≠ µ2). diyaley and chakraborty/oper. res. eng. sci. theor. appl. 5(2) 2022 1-16 10 (a) rap (b) abc algorithm (c) aco algorithm (d) pso algorithm (e) firefly algorithm (f) de algorithm (g) tlbo algorithm figure 2. optimal layouts for regular shaped parts using different metaheuristics metaheuristics-based nesting of parts in sheet metal cutting operation 11 figure 3. comparison of nested heights for regular shaped parts table 2. comparison of eur and computational time for regular shaped parts problem no. of parts rap abc aco pso fa de tlbo eur 22 0.799 0.833 0.814 0.839 0.816 0.846 0.888 computational time (min) 22 8.21 7.54 7.98 7.25 8.01 6.43 table 3. comparison of eur and computational time for irregular shaped parts problem no. of parts rap abc aco pso fa de tlbo eur 22 0.708 0.730 0.750 0.715 0.795 0.779 0.807 computational time (min) 22 12.54 11.67 11.41 11.87 11.52 10.48 table 4. paired t-tests for nested heights of regular and irregular shaped parts regular shaped parts metaheuristics abc aco pso fa de tvalue -82.4 -101.3 -81.9 -290.7 -52.1 irregular shaped parts metaheuristics abc aco pso fa de tvalue -82.4 -101.3 -81.9 -290.7 -52.1 diyaley and chakraborty/oper. res. eng. sci. theor. appl. 5(2) 2022 1-16 12 rap abc algorithm aco algorithm pso algorithm firefly algorithm de algorithm tlbo algorithm figure 4. optimal layouts for irregular shaped parts using different metaheuristics metaheuristics-based nesting of parts in sheet metal cutting operation 13 figure 5. comparison of nested heights for irregular shaped parts the population mean denotes the average value of the objective functions calculated after 1000 iterations for each of the metaheuristics considered. the results of t-test are provided in table 4 for both the problems. based on these results, the null hypotheses for two-tailed t-test can be rejected because for all the paired comparisons between the considered metaheuristic algorithms, the absolute values of the test statistic are greater than the corresponding critical value at 5% level of significance. it thus proves the uniqueness of tlbo algorithm over the other algorithms under consideration. thus, tlbo algorithm can be applied as an effective tool for determining the optimal nesting patterns for regular and irregular shaped objects with less computational effort. (a) regular (b) irregular figure 6. convergence diagrams for the considered metaheuristic algorithms diyaley and chakraborty/oper. res. eng. sci. theor. appl. 5(2) 2022 1-16 14 5. conclusions in this paper, six popular metaheuristic algorithms are applied to solve twodimensional nesting problems for regular and irregular shaped parts based on blf placement strategy during sheet metal cutting operation. the objective is set to reduce wastage of material by minimizing the nested height of two-dimensional parts resulting in reduction of the total area required for packing the parts in sheet metal. the solutions from the considered metaheuristic algorithms generate effective and optimal nesting patterns for different parts to be placed in the sheet metal before the actual cutting operation. it is observed that tlbo algorithm almost achieves the global optimal solution with minimum heights of the nested parts for both the considered problems. this algorithm also excels over the others with respect to eur value and computational time. it achieves 6.60, 9.09, 5.84, 8.82 and 4.76% improvements on eur, and 27.68, 17.26, 24.10, 12.75 and 24.57% reductions in computational time respectively against abc, aco, pso, fa and de algorithms for regular shaped objects. on the other hand, there are 10.55, 7.6, 12.87, 1.51 and 3.59% improvements in eur, and 19.65, 11.35, 8.87, 13.26 and 9.92% reductions in the computational time in tlbo algorithm as compared to abc, aco, pso, fa and de techniques respectively for irregular shapes parts. thus, it can be concluded that this algorithm can be successfully applied to determine the optimal patterns of parts to be positioned in a stock in metal cutting industries in order to minimize cutting time and trimming loss. the future scope of this paper may include determination of the optimal nesting patterns for parts with more complex configurations while applying other new metaheuristics, like ba, cuckoo search algorithm, grey wolf optimizer, jaya algorithm etc. a comparative analysis between blf algorithm and other heuristics, like rectangular placement method, quick location and movement (qlm), compact neighborhood algorithm (cla) etc. for effective placement of objects in sheet metals may be another scope of this paper. the limitations of this paper include consideration of only blf algorithm for placing two-dimensional objects in the sheet in non-overlapping patterns. references cheng, m. y., fang, y. c., & wang, c. y. 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(2014). nature-inspired optimization algorithms. london: elsevier. © 2022 by the authors. submitted for possible open access publication under the terms and conditions of the creative commons attribution (cc by) license (http://creativecommons.org/licenses/by/4.0/). https://doi.org/10.1142/s2424862218500094 plane thermoelastic waves in infinite half-space caused operational research in engineering sciences: theory and applications vol. 2, issue 2, 2019, pp. 24-39 issn: 2620-1607 eissn: 2620-1747 doi:_ https://doi.org/10.31181/oresta1902025t * corresponding author. e-mail address: gtepic@uns.ac.rs (g. tepic), sremacs@uns.ac.rs (s. sremac), moraca@uns.ac.rs (s. morača), blalic@uns.ac.rs (b. lalić), milan.kostelac@fsb.hr (m. kostelac), vladimir.stojkovicns@gmail.com (v. stojković) accidents in facilities for storing hazardous materials goran tepić1*, siniša sremac1, slobodan morača1, bojan lalić1, milan kostelac2, vladimir stojković1 1 faculty of technical science, university of novi sad, serbia 2 faculty of mechanical engineering and naval architecture, university of zagreb, croatia received: 18 april 2019 accepted: 18 july 2019 first online: 25 july 2019 original scientific paper abstract. the vital elements of numerous industrial plants include the process equipment which, depending on the nature of the technological process, can be exposed to internal pressure in the general case of a variable size. the typical examples of process equipment are available at lpg stations (distribution centers), fuel tanks, gas boilers, combustion plants, etc. practical experience and the analysis of the cause of accidents have shown that damage to process equipment is most often followed by the explosions of the tanks in which the flammable substances, such as lpg, petrol, diesel and jet fuel, oils, etc. are stored. the explosion of a tank cannot occur spontaneously, but only results from external factors. this means that the explosion of process equipment is preceded by the primary events whose harmful effects are manifested through the following phenomena: the weakening of the strength of a tank, an increase in pressure above the nominal value, or a combination of the two preceding cases. key words: risk assessment, accidents, hazardous materials, process equipment, domino effect, bleve. 1. introduction the rapid industrial development of the world's leading economies requires the increasing use of hazardous substances and chemicals in many segments of social activities. modern production conditions and strict market demands in achieving certain product properties require the presence of hazardous substances in many processes that emerge from the framework of the petrochemical industry with a relatively small product range, which has been the case in the past decades with developing countries. today, hazardous substances are present in all social spheres, accidents in facilities for storing hazardous materials 25 ranging from industrial plants, agriculture, and medicine to national security and everyday use in the household. the inevitable followers of hazardous substances are their hazardous characteristics that can adversely affect human or animal health and the environment in a direct or indirect manner. the distribution of accidents within the logistics system is based on the elementary structure of logistics subsystems and has five discrete states: production, storage, reloading, transport, and use (tanackov et al. 2018). on the one hand, no direct risk modeling in the production, storage, handling and transport of hazardous substances can be performed. the concept of dangerous goods operations is heterogeneous, starting with a range of hazardous materials, transport supplies, installed equipment, traffic intensity, the distribution concept, employee training, etc., whereas on the other, it is indirectly possible within statistical probabilities, i.e. within data from accidental databases. these data are the expensively paid mistakes that are measured by human lives, great material damage and long-term environmental consequences. the databases such as mhidas, mars, facts, mahb, carat, arip, nedies, eccairs, and irdat represent a posteriori significant data in risk modeling. accidents in the system of hazardous substances, such as a chemical release, a fire, an explosion or the bleve effect, may cause great catastrophic consequences not only for employees in their workplaces, but also for the residents and the environment. in addition, the financial losses caused by damage on objects (parts of production plants, tanks) are enormous, and rehabilitation and their re-entry into operation require a lot of time. these effects also result in other serious influences, such as, for example, the inability to provide sufficient quantities of raw materials to connected and/or related industries. the development of the oil and chemical industry has caused the use of large and complex facilities in their plants, resulting in a large increase in the storage space (tanks of different shapes and dimensions). in the meantime, due to the use of land (a lack of space) and for economic reasons, the distances between installations and warehouses have become increasingly smaller. this branch of industry continues to develop in the direction of intensive and deep processing, chemical processes end up mainly through a series of physical and chemical reactions, and their main raw materials and products are in the liquid and gaseous states that are toxic, flammable and corrosive (liu, zhang, & xu, 2013). therefore, risk for oil and chemical plants has dramatically increased, in particular so when the risk of explosions and fires is concerned. in the case of an accident (a fire or an explosion), and bearing in mind all of the foregoing, there may be a chain disaster, and therefore it may endanger human lives, environmental safety, and material assets, and may also cause high environmental pollution, as well as other secondary consequences (yu & guan, 2016), (pasley & clark, 2000), (kim et al. 2009). accidents in the process industry are most frequently a result of the release of hazardous materials, fires and explosions of process installations (hemmatian et al. 2014.). the effect of the technical-technological connection of process installations is such that the occurrence of an accident in one part of the plant may lead to the escalation and occurrence of a series of cascade accidents – a domino effect (abdolhamidzadeh et al. 2011), (dabra et al. 2011). the storage of eco-friendly tepić et al./oper. res. eng. sci. theor. appl. 2 (2) (2019) 24-39 26 substances, such as tngs, is particularly characteristic from the aspect of the appearance of a domino effect and the escalation of the initial incidents. a domino effect is a very important phenomenon in the process industry and was specifically referred to in the first version of the seveco directive (european council directive 82/501/ecc). the modifications of this directive prescribe that the dangers of a domino effect must be assessed differently, depending on whether they work on indoor or outdoor industrial plants and whether they are reflected in the application of directive 96/82/ec and 96/82/ec, or not. the occurrence of fire within technological installations is predominantly preceded by a discharge of inflammable liquids, gases or vapors (bariha et al. 2016). the explosions of process equipment are most often due to the bleve effect or a mechanical damage caused by the fragmentation of fragments (eckhoff, 2014), (sun et al. 2015). the phenomenon of the fragmentation of a tank is characterized by the cause-effect relationship between the cascading events in the accidental chain (khan & abbasi, 1999). the occurrence of critical pressure in process equipment can be due to a mechanical (physical) explosion, a cold or warm bleve effect, a closed explosion or uncontrolled chemical reactions. failures on the installations and a potential escalation of accidents due to the fragmentation of process equipment are characterized by a high degree of uncertainty (khakzad et al. 2018). therefore, the analysis of a domino effect implies a previously conducted assessment of the fragmentation risk since the subsequent fragmentation of damaged process equipment establishes a potential accidental chain. the intensive development of the modern processing industry is characterized by a considerable risk of large-scale domino effects. the prevention of potential accidents is conditioned by the use of fragmentation barriers (landucci et al. 2016), (kang et al. 2016), the identification of the fragmentation mechanism (baker et al. 1983), and the basic characteristics of the primary fragments that are defined by the number, shape, velocity, and trajectory (ccps, 1994). the procedure for predicting the number and the mass of the fragments of cylindrical storage tanks for lpg was proposed by baker et al. (baker et al. 1997). the results of their study were the basis for several recent research studies in the field of the fragmentation of tanks (hauptmanns, 2001), (hauptmanns, 2001a). the purpose of fragmentation analysis is to prevent the installations and equipment of process plants from potential fragment impacts (sun et al. 2017). the escalation of a potential damage to process installations is prevented by using the fragmentation barriers first implemented in nuclear installations (moore, 1967). risk assessment due to the fragmentation of pressure vessels requires adequate hazard modelling, and the creators of the first fragmentation models were moore and baker (moore, 1967), (baker et al. 1983). in 77% of accidents, fragmentation was a result of the explosions of the pressurized vessels generating from 1 to 9 fragments (holden & reeves, 1985). holden found that 60% of the generated fragments covered a sectoral angle of ±30° on both sides of the tank (holden, 1988). some recent studies have been based on the results of these studies (mébarki et al. 2009), (mébarki et al.2009a). mébarki et al. suggested an entropy model for estimating the number of generated fragments (mébarki et al. 2009). the typical explosions of tanks following industrial accidents were related to the bleve phenomenon (eckhoff, 2014), (zhang et al. 2016). risk assessment due to the fragmentation of a tank involves modelling the fragment flight, and in the literature a simplified model for fragmentation analysis has exclusively been applied (mannan, 2012). accidents in facilities for storing hazardous materials 27 2. bleve effect among different possible major accidents, boiling liquid expanding vapor explosions (bleves) keep occurring from time to time. a number of pieces of equipment and activities such as: steam boilers, liquefied gas storage tanks, road and rail tankers, etc. can originate them (hemmatian et al. 2019). boiling liquid expanding vapor explosions (bleves) are a major accident which can have severe consequences; they occur from time to time, both in fixed plants and in the transportation of hazardous materials. overpressure and the ejection of vessel fragments are the common effects of such an explosion; these can be followed by a fireball if the substance is flammable. if a tank containing liquid or a liquefied gas is subjected to thermal loading from a fire, an explosion of the tank is possible. such an event is called a bleve (boiling liquid expanding vapour explosion) (marshall, 1987), (baker et al. 1983). if a liquid or a liquefied gas is combustible, a fireball (a large-scale diffusion flame with strong thermal radiation) is formed. during the destruction of the tank, the shock waves of a high amplitude are produced. accidents involving bleve are characterized by the severe destruction of the plant, with people being killed. such accidents took place in fazen, france (1966), mexico (1984), and alma-ata, kazakhstan (1989). the serious consequences of bleve and a damage to the vessels containing lpg subjected to fire have drawn the attention of many investigators. impact failure (44.8%) and the human factor (30.3%) were the most common causes of bleves (hemmatian et al. 2019). the fragmentation of a tank due to the bleve effect is usually followed by the generation of two or three fragments, and very rarely four or five fragments (nguyen et al. 2009). the fragmentation of a tank due to the bleve effect is characterized by the obligatory fire occurrence in the case of the generation of a smaller number of fragments (mishra, 2016). in the literature, the assessment of the number of generated fragments is carried out by means of the entropy model using accident data (mébarki, 2009). the number of generated fragments in the explosion of a tank is usually up to five, and very rarely exceeds nine (holden, 1985), (holden,1988). nguyen et al. state that, according to the scientific reports of the ineris, typical explosions (bleve) of cylindrical tanks are most often followed by the generation of two or three primary fragments (nguyen, 2006). the application of the entropy model requires the mandatory inclusion of accident data (sun et al. 2012). the accidents accompanied by the explosion of a tank are distinguished by the three effects: a blast wave, thermal radiation and fragmentation. the fragmentation of a tank is followed by the generation of primary fragments, while the blast wave initiates the formation of secondary fragments. thermal radiation is a result of the formation of a fireball, whose influence in the explosion of the lpg tank having a volume of about 50 m3 is manifested at the distances of up to 170 m, whereas the effect of secondary fragments is intensely expressed at the distances of up to 125 m (plans et al. 2015.). the most pronounced effect of the explosion of a tank relates to fragmentation, since the range of fragments can reach as far as 1.2 km (tugnoli et al. 2014). bleve affects the previous occurrence of an incident in the form of a fire in the immediate vicinity of the tank, most often due to a discharge of inflammable substances or as a result of some other cause. a thermal impact on the walls of the tank is manifested by a reduction in the resistance of the material (a tensile tepić et al./oper. res. eng. sci. theor. appl. 2 (2) (2019) 24-39 28 strength), so that the destruction of process equipment will follow a lower critical pressure than the normal value (a value corresponding to a no-fire effect). the temperature effect is exclusively reserved for the bleve effect as there is not enough time for the other types of explosion to transfer heat to the walls of the tank (for example, in an uncontrolled chemical reaction, etc.). each type of indoor explosion (a tank) must be accompanied by shock waves, and in the case of fire-extinguishing substances by the emergence of a fireball (thermal radiation), too. the amount of these energies depends on the type of the explosion and the type of the dangerous substance. the explosion of toxic substances with nonflammable substances is not accompanied by thermal radiation, but due to the dispersion of toxic substances, additional hazardous substances arise in the form of the contamination of the surrounding area. a hazard due to thermal radiation does not exceed 200 m for an explosion of about 50 m3 of tng, whereas a toxic hazard from the same volume with unfavorable meteorological conditions may be up to several kilometers (djelosevic & tepic, 2018). 3. the domino effect in terms of production facilities and particularly refineries, it is necessary to focus (in terms of transport and production processes) on storage capacities. the storage capacities consisting of the tanks of different types, sizes and shapes are used for the permanent or temporary storage of different classes of dangerous substances (oil and oil derivatives, gas, high-pressure liquids, various corrosive substances, etc.). when an accident occurs in the production/processing or storage facilities, the physical effects of that particular accident very often lead to a damage to another surrounding equipment. taking this into account, a relatively small incident can be said to have the ability to escalate into an event causing a damage to a much larger surface and leading to far severer consequences; in practice, it is called a domino effect. such effects are usually created and caused by the physical effects of primary accidents, such as (chen et al. 2012): • overpressure, • fragments (impact fragments) • thermal radiation, and • heat flux. darbra et al. (2010) analyzed 225 accidents with the consequences of the domino effect in the processing, storage and transport plants in the period since 1961. on this occasion, the following aspects were analyzed: the accident scenario, the type of the accidents, the class/type of the substance, the causes and the consequences, as well as the most frequent accidents sequences. the analysis established the fact that the most common causes were: the external losses of 31% and the mechanical errors of 29%. even 35% of the domino-effect accidents happened in the storage area, whereas 28% of them occurred in the processing plants. the flammable substances included 89% of the accidents, most of which were lpg. in the largest number of the cases, the damaged equipment has no ability to resist, thus leading to a leakage and a loss of hazardous material and additional scenarios: a) explosion → fire (27.6%), b) fire → explosion (27.5%), and c) fire → explosion (17.8%). accidents in facilities for storing hazardous materials 29 the definitions of a domino effect contain the following three concepts (cozzani et al. 2006), (antonioni et al. 2009), (nguyen et al. 2014): 1. a “primary” event (fire, an explosion) that occurs in a certain unit; 2. the propagation of the accident towards one unit or a larger number of units or plants, in which “secondary” accidents are triggered as a result of the primary event; 3. an “escalation” effect leading to a general increase in consequences, with such secondary accidents being severer than the primary one. the oil and chemical industry include many flammable and explosive chemicals for production and storage, and manufacturing processes are performed at high temperatures or high pressures. there are many different pieces of pressure equipment in industrial plants, such as tanks (cylindrical, elliptical, and torispherical) containing gas (lpg) or high-pressure liquids. when it reaches a critical level of high pressure, overheating or mechanical stress, the tank can suddenly explode and generate many fragments (one or more, depending on the critical pressure, the crack propagation, the type of the material and the connection of the basic mechanical components) that pose a threat to another equipment or other adjacent tanks. so, the fragments caused by the explosion of the tank have an effect on other tanks, and this effect is reflected in a partial or complete breakdown and/or damage to adjacent tanks and equipment. fragments are of different shapes, sizes, initial speeds, and initial departure angles (horizontal and vertical). according to the ineris expert reports, a typical explosion (bleve) of a cylindrical tank creates a limited number of massive fragments, mainly two or three, and very rarely more than four or five. 4. the probability of a domino effect the accidents characterized by an explosion of process equipment in an installation are usually followed by a sequential sequence of events (a domino effect); so, in order to analyze risk, it is necessary to know the probability of the occurrence of the primary and secondary events of the observed accident chain. in this context, the probability of the occurrence of a domino effect requires the knowledge of the probabilistic probabilities of the consequent-causal events of one cycle of the emergency chain. the probability of producing a domino effect is presented by (1), if the primary and secondary events are marked as pd and sd, respectively. )|()()( pdsdppdpsdpdp = (1) as is known from the theory of probability, the formulation (6.10) shows that the realization of a secondary event is dependent on the realization of the primary event that is the first in an accidental chain. the primary event is an independent event in an accidental sequence and has the role of linking multiple sequential events into a unique accidental chain. the conditional likelihood of the occurrence of a secondary event, provided that the outcome of the primary one is completely certain, has the following form: tepić et al./oper. res. eng. sci. theor. appl. 2 (2) (2019) 24-39 30 )( )( )|( pdp sdpdp pdsdp  = (2) it is important to point out the fact that the analysis of a domino effect in research studies is based on a conceptual misinterpretation since it interprets the probability of an accidental sequence without the probabilistic probability of primary and secondary events. in this way, the independence of events in an accidental chain is established, which is contrary to logical and mathematical principles. the basic risk factor for a hazard that can be the generator of a domino effect encompasses the probability of its occurrence and, therefore, great attention is paid to this phenomenon for this very reason. the occurrence of a chemical accident during the technological process in the industrial plant for the production (processing) of hazardous substances is illustrated by the principle of the bajes network. in order to simplify the considered illustration, that there are only two causes in the occurrence of the accident, namely the human factor and the unreliability of equipment, will be assumed. the variables representing the human factor and the reliability of equipment are indicated by hu (human factor) and re (reliability of equipment), respectively. assign an expert assessment of the potential causes of a chemical accident due to hu and re the following probabilities: p(hu = yes) = p or p(re = no) = q, respectively. if chemical accidents are marked as chma, and if it is supposed that a) the organized hu behavior is in accordance with the prescribed procedure, and that b) the embedded process equipment works reliably, then the technological process takes place normally without any hint of a possible accident and the same is valid: p(ca = yes | hu = no, re = yes) = 0. however, the probability of the occurrence of an accident due to unreliable process equipment reads as follows: p(ca = no, re = no) = ½. since hu manages the work of the technological process, any significant deviation from the procedure of working with dangerous substances inevitably leads to the occurrence of an accident. this may be a result of unintentional omissions due to the irresponsibility of hu (the management or direct executors) and the preplanned organized activities in the form of sabotage, regardless of the motives for such actions. the probability of the occurrence of an accident, if caused by the harmful effects of hu, regardless of the degree of the reliability of process equipment, is as follows: p(ca = yes | hu = yes, re = yes) = 1 and p(ca = yes | hu = yes, re = no) = 1. the probability of the occurrence of an accident may be expressed based on the previous analysis by applying the following equation:    == == === rehu rehu rehu rephuprehuyescap reprehuprehuyescap rehuyescapyescap , , , )()(),|( )()|(),|( ),,()( (3) where p(hu | re) = p(hu) as a consequence of the assumption of the independence of hu and re events. then, after developing the sum of (3), the following equation is obtained: accidents in facilities for storing hazardous materials 31 )()(),|( )()(),|( )()(),|( )()(),|()( yesrepyeshupyesreyeshuyescap yesrepnohupyesrenohuyescap norepyeshupnoreyeshuyescap norepnohupnorenohuyescapyescap ===== +===== +===== +======= (4) qpq qpqpqpqpyescap +−= −+−−++−== )1( 2 1 )1(1)1()1(01)1( 2 1 )( (5) where p and q represent, respectively: the probability that the cause of the accident (ca) will be the human factor (hu = yes): p = p(hu = yes), and the probability that ca will be equipment unreliability (re = no): q = p(re = no). these probabilities are a result of an expert assessment and can be obtained on the basis of statistical monitoring for hu, or according to the analysis of the reliability of process equipment in the real conditions of exploitation for re. adopting, for example, that p = 0.10 and q = 0.15, the probability of chma has the value p(ca) = ½·q·(1-p)+q = ½·0.10·(1-0.10)+0.15=0.195. the obtained probability p(ca) = 0.195 represents the “a priori” probability of a chemical accident (ca) before observing any evidence.   = === = ===== re re yescap repyeshupreyeshuyescap yescareyeshupyescayeshup )( )()(),|( )|,()|( (6)   = === = ===== hu hu yescap norephupnorehuyescap yescanorehupyescanorep )( )()(),|( )|,()|( (7) by developing the sum in (6) and (7), and by replacing the concrete probability values, the following equation is obtained: 689,0 10,03 2 3 2 )1( 2 1 1)1(1 )|( = − = − = +− +− === p qpq qpqp yescayeshup (8) 379,0 10,03 10,01 3 1 )1( 2 1 )1( 2 1 1 )|( = − + = − + = +− −+ === p p qpq qpqp yescanorep (9) tepić et al./oper. res. eng. sci. theor. appl. 2 (2) (2019) 24-39 32 5. theoretical analysis of a tank horizontal cylindrical tanks for tng storage are responsible technical systems designed according to en 13445-3 (en 13445-3:2014). the projected exploitation characteristics and the achieved quality of production are checked by testing the tank according to en 13445-5 (en 13445-5:2014). the two-axis stress state of the tank indicates the longitudinal and radial deformation of the shell. the analysis of the stress state of the tank is an integral part of the design activities in terms of fulfilling exploitation requirements. a typical shape of the horizontal cylindrical tank discussed in the continuation of this paper is presented in fig. 2. the construction of the tank consists of the supports (item 1), the cylinder segments (items 2-5), the elliptical end caps (item 6), and the lifting lugs (item 7). the tank is supplied with the filling and discharging system (fdt), the measure and control system (mcs), the inspection hatch (ih), and the safety valve (sv). the empty tank mass is 12.3 t and provides storage of up to 50 m3 of tng. figure 1. a horizontal cylindrical tank with the elliptical end caps according to din 28013 horizontal cylindrical tanks have three critical cross-sections (figure 1). the a-a critical cross-section is characteristic of tanks with torispherical end caps, whereas elliptical end caps influence the tank fracture at the b-b cross-section (figure 1a). the fracture along the c-c cross-section exclusively occurs in tanks with spherical end caps (figure 1b). the wall thickness of the tank is constant δ = 14 mm (figure 1c). this condition is of great importance in the fragmentation model for the assessment of the initial velocity. accidents in facilities for storing hazardous materials 33 the critical zone of the tank in fig. 1 corresponds to the passage of the cylinder into the elliptical end cap (b-b cross-section). the critical zones of the cylindrical tank are estimated according to (10) and (11), derived from the basis of the substrate in (ciarlet, 2000). ( ) p pd h d mxxx                +=== 100 42 292685.01082.0 2 max,   (10) ( ) p pd h d mx                +=== 104 22 031418.01195.0 2 max,    (11) authoritative stress for dimensioning the pressure vessel is given by (11). permissible tress for the s355j2g3 (the tank material) is 195.83 mpa. the maximum operating pressure according to (11) is 1.88 mpa, whereas en 13445-3 prescribes 2.12 mpa. the operating pressure of the lpg storage tank ranges from 16.4 to 16.9 bars (which is an average of 16.7 bars). rationally designed tanks are characterized by a minimum difference x,max and θ,max, which is achieved by a d/2h ratio. in the case under consideration, d/2h = 2; so, it follows θ,max/x,max = 4%. the critical zone is conditioned by the criterion (d/2h) = 2.086. the critical zone 1 is considered only if the tank head is elliptical. then, it is always (d/2h) < 2; so, fragmentation is most often followed by the separation of the end cap from the tank cylinder due to the expansion of the fracture lines by circumference (θ > x). the critical zone 3 dominates when θ < x (the hemisphere head); otherwise, the b-b cross-section is authoritative (fig. 2). the estimation of critical zones according to (10) and (11) is limited to the generation of a smaller number of fragments due to the bleve effect. the real stress of the tank varies between (10) and (11) due to the axial asymmetry. therefore, the fragmentation of the tank generally requires the identification of real stress through software structural analysis. figure 2 shows the critical areas of a cylindrical tank. figure 2. the software simulation of the critical zones of the tank (the pressure of 16.7 mpa) tepić et al./oper. res. eng. sci. theor. appl. 2 (2) (2019) 24-39 34 when the crack spreads faster than the leakage of the fluid/liquid, an explosion of the tank occurs, where fragments are created, the size and velocity of which depend on the type of the cracks, i.e. the brittleness and flexibility of the material. the fragments projected due to the explosion of the tank can affect and damage adjacent objects and tanks in their surroundings. if these affected objects are, for example, pressurized containers, there is a risk that an explosion will occur, which would produce another set of projectiles/fragments. such fragments can affect other devices and generate next explosions, thus leading to a scenario known as the “domino effect” (ciarlet, 2000), (cozzani et al. 2007), (hauptmanns, 2001a), (hauptmanns, 2001b), (khan & abbasi, 2001a), (khan & abbasi, 2001b), (khan & abbasi, 2001c), (cozzani et al. 2009). according to (cozzani et al. 2007), (baum, 1998a), (baum, 1999b), (baum, 2001c), (cozzani, et al. 2006), when speaking about the reliability of industrial facilities and plants under possible explosions, it is necessary to observe and include the following development steps: 1. the analysis of conditional sources – the identification of the potentials of the plants/objects in which an explosion may occur, the knowledge of the conditions that may initiate/lead to an explosion, as well as the knowledge of the geometric dimensions, shapes, speed and frequency of the angles of the caused/generated projectiles; 2. the analysis of the influential term – the knowledge of the conditions that may cause/create the influence of other plants/facilities, the knowledge of the mechanical and geometric properties of the affected targets, the knowledge of impacts such as perforations or a partial penetration/break, as well as a possible creation of a new set of projectiles as a result of the failure/malfunction or explosion of the affected object/tank; and 3. the assessment of the reliability of the plants and facilities, and the consequences of the same. risk analysis in industrial plants often considers that random explosions generate the given categories and forms of structural fragments (fig.3), i.e. standardize projectiles, the speed of which depends on the arbitrary ratio of the total energy. in addition, a detailed analysis is needed to assess the risk of the impact and the mechanical damage that may occur on the surrounding facilities and/or tanks. accidents in facilities for storing hazardous materials 35 figure 3. the projectile penetration, a residual resisting target thickness and the domino effect, a) a global view, b) a bi-dimensional model (nguyen et al. 2009) fragments can be generated by various characteristics, such as the geometric shapes and dimensions, mass, velocity, and angles of the projection. if fragments affect the target (another tank), they can penetrate either completely or partially. the generated fragment penetrates partially or completely the second tank, which can cause an explosion of the adjacent tank (fig.3). sophisticated mechanical models are necessary or may be required in order to analyze these dynamic effects and their consequences. earlier reports (gubinelli et al. 2004), (yu, & guan, 2016) show that there are generally three forms of generated fragments after industrial accidents or tank explosions, namely cylindrical, halfsphere, or plate (fig.4). in addition, the valve parts, as well as the tubular parts, may also be transformed into cylindrical shapes during the explosion. obviously, the impact of a fragment may occur with any value of the angle between the fragment and the target, i.e. the second tank. figure 4. an illustration of fragmentation after a tank explosion tepić et al./oper. res. eng. sci. theor. appl. 2 (2) (2019) 24-39 36 the equation of the motion of the generated fragments is presented below. the vector form of the equation of motion of the fragment with mass mfr and velocity vfr is (mébarki et al., 2009) is as follows: gww dt vd m ld fr fr   ++= (12) the force of air resistance in the fragment flight is as follows: frfrddvd vvacw        −=  2 1 (13) the lift force of the fragment in flight is as follows: frfrllvl vvacw        −=  2 1 (14) 6. conclusion critical infrastructures play a key role in the normal performance of economies and society. many hazardous industrial activities provide society with indispensable goods and services. some of these activities are considered as particularly critical, such as refining, oil and gas transport and distribution, or the production of rare specialty chemicals due to their criticality for ensuring human wellbeing and the smooth functioning of society. over the past decades, the quantity and diversity of the critical infrastructure have grown rapidly and the interdependence between them has steadily increased. therefore, an increasing number of the basic services depend on the continuous performance of one, two or more critical infrastructures, such as electricity and water supply, communications, etc. observing and reviewing the extreme events that have taken place over the past two decades have revealed that, although the interdependence between 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(2016). fire and rescue combat technical training system construction for dangerous chemicals, procedia eng., 135, 655–660. zhang, j., laboureur, d., liu, y., mannan, m.s., (2016) lessons learned from a supercritical pressure bleve in nihon dempa kogyo crystal inc, j. loss prev. process ind. 41. plane thermoelastic waves in infinite half-space caused operational research in engineering sciences: theory and applications vol. 5, issue 1, 2022, pp. 107-120 issn: 2620-1607 eissn: 2620-1747 doi: https://doi.org/10.31181/oresta240322121n * corresponding author. a.nical@il.pw.edu.pl (a. nical), karolsikora@uowdubai.ac.ae (k. sikora) application of wooden modular construction for the needs of the elderly aleksander nicał 1*, karol sikora 2 1 warsaw university of technology, faculty of civil engineering, warsaw, poland 2 university of wollongong in dubai, faculty of engineering and information sciences, dubai, uae received: 08 november 2021 accepted: 25 february 2022 first online: 24 march 2022 research paper abstract: in recent years, changes in demographic structure have been observed worldwide. to sustain the growing population of elderly people with special needs, homes need a radical rethink both in designing new houses and in retrofitting new solutions to existing houses. designs that facilitate aging in place, designs that maintain thermal comfort, and designs that have net-zero energy demands and low to zero to negative carbon footprints are needed. the article discusses the issues of construction for the elderly. the trends in the demographic development of society in selected countries are presented. additionally, information on the housing stock for elderly people in poland is provided. the carbon dioxide emission limits to mitigate climate change make it necessary to find an alternative to concrete and steel, traditional construction materials. in this context, cross laminated timber (clt) fulfills the sustainability requirements. however, to select the suitable panel a detailed analysis of timber characteristics is required. it is necessary to evaluate mechanical properties in bending, tension, compression, and shear. since the mechanical properties of certain types of wood differ, their proper selection is challenging. the multi-criteria analysis could address this. in this article, four wood species, spruce, oak, ash, and beech, were evaluated using the analytic hierarchy process (ahp) analysis. based on the type of construction elements and their functions, analyses were using six mechanical properties as criteria. the optimal type of wood was indicated. key words: cross laminated timber, modular construction, elderly people, optimization, ahp. 1. introduction the studies on demographic change (pašalić et. al. 2020) reveal a relatively rapid increase in the growth of the elderly population. it is expected that in the next 30 years the ratio of elderly people (aged 65 and above) to the whole population will increase from 7% in the first decade of the 21st century to 16% in 2050 (cohen, nical and sikora/oper. res. eng. sci. theor. appl. 5(1) (2022) 107-120 108 2003; who, 2021). this trend is observed especially in the developed countries and results in a high reduction of the percentage of the population of working age. the life expectancy has increased in recent decades (roser et al., 2013). the reason for that is mainly related to the improvement of living and social conditions (nicał, 2016). although demographic changes occur worldwide, their extent and timing differ significantly in the developing countries in latin america and africa from the western european countries and japan (krueger & ludwig, 2007; bloom & williamson, 1998; united nations, 2002). due to health issues, the majority of elderly people spend most of their time at home and very often depend on other’s people with housework. the solution for these people can be robotic support systems in everyday activities at home (adls activities of daily living) (bock et al., 2012; nicał, 2017). these systems are part of a research and development program aal (active and assisted living programme) supporting projects that use information and communication technologies (ict) to improve the quality of life of older people. the implementation of the aal program usually entails the need to reconstruct the apartments where elderly people live. in many european countries (e.g. poland), elderly people live in buildings erected in the 1960s, 1970s, and 1980s. a large proportion of these buildings are made in standardized large-block and large-panel systems. figure 1. presents the share of each of these technologies in residential buildings in poland in the period between 1970-1985 (nicał, 2017; dzierżewicz & starosolski, 2010). 0 20 40 60 80 100 1970 1975 1980 1985 [% ] years panel building large-block building traditional other t echnologies figure 1. share of the various technologies in residential buildings in poland in the period between 1970-1985 (nicał, 2017; dzierżewicz & starosolski, 2010). depending on the system, these buildings were erected in spatial arrangements in which most of the walls serve as load-bearing. therefore, it is not possible to move or demolish such walls. this circumstance causes many inconveniences in terms of adapting apartments for elderly people such as widening corridors or door openings (nicał et al., 2019). therefore, it is necessary to build facilities adapted to the needs of the elderly. moreover, these buildings should be erected as quickly as possible by the implementation of advanced technologies (xing et al., 2020). panel buildings, usually made in concrete technology, are not environmentally friendly. research in this area has been carried out, inter alia, by (pierobon et al., 2019). results showed that an average of 26.5% reduction in the global warming potential is achieved in the hybrid clt building compared to the concrete building. clt compared to other application of wooden modular construction for the needs of the elderly 109 wood-based materials such as glued laminated timber (glt), has lower: emissions in global warming potential (gwp), terrestrial ecotoxicity (te), land use (lup), and ozone layer depletion (old) (balasbaneh & sher, 2021). in addition, taking into account the trends in the field of environmental protection and reduction of co2 emissions, it is necessary to use the material with the lowest carbon footprint. the material that meets these criteria is cross-laminated timber (clt). when choosing wood for clt, the decision-makers are faced with the dilemma of choosing the wood species that compose it. thus, a research gap exists at the interface between timber engineering and the decision-making process of selecting the leading parameters when selecting it. the purpose of this paper and its contribution to the field of construction for the elderly is to establish a methodology for selecting the most optimal timber spieces taking into account their six main mechanical criteria. 2. cross laminated timber (clt) 2.1. general information clt constitutes a plate-like engineered timber product, optimized for bearing loads in and out of plane and is composed of an uneven number of layers. as defined in the standard pn-en 16351 (pn-en 16351:2015), clt is structural construction timber consisting of at least three layers of wood or wood-based materials, of which at least three layers are perpendicular to each other. figure 2. below presents an example of a clt 160 l5s (40l-20w-40l-20w-40l). a detailed explanation of the individual symbols is provided below (fig. 3). figure 2. an example of clt 160 l5s (40l-20w-40l-20w-40l). figure 3. a detailed explanation of the individual symbols in the clt labeling. clt 160 l5s (40l-20w-40l-20w-40l) manufacturer symbol thickness of the element in mm orientation of outer layers number of layers thickness of a layer orientation of a layer l – longitudinal w transverse nical and sikora/oper. res. eng. sci. theor. appl. 5(1) (2022) 107-120 110 layers are quasi rigidly connected by adhesive bonding (brandner, 2013). thanks to the multilayer, alternating arrangement of layers, the significance of the natural imperfections like knots of a single wooden board are reduced and a rigid wall or a floor slab is obtained (kotarski & przepiórka, 2020). the advantages of clt as a large-sized and panel-like solid timber construction element for the construction are mostly related to its outstanding degree of prefabrication, the dry and clean construction technique, and the short erection times on site (e.g. roughly one to two days per family house) (brandner, 2013). clt is characterized by high dimensional accuracy and easy adjustment. it can also transfer loads in two dimensions. together with its low self-weight, it is particularly suitable for the conversion and modernization of existing buildings, but also for resisting exceptional loads (e.g. earthquakes). clt offers, in contrast to the lightweight timber structures (e.g. framing, post, and beam system), a clear separation of load-bearing from insulation and installation layers. additionally, clt is characterized by the low air permeability, the distinctive specific storage capacity for humidity and temperature, the independence of modular dimensions in arranging window and door openings as well as in fastening of furniture. 2.2. production and processing of clt the first stage of clt production is not much different from the production process of glued laminated timber and consists of the following activities (figure 4) (brandner, 2013): • strength or stiffness grading of already (kiln) dried boards; • cutting out of local growth characteristics which do not meet the requirements of the strength class and finger jointing of the residual board segments to endless lamellas; • division and cutting of lamellas for later use in longitudinal and transverse layers of clt. figure 4. overview of clt production process (brandner, 2013). usually, clt is composed of boards with thickness tb = (12 ÷ 45) mm (pn-en 16351:2015). there is no upper limit for the board width but due to rolling shear application of wooden modular construction for the needs of the elderly 111 stresses in-between the clt layers a minimum width of wb ≥ 4 · tb (brandner, 2013). the reference board width is proposed with wb,ref = 150 mm, as given in pn-en 338 (pn-en 338:2016-06) and pn-en 384 (pn-en 384+a1:2018-12). currently, mainly softwood species are used for clt. material moisture tolerance is 12 +/2% (kotarski & przepiórka, 2020). each of the clt layers must be made of sawn timber of the same strength class determined in accordance with pn-en 14081-1 (pn-en 14081-1+a1:2019-11), however, it is allowed to use different types of wood provided that the same technical parameters are maintained, especially swelling and shrinkage. it is also possible to use bent cross-laminated timber elements, the thickness of which depends primarily on the bend radius of the elements. the demand for bent clts is very small on the market, and the cost of setting up the production is incomparably higher than for simple elements, hence few manufacturers decided to offer this type of product. however, it is a future-proof product, offering an even greater range of design options for architects (brandner, 2013). the second stage of clt production consists of the following activities (pn-en 16351:2015) (figure 4): • adhesive bonding of lamellas to single-layer panels (optional); • assembling and adhesive bonding of lamellas or single-layer panels to clt; • cutting and joining to structural elements (customizing). melamine (muf) and polyurethane (pur) adhesives are most often used to connect the individual layers. they meet stringent standards in terms of formaldehyde emissions and are safe for health during production, use, and also during fire. the application of the adhesive to surface bonding is usually carried out mechanically and without contact on single lamellas in a continuous through-feed device or on clt layers already pre-positioned in a positioning or press bed. a linewise discrete application of adhesive is preferred (brandner, 2013). the lamellas do not have to be glued on the side surfaces and it is allowed to arrange them with a spacing of up to 6 mm. cross-glued timber is glued in hydraulic or vacuum presses (kotarski & przepiórka, 2020). in both cases, under the gluing technology, adequate pressure of the joined elements is required, which enables a permanent adhesive bond. in the case of hydraulic presses, it is from 0.1 to 1.0 n/mm2, and in the case of vacuum gluing, from 0.05 to 0.1 n/mm2 (kotarski & przepiórka, 2020), with 0.4 n/mm2 being already sufficient for most typical configurations (sikora et al., 2015). clamps, pins, and nails are very rarely used in the production of clt, this is acceptable (kotarski & przepiórka, 2020). after pressing, standard clt elements are normally trimmed on their edges. the surface of the elements after pressing is treated differently, without further processing by planning or sanding (brandner, 2013). application of additional non-load-bearing layers like osb, acoustic panels, gypsum plasterboards, or three-layered solid wood panels is possible. the additional layers are primarily connected by surface bonding (brandner, 2013). to ensure the appropriate quality of products, it is necessary to maintain the following parameters during production (brandner, 2013): • during bonding: temperature ≥ 15°c and relative humidity (40 ÷ 75) %; • during curing: temperature ≥ 18°c and relative humidity ≥ 30 %; nical and sikora/oper. res. eng. sci. theor. appl. 5(1) (2022) 107-120 112 • moisture content of adherents u = (6 ÷ 15) % (≤ 18 % in case of preservative treatment); • the maximum difference in moisture content between two parallel layers δu ≤ 5 %. 2.3. selected properties of clt mechanical properties of clt panels are determined mainly by destructive testing i.a. bending, rolling shear, compression, tension (he et al., 2020). among the conducted research, it is necessary to mention the i.a. bending and compressive properties of clt panels made from canadian hemlock that calibrated the theoretical bending stiffness using the experimental values (he, 2018), and the bending and shear properties of threeand five-layer clt panels fabricated with irish sitka spruce (sikora et al., 2016, o’ceallaigh et al., 2018). moreover, testing of rolling shear properties of clt fabricated with new zealand radiata pine and correlation between lamination thickness and its influence on rolling shear strength has been developed (li, 2017). the test results for the properties of the 3-layer and the 5-layer clt (he et al., 2020) panels show, inter alia, that 3-layer panels have about 11.3% higher stiffness parallel-to-grain direction and over 15.8% higher stiffness perpendicularto-grain direction. in addition, the average global modulus of elasticity of 3-layer panels is over 19.2% higher than 5-layer panels. 5-layer panels are characterized by, among others 11.4% higher strength parallel-to-grain direction and 9.7% higher strength perpendicular-to-grain direction. the average local bending stiffness by the 5-layer panel is 243.9% larger than for the 3-layer panel, and the average global bending stiffness by 252.5%, respectively. the average shear strength by the 5-layer panel is 3.8% higher than for the 3-layer panel, while the bending strength is 4.3% higher than for the 3-layer panel. both the 3-layer and the 5-layer clt panels were manufactured with a width of 310 mm, using the canadian black spruce lumber (no 2-grade) with the following material properties (nlga, 2010): • stiffness parallel-to-grain direction (el,0) = 10925.0 mpa; • stiffness perpendicular-to-grain direction (el,90) = 993.2 mpa; • strength parallel-to-grain direction (flc,0) = 28.7 mpa; • strength parallel-to-grain direction (flc,90) = 5.8 mpa. based on the presented results, it can be concluded that both the 3-layer and the 5-layer clt panels fabricated with the no.2-grade black spruce can provide ideal bending or shear properties. the properties can be comparable to those of the clt fabricated with other commonly used wood species (he et al., 2018). 3. housing for the elderly 3.1. general assumptions buildings intended for the stay of elderly people should meet several criteria, such as: • the building and its surroundings must not have architectural barriers; application of wooden modular construction for the needs of the elderly 113 • a multi-storey building must have a lift adapted to the needs of disabled and elderly people; • the building must be equipped with a call and alarm system and a fire alarm system. other requirements include the need to construct wide corridors, larger areas of rooms, dining rooms, guest rooms, and other technical rooms to meet the sanitary needs of residents. it is also important to remember to provide adequate conditions in the bathrooms. these are the place where a lot of accidents happen. while designing it is important to take into account the necessity of ensuring an adequate maneuver space for a wheelchair that should not be smaller than 150x150 cm (nicał, 2016), (budny, 2009). providing large living and communication areas entails the necessity to construct facilities with the use of construction elements with significant spans. additionally, the construction elements should be light and slender to ensure the largest possible cubic capacity. buildings intended for the stay of elderly people should also be made of prefabricated elements, to ensure a short construction time. in this respect, the use of clt seems to perfectly meet the expectations. 3.2. selection of wood for construction hardwood shows a higher natural strength potential than softwood, see figure 5 (franke, 2013). additionally, hardwood, with its good mechanical properties, perfectly fits for long-spanned and high stressed timber constructions. figure 5. comparison of mechanical properties of hardwood and softwood species (franke, 2016). the tensile strength perpendicular to the grain for hardwood can reach up to 260% of the softwood strength values (franke, 2016). regarding bending and compression parallel to the grain, the strength values are up to 175% and 150% higher, respectively (franke, 2016). as a result, the use of hardwood allows larger spans and smaller cross-sections. these numbers indicate that structural elements for buildings intended for the stay of elderly people could be erected of hardwood. nical and sikora/oper. res. eng. sci. theor. appl. 5(1) (2022) 107-120 114 4. methodology 4.1. ahp multicriteria assessment method for the selection of wood for construction materials one of the most difficult problems in construction, as well as, in clt material selection is to take objective decisions, especially for the selection of technology and material solutions (książek et al., 2014). construction projects planning requires a proper materials selection process that should be assessed in terms of their longterm cost (rosłon et al., 2020), durability, quality (nicał & anysz, 2020), expected construction time (ibadov, 2019), and mechanical properties. the utilization of ahp (analytic hierarchy process) multicriteria assessment method (hwang & yoon, 1981), (alosta, et al. 2021) can be beneficial. among many proven and recognized methods of multi-criteria evaluation, such as e.g. fucom (bozanic et al, 2021) or decision making trial and evaluation laboratory model (dematel) technique, integrated with analytic network process (anp) (osintsev et al. 2021), as well as, fuzzy ahp and fuzzy marcos approach (bakir et al. 2021), it was decided to use the ahp method. it is broadly spread in engineering and is very usable method that separates the problem into litter steps. the ahp is a four-step method with the following steps (saaty, 1980), (saaty, 2008), (trzaskalik, 2006). the steps are the following: • step i – hierarchy of the problem; • step ii – definition of preferences by the decision-maker; • step iii – preference matrix consistency testing; • step iv – creating a summary ranking. in step i, it is necessary to define: the problem faced by the decision-maker, available options of a solution, criteria against which the available options will be assessed, and possibly further sub-criteria. the hierarchical structure results from the decomposition of the problem into the main goal, main factors, and side factors (anysz et al., 2021). in step ii the decision-maker using numerical values from 1 to 9 (less often from 1 to 7) has to define the preferences. table 1. shows the values of the comparative assessment against each other. values not listed in table 2 (2, 4, 6, 8) characterize intermediate values (anysz et al., 2021). table 1. comparative assessment in the ahp method (anysz et al., 2021). comparative, pairwise assessment of a against b value just as good or important 1 a little better or more important 3 definitely better or more important 5 much better or more important 7 extremely better or more important 9 preferences are specified for each level within the defined hierarchical structure (anysz et al., 2021). objects that are only at one level of the hierarchy can be assessed against each other. the comparative assessment is subjective and is made by the decision-maker (grzegorzewski, 2019). the result of step ii is a square matrix a in which the terms 𝑎𝑖𝑗 concerns the preferences of the decision-maker. the digits 1 application of wooden modular construction for the needs of the elderly 115 are on the diagonal of the matrix a, there is also the reciprocal of the adopted preferences, i.e.: (1) the following sub-step is to normalize matrix a to matrix b using the dependence below: (2 ) the value bij is expressed as the quotient of the term 𝑎𝑖𝑗 to the sum of the terms in the j-th column of matrix a (anysz et al., 2021). weights of the examined elements (wi) are the arithmetic means of the rows of the matrix b according to the following formula (saaty, 1980; anysz et al., 2021; książek et al., 2014; tułecki & król, 2007). (3) in step iii only one pair of criteria is assessed by the decision-maker each time. the preference relationship between the criteria is asymmetric (anysz et al., 2021). potential inconsistencies in the assessments of the decision-maker can be avoided, with the introduction of the following control coefficients: consistency index (ci) and consistency ratio (cr) (4) (5) where: λmax the maximum eigenvalue of the matrix, ri the value of the average random consistency index ci according to the table below (table 2). table 2. the values of the average random index of ri. matrix dimension n 2 3 4 5 6 7 8 9 10 0 0.52 0.89 1.11 1.25 1.35 1.40 1.45 1.49 if 𝐶𝑅 ≤ 0.10, then the preference matrix is considered consistent. when 𝐶𝑅 > 0.150, the assumptions from step ii should be changed (saaty, 1980; saaty, 2008). nical and sikora/oper. res. eng. sci. theor. appl. 5(1) (2022) 107-120 116 in the last step iv, a ranking of the available solutions in terms of their suitability to meet the main goal is created. the order from the best to the worst needs to be kept. the total score of a single variant can be calculated according to the following formula (anysz et al., 2021): (6) where: p final score for a given solution variant, wi criterion weight according to the formula (3), ki evaluation of a given criterion. 4.2. application of ahp for the selection of wood the decision problem lies in the selection of the most advantageous type of wood for the structural elements from which the buildings intended for the stay of the elderly will be erected. for this purpose, the study of the data contained in figure 5, concerning the mechanical characteristics of wood, will be applied. the evaluation criteria, in this case, are the results obtained in the following tests: • criterion 1: bending, fm; • criterion 2: tension, ft,0; • criterion 3: tension, ft,90; • criterion 4: compression, fc,0; • criterion 5: compression, fc,90; • criterion 6: shear, fv. the variants are assigned as follows: • variant 1: spruce; • variant 2: oak; • variant 3: ash; • variant 4: beech. 4.3. results currently, the natural higher strength can potentially be mostly used for partial reinforcements in timber structures, e.g. for strengthening the lateral compression capacity at supports or loading plates or the tension capacity perpendicular to grain at notches and holes or in tapered and curved beams (franke, 2013). according to the calculations in the ahp assessment method, the following criteria weights are obtained (figure 6). application of wooden modular construction for the needs of the elderly 117 figure 6. criteria weights obtained in the ahp method. using the criteria weights from figure 6, the final result and order are as follows (table 3). table 3. final results and order in the ahp method. bending, fm tension, ft,0 tension, ft,90 compression, fc,0 compression, fc,90 shear, fv priority vector solutions vector order spruce 0.049 0.049 0.124 0.095 0.066 0.064 0.092 0.088 4 oak 0.131 0.140 0.096 0.258 0.364 0.423 0.038 0.229 3 ash 0.300 0.308 0.390 0.181 0.364 0.329 0.315 0.320 2 beech 0.520 0.503 0.390 0.466 0.207 0.185 0.229 0.363 1 0.254 0.071 the highest score of 0.363 was obtained for beech. it is followed by ash, oak, and spruce, respectively. 5. conclusion ahp analyses ranked timber species taking into account the main mechanical and criteria of main concerns for the elderly population. results indicated that the most optimum was beech, followed by ash, oak spruce. however, to provide the selection guidelines that will be generally accepted by the industry further studies should concern aspects of the cltdurability of the erected facilities and the costs of their long-term operation. it is important to take into account potential limitations in the development of clt technology, related to, inter alia, access to wood resources with the required strength parameters, and regulations for the silviculture and timber design and utilization as construction material. the aspects of the availability and cost of obtaining wood raw material, which may differ significantly from country to country, are also important. further studies on clt optimization should focus on adhesives and bonding parameters, strength, and durability, as well as, on novel fully robotized and highly efficient production technology. nical and sikora/oper. res. eng. sci. theor. appl. 5(1) (2022) 107-120 118 references alosta, a., elmansuri, o., & badi, i. 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d.mladenovic@sf.bg.ac.rs (d. mladenović), s.jankovic@sf.bg.ac.rs (s. janković), s.zdravkovic@sf.bg.ac.rs (s. zdravković), snezanam@sf.bg.ac.rs (s. mladenović), ana.uzelac@sf.bg.ac.rs (a. uzelac) night traffic flow prediction using k-nearest neighbors algorithm dušan mladenović *, slađana janković, stefan zdravković, snežana mladenović, ana uzelac university of belgrade, faculty of transport and traffic engineering, serbia received: 31 december 2021 accepted: 14 february 2022 first online: 24 march 2022 original scientific paper abstract: the aim of this research is to predict the total and average monthly night traffic on state roads in serbia, using the technique of supervised machine learning. a set of data on total and average monthly night traffic has been used for training and testing of predictive models. the data set was obtained by counting the traffic on the roads in serbia, in the period from 2011 to 2020. various classification and regression prediction models have been tested using the weka software tool on the available data set and the models based on the k-nearest neighbors algorithm, as well as models based on regression trees, have shown the best results. furthermore, the best model has been chosen by comparing the performances of models. according to all the mentioned criteria, the model based on the k-nearest neighbors algorithm has shown the best results. using this model, the prediction of the total and average nightly traffic per month for the following year at the selected traffic counting locations has been made. keywords: machine learning, traffic flow, prediction, k-nearest neighbors, weka. 1. introduction the accelerated urban development is faced with mobility challenges caused by increased transport of passengers and goods. the development of smart cities is based on the analysis of traffic data. they are used in dimensioning of road sections, connections and intersections, as well as dimensioning of road structures, environmental protection measures, economic and financial evaluation of projects, planning of management and maintenance of road infrastructure (public enterprise "roads of serbia", 2012). monitoring the road network is one way to collect real-time traffic data. various sensor technologies prevail in this type of data collection, such as technologies based on inductive loop detectors, laser radar sensors, etc. (magalhaes et al., 2021). night traffic flow prediction using k-nearest neighbors algorithm 153 the monitoring of traffic flows is important, both because of monitoring of the traffic conditions in real time, and because of predicting the characteristics of traffic flows in the future (janković et al., 2020). time determinants, such as: a day of the week, an hour of the day, the dates of state and religious holidays, holiday vacations, and so on, are some of the factors that permanently influence the formation of the usual intensity of traffic flows. some other factors, such as: weather conditions, road conditions, maintenance of road infrastructure (sénquiz-díaz, 2021), use of alternative routes and traffic accidents can influence the characteristics of traffic flows to change for the observed time interval. in the situation where the flow of vehicles exceeds the capacity of the road congestion occurs. traffic congestion leads to: prolongation of time spent in transport, increase in transport costs, increase in emissions of harmful gases, passenger delays, as well as delays in the delivery of goods. therefore, the prevention of traffic congestion is one of the most important goals of predicting the characteristics of traffic flows. supervised machine learning is a method of predictive analysis that enables prediction of future values of a target variable for independent attributes in the future, based on known values of the same target variable and known values of the same attributes in the past. collection of traffic data provides opportunities for the development of supervised machine learning models which are going to be used to predict the characteristics of future traffic flows (zhang et al., 2020; park et al., 2018; xu et al., 2013). the forecasting of traffic flows has been the subject of numerous studies over the last two decades. the second section of this paper contains an overview of the most significant studies related to this subject. the authors of this paper have limited their research to detection of night traffic patterns and the prediction of night traffic (i.e. traffic in the time period from 22.00 hours to 06.00 hours). the purpose of this research is to examine the possibilities of short term prediction of night traffic volume using the technique of supervised machine learning. the methodology according to which this research has been performed and the basic characteristics of the algorithm that has shown the best results in prediction (k-nearest neighbors, knn) are presented in the third section of this paper. the fourth section of the paper describes a case study realized within this research. in the case study predictive models have been created and the prediction of the total and average amounts of night traffic per month has been performed on selected road sections in serbia. the data collected by automatic traffic counters (atc) have been used in training and testing of machine learning models. the most significant results of the case study and discussion on the results are presented in the fifth section of the paper, while the last sixth section concludes the paper. 2. literature review all models developed for traffic prediction can be broadly classified into three categories: parametric, nonparametric and hybrid types of models. parametric models are e.g. historical average (williams et al., 1998) time series models and kalman filter (guo & williams, 2010). seasonal autoregressive integrated moving average (arima) is a classic parametric time series model used in the study (williams & hoel, 2003). in contrast, nonparametric models are mostly data-driven and use empirical prediction methods, including primarily neural networks models (vlahogianni et al., 2005; yasin mladenović et al./oper. res. eng. sci. theor. appl. 5(1) (2022) 152-168 154 çodur & tortum, 2015), nonparametric regression (marković et al., 2010; cai et al., 2016), and support vector machine (zhang & xie, 2008; peng & tang, 2015). in addition, the hybrid approach combines two or more models to generate predictions, e.g. non-linear chaotic prediction model (wang & shi, 2013), multiagent prediction model (ma et al., 2001), modular network model (vlahogianni et al., 2007), etc. the karlaftis & vlahogianni study (2011) compares traffic forecasting models based on parametric (statistical) methods and neural network-based models. boukerche & wang (2020) provide a classification and an overview of machine learning models used in traffic flow prediction. according to these authors, the mentioned models are divided into regression models, instance-based models (such as k-nn), kernel-based models (such as support vector machine svm and radial basis function rbf), neural network models (such as feed forward neural network ffnn, recurrent neural network rnn, convolutional neural network cnn) and hybrid models (combinations of two or more different models). shamshad & sarwr (2020) developed a model for predicting traffic volume at an hourly level, using two machine learning algorithms: artificial neural network (ann) and svm. traffic data obtained with the help of road sensors, as well as data on meteorological conditions have been used to train and later test different machine learning models. this study shows that ann-based machine learning models show good results in long-term predictions, while svm-based models show good results in short-term predictions. zhang et al. (2013) have developed a nonparametric regression model, based on the k-nn algorithm on the matlab platform. the experimental results of this study show that the prediction accuracy of the highway traffic volume, using the k-nn method, is over 90 percent accurate. in the study (zou et al., 2015) the authors show that, when applying k-nn methods in short-term traffic prediction, a much more accurate prediction is achieved if, in addition to temporal attributes, spatial attributes are included in independent attributes as well. in some studies, the basic k-nn method for short-term traffic prediction has been improved, in some way. for example “specifically, two screening layers based on shape similarity were introduced in the knearest neighbor non-parametric regression method, and the forecasting results were output using the weighted averaging on the reciprocal values of the shape similarity distances and the most-similar-point distance adjustment method. ”(pang et al., 2016). zheng & su (2014) have introduced a time limit when selecting the nearest neighbors. in the study (liu et al., 2018), a short-term prediction of traffic volume has been performed using a hybrid model, based on the ann and k-nn algorithms. four types of ann have been used: back-propagation (bp) neural network, radial basis function (rbf) neural network, generalized regression (gr) neural network, and elman neural network. the k-nn method has been used to reconstruct a data set on which artificial neural networks have been trained, combining similar traffic flow patterns. by applying these anns to real traffic data two important conclusions have been reached: bp and gr neural networks show better prediction performance than the other two types of networks, but are sensitive to changing the scope of the training data set. on the other hand, the rbf and elman neural networks show prediction results that are fairly stable when increasing the data set for training. the study (toan & truong, 2020) shows that applying k-nn methods to a training data set can significantly reduce the size of this data set, thus achieving faster model training using svm methods, without affecting prediction performance. night traffic flow prediction using k-nearest neighbors algorithm 155 in the research (filipovska & mahmassani, 2020) different models of machine learning for predicting traffic interruption have been developed and tested and their results have been compared to the results of traditional probabilistic approach. stojčić (2018) has given an overview of research in which the anfis (adaptive neuro-fuzzy inference system) model has been used in the prediction of traffic congestion. zaki et al. (2016), as well as shankar et al. (2012) take velocity and density as independent attributes and congestion level as a dependent variable in the prediction of congestion using the anfis model. kukadapwar & parbat (2015), among others, use traffic volume to roadway capacity ratio as an independent variable, while the target variable in their study is congestion index. recent research includes the application of deep learning methods in the prediction of traffic flow intensity (wang et al., 2018). in the study (lv et al., 2015) the application of a deep learning approach is demonstrated with stacked autoencoders (saes) to traffic data sets that have big data features. alshaykha & shaban (2021) combine the k-nn method and the broad learning system (knn-bls). “the basic structure of bls is built on the traditional rvflnn (random vector functional-link neural network), but unlike rvflnn that directly uses the original input data to build an enhanced node, bls first maps the input into a series of mapping nodes, and then uses the mapping node to build an enhanced node, and the mapping node and the enhanced node form joint nodes, and finally combine the nodes and the output layer to establish a linear connection.“ (alshaykha & shaban, 2021). mohammed & kianfar (2018) have investigated the application of four categories of predictive methods in traffic flow prediction. the results obtained using distributed random forest method slightly exceed the results obtained using other methods. 3. methodology the machine learning process takes place in the following stages: data preparation, model training, model validation, model testing and prediction. it is an iterative process in which all of the above mentioned phases are repeated as many times as necessary. the repetition of these phases ends when all attribute combinations, all available algorithms and algorithm parameter values are exhausted, or when a satisfactory model performance is reached. once the model testing shows that the model is successful, the use of the model in the prediction of the selected variable can begin. the data preparation consists of: cleaning raw data from incomplete records or records with incorrect values, converting data into the appropriate format, etc. the construction of the prediction models consists of: 1. selection of the target variable, i.e. an attribute whose value should be projected using a machine learning model; 2. selection of an algorithm, in accordance with the nature of the target variable and attributes; 3. selection of relevant attributes of the data set; 4. preparation of data sets for learning and testing of models, according to the requirements of the selected algorithm; mladenović et al./oper. res. eng. sci. theor. appl. 5(1) (2022) 152-168 156 5. model adjustment, i.e. values of hyperparameters specific to each type of machine learning algorithm; 6. model learning – implies obtaining model’s hyper-parameters through applying a training data set algorithm on the training data set. since the target variables of the data set used in this study are continuous, machine learning models based on the most popular regression algorithms have been built: linear regression, k-nearest neighbors, decision tree, support vector machines for regression (smoreg), neural network. in addition to model training and testing, a model validation has been performed in order to select the best type of model among multiple candidates, determine the optimal configuration of model parameters, and avoid problems known as overfitting and underfitting. excessive matching refers to a situation in which prediction for instances from the training set has been perfectly learned through the model, but there is a very weak ability to predict instances that are slightly different from those learned. insufficient matching refers to a case when there is failure to approximate training data through the model, so it shows poor performance even on a training data set. an approach known as cross-validation has been used to validate a model. this approach to model performance evaluation uses only training data and consists of the following phases: 1. the available data set for model training is divided into k equal parts folds. it is usually divided into 10 subsets (10-fold cross-validation). 2. the model is trained on k-1 subsets of data (e.g. on the first of k-1 subsets). 3. the model is evaluated on the only remaining (k-th) subset of data. 4. steps 2 and 3 are repeated k times. in each iteration one part of the data is taken for the purpose of model validation, while the rest (k-1 parts) is used for learning. a different subset is always selected to be used for model validation. 5. model performances are calculated as the arithmetic mean of the performances obtained in k iteration. success of the numerical prediction can be evaluated using different metrics (witten et al., 2017). the projected values of the target variable, obtained for the set of instances for model validation are: p1, p2, …, pn; while the actual values of the target variables are: a1, a2, …, an. mean-squared error eq. (1), is the average error. 𝑀𝑒𝑎𝑛 − 𝑠𝑞𝑢𝑎𝑟𝑒𝑑 𝑒𝑟𝑟𝑜𝑟 = (𝑝1−𝑎1) 2+⋯+(𝑝𝑛−𝑎𝑛) 2 𝑛 (1) mean-absolute error – eq. (2), is the mean of the absolute value of the errors. 𝑀𝑒𝑎𝑛 − 𝑎𝑏𝑠𝑜𝑙𝑢𝑡𝑒 𝑒𝑟𝑟𝑜𝑟 = |𝑝1−𝑎1|+⋯+|𝑝𝑛−𝑎𝑛| 𝑛 (2) root mean-squared error – eq. (3), is calculated in an obvious way. 𝑅𝑜𝑜𝑡 𝑚𝑒𝑎𝑛 − 𝑠𝑞𝑢𝑎𝑟𝑒𝑑 𝑒𝑟𝑟𝑜𝑟 = √ (𝑝1−𝑎1) 2+⋯+(𝑝𝑛−𝑎𝑛) 2 𝑛 (3) night traffic flow prediction using k-nearest neighbors algorithm 157 relative-squared error – eq. (4) is the square root of the mean of the squared errors. 𝑅𝑒𝑙𝑎𝑡𝑖𝑣𝑒 − 𝑠𝑞𝑢𝑎𝑟𝑒𝑑 𝑒𝑟𝑟𝑜𝑟 = (𝑝1−𝑎1) 2+⋯+(𝑝𝑛−𝑎𝑛) 2 (𝑎1−�̅�) 2+⋯+(𝑎𝑛−�̅�) 2 (4) root relative-squared error – eq. (5), is calculated in an expected way. 𝑅𝑜𝑜𝑡 𝑟𝑒𝑙𝑎𝑡𝑖𝑣𝑒 − 𝑠𝑞𝑢𝑎𝑟𝑒𝑑 𝑒𝑟𝑟𝑜𝑟 = √ (𝑝1−𝑎1) 2+⋯+(𝑝𝑛−𝑎𝑛 ) 2 (𝑎1−�̅�) 2+⋯+(𝑎𝑛−�̅�) 2 (5) relative-absolute error – eq. (6), is the total absolute error, with the same type of normalization. 𝑅𝑒𝑙𝑎𝑡𝑖𝑣𝑒 − 𝑎𝑏𝑠𝑜𝑙𝑢𝑡𝑒 𝑒𝑟𝑟𝑜𝑟 = |𝑝1−𝑎1|+⋯+|𝑝𝑛−𝑎𝑛| |𝑎1−�̅�|+⋯+|𝑎𝑛−�̅�| (6) the last measure of prediction accuracy is the correlation coefficient eq. (7), which measures the statistical correlation between the values of a and p. the correlation coefficient takes values from 1 for results that are completely correlated, over 0 when there is no correlation, to -1 when the results are in perfect negative correlation. 𝐶𝑜𝑟𝑟𝑒𝑙𝑎𝑡𝑖𝑜𝑛 𝑐𝑜𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑡 = 𝑆𝑃𝐴 √𝑆𝑃𝑆𝐴 (7) where spa, sp and sa are calculated as shown in (8): 𝑆𝑃𝐴 = ∑ (𝑝𝑖−�̅�)(𝑎𝑖−�̅�) 𝑛 𝑖=1 𝑛−1 , 𝑆𝑃 = ∑ (𝑝𝑖−�̅�) 2𝑛 𝑖=1 𝑛−1 , 𝑆𝐴 = ∑ (𝑎𝑖−�̅�) 2𝑛 𝑖=1 𝑛−1 (8) in the great number of empirical examples, the predictive model which is the best according to one measure is also the best in all other measures of error. in order to predict the performances of models using unknown data, it is necessary to determine measures of their performance on a data set that did not play any role in model training. this previously uknown data set is entitled as the test data set. the next phase is comparing the performances of models obtained on the test data set with the performances obtained on the training data set. this type of comparison enables to avoid a problem known as overfitting. if the performance of a model is good on training data but bad on the test data, then there is overfitting. in order to predict the values of the selected target variables in the future, it is necessary to prepare an appropriate set of data and apply to it the machine learning model chosen as the best. in this research, the best results have been shown by machine learning models based on the k-nn algorithm. the k-nn algorithm belongs to a class of supervised machine learning algorithms in model learning based on instances (instance-based learning). in this class of algorithms, the classification of a new instance is done by comparing it with the most similar (the closest) instances in the training set (aha et al., 1991). k is a parameter that indicates the number of most similar instances in the training set, with which the new instance is being compared. the k-nn algorithm belongs to the group of so-called lazy methods, because the decision on classification is postponed until the moment a new instance appears. mladenović et al./oper. res. eng. sci. theor. appl. 5(1) (2022) 152-168 158 the main advantage of lazy methods is that they construct a different approximation of the objective function for each new instance that needs to be classified. such local assessment of the objective function is suitable for complex objective functions. because their models are slower to train than some other classes of algorithms, this algorithm is suitable for relatively “small” data sets. this feature of the k-nn algorithm has made it a good candidate for prediction in a case study conducted as part of this research. in the weka (waikato environment for knowledge analysis) software tool used in this study, the k-nearest neighbors algorithm has been implemented under the name ibk. target variable (class), as well as attributes, with this algorithm can be: nominal, numerical, date or binary and missing values of class, as well as missing values of attributes are allowed. thus, the k-nn algorithm is applicable both in solving classification problems and regression prediction problems. in this research, it has been applied to regression predictive analysis. 4. case study a total of 391 automatic traffic counters have been installed on the network of state roads of the 1st category in the republic of serbia. through automatic traffic counters vehicles are detected and classified in real-time, using inductive loops that are placed in the asphalt layer of the road structure. one such traffic counter is shown in figure 1. figure 1. automatic traffic counter based on inductive loops the qltc-10c counters continuously count and classify vehicles into ten categories, while qltc-8c counters classify vehicles into eight categories. the qltc10c counters, classify vehicles into the following categories: a0 motorcycles, a1 passenger cars and passenger cars with trailer, a2 combined vehicles and combined vehicles with trailer, b1 light trucks and light trucks with trailer, b2 – medium heavy night traffic flow prediction using k-nearest neighbors algorithm 159 trucks, b3 heavy goods vehicles, b4 heavy goods vehicles with trailer, b5 semitrailer trucks, c1 buses, c2 articulated buses, x uncategorized (other) vehicles. for each vehicle it detects, the counter records: date, time, direction of vehicle movement, ordinal number of the vehicle on that day for the observed direction, traffic lane, vehicle category and vehicle speed. the obtained data is stored on sd (secure digital) memory cards. in this case study data used have been obtained by automatic counting of traffic on state roads in serbia at 21 counting points (figure 2), in the period from 1.1.2011 to 31.12.2020. the research was done on 4 sections of the road (ia category (road 1) and ib category (roads 22, 23 and 46)). selected counting places have the following marks, i.e. names: 1025 (kraljevo 2), 1026 (trstenik), 1027 (pojate), 1046 (vodice), 1050 (prijanovci), 1052 (pridvorica), 1057 (prijepolje), 1156 (mojsinje) , 1157 (mrčajevci), 1183 (trupale bg-ni), 1191 (ineks), 1193 (kneževići), 1194 (zlatibor), 1195 (kokin brod 2), 1196 (nova varoš), 1198 (gorjani), 1202 (međuvršje ), 1207 (prijepolje 2), 1208 (velika župa), 1225 (lučina) and 1270 (preljina). figure 2. traffic counting locations the purpose of the case study has been to predict two traffic intensity indicators: total monthly night traffic (tmnt) and average monthly night traffic (amnt), at selected counting locations, using the method of supervised machine learning. the instances of the available data set are described by the following attributes: counter, year, month, tmnt and amnt. the tmnt attribute represents the total number of vehicles that are registered by abs at night (from 22.00 hours to 06.00 hours) during the period of one month. the amnt attribute represents the average daily number of vehicles that are registered by abs at night, on a monthly basis. in order to predict the total amount of night traffic per month models of machine learning, whose target variable is the tmnt attribute, have been created, while models whose target variable is the amnt attribute have been created to predict the average night traffic per month. in both groups of machine learning models, the independent attributes are counter and month. the attribute year is used to classify the instances of the existing data set into two parts: for model training and for model testing. instances relating to period mladenović et al./oper. res. eng. sci. theor. appl. 5(1) (2022) 152-168 160 from 2011 to 2017 have been selected as a set of data for model training, while instances relating to the period from 2018 to 2020 have been used for model testing. training, validation and testing of machine learning models have been performed in the data mining software weka 3.9.5. this particular software represents a collection of machine learning algorithms used in discovery operations concerning data validity (witten et al., 2017). it enables the performance of various data mining tasks, such as: data preparation for analysis, classification, regression analysis, clustering, learning through rules of association, selection of relevant attributes and data visualization. each of these tasks is performed in a separate graphical user interface window of weka software (weka explorer) and is opened by selecting the appropriate tab of weka explorer (figure 3). the preprocess window, shown in figure 3, allows you to load and prepare the available data set for later analysis. figure 3. weka 3.9.5 software tool graphical user interface data preparation window 5. results and discussion the following eight machine learning algorithms were to predict tmnt on the training data set in the weka software tool: linear regression, multilayer perceptron, smoreg, ibk (k-nn), m5p, random forest, random tree and reptree. a 10-fold cross-validation, implemented in weka software, has been applied to validate the model. the performance of the prediction model, measured on the training data set is shown in table 1. night traffic flow prediction using k-nearest neighbors algorithm 161 table 1. the performance of eight tmnt prediction models measured on a training data set algorithm correlation coefficient meanabsolute error root meansquared error relativabsolute error (%) root relativsquared error (%) linearregression 0.6417 9718.52 14687.1 73.729 76.637 multilayerperceptron 0.6168 10197.2 15161.7 77.360 79.114 smoreg 0.6373 9430.72 14931.6 71.546 77.914 ibk 0.9803 1985.10 3784.06 15.06 19.745 m5p 0.9434 4124.44 6840.50 31.29 35.694 random forest 0.9799 2004.84 3818.77 15.209 19.926 random tree 0.9803 1990.11 3784.91 15.098 19.749 reptree 0.9701 2456.30 4650.40 18.634 24.266 models based on multilayer perceptron, smoreg algorithms, and linear regression have been rejected due to undoubtedly unsatisfactory performance (they had a correlation coefficient of 0.6417, 0.6168 and 0.6373, respectively). therefore, in the next phase – in testing the machine learning model, the remaining five algorithms have been applied. the performance of these five prediction models, measured on a test data set is shown in table 2. comparing the metrics of the selected models, shown in table 1 and table 2, it is concluded that none of these models have a problem of overfitting. in addition, in all five models on the test data set, the correlation coefficient has high value. table 2. the performances of the top five tmnt prediction models measured on a test data set algorithm correlation coefficient meanabsolute error root meansquared error relativabsolute error (%) root relativsquared error (%) ibk 0.9391 4473.81 7373.93 32.8912 35.4526 m5p 0.8854 6238.81 10205.8 45.8673 49.0681 random forest 0.9382 4495.17 7438.49 33.0482 35.763 random tree 0.9391 4473.58 7374.1 32.8895 35.4534 reptree 0.9303 4893.33 7833.42 35.9755 37.6618 li & xu (2021) propose a model for short-term traffic prediction based on the support vector regression (svr) method. the svr method is based on the basic principles of the svm method and is generalized for regression problems. the svm method is implemented in weka software called libsvm. the svr method in the weka software tool is obtained by selecting the libsvm classifier and one of its types: epsilon-svr or nu-svr. however, the libsvm classifier applied to the training data set, in this case study, gave poor results (correlation coefficient: 0.0644 (epsilon-svr) and 0.0281 (nu-svr), respectively)). therefore, the svr algorithm was rejected in the first phase of this research. in the research (filipovska & mahmassani, 2020) the best performance has been shown by models based on neural networks and svm, if it is a case of class balancing. without class balancing, the model based on a random forest algorithm has shown mladenović et al./oper. res. eng. sci. theor. appl. 5(1) (2022) 152-168 162 the best results. in this case study, the neural network model (multilayerperceptron) was rejected in the first phase because it showed worse results than all other models (table 1). in contrast, the random forest algorithm showed excellent results in this case study, along with the ibk, random tree, and reptree algorithms (table 1 and table 2). the visualization of the prediction results received on the test data set has revealed that the model based on the ibk algorithm (k-nn) gives the results closest to the actual values. therefore, the model based on the ibk algorithm has been selected as the best prediction model for tmnt. this case study confirmed the results of numerous studies, such as: zhang et al. (2013), (zou et al., 2015) and zheng & su (2014), which agree that the k-nn (ibk in weka) algorithm gives excellent results in the short-term prediction of traffic flows. figure 4. actual and projected total monthly night traffic (tmnt), at selected counters (id: 1193 and id: 1208), for the three selected years (2018, 2019 and 2020) figure 5. projected total monthly night traffic (tmnt) at selected counters for 2021 0 10000 20000 30000 40000 50000 60000 70000 80000 ja n u a ry m a rc h m a y ju ly s e p te m b e r n o v e m b e r ja n u a ry m a rc h m a y ju ly s e p te m b e r n o v e m b e r ja n u a ry m a rc h m a y ju ly s e p te m b e r n o v e m b e r 2018 2019 2020 n u m b e r o f ve h ic le s actual tmnt 1193 actual tmnt 1208 projected tmnt ibk 1193 projected tmnt ibk 1208 0 20000 40000 60000 80000 100000 120000 140000 160000 180000 n u m b e r o f ve h ic le s 1025 1026 1046 1183 1191 1193 1194 1208 night traffic flow prediction using k-nearest neighbors algorithm 163 the graph shown in figure 4 shows the ratio of actual and projected tmnt for two selected traffic counting locations (1193 kneževići and 1208 velika župa) and the period from 2018 to 2020. the tmnt projection has been performed using a model based on the ibk algorithm. the graph clearly shows that the tmnt prediction performed on the test data set closely follows the actual tmnt values in the observed period (figure 4). the results of the tmnt prediction at eight selected traffic counting locations for 2021 are shown in figure 5. for amnt prediction, the same eight machine learning algorithms have been applied to the training data set. the performance of the prediction models, measured on the training data set is shown in table 3. table 3. the performances of eight amnt prediction models measured on a training data set algorithm correlation coefficient meanabsolute error root meansquared error relativabsolute error (%) root relativsquared error (%) linearregression 0.6346 317.812 478.415 74.3936 77.2268 multilayerperceptron 0.608 334.371 494.495 78.2698 79.8224 smoreg 0.6303 308.949 486.324 72.3191 78.5034 ibk 0.9801 64.9018 122.953 15.1922 19.8474 m5p 0.9445 133.975 220.096 31.3612 35.5284 random forest 0.9797 65.5395 124.075 15.3415 20.0285 random tree 0.9801 65.069 122.985 15.2314 19.8525 reptree 0.9694 80.585 152.082 18.8634 24.5494 models based on the linear regression, multilayer perceptron and smoreg algorithms have been rejected due to unsatisfactory performance (correlation coefficients of 0.6346, 0.608 and 0.6303, respectively, have been recorded). therefore, the remaining five algorithms have been applied in testing the machine learning model. the performance of these five prediction models, measured on the test data set is shown in table 4. the best amnt prediction model has been chosen in an identical manner as the best type of tmnt prediction model. the model based on the ibk algorithm has shown the best results this time, as well. table 4. the performances of the top five amnt prediction models measured on a test data set algorithm correlation coefficient meanabsolute error root meansquared error relativabsolute error (%) root relativsquared error (%) ibk 0.939 146.428 239.814 33.1472 35.5591 m5p 0.8851 204.294 332.391 46.2465 49.2862 random forest 0.9381 147.128 241.896 33.3058 35.8678 random tree 0.939 146.420 239.819 33.1455 35.5599 reptree 0.9286 161.299 257.180 36.5137 38.1342 the graph shown in figure 6 shows the ratio of actual and projected amnt for two selected traffic counting locations (1026 trstenik and 1046 vodice) and the period mladenović et al./oper. res. eng. sci. theor. appl. 5(1) (2022) 152-168 164 from 2018 to 2020. the amnt projection has been performed using a model based on the ibk algorithm. the results of the amnt prediction at eight selected traffic counting locations for 2021 are shown in figure 7. figure 6. actual and projected average monthly night traffic (amnt), at selected counters (id: 1026 and id: 1046), for the three selected years (2018, 2019 and 2020) figure 7. projected average monthly night traffic (amnt) at selected counters for 2021 in all the diagrams shown from figure 4 to figure 7, it is easy to see that the extreme values of tmnt, as well as of amnt, occur for the months of july and august. this is because almost all counting places are located on the roads leading to popular tourist destinations, and july and august are the months when most people are on vacation and traveling. 0 200 400 600 800 1000 1200 1400 1600 1800 ja n u a ry m a rc h m a y ju ly s e p te m b e r n o v e m b e r ja n u a ry m a rc h m a y ju ly s e p te m b e r n o v e m b e r ja n u a ry m a rc h m a y ju ly s e p te m b e r n o v e m b e r 2018 2019 2020 n u m b e r o f ve h ic le s actual amnt 1026 actual amnt 1046 projected amnt ibk 1026 projected amnt ibk 1046 0 1000 2000 3000 4000 5000 6000 n u m b e r o f ve h ic le s 1025 1026 1046 1183 1191 1193 1194 1270 night traffic flow prediction using k-nearest neighbors algorithm 165 6. conclusion the aim of this research has been to train and test predictive models on the existing data set on the volume of night traffic on state roads in serbia and to predict the total and average amounts of night traffic per month for the following year. in the conducted case study, using the weka software tool, machine learning models for prediction of total monthly night traffic (tmnt) and average monthly night traffic (amnt) have been trained, based on algorithms: linear regression, multilayer perceptron, smoreg, ibk, m5p, random forest, random tree and reptree. in the training data set, the ibk (k-nn) algorithm-based model and the models based on regression trees have shown a considerably better performance than the models from the functions category (linear regression, multilayer perceptron and smoreg). therefore, only these models have been tested on the test data set. the best performances have been shown by models based 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(2015). short-time traffic flow forecasting based on the k-nearest neighbor model. fifth international conference on transportation engineering icte 2015. september 26–27, 2015, dailan, china. © 2022 by the authors. submitted for possible open access publication under the terms and conditions of the creative commons attribution (cc by) license (http://creativecommons.org/licenses/by/4.0/). https://doi.org/10.7307/ptt.v27i3.1551 https://hdl.handle.net/1887/46907 https://doi.org/10.1016/j.sbspro.2013.08.076 https://doi.org/10.3141%2f2024-11 https://doi.org/10.1109/tii.2020.2976053 https://doi.org/10.1016/j.trc.2014.02.009 night traffic flow prediction using k-nearest neighbors algorithm dušan mladenović *, slađana janković, stefan zdravković, snežana mladenović, ana uzelac 1. introduction 2. literature review 3. methodology 4. case study 5. results and discussion 6. conclusion references plane thermoelastic waves in infinite half-space caused operational research in engineering sciences: theory and applications vol. 2, issue 1, 2019, pp. 72-90 issn: 2620-1607 eissn: 2620-1747 doi:_https://doi.org/10.31181/oresta1901060c * corresponding author. prasenjit2007@gmail.com (p. chatterjee), zeljkostevic88@yahoo.com (ž. stević) a two-phase fuzzy ahp – fuzzy topsis model for supplier evaluation in manufacturing environment prasenjit chatterjee1, željko stević2* 1 department of mechanical engineering, mckv institute of engineering, india 2 university of east sarajevo, faculty of transport and traffic engineering doboj, bosnia and herzegovina received: 15 february 2019 accepted: 11 april 2019 first online: 13 april 2019 original scientific paper abstract: supplier selection is one of the most important issues in supply chain management (scm) which greatly affects its performance and market competitiveness. in the recent years, supplier selection in scm has become imperative to balance between the ordinal and cardinal criteria. this paper proposes a two-phase model which aims to evaluate and select suppliers using an integrated fuzzy analytical hierarchy process (fahp) and fuzzy technique for ordering preference by similarity to ideal solution (ftopsis) methods. a fully developed model consisting of several evaluation criteria, both quantitative and qualitative in nature, as assessed by fahp method to estimate the criteria weights, while ftopsis method is used to rank the potential suppliers that have been singled out through expert assessment. the proposed model is a support tool in the optimization of the purchasing process, and it provides the possibility of realizing additional savings by developing stronger cooperation with the optimal supplier. key words: supply chain management, supplier selection, fahp, ftopsis 1. introduction according to gunasekaran and ngai, (2004), supply chain management (scm) is one of the vital strategies in the 21st century to achieve global competitive advantage. supply logistics plays a crucial role in today’s scm. in the last few decades, and especially in recent years; there is an evidential change in the role of scm in business policies. according to knežević et. al. (2012), acquisition is treated as an integrated strategic business function that aims to connect all other functions, enable smooth execution of all processes and activities in the company, and create a high added value based on the relationship with suppliers. from all the above, it is well understood that importance of scm will continue to grow over time. a two-phase model for supplier evaluation in manufacturing environment 73 appropriate choice of suppliers is an issue of strategic importance and key activity for industries in modern scs due of its central role in deciding price, quality, delivery and service to achieve organizational objectives (kagnicioglu, 2006). according to lasch and janker, (2005) effective supplier management that begins with the identification of potential suppliers is vital for a successful scm. ghodsypour and o’brien, (2001) believed that satisfactory choice of suppliers significantly reduces costs which, according to ghodsypour and o’brien, (1998) represented up to 70% of the product price and increase competitiveness, while önüt et. al. (2009) focused on end-user satisfaction associated with it. the policy of relations and evaluation of sources of supply has a strategic importance for the whole procurement subsystem. this subsystem can effectively perform the tasks relating to the supply of the company, if it selects supplier or suppliers (not too many of them) that can meet the requirements of the procurement subsystem, and which are related to the quality, quantity, price, terms of delivery and other terms, reliability, flexibility, as well as other objectives that are to be met, satisfying other criteria too. search for suppliers that meets the above criteria is a permanent and primary task. to that end, it is necessary to continuously collect and process information about suppliers and establish and maintain adequate relations with them; further, it is necessary to develop and apply methods for the evaluation and ranking of potential suppliers. de boer et. al. (2001), have identified four stages of the selection of suppliers, as follows: problem definition, formulation of criteria, qualification and, selection. the correct choice of suppliers from the start provides opportunity for a timely, continuous and quality production which brings above mentioned benefits making the production competitive. the main activity of the company where the research was carried out is the production of pre-insulated pipes for heating; in order for the company to organize this production it is necessary to procure steel pipes. out of a large number of companies which could be potential suppliers of steel pipes it is necessary to select those whose characteristics, according to the criteria of the procurement subsystem of the company, are the most adequate. after a complete and long-term market analysis performed by the company's expert team, they selected five suppliers that represent potential solutions. in addition, the expert team had set a total of nine criteria on the basis of which it is necessary to make the evaluation of suppliers. considering the current market needs and requirements, and at the same time taking into account the knowledge and skills obtained through the years of work, the team of experts has evaluated the criteria as well in order to provide different weight value, which greatly affects the ranking of alternatives. the primary objective and the contribution of this paper is to propose a two-phase model integrating fuzzy analytical hierarchy process (fahp) and fuzzy technique for ordering preference by similarity to ideal solution (ftopsis) methods for supplier selection through establishing long-term cooperation with the selected supplier to gain additional market advantage. this paper is structured as follows. section 2 presents the literature review on supplier selection. section 3 presents fundamentals of fuzzy sets, fahp and ftopsis methods. section 4 demonstrates the considered real time example and explains the results of the integrated multi-criteria model. section 5 presents a sensitivity analysis chatterjee and stević/oper. res. eng. sci. theor. appl. 2 (1) (2019) 72-90 74 which includes the experiment of 24 sets where the values of criteria are changed. this section also discuss about the stability of the model. section 6 sets out the conclusions. 2. literature review there are numerous criteria for evaluating suppliers, but the question is how to choose the right ones from a given set, which will be used to choose the best solution. dickson, (1966) is considered to be a pioneer in this field because he was the first to create a study on the evaluation of suppliers in which he defined a set of 23 criteria by which the evaluation and selection of the best suppliers could be carried out. in his paper ellram, (1990), he tried to increase the importance of qualitative criteria that should enable long-term cooperation between the company and suppliers. he divided criteria into four groups: financial aspects, organizational culture and strategic issues, technology issues, and other. further, the authors from the end of the last century attempted to answer this question, and webber et. al. (1991) investigated the criteria for the selection of suppliers in manufacturing and retail environment. a group of authors concluded that quality, delivery and price prevail as dominant criteria, while geographical location, financial position and production capacity are secondary factors. after this, verma and pullman, (1998) conducted a survey among a large number of managers in order to examine how they reach compromise when selecting suppliers. their research indicated that managers place highest priority to quality as the most important attribute of suppliers, followed by delivery and price. research on the impact of the criteria in the sc continues at the beginning of this century, and karpak et. al. (2001) recognized reliability of delivery as a criterion for selection, whereas bhutta and huq, (2002) used four criteria for evaluating suppliers: price, quality, technology and service. research conducted in (çebi and bayraktar, 2003) singled out the following group of criteria: logistics, technology, commerce and business cooperation that contain both quantitative and qualitative criteria. combination fahp and ftopsis methods are often used for evaluation performance in sc and selection supplier, for example evaluating performance for selection of suppliers in car manufacturing factory in turkey (zeydan et. al. 2011), for evaluation of the performance of suppliers in company which produced several types of electronic cards (eraslan and atalay, 2014). shukla et. al. (2014) illustrates how fahp and ftopsis can be integrated to allow for a more consistent evaluation and prioritization of sc partner. chen and yang, (2011) are used constrained fahp and ftopsis for supplier selection. these integrated methods are also used for solving next problems: for the selection and development of reverse logistics partner in india (prakash and barua 2016), ranking of the industry alternatives for portfolio investments (dincer et. al. 2016), for handling equipment selection (yazdani, 2014), for mining method selection in zinc producer in iran (yazdani et. al. 2012) or combination more methods of mcdm with qfd for selection green supplier (yazdani et. al. 2016), combination ahp, gis and integer programming for evaluation in reverse logistics (acar et. al. 2015), combination fuzzy vikor and ar-dea method for supplier selection (mohaghar et. al. 2013) by using fahp and ftopsis, uncertainty and vagueness from subjective perception and the experiences of decision maker can be effectively represented and reached to a more effective decision (ertugrul and karakasoglu, 2008). a two-phase model for supplier evaluation in manufacturing environment 75 3. material and methods 3.1. fuzzy sets fuzzy sets are sets whose elements have degrees of membership. the theory of fuzzy sets was first introduced by zadeh, (1965), whose application enables decision makers to effectively deal with the uncertainties. in classical set theory, the membership of elements in a set is assessed in binary terms according to a bivalent condition an element either belongs or does not belong to the set. fuzzy sets used generally triangular (tfn), trapezoidal and gaussian fuzzy numbers. a fuzzy number a ̃ on r to be a tfn if its membership function lea μ_a~(x): r→[0,1] is equal to following equation (1): 𝑀𝐴~(𝑥) = { 𝑥 −𝑙 𝑚−𝑙 , 𝑙 ≤ 𝑥 ≤ 𝑚 𝑢−𝑥 𝑢−𝑚 , 𝑚 ≤ 𝑥 ≤ 𝑢 0, 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒 (1) from equation (1), l and u mean the lower and upper bounds of the fuzzy number �̃�, and m is the modal value for �̃� (figure 1). the tfn can be denoted by �̃� = (𝑙, 𝑚, 𝑢). figure 1. the membership functions of the tfn the operational laws of tfn �̌�1 = (𝑙1, 𝑚1, 𝑢1) and �̌�2 = (𝑙2, 𝑚2, 𝑢2) are displayed as following equations. addition: �̌�1 + �̌�2 = (𝑙1, 𝑚1, 𝑢1) + (𝑙2, 𝑚2, 𝑢2 ) = (𝑙1 + 𝑙2, 𝑚1 + 𝑚2, 𝑢1 + 𝑢2 ) (2) multiplication: �̌�1𝑥�̌�2 = (𝑙1, 𝑚1, 𝑢1 )𝑥(𝑙2, 𝑚2, 𝑢2) = (𝑙1𝑙2, 𝑚1𝑚2, 𝑢1𝑢2) for 𝑙1𝑙2 > 0; 𝑚1𝑚2 > 0; 𝑢1 𝑢2 > 0 (3) chatterjee and stević/oper. res. eng. sci. theor. appl. 2 (1) (2019) 72-90 76 subtraction: �̌�1 − �̌�2 = (𝑙1, 𝑚1, 𝑢1) − (𝑙2, 𝑚2, 𝑢2 ) = (𝑙1 − 𝑢2, 𝑚1 − 𝑚2, 𝑢1−𝑙2) (4) division: 𝐴1 𝐴2 = (𝑙1,𝑚1,𝑢1) (𝑙2,𝑚2,𝑢2) = ( 𝑙1 𝑢2 , 𝑚1 𝑚2 , 𝑢1 𝑙2 ) for 𝑙1𝑙2 > 0; 𝑚1𝑚2 > 0; 𝑢1𝑢2 > 0 (5) reciprocal: �̌�−1 = (𝑙1, 𝑚1, 𝑢1) −1 = ( 1 𝑢1 , 1 𝑚1 , 1 𝑙1 ) for 𝑙1𝑙2 > 0; 𝑚1𝑚2 > 0; 𝑢1 𝑢2 > 0 (6) 3.2. fuzzy ahp method analytic hierarchy process is created by thomas saaty (saaty, 1980) and according to him, ahp is a measurement theory which deals with pairwise criteria comparisons and which relies on expert opinion in order to perform the priority scale. ahp in a certain ways resolves the problem of subjective influence of the decisionmaker because it measures the degree of consistency (cr), and informs the decision makers of the result. depending on the size of the matrix the value of this ratio is recommended, so in (lee et. al. 2008) we find that the maximum permissible level of consistency for the 3x3 matrix is 0.05, for the 4x4 matrix it is 0.08, and for larger matrices it is 0.1. kwong’s method (kwong and bai, 2003) has been used to check the consistency of pairwise judgement of comparison matrix. a tfn, denoted as 𝑀=(𝑙,𝑚,𝑢), can be defuzzified to a crisp number as follows: 𝑀−𝑐𝑟𝑖𝑠𝑝 = (4𝑚+𝑙+𝑢) 6 (7) tfn, which were used in this work are marked as (lij,mij,uij). the parameters (lij,mij,uij) are the smallest possible value, the most promising value and highest possible value that describes a fuzzy event, respectively. in this study, the extent analysis method by chang, (1996) is adopted. some advantages of this method are: effectively handle both qualitative and quantitative data and easy to implement and understand (tuysuz and kahraman 2006), fuzzy ahp is preferable for widely spread hierarchies, where few importance/rating pairwise comparisons are required at lower level trees, can adopt linguistic variables (ertugrul and karakasoglu, 2008). let assume that x={x1,x2,...,xn} is number of objects, and u={u1,u2,...,um} is number of aims. according to the methodology of extended analysis set up by chang, for each object an extended goal analysis is made. values of the extended analysis "m" for each object can be represented as follows: 𝑀𝑔𝑖, 1 𝑀𝑔𝑖, 2 𝑀𝑔𝑖, 𝑚 𝑖 = 1,2, … 𝑛., (8) where 𝑀𝑔, 𝑗 𝑗 = 1,2, … 𝑚., are fuzzy triangular numbers. chang's expanded analysis includes following steps: a two-phase model for supplier evaluation in manufacturing environment 77 step 1: the value of fuzzy synthetic extent si with respect to the ith criteria is defined as: 𝑆𝑖 = ∑ 𝑀𝑔𝑖 𝑗𝑛 𝑗=1 × [∑ ∑ 𝑀𝑔𝑖 𝑗m j=1 n i=1 ] −1 (9) in order to obtain expression [∑ ∑ 𝑀𝑔𝑖 𝑗m j=1 n i=1 ] −1 (10) it is necessary to perform additional fuzzy operations with "m" values of the extended analysis, which is represented by the following expressions: ∑ 𝑀𝑔𝑖 𝑗𝑚 𝑗=1 = (∑ 𝑙𝑗 𝑚 𝑗=1 , ∑ 𝑚𝑗, ∑ 𝑢𝑗 𝑚 𝑗=1 𝑚 𝑗=1 ) (11) ∑ ∑ 𝑀𝑔𝑖 𝑗𝑛 𝑗=1 𝑛 𝑖=1 = (∑ 𝑙𝑖 𝑛 𝑖=1 , ∑ 𝑚𝑖 , ∑ 𝑢𝑖 𝑛 𝑖=1 𝑛 𝑖=1 ) (12) then it is necessary to calculate the inverse vector: [∑ ∑ 𝑀𝑔𝑖 𝑗m j=1 n i=1 ] −1 = [ 1 ∑ 𝑢𝑖 𝑛 𝑖=1 , 1 ∑ 𝑚𝑖 𝑛 𝑖=1 , 1 ∑ 𝑙𝑖 𝑛 𝑖=1 ] (13) step 2: the degree of possibility of sb ≥ sa is defined as: 𝑉(𝑆𝑏 ≥ 𝑆𝑎 ) = { 1, 𝑖𝑓 𝑚𝑏 ≥ 𝑚𝑎 0, 𝑖𝑓 𝑙𝑎 ≥ 𝑢𝑏 𝑙𝑎−𝑢𝑏 (𝑚𝑏−𝑢𝑏 )−(𝑚𝑎−𝑙𝑎) , 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒 (14) where „d“ ordinate of a largest cross-section in point d between μsa andi μsb as shown in figure 2. figure 2. intersection between sa and sb chatterjee and stević/oper. res. eng. sci. theor. appl. 2 (1) (2019) 72-90 78 to compare s1 and s2, both values v(s1 ≥ s2) and v(s2 ≥ s1) are needed. step 3: level of possibility for convex fuzzy number to be greater than „k“ convex number si (i =1,2,...,k) can be defined as follows: 𝑉(𝑆𝑖 ≥ 𝑆1, 𝑆2 , … , 𝑆𝑘 ) = min 𝑉(𝑆𝑖 ≥ 𝑆𝑘 ), = 𝑤 ′ (𝑆𝑖 ) (15) 𝑑′ (𝐴𝑖 ) = min 𝑉(𝑆𝑖 ≥ 𝑆𝑘 ), 𝑘 ≠ 𝑖, 𝑘 = 1,2, … , 𝑛 (16) the weight vector is given by the following expression: 𝑊 ′ = (d′(𝐴1), d ′(𝐴2), … , d ′(𝐴𝑛 )) 𝑇 , (17) step 4: through normalization, the weight vector is reduced to the phrase: 𝑊 = (d(𝐴1 ), d(𝐴2 ), … , d(𝐴𝑛)) 𝑇 , (18) 3.3. fuzzy topsis method due to its simple concept, topsis method has become very popular and it is applied in many areas of decision-making. however, despite that, this method is often criticized because it lacks the ability to adequately handle uncertainty and imprecision in the moment when the decision maker needs accurate results. for this reason, in this paper we use the extended ftopsis method which allows proper handling of uncertainty and imprecision, and it is completely appropriate for the ranking of alternatives. topsis was first proposed by (hwang and yoon, 1981) and a fuzzy topsis method was later introduced by (chen and hwang, 1992). the algorithm of the ftopsis method can be described as follows: (chen, 2000) step 1: form a committee of decision-makers, then identify the evaluation criteria. step 2: choose the appropriate linguistic variables for the importance weight of the criteria and the linguistic ratings for alternatives with respect to criteria. step 3: aggregate the weight of criteria to get the aggregated fuzzy weight �̃�𝑗 of criterion cj , and pool the decision maker's opinions to get the aggregated fuzzy rating 𝑥𝑖𝑗 of alternative ai under criterion cj �̃�𝑘 = (𝑎𝑘 , 𝑏𝑘 , 𝑐𝑘 ), 𝑘 = 1,2,3, … 𝐾, (19) then the aggregated fuzzy rating can be determined as 𝑅 = (𝑎, 𝑏, 𝑐), 𝑘 = 1,2,3, … 𝐾 (20) 𝑎 = 𝑚𝑖𝑛𝑘 (𝑎𝑘 ), 𝑏 = 1 𝐾 ∑ 𝑏𝑘 𝐾 𝑘=1 , 𝑐 = 𝑚𝑎𝑥𝑘 (𝑐𝑘 ) (21) step 4: construct the fuzzy decision matrix and the normalized fuzzy decision matrix. �̃�𝑘 = [𝑟𝑖𝑗 ] 𝑚𝑥𝑛 𝑖 = 1,2,3, … , 𝑚; 𝑗 = 1,2,3, … , 𝑛 (22) where b and c are the set of benefit criteria and cost criteria, respectively, and 𝑟𝑖𝑗 = ( 𝑎𝑖𝑗 𝑐𝑗 ∗ , 𝑏𝑖𝑗 𝑐𝑗 ∗ , 𝑐𝑖𝑗 𝑐𝑗 ∗ ) , 𝑗 ∈ 𝐵 (23) 𝑟𝑖𝑗 = ( 𝑎𝑗 − 𝑐𝑖𝑗 , 𝑎𝑗 − 𝑏𝑖𝑗 , 𝑐𝑖𝑗 𝑎𝑖𝑗 ) , 𝑗 ∈ 𝐶 (24) a two-phase model for supplier evaluation in manufacturing environment 79 𝑐𝑗 ∗ = maxi 𝑐𝑖𝑗 if 𝑗 ∈ 𝐵 𝑎𝑗 − = mini 𝑎𝑖𝑗 if 𝑗 ∈ 𝐶 step 5: considering the different importance of each criterion, we can construct the weighted normalized fuzzy decision matrix as: �̃� = [�̃�𝑖𝑗] 𝑚𝑥𝑛 𝑖 = 1,2, , … , 𝑚; 𝑗 = 1,2, , … , 𝑛 (25) �̃�𝑖𝑗 = 𝑟𝑖𝑗𝑊 (26) where w is the weighted vector of evaluating criteria. step 6: determine the fuzzy positive ideal solution (fpis) and fuzzy negative ideal solution (fnis) where according (yu et. al. 2011): 𝐴∗ = (�̃�1 ∗, �̃�2 ∗, … , �̃�𝑛 ∗ ) = (𝑚𝑎𝑥𝑗𝑣𝑖𝑗|𝑖 𝜖 𝐵), (𝑚𝑖𝑛𝑗𝑣𝑖𝑗|𝑖 𝜖 𝐶), 𝑖 = 1,2 … 𝑚; 𝑗 = 1,2 … 𝑛, (27) 𝐴− = (�̃�1 −, �̃�2 −, … , �̃�𝑛 −) = (𝑚𝑖𝑛𝑗𝑣𝑖𝑗|𝑖 𝜖 𝐵), (𝑚𝑎𝑥𝑗𝑣𝑖𝑗|𝑖 𝜖 𝐶), 𝑖 = 1,2 … 𝑚; 𝑗 = 1,2 … 𝑛, (28) where b and c are the set of benefit criteria and cost criteria, respectively. step 7: calculate the distance of each alternative from fpis and fnis, respectively. the distance of each alternative from a* and a− can be currently calculated as: 𝑑𝑖 ∗ = ∑ 𝑑(�̃�𝑖𝑗, �̃�𝑗 ∗𝑛 𝑗=1 ), 𝑖 = 1,2, … 𝑚, (29) 𝑑𝑖 − = ∑ 𝑑(�̃�𝑖𝑗, �̃�𝑗 −𝑛 𝑗=1 ), 𝑖 = 1,2, … 𝑚, (30) where d(.;.) is the distance measurement between two fuzzy numbers. step 8: calculate the closeness coefficient of each alternative. a closeness coefficient is defined to determine the ranking order of all alternatives once the 𝑑𝑖 ∗ and 𝑑𝑖 − of each alternative ai(i=1;2;m) has been calculated. the closeness coefficient of each alternative is calculated as: 𝐶𝐶𝑖 = 𝑑𝑖 − 𝑑𝑖 ∗+𝑑𝑖 − , 𝑖 = 1,2, … , 𝑚 (31) step 9: according to the closeness coefficient, the ranking order of all alternatives can be determined. 4. numerical example the criteria used in this study were selected based on two important factors: criteria which are commonly used in the same or similar research and based on the current needs of the company and the requirements that the company faces on the market. the criteria (puška et al. 2018) applied in this study are: the price of material, pipe length, delivery time, payment method, geographical location, quality, financial stability, flexibility and communication system, and in this paper they are marked c1c9 respectively. therefore, there are four quantitative criteria and five criteria that are qualitative, as shown in figure 3. steps of the proposed model for supplier evaluation are shown in figure 4. one of two components of multicriteria evaluation methods is chatterjee and stević/oper. res. eng. sci. theor. appl. 2 (1) (2019) 72-90 80 represented by the values of the criteria weights (ginevičius and podvezko, 2008) and one of the main features of multi-criteria decision-making process is that the different criteria cannot have the same significance, so following the methodology described for decision making which applies the extended ahp method ie. fahp to get the required results is necessary to perform criteria comparison on the basis of tfn, as shown in table 2. the comparison was made based on the scale shown in table 1. figure 3. hierarchical structure of the proposed model table 1. triangular fuzzy scale linguistic scale tf scale tf reciprocal scale just equal (1,1,1) (1,1,1) equal important (1/2,1,3/2) (2/3,1,2) weakly more important (1,3/2,2) (1/2,2/3,1) strongly more important (3/2,2,5/2) (2/5,1/2,2/3) very strongly more important (2,5/2,3) (1/3,2/5,1/2) absolutely more important (5/2,3,7/2) (2/7,1/3,2/5) a two-phase model for supplier evaluation in manufacturing environment 81 figure 4. steps of the proposed model by comparing them, weight value criteria is determined, and that criteria plays very important role in the further implementation of methods, because on the base of these values the optimal solution is determined. if some variant is better according to criteria that are very important when deciding, it increases the possibility to have excatly this variant as an optimum. fuzzy important weight of the criteria is calculated by taking geometric mean of the responses of the experts (lee, 2009), this is shown in table 3. example calculation of geometric mean for c42 is: n-= (1/2x2/5x2/5)1/3=0,431; n=(2/3x1/2x1/2)1/3=0,550; n+=(1x2/3x2/3)1/3=0,763 chatterjee and stević/oper. res. eng. sci. theor. appl. 2 (1) (2019) 72-90 82 table 2. comparison criteria by 3 experts c1 c2 c3 c4 c5 c6 c7 c8 c9 c1 e1 (1,1,1) (2/3,1,2) (1/2,2/3,1) (1/2,1,3/2) (1/2,1,3/2) (2/3,1,2) (1,1,1) (1,1,1) (1/2,1,3/2) e2 (1,1,1) (2/3,1,2) (2/3,1,2) (1,3/2,2) (1/2,1,3/2) (2/3,1,2) (1/2,1,3/2) (1/2,1,3/2) (1,3/2,2) e3 (1,1,1) (1/2,2/3,1) (2/5,1/2,2/3) (1/2,1,3/2) (1/2,1,3/2) (2/7,1/3,2/5) (1/2,1,3/2) (1,3/2,2) (1,3/2,2) c2 e1 (1/2,1,3/2) (1,1,1) (2/3,1,2) (1,3/2,2) (1,3/2,2) (1,1,1) (1/2,1,3/2) (1/2,1,3/2) (1/2,1,3/2) e2 (1/2,1,3/2) (1,1,1) (1,1,1) (3/2,2,5/2) (1,3/2,2) (1,1,1) (1,3/2,2) (1,3/2,2) (3/2,2,5/2) e3 (1,3/2,2) (1,1,1) (2/3,1,2) (3/2,2,5/2) (3/2,2,5/2) (2/5,1/2,2/3) (3/2,2,5/2) (2,5/2,3) (2,5/2,3) c3 e1 (1,3/2,2) (1/2,1,3/2) (1,1,1) (3/2,2,5/2) (3/2,2,5/2) (1/2,1,3/2) (1,3/2,2) (1,3/2,2) (3/2,2,5/2) e2 (1/2,1,3/2) (1,1,1) (1,1,1) (3/2,2,5/2) (1,3/2,2) (1,1,1) (1,3/2,2) (1,3/2,2) (3/2,2,5/2) e3 (3/2,2,5/2) (1/2,1,3/2) (1,1,1) (2,5/2,3) (2,5/2,3) (1/2,2/3,1) (2,5/2,3) (5/2,3,7/2) (5/2,3,7/2) c4 e1 (2/3,1,2) (1/2,2/3,1) (2/5,1/2,2/3) (1,1,1) (1,1,1) (2/3,1,2) (2/3,1,2) (1/2,1,3/2) (1,1,1) e2 (1/2,2/3,1) (2/5,1/2,2/3) (2/5,1/2,2/3) (1,1,1) (1/2,1,3/2) (2/5,1/2,2/3) (1/2,1,3/2) (1/2,1,3/2) (1,1,1) e3 (2/3,1,2) (2/5,1/2,2/3) (1/3,2/5,1/2) (1,1,1) (1,1,1) (2/7,1/3,2/5) (1,1,1) (1/2,1,3/2) (1/2,1,3/2) c5 e1 (2/3,1,2) (1/2,2/3,1) (2/5,1/2,2/3) (1,1,1) (1,1,1) (1/2,2/3,1) (2/3,1,2) (2/3,1,2) (1/2,1,3/2) e2 (2/3,1,2) (1/2,2/3,1) (1/2,2/3,1) (2/3,1,2) (1,1,1) (1/2,2/3,1) (1,1,1) (1,1,1) (2/3,1,2) e3 (2/3,1,2) (2/5,1/2,2/3) (1/3,2/5,1/2) (1,1,1) (1,1,1) (2/7,1/3,2/5) (1,1,1) (1/2,1,3/2) (1/2,1,3/2) c6 e1 (1/2,1,3/2) (1,1,1) (2/3,1,2) (1/2,1,3/2) (1,3/2,2) (1,1,1) (1/2,1,3/2) (1/2,1,3/2) (1,3/2,2) e2 (1/2,1,3/2) (1,1,1) (1,1,1) (3/2,2,5/2) (1,3/2,2) (1,1,1) (1,3/2,2) (1,3/2,2) (3/2,2,5/2) e3 (5/2,3,7/2) (3/2,2,5/2) (1,3/2,2) (5/2,3,7/2) (5/2,3,7/2) (1,1,1) (5/2,3,7/2) (5/2,3,7/2) (5/2,3,7/2) c7 e1 (1,1,1) (2/3,1,2) (1/2,2/3,1) (1/2,1,3/2) (1/2,1,3/2) (2/3,1,2) (1,1,1) (1,1,1) (1,1,1) e2 (2/3,1,2) (1/2,2/3,1) (1/2,2/3,1) (2/3,1,2) (1,1,1) (1/2,2/3,1) (1,1,1) (1,1,1) (2/3,1,2) e3 (2/3,1,2) (2/5,1/2,2/3) (1/3,2/5,1/2) (1,1,1) (1,1,1) (2/7,1/3,2/5) (1,1,1) (1/2,1,3/2) (1/2,1,3/2) c8 e1 (1,1,1) (2/3,1,2) (1/2,3/2,1) (2/3,1,2) (1/2,1,3/2) (2/3,1,2) (1,1,1) (1,1,1) (2/3,1,2) e2 (2/3,1,2) (1/2,2/3,1) (1/2,2/3,1) (2/3,1,2) (1,1,1) (1/2,2/3,1) (1,1,1) (1,1,1) (2/3,1,2) e3 (1/2,2/3,1) (1/3,2/5,1/2) (2/7,1/3,2/5) (2/3,1,2) (2/3,1,2) (2/7,1/3,2/5) (2/3,1,2) (1,1,1) (1,1,1) c9 e1 (2/3,1,2) (2/3,1,2) (2/5,1/2,2/3) (1,1,1) (2/3,1,2) (1/2,2/3,1) (1,1,1) (1/2,1,3/2) (1,1,1) e2 (1/2,2/3,1) (2/5,1/2,2/3) (2/5,1/2,2/3) (1,1,1) (1/2,1,3/2) (2/5,1/2,2/3) (1/2,1,3/2) (1/2,1,3/2) (1,1,1) e3 (1/2,2/3,1) (1/3,2/5,1/2) (2/7,1/3,2/5) (2/3,1,2) (2/3,1,2) (2/7,1/3,2/5) (2/3,1,2) (1,1,1) (1,1,1) a two-phase model for supplier evaluation in manufacturing environment 83 table 3. fuzzy important weight of the criteria calculated by taking geometric mean c1 c2 c3 c4 c5 c1 (1,1,1) (0.606,0.874,1.587) (0.511,0.693,1.817) (0.63,1.145,1.651) (0.5,1,1.5) c2 (0.63,1.145,1.651) (1,1,1) (0.763,1,1.587) (1.31,1.817,2.31) (1.145,1.651,2.154) c3 (0.909,1.442,1.957) (0.63,1,1.31) (1,1,1) (1.651,2.154,2.657) (1.442,1.957,2.466) c4 (0.606,0.784,1.587) (0.431,0.55,0.763) (0.376,0.464,0.606) (1,1,1) (0.794,1,1.145) c5 (0.667,1,2) (0.464,0.606,0.874) (0.405,0.511,0.693) (0.874,1,1.26) (1,1,1) c6 (0.855,1.442,1.99) (1.145,1.26,1.357) (0.874,1.145,1.587) (1.233,1.817,2.359) (1.357,1.89,2.41) c7 (0.763,1,1.587) (0.511,0.693,1.101) (0.083,0.562,0.794) (0.693,1,1.442) (0.794,1,1.145) c8 (0.693,0.874,1.26) (0.481,0.644,1) (0.415,0.693,0.737) (0.667,1,2) (0.693,1,1.442) c9 (0.55,0.763,1.26) (0.446,0.585,0.874) (0.358,0.585,0.562) (0.874,1,1.26) (0.606,1,1.817) c6 c7 c8 c9 c1 (0.503,0.694,1.17) (0.63,1,1.31) (0.794,1.145,1.442) (0.794,1.31,1.817) c2 (0.737,0.794,0.874) (0.909,1.442,1.957) (1,1.554,2.08) (1.145,1.71,2.241) c3 (0.63,0.874,1.145) (1.26,1.778,2.289) (1.357,1.89,2.41) (1.778,2.289,2.797) c4 (0.424,0.55,0.811) (0.693,1,1.442) (0.5,1,1.5) (0.794,1,1.142) c5 (0.415,0.529,0.737) (0.874,1,1.26) (0.874,1,1.442) (0.55,1,1.651) c6 (1,1,1) (1.077,1.651,2.19) (1.077,1.651,2.19) (1.554,2.08,2.596) c7 (0.457,0.606,0.928) (1,1,1) (0.794,1,1.145) (0.693,1,1.442) c8 (0.457,0.606,0.928) (0.874,1,1.26) (1,1,1) (0.763,1,1.587) c9 (0.385,0.481,0.644) (0.693,1,1.442) (0.63,1,1.442) (1,1,1) to determine fuzzy combination expansion for each one of the criteria, first we calculate ∑ 𝑀𝑔𝑖 𝑗𝑛 𝑗=1 value for each row of the matrix. c1=(1+0.606+0.511+0.630+...;1+0.874+0.693+1.145...;1+1.587+1.817+1.651+...)=(5.968; 8.861; 13.294) etc. the ∑ ∑ 𝑀𝑔𝑖 𝑗𝑛 𝑗=1 𝑛 𝑖=1 value is calculated as: (5.968;8.861;13.294)+(8.639;12.113;15.854)+(10.657;14.384;18.031)+(5.618;7.348;10.296)+(6.123;7.646;10.917)+(10.172;13.936; 17.679)+...=(64.55;87.38;118.17) chatterjee and stević/oper. res. eng. sci. theor. appl. 2 (1) (2019) 72-90 84 then, 𝑆𝑖 = ∑ 𝑀𝑔𝑖 𝑗𝑛 𝑗=1 × [∑ ∑ 𝑀𝑔𝑖 𝑗m j=1 n i=1 ] −1 : s1=(5.968;8.861;13.294)x(1/118.17;1/87.38;1/64.55)=(0.050;0.101;0.206) now, the v values are calculated using these vectors. 𝑉(s1 ≥ s2) = 0.073−0.206 (0.101−0.206)−(0.139−0.073) = 0.778 v(s1≥s3)=0.644; v(s1≥s4,s5)=1; v(s1≥s6)=0.670; v(s1≥s7,s8,s9)=1 the priorities of weights are calculated using: d'=(c1)=0.644, d'=(c2)=0.857, d'=(c3)=1, d'=(c4)=0.464, d'=(c5)= 0.503, d'=(c6)=0.974, d'=(c7)= 0.497, d'=(c8)= 0.525, d'=(c9)= 0.467 after the equation is applied (17), weight values are obtained, and from the equation (18) normalized weights of criteria are received: w'=(0.644;0.857;1;0.464;0.503;0.974;0.497;0.525;0.467) w=(0.109;0.144;0.169;0.078;0.085;0.164;0.084;0.088;0.079) table 4. defuzzification using kwong’s method c1 c2 c3 c4 c5 c6 c7 c8 c9 c1 1 0.948 0.85 1.144 1 0.742 0.99 1.136 1.309 c2 1.144 1 1.058 1.815 1.651 0.798 1.439 1.549 1.704 c3 1.439 0.99 1 2.154 1.956 0.879 1.777 1.888 2.289 c4 0.888 0.566 0.473 1 0.99 0.573 1.023 1 0.989 c5 1.111 0.627 0.524 1.022 1 0.545 1.022 1.053 1.034 c6 1.436 1.257 1.174 1.81 1.888 1 1.645 1.645 2.078 c7 1.058 0.731 0.521 1.023 0.99 0.655 1 0.99 1.023 c8 0.908 0.676 0.654 1.111 1.023 0.635 1.023 1 1.058 c9 0.81 0.61 0.543 1.023 1.071 0.492 1.023 1.012 1 after defuzzification shown in the previous table, by applying the ahp method steps, we obtain the following values: λmax = 9.262; ci = 0.033; cr = 0.023, which means that the degree of consistency is 0.023, which is much less than the maximum permitted limit of 0.1 according to the size of the matrix used in the paper. on the basis of the procedure and obtained results the most important criterion for the decision on the selection of suppliers is the third criterion: the time of delivery, which has a relative importance of 16.9%, while the quality and length of pipes follow immediately after the time of delivery with a share of 16.4%, and 14.4%, respectively. the first criterion, the price of material, has the importance of 10.9%, while other criteria are somewhat lower in value. delivery time, quality and price are the criteria that a large number of practical researches dealing with similar issues are of great importance. however, the length of the pipes as a criterion is rarely used, and even more rarely is of great importance as is the case in this study. the reason for such importance of this criteria is the activity in which the company is engaged, so this criterion can greatly contribute to an easier implementation of the finished product to the heating system, which is one of the current demands of end users in the market. table 5 shows the evaluation of suppliers by three experts using the linguistic variables. based on the characteristics of the suppliers and the expert opinion table 5 was formed. a two-phase model for supplier evaluation in manufacturing environment 85 table 5. rating of the suppliers in linguistic terms expert supp. criterion c1 c2 c3 c4 c5 c6 c7 c8 c9 e1 s1 vg vg vg f mg vg vg vg g s2 g vg vg vg mg vg g g mg s3 g g g g vg mg vg g g s4 mg g g f vg mg vg vg g s5 mg mg mp vg g g g g mg e2 s1 vg g vg mg f vg g g vg s2 g g vg vg f vg mg mg g s3 g mg mg g vg g g mg vg s4 mg f g mg vg g g vg vg s5 f mg mp vg mg g mg mg g e3 s1 g vg vg f mg vg vg vg vg s2 g vg vg vg mg g mg mg g s3 g f g g vg mg vg g vg s4 mg g g f vg mg g vg vg s5 mg vg mp g mg g mg g mg by applying the 3rd and 4th step of the ftopsis method we get the values that are presented in tables 6 and 7, which represent a fuzzy decision matrix and normalized fuzzy decision matrix. table 6. fuzzy decision matrix supp. criterion c1 c2 c3 c4 c5 s1 (7,9.667,10) (7,9.667,10) (7,9.667,10) (3,5.667,9) (3,6.333,9) s2 (7,9.333,10) (7,9.667,10) (9,10,10) (9,10,10) (3,6.333,9) s3 (7,9,10) (3,7,10) (5,8.333,10) (7,9,10) (9,10,10) s4 (5,7,9) (3,7.667,10) (7,9,10) (3,5.667,9) (9,10,10) s5 (3,6.333,9) (5,8,10) (1,3,5) (7,9.667,10) (5,7.667,10) c6 c7 c8 c9 s1 (9,10,10) (7,9.667,10) (7,9.667,10) (7,9.667,10) s2 (7,9.667,10) (5,7.667,10) (5,7.667,10) (5,8.333,10) s3 (5,7.667,10) (7,9.667,10) (5,8.333,10) (7,9.667,10) s4 (5,7.667,10) (7,9.333,10) (9,10,10) (7,9.667,10) s5 (7,9,10) (5,7.667,10) (5,8.33,10) (5,7.667,10) table 7. normalized fuzzy decision matrix criterion c1 c2 c3 c4 c5 s1 (0.3,0.31,0.429) (0.7,0.967,1) (0.1,0.103,0.143) (0.3,0.567,0.9) (0.3,0.633,0.9) s2 (0.3,0.321,0.429) (0.7,0.967,1) (0.1,0.1,0.111) (0.9,1.0,1) (0.3,0.633,0.9) s3 (0.3,0.333,0.429) (0.3,0.7,1) (0.1,0.12,0.2) (0.7,0.9,1) (0.9,1,1) s4 (0.333,0.429,0.6) (0.3,0.767,1) (0.1,0.111,0.143) (0.3,0.567,0.9) (0.9,1,1) s5 (0.333,0.474,1) (0.5,0.8,1) (0.2,0.333,1) (0.7,0.967,1) (0.5,0.767,1) c6 c7 c8 c9 s1 (0.9,1,1) (0.7,0.967,1) (0.7,0.967,1) (0.7,0.967,1) s2 (0.7,0.967,1) (0.5,0.767,1) (0.5,0.767,1) (0.5,0.833,1) s3 (0.5,0.767,1) (0.7,0.967,1) (0.5,0.833,1) (0.5,0.833,1) s4 (0.5,0.767,1) (0.7,0.933,1) (0.9,1,1) (0.7,0.967,1) s5 (0.7,0.9,1) (0.5,0.767,1) (0.5,0.833,1) (0.5,0.767,1) chatterjee and stević/oper. res. eng. sci. theor. appl. 2 (1) (2019) 72-90 86 by multiplying the values shown in table 8 with the values of criteria which obtained by fahp method we get weighted normalized fuzzy decision matrix shown in table 8, while table 9 shows the final results and ranking of alternatives. table 8. weighted normalized fuzzy decision matrix criterion c1 c2 c3 s1 (0.033,0.034,0.047) (0.101,0.139,0.144) (0.017,0.017,0.024) s2 (0.033,0.035,0.047) (0.101,0.139,0.144) (0.017,0.017,0.019) s3 (0.033,0.036,0.047) (0.043,0.101,0.144) (0.017,0.02,0.034) s4 (0.036,0.047,0.065) (0.043,0.11,0.144) (0.017,0.019,0.024) s5 (0.036,0.052,0.109) (0.072,0.115,0.144) (0.034,0.056,0.169) c4 c5 c6 s1 (0.023,0.044,0.07) (0.026,0.054,0.077) (0.148,0.164,0.164) s2 (0.07,0.078,0.078) (0.026,0.054,0.077) (0.115,0.159,0.164) s3 (0.055,0.07,0.078) (0.077,0.085,0.085) (0.082,0.126,0.164) s4 (0.023,0.044,0.07) (0.077,0.085,0.085) (0.082,0.126,0.164) s5 (0.055,0.075,0.078) (0.043,0.065,0.085) (0.115,0.148,0.164) c7 c8 c9 s1 (0.059,0.081,0.084) (0.062,0.085,0.088) (0.055,0.076,0.079) s2 (0.042,0.064,0.084) (0.044,0.067,0.088) (0.04,0.066,0.079) s3 (0.059,0.081,0.084) (0.044,0.073,0.088) (0.04,0.066,0.079) s4 (0.059,0.078,0.084) (0.079,0.088,0.088) (0.055,0.076,0.079) s5 (0.042,0.064,0.084) (0.044,0.073,0.088) (0.04,0.061,0.079) table 9 contains the final results and ranking of alternatives. table 9. closeness coefficient of alternatives and their ranking di* di¯ di*+di¯ cci rank s1 0.166 0.551 0.717 0.768 1 s2 0.185 0.546 0.731 0.747 2 s3 0.218 0.531 0.749 0.709 4 s4 0.214 0.526 0.741 0.711 3 s5 0.33 0.465 0.795 0.585 5 5. sensitivity analysis the sensitivity analysis includes the experiment of 24 sets where the values of criteria are changed. the first nine sets mean increasing each criterion separately by 8% starting from the first one to the last. since there is no significant change in the ranking of suppliers the following nine sets are formed which include increasing the value of each criterion individually by 16%. the set number 19 includes reducing the three most relevant criteria (c2, c3 and c6) by 8%, while the other six criteria increase by 4%. the set number 20 represents an increase in the three most important criteria (c2, c3 and c6) by 8%, while the remaining criteria are reduced by 4%. next set number 21 analyses the increase of the three weakest criteria (c4, c7 and c9) by 8%, while the rest are reduced by 4%. the set number 22 means equal weighting of all the criteria, a two-phase model for supplier evaluation in manufacturing environment 87 while in the set number 23 the four most important criteria (c1, c2, c3 and c6) have equal values of 0.25, and the rest of the criteria are equal to zero or not taken into account. the last set number 24 analyses the change of the criteria in the following way: the first five criteria are equal to the value of 0.12, and the other four criteria are also identical in value of 0.1. figure 5. results of sensitivity analysis after the formation of sets and the analysis shown in figure 5, it is evident that the first supplier is ranked as the most acceptable solution in 18 out of a total of 24 cases, therefore, he holds the first position. in the first nine sets only the change of the fourth criterion affect the change of preferred supplier, and then the second supplier becomes number one. in the nine sets that follow the number one supplier is ranked first in seven cases. the change occurs with the increase in the fourth criterion when the second supplier takes one the first place, i.e. with the change of the fifth criterion when supplier number three is ranked first. set 19 also places third supplier as the first, because the values of the three most important criteria are reduced. supplier number one is the most appropriate solution also in the sets number 20, 22 and 23, while in set 21 the second supplier has the rank one with a slight difference in comparison to the first supplier, while in the final set number 24 the first and the second supplier are almost identical. it is important to note that the first supplier in those six cases where he is not the most appropriate solution still holds second position, which speaks volumes about the qualities of the same. even in the situation when all criteria are equally important with the same values, this supplier is the best solution. chatterjee and stević/oper. res. eng. sci. theor. appl. 2 (1) (2019) 72-90 88 6. conclusion this paper presents a two-phase model for evaluating suppliers in the manufacturing sector. since today production is highly dependent on our own capacities but also on the capacity of suppliers, the importance of resolving this problem is evident. when it comes to a concrete example entertained in this paper, it is necessary to take into account a large number of criteria that can influence the formation of the final price of the product, and consequently the position that the company holds in the market. it is necessary to make decisions taking into account the importance of the criteria, i.e. the priorities that reflect market demands and needs, which was achieved in this paper through the creation 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the evaluation of level crossings: case study in the republic of serbia dragan pamučar*, vesko lukovac, darko božanić, nenad komazec university of defence in belgrade, military academy, belgrade, serbia received: 14 october 2018 accepted: 07 december 2018 published: 19 december 2018 original scientific paper abstract: a level crossing, as a point of the crossing of road and rail traffic in the same level, is a place of conflicts subject to traffic accidents. in serbia, the selection of the level crossings to be secured is mostly done based on the media and society pressure, as a result of an increase of the number of accidents at level crossings. this paper presents the application of a group multi-criteria fucom-mairca (full consistency method – multi attributive ideal-real comparative analysis) model that supports the process of selecting a level crossing in terms of investing in its security equipment. the fucommairca multi-criteria model is tested in a case study which included the evaluation of ten level crossings within the railway infrastructure in the republic of serbia. the evaluation of the crossings is carried out through the assessment according to seven criteria set out on the basis of representative literature and surveys of experts. sensitivity test of the fucom-mairca model is performed by changing the weight coefficients of criteria and statistically processing the results using spearman’s rank correlation coefficient. key words: railway level crossings, fucom, mairca, multi-criteria decision making, railway accidents. 1. introduction a level crossing, as a point of the crossing of road and rail traffic in the same level, is a place of conflicts subject to traffic accidents (law on road traffic safety, 2018), which can have the consequences in terms of material damage and/or perished persons (pamučar et al., 2015). at the occurrence of traffic accident between the road and the rail vehicle, there is an exchange of collision forces that are extremely high due to large mass of the two vehicles. the contact during the accident is usually made between the front part of a train and the lateral part of a road vehicle, mailto:lukovacvesko@yahoo.com mailto:dbozanic@yahoo.com mailto:nkomazec@gmail.com multi-criteria fucom-mairca model for the evaluation of level crossings: case study in the republic of serbia 109 so that such traffic accidents often result in substantial material damage or severe injuries. it is estimated that as an average 1.312 lives are lost per day in traffic accident in the world (park, 2007). according to the report of the european railway agency, 27% of total number of deaths in the railroad accidents happens at level crossings (ćirović & pamučar, 2013). traffic accidents at level crossings are mostly the result of misconduct and careless behavior of participants in road traffic. in the previous year (2017) in serbia in 57 accidents, eight people are died that shows the significance of this problem. such statistics are not only in serbia, but the indicators are approximate in other countries, and this problem has been recognized by the international rail union. according to the eu statistics (european railway agency, 2011), the volume of rail transport will be doubled over the following 30 years, which is a direct indication of the expected increase of extraordinary events at level crossings on all railroads, including those in serbia. increasing traffic volume will increase also the need for raising the level of crossing insurance at road crossings. in this context, the need for investing funds in terms of road crossings safety will also be defined. the provision of road crossings with modern safety equipment is costly investment, so when making an investment decision, the responsibility of the management is high, because the approved funds have to provide adequate effect. in serbia, 77% of level crossings are not secured according to the law on traffic safety and applicable instructions of the serbian railways (pamučar et al., 2015). on the serbian railways network with a total length of 6,974 km there are 2354 level crossings, 108 of which are pedestrian crossings. out of this number, 588 crossings are secured with automatic or mechanical devices. securing level crossings represents significant material expenditure, so it is necessary to be grounded on reliable strategies for the selection of a level crossing that needs to be secured, as well as to be supported by the investments realization plan in terms of its security. in this paper is proposed the fucom-mairca multi-criteria model for the evaluation of level crossings and the creation of a strategy for the selection of priority level crossings that need to be secured. the criteria affecting the selection of the level crossing for the installation of necessary equipment to increase the security are defined. the survey of experts is conducted in the research in order to collect necessary data for determining relative weight criteria using the fucom model. the final evaluation and selection of priority crossings is carried out using the mairca model. through the research and development of the model in this paper several goals are presented: (1) review of the existing methodologies for the evaluation of level crossings; (2) improving the methodology for crossings evaluation and selecting priority crossings for the installation of security equipment through the development of original multi-criteria fucom-mairca model; (3) proposal of new methodology for the identification of high-risk crossings; (4) bridging the gap that currently exists in the methodology for evaluating and selecting priority crossings for the installation of safety equipment; and (5) popularizing and affirming new models of multi-criteria pamučar et al./oper. res. eng. sci. theor. appl. 1 (1) (2018) 108-129 110 decision making (fucom and mairca models) through their application in making complex decisions. the remaining sections of the paper are organized as follows. in the second part, a brief overview of the literature is presented and a review of similar research topics in which are applied the models for the selection and evaluation of crossings. in the third part, the models used are briefly presented and the fucom-mairca algorithm is shown. the fourth part presents a case study in which is carried out the evaluation of ten railway crossings within the railway infrastructure in the republic of serbia. the fifth part includes the sensitivity analysis in terms of testing the stability of the results by changing the weight coefficients of criteria in the fucommairca model. the sixth part presents key contributions of the developed model, as well as suggestions for future research. 2. literature review the first mathematical models for the evaluation and ranking of crossings were developed in the mid 20th century (berg, 1966). berg (1966) presented the model for the evaluation and ranking of level crossings on the basis of a statistical model for predicting the number of traffic accidents. later qureshi et al. (2003) improved the statistical model shown by berg (1966) through the application of data mining. in addition to the above mentioned models, in many countries of the world the evaluation of crossings is performed using quantified risk analysis (qra). qra provides a suitable basis for establishing level crossing improvement priorities. this it does by allowing a ranking of level crossings in terms of their accident risk probability. those crossings with high accident probabilities would normally qualify for funding allocations, while those with low accident probabilities would be assigned a low priority for improvement funding. the oregon state highway department completed a study concerned with measuring the relative hazards of railroad grade crossings located on state and federal-aid highway systems (tey et al., 2009). the majority of the 400 grade crossings considered were located in incorporated areas. application of qra can be see in papers of many authors (reiff et al., 2003; tey et al., 2009; anandarao & martland, 1998; woods et al., 2008). the armour research foundation has conducted two grade crossing accident studies for the association of american railroads results of an analysis of 2.291 grade crossings in the state of iowa were reported in 1958 (crecink, 1958). regression analysis techniques were utilized to develop risk factors (the expected accident rates at grade crossings over a 16year period) as a function of type of protection, highway traffic volume, number of tracks, and a measure of visibility. however, the regression model lacked consistency with accepted a priori assumptions concerning the relationships between the study variables. the second study performed by the armour research foundation was an investigation of the relationships between accidents and nine grade crossing characteristics at 7.416 locations in the state of ohio (crecink, 1958). a regression analysis routine was used to develop models predicting a ten-year expected accident rate. equations were developed for four separate types of protection: painted crossbucks, reflectorized crossbucks, flashers, and gates. multi-criteria fucom-mairca model for the evaluation of level crossings: case study in the republic of serbia 111 in addition to the above mentioned models, there are also numerous models used by different states in the usa to prioritize rail-highway level crossings (elzohairy & benekohal, 2000): (1) the department of transportation accident prediction formula (usdot accident prediction model), (2) california s hazard rating formula, (3) connecticut s hazard rating formula, that is very similar to that of california, (4) kansas's design hazard rating formula, (5) the missouri crossing improvement program currently uses a calculated exposure index (missouri s exposure index formula) to prioritize crossings for possible improvements, (6) nois s modified expected accident frequency formula used to rank grade crossings (elzohairy & benekohal, 2000). as compare to conventional cost-benefit approach, multicriteria analysis allows effective comparative evaluation among options and stakeholders over a common set of evaluation objectives. furthermore, multi-criteria analysis could overcome the limitation of cost-benefit analysis whereby all the costs and benefits have to be expressed in monetary terms (ćirović & pamučar, 2013). ford and matthews (2002) and roop et al. (2005) adoped multi-criteria analysis technique to assess the relative merits of the candidate protection systems and evoluation of railway level crossings. in addition to classic multi-criteria techniques, ćirović & pamučar (2013) presented the modeling of the neuro-fuzzy system for the prioritizing of crossings. the study showed successful use of adaptive artificial intelligence models for predicting risks at the crossings. therefore, the managers of railway companies and agencies involved in improving road safety should try to answer several questions, such as how to prioritize level crossings and how to build a strategy of investing in the improvement of their security. in such cases, multi-criteria decision making models offer practical solutions. however, the design of multi-criteria framework for the evaluation of level crossings is a complex process that is still being developed to improve the area under consideration in this paper (roop et al., 2005). accordingly, in order to face the above challenges, it is necessary to develop a model for the evaluation and ranking of crossings. it is precisely this purpose that the goal of this study results from, and that is to provide a comprehensive model for making sustainable investment strategy in improving the security of crossings using multi-criteria models. in order to achieve this goal, the main research question of this study is how to form a decision-making model in which key risk indicators on the crossings are implemented and which allows determining priority of crossings while creating sustainable strategy for investing in security equipment? in order to solve this problem, this study suggests the evaluation of crossings using the fucom and mairca models. the implementation of multi-criteria approach in the models for evaluating crossings has been very limited so far. more precisely, there are no studies that consider the integration of the fucom and mairca models, not only in the field of evaluation of crossings, but neither in literature in the field of multi-criteria decision making (mcdm). the fucom-mairca model is new comprehensive multi-criteria model that can be very successfully applied in other studies that are not covered by this paper. pamučar et al./oper. res. eng. sci. theor. appl. 1 (1) (2018) 108-129 112 3. methodological presentation of the fucom and mairca models the fucom-mairca model is implemented through two phases. in the first phase, through the application of the fucom model the expert evaluation of criteria is carried out and determining of weight coefficients of criteria. the obtained values of the weight coefficients are further used in the second phase of the model for determining the values of theoretical assessments of the mairca model. in the following sections (sections 3.1 and 3.2), the steps of the fucom and mairca model are presented in detail. 3.1. full consistency method (fucom) the fucom (pamučar et al, 2018a) belongs to new models for subjective determining of weights of criteria in multi-criteria decision making. the fucom is a tool that helps managers deal with their own subjectivity in prioritizing criteria through simple algorithm and using a scale acceptable for them. some advantages that make the authors opt for the fucom are the following: (1) fucom allows obtaining optimal weight coefficients with the ability to validate them by consistency of the results; (2) applying fucom, the optimal values of weight coefficients are obtained with simple mathematical apparatus that allows favoring certain criteria in evaluating phenomena in accordance with current requirements of decision-makers and minimizing the risks in decision-making; (3) fucom provides optimal values of weight coefficients with minimal subjective influence and minimal impact of inconsistencies of expert preferences on the final values of the weights of criteria; (4) only the n-1 comparison of criteria is required; (5) the model is flexible and suitable for application to different measurement scales representing expert preferences. in the next section is presented the fucom algorithm including the following steps: step 1. in the first step, the criteria from the predefined set of the evaluation criteria  1 2 nc c , c ,..., c are ranked. the ranking is performed according to the significance of the criteria, i.e. starting from the criterion which is expected to have the highest weight coefficient to the criterion of the least significance. thus, the criteria ranked according to the expected values of the weight coefficients are obtained: j(1) j(2) j(k) c c ... c   (1) where k represents the rank of the observed criterion. if there is a judgment of the existence of two or more criteria with the same significance, the sign of equality is placed instead of “>” between these criteria in the expression (1) step 2. in the second step, a comparison of the ranked criteria is carried out and the comparative priority ( k / (k 1)   , k 1, 2,..., n , where k represents the rank of the criteria) of the evaluation criteria is determined. the comparative priority of the evaluation criteria ( k / (k 1)   ) is an advantage of the criterion of the j( k ) c rank compared to the criterion of the j(k 1) c  rank. thus, the vectors of the comparative priorities of the evaluation criteria are obtained, as in the expression (2)  1/ 2 2 / 3 k / ( k 1), ,...,     (2) multi-criteria fucom-mairca model for the evaluation of level crossings: case study in the republic of serbia 113 where k / (k 1)   represents the significance (priority) that the criterion of the j( k ) c rank has compared to the criterion of the j(k 1) c  rank. the comparative priority of the criteria is defined in one of the two ways defined in the following part: a) pursuant to their preferences, decision-makers define the comparative priority k / (k 1)   among the observed criteria. thus, for example, if two stones a and b, which, respectively, have the weights of a w 300 grams and b w 255 grams are observed, the comparative priority ( a / b  ) of stone a in relation to stone b is a/ b 300 / 255 1.18   . also, if the weights a and b cannot be determined precisely, but a predefined scale is used, e.g. from 1 to 9, then it can be said that stones a and b have weights a w 8 and b w 7 . respectively. then the comparative priority ( a / b  ) of stone a in relation to stone b can be determined as a/ b 8 / 7 1.14   . this means that stone a in relation to stone b has a greater priority (weight) by 1.18 (in the case of precise measurements), i.e. by 1.14 (in the case of application of measuring scale). in the same manner, decision-makers define the comparative priority among the observed criteria k / (k 1)   . when solving real problems, decision-makers compare the ranked criteria based on internal knowledge, so they determine the comparative priority k / (k 1)   based on subjective preferences. if the decision-maker thinks that the criterion of the j( k ) c rank has the same significance as the criterion of the j(k 1) c  rank, then the comparative priority is k / (k 1) 1   . b) based on a predefined scale for the comparison of criteria, decision-makers compare the criteria and thus determine the significance of each individual criterion in the expression (1). the comparison is made with respect to the first-ranked (the most significant) criterion. thus, the significance of the criteria ( j( k )c  ) for all of the criteria ranked in step 1 is obtained. since the first-ranked criterion is compared with itself (its significance is j(1)c 1  ), a conclusion can be drawn that the n-1 comparison of the criteria should be performed. as we can see from the example shown in step 2b, the fucom model allows the pairwise comparison of the criteria by means of using integer, decimal values or the values from the predefined scale for the pairwise comparison of the criteria. step 3. in the third step, the final values of the weight coefficients of the evaluation criteria   t 1 2 n w , w ,..., w are calculated. the final values of the weight coefficients should satisfy the two conditions: a) that the ratio of the weight coefficients is equal to the comparative priority among the observed criteria ( k / (k 1)   ) defined in step 2, i.e. that the following condition is met: k k / ( k 1) k 1 w w     (3) pamučar et al./oper. res. eng. sci. theor. appl. 1 (1) (2018) 108-129 114 b) in addition to the condition (3), the final values of the weight coefficients should satisfy the condition of mathematical transitivity, i.e. that k / (k 1) (k 1)/ (k 2) k / (k 2)          . since k k / ( k 1) k 1 w w     and k 1 ( k 1) / ( k 2) k 2 w w       , that k k 1 k k 1 k 2 k 2 w w w w w w       is obtained. thus, yet another condition that the final values of the weight coefficients of the evaluation criteria need to meet is obtained, namely: k k / ( k 1) ( k 1) / ( k 2) k 2 w w         (4) full consistency i.e. minimum dfc (  ) is satisfied only if transitivity is fully respected, i.e. when the conditions of k k / ( k 1) k 1 w w     and k k / ( k 1) ( k 1) / ( k 2) k 2 w w         are met. in that way, the requirement for maximum consistency is fulfilled, i.e. dfc is 0  for the obtained values of the weight coefficients. in order for the conditions to be met, it is necessary that the values of the weight coefficients   t 1 2 n w , w ,..., w meet the condition of k k / (k 1) k 1 w w       and k k / (k 1) (k 1) / (k 2) k 2 w w           , with the minimization of the value  . in that manner the requirement for maximum consistency is satisfied. based on the defined settings, the final model for determining the final values of the weight coefficients of the evaluation criteria can be defined. j( k ) k / ( k 1) j( k 1) j( k ) k / ( k 1) ( k 1) / ( k 2) j( k 2) n j j 1 j min s.t. w , j w w , j w w 1, j w 0, j                          (5) by solving the model (5), the final values of the evaluation criteria   t 1 2 n w , w ,..., w and the degree of dfc (  ) are generated. in order to achieve a better understanding of the presented model, two simple examples will demonstrate the process of determining weight coefficients by applying fucom. in the first example, the procedure for determining the comparative priority ( k / (k 1)   ) is shown by applying step 2a, whereas in the second example, k / (k 1)   is determined by applying step 2b. multi-criteria fucom-mairca model for the evaluation of level crossings: case study in the republic of serbia 115 3.2. multi-attributive ideal-real comparative analysis (mairca) the basic mairca set-up is to define the gap between ideal and empirical ratings (gigović et al., 2016; pamučar et al., 2017, 2018b; chatterjee et al., 2018). summing up the gap by each criterion generates the total gap for each alternative observed. ranking the alternatives comes at the end of the process, where the bestranked alternative is the one with the lowest gap value. the alternative with the lowest total gap value is the alternative, by most of the criteria, with the values closest to the ideal ratings (the ideal criteria values). the mairca method is carried out in seven steps: step 1. formulation of the initial decision-making matrix ( x ). the initial decision-making matrix (6) determines the criteria values ( ij x , i 1, 2,...n; j 1, 2,...m  ) for each alternative observed. 1 2 n 1 11 12 1n 2 21 22 2n m m1 22 mn c c ... c a x x ... x a x x x x ... ... ... ... ... a x x ... x             (6) the criteria from the matrix (6) can be quantitative (measurable) and qualitative (descriptive). the quantitative criteria values in the matrix (6) are obtained by quantification of real indicators which present the criteria. the qualitative criteria values are determined by decision-maker’s preferences or, in a case of a large number of experts, by aggregating the experts’ opinions. step 2. defining preferences for the choice of alternatives ia p . while selecting the alternatives, the decision maker (dm) is neutral, meaning there’s no preference for any of the offered alternatives. the assumption is that the dm does not take into account the probability of choosing any particular alternative, and has no preference in the alternative selection process. the dm can then view the alternatives as if each can materialize with the same probability, and the preference for any of the m possible alternatives is i i m a a i 1 1 p ; p 1, i 1, 2,..., m m     (7) where m is the total number of the alternatives being selected. in a decision-making analysis with a priori probabilities we proceed from the point that the dm is neutral to selection probability of each alternative. in that case, all preferences for the selection of individual alternatives are equal, i.e. 1 2 ma a a p p ... p   (8) where m is the total number of the alternatives being selected. step 3. calculation of the elements of the theoretical ratings matrix ( p t ). pamučar et al./oper. res. eng. sci. theor. appl. 1 (1) (2018) 108-129 116 the format of the matrix ( p t ) is n x m (where n is the total number of criteria, m is the total number of alternatives). the elements of the theoretical ratings matrix ( pij t ) are calculated as a product of preferences for the selection of alternatives ia p and criterion weights ( i w , i 1, 2,..., n ) 1 1 1 1 1 2 2 2 2 2 m m m m 1 2 n1 2 n a a a 1 a 2 a np11 p12 p1n a a a 1 a 2 a np 21 p 22 p 2n p pm1 pm 2 pmna a a 1 a 2 w w ... ww w ... w p p p w p w ... p wt t ... t p p p w p w p wt t t t ... ... ... ...... ... ... ... ... ... t t ... tp p p w p w ... p               ma n w               (9) since the dm is neutral towards the initial alternative selection, the preferences ( ia p ) are the same for all alternatives. as the preferences ( ia p ) are the same for all the alternatives, we can also present the matrix (9) in the format n x 1 (where n is the total number of criteria). i i i i i 1 2 n1 2 n p a p1 p2 pn a a 1 a 2 a n w w ... ww w ... w t p t t ... t p p w p w ... p w       (10) where n is the total number of criteria, and pi t theoretical rating. step 4. definition of the elements of real ratings matrix ( r t ). 1 2 n 1 r11 r12 r1n 2 r 21 r 22 r 2n r m rm1 rm 2 rmn c c ... c a t t ... t a t t t t ... ... ... ... ... a t t ... t             (11) where n represents the total number of criteria, and m the total number of alternatives. in calculation of the elements of the real ratings matrix ( r t ) the elements of the theoretical ratings matrix ( p t ) are multiplied by the elements of the initial decision-making matrix ( x ) using the following formulas: for the benefit type criteria (preferred higher criteria value) ij i rij pij i i x x t t x x            (12) for the cost type criteria (preferred lower criteria value) ij i rij pij i i x x t t x x            (13) multi-criteria fucom-mairca model for the evaluation of level crossings: case study in the republic of serbia 117 where ij x , i x  and i x  represent the elements of the initial decision-making matrix ( x ), and i x  i i x  are defined as:  i 1 2 mx max x , x ,..., x   , representing the maximum values of the observed criterion by alternatives.  i 1 2 mx min x , x ,..., x   , representing the minimum values of the observed criterion by alternatives. step 5. the calculation of the total gap matrix ( g ). the elements of the g matrix are obtained as a difference (gap) between the theoretical ( pij t ) and real ratings ( rij t ), i.e. , a difference between the theoretical ratings matrix ( p t ) and the real ratings matrix ( r t ) p11 r11 p12 r12 p1n r1n11 12 1n p 21 r 21 p 22 r 22 p 2n r 2n21 22 2n p r pm1 rm1 pm 2 rm 2 pmn rmnm1 m 2 mn t t t t ... t tg g ... g t t t t ... t tg g ... g g t t ... ... ... ...... ... ... ... t t t t ... t tg g ... g                               (14) where n represents the total number of criteria, m is the total number of the alternatives being selected. the gap ij g takes the values from the interval  ijg 0,  , by the equation (15) ij pij rij g t t  (15) the preferable option is that ij g gravitates towards zero ( ij g 0 ), since we are choosing the alterative with the smallest difference between theoretical ratings ( pij t ) and real ratings ( rij t ). if for the criterion i c the alternative i a has the theoretical rating value equal to the real rating value ( pij rij t t ), the gap for the alternative i a , by the criterion i c , is ij g 0 . in other words, by the criterion i c , the alternative i a is the best (ideal) alternative ( i a  ). if by the criterion i c the alternative i a has the value of theoretical ratings pij t , and the value of real ratings rij t 0 , the gap for the alternative i a , by the criterion i c , is ij pij g t . in other words, the alternative i a is the worst (anti-ideal) alternative ( i a  ) by the criterion i c . step 6. the calculation of the final values of criteria functions ( i q ) by alternatives. the values of criteria functions are obtained by summing the gap ( ij g ) by alternatives, that is, by summing the elements of matrix ( g ) by columns, eqn. (16) pamučar et al./oper. res. eng. sci. theor. appl. 1 (1) (2018) 108-129 118 n i ij j 1 q g , i 1, 2,..., m    (16) where n is the total number of criteria, and m is the total number of the alternatives being selected. step 7. defining the dominance index  d,1 ja  of the best-ranked alternative and final rank of alternatives. the dominance index of the best-ranked alternative defines its advantage in relation to the other alternatives, and determined here by applying eqn. (17). j 1 d,1 j n q q a , j 2, 3,.., m q     (17) where 1 q denotes the criterion function of the best-ranked alternative, n q denotes the criterion function of the last ranked alternative, j q denotes the criterion function of the alternative which is compared to the best-ranked alternative, and m denotes the number of alternatives. once the dominance index is determined, the dominance threshold d i is determined by applying eqn.(18) d 2 m 1 i m   (18) where m denotes the number of alternatives. provided that the dominance index d,1 j a  is greater or equal to dominance threshold d i ( d,1 j d a i   ), the obtained rank will be retained. however, if the dominance index d,1 j a  is smaller than the dominance threshold d i ( d,1 j d a i   ), then it cannot be said with certainty that the first ranked alternatives have an advantage over the alternative being analyzed. the said restrictions can be shown by applying the following eqn. (19) d,1 j d final, j initial, j final, j d,1 j d final, j initial,1 a i r r r a i r r           (19) where initial, j r and final, j r denotes the initial and final rank of the alternative, respectively, that is compared with the best-ranked alternative, d i denotes the dominance threshold, and d,1 j a  denotes the dominance index of the best-ranked alternative in relation to the alternative. provided that criterion d,1 j d a i   is satisfied, then the rank of the alternative that is compared to the best-ranked alternative will be corrected and then treated as the best-ranked alternative and assigned the value "1*". in this way it is emphasized that the best-ranked alternative is characterized by a smaller advantage than the one specified in eqn. (18). multi-criteria fucom-mairca model for the evaluation of level crossings: case study in the republic of serbia 119 assume, for example, that the best-ranked alternative is compared to the second-ranked alternative and that the criterion d,1 2 d a i   is satisfied. then the second-ranked alternative will be assigned rank "1*". the comparison may proceed with the third-ranked alternative. if for the third-ranked alternative criterion d,1 3 d a i   is satisfied, then the third-ranked alternative will be assigned rank "1**" and so on, until reaching the last alternative. finally, correction of the initial ranks ( initial r ) is carried out for all alternatives satisfying criterion d,1 j d a i   , while the ranks of alternatives satisfying the criterion d,1 j d a i   remain unchanged. therefore, the final rank of alternatives ( final r ) which is presented simultaneously with the initial rank of alternatives ( initial r ) is obtained. 4. application of the fucom-mairca model the most important task of the safety management in road and rail traffic is to raise safety level of traffic at level crossings (jankovic & mladenovic, 2011). in order to identify the crossings which requires the intervention, either in terms of changes in safety method, or in terms of reconstruction and maintenance of road and railway infrastructure, it is necessary to dispose of various data which can be classified in three categories (jankovic et al., 2014): (1) data on current condition of the level crossings: location of the crossing from the aspect of railway (station area or open rail) and from the aspect of road (main, regional or local), existing safety system on the level crossing, existing road and railway signalization condition in the level crossing area, type and condition of road surface at the crossing, barriers and drainage systems in the crossing area, geometric parameters of the crossing, sight triangle and distance visibility, (non) existence of opportunities for level separation, prescribed speed of trains and road vehicles in the crossings area; (2) data on traffic accidents at crossings for a selected period: total number of accidents, structure of accidents by consequences, total number of minor, serious injuries and killed persons, total material damage and (3) data on volume and structure of road and rail traffic at crossings. on the basis of the recommendations from the literature (jankovic & mladenovic, 2011; ćirović & pamučar, 2013; jankovic et al., 2014), as well as the empirical knowledge of four experts collected through the survey, the criteria for the evaluation of level crossings are defined and shown in the table 1. pamučar et al./oper. res. eng. sci. theor. appl. 1 (1) (2018) 108-129 120 table 1. criteria for the evaluation of level crossings criterion brief description frequency of rail traffic at the observed level crossing (c1) max a parameter with a major impact on the probability of occurrence of extraordinary events at road crossings. traffic volume and frequency are influenced by trains in internal traffic, as the needs of certain regional or other centers at the part of the railway. the number of truck/month road traffic frequency at the observed level crossing (c2) max this factor is particularly significant in urban areas where the railway line divides city zones, where road traffic is loaded with more vehicles and pedestrians and where, due to poor technical possibilities of railway traffic equipment, waiting time for passing of a train is larger than usual (even up to 10 minutes). in urban zones, there are crossings where the road crosses several tracks. this increases the likelihood of occurrence of extraordinary events at the crossings. the number of vehicles/h number of tracks at the observed level crossing (c3) max the number of tracks directly affects the time that road users spend on the railroad. with the increase of the number of tracks, the time from the moment of moving of the vehicle from the stop line from one side of the crossing to the pass of the rear part of the vehicle out of the rail profile at the given crossing also increases. the number of tracks at road crossings maximum permitted speed of trains at the level crossing chainage (c4) max a parameter that is particularly significant for crossings that are only secured by road signs. this parameter is indirectly related to the visibility of the crossing for road vehicle drivers or pedestrians. maximum permitted speed of trains at road section angle of crossing of road and rail (c5) max the optimum angle of crossing of rail and road at the crossing is 90 degrees. however, the construction possibilities, the terrain configuration, the position of the existing roads and other circumstances make the road and rail crossing angle in practice range from 30 to 175 degrees. angle of crossing of road and rail number of extraordinary events at the observed level crossing (c6) max extraordinary events are followed by great material damage, killed and severely injured persons. number of extraordinary events at level crossing sight of the observed crossing from the aspect of road traffic (c7) min sight at a given road crossing is a parameter that has an impact on the decision of a road vehicle driver to start driving over the crossing in cases where the crossing is not secured by active protection devices (semi-barriers or barriers). sight of the crossing means that when a driver stops his vehicle on the stop line, he can observe the traffic situation. the qualitative criterion that evaluating using linguistic scale 1 9 multi-criteria fucom-mairca model for the evaluation of level crossings: case study in the republic of serbia 121 as defined in the previous section, the first phase of the model implies the application of the fucom to determine weight coefficients of criteria. step 1. in the first step, the criteria are ranged from the defined set of criteria, which is shown in the table 1. ranking of the criteria according to its significance is carried out by four experts. table 2. rank of criteria expert rank e1 c2>c5>c7>c1>c6>c3>c4 e2 c2>c5>c7>c1=c6>c3>c4 e3 c2>c5>c7>c1>c6>c4>c3 e4 c2>c7>c5>c1=c6>c3>c4 step 2. in the second step, comparison of the ranked criteria is done and comparative significance of the evaluation criteria is determined. comparative significance of the evaluation criteria is obtained by the survey of experts and it is shown in the table 3. table 3. comparative significance of criteria expert comparative significance ( k / (k 1)  ) e1 c2 c5 c7 c1 c6 c3 c4 1 1.28 1.10 1.18 1.05 1.10 1.38 e2 c2 c5 c7 c1 c6 c3 c4 1 1.31 1.08 1.15 1.00 1.15 1.25 e3 c2 c5 c7 c1 c6 c4 c3 1 1.22 1.13 1.20 1.03 1.15 1.20 e4 c2 c7 c5 c1 c6 c3 c4 1 1.18 1.12 1.17 1.00 1.17 1.30 step 3. in this step, the final values of the weight coefficients of the evaluation criteria are calculated   t 1 2 7 w , w ,..., w forming the model (5). by applying both the expressions (3) and (4) and the data from the table 3, it is formed special model for determining the weight coefficients of the criteria for every expert: pamučar et al./oper. res. eng. sci. theor. appl. 1 (1) (2018) 108-129 122 5 72 5 7 1 6 31 6 3 4 5 72 7 1 6 61 3 4 7 j j j 1 expert 1 min w ww 1.28 , 1.10 , 1.18 , w w w w ww 1.05 , 1.10 , 1.38 , w w w w ww s.t. 1.408 , 1.298 , 1.239 , w w w ww 1.155 , 1.518 , w w w 1, w 0, j expe                                                        7 52 7 5 1 6 31 6 3 4 7 52 5 1 6 61 3 4 7 j j j 1 rt 4 min w ww 1.18 , 1.12 , 1.17 , w w w w ww 1.00 , 1.17 , 1.30 , w w w w ww s.t. 1.322 , 1.310 , 1.17 , w w w ww 1.17 , 1.521 , w w w 1, w 0, j                                                        by solving the presented models in the lingo 17.0 software, we obtain the weight coefficients of the criteria for every expert, as shown in table 4. table 4. weight coefficients of criteria expert w1 w2 w3 w4 w5 w6 w7 dfc (  ) e1 0.1318 0.2190 0.1141 0.0827 0.1711 0.1256 0.1556 0.0000 e2 0.1319 0.2145 0.1147 0.0917 0.1638 0.1319 0.1516 0.0000 e3 0.1294 0.2140 0.0910 0.1093 0.1754 0.1256 0.1553 0.0002 e4 0.1327 0.2051 0.1134 0.0872 0.1552 0.1326 0.1738 0.0002 average 0.1314 0.2132 0.1083 0.0927 0.1664 0.1289 0.1591 from the table 4, it can be observed that the fucom provides fully consistent values of weight coefficients, since for every of the four models dfc≈0. final values of the weight coefficients are obtained by averaging the weights obtained from every of the four models shown. after calculating the weight coefficients of the criteria ( i w ), the evaluation of the crossings is carried out using the mairca method. in the table 5 are shown the characteristics of ten level crossings (alternatives). the evaluation of the qualitative criteria c7 is made based on the assessments of the observed level crossing changing through the nine-degree scale. multi-criteria fucom-mairca model for the evaluation of level crossings: case study in the republic of serbia 123 table 5. evaluation of level crossings alternative c1 c2 c3 c4 c5 c6 c7 a1 61 226 3 65 70 7 2 a2 91 33 2 60 88 4 8 a3 36 235 3 55 68 5 3 a4 99 122 2 80 62 3 2 a5 74 181 2 55 45 2 9 a6 86 33 3 55 78 6 6 a7 55 155 3 80 63 7 9 a8 111 128 4 75 60 3 7 a9 52 76 4 85 45 5 5 a10 77 123 2 50 85 5 3 after forming the initial decision matrix, as in the table 5, the preferences are made according to the selection of the alternatives ia p . since during the evaluation of the level crossing, experts do not have clear preference for selecting certain alternatives, then ia p is determined by applying the expression (7) ia 1 1 p 0.10 m 10    in this case, all preferences for the selection of certain alternatives are the same (8) 1 2 10a a a p p ... p 0.10    the calculation of the elements of the matrix of theoretical assessments ( p t ), from the table 6, is performed using the expression (9), respectively (10). matrix elements are calculated by multiplying the preferences of selected alternatives ia p and the weight coefficients of criteria ( i w ). table 6. matrix of theoretical weights p t alternative c1 c2 c3 c4 c5 c6 c7 a1 0.0131 0.0213 0.0108 0.0093 0.0166 0.0129 0.0159 a2 0.0131 0.0213 0.0108 0.0093 0.0166 0.0129 0.0159 a3 0.0131 0.0213 0.0108 0.0093 0.0166 0.0129 0.0159 a4 0.0131 0.0213 0.0108 0.0093 0.0166 0.0129 0.0159 a5 0.0131 0.0213 0.0108 0.0093 0.0166 0.0129 0.0159 a6 0.0131 0.0213 0.0108 0.0093 0.0166 0.0129 0.0159 a7 0.0131 0.0213 0.0108 0.0093 0.0166 0.0129 0.0159 a8 0.0131 0.0213 0.0108 0.0093 0.0166 0.0129 0.0159 a9 0.0131 0.0213 0.0108 0.0093 0.0166 0.0129 0.0159 a10 0.0131 0.0213 0.0108 0.0093 0.0166 0.0129 0.0159 pamučar et al./oper. res. eng. sci. theor. appl. 1 (1) (2018) 108-129 124 after forming the matrix of theoretical assessments ( p t ), it is calculated the matrix of real assessments ( r t ). the calculation of the real assessment matrix elements (table 7) is carried out by multiplying the elements of the matrix of theoretical assessment ( p t ) and normalized elements of the initial decision making matrix. normalization of elements of the initial decision making matrix is performed using the expressions (12) and (13). table 7. matrix of real assessments alternative c1 c2 c3 c4 c5 c6 c7 a1 0.0044 0.0204 0.0054 0.0041 0.0104 0.0129 0.0159 a2 0.0096 0.0000 0.0000 0.0022 0.0166 0.0052 0.0023 a3 0.0000 0.0213 0.0054 0.0011 0.0077 0.0077 0.0136 a4 0.0110 0.0094 0.0000 0.0082 0.0063 0.0026 0.0159 a5 0.0067 0.0156 0.0000 0.0014 0.0002 0.0000 0.0000 a6 0.0088 0.0000 0.0054 0.0008 0.0147 0.0103 0.0068 a7 0.0033 0.0129 0.0054 0.0079 0.0104 0.0129 0.0000 a8 0.0131 0.0100 0.0108 0.0065 0.0039 0.0026 0.0045 a9 0.0028 0.0045 0.0108 0.0093 0.0000 0.0077 0.0091 a10 0.0072 0.0095 0.0000 0.0000 0.0159 0.0077 0.0136 the elements of the total gap matrix ( g ) are obtained as the difference (gap) between theoretical ( pij t ) and real assessments ( rij t ), respectively, by subtracting the elements of the matrix of theoretical assessments ( p t ) and the elements of the real assessment matrix ( r t ). by applying the expression (14) we obtain final total gap matrix, as shown in the table 8. it is desirable that the value ij g tends to zero ( ij g 0 ), since we select the alternative with the slightest difference between theoretical ( pij t ) and real assessments ( rij t ). table 8. total gap matrix alternative c1 c2 c3 c4 c5 c6 c7 a1 0.0088 0.0009 0.0054 0.0052 0.0063 0.0000 0.0000 a2 0.0035 0.0213 0.0108 0.0071 0.0000 0.0077 0.0136 a3 0.0131 0.0000 0.0054 0.0082 0.0089 0.0052 0.0023 a4 0.0021 0.0119 0.0108 0.0011 0.0104 0.0103 0.0000 a5 0.0065 0.0057 0.0108 0.0079 0.0164 0.0129 0.0159 a6 0.0044 0.0213 0.0054 0.0085 0.0019 0.0026 0.0091 a7 0.0098 0.0084 0.0054 0.0014 0.0063 0.0000 0.0159 a8 0.0000 0.0113 0.0000 0.0027 0.0128 0.0103 0.0114 a9 0.0103 0.0168 0.0000 0.0000 0.0166 0.0052 0.0068 a10 0.0060 0.0118 0.0108 0.0093 0.0007 0.0052 0.0023 the values of the criteria functions ( i q ) by alternatives (table 9) are obtained by summing the gap ( ij g ) by alternatives, as in the expression (16). multi-criteria fucom-mairca model for the evaluation of level crossings: case study in the republic of serbia 125 table 9. ranking alternatives according to the mairca method alternative q initialr finalr a1 0.0266 1 1 a2 0.0641 9 9 a3 0.0431 2 2 a4 0.0466 4 4 a5 0.0761 10 10 a6 0.0532 7 7 a7 0.0472 5 5 a8 0.0485 6 6 a9 0.0557 8 8 a10 0.0460 3 3 a1>a3>a10>a4>a7>a8>a6>a9>a2>a5 based on the obtained values of the criteria functions ( i q ) is determined the initial rank of alternatives ( initial r ). according to the initial ranking, the best-ranked alternative is the alternative a1. in order to conclude whether the a1 is also the best alternative, it is necessary to determine if it sufficiently dominates over the other alternatives. it is therefore necessary to determine the index of domination of the alternative a1 ( d,a1 j a  ) over the other alternatives, as in the expression (17). before determining the index of domination d,a1 j a  , using the expression (16), the dominance threshold d i is to be defined which must be met by the alternative a1 so as to be ranked as the first one in final ranking. d 2 2 n 1 10 1 i 0.090 n 10      since the condition d,1 j d a i   is fulfilled for all the alternatives, we can conclude that all initial ranks of the alternatives are retained, respectively, that initial final r r , as shown in the table 9. on the basis of the obtained results, we conclude that the a1 alternative is first-ranked, respectively, a1> a3> a10> a4> a7> a8> a6> a9> a2> a5. 5. sensitivity analysis and validation of results the results of the multi-criteria models can significantly be influenced by the values of weight coefficients of the evaluation criteria. that is why the analysis of the influence of altering weight coefficients on the results of the research is a logical step to test the robustness of the applied model and the obtained results. therefore, in this part of the paper is carried out the sensitivity analysis of the ranks of alternatives to changes in weight coefficients of the criteria. the sensitivity analysis is performed through seven situations. in every situation, one criterion is favorized whose weight coefficient is increased by 50 %. in the same situation, the weight coefficients are pamučar et al./oper. res. eng. sci. theor. appl. 1 (1) (2018) 108-129 126 reduced by 50 % in the remaining criteria. changes in the ranks of alternatives in seven situations are shown in the figure 1. 0 2 4 6 8 10 s1 s2 s3 s4 s5 s6 s7 sensitivity anaysis a1 a2 a3 a4 a5 a6 a7 a8 a9 a10 figure 1. sensitivity analysis of the ranks of alternatives through seven situations the results (figure 1) show that assigning different weights of criteria through situations leads to minor variations in the ranking of alternatives, which confirms that the model is sensitive to changes in weight coefficients. by comparing the firstranked alternatives (a1 and a3), we note that the alternative a1 retains its rank in all situations (it remained the first-ranked), while the alternative a3 in five situations keeps its ranking, and in two situations it is third-ranked. during sensitivity analysis there was a change of ranks of the alternatives a2, a9 and a6. however, we can conclude that these changes were not drastic, as evidenced by high rank correlation through situations (figure 2). the correlation was determined using spearman’s coefficient of correlation (chatterjee et al, 2018). 0.960 0.965 0.970 0.975 0.980 0.985 0.990 0.995 1.000 s1 s2 s3 s4s5 s6 s7 figure 2. correlation of ranks through seven situations of sensitivity analysis multi-criteria fucom-mairca model for the evaluation of level crossings: case study in the republic of serbia 127 the values of spearman’s coefficient of correlation were obtained by comparing the initial rank of the fucommairca model (table 9) with the ranks obtained through the situations (figure 1). in the figure 2, we note that there is extremely high correlation of ranks, since in all situations the value of the correlation coefficient is higher than 0.970. mean value of the correlation coefficient through all the situations amounts to 0.990, which shows extremely high correlation. since all values of the correlation coefficient are significantly greater than 0.90, we can conclude that there is a very high correlation (closeness) of ranks and that the proposed ranking is confirmed and credible. 6. conclusion in this research is presented the use of multi-criteria fucom-mairca model for evaluating level crossings. the key contribution of this paper is new fucommairca model for the evaluation of crossings. presented model allows consideration of subjectivity in the process of group decision making through linguistic evaluation of the evaluation criteria. in addition, the model presented in this paper introduces new methodological principles for the evaluation of the crossings, which at the same time contributes to the improvement of theoretical basis of multi-criteria decision making in general. the developed approach allows bridging the gap that currently exists in the methodology for evaluating the crossings. the fucom-mairca model was applied in the evaluation of ten level crossings on the territory of the republic of serbia. the results obtained were verified through sensitivity analysis carried out based on seven situations. the stability of the model is verified through statistical correlation coefficient showing high correlation of ranks in all situations. consideration of the results and sensitivity analysis of the fucom-mairca model show significant stability of the results and promising applicability of the model shown. securing level crossings represents significant material expenditure, so it is necessary to be grounded on reliable strategies for the selection of a level crossing that needs to be secured, as well as to be supported by the investments realization plan in terms of its security. also, this integrated fucommairca model can be applied for evaluation of reliable strategies for the selection of a level crossing that needs to be secured in the next phase. since these are new models of multi-criteria decision making, the directions of future research should focus on the application of uncertainty theories (fuzzy sets, rough numbers, gray numbers, neutrosophic sets etc.) in the fucom and mairca models. the integration of the uncertainty theories in the fucom and mairca models would allow significant exploitation of uncertainty and subjectivity existing in the decision-making process. references anandarao, s., & martland, c. d. 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(in serbian). © 2018 by the authors. submitted for possible open access publication under the terms and conditions of the creative commons attribution (cc by) license (http://creativecommons.org/licenses/by/4.0/). plane thermoelastic waves in infinite half-space caused operational research in engineering sciences: theory and applications vol. 5, issue 1, 2022, pp. 185-204 issn: 2620-1607 eissn: 2620-1747 doi: https://doi.org/10.31181/oresta040422196m * corresponding author. saimamustafa28@gmail.com (s. mustafa), arfajutt60@gmail.com (a. a. bajwa), shafqat905@e.gzhu.edu.cn (s. iqbal), a new fuzzy garch model to forecast stock market technical analysis saima mustafa 1, arfa amjad bajwa 1, shafqat iqbal 2* 1 department of mathematics and statistics, pmas arid agriculture university, rawalpindi, pakistan 2 school of economics and statistics, guangzhou university, guangzhou, china received: 15 january 2022 accepted: 14 march 2022 first online: 04 april 2022 original scientific paper abstract: decision making process in stock trading is a complex one. stock market is a key factor of monetary markets and signs of economic growth. in some circumstances, traditional forecasting methods cannot contract with determining and sometimes data consist of uncertain and imprecise properties which are not handled by quantitative models. in order to achieve the main objective, accuracy and efficiency of time series forecasting, we move towards the fuzzy time series modeling. fuzzy time series is different from other time series as it is represented in linguistics values rather than a numeric value. the fuzzy set theory includes many types of membership functions. in this study, we will utilize the fuzzy approach and trapezoidal membership function to develop the fuzzy generalized auto regression conditional heteroscedasticity (fgarch) model by using the fuzzy least square techniques to forecasting stock exchange market prices. the experimental results show that the proposed forecasting system can accurately forecast stock prices. the accuracy measures rmse, mad, mape, mse, and theil-u-statistics have values of 18.17, 15.65, 2.339, 301.998, and 0.003212, respectively, which confirmed that the proposed system is considered to be useful for forecasting the stock index prices, which outperforms conventional garch models. key words: fuzzy time series, membership function, trapezoidal fuzzy approach, garch model, forecasting. 1. introduction forecasting is a significant feature in economics, commerce, various branches of science and marketing. it is a technique that predicts the future behavior of output on the basis of present and past output of yield and past trends. the economy of a nation to a great extent relies on upon capital business sector on upon capital s. mustafa et al./oper. res. eng. sci. theor. appl. 5(1) (2022) 185-204 186 business sector, forecasting of stock market and their drifts are important factor in attaining significant gains in financial market. in capital and derivative pricing, investment plans, fund distribution and risk control processes, the accurately computation and prediction of financialvolatility plays a vital role (franke & westerhoff, 2011; haugom, langeland, molnár, & westgaard, 2014; a. y. huang, 2011), also fuzzy-garh models for forecasting financial volatility (hung, 2011a, 2011b; maciel, gomide, & ballini, 2016). the stock price has deep impact in financial event of the country and large-scale economics approach. however, predicting and forecasting the stocks trading, prices and movement is not an easy task because of the serious impact of full-scale financial variable, including general monetary condition, political interference, financial specialist’s decision, sudden and unexpected change in security exchanges. apart from the statistical models that have been used to understand and forecast variations in the stock market, a lot of attention has also been shifted to the applications of various soft computing application. there are different time series models proposed by the different researchers. due to appropriateness and efficiency fuzzy time series models are used in different studies (bisht, joshi, & kumar, 2018; iqbal & zhang, 2020; yu, 2005). fuzzy set theory, provides an authoritative framework to handle with vague or ambiguous problems and can express linguistic values and human subjective decisions of natural language, (zadeh, 1965). fuzzy time series was first presented by (song & chissom, 1993, 1994). furthermore, many fuzzy time series models were developed by researchers using different theories (chen & tanuwijaya, 2011; egrioglu, bas, yolcu, & chen, 2020; hassan et al., 2020; iqbal, zhang, arif, hassan, & ahmad, 2020; lu, chen, pedrycz, liu, & yang, 2015; wang, lei, fan, & wang, 2016; xiao, gong, & zou, 2009). some analysts developed fts forecsting models using probabilistic fuzzy set theory and reported significant results (gupta & kumar, 2019; w.-j. huang, zhang, & li, 2012). some fuzzy forecasting models in the environment of intuitionistic fuzzy set theory with equal length intervals are developed by (abhishekh, gautam, & singh, 2018),(bas, yolcu, & egrioglu, 2021) and also some work with unequal length intervals introduced by (lei, lei, & fan, 2016) and (iqbal & zhang, 2020). in addition, a novel method to forecast time series data was introduced by (soto, melin, & castillo, 2018), using ensembles of it2fnn models with fuzzy integrator optimization. there also some studies in which fuzzy based forecasting techniques are compared with classical models like arima (iqbal, zhang, arif, wang, & dicu, 2018). technical analysis is a tool to predict future stock value developments by analyzing the past succession of stock costs. the generalized autoregressive conditional heteroscedasticity (garch) model is one of the famous econometric models used to estimates the volatility in financial market, stock markets. garch model is an econometric model, to describe an appropriate approach to estimate the in-monetarist markets volatility in monetarist markets, (engle, 1982). garch models are useful across an extensive range of applications, also they do have boundaries as this model is only part of a solution. although these models are usually applied to return series, financial decisions are rarely based solely on expected returns and volatilities. these models are parametric specifications that operate best under relatively stable market conditions. garch is explicitly designed to model time-varying conditional variances, generalized auto-regressive conditional heteroscedasticity models often failed to capture highly irregular phenomena, including wild market fluctuations (e.g., crashes and subsequent a new fuzzy grach model to forecast stock market technical analysis 187 rebounds), and other highly unanticipated events that can lead to significant structural change. garch models often fail to fully capture the fat tails distribution observed in asset return series. a fat-tailed distribution is a probability distribution that has the property, along with the other heavy-tailed distributions, that its revelations excess skewness or kurtosis. this comparison is often made relative to the normal distribution, or to the exponential distribution. heteroscedasticity explains some of the fat tail behavior, but typically not all of it. fat tail distributions, such as student-t, have been applied in garch modeling, but often the choice of distribution is a matter of trial and error. for this purpose, fuzzy model is proposed known as fuzzy generalized auto-regressive conditional heteroscedasticity (fgarch) model in this paper. although several fuzzy garch models based on different statistical and machine learning approaches are developed, such as (hung, 2009, 2011a; popov & bykhanov, 2005), and (maciel et al., 2016), but our proposed fuzzy generalized auto-regressive conditional heteroscedasticity (fgarch) model is the best option because it is useful in investment on assets returns but also operates best under wide market fluctuation. in this paper, a new fuzzy model is proposed known as fuzzy generalized autoregressive conditional heteroscedasticity (fgarch) with fuzzy least square techniques and fuzzy trapezoidal approach. the motivation to use trapezoidal membership function is that it outperforms the different types of membership functions when it comes to develop a fuzzy-model for decision making and applicable to real-world applications. the proposed fuzzy model is the best option because it is useful in investment on assets returns but also operates best under wide market fluctuation. the objectives of the current study are explained as: (i) to estimate the unknown parameter by using the generalized auto-regressive conditional heteroscedasticity and forecasting fuzzy models, (ii) to articulate the fuzzy model by using the fuzzy least square technique, (iii) to evaluate the comparison between forecast produced from classical model and proposed fuzzy model and also select the best performance model from them. the remaining paper comprises in the following stages. first section describes the introduction part. second section briefly explains the earlier work done by the researchers in classical and fuzzy forecasting model. in third section, briefly described the methodology of the classical econometric model “generalized autoregressive conditional heteroscedasticity (garch)” and fuzzy model “proposed fuzzy generalized auto-regressive conditional heteroscedasticity (fgarch)”by using fuzzy least square method. this section also comprises concept of limitation in generalized auto-regressive conditional heteroscedasticity (garch), perceptive to move towards fuzzy model. fourth section included the results obtained from classical and proposed models with comparing the efficiency of the both models by using different endorsements. 2. basic theories 2.1. fuzzy set a fuzzy set z˜ in the universe of information u can be defined as a set of ordered pairs and it can be represented mathematically as s. mustafa et al./oper. res. eng. sci. theor. appl. 5(1) (2022) 185-204 188 (1) here (x) is degree of membership of x, which assumes values in the range from 0 to 1, i.e., (x) ∈ [0,1]. 2.2. trapezoidal membership function trapezoidal membership function is described using the following equation t = (2) where, x represents real value within the universe of discourse. a, b, c, d represent a xcoordinates of the four heads of trapezoidal and values should validate the following condition a<b<c<d. 2.3. fuzzy time series the first time (zadeh, 1965), proposed the fuzzy set theory, it provides a authoritative framework to handle with vague or ambiguous problems and can express linguistic values and human subjective decisions of natural language. time series models had failed to consider the application of forecasting theory until fuzzy time-series was defined by (song & chissom, 1993, 1994). 3. proposed fuzzy-based methodology 3.1. generalized auto-regressive conditional heteroscedasticity (p,q) model the generalized autoregressive conditional heteroscedasticity (garch) process is an econometric term proposed in 1982 by robert f. engle, an economist. in the year 2003, awarded by the nobel memorial prize for economics, to propose an approach to econometric model to estimate volatility in monetary markets. engle (engle, 1982) and (bollerslev, 1986) proposed the generalized arch (p,q) model. the general representation of garch (p,q) process ( is defined as, , (3) where is white noise with and   = = −− ++= q i p j titit hh 1 1 1 2 10  (4) a new fuzzy grach model to forecast stock market technical analysis 189 where, in eq. (4), 0 is a constant,  = − q i ti 1 2 1  shows the auto-regressive conditional heteroscedasticity term,  = − p j ti h 1 1  shows the generalized autoregressive conditional heteroscedasticity term with the parameters q  ,...,, 10 and p  ,...,, 10 . if , the shocks have a decaying impact of the future volatility (fryzlewicz, 2007). the general process for a garch model involves three steps. the first is to estimate a best-fitting of auto-regressive model. the second is to compute autocorrelations of the error terms. the third step is to test for implication. two other widely used approaches to estimate and predict the financial volatility are the classic historic volatility method, and the exponentially weighted moving average volatility method. heteroscedasticity describes the irregular pattern of variation of an error terms, or variable, in a statistical model. in data where heteroscedasticity present, observations do not confirm to a linear pattern, instead, they tend to clusters. the result is that the conclusions and predictive values drawn from the model will not be reliable. garch an econometric model, that can be used to analyze a number of different types of financial data series, for instance, macroeconomic data. financial institutions classically use this model to estimate the volatility of stock returns, bonds and market indices. they resulting information helps to determine the pricing and as well as supports to judge that, which assets will potentially provide higher returns. furthermore, it helps to forecast the returns of current investments to support in their asset allocation, hedging, risk management and portfolio optimization decisions. 3.2. fuzzy generalized auto-regressive conditional heteroscedasticity proposed fuzzy generalized auto-regressive conditional heteroscedasticity model is given as follows with fuzzy parameters: ptpttqtqttt hhhh −−−−−− ++++++++=  ~...~~~...~~ ~ 2211 22 22 2 110 (5) in the eq. (5) th ~ is the estimated fuzzy variable used as output variable, ( qpq ++  ~,...,~,...,~,~ 121 ) are the parameters with q term known as fuzzy autocorrelation parameters and fuzzy parameters with p term known as fuzzy partial autocorrelation. the impreciseness and conciseness have been tackled by connecting parameters with p and q order into fuzzy parameters. 3.2.1. fuzzy least square approach fuzzy least square approach is an accumulation form of ordinary least square technique. this technique incorporates of goodness of fit and requires a distance between the fuzzy values estimated by the model and vague data that is really pragmatic. mathematically it is expressed as: https://www.investopedia.com/terms/a/autoregressive.asp https://www.investopedia.com/terms/a/autocorrelation.asp https://www.investopedia.com/terms/a/autocorrelation.asp https://www.investopedia.com/terms/e/errorterm.asp https://www.investopedia.com/terms/s/statistical-significance.asp https://www.investopedia.com/terms/h/historicalvolatility.asp https://www.investopedia.com/terms/e/ema.asp https://www.investopedia.com/terms/e/ema.asp https://www.investopedia.com/terms/h/heteroskedasticity.asp https://www.investopedia.com/terms/l/linearrelationship.asp https://www.investopedia.com/terms/m/marketindex.asp s. mustafa et al./oper. res. eng. sci. theor. appl. 5(1) (2022) 185-204 190 where are two fuzzy numbers. is a trapezoidal fuzzy number with four points such as  vurm aaaa 00000 ,,,= and is another trapezoidal fuzzy number with four points such that  vurm aaaa 11111 ,,,= , and is the weighting function for determining the distance square between two fuzzy numbers. in both fuzzy numbers , parameters mm aa 10 , represent the left fuzzy points, mr aa 10 , represent the left center points, mu aa 10 , represent the right center fuzzy points, mv aa 10 , represented the right fuzzy points. 3.2.2. estimation of parameter of model by fuzzy least square approach the parameter of model is estimated by using the fuzzy least square method to gain a unique solution. the fuzzy least square method is defined by the sum of error distance between observed value )( t o and estimated output value . mathematically sum of error distance is represented as: 2 1 )]}(,)([{  t q i t eodsse  = = (6) where, in eq. (6) ))(),((  tt eod is mathematically represented as: 2 11 0 2 ]))(,)(()([))(),((   deodfeod tttt = (7) where index denotes the non-fuzzy series of data used in observed value input )( t o and estimated output value . )( t e =  )(),(),(),( vurm afafafaf now from the equation, each fuzzy parameter converted into a generalized autoregressive conditional heteroscedasticity in the form of functions given below:  = − = − ++= p ij jtm q i itmm haaaf ,)( 1 2 0  (8)  = − = − ++= p ij jtr q i itrr haaaf ,)( 1 2 0  (9) a new fuzzy grach model to forecast stock market technical analysis 191  = − = − ++= p ij jtu q i ituu haaaf ,)( 1 2 \0  (10)  = − = − ++= p ij jtv q i itvv haaaf ,)( 1 2 0  (11) where in the above equations, represent the left point function, represent the left center point function, represent the right center function, and represent the right point function. now, estimated output value expressed on = ],[ 10 ll , with α-cut fuzzy interval for trapezoidal number can be represent as: )}],()({)(),()}()([{)( uvvmmrt afafafafafafe −−+−=  (12) similarly, observed value is )(to expressed on )(to = ],[ 10 ll , such as )},()({)(),()}()({ 10 uvvmmr afafaflafafafl −−=+−=  (13) where represent the lower bound and represent the higher bound. now using the values, the observed and estimated output value is obtained by the sum of square error distance: 2 1 [ ( ), ( )] q t t i sse d o e  = =  , in the above expression, )](),([  tt eod stands the square distance between the observed and estimated output which is shown as given below: ( ))(),(2  tt eod =     ++−− 2 0 )()()( mmr afafafl    2 1 )()([)( vuu afafafl −+−  now putting the above expression and weighting function in sum of square error (sse) equation which is given below:  = = q i fsse 1 1 0 )(    2 0 )()()( mmr afafafl +−−  jtt h −− − 1  +   2 1 )()([)( vuu afafafl −+−  jtt h −− − 1  ,d (14) using the equation (12) for finding the partial derivation with respect to to the get simplified form of equations given as: s. mustafa et al./oper. res. eng. sci. theor. appl. 5(1) (2022) 185-204 192   = −   1 1 0 )1(2 i ij x    0()()( )0 =+−−  dafafafl mmr (15)   =   1 1 0 2 2 i ij x    ,0()()( )0 =+−+−  dafafafl mmr (16)   = q i 1 1 0 2  ,0)}]()({)([ 1 =−−+−  dafafaflx uvvij (17)   0)()()([)1(2 1 1 1 0 =−+−−  =  dafafaflx uvv q i ij , (18) now by solving the integral of the above equations and putting the values in the equations, encompassing the following equation: ij q i im xxa  =1 00 ij q i im xxa  = + 1 11 ij q i im xxa  = ++ 1   where 0ix =1 and pj ,2,1,0= after simplification, the standard form of above equation is given as: ij q i im xxa  =1 00 ij q i im xxa  = + 1 11 ij q i im xxa  = ++ 1   ij q i i xc = = 1 , now ij q i imij q i irij q i ir xxaxxaxxa  === +++ 11 1 1 0 1   where 0ix =1 and pj ,2,1,0= after simplification, the standard form of above equation is: ij q i imij q i irij q i ir xxaxxaxxa  === +++ 11 1 1 0 1   ij q i i xk = = 1 , now + = ij q i iu xxa 1 00  == ++ q i ijiuij q i iu xxaxxa 11 11   where 0ix =1 and pj ,2,1,0= after simplification, the standard form of above equation is: + = ij q i iu xxa 1 00  == ++ q i ijiuij q i iu xxaxxa 11 11   ij q i i xg = = 1 , (19) a new fuzzy grach model to forecast stock market technical analysis 193  === +++ q i ijivij q i ivij q i iv xxaxxaxxa 11 1 1 0 10   where 0ix =1 and pj ,2,1,0= after simplification, the standard form of above equation is:  === +++ q i ijivij q i ivij q i iv xxaxxaxxa 11 1 1 0 10   ij q i i xs = = 1 , (20) in these above equations i=1, 2…, q, are the outcomes of integral calculation of the above equations. these simple form of equations (15), (16), (17), (18) are represented in the form of matrix. (21) in eq. (21), m represents the left point matrix, r represents the left center point matrix, u represent the right center point matrix, v and represent the right center point matrix of trapezoidal membership function. where c, k, g and s represent the matrix which are obtained after solving the integral. these matrixes are represented as: nmmm aaam  10 ,{= } t , t t q i t xcc )( 1 1 1 += − = − t rrr n aaar },{ 10 = , t t q i t xkk )( 1 1 1 += − = − t uuu n aaau },{ 10 = , t t q i t xgg )( 1 1 1 += − = − t vvv n aaav },,{ 10 = , t q i tt xss )( 1 11 +=  = −− where and matrix, x is a data matrix and a is the positive definite with rank = n+1. if matrix , then inverse of matrix a can be easily determined. then equation problem consists of unique solution: s. mustafa et al./oper. res. eng. sci. theor. appl. 5(1) (2022) 185-204 194 cam 1− = , kar 1− = , , 1 gau − = sav 1−= 4. computational analysis the stock prices index of gold as input variable from year 2009 to 2017 is given in appendix a. step 1. in our proposed model, possibility of successes is given into five linguistic terms, each linguistic term is represented by the degree of trapezoidal fuzzy numbers. for example, very low interval = = = low interval = = = similarly, other computations are also computed regarding average interval, high interval and very high interval, and further arranged the linguistic variable according to the order as follows i. nverylow k ~ = = ii. nlow k ~ = iii. naverage k ~ = iv. nhigh k ~ = a new fuzzy grach model to forecast stock market technical analysis 195 v. nveryhigh k ~ = the above expression (i), (ii), (iii), (iv) and (v) shows very low, low, average, high and very high possibility of success for the nth observations. each linguistics variables are represented as observed prospective output. step 2. now, used the partial derivation of eqs. (12), (13), (14) and (15) which is show into a following simplified form of equation given as:   = −   1 1 0 )1(2 i ij x    0()()( )0 =+−−  dafafafl mmr 0)( 2 1 1 0 =      − = p i ijmij lxafx (22)   =   1 1 0 2 2 i ij x    ,0()()( )0 =+−+−  dafafafl mmr   0)()(54 1 0 =+− = p i ijmijrij xafxaflx (23)   = q i 1 1 0 2  ,0)}]()({)([ 1 =−−+−  dafafaflx uvvij  − =      +− p i ijvijiju xafxlxaf 1 1 0)( 3 1 )( 3 2 (24)   0)()()([)1(2 1 1 1 0 =−+−−  =  dafafaflx uvv q i ij  = =      − p i ijijv xlxaf 1 1 0)( 2 1 (25) step 3. after solving the integral and putting the values of above equations we get the matrix form of equations shown as: cam 1− = , kar 1− = , , 1 gau − = sav 1− = where and , s. mustafa et al./oper. res. eng. sci. theor. appl. 5(1) (2022) 185-204 196 matrix a is the positive definite with rank = n+1. if matrix , then inverse of matrix a can be easily determined. then equation problem consists of unique solution. a= 0.2032 0.0482 0.0173 0.0737 0.0532 0.0626 0.0613 0.0387 0.0482 0.4229 0.3145 0.1760 0.4474 0.4718 0.2032 0.5697 0.0173 0.3145 0.3816 0.1533 0.3684 0.3459 − − − − − − − − − 0.1657 0.5291 0.0737 0.1760 0.1533 0.1481 0.1800 0.2208 0.1043 0.2478 0.0532 0.4474 0.3684 0.1800 0.7109 0.5123 0.2705 0.5616 0.0626 0.4718 0.3459 0.2208 0 − − − − − − − − − − − .5123 0.7365 0.1598 0.7122 0.0613 0.2032 0.1657 0.1043 0.2705 0.1598 0.2270 0.1765 0.0387 0.5697 0.5291 0.2478 0.5616 0.7122 0.1765 1 .1042                    − − − − − −    − − − −   “very low” opportunity of interval the possibility of very low interval for the th n observation is written as: nverylow k ~ = = (26) using equation (26), interval of very low possibility for the th n observation is to estimate the observed value at different η values. here we have selected the η values that lies between [0, 1] from table .after putting the value of η = 0.086 in the equation (26), we have evaluated the value of 073.0 0 −=l and 0361.0 1 =l now following the procedure described in section 3 of this paper, the estimated model of “very low opportunity interval” obtained from observations is shown as: t h ~ = (26.523 32.7861 42.667 103.37) + (25.409 32.014 51.406 101.881) 2 1−t  + (15.1531 27.179 36.716 82.8758) 2 2−t  + (28.355 34.023 45.5677 106.771) 2 3−t  + (22.942 31.841 42.475 123.931) 2 4−t  + (25.043 29.587 38.879 79.749) 1−th + (30.048 43.198 65.913 131.927) 2−th + (22.945 38.4413 64.478 92.9316) 3−th + the above equation of model represents the “very low” linguistic category case that consist of fuzzy parameter in the form of trapezoidal membership function parameters. similarly, at other levels, the possibility intervals can be computed by following this procedure. step 4. fuzzy logical relationships to find the fuzzy logical relationship, fuzzified datasets are arranged according to the years. the fuzzified values are given in table 1. a new fuzzy grach model to forecast stock market technical analysis 197 table 1. actual prices of gold stock index with sets of fuzzy years stock index prices (returns*100) fuzzy sets 2010 1.485 2011 60.39 2012 21.89 2013 44.96 2014 29.064 2015 99.956 2016 69.98 2017 13.88 fuzzy logical relationships are designed from above fuzzified datasets and are presented in table 2. according to the rule of fuzzification, if the time series observation f(t-1) is fuzzified as in year 2010 and f(t) as in year 2011, then is mapping into . in the same manner sets of fuzzy in year 2011 is interrelated to in year 2012, sets of fuzzy in year 2012 is interrelated to in year 2013, sets of fuzzy in year 2013 is interrelated to in year 2014, sets of fuzzy in year 2014 is interrelated to in year 2015, sets of fuzzy in year 2015 is interrelated to in year 2016, sets of fuzzy in year 2016 is interrelated to in year 2017 so in this way all year fuzzy relationship datasets are formed. table 2. fuzzy logical relationships years relationships fuzzy logical relationships 2010 → 2011 → 2011 → 2012 2012 → 2013 2013 → 2014 2014 → 2015 2015 → 2016 2016 →2017 fuzzy logical relationship groups (flrg’s) using the table 2, fuzzy logical relationship groups (flrg’s) are formed which are given in the table 3. in group 1, relationship of fuzzy related to is mapping in the same way, the fuzzy relationship of is mapping on , is mapping on in group 3, is mapping on in group 4, is mapping on in group 5, is mapping on in group 6, is mapping on in group 7. there is no relationship of fuzzy that consist of more than one set that can be merged into another group. relationship of fuzzy group are shown in below given table. s. mustafa et al./oper. res. eng. sci. theor. appl. 5(1) (2022) 185-204 198 table 3. fuzzy logical relationship groups fuzzy relationship groups fuzzy set groups group 1 → group 2 group 3 group 4 group 5 group 6 group 7 step 5. fuzzy forecasted prices using the methods of fuzzy logical relationship groups by song (song & chissom, 1994), forecasted output is determined. all the relationship groups from the above table consist of case 1 which is stated as that in one to one relationship such as → then highest degree occurred in at interval . forecasted output of the fuzzy generalized auto-regressive conditional heteroscedasticity model is written in below column of table. in this table, year 2011 is forecasted value using the fuzzified interval midpoint values of 2010. the relationship of fuzzy group of year 2010 is → , according to fuzzification case 1, the highest degree of interval is = [1.489, 38.525], so the forecasted output of the year 2011 is the midpoint of which is equal to 20.005. in the same manner all the forecasted prices are obtained which are given in table 4. table 4. forecasted prices of stock index year actual prices of index (returns*100) forecasted prices of index fuzzy relationship groups midpoints of intervals 2010 1.485 → 20.005 2011 13.88 20.005 30.649 2012 21.89 30.649 37.646 2013 29.064 37.646 52.064 2014 44.96 52.064 72.148 2015 60.39 72.148 99.132 2016 69.98 99.132 128.569 2017 99.956 128.569 a new fuzzy grach model to forecast stock market technical analysis 199 figure 1. comparison graph of actual and forecasted prices of stock index in figure.1, it is shown that the actual prices of gold prices of stock index from year 2010 to 2017 are near to forecasted prices obtained from fuzzy generalized auto-regressive conditional heteroscedasticity from year 2010 to 2017. this graph reflects the regular component which means year to year variation existing in the fuzzy forecasted prices which do not follow any pattern. in actual prices of stock index, from year 2010 to 2013, price pattern shows minor change in trend movement and from year 2013 to 2016 there is a slightly movement and from year 2016 to 2017 there is a slightly downward movement seen in the prices pattern. the forecasted prices pattern shows slightly movement from year 2011 to 2013 and from 2013 to 2015, there is a upward trend seen in prices trend. from year 2016 to 2017, drastic upward movement are seen in forecasted prices. 4.2. comparison between (garch) (p,q) model and (fgarch) (p,q) model it is important to know that, which model is performing best and give significant results among classical and proposed fuzzy models. comparison between garch model and proposed fgarch model is evaluated by using different estimation criteria. results obtained through garch and proposed fgarch models by using different evaluation methods are given in the table 5. from above evaluation empirically, criteria’s results of proposed fuzzy generalized auto-regressive conditional heteroscedasticity (fuzzy-garch) is smaller and efficient than generalized auto-regressive conditional heteroscedasticity (garch), which depict that proposed fuzzy generalized autoregressive conditional heteroscedasticity (fuzzy-garch) perform effectively and efficient as compared to generalized auto-regressive conditional heteroscedasticity (garch). s. mustafa et al./oper. res. eng. sci. theor. appl. 5(1) (2022) 185-204 200 table 5. different evaluation criteria result obtained from garch and proposed fuzzygarch evaluation criteria garch fuzzy-garch root mean square (rmse) 72.5341 18.170093 mean absolute deviation (mad) 62.009312 15.6507 mean absolute percentage error (mape) 101.48869 2.339601 mean square error (mse) 2081.9607 301.998 theil-u-statistics 0.003212 to determine whether proposed fuzzy garch is appropriate and best model in forecasting than garch, we compare the properties of the both classical and proposed model which are given below: i. input and output information used in garch depend upon a previous function whereas in proposed fgarch model information are totally based on the fuzzy function. ii. garch model work on the larger observation datasets whereas proposed fgarch is applicable on small observation as well as larger observations. iii. garch model provides confidence interval whereas proposed fgarch models give the possibility parameters intervals, which make informal for the forecasted to deal with the possible conditions. iv. garch deals with the conventional fact such as time-fluctuating volatility and volatility crowding, whereas proposed fgarch deals with forecasting of volatility effect and give more accurate result than classical garch. from above comparison, proposed fgarch model provides the best forecasted results and best scenario in possibility situation and provide to be effective in spotting the small data outliers. 5. conclusions this study is based on basic idea of generalized auto-regressive conditional heteroscedasticity (garch) in forecasting the prices of stock exchange. a new method based on fuzzy theory is proposed with different mathematical computations and relate this computation in forecasting the stock exchange to determine the efficiency of this model with existing garch model. the pragmatic results of the mse, mfe, mape, mad and rmse, normalized mean square error (nmse) of fgarch model shown in table 4.7 are smaller as compared to garch model, which indicates that proposed fgarch forecasting accuracy is better and perform well than garch model. theil –u-statistic of both models is equal to zero which depicts that generalized auto-regressive conditional heteroscedasticity (garch) and proposed fuzzy generalized auto-regressive conditional heteroscedasticity (garch) perfectly forecast the stock prices. the likelihood practice is sensitive to the preliminary value selection and the distribution of data. the presence of uncertainty in data series makes questionable of using the likelihood technique to resolve the uncertainty due to unknown distribution. this limitation is vital in aspects of the forecasting with low accuracy. future research needs improvement in fuzzy garch model regarding a new fuzzy grach model to forecast stock market technical analysis 201 estimation of parameters and variability in order to improve the accuracy of model to forecast time series data. appendix a: stock prices index of gold (base 2009-2017) date gold prices index returns of gold prices date gold prices index returns of gold prices 12/31/2009 1134.72 1/31/2014 1244.27 0.018292 1/31/2010 1117.96 -0.01499 2/28/2014 1299.58 0.04256 2/28/2010 1095.41 -0.02059 3/31/2014 1336.08 0.027319 3/31/2010 1113.34 0.016105 4/30/2014 1298.45 -0.02898 4/30/2010 1148.69 0.030774 5/31/2014 1288.74 -0.00753 5/31/2010 1205.43 0.04707 6/30/2014 1279.1 -0.00754 6/30/2010 1232.92 0.022297 7/31/2014 1310.59 0.024027 7/31/2010 1192.97 -0.03349 8/31/2014 1295.13 -0.01194 8/31/2010 1215.81 0.018786 9/30/2014 1236.55 -0.04737 9/30/2010 1270.98 0.043407 10/31/2014 1222.49 -0.0115 10/31/2010 1342.02 0.052935 11/30/2014 1175.33 -0.04012 11/30/2010 1369.89 0.020345 12/31/2014 1200.62 0.021064 12/31/2010 1390.55 0.014857 1/31/2015 1250.75 0.04008 1/31/2011 1360.46 -0.02212 2/28/2015 1227.08 -0.01929 2/28/2011 1374.68 0.010344 3/31/2015 1178.63 -0.04111 3/31/2011 1423.26 0.034133 4/30/2015 1198.93 0.016932 4/30/2011 1480.89 0.038916 5/31/2015 1198.63 -0.00025 5/31/2011 1512.58 0.020951 6/30/2015 1181.5 -0.0145 6/30/2011 1529.36 0.010972 7/31/2015 1128.31 -0.04714 7/31/2011 1572.75 0.027589 8/31/2015 1117.93 -0.00929 8/31/2011 1759.01 0.105889 9/30/2015 1124.77 0.006081 9/30/2011 1772.14 0.007409 10/31/2015 1159.25 0.029743 10/31/2011 1666.43 -0.06344 11/30/2015 1086.44 -0.06702 11/30/2011 1739 0.041731 12/31/2015 1075.74 -0.00995 12/31/2011 1639.97 -0.06039 1/31/2016 1097.91 0.020193 1/31/2012 1654.05 0.008512 2/29/2016 1199.5 0.084694 2/29/2012 1744.82 0.052023 3/31/2016 1245.14 0.036655 3/31/2012 1675.95 -0.04109 4/30/2016 1242.26 -0.00232 4/30/2012 1649.2 -0.01622 5/31/2016 1260.95 0.014822 5/31/2012 1589.04 -0.03786 6/30/2016 1276.4 0.012104 6/30/2012 1598.76 0.00608 7/31/2016 1336.66 0.045083 7/31/2012 1594.29 -0.0028 8/31/2016 1340.17 0.002619 8/31/2012 1630.31 0.022094 9/30/2016 1326.61 -0.01022 9/30/2012 1744.81 0.065623 10/31/2016 1266.55 -0.04742 10/31/2012 1746.58 0.001013 11/30/2016 1238.35 -0.02277 11/30/2012 1721.64 -0.01449 12/31/2016 1157.36 -0.06998 12/31/2012 1684.76 -0.02189 1/31/2017 1192.1 0.029142 1/31/2013 1671.85 -0.00772 2/28/2017 1234.2 0.034111 2/28/2013 1627.57 -0.02721 3/31/2017 1231.42 -0.00226 3/31/2013 1593.09 -0.02164 4/30/2017 1266.88 0.02799 4/30/2013 1487.86 -0.07073 5/31/2017 1246.04 -0.01672 5/31/2013 1414.03 -0.05221 6/30/2017 1260.26 0.011283 6/30/2013 1343.35 -0.05261 7/31/2017 1236.84 -0.01894 7/31/2013 1285.52 -0.04499 8/31/2017 1283.04 0.036008 9/30/2013 1348.6 -0.00233 9/30/2017 1314.07 0.023614 10/31/2013 1316.58 -0.02432 10/31/2017 1279.51 -0.02701 11/30/2013 1275.86 -0.03192 11/30/2017 1281.9 0.001864 12/31/2013 1221.51 -0.04449 12/31/2017 1264.45 -0.0138 s. mustafa et al./oper. res. eng. sci. theor. appl. 5(1) (2022) 185-204 202 references abhishekh, gautam, s. s., & singh, s. 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(1965). fuzzy sets. information and control, 8(3), 338-353. © 2022 by the authors. submitted for possible open access publication under the terms and conditions of the creative commons attribution (cc by) license (http://creativecommons.org/licenses/by/4.0/). https://doi.org/10.1016/j.cam.2008.09.033 https://doi.org/10.1016/j.physa.2004.11.006 operational research in engineering sciences: theory and applications vol. 4, issue 3, 2021, pp. 59-81 issn: 2620-1607 eissn: 2620-1747 doi: https://doi.org/10.31181/oresta081221059t * corresponding author. spturkoglu@ybu.edu.tr (s. türkoğlu), stuzcu@politics.ankara.edu.tr (s. tuzcu) assessing country performances during the covid-19 pandemic: a standard deviation based range of value method serap pelin türkoğlu1, sevgi eda tuzcu2* 1 department of management and organization, ankara yıldırım beyazıt university, ankara, turkey 2 department of business administration, ankara university, ankara, turkey received: 22 april 2021 accepted: 24 september 2021 first online: 09 december 2021 original scientific paper abstract: in this paper, we compare the pandemic management performance of 22 countries that belong to the middle-high income class based on criteria including the pandemic data, population characteristics, and health system capacity. the management of the covid-19 pandemic requires considering many and often conflicting aspects at the same time which necessitates an mcdm approach. we use a standard deviation (sdv) based range of value (rov) method which coincides with the black-box nature of the disease. the weights obtained from the sdv method reveal that the number of covid-19 deaths, current health expenditure, and deaths due to cardiovascular diseases are the most important criteria. the rov method indicates that most asian countries are ranked in higher positions due to their strong healthcare systems and quick implementation of social distancing rules. the lowest performances belong to bulgaria, montenegro, and bosnia and herzegovina. they have experienced an elevated number of deaths due to having an elderly population and inefficient usage of healthcare resources. we also show that extreme poverty is an important determinant of country performance. in countries where poverty is higher, as the case with indonesia, implementing the social distancing rules becomes almost impossible which affects the overall country performance significantly. keywords: covid-19 pandemic, rov method, sdv method, mcdm, middle-high income countries 1. introduction it has been more than a year since the world health organization first declared the new coronavirus disease (covid-19) was a pandemic. after one year and several türkoğlu and tuzcu/oper. res. eng. sci. theor. appl. 4 (3) (2021) 59-81 60 waves, covid-19 caused 113,051,293 cases and more than 2,500,000 deaths1. although we have learned many things about the disease, and several covid-19 vaccines have been developed, the importance of the studies to clarify the effects of the disease has not been reduced. any research that helps reduce the burden on the healthcare system and flatten the spread rate is still valuable. in this study, we aim to compare the performance of a relatively homogenous group of countries in their fight against the covid-19 during the ongoing pandemic. more specifically, we rank the pandemic management performance of 22 countries that belong to the middle-high income class according to the world bank classifications based on many criteria, namely pandemic data, population characteristics, and health system capacity. the existence of various factors and often conflicting criteria at the same time makes the issue of ranking country performances as a multi-criteria decision making (mcdm) problem. for this aim, we use a combination of two mcdm techniques, namely the standard deviation approach (sdv) for the criteria weights and range of value (rov) method in order to compare country performances against covid-19. regarding the aim of our study, we note two related fields of research: the first field investigates how well countries all over the world cope with the pandemic. adabavazeh et al. (2020) note that benchmarking is essential for the healthcare systems to improve their working process and to be prepared for future public health crises. hence, it is natural to observe a specific line of research in the covid-19 literature. these studies concentrate on the performance rankings of different countries with various methodologies. jamison et al. (2020) examine the performances of 35 countries according to the doubling times of confirmed cases and deaths at three different points in time during the beginning of the pandemic. they demonstrate that although the variation among the cross-country performances is modest initially, the difference between countries gets wider between later days. aydin and yurdakul (2020) rank the country performances against covid-19 by using an extension of data envelopment analysis (dea) and different machine learning algorithms. they aim to show which factors affect the number of confirmed cases and deaths the most. maroko et al. (2020) aim to compare the neighborhoods in new york city, the usa, in terms of population characteristics. olivia et al. (2020) evaluate the current pandemic management of indonesia by comparing its performance with lombardy (italy) and new york (the usa) as well as other asian countries. the second group of related works is the ones that apply different decision-making approaches to covid-19 studies. among those studies, shirazi et al., (2020) rank the performance of hospitals in iran and their capability to meet patients’ needs during the pandemic by using fahp – promethee methods. samanlioglu and kaya (2020) evaluate the intervention strategies that countries have adopted to flatten the epidemiological curve by using the hesitant fuzzy ahp method. kayapinar kaya (2020) assesses the impact of covid-19 on the sustainable development levels of the oecd countries by employing the mairca technique and compares the findings with two other mcdm models, i.e. mabac and waspas. yiğit (2020) analyzed the performance of oecd countries during the current pandemic by employing the topsis approach. in this study, the healthcare system performance proxies, such as health expenditures, the number of medical staff, and covid-19 related indicators are employed as criteria, 1 data from: https://www.worldometers.info/coronavirus/ access date: 24.02.2021 https://www.worldometers.info/coronavirus/ assessing country performances during the covid-19 pandemic: a standard deviation based range of value method 61 while 36 oecd countries constitute the alternatives. this study reveals that asian pacific countries are the more successful ones in this struggle whereas the european and middle eastern countries demonstrate bad performance. determining a good country performance against covid-19 requires considering many types of criteria at the same time. population characteristics, such as age, accompanying chronic diseases, the level of poverty are important factors in this struggle. still, the biggest burden is on the healthcare system components. among the primary determinants of pandemic management success, we can observe the timely detection of the newly infected ones, providing good healthcare, and limiting the number of deaths. the existence of various and conflicting criteria creates a need for mcdm techniques. hence, we use two mcdm techniques combinedly, namely the sdv and the rov approaches, to determine the rankings of the countries. to the extent of our knowledge, this is the first study that applies an sdv based rov method to analyze the country’s performances in the battle against the current pandemic. by doing so, we aim to contribute to both lines of the above-mentioned researches. mcdm is a very common methodology to rank the decision options according to a group of criteria (hajkowicz & higgins, 2008). this particular nature allows us to compare the country’s performances in the fight against covid-19. in this sense, the aim of our study is related to the paper by yiğit (2020). here, we must mention the significant differences between this paper and ours. yiğit (2020) considers the early phases of the pandemic with only healthcare-related criteria. however, covid-19 created a very fast-changing environment in all areas. therefore, re-evaluating the performance of the countries and showing the differences between the ongoing situation and the early stages even for a short period of time still adds to the efforts that aim to decrease its negative effects. it is also known that the struggle against the covid-19 does not only depend on healthcare system, but also the characteristics of vulnerable population. these criteria must be added into country comparisons. unlike yiğit (2020), we consider population-related criteria such as the prevalence of chronic diseases and the percentage of elderly population. besides, we focus on a different and more homogenous group of countries. it is natural to draw different conclusions from this comparison relative to a more heterogeneous country group. last, we use a different combination of mcdm techniques. as a result, we believe that benchmarking the countries in the first year of the pandemic is still important to suggest policy changes for the worst-performing ones. bedford et al. (2020) indicate that the struggle against the covid-19 pandemic is harder for the countries in the low and middle-income groups than the higher-income group countries. the literature, however, mostly concentrates on the usa and european countries where the pandemic hit hard initially. the burden of the pandemic on the healthcare workers and units is devastating even for the better prepared higher-income countries. de nardo et al. (2020) state that the situation is, even more, overwhelming for lowand middle-income countries where the healthcare facilities are limited and mobility restrictions are difficult to be applied. in this study, we consider the middle-high income group countries, a less examined sample that also includes the origin of the pandemic, i.e. mainland china. we believe that such a comparison will help more disadvantaged countries to be prepared for future infection spreads, to decrease the economic and social effects of pandemics, and to allocate healthcare resources efficiently. türkoğlu and tuzcu/oper. res. eng. sci. theor. appl. 4 (3) (2021) 59-81 62 our findings reveal that asian countries like thailand, mainland china and malaysia produce better rankings in this comparison. these countries are more experienced in the management of infectious diseases due to previous epidemics, i.e. sars. however, bosnia and herzegovina, bulgaria, and montenegro have more disadvantaged rankings. their relative low performance can be attributed to the higher levels of the elderly population and their related co-morbidities as well as the inefficient management of the existing healthcare resources. we clearly show that countries that are successful in pandemic management have stronger healthcare systems and they have been more prepared for such a disaster. countries that are ranked in the lower positions either have limited capacity or cannot manage their resources efficiently. delaying to take necessary social distancing precautions is likely to increase the number of covid-19 deaths and lowers the country's performance. the success in pandemic management also depends on population characteristics. having an elderly population increases the overall burden in the healthcare system because it increases the requirement for long term attention. in distressing times, like the covid-19 pandemic, along with the co-morbidities, countries experience many difficulties to manage the crisis, no matter how high the level of the current expenditure is. in countries, where poverty is higher, implementing the social distancing rules becomes almost impossible. with that limited access to clean water and other hygiene products, the number of cases and deaths rapidly escalates. authorities must adopt policies regarding elderly care and people living below the poverty line. this paper continues with the literature review section that summarizes the related lines of research. the data and methodology section explains the details of the data and the selected mcdm method. section 4 presents the findings and the policy discussions based on these results. we compare the robustness of our results in section 5. the last section concludes. 2. related literature since the beginning of the covid-19 pandemic, there has been vast literature discussing its effects in every aspect of our lives. besides discussing the impact of the pandemic on our social and professional lives, many studies examine the effectiveness of different precautions to deal with the covid-19. in this paper, we aim to compare the performances of countries in the battle against the current pandemic by using a combination of two mcdm techniques. therefore, in this literature review we specifically focus on the two lines of research: first, we look at the literature that investigates how well countries all over the world cope with the pandemic. in this group, jamison et al. (2020); aydin and yurdakul (2020); adabavazeh et al. (2020) are highlighted. second, we examine how different decision-making techniques are used in the covid-19 studies. in the second group, the studies by de nardo et al. (2020); shirazi, et al. (2020); yiğit (2020), and kayapinar kaya (2020) are stand out among the others. the study by jamison et al. (2020) is one of the first ones that investigate the county performances against covid-19. they compare the performance of 35 countries with different characteristics in the early times of the pandemic depending on the doubling assessing country performances during the covid-19 pandemic: a standard deviation based range of value method 63 times of new cases and covid-19 related deaths per 1,000,000 population. they aim to show which policy choices of different governments provide better health and economic results. their results indicate that in the less populated countries, the pandemic started with more severity, but in time, the more populated countries were affected more. brazil and india have always shown a bad performance in terms of controlling the pandemic. the cases in iran and indonesia doubled more quickly in the later comparisons than the initial times. turkey showed a good performance and its ranking is above the average of 35 countries in terms of both new cases and deaths. aydin and yurdakul (2020) and adabavazeh et al (2020) employ the dea method in the analysis of country efficiency. more specifically, aydin and yurdakul (2020) develop a novel three-stage dea model called wsidea to identify country performances based on the number of covid-19 cases and deaths and other population and economic characteristics. they cluster 142 countries into 3 groups and obtain their efficiencies according to the wsidea method. the factors that affect country efficiency levels are examined with decision trees and random forest algorithms. adabavazeh, et al. (2020), on the other hand, employ the traditional dea method to analyze the efficiency of healthcare units in 71 different countries where population, gdp per capita, day of infection, and the total number of cases are inputs and the number of total recovered patients and total deaths are outputs. they employ a bcc type output-oriented dea model. among them, 16 healthcare units including those located in mainland china and iran are found efficient. the second line of research applies different decision-making tools in covid-19 studies, such as mcdm techniques, fuzzy sets, and artificial intelligence. these applications include many different fields, ranging from the prediction of future risks and the effectiveness of the non-healthcare precautions to medicine selection and hospital admissions. among the examples of fuzzy sets and artificial intelligence applications in the struggle against covid-19, the following studies can be examined: pal et al. (2020) benefit from artificial intelligence to predict long term country-specific risks and to group them as high-risk, low-risk, and recovering countries. majumder et al. (2020) develop a decision-making tool based on topsis. they try to identify the possible covid-19 patients depending on their linguistic information in order to help early detection of newly infected people and to send them self-isolation or home quarantine. they replace the euclidian distance computation of proximity to ideal solutions with supremum distance. next, they apply an artificial neural network approach to provide real-time monitoring for death values. si et al. (2021) propose a decision-making approach for appropriate medicine selection by employing fuzzy sets and grey relational analysis. mishra et al. (2021), following si et al. (2021), rank alternative medical treatments to apply for the mild cases of covid-19. they employ an aras framework with hesitant fuzzy information. the attribute weights are obtained through the hf-divergence measure. khatua et al. (2020) employ granular differentiability based fuzzy seiahrd model to control the current pandemic in india. their results indicate that an optimal pandemic control requires more testing to detect the infections, hospital quarantine, and long-term partial lockdowns in the country. the following group of studies constitutes examples for the application of mcdm techniques to the covid-19 studies. sayan et al. (2020) employ two different mcdm türkoğlu and tuzcu/oper. res. eng. sci. theor. appl. 4 (3) (2021) 59-81 64 techniques, namely fuzzy promethee and fuzzy topsis to rank seven diagnostic alternatives of covid-19 based on different criteria such as test sensitivity, cost, usability, false result rates, accessibility, equipment. samanlioglu and kaya (2020) assess the non-healthcare precautions, including mobility and border restrictions, lockdowns, school closures, declaration of a state of emergency in the struggle against the current pandemic by employing a hesitant fuzzy ahp method. de nardo et al. (2020) use paprika as an mcdm technique to detect and prioritize the hospital admissions of covid-19 patients with the potential of quick clinical deterioration in italy. the criteria weights are based on a survey applied to the experts who deal actively with covid-19 patients. the paprika method compares all combinations of criteria pairs. shirazi, et al. (2020) examine patient satisfaction under normal terms and under times of health crisis, such as the current pandemic. to do so, they rate the hospitals in iran and determine the factors of patient satisfaction by using a combination of the fuzzy ahp-promethee approach. kayapinar kaya (2020) assesses the sustainable development performance of oecd countries before and during the covid-19 pandemic by using mairca as the main analysis method. she compared the rankings of mairca with two other mcdm techniques namely waspas and mabac. she showed that although the pandemic affects negatively all countries’ sustainable development levels, developing countries are more negatively impacted. sangiorgio and parisi (2020) develop an index to forecast the contagion risk under different mobility scenarios in urban areas to support the decision-making process of local authorities. to do so, they collect data from 257 urban areas in italy and they design the problem as ahp based multi-criteria approach. next, they calibrate the model by using the grg-optimization method and compared the results with an analysis based on the artificial neural networks. yiğit (2020) compares the performance of 36 oecd countries by using the topsis method in their struggle against the current disease. she considers the countries as alternatives to rank and employs healthcare indicators as equally weighted criteria. these criteria include the number of covid-19 patients and deaths, healthcare system expenditures by governments, and current healthcare capacities, such as hospital beds and the number of physicians. she states that although one may observe a high correlation between healthcare expenditures and life expectancy, some countries do not comply with this anticipation. for example, portugal, spain, and israel are among the countries with high life expectancy but their healthcare expenditures are lower than the oecd average. as a result, as indicated by yiğit (2020), in a worldwide healthcare crisis, this situation leads to different performance rankings. the findings of yiğit (2020) suggest that asian countries in the oecd sample react more proactively to the ongoing pandemic relative to european countries and the usa. the studies applying several decision-making tools on covid-19 are summarized below in table 1. our study aims to combine these two lines of research mentioned above. in particular, we aim to rank the countries in the middle-high income group based on their performances against the current pandemic while employing mcdm techniques. although these techniques provide transparent and consistent comparisons as noted by de nardo et al. (2020), the studies applying mcdm to the country performances are rather scarce. in this sense, our aim coincides most with the study by yiğit (2020). assessing country performances during the covid-19 pandemic: a standard deviation based range of value method 65 table 1. the studies applied decision-making tools in the struggle against covid-19 authors the aim of the paper the decision-making tool yiğit (2020) to compare the country performances based on the healthcare criteria in the battle against the current pandemic topsis sayan et al. (2020) to compare the covid-19 diagnostic tool alternatives fuzzy promethee and fuzzy topsis samanlioglu and kaya (2020) to rank the precautions other than the healthcare system measures against covid-19 hesitant fuzzy ahp de nardo et al. (2020) to prioritize the hospital admissions of not currently but potentially urgent patients. paprika kayapinar kaya (2020) to rank the sustainable development levels of countries before and during the covid-19 pandemic mairca results compared with waspas and mabac shirazi, et al. (2020) to rate the hospitals in iran according to the patient satisfaction under normal and pandemic conditions a combination of fuzzy ahppromethee sangiorgio and parisi (2020) to predict the contagion risk of covid-19 based on different mobility restriction scenarios ahp based multi-criteria approach and grgoptimization method. the results are compared with those obtained from ann. khatua et al. (2020) to find the requirements for an optimal pandemic control in india granular differentiability based fuzzy seiahrd majumder et al. (2020) to detect the potential covid-19 patients based on their verbal information supremum distance topsis method combined with ann pal et al. (2020) to determine the long term covid19 risks of a country artificial intelligence si et al. (2021) to choose appropriate medicine to treat covid-19 patients fuzzy sets and grey relational analysis mishra et al. (2021) to rank medical treatment alternatives of mild covid-19 patients aras framework with hesitant fuzzy information however, there are important differences between these two papers. we consider a more homogenous and less investigated sample of countries than yiğit (2020). benchmarking of countries is more intuitive when the sample becomes less heterogeneous. in addition to the healthcare indicators employed in yiğit (2020), we also consider population-based criteria, such as the elderly ratio, extreme poverty, and the existence of co-morbidities in our analysis. these criteria are also known as important determinants of the number of covid-19 deaths and cases. therefore, the performance comparison of countries in this battle must consider these criteria as well. the criteria ranking is done based on an objective weighting method called the sdv approach. the country comparisons are realized based on the rov method. we believe that our selection of criteria weighting and alternative ranking methods overlap the black-box nature of the ongoing pandemic. last, we employ a later time period for the ongoing pandemic to compare the performances. such a comparison in this fast-changing environment is very valuable. türkoğlu and tuzcu/oper. res. eng. sci. theor. appl. 4 (3) (2021) 59-81 66 3. data and methodology this study collects data for 22 countries that are classified as middle-high income group by the world bank2. these countries are albania, argentina, armenia, bosnia and herzegovina, brazil, bulgaria, mainland china, columbia, costa rica, dominican republic, ecuador, georgia, indonesia, iran, kazakhstan, malaysia, mexico, montenegro, paraguay, russia, thailand, and turkey. as of the date of the analysis, this sample covers 25% of the total cases and 32% of the covid-19 related deaths worldwide. these countries create a rather homogeneous group to provide a ranking for their performances and also contain mainland china, which is the origin of the pandemic and the most discussed country for its crisis management methods. the study begins with the identification of performance criteria and application of the sdv method to weight them. next, the rov method will be applied as the main analysis method, where the results are compared topsis and edas approaches. for clarity, we show the general framework of our work in figure 1. figure 1. general working diagram of the study 2 the world bank, https://datahelpdesk.worldbank.org/knowledgebase/articles/906519-world-bankcountry-and-lending-groups, access date: 24.02.2020 https://datahelpdesk.worldbank.org/knowledgebase/articles/906519-world-bank-country-and-lending-groups https://datahelpdesk.worldbank.org/knowledgebase/articles/906519-world-bank-country-and-lending-groups assessing country performances during the covid-19 pandemic: a standard deviation based range of value method 67 for the comparisons, 12 evaluation criteria have been selected based on the studies by adabavazeh et al. (2020), aydin and yurdakul (2020), george et al. (2020), and khafaie and rahim (2020). those criteria, their codes, and the sources from which the data is obtained are provided in table 2. table 2. the criteria used in the analyses, their codes and data sources criteria codes definition data source total cases c1 the number of patients that have positive pcr tests per 100.000 people https://www.worldometers.info/coronavirus (access date: 20.01.2021) total deaths c2 total number of deaths due to covid-19 per 100.000 people https://www.worldometers.info/coronavirus (access date: 20.01.2021) extreme poverty c3 the percentage of the population living less than daily $1.90 https://ourworldindata.org (access date: 20.01.2021) cardiovascular death rate c4 the annual number of deaths due to cardiovascular diseases per 100.000 people in a given country. https://ourworldindata.org (access date: 20.01.2021) diabetes prevalence c5 the rate of people aged between 20 and 79 with type 1 and type 2 diabetes https://ourworldindata.org (access date: 20.01.2021) female smokers c6 the number of women who smoke in a given country. https://ourworldindata.org (access date: 20.01.2021) population aged 65 + c7 the rate of people aged 65 and above to the total population in a given country. the world bank database (2019) male smokers c8 the number of men who smoke in a given country. https://ourworldindata.org (access date: 20.01.2021) current health expenditure c9 the amount of health expenditures as a percentage of the gdp of a given country. the world bank database (2018) total recovered c10 the number of patients recovered from covid-19 infection per 100.000 people. https://www.worldometers.info/coronavirus (access date: 20.01.2021) hospital beds per thousand c11 the number of hospital beds per 1000 people in a given country. https://ourworldindata.org (access date: 20.01.2021) total tests c12 the number of total pcr tests to diagnose covid19 infections per 100.000 people. https://www.worldometers.info/coronavirus (access date: 20.01.2021) 3.1. standard deviation method the standard deviation method is used to weight the criteria in this analysis. this method is developed by diakoulaki et al. (1995) and the weights are determined according to the standard deviations of criteria. this is an objective weighting method in which decision-makers do not influence establishing the relative importance of criteria. this method gives lower weights to an attribute as long as the attribute has similar values in different alternatives. as a result, the contrasting attribute in the https://ourworldindata.org/ https://ourworldindata.org/ https://ourworldindata.org/ https://ourworldindata.org/ https://ourworldindata.org/ türkoğlu and tuzcu/oper. res. eng. sci. theor. appl. 4 (3) (2021) 59-81 68 alternatives becomes much highlighted (diakoulaki et al., 1995; hassan et al., 2015). diakoulaki et al. (1995) indicate that when the criteria are interdependent, the results might be misleading. however, removing some of these interdependent criteria might cause a loss of important information as well. in this case, using the standard deviation method in the weight determination might be a solution. this feature of the standard deviation method becomes more important when the nature of the covid-19 pandemic is considered. as an example, the criteria in table 2 include total confirmed cases, total tests, and deaths. naturally, as more testing is performed, more cases will be confirmed and more covid-19 deaths will be detected. however, the omission of any of these criteria will result in a loss of information. while obtaining the weights into the standard deviation method, first, a normalization process is applied through eq. (1) and eq. (2) to provide a common and measurable basis for criteria that differ in scale and units (diakoulaki et al., 1995; elsantawy & ahmed, 2012): 𝑥𝑖𝑗 ′ = 𝑥𝑖𝑗−min (𝑥𝑖𝑗)𝑖=1 𝑚 max (𝑥𝑖𝑗)𝑖=1 𝑚 −min (𝑥𝑖𝑗)𝑖=1 𝑚 i= 1,2,…,m; j = 1,2,… ,n (for beneficial) (1) 𝑥𝑖𝑗 ′ = max (𝑥𝑖𝑗)𝑖=1 𝑚 −𝑥𝑖𝑗 max (𝑥𝑖𝑗)𝑖=1 𝑚 −min (𝑥𝑖𝑗)𝑖=1 𝑚 i=1,2,…,m; j=1,2,…,n (for non-beneficial) (2) there are m alternatives and n criteria. here, xij is the raw score of ith alternative for criterion j. (x')mxn is the matrix after the normalization process, while max xij and min xij are the maximum and minimum values of xij respectively. the standard deviation for each criterion is computed with the aid of eq. (3). 𝑆𝐷𝑉𝑗 = √ 1 𝑚 ∑ (𝑥𝑖𝑗 ′ − 𝑥𝑗 ′̅)2𝑚𝑖=1 (3) 𝑥𝑗 ′̅ is the average of the values of the jth criterion after the normalization process, and j=1,2,…,n. after obtaining standard deviation values, the weightings of criteria are computed by using eq. (4). 𝑤𝑗 = 𝑆𝐷𝑉𝑗 ∑ 𝑆𝐷𝑉𝑗 𝑛 𝑗=1 j = 1,2,…, n (4) 3.2. range of value (rov) method rov approach is developed by yakowitz and szidarovxzky (1993). hajkowicz and higgins (2008) state that this method is especially beneficial when it is not possible or meaningful to provide quantitative weights. after one year of the pandemic, covid-19 still protects its black box nature in many aspects. therefore, instead of assigning quantitative weights, we find the rov method more suitable to assess the country's performances during the pandemic. to the extent of our knowledge, this is to first paper that combines the rov approach with the standard deviation method in both mcdm and covid-19 literature. rov method basically computes the best and worst utility values for each alternative (hajkowicz & higgins, 2008). to calculate those values, the utility function is maximized and minimized, respectively. as a result, the performance rankings of alternatives are obtained. assessing country performances during the covid-19 pandemic: a standard deviation based range of value method 69 the procedure for the application of the rov method is simple which constitutes another strong point for this approach. the application steps are as follows (madić et al., 2016): step 1: the relevant criteria to assess the existing alternatives are set. step 2: the decision matrix is formed. in this matrix, each row represents an alternative whereas each column reflects a criterion. step 3: the decision matrix is normalized at this stage. for beneficial criteria, where maximization is applied, the normalization is done by using eq. (5) below: 𝑥𝑖𝑗 = 𝑥𝑖𝑗−min (𝑥𝑖𝑗)𝑖=1 𝑚 max (𝑥𝑖𝑗)𝑖=1 𝑚 −min (𝑥𝑖𝑗)𝑖=1 𝑚 (5) for the non-beneficial criteria, however, where minimization is applied, the normalization is done by using eq. (6) below: 𝑥𝑖𝑗 = max (𝑥𝑖𝑗)𝑖=1 𝑚 −𝑥𝑖𝑗 max (𝑥𝑖𝑗)𝑖=1 𝑚 −min (𝑥𝑖𝑗)𝑖=1 𝑚 (6) in both eq (5) and (6), xij is the raw score of ith alternative for criterion j. there are m alternatives. max xij and min xij are the maximum and minimum values of xij, and the �̅�𝑖𝑗 is the normalized values. step 4: for each alternative, the best and worst utility values are computed as in eq. (7) and (8). max: 𝑢𝑖 + = ∑ 𝑥𝑖𝑗 𝑛 𝑗=1 ∗ 𝑤𝑗 (7) min: 𝑢𝑖 − = ∑ 𝑥𝑖𝑗 𝑛 𝑗=1 ∗ 𝑤𝑗 (8) where ui+ and uirepresent utility values and wj reflects the criterion weight. the summation of the criterion weights must be equal to 1, and wj≥0. when ui-≥ui’+, the ith alternative shows a better performance than the alternative i’ without looking at the quantitative weights. if this basis is not sufficient to distinguish the alternatives, a midpoint scoring (ui) can be used to allow the following ranking as such: 𝑢𝑖 = 𝑢𝑖 −+ 𝑢𝑖 + 2 (9) step 5: in this last step, the alternatives are ordinally ranked based on their ui values. the best alternative has the highest ui, whereas the worst one has the lowest ui. 4. findings following the above procedure, the criteria that are presented in table 2 are first weighted by using the standard deviation method. next, the decision matrix is formed. here, c1,…., c8 represent non-beneficial criteria to be minimized, while c9, c10, c11, and c12 are beneficial criteria, to be maximized. the decision matrix can be seen in table 3. türkoğlu and tuzcu/oper. res. eng. sci. theor. appl. 4 (3) (2021) 59-81 70 table 3. the initial decision matrix countries c1 c2 c3 c4 c5 c6 c7 c8 c9 c10 c11 c12 albania 2381.8 44.8 1.1 304.2 10.1 7.1 14.2 51.2 5.3 1470.4 2.9 11105.5 argentina 4021.9 101.9 0.6 191.0 5.5 16.2 11.2 27.7 9.6 3591.0 5.0 12677.7 armenia 5567.6 101.3 1.8 341.0 7.1 1.5 11.5 52.1 10.0 5201.8 4.2 21246.1 bosnia and herzegovina 3577.1 135.8 0.2 329.6 10.1 30.2 17.2 47.7 8.9 2698.4 3.5 17304.2 brazil 4033.0 99.6 3.4 178.0 8.1 10.1 9.3 17.9 9.5 3584.2 2.2 13551.3 bulgaria 3044.5 122.7 1.5 424.7 5.8 30.1 21.3 44.4 7.3 2510.0 7.5 18543.8 mainland china 7.0 0.3 0.7 261.9 9.7 1.9 11.5 48.4 5.4 5.8 4.3 11447.2 colombia 3820.3 97.3 4.5 124.2 7.4 4.7 8.8 13.5 7.6 3548.2 1.7 18555.9 costa rica 3685.2 48.6 1.3 138.0 8.8 6.4 9.9 17.4 7.6 2870.2 1.1 11012.0 dominican republic 1815.5 22.7 1.6 266.7 8.2 8.5 7.3 19.1 5.7 1356.5 1.6 9065.9 ecuador 1333.3 82.4 3.6 140.4 5.6 2.0 7.4 12.3 8.1 1147.3 1.5 4742.1 georgia 6663.6 79.5 4.2 496.2 7.1 5.3 15.1 55.5 7.1 6368.2 2.6 54798.1 indonesia 338.8 9.7 5.7 342.9 6.3 2.8 6.1 76.1 2.9 282.1 1.0 3138.1 iran 1611.5 68.6 0.2 270.3 9.6 0.8 6.4 21.1 8.7 1372.2 1.5 10413.8 kazakhstan 1171.8 15.6 0.1 466.8 7.1 7.0 7.7 43.1 2.9 839.3 6.7 32097.7 malaysia 506.2 1.8 0.1 260.9 16.7 1.0 6.9 42.4 3.8 399.5 1.9 13036.4 mexico 1292.9 110.7 2.5 152.8 13.1 6.9 7.4 21.4 5.4 981.2 1.4 3284.4 montenegro 8969.5 119.9 1.0 387.3 10.1 44.0 15.4 47.9 8.4 7592.0 3.9 34205.6 paraguay 1740.1 35.7 1.7 199.1 8.3 5.0 6.6 21.6 6.7 1420.7 1.3 8769.1 russia 2460.8 45.0 0.1 431.3 6.2 23.4 15.1 58.3 5.3 2096.8 8.1 67602.4 thailand 18.0 0.1 0.1 109.9 7.0 1.9 12.4 38.8 3.8 13.8 2.1 1749.1 turkey 2868.2 28.9 0.2 171.3 12.1 14.1 8.7 41.1 4.1 2737.5 2.8 33402.3 the next step is to normalize each element in the decision matrix. this process is done according to eq. (1) for beneficial criteria and according to eq. (2) for nonbeneficial criteria. the normalized decision matrix is presented in table 4. table 4. normalized decision matrix countries criteria c1 c2 c3 c4 c5 c6 c7 c8 c9 c10 c11 c12 albania 0.74 0.67 0.82 0.50 0.59 0.85 0.46 0.39 0.33 0.19 0.26 0.14 argentina 0.55 0.25 0.91 0.79 1.00 0.64 0.66 0.76 0.94 0.47 0.56 0.17 armenia 0.38 0.25 0.70 0.40 0.86 0.98 0.64 0.38 1.00 0.68 0.45 0.30 bosnia and herzegovina 0.60 0.00 0.98 0.43 0.59 0.32 0.27 0.45 0.84 0.35 0.35 0.24 brazil 0.55 0.27 0.41 0.82 0.77 0.78 0.79 0.91 0.93 0.47 0.17 0.18 bulgaria 0.66 0.10 0.75 0.19 0.97 0.32 0.00 0.50 0.63 0.33 0.91 0.26 mainland china 1.00 1.00 0.89 0.61 0.62 0.97 0.64 0.43 0.35 0.00 0.47 0.15 colombia 0.57 0.28 0.21 0.96 0.83 0.91 0.82 0.98 0.67 0.47 0.10 0.26 costa rica 0.59 0.64 0.79 0.93 0.71 0.87 0.75 0.92 0.66 0.38 0.01 0.14 dominican republic 0.80 0.83 0.73 0.59 0.76 0.82 0.92 0.89 0.40 0.18 0.08 0.11 ecuador 0.85 0.39 0.38 0.92 1.00 0.97 0.91 1.00 0.74 0.15 0.07 0.05 georgia 0.26 0.42 0.27 0.00 0.86 0.90 0.41 0.32 0.59 0.84 0.22 0.81 indonesia 0.96 0.93 0.00 0.40 0.93 0.95 1.00 0.00 0.00 0.04 0.00 0.02 iran 0.82 0.50 0.98 0.58 0.64 1.00 0.98 0.86 0.81 0.18 0.07 0.13 kazakhstan 0.87 0.89 1.00 0.08 0.86 0.86 0.89 0.52 0.01 0.11 0.81 0.46 malaysia 0.94 0.99 1.00 0.61 0.00 1.00 0.94 0.53 0.12 0.05 0.12 0.17 mexico 0.86 0.19 0.57 0.89 0.33 0.86 0.91 0.86 0.35 0.13 0.05 0.02 montenegro 0.00 0.12 0.84 0.28 0.59 0.00 0.39 0.44 0.78 1.00 0.40 0.49 paraguay 0.81 0.74 0.71 0.77 0.75 0.90 0.96 0.85 0.53 0.19 0.04 0.11 russia 0.73 0.67 1.00 0.17 0.94 0.48 0.41 0.28 0.34 0.28 1.00 1.00 thailand 1.00 1.00 1.00 1.00 0.86 0.97 0.58 0.58 0.13 0.00 0.15 0.00 turkey 0.68 0.79 0.98 0.84 0.41 0.69 0.82 0.55 0.18 0.36 0.25 0.48 assessing country performances during the covid-19 pandemic: a standard deviation based range of value method 71 in the last step of this method, the standard deviation of each performance criterion and its relevant weight is computed by using eq. (3) and eq. (4). the results are shown in table 5. table 5. standard deviations and criterion weights sdvj is the calculated standard deviation for each criterion. wj is the weight for each criterion it is observed from the criteria weights in table 5 that the most important criteria determining the country's performances are total deaths (c2), current health expenditures (c9), and cardiovascular death rate (c4). the least important criteria are, however, diabetes prevalence (c5), total cases (c1), and total tests (c12). table 6. criteria weights comparison matrix t o ta l c a se s (c 1 ) t o ta l d e a th s (c 2 ) e x tr e m e p o v e rt y (c 3 ) c a rd io v a sc u la r d e a th r a te ( c 4 ) d ia b e te s p re v a le n ce ( c 5 ) f e m a le s m o k e rs (c 6 ) a g e d 6 5 + ( c 7 ) m a le s m o k e rs ( c 8 ) c u rr e n t h e a lt h e x p e n d it u re s (c 9 ) t o ta l r e co v e re d (c 1 0 ) h o sp it a l b e d s p e r 1 0 0 0 ( c 1 1 ) t o ta l t e st s (c 1 2 ) wj 7 .4 0 % 9 .7 8 % 8 .8 0 % 9 .1 1 % 7 .2 3 % 7 .9 7 % 8 .0 6 % 8 .1 0 % 9 .2 8 % 7 .9 1 % 8 .8 4 % 7 .5 4 % total cases (c1) 7.40% 0.76 0.84 0.81 1.02 0.93 0.92 0.91 0.80 0.93 0.83 0.98 total deaths (c2) 9.78% 1.32 1.11 1.07 1.35 1.23 1.21 1.21 1.05 1.24 1.11 1.30 extreme poverty (c3) 8.80% 1.19 0.90 0.97 1.22 1.10 1.09 1.09 0.95 1.11 1.00 1.17 cardio. death rate (c4) 9.11% 1.23 0.93 1.04 1.26 1.14 1.13 1.13 0.98 1.15 1.03 1.21 diabetes prevalence (c5) 7.23% 0.98 0.74 0.82 0.79 0.91 0.90 0.89 0.78 0.91 0.82 0.96 female smokers (c6) 7.97% 1.08 0.81 0.91 0.87 1.10 0.99 0.98 0.86 1.01 0.90 1.06 aged 65 + (c7) 8.06% 1.09 0.82 0.92 0.88 1.11 1.01 1.00 0.87 1.02 0.91 1.07 male smokers (c8) 8.10% 1.09 0.83 0.92 0.89 1.12 1.02 1.00 0.87 1.02 0.92 1.07 current health exp. (c9) 9.28% 1.25 0.95 1.05 1.02 1.28 1.16 1.15 1.15 1.17 1.05 1.23 total recovered (c10) 7.91% 1.07 0.81 0.90 0.87 1.09 0.99 0.98 0.98 0.85 0.89 1.05 hospital beds per 1000 (c11) 8.84% 1.20 0.90 1.00 0.97 1.22 1.11 1.10 1.09 0.95 1.12 1.17 total tests (c12) 7.54% 1.02 0.77 0.86 0.83 1.04 0.95 0.94 0.93 0.81 0.95 0.85 wj is the weight for each criterion t o ta l c a se s (c 1 ) t o ta l d e a th s (c 2 ) e x tr e m e p o v e rt y ( c 3 ) c a rd io v a sc u la r d e a th r a te (c 4 ) d ia b e te s p re v a le n ce ( c 5 ) f e m a le s m o k e rs ( c 6 ) a g e d 6 5 + ( c 7 ) m a le s m o k e rs ( c 8 ) c u rr e n t h e a lt h e x p e n d it u re s (c 9 ) t o ta l r e co v e re d ( c 1 0 ) h o sp it a l b e d s p e r 1 0 0 0 (c 1 1 ) t o ta l t e st s (c 1 2 ) sdvj 0.25 0.33 0.30 0.31 0.24 0.27 0.27 0.27 0.31 0.27 0.30 0.25 wj 0.07 0.10 0.09 0.09 0.07 0.08 0.08 0.08 0.09 0.08 0.09 0.08 türkoğlu and tuzcu/oper. res. eng. sci. theor. appl. 4 (3) (2021) 59-81 72 as noted before, the standard deviation method determines the criteria weights based on the contrasting attributes. in other words, this method puts less importance if the attribute distributes more evenly among the alternatives, but places more emphasis if it differs significantly. from table 5, it is seen that the number of cases and number of tests per one hundred thousand people are similar for the countries in the sample. however, the differences in the number of deaths per one hundred thousand and current health expenditures become prominent across countries. based on the weights in table 5, we also construct the matrix in table 6 to show the relative importance for any pair of criteria following de nardo et al. (2020). this matrix is interpreted from left to right and it is not symmetric. for example, table 6 indicates that the number of covid-19 deaths is slightly more important than the deaths due to cardiovascular diseases (1.07) and the current health expenditures (1.05), but 1.32 times more important than the number of confirmed cases. the extreme poverty level is as important as the number of hospital beds. in fact, current health expenditures and the extreme poverty level are two of the criteria that show the biggest discrepancies among the sample countries. the diabetes level in a population, however, is the least important criterion in this analysis. table 7. the results of the rov method countries results uiui+ ui rankings thailand 0.59 0.03 0.60 1 iran 0.52 0.11 0.58 2 paraguay 0.54 0.08 0.58 3 ecuador 0.52 0.09 0.57 4 costa rica 0.52 0.10 0.57 5 dominican republic 0.53 0.07 0.56 6 mainland china 0.52 0.08 0.56 7 argentina 0.46 0.19 0.55 8 kazakhstan 0.49 0.12 0.55 9 turkey 0.49 0.10 0.54 10 malaysia 0.51 0.04 0.53 11 colombia 0.45 0.13 0.52 12 brazil 0.43 0.15 0.51 13 russia 0.38 0.22 0.49 14 armenia 0.37 0.21 0.48 15 mexico 0.45 0.05 0.47 16 albania 0.42 0.08 0.46 17 indonesia 0.42 0.00 0.42 18 georgia 0.28 0.20 0.38 19 bosnia and herzegovina 0.30 0.16 0.37 20 bulgaria 0.28 0.18 0.37 21 montenegro 0.22 0.22 0.33 22 average 0.50 after obtaining the criterion weights, we find the rankings of country performances in the struggle against covid-19 by employing the rov approach. since the first three steps in the rov approach are the same as the weighting procedure of the standard deviation model, the normalized decision matrix shown in table 4 is used for the rov method as well. the best and worst utility values are computed according to eq. (7) assessing country performances during the covid-19 pandemic: a standard deviation based range of value method 73 and eq. (8). next, for each alternative, the mid values (ui) are calculated by using eq. (9). according to these values, countries, which constitute the alternatives, are ranked. the overall results of the rov method are given in table 7. the results in table 7 demonstrate that thailand, iran, and paraguay perform the best in the fight against the covid-19 pandemic, while bosnia and herzegovina, bulgaria, and montenegro are the worst-performing countries. the average performance score is 0.4984. the starting point of the pandemic, mainland china has the 7th ranking. from table 7, it is seen that the high-performing countries have lower covid-19 deaths, higher healthcare expenditures, lower poverty rates, and much lower rates of cardiovascular diseases. bosnia and herzegovina and bulgaria, the countries with the lowest performance, have higher covid-19 deaths and the highest elderly population in the sample. montenegro is one of the countries with the lowest covid-19 deaths. since the beginning of the pandemic, montenegro has applied strict physical distancing rules. however, when the population characteristics are closely observed, it is seen that smoking and diabetes are very common. the cardiovascular death rates are elevated. together with the large elderly population, the struggle against the current pandemic becomes tougher. interestingly, the countries with the lowest performance have relatively high levels of current health expenditures and hospital bed capacity. in the case of bulgaria, the lack of the medical workforce, especially in terms of nursing staff created difficulties for the treatment of covid-19 disease. particularly during the wave of october 2020, the number of infected medical professionals increased heavily and generated a shortage in workforce capacity3. the bulgarian government was also criticized for not putting into force necessary non-healthcare precautions timely. the physical distancing rules were started to be applied late. bosnia and herzegovina, on the other hand, caught relatively short of the covid-19 pandemic. there was no initial emergency action plan in the country for such a disaster. although the healthcare resources are higher than the sample average in terms of expenditures and hospital beds, the resources seem to be inefficiently managed during the pandemic4. these findings indicate that each country struggles with this global health crisis with its own resources. healthcare capacity and the amount of healthcare expenditure matter, albeit, are not enough. the efficient management of available resources and the existence of an emergency action plan are also necessary. in addition, these three countries have the highest elderly percentage in the sample. an older population increases the demand for long term healthcare attention (yiğit, 2020). this situation raises the burden on the overall system particularly in times of crisis and limits the success of the “flattening the curve” efforts. 3covid-19 health system response monitor (hsrm) https://www.covid19healthsystem.org/countries/bulgaria/livinghit.aspx?section=2.2%20wo rkforce&type=chapter#7physicalinfrastructure access date: 09.07.2021 4 covid-19 health system response monitor (hsrm) https://www.covid19healthsystem.org/countries/bosniaandherzegovina/livinghit.aspx?secti on=2.1%20physical%20infrastructure&type=section access date: 09.07.2021 https://www.covid19healthsystem.org/countries/bulgaria/livinghit.aspx?section=2.2%20workforce&type=chapter#7physicalinfrastructure https://www.covid19healthsystem.org/countries/bulgaria/livinghit.aspx?section=2.2%20workforce&type=chapter#7physicalinfrastructure https://www.covid19healthsystem.org/countries/bosniaandherzegovina/livinghit.aspx?section=2.1%20physical%20infrastructure&type=section https://www.covid19healthsystem.org/countries/bosniaandherzegovina/livinghit.aspx?section=2.1%20physical%20infrastructure&type=section türkoğlu and tuzcu/oper. res. eng. sci. theor. appl. 4 (3) (2021) 59-81 74 when we turn our attention to the asian countries, we observe that thailand, malaysia, and mainland china are among the least affected countries by the covid-19 pandemic in the world (olivia et al., 2020). thailand has a very low rate of covid-19 deaths which brings the country to the first ranking. in fact, it is the only middle-high income country that has a position in the top ten health systems in the global health security index ratings5. together with mainland china, thailand is among the countries that apply very strict measures since the beginning of the pandemic. the country had an influenza pandemic plan and people have been used to wear face masks because of previous epidemics and air pollution (issac et al., 2021). issac et al. (2021) indicate that the success behind thailand’s covid-19 management is due to the primary healthcare workers that also surveil individual mobility and high usage of technological tools. mainland china has the 7th ranking in this comparison. china is known for its very restrictive measures since the beginning of the pandemic. on the global level, it has a low amount of total deaths due to effective coordination between its local and central administrations and the applied social control levels (jiang, 2020). comparing to the country figures in our sample, mainland china has covid-19 deaths less than the sample average as well. it is position is mostly due to its averaged current healthcare expenditure levels and relatively higher cardiovascular death rates in society. malaysia has the average performance ranking according to our analysis (11th place). the country has lower covid-19 deaths. its population is relatively young and the cardiovascular deaths rates are close to the sample average. hamzah et al. (2021) investigate the performance of malaysia against covid-19 very thoroughly with a network dea approach. they examine the performance into three sub-areas, namely community surveillance, non-critical and critical medical care needs. they show that the highest inefficiency is originated from the medical care that must be applied to patients with critical conditions. the country demonstrates efficient contact tracking and surveillance, on the other hand. hamzah et al. (2021) point out that this is mostly because of the existing emergency plans and the country’s elevated preparedness levels. the inference of hamzah et al. (2021) is also confirmed by our analysis. we observe that malaysia has much lower current health expenditures than the sample average which lowers the position of the country and causes a middle ranking despite its high preparedness level. in contrast to most asian countries, indonesia produces a much lower performance in the struggle against the pandemic. de nardo et al. (2020) indicate that in low and middle-income countries, the poverty rates are higher, so implementing the social distancing rules is much difficult as well as accessing clean water. this is the case with indonesia. it is mostly due to very high rates of extreme poverty, cardiovascular disease prevalence, low amount of hospital beds per capita (olivia et al., 2020). setiati and azwar, (2020) point out that the number of beds in intensive care units per capita is among the lowest in asian countries. they are mostly located in specific areas, so 5 this global index compares 195 countries according to 6 categories, including disease prevention, detection and reporting, and health system capabilities. according to this index, thailand has an 73.2 index score and had 6th place out of 195 countries in 2019. https://www.ghsindex.org/about/ and ghs homepage https://www.ghsindex.org/ access date: 06.08.2021 https://www.ghsindex.org/about/ https://www.ghsindex.org/ assessing country performances during the covid-19 pandemic: a standard deviation based range of value method 75 not evenly distributed. healthcare workers cannot reach enough protective suits while dealing with covid-19 patients. the country has also been criticized for reacting late to the initial cases while its neighbors, malaysia and singapore, had already started mass testing (olivia et al., 2020). turkey has 10th place in the performance ranking. the country has lower health expenditures and hospital bed capacity than the sample average. it owes its relatively high position to the low number of covid-19 deaths, much lower cardiovascular disease rates, and younger population. it had an influenza pandemic plan before the current pandemic which facilitated being prepared for the spread of this disease. as noted by jamison et al. (2020), the efforts of “flattening the curve” play a significant role in those rankings. the delay in the implementation of such measures can also be a determinant. brazil, for instance, does not have a high rate of chronic diseases or deaths, has a relatively younger population and expenditures for the healthcare system as a percentage of gdp are relatively higher. however, the brazilian government has minimized the necessary precautions. the social distancing implementations are very weak and the extreme poverty in the country is high. this explains the very high rates of deaths related to covid-19. in contrast to brazil, the countries located in central and south america mostly demonstrated good performance against covid-19. paraguay, ecuador, costa rica, and the dominican republic have positions from 3rd to 6th in the sample. among these countries, ecuador and costa rica have advanced global health index rankings 6. the population percentage of 65 years and over is relatively small in paraguay. the country also experiences a small number of covid-19 deaths. undp paraguay report (2020) reveals that the country was fighting the dengue epidemic when the covid-19 pandemic started. because of the previous experience from the dengue outbreak, the paraguay government responded quickly to this new disease and applied physical distance measures and movement restrictions early. we observe that a bigger healthcare capacity and lower poverty levels maintain a strong stance against health system crises even with higher levels of disease spread. as the healthcare system becomes larger and more evenly distributed, this battle gets easier. however, as we see from the bosna and herzegovina example, the efficient usage of the existing capacity is crucial to be successful. the initial preparedness of the countries and their willingness to apply social distancing measures are also important to limit the number of deaths. brazil, for example, has a relatively greater overall score in the rankings of the global health security index. however, the government’s reluctance to put in force necessary measures caused a significant number of deaths. poverty levels, on the other hand, determine the applicability of non-healthcare precautions. in the countries where most of the population lives below the poverty line, it is almost impossible to achieve physical distancing and personal hygiene. this environment accelerates the new numbers of covid-19 cases. taken together with the limited healthcare facilities, it is natural to observe a higher number of deaths. 6https://www.ghsindex.org/country/ecuador/ and https://www.ghsindex.org/country/costarica/ access date: 06.08.2021. https://www.ghsindex.org/country/ecuador/ https://www.ghsindex.org/country/costarica/ türkoğlu and tuzcu/oper. res. eng. sci. theor. appl. 4 (3) (2021) 59-81 76 5. sensitivity analysis to show that our findings from the sdv based rov approach are robust, we also conduct topsis and edas analyses and compare the results. as discussed before, the rov method depends on the comparison of best and worst utility functions for each alternative. based on these utility functions, we obtain the rankings of alternatives in an easy manner. topsis method, which is widely used in different areas (for example, mimović et al. 2021), computes distances from positive ideal and negative ideal solutions. the alternative is ranked based on its proximity to the positive ideal and its remoteness from the negative ideal. the edas method, however, calculates the distances from average solutions. the positive and negative ideals are not required to be estimated (ghorabaee et al., 2015). we apply both topsis and edas methods by employing the criteria weights obtained from sdv analysis. the comparisons of the rankings from these three methods are demonstrated in figure 2. figure 2: the rankings from rov, edas, and topsis methods respectively the comparisons show that the rankings from these three methods are quite parallel to each other. particularly, the rankings of the low-performing countries stay very similar. in addition to the visual analysis, we also look at the spearman rank correlations and wilcoxon rank tests. the former one is applied to observe the direction and strength of the relation between the ranks obtained from these three methods. the latter test shows whether the mean ranks are statistically different. both are non-parametric tests since mcdm analysis provides results that are not normally distributed. the findings are presented in table 8. 0 5 10 15 20 25 a lb a n ia a rg e n ti n a a rm e n ia b o sn ia a n d h e rz e g o v in a b ra zi l b u lg a ri a c o lo m b ia c o st a r ic a d o m in ic a n r e p u b li c e cu a d o r g e o rg ia in d o n e si a ir a n k a za k h st a n m a in la n d c h in a m a la y si a m e xi co m o n te n e g ro p a ra g u a y r u ss ia t h a il a n d t u rk e y rov edas topsis assessing country performances during the covid-19 pandemic: a standard deviation based range of value method 77 table 8. the results for spearman rank correlations and wilcoxon rank tests spearman rank correlations rov edas topsis rov 1 edas 0.69 1 topsis 0.61 0.97 1 wilcoxon rank tests h0 rov=edas rov=topsis z 0.488 0.261 p-value 0.626 0.806 the findings from spearman rank correlations indicate that the rov method produces positive and fairly high association with edas and topsis methods (0.69 and 0.61 respectively). in the second part of table 8, the mean ranking of rov is tested against edas and topsis. the null hypotheses here are the mean ranking of rov is not different than the mean ranking of edas and topsis respectively (first and second columns). the p-values for both tests are much higher than any acceptable significance levels, so the null hypotheses cannot be rejected. the overall results suggest that the rov method has a computational advantage over more popular methods such as topsis and edas and offers similar rankings. 6. conclusion this study aims to shed light on the black-box nature of the covid-19 pandemic by comparing the country's performances in this global struggle. to do so, the performance of 22 countries, which all belong to high–middle income group according to the world bank classifications, are assessed. since several and conflicting criteria are used, the performance ranking against managing the current pandemic is considered a multicriteria decision-making problem. the benchmarking is made with the standard deviation-based rov approach. to the extent of our knowledge, this is the first study that combines these two methods and applies them to the covid-19 pandemic. in the struggle against covid-19, there are some important parameters such as the properties of the healthcare system, application of physical distancing rules and mobility restrictions, and the population characteristics. among them, particularly the healthcare capacity, proxied by the number of hospital beds and the current healthcare expenditures, becomes prominent. our analysis confirms this expectation and demonstrates that thailand has the highest ranking in our sample. the country’s very high position in the global health security index and the very low number of covid-19 deaths are no surprise, in this sense. however, the findings from the lowest ranking countries reveal that the efficient usage of healthcare resources matters as much as its amount. these countries have a relatively high amount of healthcare resources, but they have still experienced elevated numbers of covid-19 deaths. as seen from the bosnia and herzegovina case, the lack of an emergency healthcare plan makes much more difficult to obtain efficiency in the usage of resources. we also observe that the high-ranked countries are mostly praised for their quick response to take necessary non-healthcare restrictive precautions and the low-ranked türkoğlu and tuzcu/oper. res. eng. sci. theor. appl. 4 (3) (2021) 59-81 78 ones are highly criticized for the same reason. it is seen that many asian countries, for instance, thailand, mainland china, and malaysia, applied strict social distancing rules, whereas brazil, bulgaria, and indonesia are the ones where these rules are weak or sometimes non-existent. our analysis also confirms that population characteristics are other determinants of country performances against covid-19. the low-ranking countries mostly have an elder population. age brings co-morbidities with itself which increases the likelihood of covid-19 deaths. it also boosts the requirement of long-term healthcare attention, which creates another burden on the already overwhelmed healthcare system. another population characteristic that affects country rankings is the level of poverty. in countries, where the poverty level is higher, implementing the social distancing rules and distant working becomes almost impossible. in fact, we show that extreme poverty is as crucial as the number of hospital beds in this battle. combining the fact that these areas have diminished access to clean water, the spread of the disease is inevitable. this is one of the social consequences of covid-19: it contributes to the gap between rich and poor. policymakers should consider policies that decrease the level of poverty to control future pandemics as well. the vaccination policies against covid-19 will also have importance. since the delivery of vaccines requires more time in the middle-high income countries in comparison to their developed counterparts, the public must comply with the social distancing rules to avoid future deaths. for future pandemics, countries that manage their healthcare resources more efficiently and that are quick to apply social distancing rules will be more successful to eliminate the negative impacts. however, policymakers must also focus on elderly care and poverty levels in their countries. there are some limitations of this study that must be mentioned: first, the very quick changes in the pandemic landscape restrict the generalizability of the findings to some extent. this is why the covid-19 studies that compare the beginning of the pandemic to the ongoing situation are valuable. second, we have only used quantitative data in this analysis. further researches may consider qualitative data and appropriate techniques such as fuzzy mdcm to compare the performance of countries. last, at the beginning of the pandemic, the definitions of covid-19 deaths and patients were not clear for all countries7. in time, there has been a convergence in these definitions. however, this situation may create a limitation for this study in terms of comparability. acknowledgments: a preliminary version of this paper was presented at the international covid-19 and current issues congress, march 12-14, 2021. the authors would like to thank the participants and reviewers of the conference for their valuable comments and suggestions. 7some countries have made a distinction between “deaths from covid-19” and “deaths with covid-19”. the same difference was valid at the beginning of the pandemic for the positive cases. some counted a person as covid-19 patient depending on the clinical diagnosis, others required a positive test result. source:https://eurohealthobservatory.who.int/monitors/hsrm/analyses/hsrm/howcomparable-is-covid-19-mortality-across-countries access date: 05.08.2021 https://eurohealthobservatory.who.int/monitors/hsrm/analyses/hsrm/how-comparable-is-covid-19-mortality-across-countries https://eurohealthobservatory.who.int/monitors/hsrm/analyses/hsrm/how-comparable-is-covid-19-mortality-across-countries assessing country performances during the covid-19 pandemic: a standard deviation based range of value method 79 author contributions: all authors contributed equally to this paper and have approved this version. conflicts of interest: the authors declare no conflict of interest. references adabavazeh, n., nikbakht, m., & amirteimoori, a. 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(2020). the performance of oecd countries in combating with covid 19 pandemics: a cross-sectional study. journal of current researches on social sciences, 10(10 (2)), 399–416. https://doi.org/10.26579/jocress.372 © 2021 by the authors. submitted for possible open access publication under the terms and conditions of the creative commons attribution (cc by) license (http://creativecommons.org/licenses/by/4.0/). assessing country performances during the covid-19 pandemic: a standard devıatıon based range of value method serap pelin türkoğlu1, sevgi eda tuzcu2* 1. introduction 2. related literature 3. data and methodology 3.1. standard deviation method 3.2. range of value (rov) method 4. findings 5. sensitivity analysis 6. conclusion references plane thermoelastic waves in infinite half-space caused operational research in engineering sciences: theory and applications vol. 2, issue 1, 2019, pp. 91-107 issn: 2620-1607 eissn: 2620-1747 doi:_https://doi.org/10.31181/oresta1901085d * corresponding author. elma_durmic@hotmail.com the evaluation of the criteria for sustainable supplier selection by using the fucom method elmina durmić university of east sarajevo, faculty of transport and traffic engineering doboj received: 20 february 2019 accepted: 12 april 2019 first online: 13 april 2019 original scientific paper abstract. the selection of a sustainable supplier has a strategic significance and represents the critical phase for the whole sustainable supply chain. the process of the functioning of the supply chain depends on this activity. this paper is aimed at defining the most important criteria for the assessment and selection of a sustainable supplier in the company for lime production. for the purpose of decision-making in this process, a team of experts was formed for the comparison and assessment of the criteria grouped at two levels. at the first level, there are the economic, social and environmental criteria which consist of the seven sub-criteria for each of the main groups. in order to determine the significance of the criteria, the full consistency method (fucom) was applied. the obtained results show the significance of the criteria at both decision-making levels with respect to the selection of a sustainable supplier. an adequate supplier selection is carried out by using the sustainable criteria that will ensure a possibility of having both timely and quality production. this generates competition growth in the market for companies. key words: sustainable supplier selection, fucom, evaluation of criteria, decision-making 1. introduction sustainable supply chains have a large influence on the modern market, so the problem of the selection of a sustainable supplier is very important and frequent in all fields. the selection of sustainable suppliers is a constant process that requires the consideration of a certain number of the criteria needed to make a decision on the selection of the most suitable suppliers (büyüközkan and çifçi, 2011; luhtra et al. 2017; ayadnia et al. 2015). modern business conditions require a business to quickly adapt to changes in the environment. in line with developments in the market, business entities need adequate sustainable supply chains (stojanović et al., 2017; stević et al. 2019). a well-designed supply chain management system is important for improving competitive advantage in the era of international economics and the rapid development of information technology (liu and wang, 2007). manufacturing companies are highly dependent on their suppliers. due to the constant changes that the market is exposed to durmić/oper. res. eng. sci. theor. appl. 2 (1) (2019) 91-107 92 and the ever-growing demands, it is certainly challenging to maintain a competitive position (stević, 2017). according to kagnicioglu (2006), the selection of suppliers is a critical procurement activity in the supply chain management due to the key role of the supplier characteristics on the price, quality, delivery, and service in achieving the supply chain objectives. the aim of the supplier selection is to identify suppliers with the greatest potential to meet the company’s needs and at an acceptable price (de boer et al. 2001). one of the important issues in the process of selecting a sustainable supplier is choosing the appropriate method and criteria for the selection of a supplier. essentially, group decision-making according to multiple criteria is the problem in choosing a sustainable supplier in the supply chain system. in solving this problem, the degree of uncertainty, the number of decision-makers, and the nature of the criteria must be taken into account (chen et al., 2006). the rest of the paper is structured as follows: the second section describes the steps of the used method, i.e. the fucom method. in the third section, the problem postulate with the hierarchical structure of the model and a detailed explanation of the used criteria. in the fourth section, the fucom method is applied in the group decision-making process for the two levels of hierarchy. after that, the fifth section shows a discussion of the obtained results, while in the sixth section the conclusions of the study are presented. 2. fucom (full consistency method) the fucom method was developed by pamučar et al. (2018) for the purpose of determining criteria weights. so, for now, the method has been applied in a few studies (prentkovskis et al. 2018; zavadskas et al. 2018; fazllolahtabar 2019; matić et al 2019). the steps of the fucom method are as follows: step 1 in this step, the criteria from the predefined set of the evaluation criteria  1 2, ,..., nc c c c= . the ranking is performed according to the significance of the criteria, i.e. starting from the criterion which is expected to have the highest weight coefficient to the criterion of the least significance: (1) (2) ( ) ... j j j k c c c   (1) step 2 in this step, a comparison of the ranked criteria is carried out and the comparative priority ( / ( 1)k k  + , 1, 2,...,k n= , with k representing the rank of the criteria) of the evaluation criteria is determined: ( )1/ 2 2/3 / ( 1), ,..., k k   + = (2) step 3 in this step, the final values of the weight coefficients of the evaluation criteria ( )1 2, ,..., t n w w w are calculated. the final values of the weight coefficients should satisfy the following two conditions: (1) the ratio of the weight coefficients is equal to the comparative priority among the observed criteria ( / ( 1)k k  + ) defined in step 2, i.e. the following condition is met: the evaluation of the criteria for sustainable supplier selection by using the fucom method 93 / ( 1) 1 k k k k w w  + + = (3) (2) in addition to the condition (2), the final values of the weight coefficients should satisfy the condition of mathematical transitivity, i.e. t / ( 1) ( 1) / ( 2) / ( 2) k k k k k k    + + + +  = . then / ( 1) 1 k k k k w w  + + = and 1 ( 1) / ( 2) 2 k k k k w w  + + + + = 1 1 2 2 k k k k k k w w w w w w + + + +  = are obtained. thus, the second condition that the final values of the weight coefficients of the evaluation criteria should meet is obtained, namely: / ( 1) ( 1) / ( 2) 2 k k k k k k w w   + + + + =  (4) based on the defined settings, the final model for determining the final values of the weight coefficients of the evaluation criteria can be defined as: (5) 3. problem postulate this research study was performed with the aim of determining the most important criteria for the selection of a sustainable supplier, which depends on the precise determination and selection of adequate criteria. the evaluation of the criteria was performed by a group of the experts employed in the company which is the subject matter of the research study (a lime production company). figure 1 shows the hierarchical structure of the criteria evaluation at both levels of decision-making: ( ) / ( 1) ( 1) ( ) / ( 1) ( 1)/ ( 2) ( 2) 1 min . . , , 1, 0, j k k k j k j k k k k k j k n j j j s t w j w w j w w j w j       + + + + + + = − =  −  =  =     durmić/oper. res. eng. sci. theor. appl. 2 (1) (2019) 91-107 94 figure 1. the hierarchical structure of the proposed model table 1 shows the criteria for the selection of a sustainable supplier and their respective definitions. all of the criteria displayed below were used in this study. table 1. the criteria for the selection of a sustainable supplier and their respective definitions seq. no name definition c1 economic c11 costs/prices the final cost of purchasing a unit of raw or semi-finished product c12 quality quality is the degree to which a set of product characteristics meet customer requirements c13 flexibility the demand that can be profitably sustained, and the time or the cost required for adding new products to the existing production operations c14 productivity satisfying customer needs and delivery on time c15 financial ability the capital needed to maintain the normal business activities of an enterprise during a certain period of time c16 partnership relations determining the willingness to establish long-term and close business relations with suppliers to jointly develop the market c17 technology capability the sum of all the knowledge of an enterprise in support of technological innovation. c2 social c21 reputation reputation marks the general opinion of the supplier which relates to the supplier’s reputation c22 safety and health at work this criterion concerns the safety, health, and welfare of people at work c23 employees’ rights a group of legal rights and claimed human rights related to the labor relations between workers and their employers the evaluation of the criteria for sustainable supplier selection by using the fucom method 95 c24 local community influence neighboring relations between the company and the local government, the community and all the residents, representing the public image of the organization c25 training of employees the process of enhancing the employees’ skills and capabilities for and knowledge of a particular job c26 respect of rights and policies enterprises comply with all the laws and regulations of the country, assume legal obligations, and promote good social public morals c27 disclosing information providing information to stakeholders about the materials used, carbon emissions, toxins released during production, and so on c3 environmental c31 green image the identity that consumers prioritize environmental conservation and sustainable business practices c32 recycling the reuse of the used materials and energy c33 pollution control the control of the pollutants released into the air, water, or soil c34 environmental protection management system a system that comprehensively evaluates the internal and external environmental performances of an organization. c35 eco design an approach to designing products, with a special consideration for the environmental impacts of a product during its whole lifecycle. c36 consumption of resources the use of nonrenewable or, less frequently, renewable resources c37 green competences the capacity to balance the containment relationships between economic and environmental performance 4. the evaluation of the criteria for the selection of a sustainable supplier 4.1. the determination of the criteria weights at the first level of decisionmaking first, the decision-makers (dms) ranked and made a comparison of the criteria at the first level of decision-making. after that, the steps of the fucom method for the calculation of their normalized values were applied as follows: step 1: in this step, the team of experts performed the ranking of the criteria. dm1: c1>c2>c3; dm2: c1>c2>c3; dm3: c1>c2>c3; step 2: in this step, the decision-makers performed a comparison of the previously ranked criteria. in that way, the significance of the criteria ( ) (table 2) was obtained. table 2. the significance of the criteria at the first level dm1 criteria c1 c3 c2 significance ( ( )j kc  ) 1 1.9 2.5 dm2 criteria c1 c2 c3 significance ( ( )j kc  ) 1 2.1 2.5 dm3 criteria c1 c3 c2 significance ( ( )j kc  ) 1 1.8 2.4 ( )j kc  durmić/oper. res. eng. sci. theor. appl. 2 (1) (2019) 91-107 96 based on the obtained significance of the criteria, it is necessary to calculate the comparative priority of the criteria for each one of the decision-makers: dm1: 1 2/ 1.9 / 1 1.9 c c  = = , 2 3/ 2.5 / 1.9 1.32 c c  = = ; dm2: 1 2/ 2.1 / 1 2.1 c c  = = , 2 3/ 2.5 / 2.1 1.19 c c  = = ; dm3: 1 2/ 1.8 / 1 1.8 c c  = = , 2 3/ 2.4 / 1.8 1.33 c c  = = step 3: in this step, the final values of the weight coefficients were calculated and they should meet the two conditions (3) and (4): condition (3): dm1: 1 2 / 1.9w w = , 2 3 / 1.32w w = ; dm2: 1 2 / 2.1w w = , 2 3 / 1.19w w = ; dm3: 1 2 / 1.8w w = , 2 3 / 1.33w w = and the condition (4): 1 3 / 2.51w w = , 1 3 / 2.50w w = , 1 3 / 2.39w w = by applying expression (5), the final model for the determination of the weight coefficients can be defined as follows: 1 2 2 3 1 3 3 1 1 min 1.9 , 1.32 , . . 2.51 , 1, 0, j j j dm w w w w w s t w w w j    =  − = − =    −    =      1 2 2 3 1 3 3 1 2 min 2.1 , 1.19 , . . 2.50 , 1, 0, j j j dm w w w w w s t w w w j    =  − = − =    −    =      1 2 2 3 1 3 3 1 3 min 1.8 , 1.33 , . . 2.39 , 1, 0, j j j dm w w w w w s t w w w j    =  − = − =    −    =      by solving the presented model by using the lingo 17 software, the final values of the weight coefficients were obtained for the first level of decision-making (table 3). the evaluation of the criteria for sustainable supplier selection by using the fucom method 97 table 3. the final values of the weight coefficients obtained for the first level of decision-making dm1 dm2 dm3 c1 0.519 0.533 0.507 c2 0.273 0.254 0.282 c3 0.208 0.213 0.211 dfc 0.000 0.000 0.000 4.2. the determination of the criteria weights at the second level of decisionmaking the dms performed the ranking of the criteria at the second level, and the significances of the criteria were obtained for each group. the calculation of the criteria weights for the second level of decision-making was done in the same way as for the first level. the obtained final values for the sub-criteria are shown in tables 4 and 5 for the group of the economic criteria, in tables 6 and 7 for the group of the social criteria, and in tables 8 and 9 for the group of the environmental criteria. 4.2.1. determining the sub-criteria weights of the group of the economic criteria step 1: dm1: c2>c1>c4>c6>c5>c7>c3; dm2: c2>c4>c3>c5>c1>c6>c7; dm3: c2>c1>c4>c6>c3>c5>c step 2: table 4. the significance of the criteria at the second level for the group of the economic criteria dm1 economic factors c12 c11 c14 c16 c15 c17 c13 ( )j kc  1 1.2 1.7 2.0 2.4 2.8 3.1 dm2 economic factors c12 c14 c13 c15 c11 c16 c17 ( )j kc  1 1.4 1.7 2.2 2.4 2.6 3.0 dm3 economic factors c12 c11 c14 c16 c13 c15 c17 ( )j kc  1 1.6 1.8 2.2 2.6 2.9 3.1 dm1: 2 1/ 1.2 / 1 1.2 c c  = = , 1 4/ 1.7 / 1.2 1.42 c c  = = , 4 6/ 2.0 / 1.7 1.18 c c  = = 6 5/ 2.4 / 2.0 1.2 c c  = = 5 7/ 2.8 / 2.4 1.17 c c  = = , 7 3/ 3.1 / 2.8 1.11 c c  = = ; dm2: 2 4/ 1.4 / 1 1.4 c c  = = , 4 3/ 1.7 / 1.4 1.21 c c  = = , 3 5/ 2.2 / 1.7 1.29 c c  = = 5 1/ 2.4 / 2.2 1.09 c c  = = , 1 6/ 2.6 / 2.4 1.08 c c  = = , 6 7/ 3.0 / 2.6 1.15 c c  = = ; durmić/oper. res. eng. sci. theor. appl. 2 (1) (2019) 91-107 98 dm3: 2 1/ 1.6 / 1 1.6 c c  = = , 1 4/ 1.8 / 1.6 1.13 c c  = = , 4 6/ 2.2 / 1.8 1.22 c c  = = 6 3/ 2.6 / 2.2 1.18 c c  = = , 3 5/ 2.9 / 2.6 1.12 c c  = = , 5 7/ 3.1 / 2.9 1.07 c c  = = ; step 3: 1) dm1: 2 1 / 1.2w w = , 1 4 / 1.42w w = , 4 6 / 1.18w w = , 6 5 / 1.2w w = , 5 7 / 1.17w w = , 7 3 / 1.11w w = ; dm2: 2 4 / 1.4w w = , 4 3 / 1.21w w = , 3 5 / 1.29w w = , 5 1 / 1.09w w = , 1 6 / 1.08w w = , 6 7 / 1.15w w = ; dm3: 2 1 / 1.6w w = , 1 4 / 1.13w w = , 4 6 / 1.22w w = , 6 3 / 1.18w w = , 3 5 / 1.12w w = , 5 7 / 1.07w w = ; 2) dm1: 2 4 / 1.7w w = , 1 6 / 1.68w w = , 4 5 / 1.42w w = , 6 7 / 1.4w w = , 5 3 / 1.3w w = ; dm2: 2 3 / 1.69w w = , 4 5 / 1.56w w = , 3 1 / 1.41w w = , 5 6 / 1.18w w = , 1 7 / 1.24w w = ; dm3: 2 4 / 1.81w w = , 1 6 / 1.38w w = , 4 3 / 1.44w w = , 6 5 / 1.32w w = , 3 7 / 1.20w w = ; 6 52 1 4 1 4 6 5 7 7 62 1 4 3 4 6 5 7 5 3 3 1 1 min 1.2 , 1.42 , 1.18 = , 1.2 , 1.17 , 1.11 , 1.7 , 1.68 , 1.42 , 1.4 , . . 1.3 , 1, 0, j j j dm w ww w w w w w w w w ww w w w w w w w s t w w w w j             =  − = − = − − = − =    − = − = − = − = − =    − =   =     3 52 4 1 4 3 5 1 6 6 3 52 4 7 3 5 1 6 1 7 3 1 2 min 1.4 , 1.21 , 1.29 = , 1.09 , 1.08 , 1.15 , 1.69 , 1.56 , 1.41 , 1.18 , . . 1.24 , 1, 0, j j j dm w ww w w w w w w w w w ww w w w w w w s t w w w w j             =  − = − = − − = − =    − = − = − = − = − =    − =   =     the evaluation of the criteria for sustainable supplier selection by using the fucom method 99 6 32 1 4 1 4 6 3 5 5 62 1 4 7 4 6 3 5 3 7 3 1 3 min 1.6 , 1.13 , 1.22 = , 1.18 , 1.12 , 1.07 , 1.81 , 1.38 , 1.44 , 1.32 , . . 1.2 , 1, 0, j j j dm w ww w w w w w w w w ww w w w w w w w s t w w w w j             =  − = − = − − = − =    − = − = − = − = − =    − =   =     table 5. the values of the criteria for the second level of decision-making for each of the dms for the group of the economic criteria 4.2.2. determining the sub-criteria weights for the group of the social criteria step 1: dm1: c2>c6>c1>c3>c5>c7>c4; dm2: c2>c7>c5>c6>c3>c1>c4; dm3: c1>c2>c6>c7>c3>c5>c4 step 2: table 6. the significance of the criteria at the second level for the group of the social criteria dm1 dm2 dm3 c1 0.207 0.107 0.170 c2 0.249 0.257 0.271 c3 0.080 0.151 0.104 c4 0.146 0.184 0.151 c5 0.104 0.117 0.094 c6 0.124 0.099 0.123 c7 0.089 0.086 0.087 dfc 0.000 0.000 0.000 dm1 social factors c22 c26 c21 c23 c25 c27 c24 ( )j kc  1 1.5 1.6 1.9 2.1 2.3 2.5 dm2 social factors c22 c27 c25 c26 c23 c21 c24 ( )j kc  1 1.3 1.6 1.9 2.3 2.5 2.8 dm3 social factors c21 c22 c26 c27 c23 c25 c24 ( )j kc  1 1.3 1.6 2.0 2.2 2.5 3.0 durmić/oper. res. eng. sci. theor. appl. 2 (1) (2019) 91-107 100 dm1: 2 6/ 1.5 / 1 1.5 c c  = = , 6 1/ 1.6 / 1.5 1.07 c c  = = , 1 3/ 1.9 / 1.6 1.19 c c  = = , 3 5/ 2.1 / 1.9 1.11 c c  = = , 5 7/ 2.3 / 2.1 1.10 c c  = = , 7 4/ 2.5 / 2.3 1.09 c c  = = ; dm2: 2 7/ 1.3 / 1 1.3 c c  = = , 7 5/ 1.6 / 1.3 1.23 c c  = = , 5 6/ 1.9 / 1.6 1.19 c c  = = , 6 3/ 2.3 / 1.9 1.21 c c  = = , 3 1/ 2.5 / 2.3 1.09 c c  = = , 1 4/ 2.8 / 2.5 1.12 c c  = = ; dm3: 1 2/ 1.3 / 1 1.3 c c  = = , 2 6/ 1.6 / 1.3 1.23 c c  = = , 6 7/ 2.0 / 1.6 1.25 c c  = = , 7 3/ 2.2 / 2.0 1.1 c c  = = , 3 5/ 2.5 / 2.2 1.14 c c  = = , 5 4/ 3.0 / 2.5 1.2 c c  = = ; step 3: 1) dm1: 2 6 / 1.5w w = , 6 1 / 1.07w w = , 1 3 / 1.19w w = , 3 5 / 1.11w w = , 5 7 / 1.1w w = , 7 4 / 1.09w w = ; dm2: 2 7 / 1.3w w = , 7 5 / 1.23w w = , 5 6 / 1.19w w = , 6 3 / 1.21w w = , 3 1 / 1.09w w = , 1 4 / 1.12w w = ; dm3: 1 2 / 1.3w w = , 2 6 / 1.23w w = , 6 7 / 1.25w w = , 7 3 / 1.1w w = , 3 5 / 1.14w w = , 5 4 / 1.2w w = ; 2) dm1: 2 1 / 1.61w w = , 6 3 / 1.27w w = , 1 5 / 1.32w w = 3 7 / 1.22w w = 5 4 / 1.2w w = ; dm2: 2 5 / 1.6w w = , 7 6 / 1.46w w = , 5 3 / 1.44w w = , 6 1 / 1.32w w = , 3 4 / 1.22w w = ; dm3: 1 6 / 1.6w w = , 2 7 / 1.54w w = , 6 3 / 1.38w w = , 7 5 / 1.25w w = , 3 4 / 1.37w w = ; 6 3 52 1 6 1 3 5 7 7 6 32 1 4 1 3 5 7 5 4 3 1 1 min 1.5 , 1.07 , 1.19 = , 1.11 , 1.1 , 1.09 , 1.61 , 1.27 , 1.32 , 1.22 , . . 1.2 , 1, 0, j j j dm w w ww w w w w w w w w ww w w w w w w s t w w w w j             =  − = − = − − = − =    − = − = − = − = − =    − =   =     the evaluation of the criteria for sustainable supplier selection by using the fucom method 101 7 5 6 32 7 5 6 3 1 7 5 61 2 4 5 6 3 1 3 4 3 1 2 min 1.3 , 1.23 , 1.19 = , 1.21 , 1.09 , 1.12 , 1.60 , 1.46 , 1.44 , 1.32 , . . 1.22 , 1, 0, j j j dm w w w ww w w w w w w w ww w w w w w w s t w w w w j             =  − = − = − − = − =    − = − = − = − = − =    − =   =     6 7 31 2 2 6 7 3 5 5 6 71 2 4 6 7 3 5 3 4 3 1 3 min 1.3 , 1.23 , 1.25 = , 1.1 , 1.14 , 1.2 , 1.6 , 1.54 , 1.38 , 1.25 , . . 1.37 , 1, 0, j j j dm w w ww w w w w w w w w ww w w w w w w s t w w w w j             =  − = − = − − = − =    − = − = − = − = − =    − =   =     table 7. the values of the criteria for the second level of decision-making for each of the dms for the group of the social criteria dm1 dm2 dm3 c1 0.151 0.097 0.245 c2 0.242 0.243 0.188 c3 0.127 0.106 0.111 c4 0.097 0.087 0.082 c5 0.115 0.152 0.098 c6 0.161 0.128 0.153 c7 0.105 0.187 0.122 dfc 0.000 0.000 0.000 durmić/oper. res. eng. sci. theor. appl. 2 (1) (2019) 91-107 102 4.2.3. determining the sub-criteria weights for the group of the environmental criteria step 1: dm1: c3>c1>c5>c2>c4>c7>c6; dm2: c3>c2>c4>c5>c7>c6>c1; dm3: c3>c2>c1>c5>c7>c4>c6; step 2: table 8. the significance of the sub-criteria for the group of the environmental criteria dm1 environmental factors c33 c31 c35 c32 c34 c37 c36 ( )j kc  1 1.2 1.3 1.4 1.7 2.0 2.3 dm2 environmental factors c33 c32 c34 c35 c37 c36 c31 ( )j kc  1 1.1 1.3 1.6 1.9 2.3 2.5 dm3 environmental factors c33 c32 c31 c35 c37 c34 c36 ( )j kc  1 1.3 1.6 1.9 2.1 2.4 2.9 dm1: 3 1/ 1.2 / 1 1.2 c c  = = , 1 5/ 1.3 / 1.2 1.08 c c  = = , 5 2/ 1.4 / 1.3 1.08 c c  = = , 2 4/ 1.7 / 1.4 1.21 c c  = = , 7 4/ 2.0 / 1.7 1.18 c c  = = , 7 6/ 2.3 / 2.0 1.15 c c  = = ; dm2: 3 2/ 1.1 / 1 1.1 c c  = = , 2 4/ 1.3 / 1.1 1.18 c c  = = , 4 5/ 1.6 / 1.3 1.23 c c  = = , 5 7/ 1.9 / 1.6 1.19 c c  = = , 7 6/ 2.3 / 1.9 1.21 c c  = = , 6 1/ 2.5 / 2.3 1.09 c c  = = ; dm3: 3 2/ 1.3 / 1 1.3 c c  = = , 2 1/ 1.6 / 1.3 1.23 c c  = = , 1 5/ 1.9 / 1.6 1.19 c c  = = , 5 7/ 2.1 / 1.9 1.11 c c  = = , 7 4/ 2.4 / 2.1 1.14 c c  = = , 4 6/ 2.9 / 2.4 1.21 c c  = = ; step 3: 1) dm1: 3 1 / 1.2w w = , 1 5 / 1.08w w = , 5 2 / 1.08w w = , 2 4 / 1.21w w = , 4 7 / 1.18w w = , 7 6 / 1.15w w = ; dm2: 3 2 / 1.1w w = , 2 4 / 1.18w w = , 4 5 / 1.23w w = , 5 7 / 1.19w w = , 7 6 / 1.21w w = , 6 1 / 1.09w w = ; dm3: 3 2 / 1.3w w = , 2 1 / 1.23w w = , 1 5 / 1.19w w = , 5 7 / 1.11w w = , 7 4 / 1.14w w = , 4 6 / 1.21w w = ; 2) dm1: 3 5 / 1.3w w = , 1 2 / 1.17w w = , 5 4 / 1.31w w = , 2 7 / 1.43w w = , 4 6 / 1.36w w = ; dm2: 3 4 / 1.3w w = , 2 5 / 1.45w w = , 4 7 / 1.46w w = , 5 6 / 1.44w w = , 7 1 / 1.32w w = ; dm3: 3 1 / 1.6w w = , 2 5 / 1.46w w = , 1 7 / 1.32w w = , 5 4 / 1.27w w = , 7 6 / 1.38w w = ; the evaluation of the criteria for sustainable supplier selection by using the fucom method 103 3 51 2 4 1 5 2 4 7 7 3 51 2 6 5 2 4 7 4 6 3 1 1 min 1.2 , 1.08 , 1.08 = , 1.21 , 1.18 , 1.15 , 1.3 , 1.17 , 1.31 , 1.43 , . . 1.36 , 1, 0, j j j dm w ww w w w w w w w w w ww w w w w w w s t w w w w j             =  − = − = − − = − =    − = − = − = − = − =    − =   =     3 5 72 4 2 4 5 7 6 6 3 52 4 1 4 5 7 6 7 1 3 1 2 min 1.1 , 1.18 , 1.23 = , 1.19 , 1.21 , 1.09 , 1.3 , 1.45 , 1.46 , 1.44 , . . 1.32 , 1, 0, j j j dm w w ww w w w w w w w w ww w w w w w w s t w w w w j             =  − = − = − − = − =    − = − = − = − = − =    − =   =     3 5 72 1 2 1 5 7 4 3 54 2 1 6 1 5 7 4 7 6 3 1 3 min 1.3 , 1.23 , 1.19 = , 1.11 , 1.14 , 1.21 , 1.6 , 1.46 , 1.32 , 1.27 , . . 1.38 , 1, 0, j j j dm w w ww w w w w w w w ww w w w w w w w s t w w w w j             =  − = − = − − = − =    − = − = − = − = − =    − =   =     durmić/oper. res. eng. sci. theor. appl. 2 (1) (2019) 91-107 104 table 9. the values of the criteria for the 2nd level of decision-making for each of the dms for the group of the environmental criteria table 10 accounts for the final values of the criteria and the sub-criteria weights (the global and the local ranks). the final values for the global rank were obtained by the multiplication of the values of the main criteria by the obtained values within the group which they belong to. table 10. the final results of the proposed model criteria wj sub-criteria local weights global weights local rank global rank 1. economic 0.520 1.1 cost/prices 0.161 0.084 2 2 1.2 quality 0.259 0.135 1 1 1.3 flexibility 0.112 0.058 5 6 1.4 productivity 0.160 0.083 3 3 1.5 financial ability 0.105 0.055 6 7 1.6 partnership relations 0.115 0.060 4 4 1.7 tech.-innovation 0.087 0.045 7 9 2. social 0.270 2.1 reputation 0.164 0.044 2 10 2.2 safety at work 0.224 0.060 1 5 2.3 employees’ rights 0.115 0.031 6 15 2.4 local community influence 0.089 0.024 7 19 2.5 training of employees 0.122 0.033 5 14 2.6 respect of rights and policies 0.147 0.040 3 11 2.7 disclosing information 0.138 0.037 4 13 3. environmental 0.211 3.1 green image 0.136 0.029 4 17 3.2 recycling 0.176 0.037 2 12 3.3 pollution control 0.220 0.046 1 8 3.4 environmental protection management system 0.129 0.027 5 18 3.5 green products 0.140 0.030 3 16 3.6 consumption of resources 0.089 0.019 7 21 3.7 green competences 0.110 0.023 6 20 dm1 dm2 dm3 c1 0.172 0.086 0.150 c2 0.148 0.195 0.185 c3 0.207 0.214 0.240 c4 0.122 0.165 0.100 c5 0.159 0.134 0.127 c6 0.090 0.093 0.083 c7 0.103 0.113 0.115 dfc 0.000 0.000 0.000 the evaluation of the criteria for sustainable supplier selection by using the fucom method 105 5. discussion according to the respective decisions of all the three experts, when selecting a sustainable supplier, the economic factors have the greatest influence at the first level of decision-making. those factors are followed by the social and, finally, the ecological factors, as the secondand the third-ranked (having the least influence), respectively. the obtained results showing the criteria values were expected at the beginning of the research study because the standards of environmental protection and human life and health are still insufficiently developed in the territory of bosnia and herzegovina, where the company is located and operates. at the second level of decision-making, quality is the most important criterion in the group of the economic factors, and is also the most important criterion in general our of all the other criteria, which is understandable given the fact that the selection of a sustainable supplier of input resources for production is carried out. in order to achieve a good quality of the output product, it is necessary that the quality of the input resource should be satisfactory. the price, productivity and partner relationships are also the criteria ranked the same in the local and the global ranks of the criteria. once, the price was the most important criterion; with the development of the market and an increase in the number of competitors, however, quality began gaining in importance, whereas the price became less important; in this case, it ranks the second. in order to meet the conditions and the needs of the customers of the final product, it is important to provide the required quantity of products at the required time, which is achieved by timely and continuous production, for which reason it is important that the selected supplier should be reliable and make his/her deliveries at the right time. for this reason, reliability is the decision-makers’ third highest priority in this research study. the selection of a supplier is a strategic decision, and therefore it is very important that the supplier should be ready to develop long-term partnerships and joint market development, due to which fact partnership relations rank the fourth. the fifth-ranked is safety at work in the global ranking, simultaneously being the firstranked in the group of the social factors. in the course of its business, the company pays great attention to its employees’ safety at work, for the reason of which fact this criterion is of great importance in the selection of suppliers. the sixth and the seventh ranks in the global ranking are assigned to the criteria of the group of the economic factors, namely to flexibility and the financial ability. as a consequence of the lesser importance of the group of the social factors, the reputation ranked the second in the local ranking, whereas it ranked the tenth in the global ranking. out of the group of the environmental factors, pollution control is highlighted, which ranks much more importantly than the other criteria belonging to this group, out of which it ranks the eighth in the global ranking, and it is understandable for that reason that it is of the highest importance and ranks the first at the local level. given the fact that green competence and resource consumption rank the last in the global ranking, they are the criteria least considered in the evaluation and selection of suppliers. 6. conclusion nowadays, increasing attention is paid to the selection of a supplier given the fact that the establishment of long-term cooperation with a reliable supplier can affect a reduction in the total production costs and reaching a competitive position on the market. considering the fact that manufacturing processes are both numerous and complex, the durmić/oper. res. eng. sci. theor. appl. 2 (1) (2019) 91-107 106 manufacturer’s requirements for suppliers are very complex as well. such requirements, i.e. criteria, have increasingly been growing in number, making it difficult for decisionmakers to choose suppliers. in order to facilitate the selection of a sustainable supplier, the multi-criteria fucom method for criteria evaluation was applied in this paper. in order to assess the significance of the criteria formed at two levels, an expert team of three decision-makers was selected. the results obtained by the applied methodology demonstrate that the most important criteria for the selection of suppliers are the quality, the price, productivity, partnership relations, safety at work, flexibility and the financial ability. based on the most important criteria mentioned in this paper, future research should study the application of certain mcdm methods for the assessment and selection of suppliers in the company for the production of lime. references azadnia, a. h., saman, m. z. m., & wong, k. y. 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(2018). a new model for determining weight coefficients of criteria in mcdm models: full consistency method (fucom). symmetry, 10(9), 393 prentkovskis, o., erceg, ž., stević, ž., tanackov, i., vasiljević, m., & gavranović, m. (2018). a new methodology for improving service quality measurement: delphi-fucomservqual model. symmetry, 10(12), 757. the evaluation of the criteria for sustainable supplier selection by using the fucom method 107 stević, ž. (2017). evaluation of supplier selection criteria in agricultural company using fuzzy ahp method. 22th international scientific conference: strategic management and decision support systems in strategic management, 607-612 stević, ž., vasiljević, m., puška, a., tanackov, i., junevičius, r., & vesković, s. (2019). evaluation of suppliers under uncertainty: a multiphase approach based on fuzzy ahp and fuzzy edas. transport, 34(1), 52-66. stojanović, m., popović, p., & milovanović, ž. (2017). višekriterijumski izbor dobavljača primjenom ahp metodologije i spoftverskog paketa expert choise. internacional scientific conference on information technology and data related research, 400-408 zavadskas, e. k., nunić, z., stjepanović, ž., & prentkovskis, o. (2018). a novel rough range of value method (r-rov) for selecting automatically guided vehicles (agvs). studies in informatics and control, 27(4), 385-394. operational research in engineering sciences: theory and applications vol. 5, issue 3, 2022, pp. 17-39 issn: 2620-1607 eissn: 2620-1747 doi: https://doi.org/10.31181/oresta060722075b * corresponding author. prasad.bari@fcrit.ac.in (p. bari), pmkarande@me.vjti.ac.in (p. karande), jaystonmenezes@gmail.com (j. menezes) simulation of job sequencing for stochastic scheduling with a genetic algorithm prasad bari 1,2*, prasad karande 1, jayston menezes 2 1 department of mechanical engineering, veermata jijabai technological institute, mumbai, india 2 department of mechanical engineering, fr. c. rodrigues institute of technology, vashi, navi-mumbai, india received: 15 april 2022 accepted: 18 june2022 first online: 06 july 2022 research paper abstract: sequencing is done to determine the order in which the jobs are to be processed. extensive research has been carried out with an aim to tackle real-world scheduling problems. in industries, experimentation is performed before an ultimate choice is made to know the optimal priority sequencing rule. therefore, an extensive approach to selecting the correct choice is necessary for the management decisionmaking perspective. in this research, the genetic algorithm (ga) and working of a simulation environment are explained, in which a scheduling operator, under any given circumstances, can obtain the appropriate sequence for job scheduling in a shop. the paper also explains the stochastic based linguistic, scenarios and probabilistic approaches to solve sequencing problem. the simulation environment allows the operator to select the tardiness and non-tardiness related performance measures. the simulator takes input values such as number of jobs, processing time and due date and discovers a near-optimal sequence for scheduling of jobs that minimizes the performance measures selected by the operator as per requirement. the case study considered is solved using scenarios based stochastic scheduling approach and results are shown. the results are compared with the classical method used in the company and observed that the proposed approach gives a better result. key words: stochastic scheduling, genetic algorithm, sequencing, tardiness 1. introduction job scheduling defines the order in which jobs are to be completed at one or more workplaces in a workshop. job scheduling is critical to avoid long lines or production delays, which can result in financial losses or penalties for the firm. scheduling of the mailto:pmkarande@me.vjti.ac.in mailto:jaystonmenezes@gmail.com bari et al. / oper. res. eng. sci. theor. appl. 5(3)2022 17-39 18 jobs can be done by keeping the main focus on one of the factors like priority sequencing rules (sharma & jain, 2015), performance measures (oyetunji, 2009), cost minimization (bari & karande, 2020)(bari & karande, 2022), preference to weighted jobs, etc. oyetunji (2009) formulated expressions of performance measures for computing their values. in this paper, the primary focus is on the minimization of the performance measures for scheduling. performance measures can be minimized by arranging jobs in a particular sequence. in order to obtain the optimum sequence of the jobs, it is essential to know the number of jobs, their corresponding processing time (pt), and their due date (dd). a job sequence is created by applying sequencing rules such as shortest processing time (spt), in which the job that requires the least amount of machine processing time is scheduled first. it is applicable in the need of reduction of average completion time. under the earliest due date (edd) rule, jobs are completed in the order of their earlier due date. it can be used to cut down on tardiness. jobs are processed in the order they arrive on the machine under the first-come, first-served (fcfs) rule. it is effective at lowering the variance in completion time for any dataset. the operator follows one of the sequencing rules as per their industry requirement. the operator's primary focus is primarily on the performance measure values of the sequence so that he can process the operation in the lowest possible time. in the scheduling operations, kumar et al. (2017) discussed about 13 significant performance measures: completion time, flow time, total flow time, average job completion time, average number of jobs in the system, percentage utilization, lateness, average lateness, tardiness, total tardiness, maximum tardiness, average tardiness, and number of tardy jobs. section 2 explains these performance measures in detail. to maximize production efficiency, all performance measurements except the percentage utilization from the considered performance measures should be minimized. maximum percentage utilization indicates that the processing of the job is being done effectively on the machines in the job shop. applying a promethee-gaia technique can optimize these performance measures (bari & karande, 2021). considering the deterministic scheduling model, the optimum sequence with reference to these performance measures can be attained. however, in real-world scheduling problems, various factors affect the pt of the jobs that cannot be neglected. therefore, such problems can be solved using the stochastic model. the stochastic approaches are more significant because of their capability to handle non-linear and multi-objective formulations effortlessly. the stochastic model can be solved using either the exact method or heuristic approach. however, the computational time required to solve deterministic and stochastic problems using the exact method is more than the heuristic approach. one of the popular heuristic methods is the genetic algorithm (ga). the trend for using stochastic techniques with ga is increasing for solving industrialized problems because ga finds a better objective function value for each iteration in less computational time. (deb et al., 2002), (sarkar & modak, 2005), (koratiya et al., 2010), (ramteke & srinivasan, 2012). shrouf et al. (2014) proposed the application of ga to solve the single machine scheduling in the time off use tariff with respect to the machine's status, which consists of processing, idle, turning on and turning off. roy et al. (2019) introduced novel ga concerning selection and crossover operation and found it effective to solve the travelling salesman problem. they have also mentioned that the algorithm proved effective for solving other problems like network optimization. kurniawan et al. (2020) implemented ga to determine the job simulation of job sequencing for stochastic scheduling with a genetic algorithm 19 sequencing, the job assignment, and the starting time of the job. bayu et al. (2020) applied ga by considering stochastic conditions for sequencing the operations of gasoline blending and distribution plants to give gasoline a high commercial latent without negotiating quality and the clients' demand. stanković et al. (2020) presented a model for solving flexible job shop scheduling problem (fjsp) built on meta-heuristic algorithms, tabu search, ga, and ant colony optimization. they have demonstrated the effectiveness of the ga method in resolving the fjsp problem, which gives commendatory results after testing. garg (2016, 2019) solved the constraint optimization problem by feeding genetic operators of ga with particle swarm optimization and a gravitational search algorithm and discovered that these combined algorithms were efficient in finding solution to engineering design problems. souza et al. (2022) proposed ga with simulated annealing approach to generate schedules in deterministic and stochastic machine unavailability restrictions. as a result, the authors demonstrated the significance of ga in their research. researchers are also researching other combinatorial optimization strategies to solve and improve solutions to optimization problems. kundu t., & garg h. (2021) combined harris hawks optimization and teaching–learning-based optimization algorithm and found to be better to find solution to numerical optimization problems. the paper is further divided into the sections listed below. section 2 discusses methodology, including performance measures, deterministic and stochastic scheduling, and their approaches. section 3 describes the optimization of the nontardiness and tardiness-related measures, as well as the ga algorithm. section 4 includes a case study of a manufacturing company as well as the model developed for it. section 5 discusses the case study results. finally, section 6 shows the conclusions of the article. 2. methodology the main objective of this article is to develop a model to find the optimal solution to scheduling problems using ga. the model was created using the python programming language on a computer with 8 gb of ram, a 500 gb hard drive, and the windows 10 operating system. this model aids in determining the best sequence for minimizing performance measures in accordance with industry standards. for deterministic, stochastic linguistic, stochastic probabilistic, and stochastic scenariosbased scheduling problems, the model finds the best solution. the following are the scheduling performance measures: 1. completion time (cj): it is the period necessary to finish a single job j. consider five jobs, j1, j2, j3, j4 and j5, with their respective pt and dd as p1, p2, p3, p4, p5 and d1, d2, d3, d4, d5. additionally, job's in-time and out-time, that is, the time at which the processing operation of a specific job, from a list of jobs, begins and ends, respectively, is also required. table 1 shows the completion time of each job under the out-time column. çetinkaya & duman, (2021) developed an approach to minimize completion time of the sublots and job lots with a single job and multiple jobs. bari et al. / oper. res. eng. sci. theor. appl. 5(3)2022 17-39 20 table 1. data of 5 jobs job number (j) pt (pj) in-time out-time (cj) dd (dj) j1 p1 0 p1 d1 j2 p2 p1 p1 + p2 d2 j3 p3 p1 + p2 p1 + p2 + p3 d3 j4 p4 p1 + p2 + p3 p1 + p2 + p3 + p4 d4 j5 p5 p1 + p2 + p3 + p4 p1 + p2 + p3 + p4 + p5 d5 2. flow time (fj): it is the period between the finishing time of a job and the starting time, that is, the difference between the out-time and release time of the job. for the deterministic model, rj = 0, where rj is the job's release time or starting time. the relationship is defined by equation 1. fj = cj rj (1) 3. total flow time (tft): it is the cumulative flow time for all the jobs and represented by equation 2. from table 1, tft is the summation of the values in the out-time column. 𝑇𝐹𝑇 = ∑ 𝐹𝑗 𝑛 𝑗=1 (2) 4. average job completion time (tavg): it is the ratio of tft to the number of jobs (n) in a given set and shown in equation 3. 𝑇𝑎𝑣𝑔 = 𝑇𝐹𝑇 𝑛 (3) 5. average number of jobs in the system (navg): it is the ratio of tft and the job with the maximum flow time, i.e. 𝑚𝑎𝑥(𝐹𝑗 ) formulated as equation 4. 𝑁𝑎𝑣𝑔 = 𝑇𝐹𝑇 𝑚𝑎𝑥(𝐹𝑗 ) (4) 6. percentage utilization (% utilization): it is the reciprocal of the average number of jobs in the system given in equation 5. it is defined as the number of machines available in a job shop used to process a job. % utilization = 𝑚𝑎𝑥(𝐹𝑗 ) 𝑇𝐹𝑇 (5) 7. lateness (lj): it is the difference between the completion time and the dd of a job expressed in equation 6. from table 1, the lateness of a job is the difference between the out-time and corresponding dd. it can have either a positive, negative or zero value. if lateness is positive, the job will be delayed, whereas, if it is negative, the job will be completed before the dd. if lateness is zero, the job will be completed on time. simulation of job sequencing for stochastic scheduling with a genetic algorithm 21 𝐿𝑗 = 𝐶𝑗 − 𝑑𝑗 (6) 8. average lateness (lavg): it is the ratio of the lateness of all the jobs in the system to the number of jobs shown in equation 7. 𝐿𝑎𝑣𝑔 = 1 𝑛 ∑ 𝐿𝑗 𝑛 𝑗=1 (7) 9. tardiness (tj): it is the measure of the delay in the completion of a job beyond the dd formulated as equation 8. tardiness can have either a positive or zero value. if the difference between completion time and dd is negative, the job is early and not tardy; hence, the tardiness in such a case will be 0. 𝑇𝑗 = 𝑚𝑎𝑥(0, 𝐶𝑗 − 𝑑𝑗 ) (8) 10. total tardiness (t): it is the cumulative delay of all the jobs in the set represented in equation 9. it is the summation of the tardiness of all jobs. 𝑇 = ∑ 𝑇𝑗 𝑛 𝑗=1 (9) 11. maximum tardiness(tmax): it is the measure of the maximum delay of a job beyond the dd. 12. average tardiness (tavg): it is the ratio of total tardiness and the number of jobs in the system shown in equation 10. 𝑇𝑎𝑣𝑔 = 𝑇 𝑛 (10) 13. number of tardy jobs (ntj): it is a measure of the number of delayed jobs in the system and is expressed in equation 11. 𝑁𝑡𝑗 = ∑ 𝛿(𝑇𝑗 ) { 𝛿(𝑥) = 1 𝑖𝑓 𝑥 > 0 𝛿(𝑥) = 0 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒 𝑛 𝑗=1 (11) 2.1. deterministic scheduling the deterministic scheduling operation is done considering only the present scenario at hand. this type of scheduling requires only the jobs' pt and dd. the dd given by the client remains fixed. the pt changes depending on the nature of the factors affecting the jobs. deterministic scheduling does not take into account these factors. hence, deterministic scheduling can be referred to as an idealistic operation. the deterministic model considers assumptions like jobs are available simultaneously for processing, a machine can process only one job at a time, set up times are included in the pt, input data is deterministic and known in advance, machines are available bari et al. / oper. res. eng. sci. theor. appl. 5(3)2022 17-39 22 continuously, and never kept idle, once an operation begins on the machine it proceeds without interruption (french, 1982). an illustration of the data required for deterministic scheduling is given in table 2. consider five jobs, j1, j2, j3, j4 and j5, with their respective pt and dd as p1, p2, p3, p4, p5 and d1, d2, d3, d4, d5. table 2. data format for deterministic scheduling job number (j) pt (pj) dd (dj) j1 p1 d1 j2 p2 d2 j3 p3 d3 j4 p4 d4 j5 p5 d5 2.2. stochastic scheduling in real-world scheduling problems, various factors affect the pt of jobs and cannot be neglected. the deviation that occurred in the accuracy of the pt values can hamper the efficacy of the job shop. this further can cause a delay in circumstances where these factors are in the worst case. to assist the industry in scheduling of jobs with real-time data, stochastic scheduling is preferred, which provides more accurate results. this also gives an idea to the operators about when and how to sequence the jobs and provides the client with a view to set the dd of procurement. the assumptions like input data is deterministic and known in advance, and machines are available continuously and never kept idle made in deterministic scheduling are relaxed in stochastic scheduling. through the literature review, three stochastic scheduling models, as mentioned below (baker & trietsch, 2009), have been identified that can provide the required results. 2.2.1. scenarios method in this method, scheduling is done considering more than one scenario of the jobs as mentioned in table 3. these scenarios are for the same jobs; that is, the end product is the same. however, the path to preparing the end product in different scenarios may be different. for example, in some scenarios, jobs can be made of different materials or the size of the raw material can be different, or the machine used to process can be different. these various factors affecting the jobs can increase or decrease the pt of the jobs. thus, different scenarios are created to assist in stochastic scheduling with real-time data. consider five jobs, j1, j2, j3, j4, and j5 with the respective pt of p11, p12, p13, p14, p15, (for scenario 1) p21, p22, p23, p24, p25, (for scenario 2) and p31, p32, p33, p34, p35. (for scenario 3). the dd for the five jobs are d1, d2, d3, d4, and d5. this data is shown in table 3. table 3. data format for scenarios scheduling job number scenario 1 pt scenario 2 pt scenario 3 pt dd j1 p11 p21 p31 d1 j2 p12 p22 p32 d2 j3 p13 p23 p33 d3 j4 p14 p24 p34 d4 j5 p15 p25 p35 d5 simulation of job sequencing for stochastic scheduling with a genetic algorithm 23 in deterministic scheduling, only the pt of one scenario is considered at a given time. the scenario can be 1, 2 or 3 from table 3. however, in the stochastic model, the pt of every job is considered by taking the average of the pt from all the possible scenarios that can occur and shown in equation 12. thus, the pt for any job concerning the above table can be given as: 𝐸𝑥𝑝𝑒𝑐𝑡𝑒𝑑 𝑃𝑇 𝑜𝑓 𝑗𝑡ℎ 𝑗𝑜𝑏 = 𝑝𝑗 = 𝑝𝑗 1 + 𝑝𝑗 2 + 𝑝𝑗 3 3 = 1 3 ∑ 𝑝𝑗 𝑖 3 𝑖=1 hence, the formula can be given as: 𝑝𝑗 = 1 𝑛𝑠 ∑ 𝑝𝑗 𝑛𝑠 𝑗=1 (12) where, ns – number of scenarios and j – scenario number 2.2.2. linguistic method the linguistic method stands out when selecting real-time data of jobs. in this method, the pt of jobs is estimated by considering various factors that affect their operation. for instance, to perform a turning operation on a job, some of the factors affecting are the condition of the tool, the machine, the material of the job or coolant type. these and many other factors can either increase or decrease the pt. if a particular factor increases the pt of a job, it may not be in its best form. for example, an increase in pt concerning the above factors can be because the tool is blunt, the machine is not operating as it should, the material of the job is rough, or the coolant is not effective enough. conversely, if the same factors are in their best form, the pt of the job will decrease. in the linguistic method, either one or all the factors can be in their best or worst shape under different circumstances. thus, if there are 'nf' factors affecting the pt of a job and each factor can have either good (g) or bad (b) form, the number of conditions is given by 2𝑛𝑓 . in a more general aspect, the number of conditions can be given by 𝑁𝑐 = 𝑥 𝑛𝑓 where, 'nf' is the number of factors and x is the number of forms each factor can have. consider there are five jobs, and three factors are taken into account that can affect the processing of each job. each factor can have two forms that is g or b. hence, there will be eight (23) conditions for each job like bbb, which means all factors for jobs are in bad conditions, bbg means the first two factors are in bad conditions whereas the third factor is in good condition and so on. table 4 shows the data format of the linguistic method with eight conditions for each job. table 4. data format for linguistic scheduling job number bbb bbg bgb bgg gbb gbg ggb ggg dd 1 32 28 27 25 22 20 16 15 23 2 30 26 23 22 19 17 14 13 21 3 33 29 25 24 20 19 16 11 17 4 28 27 26 21 17 16 13 9 13 5 35 28 25 20 16 15 13 10 15 bari et al. / oper. res. eng. sci. theor. appl. 5(3)2022 17-39 24 from the table, the real-time data of the jobs can be selected by the form of each factor. for example, if the condition chosen for job number 1, 2, 3, 4 and 5 is bgb, gbb, bbb, gbg and ggg, respectively, the new data for the scheduling operation will be shown in table 5. table 5. stochastic scenarios scheduling data after operator selection job number (j) pt (pj) dd (dj) 1 27 23 2 19 21 3 33 17 4 16 13 5 10 15 thus, the pt of the jobs is now based on the form of the individual factors in the present scenario. 2.2.3. probabilistic method the probabilistic scheduling method is similar to the scenarios method, wherein each job has a different pt in each scenario. however, this method does not take an average of the pt; instead, a probability of occurring is associated with each scenario. therefore, the sum of the probabilities of each scenario happening is equal to 1. the probabilistic approach is used for repetitive jobs carried out in industry. ideally these jobs should have the same pt, but this pt can be different for different scenarios and thus the probability of occurring in the scenarios may vary due to different elements. the probability of scenarios is determined by elements such as machine breakdown, power failure, worker absenteeism, technology failure, material shortages, unavoidable delays, and so on. the decision-maker computes these probabilities by analyzing historical data. while calculating the performance measure, each scenario has to be arranged in the sequence, and the performance value is then calculated for the individual scenarios. next, the expected value of the performance measure is calculated by taking the summation of the product of individual scenarios' performance measure and the probability of the scenario. consider the data of 5 jobs, j1, j2, j3, j4, and j5, as shown in table 6, with the respective pt for scenario 1 are p11, p12, p13, p14, p15 for scenario 2 are p21, p22, p23, p24, p25 and for scenario 3 are p31, p32, p33, p34, p35. the dd for the five jobs are d1, d2, d3, d4, and d5. the probability of scenario 1, 2 and 3 occurring is p1, p2 and p3, respectively. table 6. data format for stochastic probabilistic scheduling job number scenario 1 pt scenario 2 pt scenario 3 pt dd j1 p11 p21 p31 d1 j2 p12 p22 p32 d2 j3 p13 p23 p33 d3 j4 p14 p24 p34 d4 j5 p15 p25 p35 d5 if the performance measure, tft calculated for the above 3 scenarios is tft1, tft2 and tft3, then the expected tft is given in equation 13, simulation of job sequencing for stochastic scheduling with a genetic algorithm 25 𝐸𝑥𝑝𝑒𝑐𝑡𝑒𝑑 𝑇𝐹𝑇 = 𝑇𝐹𝑇1 ∗ 𝑃1 + 𝑇𝐹𝑇2 ∗ 𝑃2 + 𝑇𝐹𝑇3 ∗ 𝑃3 (13) the same approach can be implemented for finding the expected values of all the performance measures. 3. optimizing performance measures the performance measures are divided into two categories, non-tardiness performance measures and tardiness performance measure. the non-tardiness performance measures are optimized with the spt rule, while for tardiness related measures, ga is applied to generate an optimal sequence. 3.1. non-tardiness performance measures non-tardiness performance measures are total flow time, average flow time, total pt, percentage utilization, the average number of jobs in the system, total lateness and average lateness. all these measures, except percentage utilization, can be reduced by arranging the jobs in the spt sequence. if the jobs are arranged in an spt sequence, percentage utilization will have a maximum value. the explanation for this approach has been given using the following example. consider five jobs j1, j2, j3, j4 and j5 with pt p1, p2, p3, p4 and p5. the dd of the jobs are d1, d2, d3, d4 and d5. this data is summarized in table 2. to calculate the non-tardiness related performance measures, two additional columns must be added, in-time and out-time of each job. in-time indicates when a job arrives on a machine, more specifically, after completing the preceding job, if any. out-time indicates the time at which a job leaves the machine that is after completion of its pt. 1. total flow time it is given by the sum of the values in the out-time column. therefore, in this case, 𝑇𝐹𝑇 = 𝑝1 + 𝑝1 + 𝑝2 + 𝑝1 + 𝑝2 + 𝑝3 + 𝑝1 + 𝑝2 + 𝑝3 + 𝑝4 + 𝑝1 + 𝑝2 + 𝑝3 + 𝑝4 + 𝑝5 𝑇𝐹𝑇 = 5𝑝1 + 4𝑝2 + 3𝑝3 + 2𝑝4 + 𝑝5 (14) to minimize the value of tft shown in equation 14, the job with the least pt has to be multiplied with the largest coefficient and so on from left to right in increasing order of pt. 2. average job completion time 𝑇𝑎𝑣𝑔 = 5𝑝1 + 4𝑝2 + 3𝑝3 + 2𝑝4 + 𝑝5 𝑛 (15) to reduce tavg, shown in equation 15, the number of jobs is constant, and hence the sequence which will reduce the tft will also reduce tavg. 3. percentage utilization bari et al. / oper. res. eng. sci. theor. appl. 5(3)2022 17-39 26 % utilization = max (𝐹𝑙𝑜𝑤 𝑇𝑖𝑚𝑒) 𝑇𝐹𝑇 ∗ 100 the performance measure shown in equation 16 requires to be maximum to make the utmost utilization of the machine for the given set of jobs. for example, from table 1, job number 5 will have the maximum flow time, and the tft must be minimized to maximize the performance measure. % utilization = 𝑝1 + 𝑝2 + 𝑝3 + 𝑝4 + 𝑝5 5𝑝1 + 4𝑝2 + 3𝑝3 + 2𝑝4 + 𝑝5 ∗ 100 (16) 4. average number of jobs in the system 𝑁𝑎𝑣𝑔 = 1 % utilization (17) to minimize this performance measure shown in equation 17, the percentage utilization performance measure must be maximum. hence, this value can be minimized using the same approach from the previous performance measure. 5. total lateness total lateness is the sum of the difference between the out-time of a job and its dd. from the table 1, the equation obtained is, total lateness = (𝑝1 − 𝑑1) + (𝑝1 + 𝑝2 − 𝑑2) + (𝑝1 + 𝑝2 + 𝑝3 − 𝑑3) + (𝑝1 + 𝑝2 + 𝑝3 + 𝑝4 − 𝑑4) + (𝑝1 + 𝑝2 + 𝑝3 + 𝑝4 + 𝑝5 − 𝑑5) total lateness = (5𝑝1 + 4𝑝2 + 3𝑝3 + 2𝑝4 + 𝑝5) − ( 𝑑1 + 𝑑2 + 𝑑3 + 𝑑4 + 𝑑5) total lateness = 𝑇𝐹𝑇 − ( 𝑑1 + 𝑑2 + 𝑑3 + 𝑑4 + 𝑑5) (18) the summation of the dd is the same irrespective of the job sequence. hence, the tft must be minimum to reduce the lateness shown in equation 18. therefore, a minimum value can be obtained using the same sequence of jobs from the previous measures. 6. average lateness the average lateness is shown in equation 19. the number of jobs is constant. so, to minimize the numerator, the same approach from the previous performance measure can be used. 𝐿𝑎𝑣𝑔 = total lateness 𝑛 (19) 7. total pt simulation of job sequencing for stochastic scheduling with a genetic algorithm 27 it is the summation of the pt of all jobs in the scheduling problem. the total pt is a constant value for any given sequence of jobs and cannot be minimized. 3.2. tardiness performance measures for the tardiness related parameters, a few of the approaches tested to minimize the performance measures were the branch and bound algorithm (tyagi et al., 2016), excel workbook tool, sequentially searching through each of the 'n!' sequences possible. however, these approaches were limited by various factors, including computing time and data size variation. hence, a randomized search approach was implemented like ga (bancila & buzatu, 2008). the ga initiates by using random sequences of the jobs as starting population. then, it proceeds with each sequence of the population over a fitness function. later, it chooses the fittest sequence of the population to reproduce using the reproduction function of ga and repeats the assessment and reproduction until a selected number of iterations. in the end, the algorithm presents the optimal sequence of the population according to the fitness function. following are the steps in the ga used in the simulation model: step 1: select the initial population randomly the initial population is a set of randomly generated chromosomes (sequence of jobs) as input to the ga. ga chooses a set of samples randomly from n! sequences as the initial population. for example, the 30 sequences are selected randomly for five jobs 0,1,2,3,4 from 5! that is 120 sequences as an initial population shown below. [2, 0, 1, 4, 3] [1, 4, 2, 0, 3] [4, 1, 2, 3, 0] [3, 2, 0, 4, 1] [1, 2, 4, 0, 3] [3, 4, 1, 0, 2] [0, 4, 2, 1, 3] [2, 4, 1, 3, 0] [4, 1, 0, 3, 2] [3, 0, 2, 4, 1] [0, 1, 2, 3, 4] [1, 3, 4, 2, 0] [4, 2, 1, 0, 3] [4, 2, 0, 3, 1] [1, 3, 4, 2, 0] [4, 3, 2, 1, 0] [4, 0, 2, 3, 1] [4, 3, 0, 2, 1] [0, 3, 2, 1, 4] [4, 1, 3, 0, 2] [2, 4, 1, 3, 0] [1, 3, 2, 4, 0] [4, 1, 0, 3, 2] [2, 1, 4, 0, 3] [2, 1, 3, 4, 0] [0, 1, 4, 2, 3] [4, 0, 3, 1, 2] [2, 4, 1, 3, 0] [3, 0, 4, 1, 2] [4, 3, 2, 1, 0] step 2: application of ga operators crossover operator: crossover is a genetic operator used to modify a chromosome or chromosomes by combining chromosomes from one generation to the next. randomly select two parents, just for manageable iteration, number all the sequences and shuffle it for reproduction operation on the population to get offspring. 0 6 12 18 24 1 7 13 19 25 2 8 14 20 26 3 9 15 21 27 4 10 16 22 28 5 11 17 23 29 [26, 7, 9, 29, 3, 10, 2, 28, 8, 27, 21, 16, 25, 12, 20, 15, 4, 24, 6, 19, 5, 18, 14, 0, 13, 23, 11, 22, 17, 1] bari et al. / oper. res. eng. sci. theor. appl. 5(3)2022 17-39 28 let's select the first two sequences as parents 26 and 7. p1 [1, 3, 4, 2, 0] p2 [0, 4, 2, 1, 3] randomly select half of the number of jobs and create the sequences just by swapping the jobs at that positions to get children. now remaining places are filled with jobs that are not in children. let’s select [0,4] child_1 = [0, 'na', 'na', 'na', 3] child_2 = [1, 'na', 'na', 'na', 0] ‘na’ represents the blank place thus in child_1, jobs [1, 4, 2] are not present. similarly, in child_2, jobs [4, 2, 3] are not present. now just put these jobs to get child_1 and child_2 as follows child_1 = [0,1,4,2,3] child_2 = [1,4,2,3,0] this process needs to repeat for the remaining sequences, producing the different sequences as offspring list. mutation: mutation operators are generally viewed as a random disturbance term of the individual chromosome. the children list of sequences produced by the crossover function of ga is used as input to this mutation function. first, randomly select the sequence and swap the position of jobs that gives the new list of offspring sequences. let’s take child_2 = [1,4,2,3,0] select any two positions and swap the jobs. for example, let's select 2nd and 3rd positions and change the jobs to produce a new sequence [1,2,4,3,0]. this process repeats for all sequences present in the children list, input for mutation function to get new offspring. step3: evaluation of offspring evaluation of offspring is finding the sequence with the lowest tardiness value. now parent list and offspring list are merged to get the whole list of sequences to find optimal sequences. the tardiness performance measures are needed to minimize. the total tardiness of all the sequences is calculated, and the sequence with minimum tardiness is selected as the optimal sequence. the exact sequence is used to calculate other tardiness based measures. step 4: termination condition the termination condition is the stopping criterion for the algorithm. in this paper, the user gives the number of iterations as a termination condition for finding the best sequence. after a specified iteration, the algorithm stops and produces the optimal sequence for minimizing total tardiness. simulation of job sequencing for stochastic scheduling with a genetic algorithm 29 based on the ga implemented, figure 1 shows a graph that indicates the time required to compute total tardiness, average tardiness, number of tardy jobs and maximum tardiness in one iteration against the number of jobs in the dataset. figure 1. number of jobs and time required for 1 iteration from figure 1, it is observed that the time required to compute one iteration roughly increases as the number of jobs increases. this gives the operator an idea of how much time will be required for computing the required number of iterations. another benefit of the implemented algorithm is that if the values reach a minimum value, the algorithm will check the value for a few more iterations and exit the loop after a few iterations to save the operator's time from computing the remaining number of iterations. hence implementing the spt approach and a ga, an optimizing stochastic model can be developed for any scheduling application. 4. case study a case study was performed in association with a manufacturing company specializing in pipe fittings and flanges to verify the methodology and compare results with the real-world scenario. figure 2 shows sample data from a datasheet of the company. the model developed for the case study uses the scenarios method of scheduling explained earlier in section 2.2.1. the model is limited to n jobs one machine scenario that is scheduling will be done for any number of jobs as long as they are processed on one machine. with respect to figure 2, the simulation model assigns job numbers based on the sizes of the individual components; that is, job numbers are assigned based on the 'size' column. the model also calculates the pt of the respective job, in minutes, by taking the product of the values from the column 'qty.' and 'processing time'. the pt is then converted to hours because the dd of the jobs is also accepted in terms of hours. thus, the data required for performing scheduling operations is prepared. the model is created using python programming language on a computer system with 8 gb ram and 500 gb hard disk and windows 10 operating system. this model can also run on other versions of the operating system like windows 7, windows 8 and other operating systems. other than this, no other special hardware and software requirements are needed. 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 0 10 20 30 40 50 60 70 80 90 100 110 120 130 t im e ( in s e c o n d s) number of jobs bari et al. / oper. res. eng. sci. theor. appl. 5(3)2022 17-39 30 figure 2. sample data of case study a similar approach is followed if there are more than one scenario. if there are more than one scenario, the simulation model requires the same number and similar jobs in all the datasheets. figure 3 shows the main window of the job shop scheduling simulator. all four scheduling methods explained earlier are included in this simulator. a new window will open for the respective scheduling model on clicking any button. the 'about' button provides information about the simulator. for example, the case study model developed can be located by clicking the 'stochastic scheduling (scenarios) company model' button. on clicking the company model button, the main window of the model will open up, as shown in figure 4. the model has two ways of data input, manual input or importing an excel file. the 'enter number of iterations' box is required only for the tardiness related performance measures, without which error will be displayed. if there are more than one scenario, the operator can select the individual scenarios by entering in the 'enter scenarios of jobs' box. the 'instructions' give information about the file format and the format of input wherever required. figure 3. main window of simulator simulation of job sequencing for stochastic scheduling with a genetic algorithm 31 figure 4. main window of company model if the operator chooses to import the data, a 'browse' window will appear to select one or more files from the device storage. an error will be displayed if the datasheet is not in the proper format. after selecting the file(s), the software will read through the 'process used' column of the datasheet(s) to identify different machines. now the operator has to enter for which machine scheduling has to be performed, as the simulation will be done for n jobs one machine. this input will be taken in the 'select process' window, as shown in figure 5. the operator can also enter the dd of the jobs, in hours, in the same window. on clicking the 'submit' button, the data will be ready for scheduling operation. figure 5. process used and due date the operator can also enter the data of the jobs manually, that is, the dd and pt of the jobs, by clicking the 'enter data' button in the main window. on clicking, a window, as shown in figure 6, will appear. the simulator will automatically assign the job number in the order the input is given. the pt of more than one scenario can also be added there. the units, however, of both the inputs have to be the same as no units are assumed or assigned here. bari et al. / oper. res. eng. sci. theor. appl. 5(3)2022 17-39 32 figure 6. window to manually enter data the operator must select the performance measures for which the minimizing sequence has to be found and the corresponding minimum value. the individual performance measures can be chosen, or the 'all performance measures' can be selected as a whole. if the operator selects 'all performance measures' or any of the tardiness related performance measures, input will be required from the operator for the number of iterations. the computing time will increase if the number of iterations are more or if the number of jobs are more. the operator can give the appropriate value based on the time at hand. the operator is required to enter the scenarios of the jobs. this can be done in the following ways. 1. for selecting single scenarios, the scenario number can be given, that is, 1 or 2 2. for more than one scenario, each scenario should be separated with a comma, 3, 4, 5, 6, 7. 3. the hyphen symbol can be used for selecting a range of scenarios; that is, 410 will select all the scenarios within this range, including 4 and 10. 4. for a combination of individuals and a range of scenarios, the following format can be followed that is, 4-10, 12, 13, 16. this will select the scenarios from the range of 4 and 10, including the individual scenarios of 12, 13, and 16. the operator can also view the data table, that is, the job number, pt and dd of every job and scenario, by clicking on the 'preview table' button. on clicking, a window, as shown in figure 7, will appear. the data, here, cannot be manipulated. after all the required input is given for the scheduling operation, as shown in figure 8, the scheduling operation is ready to be performed. simulation of job sequencing for stochastic scheduling with a genetic algorithm 33 figure 7. sample preview table window figure 8. performance measure selection a new window will appear after clicking the 'submit’ button, as shown in figure 9. this window will consist of all the names of the performance values selected by the operator and the corresponding minimum value in the top table. next, in the bottom table, the job details will be provided. finally, in the right-hand side section of the window, the names of the performance measures will be given and the sequence that will minimize performance measures. thus, the result window consists of all the data required to perform the scheduling operation. bari et al. / oper. res. eng. sci. theor. appl. 5(3)2022 17-39 34 figure 9. results for due date 700 the dd given by the client was four months, that is, 700 hours (assuming 25 working days in a month and seven working hours per day). after running the model with dd of 700 hours, the tardiness comes to be 0, as shown in figure 9. this indicates that all the jobs are completed early. the just-in-time approach in manufacturing industries stimulates the notion of tardiness and earliness also. in industry, in view of due-dates, the primary intent is to complete all the jobs on time. the intent may be achieved by permitting the loose dd as 700 hours as dd in the case study. in this case of unrestricted dd situation, all jobs can be completed before dd by any sequence. completing the jobs before time affects inventory carrying costs like storage and protection costs. however, due dates should be chosen carefully, as dd that is tight or restricted invite more customers. the above discussion indicates that the dd should be tighter. if the dd is negotiable with the customers and can be made still tighter, it will attract more customers, and there will be no need to keep a loose dd. after several runs with a different dd, it is found that the dd of 548 hours, approximately 3 months and 3 days is optimum for the case study. the dd produces the same result for tardiness measures, as shown in figure 10. it is noted that the sequence of jobs for non-tardiness performance measures is the same as it is based on the spt priority sequencing rule; however, the sequence for tardiness performance measure is different for both cases shown in figure 9 and figure 10. the average lateness is reduced from 627.457 to 475.457, which indicates that the inventory level of the completed job can be minimized. simulation of job sequencing for stochastic scheduling with a genetic algorithm 35 figure 10. results for due date 548 5. results and discussion of case study the case study is conducted using the dd given by the client with a stochastic scenario model. the company sequenced the jobs in the fcfs rule. there were 90 jobs for the company to schedule on the lathe machine for sequencing. the performance measures were calculated for the dataset, with the dd as four months for the dataset. the company followed a deterministic approach to job scheduling. hence, only one datasheet was considered, whereas the model developed uses the stochastic approach and therefore uses two datasheets for two scenarios. table 7 shows the calculated values for the dataset and the values calculated by the model. table 7. deterministic and stochastic results for data set sr. no. performance measures deterministic approach stochastic approach 1. total flow time 32967.75 hours 6528.85 hours 2. average job completion time 366.30 hours 72.543 hours 3. total processing time 547.6 hours 547.6 hours 4. percentage utilization 1.442 % 8.387 % 5. average number of jobs in the system 69.338 11.923 6. total lateness -30032.2 hours -56471.15 hours 7. average lateness -333.69 hours -627.457 hours 8. total tardiness 0 0 9. average tardiness 0 0 10. maximum tardiness 0 0 11. number of tardy jobs 0 0 both the approaches assign job numbers based on the sizes and consider the quantity of those sizes as one job. there were 90 jobs in the dataset, and to calculate the tardiness performance measures, ten iterations as termination condition were given for ga. from table 7, it is observed that the developed model, which uses spt bari et al. / oper. res. eng. sci. theor. appl. 5(3)2022 17-39 36 and ga methods for calculating non-tardiness and tardiness performance measures, respectively, provides a better value. due to the proposed approach, the company will have more time after completing a set, which can be used for various tasks like maintaining the machines or beginning the operations on the next set of jobs. it is further suggested that if the dd is negotiable, that means a tighter dd as compared to the given dd by the client; the company can clear out the inventory of finished products without affecting performance measures. finishing the jobs well beforehand also reduces inventory costs in terms of storage or protection and improves the company's value. by lowering the tardiness performance measures company can lessen the delaying cost. the total tardiness for each iteration with different dd is shown in table 8. figure 11 shows the tardiness with respect to iteration for dd 400, 450, 500 and greater than equal to 548 hours. table 8 and figure 11 suggest that the dd can be tighter as 548 hours without affecting tardiness measures. it is observed that dd of less than 548 hours affects the total tardiness. further decrease in dd increases the total tardiness. this total tardiness can be improved as the number of iterations in ga are increased. after specific iterations, it gives a constant value, but an increase in the number of iterations will increase computational time. table 8. total tardiness for each iteration with different due date number of iterations dd (in hours) 700 650 600 550 548 500 450 400 tardiness (in hours) 1 0 0 0 0 0 93 144.9 5 203.8 2 0 0 0 0 0 47.6 144.9 4 203.8 3 0 0 0 0 0 47.6 144.9 4 175.2 7 4 0 0 0 0 0 47.6 138.0 4 140.4 4 5 0 0 0 0 0 47.6 137.5 2 140.4 4 6 0 0 0 0 0 47.6 137.7 3 129.9 4 7 0 0 0 0 0 47.6 137.1 7 129.9 4 8 0 0 0 0 0 47.6 137.1 7 129.9 4 9 0 0 0 0 0 47.6 137.0 7 129.9 4 10 0 0 0 0 0 47.6 137.0 7 129.9 4 figure 11. total tardiness for different due date -10 10 30 50 70 90 110 130 150 170 190 210 230 0 1 2 3 4 5 6 7 8 9 10 11 t a rd in e ss number of iterations due date>=548 due date=500 due date=450 due date=400 simulation of job sequencing for stochastic scheduling with a genetic algorithm 37 in comparison to traditional methods such as an excel workbook or manual calculation, the proposed work advocates using ga to reduce the computing time required to calculate performance measures and find the best sequence of jobs in a scheduling problem. in addition, the proposed work uses stochastic scenarios, linguistics, and probabilistic approaches to find job sequences that minimize performance measures. when the proposed model is applied to real data from a company, it is discovered that the sequence obtained by the model produces the lowest performance measure value when compared to the company's method. the proposed method is a unique application that allows for faster computation and better results. 6. conclusions the developed simulation model can handle the stochastic scheduling problem with linguistic, scenarios and probabilistic data to discover an optimal sequence of jobs for scheduling on a single machine. it also helps to solve the problem in a deterministic way. if the number of jobs and iterations increases, the computational time required to discover the optimal sequence also increases. when the problem was solved using the excel solver, it took more time in discovering the near-optimal sequence. the developed simulation model not only produces results with lesser time, but also improves solution. stochastic models allow the operator to select real-time data, whereas deterministic scheduling does scheduling based on the data at hand. the spt rule minimizes tft and minimizes all the non-tardiness related performance measures. the developed ga model also minimizes the tardiness related performance measures. as an outcome, the proposed stochastic technique assisted the company in reducing the average completion time of job from 366.30 hours to 72.543 hours. additionally, increased the percentage utilization from 1.442 percent to 8.387 percent. while doing the analysis of the company dataset using the developed model, it is revealed that a tighter dd is beneficial for reducing inventory costs. the work is restricted to a single machine with an unlimited number of jobs. ga generates optimal sequences for scheduling problems, however, for different runs, it generates different sequences with the minimized performance values. to tackle this issue, a combinatorial approach of ga with other optimization techniques can be used. future work on this project may include developing simulation environments for n jobs m machines which will provide a broader range of options as per the industry’s needs. modifying the simulation environment from software to web application will not require instalment on the device, and the operator can use it remotely on any device. this paper focuses on stochastic scheduling and the reduction in time for completion of job. however, another factor that majorly affects scheduling is cost, which may be further analyzed. delay of jobs can incur costs to the company of a by considerable amount. hence, developing a simulation environment to minimize both time and cost will assist the manufacturing industries with better insight into the scheduling and sequencing of jobs. bari et al. / oper. res. eng. sci. theor. appl. 5(3)2022 17-39 38 references baker, k. r., & trietsch, d. 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(2016). single machine scheduling model with total tardiness problem. indian journal of science and technology, 9(37), 1–14. https://doi.org/10.17485/ijst/2016/v9i37/97527 © 2022 by the authors. submitted for possible open access publication under the terms and conditions of the creative commons attribution (cc by) license (http://creativecommons.org/licenses/by/4.0/). simulation of job sequencing for stochastic scheduling with a genetic algorithm prasad bari 1,2*, prasad karande 1, jayston menezes 2 1. introduction 2. methodology 2.1. deterministic scheduling 2.2. stochastic scheduling 2.2.1. scenarios method 2.2.2. linguistic method 2.2.3. probabilistic method 3. optimizing performance measures 3.1. non-tardiness performance measures 3.2. tardiness performance measures 4. case study 5. results and discussion of case study 6. conclusions references operational research in engineering sciences: theory and applications vol. 4, issue 2, 2021, pp. 13-35 issn: 2620-1607 eissn: 2620-1747 doi: https://doi.org/10.31181/oresta20402013b * corresponding author. mouba121286@yahoo.fr (m.b. bouraima), zeljko.stevic@sf.ues.rs.ba (ž. stević ), ilijat@uns.ac.rs (i. tanackov), publicqiu@vip.163.com (y. qiu)(m.b. bouraima) assessing the performance of sub-saharan african (ssa) railways based on an integrated entropy-marcos approach mouhamed bayane bouraima 1, 2, željko stević 3*, ilija tanackov 4, yanjun qiu 1 1 school of civil engineering, southwest jiaotong university, china 2 organization of african academic doctors (oaad), nairobi, kenya 3 university of east sarajevo, faculty of transport and traffic engineering doboj, bosnia and herzegovina 4 university of novi sad, faculty of technical sciences, novi sad, serbia frican academic doctors (oaad), off kamiti road, p.o box 25305 received: 31 march 2021 accepted: 11 may 2021 first online: 16 june 2021 research paper abstract: in this study, the performance of sub-saharan african railways systems (ssa) is assessed by using an integrated entropy-marcos (measurement alternatives and ranking according to compromise solution) based methodology. in the first phase, the entropy method is employed to determine the weights of each sub-criterion of the decision model. this process identifies six main criteria, i.e., safety, security, internal business aspect, intermodal aspect, innovation, and learning aspect, and customer satisfaction which are further supplemented by 13 sub-criteria. in the second phase, the marcos method is used to rank the countries based on their railway performance assessment. based on the results from the proposed method, a sensitivity analysis was carried out through a comparative analysis with seven other multicriteria decision-making (mcdm) methods. the results of the study indicate that the most weighted sub-criterion is the labor productivity (internal business perspective criteria) followed by the terrorist incidence (security criteria) and the number of employees going through training/exposure sessions (innovation and learning perspective criteria). moreover, it was revealed that kenya is the best alternative in terms of its railway performance followed by ethiopia, cameroon, nigeria, and ghana. based on the findings from this study, decision-makers can be assisted during the operative, designing, and planning investigations of the railway system through the consideration of these parameters as insert indicators. also, the findings can help as a benchmark for the performance analysis of other railway systems in other african countries. keywords: railways, sub saharan africa, performance, entropy, marcos, multicriteria decision making bouraima et al./oper. res. eng. sci. theor. appl. 3 (x) (2020) 1-20 bouraima et al./oper. res. eng. sci. theor. appl. 4 (2) (2021) 13-35 14 1. introduction in the present’s severe rivalries between railway and road transportation modes in the major corridors of the african sub-region, a distinguished service distribution change into a regional trade demand. one of the pivotal constituents for modern railway corporations is performance appraisal and efficacy. this can reinforce reaching the organization's goals and analyze their achievement with identical leading policies marketing. to meet these excellent positions, a method should be elaborated by the railway corporation to create this evaluation in a beneficial approach. railway has lately undergone a universal renaissance via its network expansion and yearly traffic values. according to bayane and yanjun (2017) and bouraima, yang, and qiu (2017), this improvement of railways is related to socio-economic and environmental advantages produced by the transport sector. railway plays a considerable role through the assistance of economy and commerce of any country due to heavy traffic transportation of people and goods over long distances. a relative evaluation of air, road, and railway mode showed its potentiality in terms of cost, greenhouse gas, and carbon emission (bouraima et al., 2020). in 2010, a coherent performance and demand development was universally reported in the railway system through a 40% rise in cargo and passenger traffic in comparison to an antecedent year. however, an opposite trend in the performance was noticed in africa. while dynamic growth has been recorded in asia, europe, and america, africa has seen a drop in passengers’ services and freight transport. due to the recent powerful rise of the transport market worldwide, the contradictory trend in sub saharan africa (ssa) revealed the crucial deficient railway system (olievschi, 2013). in 2010, the africa union commission has expressed the will to ameliorate the infrastructure condition through the infrastructure development program in the continent (union, 2009). during this period, political leaders have expressed the connectivity ambition at both regional and continental levels (commission, 2012). nonetheless, this ambition has been rapidly impeded by several factors that affect railway development. several endogenous and exogenous factors restrict the competitiveness of african railway systems. while poor connectivity and interoperation of railways have seen to be the endogenous factors (bouraima & qiu, 2018; bouraima & yanjun, 2020), exogenous parameters are related to rivalry with road transport and the lack of policy related to transport (bayane, yanjun, & bekhzad, 2020; bouraima & dominique, 2018; bouraima, et al., 2020). literature available so far indicates the dramatic status of the railway sector in sub-saharan africa (bullock, 2009). a study by mbangala mapapa (2004) on the measurement of african railways productivity over 21 years indicated that the average efficiency is relatively low. as consequence, a need of improving the sector performance is imperative. sabri, colson, and mbangala (2008) used data enveloped analysis (dea) and preference ranking organization method for enrichment of evaluations (promethee) ii methods for the financial and technical performance analyses of five firms in north africa. sabri (2016) provided complimentary detailed information on the productivities of north african railways using a malmquist quantity index. de bod and havenga (2010) highlighted the considerable cost assessing the performance of sub-saharan african (ssa) railways based on an integrated entropy-marcos approach 15 depletion benefits feasible via the condensation of railway goods through prolonged distances, with related indications for profitability rise for rail operators. olievschi (2013) suggested an extensive improvement method for the performance of the railway sector together with its governance modes. wangai, rohacs, and boros (2020) introduced a harmonized interaction methodology including socio-economic needs, technical expansion, and rule for the development process of railway systems in low-income countries. kutlar, kabasakal, and sarikaya (2013) measured the technical and allocative efficiencies scores of 31 railways companies using dea and tobit analyses, respectively. blumenfeld et al., (2019) proposed a technical strategy that captured the crucial capacity to be recommended to reach upcoming achievement in railway infrastructure in low-income countries while highlighting the necessity for arising technologies to be employed for appropriate solution. among these studies (blumenfeld et al., 2019; bullock, 2009; mbangala mapapa, 2004; sabri, 2016; sabri et al., 2008; wangai et al., 2020), none of them have examined the key performance indicators (kpi’s) of ssa’s railways. moreover, none of them have applied the mcdm method for the performance assessment of subsaharan african railways. this paper proposed an integrated entropy-marcos approach for the assessment of ssa’s railways. the criteria and alternatives associated with the kpi’s of railways are defined. a questionnaire survey was prepared for data collection and assigned to the railway experts from different countries. all experts hold senior positions with associated working experience and most of them had practiced in the field for 15 years at least. they all belong to the railway corporation in their respective countries: cameroon railway corporation (camrail), ethiopian railway corporation (erc), ghana railway corporation (grc), nigeria railway corporation (nrc), and kenya railway corporation (krc). the survey of experts is carried out in the study so that necessary data will be collected to determine relative criteria weight using the entropy method. the measurement and ranking of alternatives are assessed through the marcos method. through the proposed model in this study, various objectives are elucidated: 1) review of the existing methodologies for the evaluation of different areas of the railway transport; 2) enhancing the methodology for railway performance assessment and determining criteria weights and alternatives ranks through the development of the original multi-criteria entropy-marcos model; 3) proposal of new methodology for the railway performance assessment; and (4) cross over the existing gap for the railway performance evaluation approach in sub-saharan africa. the remaining sections of the paper are as follows. section 2 includes the review of similar research topics in which are applied the models for the analysis of railway transport. section 3 deals with the materials and methods. in section 4, the results and the discussion of the entropy-marcos methods are provided. section 5 presented and discussed a comparative analysis of the proposed method with others mcdm methods. section 6 ends with the conclusion along with the benefit of the research and the guidance for upcoming research. 2. literature review the analytical hierarchy process (ahp) introduced by saaty (1990), is the most frequently applied mcdm approach in transport sector problems (yannis et al., bouraima et al./oper. res. eng. sci. theor. appl. 3 (x) (2020) 1-20 bouraima et al./oper. res. eng. sci. theor. appl. 4 (2) (2021) 13-35 16 2020). vesković et al., (2016) used the fuzzy ahp approach to examine the operation of railways. vesković et al., (2018) evaluate the management of railway through the combination of the delphiswara mabac approaches. the performance of goods transport in the railway sector is measured by blagojević et al., (2020) through the usage of fuzzy-ahp-dea approaches. simić, soušek, and jovčić (2020) assessed the risk related to the railway infrastructure through the application fuzzy mcdm picture. blagojević et al., (2021) examined the safety degree of the railway crossings with a new hybrid fuzzy mcdm approach so that durable traffic management can be reached. a new hybrid saw (simple additive weighting) rn (rough numbers) method introduced by stević et al., (2017) was used to choose wagons for the internal logistic transport enterprise. a choice of suitable alternative for the passenger rail operators business was done by vesković et al. (2020) through a new hybrid fuzzy piprecia (pivot pairwise relative criteria importance assessment)fuzzy -edas approach. blagojević et al., (2020) assessed the safety of railway traffic using a new integrated fuzzy piprecia-entropy-dea. not much structural performance has been achieved in most of ssa’s countries' railways, especially in recent times. nonetheless, new investments and developments have been noticed on the rail and some actions are taken in place to rejuvenate the railway system in most of ssa’s countries. a renaissance has been felt in the railway system through the development of new lines and modernization and rehabilitation of old lines. as consequence, performance criteria are very important to measure and manage the railway sub-sector. the performance indicators for the railway system have been elucidated by onatere, nwagboso, and georgakis (2014) in nigeria. however, no research has been conducted regarding a comparative analysis of these performance indicators between countries from different regions of sub-saharan africa. as consequence, this research is new and different from previous studies related to african railway performance since it takes into account countries from west africa (ghana and nigeria), east africa (ethiopia and kenya), and central africa (cameroon). 3. materials and methods section 3 is divided into two sub-sections. the first sub-section presents the materials which are the case study, where thirteen parameters are used to assess the railway performance of five selected ssa countries. the second sub-section deals with the presentation of the models used and the entropy-marcos algorithm is shown 3.1 materials (case study) section 3.1 includes the background of the railway system in the selected countries (section 3.1.1), the definition of key performance indicators (section 3.1.2), and the formation of the multi-criteria model (section 3.1.3). 3.1.1. overview of the railway in selected countries in this study, five countries have been selected for the performance analysis based on the recent construction of new lines and maintenance and rehabilitation of assessing the performance of sub-saharan african (ssa) railways based on an integrated entropy-marcos approach 17 existing networks. they comprise ghana and nigeria in west africa, ethiopia and kenya in east africa, and cameroon in central africa, as can be seen in figure 1. the construction of the existing railway in cameroon dates back to the 1900s. being single track, it consists of the metric gauge with wood and iron sleepers. the cameroonian railway network may be categorized into three routes: transcam i line (also referred to as the central railway line), connecting douala to yaoundé, is camrail’s central line; transcam ii line (also referred to as the northern line) connecting yaoundé to ngaoundere; and the western line running between douala and kumba (douala-mbanga-nkongsamba line, mbanga~kumba line). the total length of the railways is 1, 270km (figure 2-a). although the country has the most important and heaviest railway structures among countries of the sub-region, it is less extensive and operational in only part of the country. the only line that is functional provides a durable communication link between the north and south of the country, whereas it is still not operating at the international level. as consequence, the cameroonian government commissioned the national railway master plan in cameroon project in 2009 intending to construct 6000 km of lines categorized into short (s), mid (m), and long (l) term; with double track and standard gauge and in the same time develop urban railway for yaoundé and douala. figure 1. countries of sub-saharan african contemplated in the study the first railway line built in ethiopia dates back to 1917 and links ethiopia to djibouti (figure 2-b). it is a 784km metric gauge railway of which 475 km are destroyed and abandoned due to poor maintenance. the national railway network of ethiopia (nrne) is in charge of the management and operation of the railway. in recent years, the national railway has been modernized through the completion of the addis ababa–djibouti electrified standard gauge railway and the ongoing construction of the awash–weldiya and weldiya–mekelle lines. additionally, there is an urban light rail system in the capital which started operation in 2015 and represents the first light rail and rapid transit in the eastern and sub-saharan africa region. the existing 947 km ghanaian railway network (figure 2 c) comprises three lines: the eastern line (kumasi –accra: 303.9 km), the western line (kumasi to sekondi-takoradi: 266.8 km), and the central line (eastern-western). most of the existing lines are single track, except a 32 km double-track line from takoradi to manso. bouraima et al./oper. res. eng. sci. theor. appl. 3 (x) (2020) 1-20 bouraima et al./oper. res. eng. sci. theor. appl. 4 (2) (2021) 13-35 18 the kenyan narrow-gauge railway (ngr) still plays a crucial role in the country’s transport and logistics. its construction began in the year 1896 under british rule. the mainline is composed of the 530.3km mombasa-nairobi section and the 551.88km nairobinakuru-malaba, at kenya’s border with uganda (figure 2-d). this line is operational mostly for freight with a speed range of 20km/h to 30km/h from the mombasa to malaba border. the kenya vision 2030 which is the country’s future development blueprint puts forward expansion and development of the railway system as one of the key flagship projects. the kenya government identified the northern corridor and the lapsset corridor for the development of the modern standard gauge railway (sgr). the northern corridor is made up of; mombasanairobi, nairobi-naivasha, naivasha–narok–bomet–nyamira–kisumu, and kisumu– yala–mumias–malaba. the lamu port south sudan ethiopia transport (lapsset) corridor is a regional project intended to create seamless connectivity between kenya and her neighbors ethiopia and south sudan. the construction of nigeria’s existing railway network began in 1898 under british colonial power. this includes a 3,505 km old narrow-gauge single track running through three main north-south branch lines that run diagonally through the country (figure 2-e). these lines initially played a significant economic role. to develop and refurbish the railway network, as mentioned in the 25-year strategic plan, all the existing 3505-km network of the narrow-gauge track will be converted for commercial freight and new standard-gauge lines will be built for passenger traffic that will link the economic centers and all the main states. this explains the construction of two main standard gauge railway (sgr) greenfield projects that have been backed by chinese funding: the new 2,733 km lagos-kano sgr line project is the first one substituting the colonial track, and split into four portions: lagos-ibadan, ibadan-kaduna, kaduna-kano, and abuja-kaduna and the new coastal railway line linking lagos to calabar through port harcourt and warri. (a) assessing the performance of sub-saharan african (ssa) railways based on an integrated entropy-marcos approach 19 (b) (c) (d) bouraima et al./oper. res. eng. sci. theor. appl. 3 (x) (2020) 1-20 bouraima et al./oper. res. eng. sci. theor. appl. 4 (2) (2021) 13-35 20 (e) figure 2. railway networks of different countries (a) cameroon, (b) ethiopia, (c) ghana, (d) kenya, (e) nigeria. 3.1.2. defining key performance indicators different actions were employed to examine and trace an organization’s development upon its objective. according to henning, essakali, and oh (2011), the quality of an organization's performance is quantified through kpis. the choice and operation of adequate kpis might be completely difficult, particularly when handling an organization like the railway sector in sub-saharan africa. for this purpose of evaluating sub-saharan african railway performance, thirteen indexes were applied, as shown in figure 3. in this study, we follow the indexes based on the literature reviews related to kpis (onatere et al., 2014) as follows: safety, security, internal business aspect, intermodal aspect, innovation, and learning aspect, and customer satisfaction. safety is related to the preservation of property and life through the advanced technology, rule, and management of all kinds of the railway sector. some railway accidents have been noticed in some of the sub-saharan african countries because of the poor safety measures. there is the occurrence of the death of some individuals because of the disposition of wares by traders along rail lines and carelessness of people when traversing lines. also, the congested state of trains with people on the rooftop causes deaths of people who fall from trains. the kpis for the safety criteria are shown in figure 3. security is a component of safety, from the substantial preservation of infrastructure to techniques that protect the information network. appropriate security actions are very important in the country where there is the occurrence of terrorist attacks and the presence of hard drugs and hemp used by people during the train journey. the kpis for the security criteria are shown in figure 3. internal business viewpoint is an ameliorated inner performance of the railway transport which is important for the customer satisfaction requirements. as consequence, the evaluation of whether the inner performance directed the necessity assessing the performance of sub-saharan african (ssa) railways based on an integrated entropy-marcos approach 21 or prediction of the client is pivotal. the kpis for the internal business viewpoint are shown in figure 3. figure 3. performance indicators for railway system measurement intermodality is the involvement of diverse transportation modes for travel. as consequence, the construction of stations of different types of public transport modes such as rail, airport, and bus should be close to each other. by preference, they should just step away, which makes it convenient for the traveler to link with other transport means. the kpis for intermodal perspective are shown in figure 3. innovation and learning perspective is considered as the design and application of the business management initiatives emphasized by the company that foster increased innovation and learning among the workforce. the sector in most africans has endured deterioration with regards to high profile personnel. the kpis for innovation and learning criteria are shown in figure 3. bouraima et al./oper. res. eng. sci. theor. appl. 3 (x) (2020) 1-20 bouraima et al./oper. res. eng. sci. theor. appl. 4 (2) (2021) 13-35 22 customers’ satisfaction has mostly been ignored in the existing african rail transport system due to poor facilities. the satisfaction of commuters should become a preference and vital for sustainable railway development since under normal cases, transport services are required by commuters. as consequence, in the case of dissatisfaction, they will refer to other modes of transport. the kpis for customer satisfaction are shown in figure 3. among these criteria, the number of collisions, the recorded accidents and incidents, the terrorist incidence, and the number of customer complaints are criteria of underestimate type and are included in the cost group. meanwhile, others are criteria of interest type, i.e. they need to be enhanced. 3.1.3. forming a multi-criteria model based on criteria associated with the kpis, experts from different countries have evaluated each criterion based on the linguistic scale (table 1) to make a decision matrix (table 2). table 1. linguistic scale for the evaluation of alternatives depending on the type of criteria criteria scale 1 very poor-vp 2 poor -p 3 medium poor-mf 4 fair -f 5 medium good -mg 6 good-g 7 very good-vg table 2. decision matrix a1 a2 a3 a4 a5 cam nig gha eth ken c11 3 3 3 2 2 c12 3 3 2 2 2 c21 3 3 2 2 1 c22 4 4 5 6 6 c31 4 4 2 5 5 c32 4 4 2 6 5 c33 2 2 3 4 5 c41 2 2 2 2 4 c42 2 2 4 3 4 c51 4 4 2 6 5 c52 4 4 3 5 5 c61 4 4 4 4 4 c62 4 4 3 5 4 note: cam (cameroon), nig (nigeria), gha (ghana), eth (ethiopia), ken (kenya) assessing the performance of sub-saharan african (ssa) railways based on an integrated entropy-marcos approach 23 3.2. methods the entropymarcos model is implemented in two steps. in the first step, the determination of criteria weights is done using the entropy model (shannon, 1948) right after their evaluation by experts. in the second step, these weight coefficients are employed to rank alternatives through the marcos model. in the following sections (sections 3.2.1 and 3.2.2), the steps of the entropy and marcos model are presented. 3.2.1. entropy method the entropy method, originally obtained from thermodynamics (clausius, 1865), and employed to examine the irremediable situation of a procedure (mon, cheng, & lin, 1994), is a means of ambiguity in information produced regarding the hypothesis of the probability. the entropy theory is firstly initiated by shannon (1948) as a concept to determine weights in an objective manner(zou, yi, & sun, 2006). it includes successive steps: at first, the initial matrix is normalized through equation (1). (1) where stands for normalized values and represents primary decisionmaking matrix values. secondly, equation (2) is employed to compute the entropy measure (2) where m stands for the number of alternatives. thirdly, equation (3) is used to compute the criterion weight (3) where n stands for criteria quantity 3.2.2. marcos method the marcos method depends on the interaction between ideal and anti-ideal options and alternatives. regarding the established correlations, the beneficial functions of options are settled and the compromise classification is produced according to both options. the beneficial function is the location of an alternative concerning both options. the best option is the one that is the nearest to ideal and concomitantly the anti-ideal mentioning point. the marcos method is performed through the following steps (đalić et al., 2020; mitrović simić et al., 2020; puška, stević, & stojanović, 2021; stanković et al., 2020; stević & brković, 2020; puška, & chatterjee, 2020; stević, tanackov, & subotić, 2020): step 1: initial decision-making matrix creation through the evaluation by experts. step 2: extended initial matrix modeling through the setting of the ideal (ai) and anti-ideal (aai) solution. bouraima et al./oper. res. eng. sci. theor. appl. 3 (x) (2020) 1-20 bouraima et al./oper. res. eng. sci. theor. appl. 4 (2) (2021) 13-35 24 (4) the anti-ideal solution (aai) is the least effective option while the ideal solution (ai) represents the best option. regarding the criteria aspect, equations (2) and (3) are respectively applied to determine the aai and ai: (5) (6) where there is benefit group criteria (b) and cost group criteria (c) step 3: extended initial matrix normalization (x). in this step, equations (7) and (8) are used to get the components of the normalized matrix: n= = if j c (7) if j b (8) where and are the components of the matrix x step 4: weighted matrix v= calculation through equation (9) multiplying the normalized matrix n with the weight coefficients of the criterion (9) step 5: computation of utility degree ki, using equations (10) and (11) concerning the anti-ideal and ideal options. (10) (11) where (i=1, 2,…, m) stands for the aggregates of the components of the weighted matrix v, and calculation through equation (12) (12) step 6: use equation (13) to compute the utility function of alternatives f (ki). the utility function is the arrangement of the detected option concerning both solutions. (13) assessing the performance of sub-saharan african (ssa) railways based on an integrated entropy-marcos approach 25 where the utility function (anti-ideal solution, see equation 14) and the utility function (ideal solution, see equation 15) (14) (15) step 7: classification of the alternatives according to the utility function results. alternative with greater utility function value is advisable. 4. results and discussion 4.1 entropy method the entropy method is used for the determination of weights for each criterion. at first, equation (1) is employed to normalize the decision matrix (table 3) for profitable and non-profitable criteria, respectively. then, the determination of entropy measures of each criterion is made. next, equations (2) and (3) are used for the weight calculation (table 4). the results from table 4 showed that labor productivity (internal business perspective) is the most significant criterion with a higher value (0.138). this is understandable because most considerable growth in resources is predicted from it. this is succeeded by the terrorist incidence (security) which is a non-profitable criterion at a value of 0.133. the quantity of employees that are exposed to the training (innovative and learning viewpoint) which is of beneficial type comes in the third position with a value of 0.114. the other criteria are classified as follows: c31 (benefit type) > c41 (benefit type) > c42 (benefit type) > c33 (benefit type) > c52 (benefit type) > c12 (cost type) > c11 (cost type) > c62 (benefit type) > c22 (benefit type) > c61 (cost type). table 3. normalized matrix a1 a2 a3 a4 a5 c11 0.231 0.231 0.231 0.154 0.154 c12 0.250 0.250 0.167 0.167 0.167 c21 0.273 0.273 0.182 0.182 0.091 c22 0.160 0.160 0.200 0.240 0.240 c31 0.158 0.211 0.105 0.263 0.263 c32 0.150 0.200 0.100 0.300 0.250 c33 0.176 0.118 0.176 0.235 0.294 c41 0.167 0.167 0.167 0.167 0.333 c42 0.133 0.133 0.267 0.200 0.267 c51 0.227 0.182 0.091 0.273 0.227 c52 0.261 0.174 0.130 0.217 0.217 c61 0.238 0.190 0.190 0.190 0.190 c62 0.238 0.190 0.143 0.238 0.190 bouraima et al./oper. res. eng. sci. theor. appl. 3 (x) (2020) 1-20 bouraima et al./oper. res. eng. sci. theor. appl. 4 (2) (2021) 13-35 26 table 4 entropy values and entropy weights entropy value entropy weight c11 0.989 0.039 c12 0.987 0.043 c21 0.961 0.133 c22 0.990 0.034 c31 0.969 0.107 c32 0.960 0.138 c33 0.972 0.095 c41 0.970 0.103 c42 0.972 0.096 c51 0.967 0.114 c52 0.984 0.054 c61 0.997 0.009 c62 0.990 0.035 4.2. marcos method table 5 shows the extended initial matrix based on step 2 of the marcos approach through equations (4)– (6). the rate of collisions (c11), the terrorist incidence (c21), and the number of customer complaints (c61) are of a nonprofitable type and using equation (5), the anti-ideal solution (aai) has been calculated and represents the maximum attribute, with a value of 3 for c11, c12, and c21, and a value of 5 for c61. table 5. extended initial decision matrix criteria aai a1 a2 a3 a4 a5 ai c11 3 3 3 3 2 2 2 c12 3 3 3 2 2 2 2 c21 3 3 3 2 2 1 2 c22 4 4 4 5 6 6 6 c31 2 3 4 2 5 5 5 c32 2 3 4 2 6 6 6 c33 2 3 2 3 4 5 4 c41 2 2 2 2 2 4 2 c42 2 2 2 4 3 4 3 c51 2 5 4 2 6 6 6 c52 3 6 4 3 5 6 5 c61 5 5 4 4 4 4 4 c62 3 5 4 3 5 5 5 for the security of human being and belongings in the station (c22), the wagon and locomotive availability (c31), the labor productivity (c32), the line availability (c33), the ease of connection with another transportation mode (c41), the ease connection with other train services (c42), the number of employees for training/exposure sessions (c51), quantity of trained/exposed employees (c52), and the facilities at station (c62), 4, 2, and 3 are the lowest values for (c22); (c31, c32, c33, c41, c42, c51); and (c52, c62) respectively and are involved in the aai solution. the determination of values comprised of the ideal solution (ai) is made using assessing the performance of sub-saharan african (ssa) railways based on an integrated entropy-marcos approach 27 equation (6). the values of 2, 1, and 4 are the smallest ones for (c11, c12), (c21), and (c61), whereas 6, 5, and 4 are the highest ones for (c22, c32, c51, c52), (c31, c33, c62), and (c41, c42), respectively for non-beneficial type (cost). following the extension of the initial matrix, equation (7) is used for the normalization of nonprofitable type while equation (8) is applied in the case of the profitable type. table 6 illustrated the normalization of the decision matrix. = if j c =2/3=0.667, for non-beneficial type if j b =3/4=0.750, for benefit type table 6. normalized decision matrix aai a1 a2 a3 a4 a5 ai c11 0.667 0.667 0.667 0.667 1.000 1.000 1.000 c12 0.667 0.667 0.667 1.000 1.000 1.000 1.000 c21 0.333 0.333 0.333 0.500 0.500 1.000 1.000 c22 0.667 0.667 0.667 0.833 1.000 1.000 1.000 c31 0.400 0.600 0.800 0.400 1.000 1.000 1.000 c32 0.333 0.500 0.667 0.333 1.000 0.833 1.000 c33 0.400 0.600 0.400 0.600 0.800 1.000 1.000 c41 0.500 0.500 0.500 0.500 0.500 1.000 1.000 c42 0.500 0.500 0.500 1.000 0.750 1.000 1.000 c51 0.333 0.833 0.667 0.333 1.000 0.833 1.000 c52 0.500 1.000 0.667 0.500 0.833 0.833 1.000 c61 0.800 0.800 1.000 1.000 1.000 1.000 1.000 c62 0.600 1.000 0.800 0.600 1.000 0.800 1.000 the weight normalized matrix is then computed through the multiplication of the precedent normalized matrix by the alternatives/ criteria values acquired in the entropy approach. table 7 indicates the normalized weighted matrix. table 7. weight normalized decision matrix aai a1 a2 a3 a4 a5 ai c11 0.026 0.026 0.026 0.026 0.039 0.039 0.039 c12 0.029 0.029 0.029 0.043 0.043 0.043 0.043 c21 0.044 0.044 0.044 0.067 0.067 0.133 0.133 c22 0.023 0.023 0.023 0.028 0.034 0.034 0.034 c31 0.043 0.064 0.085 0.043 0.107 0.107 0.107 c32 0.046 0.069 0.092 0.046 0.138 0.115 0.138 c33 0.038 0.057 0.038 0.057 0.076 0.095 0.045 c41 0.052 0.052 0.052 0.052 0.052 0.103 0.103 c42 0.048 0.048 0.048 0.096 0.072 0.096 0.096 c51 0.038 0.095 0.076 0.038 0.114 0.095 0.114 c52 0.027 0.054 0.036 0.027 0.045 0.045 0.054 c61 0.007 0.007 0.009 0.009 0.009 0.009 0.009 c62 0.021 0.035 0.028 0.021 0.035 0.028 0.035 bouraima et al./oper. res. eng. sci. theor. appl. 3 (x) (2020) 1-20 bouraima et al./oper. res. eng. sci. theor. appl. 4 (2) (2021) 13-35 28 through the marcos approach, the final results have been obtained in table 8 with the application of equations from (10) to (15). the summarization of all values for the alternatives (by rows) is shown below through equation (12). =0.026+0.029+0.044+0.023+0.043+0.046+0.038+0.052+0.048+0.038+0.026+0. 007+0.021=0.441 at the same time, the values for the remained alternatives are procured. the calculation of the utility of degree concerning the anti-ideal solution is done through equation (10). an illustration calculation is shown bellows. meanwhile, the utility degrees concerning the ideal solution are acquired by applying equation (11), e.g.: equation (14) is used to set the utility function regarding the anti-ideal solution as follows: at the same time, equation (15) is used for the utility function regarding the ideal solution as follows: at last, equation (13) is used to get the utility function of alternative a1: the remained values that appeared in the final results are got identically as elucidated in table 8. based on the results of the new integrated method, the performance evaluation showed that the alternative with code 5 (kenya) has the best performance followed by alternatives under codes 4 and 1 (ethiopia and cameroon) in the classification, respectively. a look in the classification showed that no much difference exists between the third and fourth positions and a variation in the classification can be predicted for future evaluation based on expert judgment. although the railway system in nigeria is being rejuvenated through the construction of new standard gauge railway lines, its railway performance is lower in comparison to cameroon. assessing the performance of sub-saharan african (ssa) railways based on an integrated entropy-marcos approach 29 this can be explained by the fact that there are security challenges, poor facilities at a station in the old railway networks, and a higher rate of commuter complaints. table 8 finding of the marcos approach. rank aai 0.441 1.000 a1 0.602 1.365 0.602 0.306 0.694 0.531 3 a2 0.586 1.327 0.586 0.306 0.694 0.516 4 a3 0.553 1.252 0.553 0.306 0.694 0.487 5 a4 0.830 1.880 0.830 0.306 0.694 0.731 2 a5 0.942 2.135 0.942 0.306 0.694 0.830 1 ai 1.000 1.000 5. sensitivity analysis a comparative evaluation is carried with other seven methods: edas – evaluation based on distance from average solution (keshavarz ghorabaee et al., 2015), saw – simple additive weighting method (kishore et al., 2020, durmić et al. 2020), aras – additive ratio assessment (zavadskas & turskis, 2010), cocoso combined compromise solution (yazdani et al., 2019), mabac – multi-attributive border approximation area comparison (pamučar & ćirović, 2015, pamučar et al. 2021), topsis – technique for order of preference by similarity to ideal solution (anthony et al., 2019), and waspas – weighted aggregated sum product assessment (zavadskas et al., 2012). the results of this comparative analysis are shown in figure 4. as can be seen from it, there were certain changes in the ranks, which is a consequence of a diverse normalization approach in applying other approaches. as consequence, one of the sources of variations in the rankings is emulated in a very small variation in the values of some alternative solutions obtained in the initial model. a look at figure 5 indicates that the greatest alternative does not vary from its initial position whichever method is applied. as consequence, the fifth alternative keeps its first place. the second place is assigned to the fourth alternative for all the methods, with exception of topsis, where it takes the fourth place. there is no variation in position for all the alternatives when using the marcos, waspas, aras, edas, and saw approaches. however, when using mabac and the five antecedent methods, there is only one variation in the classification where a2 and a3 replace their positions occupying the fifth and the fourth place, respectively. when applying the marcos and cocoso methods for a comparative analysis for the classification, some moderate variations are noticed whereas in the case of the topsis method, the variation in the classification is a little bit more. bouraima et al./oper. res. eng. sci. theor. appl. 3 (x) (2020) 1-20 bouraima et al./oper. res. eng. sci. theor. appl. 4 (2) (2021) 13-35 30 figure 4. values of alternatives through a comparative analysis figure 5. ranking in a comparative analysis of different methods the ws coefficient developed by salabun and urbaniak (2020) was computed to examine the rankings similarity as shown in figure 6. the benefit of this coefficient relies on the fact that locations at the summit of the classification have a powerful influence on the similarity than those more distant, which is accurate in the process of decision making. assessing the performance of sub-saharan african (ssa) railways based on an integrated entropy-marcos approach 31 figure 6. determination of the ws coefficient as can be seen in figure 6, the previous discussion where the ws coefficient has values 1 (waspas, aras, edas, and saw), and 0.971 (mabac) show an extremely high correlation in ranking alternatives. a little bit of correlation of marcos method with cocoso exists and the value is 0.901, whereas the difference is large for marcos method in comparison to the topsis method, i.e., the smallest correlation with a value of 0.792. 6. conclusion in this paper, an assessment of sub-saharan african railways performance was conducted. a multi-criteria model consisting of six main criteria and five alternatives was formed. for their evaluation, a new integrated entropy-marcos model was proposed and applied. the results showed that labor productivity is the most weighted sub-criterion. considering the ranking of the railway's performance, kenya is the best alternative with a higher utility function value of 0.830 followed by ethiopia with 0.731 as the utility function value. cameroon and nigeria came in the third and fourth positions with approximately the same utility function value of 0.531 and 0.516, respectively. ghana represents the worst alternative with the lowest utility function value of 0.487. the results obtained in the paper were validated through an extensive sensitivity analysis. the findings of this paper can assist decision-makers to consider these parameters as insert indicators for all operative, designing, and planning investigations. in addition, the findings can also serve as a benchmark for the performance analysis of other railway systems in other african countries. the continuity of this study pertains to the incessant surveying and repeated assessment of the railway transportation system in the sub-saharan africa region bouraima et al./oper. res. eng. sci. theor. appl. 3 (x) (2020) 1-20 bouraima et al./oper. res. eng. sci. theor. appl. 4 (2) (2021) 13-35 32 together with the newly built standard gauges’ railways across the region, which can contribute to the socio-economic and regional inter-trade integration and wealth of the region. although a new integrated entropy-marcos is proposed in this research, the future study may apply the use of integrated fucommarcos, fuzzy pipreciadea, delphi-swara-mabac, and fuzzy-ahp for the evaluation of railway transportation system or factors that impede its sustainability. also, the analysis of the railway system should be at the continental level. references anthony, p., behnoee, b., hassanpour, m., & pamucar, d. 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(2006). entropy method for determination of weight of evaluating indicators in fuzzy synthetic evaluation for water quality assessment. journal of environmental sciences, 18(5), 1020-1023. © 2021 by the authors. submitted for possible open access publication under the terms and conditions of the creative commons attribution (cc by) license (http://creativecommons.org/licenses/by/4.0/). assessing the performance of sub-saharan african (ssa) railways based on an integrated entropy-marcos approach mouhamed bayane bouraima 1, 2, željko stević 3*, ilija tanackov 4, yanjun qiu 1 1. introduction 2. literature review 3. materials and methods 3.1 materials (case study) 3.1.1. overview of the railway in selected countries 3.1.2. defining key performance indicators 3.1.3. forming a multi-criteria model 3.2. methods 3.2.1. entropy method 3.2.2. marcos method 4. results and discussion 4.1 entropy method 4.2. marcos method 5. sensitivity analysis 6. conclusion references plane thermoelastic waves in infinite half-space caused operational research in engineering sciences: theory and applications vol. 5, issue 1, 2022, pp. 90-106 issn: 2620-1607 eissn: 2620-1747 doi: https://doi.org/10.31181/oresta180222016p * corresponding author. 2017476603@ufs4free.ac.za (d. pavolo), chikobvu@ufs.ac.za (d. chikobvu) estimating rubber covered conveyor belting cure times using multiple simultaneous optimisations ensemble domingo pavolo*, delson chikobvu department of mathematical statistics and actuarial science, faculty of natural and agricultural sciences, university of the free state, south africa received: 15 july 2021 accepted: 08 november 2021 first online: 18 february 2022 research paper abstract: multiple response surface methodology (mrsm) has been the favorite method for optimizing multiple response processes though it has two weaknesses which challenge the credibility of its solutions. the first weakness is the use of experimentally generated small sample size datasets, and the second is the selection, using classical model selection criteria, of single best models for each response for use in simultaneous optimization to obtain the optimum or desired solution. classical model selection criteria do not always agree on the best model resulting in model uncertainty. the selection of single best models for each response for simultaneous optimization loses information in rejected models. this work proposes the use of multiple simultaneous optimizations to estimate multiple solutions that are ensembled in solving a conveyor belting cure time problem. the solution is compared with one obtained by simultaneous optimization of single best models for each response. the two results were different. however, results show that it is possible to obtain a more credible solution through ensembling of solutions from multiple simultaneous optimizations. key words: multiresponse surface methodology, ensembling, credibility of results, solution uncertainty, small sample size problems, simultaneous optimisation 1. introduction the mining industry is at the heart of the southern african development community (sadc) region’s economic activities and development. conveyor belts are critical for conveyance of bulk ore over distances and through various stages of processing. the regional product quality standard minimum requirements for general purpose rubber covered conveyor belts for the mining industry were amended. the component adhesion requirement was increased from 5n/mm to 7n/mm. however, key customers were insisting on a minimum of 10n/mm adhesion and 60⁰ shore a rubber compound cover hardness. after redesigning of the specifications of rubber pavolo & chikobvu/oper. res. eng. sci. theor. appl. 5(1) (2022) 90-106 91 compounds, a client manufacturing company required optimum cure times (tc), which would ensure a minimum of 12n/mm adhesion and 60⁰ shore a hardness, to be determined for the vulcanisation of different conveyor belt thicknesses (rt) for use in shop-floor work instructions. figure 1. illustrating the conveyor belting vulcanization process problem given the illustrated process in figure 1, it was thus intended to estimate credible cure times (tc) for given rubber thicknesses (rt), as shown in table 1 below. table 1. showing the expected solution 𝐑𝐭 (𝐦𝐦) 7 8 9 10 11 12 13 14 15 16 17 18 19 20 𝐓𝐜(𝐦𝐢𝐧. ) 𝐓𝟕 𝐓𝟖 𝐓𝟗 . . . . . . . . . . 𝐓𝟐𝟎 for manufacturers, optimum cure time (tc) is critical for product quality and production process productivity. good adhesion between conveyor belt components (covers, skims and reinforcement fabrics) ensures that they do not separate during heavy duty operations in the mines. the top and bottom rubber covers protect the reinforcement fabrics, therefore hardness is essential for wear resistance to the abrasive mining operational environments. the separation of belting components during heavy duty operation and excessive rubber cover wear are the two major failures of conveyor belting during mining operations. increasing adhesion between belting components and cover hardness ensures more belting life and therefore lower mining operational costs. beyond just providing a solution to the client company, the study sought to recommend to the conveyor belt manufacturing industry a credible and efficient tool for converting changes in product standard requirements to production process input parameters. quality and productivity are critical manufacturing industry competitive factors and the speed of successfully implementing change is critical in any industry as it gives first mover advantages. this work is of interest, therefore, to operations researchers, industrial engineers and business management strategists in the conveyor belting manufacturing industry. estimating rubber covered conveyor belting cure times using multiple simultaneous optimizations ensemble 92 the authors could not find anywhere in literature were cure times per given conveyor belt thickness were estimated for the vulcanisation process of general purpose rubber covered conveyor belting. literature only gives methodologies for estimating the cure times of different rubber compounds. a rubber covered conveyor belt is constructed from a rubber cover compound, a rubber skim compound (which provides the bonding strength between components) and reinforcement fabric. these components individually contribute to the overall vulcanization time due to different heat conductivities. in this work, the sufficiency of the contemporary multiple response surface methodology (mrsm) framework in estimating a credible solution to the problem was critiqued and two major weaknesses identified. firstly, it is statistically difficult to extract credible process information from small sample size mrsm datasets. secondly, the selection of single best models for each response for simultaneous optimization is prone to (1) loss of information in the rejected response models and (2) model uncertainty as model selection criteria do not always agree on the best model. this work proposes the use of multiple simultaneous optimizations to estimate multiple solutions that are then ensembled, to account for the two weaknesses in the mrsm framework, in solving the conveyor belting cure time problem. results suggest that the proposed ensemble system can provide a credible solution to the problem. 2. literature review 2.1. rubber technology perspective a number of techniques have been proposed in rubber technology literature to estimate the cure time of rubber products such as nuclear magnetic resonance spectroscopy, differential scanning calorimetry, dynamic mechanical analysis, adaptive neuro-fuzzy inference systems, equivalent cure concept, and artificial neural networks and finite element analysis (gatos and karger-kocsis, 2004; karaagâc et al., 2011; gough, 2017). the accepted basic tool of cure time estimation is the rheograph (appendix a) which shows how the shear strength of a sample of rubber changes with time during vulcanisation. the rheograph does not consider the case where there are different layers of constituent rubber compounds and other materials such as conveyor reinforcement fabric (nylon and/or polyester). the conveyor belting case requires a multiple factor and multiple response simultaneous optimisation solution methodology, hence the shift to multiple response surface methodology (mrsm). 2.2 multiple response surface methodology (mrsm) figure 2. showing the contemporary mrsm framework pavolo & chikobvu/oper. res. eng. sci. theor. appl. 5(1) (2022) 90-106 93 mrsm is an important tool for optimising manufacturing processes in industry. it is a collection of mathematical and statistical techniques that are useful for the modelling and analysis of problems in which multiple responses are influenced by several variables and the objective of the analysis is to optimize the responses by determining the best settings of the input variables (myers et al., 2016; hejazi et al., 2017; khuri, 2017). in figure 2, the mrsm dataset generation stage, stage (1), involves designing and running screening and mrsm experiments (myers et al., 2016). the stage (3) are the solution methodologies for estimating the operating conditions that optimise all the responses or at least keep them in desired ranges. mrsm experimental designs are constructed to eliminate or minimise correlations between chosen variables which allows independent estimation of variable effects and their potential interactions (myers et al., 2016; khuri, 2017; mäkelä, 2017). examples include central composite designs (ccd), box-behnken, orthogonal arrays, placketburman, and computer-generated optimal designs (myers et al., 2016; khuri, 2017; alhorn et al., 2019). the strength of mrsm is in efficient experimental designs (khuri, 2017). however, statistically, it is difficult to extract credible population information from small sample size datasets (rawlings et al., 1998; yuan and yang, 2005; xu and goodacre, 2018; jenkins and quintana-ascencio, 2020). this is the first weakness that requires to be accounted for to obtain credible solutions. optimisation in mrsm is multi-objective in nature, and is performed after regression modelling and model selection of single “best” models for each response (myers et al., 2016; khuri, 2017). mrsm solution methodologies rely heavily on classical model selection criteria for choosing the best model for each response for simultaneous optimisation. this the second weakness of the contemporary mrsm framework. problems associated with the contemporary mrsm contextual framework are presented in figure 3 below. figure 3. problems related to the current mrsm contextual framework estimating rubber covered conveyor belting cure times using multiple simultaneous optimizations ensemble 94 in this paper, the authors proposed and utilised a novel solution methodology that accounted for the two weaknesses to obtain a credible solution. 3. solution methodology the mrsm dataset generation for the rubber covered conveyor belting problem is explained in detail in pavolo and chikobvu (2020). the dataset was adopted as is and is shown in table 2. table 2. the two-factor ccd experiment mrsm dataset run t (min.) rt (mm) ave. hardness (0shore a) ave. adhesion(n/mm) 1 16 7.2 60 10.60 2 30 7.2 63 13.34 3 16 22.8 53 6.20 4 30 22.8 61 12.10 5 23 15 58 11.80 6 23 15 58 12.10 7 13 15 44 6.5 8 33 15 63 13.30 9 23 4 63 13.30 10 23 26 56 3.50 11 23 15 58 12.20 12 23 15 57 12.30 13 23 15 58 12.10 ensemble-based systems have been recommended for small sample size situations in literature (kittler, 1998; burnham and anderson, 2002; polikar, 2006; yang et al., 2016; ahangi et al., 2019). an ensemble system was considered the best option for accounting for the weaknesses of the contemporary mrsm framework and delivering a credible solution. the solution methodology is summarised in figure 4. figure 4. showing the solution methodology flow diagram pavolo & chikobvu/oper. res. eng. sci. theor. appl. 5(1) (2022) 90-106 95 at response surface analysis, the one hardness model with response surface conformity was adopted as is from pavolo and chikobvu (2020). however, in this work, all the adhesion response models were assumed to be response surface conforming. the estimated cure time solution was compared with one from a methodology structured after the contemporary mrsm contextual framework. figure 5 shows the strategies used in the solution methodology to deal with each problem listed in figure 3. figure 5. showing the strategies employed to deal with problems figure 6 summarises the problems of the contemporary solution methodologies and presents the advantages of the ensembling methodology from literature. figure 6. the advantages of the solution methodology vs. problems of contemporary mrsm estimating rubber covered conveyor belting cure times using multiple simultaneous optimizations ensemble 96 the formulae used for computation of theoretical accuracy are shown below. validation was computed against the minimum targeted response values as the sample size was too small to be split into a fitting set and a validation set. mspeval(min.): the validation minimum mean squared prediction error (mspeval(min.)) of a response model measures the minimum squared deviation of the model predictions from the targeted. mspeval(min.) is given below for a sample size n. mspeval(min.)= ∑ (𝒏𝒊=𝟏 𝒀𝒊−𝒀𝑻) 𝟐 𝒏 , (1) where 𝒀𝒊 is the ith estimated response, 𝒀𝑻 is the a response value. mspesimul: the mean squared prediction error at simultaneous optimisation (mspesimul) of a response model in an adhesion – hardness model pair indicates the mean squared deviation of the model predictions from the targeted and is given below for a sample size n as: mspesimul= ∑ (𝒏𝒊=𝟏 𝒀𝒊−𝒀𝑻) 𝟐 𝒏 , (2) where 𝒀𝒊 is the ith estimated response value at simultaneous optimisation. the mspesimul bias-variance decomposition estimates were integrated by arithmetic averaging to estimate the bias-variance-covariance decomposition of the mspesimul of the ensembled results (geman et al., 1992; ueda and nakano, 1996). mse(𝑓) = bias(𝑓)2 + var(𝑓) (3) and the expected ensemble mse is, e{mse(𝑓𝑒𝑛𝑠. )} = bias2 + ( 1 𝑘 ) ×variance + (1 1 𝑘 ) ×covariance (4) where k is the number of base models in the ensemble. prediction accuracy compromise: define prediction accuracy compromise (pac) as the difference between mspesimul and the mspeval(min.) of a response model. pac gives a picture of how models compromise their accuracy in the process of simultaneous optimisation. then % pac will be the percentage change in mspeval(min.) to achieve simultaneous optimisation. % pac = 100% x (mspesimul mspeval(min.)) / mspeval(min.) (5) relative accuracy: the relative accuracy is computed for each base model in the ensemble relative to the ensemble result and is given by: relative accuracy = 𝑵𝒖𝒎𝒃𝒆𝒓 𝒐𝒇 𝑩𝒂𝒔𝒆 𝑴𝒐𝒅𝒆𝒍 𝒐𝒓 𝑬𝒏𝒔𝒆𝒎𝒃𝒍𝒆 𝑪𝒐𝒓𝒓𝒆𝒄𝒕 𝑷𝒓𝒆𝒅𝒊𝒄𝒕𝒊𝒐𝒏𝒔 𝑻𝒐𝒕𝒂𝒍 𝑵𝒖𝒎𝒃𝒆𝒓 𝒐𝒇 𝑰𝒏𝒔𝒕𝒂𝒏𝒄𝒆𝒔 (6) pavolo & chikobvu/oper. res. eng. sci. theor. appl. 5(1) (2022) 90-106 97 4. results 4.1 all possible regression modelling results tables 3 and 4 below show the all possible ordinary least squares (ols) regression models for both responses after removal of response models that did not conform to the recommendations of the screening experiment at dataset generation. table 3. the twenty-five ols adhesion all possible regression response models model 𝛃𝟎 𝛃𝟏 𝛃𝟐 𝛃𝟏𝟐 𝛃𝟏𝟏 𝛃𝟐𝟐 tc.rt 12.2600 -0.0039 tc, rt 7.9500 0.3244 -0.3127 tc, tc .rt 3.2600 0.5100 -0.0124 tc, rt2 6.1800 0.3244 -0.0111 r, tc.rt 15.4100 -0.7910 0.0208 rt, tc 2 11.6700 -0.3127 0.0067 tc.rt, tc 2 8.9600 -0.0119 0.0105 tc.rt, rt2 10.4970 0.0203 -0.0258 tc 2, rt2 9.9100 0.0066 -0.0111 tc, rt, tc.rt 12.9400 0.1070 -0.6460 0.0145 tc, rt, tc 2 2.4100 0.8350 -0.3127 -0.0111 tc, rt, rt 2 3.6100 0.3244 0.3800 -0.0231 tc, tc.rt, tc 2 -2.2800 1.0200 -0.0124 -0.0111 tc, tc.rt, rt 2 9.1400 0.0910 0.0156 -0.0224 tc, tc 2, rt 2 -0.2500 0.9190 -0.0129 -0.0112 rt, tc.rt, tc 2 15.2400 -0.7710 0.0199 0.0003 rt, tc.rt, rt 2 11.0800 -0.0980 0.0208 -0.0231 rt, tc 2, rt 2 7.5200 0.3580 0.0066 -0.0224 tc.rt, tc 2, rt 2 10.3900 0.0189 0.0005 -0.0249 tc, rt, tc.rt, tc 2 7.4000 0.6180 -0.6460 0.0145 -0.0111 tc, rt, tc.rt, rt 2 8.6100 0.1070 0.0470 0.0145 -0.0231 tc, rt, tc 2, rt 2 -4.2500 1.0210 0.4300 -0.0151 -0.0248 tc, tc.rt, tc 2, rt 2 1.9500 0.7590 0.0168 -0.0149 -0.0234 rt, tc.rt, tc 2, rt 2 11.2100 -0.1130 0.0215 -0.0003 -0.0232 tc, rt, tc.rt, tc 2, rt 2 0.7400 0.8040 0.0970 0.0145 -0.0151 -0.0248 table 4. the twenty-five ols hardness all possible regression response models model 𝛃𝟎 𝛃𝟏 𝛃𝟐 𝛃𝟏𝟐 𝛃𝟏𝟏 𝛃𝟐𝟐 tc.rt 56.1800 0.0040 tc, rt 48.4600 0.5130 -0.1800 tc, tc .rt 45.7500 0.6040 0.0061 tc, rt2 46.5300 0.5130 -0.0030 r, tc.rt 60.2500 -0.9610 0.0339 rt, tc 2 54.8400 -0.1800 -0.0097 tc.rt, tc 2 52.8900 0.0045 -0.0111 tc.rt, rt2 55.0800 0.0209 -0.0181 tc 2, rt2 52.9000 0.0097 -0.0030 tc, rt, tc.rt 57.5000 0.0320 -0.7180 0.0321 tc, rt, tc 2 18.0000 3.3200 -0.1800 -0.0610 tc, rt, rt 2 57.5100 0.5130 -1.6290 0.0483 tc, tc.rt, tc 2 15.3000 3.4100 -0.0061 -0.0610 tc, tc.rt, rt 2 41.9300 0.8760 -0.0242 0.0146 tc, tc 2, rt 2 15.9000 3.3400 -0.06160 -0.0034 rt, tc.rt, tc 2 65.0600 -1.4960 0.0572 -0.00860 estimating rubber covered conveyor belting cure times using multiple simultaneous optimizations ensemble 98 rt, tc.rt, rt 2 69.3100 -2.4090 0.0339 0.0483 rt, tc 2, rt 2 64.0100 -1.6610 0.0098 0.0494 tc.rt, tc 2, rt 2 52.6600 -0.0094 0.0127 0.0039 tc, rt, tc.rt, tc 2 29.1000 2.8400 -0.9180 0.0321 -0.0610 tc, rt, tc.rt, rt 2 68.6000 0.0320 -2.3660 0.0321 0.0483 tc, rt, tc 2, rt 2 13.4000 3.5300 -0.0196 -0.0592 0.0108 tc, tc.rt, tc 2, rt 2 29.4200 3.0020 -1.4500 -0.0541 0.0423 rt, tc.rt, tc 2, rt 2 73.31000 -2.8470 0.0540 -0.0074 0.0048 tc, rt, tc.rt, tc 2, rt 2 40.5000 2.5210 -2.1870 0.0321 -0.0541 0.0423 hardness response model [tc, rt, tc.rt, tc2] was the only hardness model with a conforming response surface. 4.2. simultaneous optimisation results table 5 shows the simultaneous optimisation of the adhesion-hardness model pair [tc.rt, rt2] [tc, rt, tc.rt, tc2] using an excel spreadsheet tool. the rest of the adhesion response models were similarly optimised with the same hardness model. table 5. showing simultaneous optimisation on an excel spreadsheet tc rt adhesion hardness (min.) (mm) [t*rt, rt2] e2 [t, rt, t* rt, t2 ] e2 21 7 12 12.2169 0.0470 60 60.1317 0.0173 22 8 12 12.4186 0.1752 60 60.3616 0.1308 22 9 12 12.4266 0.1820 60 60.1498 0.0224 23 10 12 12.5860 0.3434 60 60.3540 0.1253 23 11 12 12.5111 0.2612 60 60.1743 0.0304 24 12 12 12.6282 0.3946 60 60.3528 0.1245 24 13 12 12.4704 0.2213 60 60.2052 0.0421 24 14 12 12.2610 0.0681 60 60.0576 0.0033 25 15 12 12.3045 0.0927 60 60.2425 0.0588 25 16 12 12.0122 0.0001 60 60.1270 0.0161 26 17 12 12.0134 0.0002 60 60.2862 0.0819 27 18 12 12.0036 0.0000 60 60.3876 0.1502 29 19 12 12.3685 0.1358 60 60.4041 0.1633 30 20 12 12.3570 0.1274 60 60.3000 0.0900 ave. 12.3270 mpse:0.1464 ave.: 60.2525 mpse: 0.0755 bias: 0.3270 var.: 0.0394 bias: 0.2525 var.: 0.0117 table 6 shows cure time estimates which each adhesion response model gave at simultaneous optimisation. table 6. showing the cure time estimate results for each adhesion response model rt (mm) 7 8 9 10 11 12 13 14 15 16 17 18 19 20 tc.rt 21 22 22 23 24 25 26 26 27 28 29 30 tc, tc.rt 21 22 22 23 24 25 26 27 28 29 30 tc, rt 2 21 22 22 23 23 24 24 25 26 27 28 30 rt ,tc.rt, 21 22 22 23 24 25 26 27 28 28 29 29 30 30 tc, rt 2 21 22 22 23 24 25 26 27 28 29 30 30 tc.rt, tc 2 22 23 23 24 25 26 26 27 28 29 30 tc.rt, rt 2 21 22 22 23 23 24 24 24 25 25 26 27 29 30 tc 2, rt 2 21 22 22 23 24 25 26 27 28 29 30 30 tc, rt, tc.rt 21 22 22 23 24 25 26 27 27 28 29 30 30 31 tc ,rt, tc 2 21 22 22 23 24 25 26 27 28 29 30 tc, rt, rt 2 22 22 22 23 23 24 24 24 25 26 27 28 30 31 tc, tc.rt, tc 2, 21 22 22 23 24 25 26 27 28 29 30 tc, tc.rt, rt 2 21 22 22 23 23 24 24 24 25 26 27 28 29 30 pavolo & chikobvu/oper. res. eng. sci. theor. appl. 5(1) (2022) 90-106 99 tc, tc 2, rt 2 21 22 22 23 23 23 24 24 25 26 28 30 rt ,tc.rt, tc 2 21 22 22 23 24 25 26 27 28 28 29 29 30 30 rt ,tc.rt, rt 2 21 22 22 23 23 24 24 24 25 26 26 28 29 30 rt, tc 2, rt 2 22 22 22 22 23 23 24 25 26 27 28 29 30 31 tc.rt, tc 2, rt 2 21 22 22 23 23 24 24 24 25 26 27 28 29 30 tc, rt, tc.rt, tc 2 21 22 22 23 23 24 25 26 27 28 29 30 tc, rt, tc.rt, rt 2 21 22 22 23 23 24 24 24 25 26 27 28 29 30 tc, tc.rt, tc 2, rt 2 21 22 22 23 23 24 24 24 25 25 26 27 29 30 tc, tc.rt, tc 2, rt 2 21 22 22 23 23 23 24 24 25 25 26 27 30 rt, tc.rt, tc 2, rt 2 21 22 22 23 23 24 24 24 25 26 27 28 29 30 tc, rt, tc.rt, tc 2, rt 2 21 22 22 23 23 24 24 24 25 25 25 27 28 31 table 7 shows the remaining thirteen adhesion response models with their cure time estimates after dropping those results that did not give estimates for the full rubber thickness range. table 7. showing the adhesion response models with simultaneous optimisation cure time estimates for the full rubber thickness range rt(mm) 7 8 9 10 11 12 13 14 15 16 17 18 19 20 model rt ,tc.rt, 21 22 22 23 24 25 26 27 28 28 29 29 30 30 tc.rt, rt 2 21 22 22 23 23 24 24 24 25 25 26 27 29 30 tc, rt, tc.rt 21 22 22 23 24 25 26 27 27 28 29 30 30 31 tc, rt, rt 2 22 22 22 23 23 24 24 24 25 26 27 28 30 31 tc, tc.rt, rt 2 21 22 22 23 23 24 24 24 25 26 27 28 29 30 rt ,tc.rt, tc 2 21 22 22 23 24 25 26 27 28 28 29 29 30 30 rt ,tc.rt, rt 2 21 22 22 23 23 24 24 24 25 26 26 28 29 30 rt, tc 2, rt 2 22 22 22 22 23 23 24 25 26 27 28 29 30 31 tc.rt, tc 2, rt 2 21 22 22 23 23 24 24 24 25 26 27 28 29 30 tc, rt, tc.rt, rt 2 21 22 22 23 23 24 24 24 25 26 27 28 29 30 tc, tc.rt, tc 2, rt 2 21 22 22 23 23 24 24 24 25 25 26 27 29 30 rt, tc.rt, tc 2, rt 2 21 22 22 23 23 24 24 24 25 26 27 28 29 30 tc, rt, tc.rt, tc 2, rt 2 21 22 22 23 23 24 24 24 25 25 25 27 28 31 a frequency analysis of the occurrence of the different cure time results is given in table 8. there were only seven possible cure time estimate solutions in table 7. the solution with the highest occurrence had a frequency of five. table 8. showing frequency of occurrence of cure time estimates results rt 7 8 9 10 11 12 13 14 15 16 17 18 19 20 frequency 1 21 22 22 23 24 25 26 27 27 28 29 30 30 31 1 2 22 22 22 23 23 24 24 24 25 26 27 28 30 31 1 3 22 22 22 22 23 23 24 25 26 27 28 29 30 31 1 4 21 22 22 23 23 24 24 24 25 25 25 27 28 31 1 5 21 22 22 23 24 25 26 27 28 28 29 29 30 30 2 6 21 22 22 23 23 24 24 24 25 25 26 27 29 30 2 7 21 22 22 23 23 24 24 24 25 26 27 28 29 30 5 estimating rubber covered conveyor belting cure times using multiple simultaneous optimizations ensemble 100 4.3 integration results table 9 shows the results of integrating the cure time estimates of table 6 using arithmetic averaging (a. ave.) and majority vote (m. vote). table 9. showing the integration of the thirteen cure time estimate results 7 8 9 10 11 12 13 14 15 16 17 18 19 20 rel. model acc. rt ,tc.rt, 21 22 22 23 24 25 26 27 28 28 29 29 30 30 36% tc.rt, rt 2 21 22 22 23 23 24 24 24 25 25 26 27 29 30 79% tc, rt, tc.rt 21 22 22 23 24 25 26 27 27 28 29 30 30 31 29% tc, rt, rt 2 22 22 22 23 23 24 24 24 25 26 27 28 30 31 86% tc, tc.rt, rt 2 21 22 22 23 23 24 24 24 25 26 27 28 29 30 100% rt ,tc.rt, tc 2 21 22 22 23 24 25 26 27 28 28 29 29 30 30 36% rt ,tc.rt, rt 2 21 22 22 23 23 24 24 24 25 26 26 28 29 30 100% rt, tc 2, rt 2 22 22 22 22 23 23 24 25 26 27 28 29 30 31 29% tc.rt, tc 2, rt 2 21 22 22 23 23 24 24 24 25 26 27 28 29 30 100% tc, rt, tc.rt, rt 2 21 22 22 23 23 24 24 24 25 26 27 28 29 30 100% tc, tc.rt, tc 2, rt 2 21 22 22 23 23 24 24 24 25 25 26 27 29 30 79% rt, tc.rt, tc 2, rt 2 21 22 22 23 23 24 24 24 25 26 27 28 29 30 100% tc, rt, tc.rt, tc 2, rt 2 21 22 22 23 23 24 24 24 25 25 25 27 28 31 64% ave 21 22 22 23 23 24 24 25 26 26 27 28 29 30 m. vote 21 22 22 23 23 24 24 24 25 26 27 28 29 30 three observations to note: (1)the two integration methods did not agree on two cure time estimates for rubber thicknesses 14 and 15 mm; (2) some adhesionhardness pairs had relative accuracy less than 50%; and (3) the majority vote result was equivalent to the result with the highest frequency in table 8. table 10 shows the bias-variance-covariance decomposition of the mspesimul of the ensemble of results. table 10. showing the bias-variance-covariance decomposition of the mspesimul mspe bias var. covar mspe bias var. covar. model rt ,tc.rt, 0.1430 0.3849 0.0609 0.1841 0.4015 0.0229 tc.rt, rt 2 0.1464 0.3270 0.0394 0.0755 0.2500 0.0117 tc, rt, tc.rt 0.1298 0.2980 0.0410 0.1726 0.3738 0.0329 tc, rt, rt 2 0.1121 0.2878 0.0292 0.1048 0.2890 0.0202 tc, tc.rt, rt 2 0.1417 0.3543 0.0162 0.0957 0.2852 0.0144 rt ,tc.rt, tc 2 0.1297 0.2636 0.0602 0.1841 0.4015 0.0229 rt ,tc.rt, rt 2 0.1513 0.3699 0.0144 0.0957 0.2852 0.0144 rt, tc 2, rt 2 0.5463 0.3323 0.0161 0.0957 0.2852 0.0144 tc.rt, tc 2, rt 2 0.1051 0.3006 0.0147 0.0957 0.2852 0.0144 tc, rt, tc.rt, rt 2 0.0992 0.2774 0.0223 0.0957 0.2852 0.0144 tc, tc.rt, tc 2, rt 2 0.4951 0.6186 0.1125 0.0755 0.2500 0.0117 rt, tc.rt, tc 2, rt 2 0.1265 0.3323 0.0161 0.0957 0.2852 0.0144 tc, rt, tc.rt, tc 2, rt 2 0.1561 0.6155 0.1373 0.0651 0.2200 0.0117 ave 0.21864 0.3586 0.0446 0.0937 0.1105 0.2998 0.0174 0.0209 there were six adhesion-hardness model pairs that have the same accuracy values on the hardness side. generally, for a high adhesion side mspesimul, there was a low mspesimul on the hardness side. this pattern, however, did not seem to have any significant relationship with the accuracy of the cure time estimates. pavolo & chikobvu/oper. res. eng. sci. theor. appl. 5(1) (2022) 90-106 101 table 11 gives the percentage accuracy compromise of the base model pairs of the ensemble at simultaneous optimisation. table 11. showing the pac results at simultaneous optimisation rt mspevalmin mse pac(h) pac(a) adhesion model % % rt, tc.rt 0.0242 2.3855 310 487 tc.rt, rt2 0.0321 1.3382 69 357 tc, rt, tc.rt 0.0405 2.3441 285 221 tc, rt, rt 2 0.0458 1.4710 145 134 tc, tc.rt, rt 2 0.0456 1.2815 114 211 rt, tc.rt, tc 2 0.0194 2.5300 114 569 rt, tc.rt, rt 2 0.0226 1.3200 114 220 rt, tc 2, rt 2 0.0445 1.8069 114 1128 tc.rt, tc 2, rt 2 0.0474 1.3377 114 219 tc, rt, tc.rt, rt 2 0.0407 1.2789 113 144 tc, tc.rt, tc 2, rt 2 0.0348 0.9842 33 1323 rt, tc.rt, tc 2, rt 2 0.0345 1.3689 114 267 tc, rt, tc.rt, tc 2, rt 2 0.0366 0.9762 69 1323 table 11 shows that it’s very difficult, were simultaneous optimisation is concerned, to find a model pair that has all the model accuracy criteria aligning. ➢ the response model pair with best mspevalmin (0.0194) had the worst mse (2.53). ➢ the adhesion response model with the best mse (0.9762) compromised the worst (% accuracy compromise, pac(a) = 1323%) to achieve simultaneous optimisation. ➢ the response model pair with the best pac on the hardness side (33%), had the worst pac on the adhesion side (1323%). ➢ there were six adhesion-hardness model response pairs with the same pac(h) value. these six were not necessarily the same ones with similar mspesimul values on the hardness side. the average pac(h) was lower compared to the pac(a). this suggests that response models do not necessary compromise the same to achieve simultaneous optimisation. 4.4 ensemble review results elimination of model pairs with relative accuracy less than 50% left nine adhesionhardness pairs in the ensemble. the arithmetic average and majority vote results of the reviewed ensemble were equal throughout the whole rubber thickness range as shown in table 12. estimating rubber covered conveyor belting cure times using multiple simultaneous optimizations ensemble 102 table 12. showing the result of eliminating response models with relative accuracy<50% rt (mm) 7 8 9 10 11 12 13 14 15 16 17 18 19 20 rel. model acc. tc.rt, rt 2 21 22 22 23 23 24 24 24 25 25 26 27 29 30 79% tc, rt, rt 2 22 22 22 23 23 24 24 24 25 26 27 28 30 31 86% tc, tc.rt, rt 2 21 22 22 23 23 24 24 24 25 26 27 28 29 30 100% rt ,tc.rt, rt 2 21 22 22 23 23 24 24 24 25 26 27 28 29 30 100% tc.rt, tc 2, rt 2 21 22 22 23 23 24 24 24 25 26 27 28 29 30 100% tc, rt, tc.rt, rt 2 21 22 22 23 23 24 24 24 25 26 27 28 29 30 100% tc, tc.rt, tc 2, rt 2 21 22 22 23 23 24 24 24 25 25 26 27 29 30 79% rt, tc.rt, tc 2, rt 2 21 22 22 23 23 24 24 24 25 26 27 28 28 30 100% tc, rt, tc.rt, tc 2, rt 2 21 22 22 23 23 24 24 24 25 25 25 27 28 31 64% ave 21 22 22 23 23 24 24 24 25 26 27 28 29 30 m. vote 21 22 22 23 23 24 24 24 25 26 27 28 29 30 table 13 shows that the accuracy results at simultaneous optimisation significantly improved, but more on the hardness side than the adhesion side. table 13. showing the accuracy results of the reviewed ensemble mspe bias var. covar mspe bias var. covar. model tc.rt, rt 2 0.1464 0.3270 0.0394 0.0755 0.2500 0.0117 tc, rt, rt 2 0.1121 0.2878 0.0292 0.1048 0.2890 0.0202 tc, tc.rt, rt 2 0.1417 0.3543 0.0162 0.0957 0.2852 0.0144 rt ,tc.rt, rt 2 0.1513 0.3699 0.0144 0.0957 0.2852 0.0144 tc.rt, tc 2, rt 2 0.1051 0.3006 0.0147 0.0957 0.2852 0.0144 tc, rt, tc.rt, rt 2 0.0992 0.2774 0.0223 0.0957 0.2852 0.0144 tc, tc.rt, tc 2, rt 2 0.4951 0.6186 0.1125 0.0755 0.2500 0.0117 rt, tc.rt, tc 2, rt 2 0.1265 0.3323 0.0161 0.0957 0.2852 0.0144 tc, rt, tc.rt, tc 2, rt 2 0.1561 0.6155 0.1373 0.0651 0.2200 0.0117 arithmetic ave 0.2104 0.3870 0.0447 0.0619 0.0888 0.2706 0.0148 0.0157 if the base models were the five adhesion response models with the same cure time estimates the theoretical accuracy of the ensemble would be as shown in table 14. it appeared, for this problem, that when the cure time estimates for different adhesionhardness pairs were the same, the theoretical accuracy on the hardness response side was the same. pavolo & chikobvu/oper. res. eng. sci. theor. appl. 5(1) (2022) 90-106 103 table 14. accuracy results of the ensemble with five base models with similar tc estimates mspe bias var. covar mspe bias var. covar. model tc, tc.rt, rt 2 0.1417 0.3543 0.0162 0.0957 0.2852 0.0144 rt, tc.rt, rt 2 0.1513 0.3699 0.0144 0.0957 0.2852 0.0144 tc.rt, tc 2, rt 2 0.1051 0.3006 0.0147 0.0957 0.2852 0.0144 tc, rt ,tc.rt, rt 2 0.0992 0.2774 0.0223 0.0957 0.2852 0.0144 rt, tc.rt, tc 2, rt 2 0.1265 0.3323 0.0161 0.0957 0.2852 0.0144 arithmetic ave 0.1248 0.3269 0.0167 0.0182 0.0957 0.2852 0.0144 0.0144 4.5 multiple ms criteria best model selection methodology results the first result was for the selection of the best model using majority vote of fifteen different model selection criteria. the formulae used to compute the criteria values are shown in the appendix. table 15 shows the model selection criteria values and their votes. adhesion response model [tc.rt, rt2] is the obvious best with a vote of 10. this minimises uncertainty. model [tc, tc.rt, tc2, rt2] follows behind with a vote of 6. table 15. showing multiple ms criteria selections model tc, rt, tc.rt, tc 2, rt 2 tc, tc.rt, tc 2, rt 2 rt, tc.rt, rt 2 tc.rt, rt 2 tc, rt, rt 2 tc, tc.rt, r2 (pr.) 26.5 51.5 49.9 65.4 49.4 52 adeq. pr. 10.4 4.1 5.7 1.8 11.9 5.4 cp-k 1.0 0.1 0 0 2.1 0 press 88.1 59.3 81.3 42.1 62.2 58.6 aic 11.7 9.8 11.6 9.8 13 17.3 bic 15.1 12.6 13.9 11.5 15.3 19 aicc 20.2 14.8 14.3 11 15.7 18.5 apcp 2.9 2.4 2.6 2.9 2.6 4.0 sbc 1.9 1.7 4.9 4.8 6.1 11.9 hqc 1.1 1.1 4.3 4.5 5.6 11.5 kicc 87.3 64.4 51.2 38.1 52.6 45.6 hq 0.5 0.5 4.2 4.2 5.6 11.7 kic 20.7 17.8 18.6 15.8 20 23.3 mkic 18.2 12 9.1 5.4 9.8 10.7 tic 13.7 11.8 13.6 11.8 15 19.3 vote 2 6 1 10 1 1 the simultaneous optimisation results of both response models [tc.rt, rt2] and [tc, tc.rt, tc2, rt2] are shown in tables 12 and 13. the two have the same cure time estimate and theoretical accuracy results on the hardness side. the cure time estimate result, however, was different from the multiple simultaneous optimisations ensemble one. 5. conclusion the dilemma of choosing from two different solutions, see table 16, both of which standing on strong positions makes the problem at hand challenging. however, an objective analysis and critic of each position helps in separating the two. estimating rubber covered conveyor belting cure times using multiple simultaneous optimizations ensemble 104 table 16. multiple ms criteria solution (s6) vs. ensemble solution (s7) rt 7 8 9 10 11 12 13 14 15 16 17 18 19 20 vote s6 21 22 22 23 23 24 24 24 25 25 26 27 29 30 2 s7 21 22 22 23 23 24 24 24 25 26 27 28 29 30 5 the multiple simultaneous optimisations ensemble cure time estimate solution (s7) shows credibility in that (i) it is the most frequent solution from the adhesionhardness model pairs, (ii) there is agreement between the two integration methodologies used, and (iii) by design, it fairly accounts for all the listed problems of the contemporary mrsm contextual framework. it accounts for dataset uncertainty, loss of information, model over-/underfitting, and model parameter bias by utilising multiple models and minimising discarded models. it minimises model uncertainty and small sample size inefficiency by totally avoiding the use of classical model selection criteria. on the other hand, seven of the ten model selection criteria that voted for the best single adhesion response model [tc.rt, rt2] are information criteria and three are prediction model selection criteria. this implies that the response model has the best parsimonious fit to the mrsm dataset, of all the 25 ols adhesion response models, and has good prediction capability. however, the cure time estimate solution (s6) is not considered the best in credibility because (i) model selection criteria have a small sample size inefficiency problem, (ii) they do not deal with the problem of model parameter bias, (iii) dataset uncertainty and (iv) since the methodology is structured as the contemporary mrsm framework, it loses information in discarded models by the selection and use of one model per response in simultaneous optimisation. it should be emphasised that where the model with the best parsimonious fit to the dataset is required, response model [tc.rt, rt2] is the model. the arguments above clearly separate the most credible cure time solution (s7) from the model with the best parsimonious fit to the mrsm dataset (s6]. the multiple simultaneous optimisations ensemble, therefore, is both logically and empirically a better way of obtaining credible results compared to the current mrsm contextual framework which must first select a best model for each response before simultaneous optimisation. the multiple simultaneous optimisations ensemble is thus recommended to the rubber covered conveyor belting manufacturing industry for use in reviewing cure times when adhesion and cover hardness minimum quality standard requirements change. the use of targeted values in validation is worth mentioning here, as well, since the size of the mrsm dataset is small and it would be senseless to split it. the other option would have been to use cross validation which would have taken back the solution methodology to the weakness of the contemporary mrsm framework. in itself, the practice is worth considering where targeted quality values have to be effectively converted to production process parameters. noting the fact that the multiple simultaneous optimisations ensemble worked well on a two factors and two responses problem, it then makes it imperative to investigate its generalisability to other more complex mrsm problems. as the number of factors and 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(2005). combining linear regression models: when and how?. journal of the american statistical association, 100(472), 1202-1214. https://doi.org/10.1198/016214505000000088 © 2022 by the authors. submitted for possible open access publication under the terms and conditions of the creative commons attribution (cc by) license (http://creativecommons.org/licenses/by/4.0/). https://doi.org/10.1109/icnn.1996.548872 https://doi.org/10.1007/s41664-018-0068-2 https://doi.org/10.1198/016214505000000088 operational research in engineering sciences: theory and applications vol. 4, issue 3, 2021, pp. 21-38 issn: 2620-1607 eissn: 2620-1747 doi: https://doi.org/10.31181/oresta20402021k * corresponding author. ckaramasa@gmail.com (ç. karamaşa), mustafa.ergun@giresun.edu.tr (m. ergün), bgulcan@kmu.edu.tr (b. gülcan) selcuk.korucuk@giresun.edu.tr (s. korucuk), salih.memis@giresun.edu.tr (s. memiş), draganvojinovi123@gmail.com (d. vojinović) ranking value-creating green approach practices and choosing ideal green marketing strategy for logistics companies çağlar karamaşa 1*, mustafa ergün 2, bayezid gülcan 3, selçuk korucuk 2, salih memiş 2, dragan vojinović 4 1 anadolu university, faculty of business, turkey 2 giresun university, bulancak kadir karabaş vocational high school, department of international trade and logistics, turkey 3 karamanoğlu mehmetbey university, faculty of economics and administrative sciences, department of business administration, turkey 4 university of east sarajevo, faculty of economics pale, bosnia and herzegovina received: 10 june 2021 accepted: 18 august 2021 first online: 22 september 2021 research paper abstract: the deterioration of environmental factors, economic and technological development, the formation of complexity in societies, the rise of complex structures have made the environment and green management practices more important. especially value-creating green approaches are considered as critical components in both public and private sector applications and defined as indicators of success in terms of sustainability. on the other hand, green marketing strategies are also important practices that have a positive impact on the environment and should be carefully emphasized for the inheritance of nature to future generations. recently, it has been on the agenda quite a lot and it is understood for all sectors.in this study, it is aimed to determine the criteria for value-creating green approach practices in logistics companies operating in the tr a1 region due to the above mentioned importance and to choose the most ideal green marketing strategy. in solving this problem, multi criteria decision making (mcdm) methods, which are a complex decision-making method, have been used. according to the results of the research, it was determined that the most important criterion in value creating green approach applications as environmental focused strategic decisions (c3), and the least important criterion as environmental life cycle analysis (c2). it has been determined that the most ideal green marketing strategy is green innovation (a1). accordingly the importance of the environmental based strategic decisions is revealed in terms of creating green marketing strategy for companies. key words: green approaches, value creating green approaches, green marketing strategy, entropy, maut. karamaşa et al./oper. res. eng. sci. theor. appl. 4 (3) (2021) 21-38 22 1. introduction nowadays, waste and gas emissions generated by supply chains are a major source of serious environmental problems, leading to global warming and acid rain (bloemhuf et. al., 1995). within the scope of supply chains, various studies are carried out to minimize the damages to the ecosystem. with globalization, solutions in all areas of supply chains have increased. these fields are; environmental compliance requirements, supply chain requirements and consumer demands, sustainability and corporate social responsibility projects (shecterle and senxian, 2008). in addition to reducing costs in a competitive market environment, businesses were forced to adopt more environmentally friendly policies as a result of the kyto protocol signed in 1997. logistics is one of the main operations of the company. for this reason, logistics is costly and damages the environment. the purpose of green logistics is to reduce the environmental impacts of businesses while continuing their logistics activities. environmental negativities related to global warming in recent years have caused consumers to take part in activities aimed at protecting the environment. as a result, consumers began to act in a way that could affect their purchasing process. therefore, it has become necessary for companies to change their business models in order to adapt their activities to green trends. the decision theory approach has become an important tool for providing real-time solutions to uncertainty problems, especially for sustainable engineering and environmental sustainability problems in engineering processes (stojčić et al, 2019). perceived value is the value that the product or service has in the mind of the consumer. in other words, it is a consumer's general assessment of net benefit (bolton & drew, 1991; patterson & spreng, 1997). based on this definition, green value, which is a new concept for this study, it can be expressed as the evaluation of a product or service consisting of the net benefit between what is received and what is given according to the consumer's environmental desires, sustainable expectations and environmentally sensitive needs. green logistics is an issue that has recently developed and become widespread in the transportation sector. the world's leading transport companies have begun to transition to green logistics since the early 2000s and local companies since 2010. along with the laws and incentives applied in developed countries, railway, maritime and inland waterway transportation has also been used as a substitute for the road. green marketing activities are carried out with support from all relevant departments of the business in order to focus on customer needs and values. the adoption of a green marketing strategy is reorienting a business in terms of how it launches and manages its green practices, it also affects how it reacts to rapidly growing green customer demand and changes in dynamic market conditions, how it targets its customers, how it promotes market offers and how it uses green initiatives to create a sustainable competitive advantage (d’souza et al., 2015). while applying green marketing strategies of businesses; it is important for them to know how to initiate and manage green activities, define their target customers, and encourage market resources to benefit from green activities in building sustainable competitiveness (shi & yang, 2019). rankıng value-creatıng green approach practıces ın logıstıcs companıes operatıng ın the tr a1 regıon and choosıng ıdeal green marketıng strategy 23 in an environment where competition is increasing, in order to gain competitive advantage, it is very important to integrate green marketing practices with every function of the business for a trustworthy corporate reputation, a green image for trustworthy corporate reputation, green marketing strategies to create a green image and strong green marketing strategies. in particular, green approaches that create value are seen as critical components in both public and private sector applications and are defined as indicators of success in terms of sustainability. in this context, determining the difficult and value-creating green approach marketing strategies, which is a complex process, and combining multiple variables to make decisions can be considered as a problem. firms need to be careful in creating green products and services and differentiating from competitors before selecting the green marketing strategies. that complicates the process of selecting and applying profitable green marketing strategy by managers too. hence it is important to form value creating green marketing strategies for managers. in this context, it was aimed to determine the criteria for value-creating green approach practices in logistics companies operating in the tr a1 region (covering the provinces of erzurum, erzincan and bayburt in northeastern region of turkey) and to choose the most ideal green marketing strategy. reasons for selecting the region of tra1 are recent positive foreign trade based developments and the positive effects on the logistic activities. according to the authors’ view there is not any study in the literature which aims to prioritize the value creating green approach practices and select the most ideal green marketing strategy with respect to logistics companies, and that shows the originality and novelty of the work. the criterion weights were determined by the entropy method and the maut method was used in the selection of the most ideal green marketing strategy. in the later stages of the study, a detailed literature review was made for green values and green marketing strategies, entropy and maut method were applied to the study, and the study was completed with the results and recommendations section. 2. literature review a detailed literature review on the value creating green approach and green marketing strategies is given below: confente and ruso (2009) argued that the recyclability of products and packaging and the creation of limited spaces for logistics applications are examples of green logistics practices. lopes et al. (2010), green value indicators are based on the certification of environmental management system, reducing energy consumption and using renewable energy. in addition, it is seen that product and packaging refer to environmentally friendly and coordinated transportation to recycling by acting with green awareness in product design. as a result of a study conducted by hu and hsu (2010) on companies in taiwan, green supply chain implementation has been dealt with in four dimensions: supplier management, product recycling, enterprise relationship and life cycle management. kim and han (2011) demonstrated that both freight transport and storage actions are among the green logistics indicators. zhang and zhao (2012) demonstrate the importance of disposal of waste within the enterprise, stating that measures should also be taken for freight transport. evangelista et al. (2012), it is seen that the legal regulations and the actions related to karamaşa et al./oper. res. eng. sci. theor. appl. 4 (3) (2021) 21-38 24 freight transportation are added to the green logistics indicators. according to seroka (2014), it connects green logistics indicators to the cooperation between product designer and supplier, environmental cooperation with customers, legal regulations, green design and reverse logistics. wichaisri and sopadang (2014) showed that activities aiming to minimize waste rate, intermodal transportation systems, cargo transportation activities and raising awareness of the organizational structure are among the green logistics indicators. jaller et al. (2015), in addition to the legal regulations, the use of environmentally friendly vehicles and intermodal transport systems and the prevention of traffic congestion that may occur during the distribution of the cargo are presented as green logistics indicators. atrek and özdağoğlu (2016) provided data on the current status of green supply chain applications in the aluminum joinery sector in i̇zmir. as a result of the study, it was concluded that green supply chain applications are not at the desired level and should be developed. zengin (2017) examined the effects of green logistics practices in sustainable development and aims to evaluate the situation in turkey on green logistics. there are businesses that consider the practice green logistics in turkey. korucuk (2018) determined the effect of green logistics applications on the competitiveness and hospital performance with the application it has applied to 31 public-private-university hospitals operating in ankara. korucuk and memiş (2019) have been prioritized by determining the performance factors of green port practices in enterprises that have received a green port certificate in istanbul. research on green marketing strategies, on the other hand; kumar et al. (2012), as a result of their study, emphasized the necessity of including environmental awareness in this process while developing the strategies of businesses that want to be successful in an intense competitive environment. leonidou et al. (2013) in a study on hotel businesses operating in greece, it was concluded that green marketing strategies can provide a competitive advantage, especially for hotel businesses operating in a highly competitive environment. nadanyiova et al. (2013), in their study on small, medium and large-scale enterprises operating in slovakia, stated that the inclusion of green marketing activities in the business processes of the enterprises will provide a competitive advantage against their competitors. eneizan et al. (2016) stated that green marketing strategies are effective on perceived business performance. simao and lizboa (2017), in their research on toyota, determined that maintaining their activities in an environmentally conscious manner will provide them with some advantages such as low cost, improvement of production process, and increasing the corporate image. karimi et al. (2017) tried to bring together the proposed two-stage messenger problem and supplier selection problem in a green supply chain, where the seller must select suitable suppliers to purchase raw materials and finished products. it is assumed that the seller has several types of vehicles that can send them to receive raw materials purchased from selected suppliers. it is also assumed that the greenhouse gas (ghg) emissions emitted by vehicles depend on the total distance between vendors and suppliers. a limitation on the total ghg emissions of selected vehicles is also considered. the aim of the study is to maximize the expected total vendor profit relative to the total cost of supplier selection and the total transportation cost of vehicles subject to budget and storage space constraints. as a rankıng value-creatıng green approach practıces ın logıstıcs companıes operatıng ın the tr a1 regıon and choosıng ıdeal green marketıng strategy 25 result of the calculations, it has been shown that an increase in the number of raw materials will cause a decrease in the purchased quantity of each raw material and final product at the beginning of the sales period. suresh et al. (2018) investigated the attitudes of consumers towards environmentally friendly products developed by the e-commerce site tamil nadu business towards green marketing strategies. dzulkarnain et al. (2019), using swot analysis, aimed to formulate a green marketing strategies that can be applied in local private agricultural industry development. gedik (2020), the existence of environmental strategies of the enterprise; it aimed to measure whether it differs according to green marketing practices, environmental protection studies, elements of the green marketing mix, environmental responsibilities and customer relations. kumar and rodrigues, (2020) considered two uk-based manufacturing companies. one of them is semiconductor manufacturing company (case a) and other is furniture manufacturing company (case b). case a and case b are considered 'polar types' and are similar in different respects. they are similar in their commitment to integrating lean and green practices and have formed crossfunctional teams to maximize the potential benefits from the integrated approach. they found that the real benefit of integrated lean and green practices can be realized when a cross-functional team works together across organizational boundaries from design to product delivery and after-sales service. handoko et al. (2021) made a case study of the pallet problem for the pulp and paper industry in indonesia. they aimed to establish pallet material strategy and innovation using the concept of reduce, reuse and recycle (3r) in the pallet supply unit to meet the needs of the production unit and avoid product delivery delays. in a closed-loop system, (solid) finished products were sent to consumers on wooden pallets, and the pallets were stored and reused at the consumer's site for later return (to the manufacturer); pallets used can carry a payload of more than 600 kg. with this green approach, it is aimed to overcome the pallet shortage of the pulp and paper manufacturing industry. the fact that there is no study on value-creating green approach practices and choosing the most ideal green marketing strategy in the detailed literature review makes the subject valuable. on the other hand, it is thought that the study will contribute to the literature in terms of the field of application and the methods used. in tr a1 region, entropi and maut, which are among the multi criteria decision making (mcdm) methods for value-creating green approach practices and choosing the most ideal green marketing strategy, have been utilized. because mcdm methods; it is one of the methods applied differently from statistical analysis techniques, that is, objective and non-objective factors are evaluated together. analyzes are carried out within the framework of expert opinions, and at the same time, the study can be shaped according to the opinion of a single expert or a group of experts. (korucuk, 2019). karamaşa et al./oper. res. eng. sci. theor. appl. 4 (3) (2021) 21-38 26 3. methodology in this section, value creating green approach applications and entropy and maut methods used in choosing the most ideal green marketing strategy are explained. 3.1. entropy entropy is one of the weighting methods that reflect reality. entropy, an effective method used to explain the maximum uncertainty or minimum certainty of the problem, also eliminates human-induced errors. in practice, the smaller the value in the method, the smaller the degree of irregularity (wu et al., 2011: 5163-5165; çiçek, 2013: 59; korucuk et al., 2019). the application steps of entropy weight method are given below (abdullah and otheman, 2013: 26; korucuk et al., 2020). step 1. creating the initial decision matrix for a multi-criteria decision problem with m decision alternatives and n evaluation criteria, an initial decision matrix is created as follows: 11 12 1 21 22 2 1 2  j mxn j iji i x x x x x x x xx x (1) step 2. normalization of the initial decision matrix in the normalization process, the following formulas apply according to whether the criteria are benefit (2) or cost (3): 1, 2, , ; 1, 2, ,        min ij j ij max min j j x x r i m j n x x (2) 1, 2, , ; 1, 2, ,        max j ij ij max min j j x x r i m j n x x (3) after the initial matrix is normalized, equation (4) is used by showing r = [rij]mxn in the matrix. 1   ij ij m iji r p r (4) step 3. calculation of entropy value the entropy value (ej) is calculated using the following equation (5):   1    m j ij ij i e k p ln p (5) where k is calculated by the formula k = (ln(m))-1 . rankıng value-creatıng green approach practıces ın logıstıcs companıes operatıng ın the tr a1 regıon and choosıng ıdeal green marketıng strategy 27 step 4. calculation of degree of differentiation the degree of differentiation of the entropy value (dj) is calculated using the equation (6): 1 ;    j j d e j (6) step 5. calculation of entropy weight the objective weight (wj) of each criterion is defined according to equation (7): 1 ;     j j n jj d w j d (7) 3.2. maut maut method is a method used by fisburn (1967) and keeney (1974) to find the most useful alternative based on both qualitative and quantitative criteria. this method is aimed at finding the most useful alternative based on both qualitative and quantitative criteria. in fact, in the maut method, it is aimed to find the most beneficial alternative by making subjective data computable (loken & botterud, 2007). basically, every decision maker consciously or indirectly tries to optimize by bringing all his perspectives together. the decision maker's preferences are also the utility function represented. the decision maker does not need to know this function at the beginning of the decision-making process, so first he has to build the function. the utility function is a way of measuring preferability or alternatives (tunca et al., 2016). in addition, decision makers may not be able to clearly reflect their opinions or express their thoughts clearly in determining the complex structure and relationships of real-life problems. in other words, there may be situations where the criterion values cannot be stated with exact expressions (ergün, et al., 2020). in this direction, the steps of the maut method are given below (ishizaka & nemery, 2013; talkan and uygun, 2014 and ergün, et al., 2020); step 1: determination of criteria and alternatives the criteria (an) in the decision problem and the alternatives (xm) that will help in selecting the criteria should be determined. step 2: determination of weight values assignment is made to the weight values (wj) that allow the alternatives to be evaluated correctly and for which priorities are determined. the sum of all (wj) values must equal 1. 1 1   m j i w (8) step 3: determining the decision matrix the value measures of the criteria are assigned. this assignment is made by considering paired comparisons for qualitative criteria, while quantitative values are karamaşa et al./oper. res. eng. sci. theor. appl. 4 (3) (2021) 21-38 28 for quantitative criteria. based on all these, value assignments are made in systems of 5, 100 and so on (xm). step 4: calculation of normalized benefit values in the normalization process, firstly the best and worst values are determined for each feature and a value of 1 is assigned to the best value and 0 to the worst value. for the calculation of other values, the formula in equation (9) below is used.              i i i j i i i f a min f f a max f min f (9) step 5: calculation of total benefit values after the normalization process, the process of determining the benefit values is started. the utility function formula is as in equation (10).     1 .   q i i i j j u a f a w (10) 4. findings under this title, a presentation of the findings obtained by applying entropy and maut methods for value-creating green approach practices and the most ideal green marketing strategy in the tr a1 region and the evaluations regarding these findings will be presented. in this study, the criteria for value-creating green approach practices were created by using expert opinions and literature review (van hoek, 1999, sarkis, 2003 and zhu et al. 2007) and shown in table 1. green marketing strategies options are formed (rodrigue et al., 2001, kemp and pearson, 2007, fargnoli et al., 2012 and eneizan et al., 2016) are presented in table 2. table 1. criteria for value-creating green aprroach practices criteria coded values systematic environmentally friendly applications (c1) environmental life cycle analysis (c2) environmental focused strategic decisions (c3) designing recyclable and reusable products (c4) product, process and service valuation (c5) decision making and tracking for environmentally friendly products (c6) green supply chain initiative (c7) in table 2 below, green marketing strategy options are given. rankıng value-creatıng green approach practıces ın logıstıcs companıes operatıng ın the tr a1 regıon and choosıng ıdeal green marketıng strategy 29 table 2. alternatives for green marketing strategy alternatives coded values green innovation (a1) green logistics (a2) green pricing (a3) green design and positioning (a4) green segmentation and targeting (a5) green communication (a6) green alliance (a7) academicians (3) who are the stakeholders of the subject; erzurum (8 managers), erzincan (4 managers), and bayburt (2 managers). a total of 17 questionnaires were submitted to the managers of international logistic firms. 4.1. weighting criteria at this stage, the initial decision matrix has been established to evaluate the criteria and seen as table 3. table 3. initial decision matrix for entropy criteria c1 c2 c3 c4 c5 c6 c7 c1 1 7.10 3.63 4.70 4.19 5.49 5.61 c2 3.34 1 2.76 3.81 5.80 3.39 2.70 c3 4.56 6.44 1 2.73 2.99 4.13 3.89 c4 5.15 6.01 6.60 1 3.15 5.44 2.74 c5 6.44 5.90 3.11 5.04 1 6.10 5.79 c6 5.33 4.84 2.49 4.19 5.44 1 3.89 c7 3.17 5.39 3.90 6.15 6.17 3.96 1 following to that the normalization process is made and the normalized decision matrix is formed as table 4. table 4. normalized decision matrix for entropy criteria c1 c2 c3 c4 c5 c6 c7 c1 0.035 0.193 0.155 0.170 0.146 0.186 0.219 c2 0.115 0.027 0.119 0.138 0.202 0.115 0.105 c3 0.157 0.176 0.043 0.099 0.104 0.14 0.152 c4 0.178 0.164 0.28 0.036 0.11 0.184 0.107 c5 0.222 0.161 0.132 0.183 0.035 0.207 0.226 c6 0.184 0.132 0.106 0.151 0.189 0.034 0.152 c7 0.109 0.147 0.165 0.223 0.214 0.134 0.039 after computing entropy and degree of differentiation values, the objective weights of each criterion are obtained as table 5. table 5. weights (wj ) of criteria criteria c1 c2 c3 c4 c5 c6 c7 wj 0.13 9 0.12 8 0.16 2 0.13 6 0.15 1 0.13 0 0.15 4 karamaşa et al./oper. res. eng. sci. theor. appl. 4 (3) (2021) 21-38 30 according to table 5, “environmental focused strategic decisions”, “green supply chain initiative”, ”product, process and service valuation” and “systematic environmentally friendly applications” were determined as the most important main criteria for internationally qualified logistics companies. on the other hand, the least important criteria were found to be “environmental life cycle analysis”, “decision making and tracking for environmentally friendly products” and “designing recyclable and reusable products” respectively. 4.2. ranking alternatives in this section, maut method is used to choose the most ideal green marketing strategy. using the weights of the criteria obtained by the entropy method, the most ideal green marketing strategy was selected with the maut method. each alternative was evaluated using the maut questionnaire within the framework of the previously determined decision criteria. during the evaluation, the participants were asked to give each alternative a score of 1-5 (1worst, 5best). firstly inintial decsion matrix for alternatives in terms of maut method is created as table 6. table 6. initial decision matrix for maut alternatives c1 c2 c3 c4 c5 c6 c7 a1 4 5 3 4 4 5 4 a2 4 5 3 3 4 4 3 a3 3 4 4 4 3 4 4 a4 4 3 3 2 2 2 3 a5 3 4 2 3 1 2 3 a6 4 4 1 2 3 5 3 a7 2 2 3 3 2 3 2 then normalization process is applied and normalized decision matrix is obtained as table 7. table 7. normalized decision matrix for maut alternatives c1 c2 c3 c4 c5 c6 c7 a1 1 1 0.667 1 1 1 1 a2 1 1 0.667 0.500 1 0.667 0.500 a3 0.500 0.667 1 1 0.667 0.667 1 a4 1 0.333 0.667 0 0.333 0 0.500 a5 0.500 0.667 0.333 0.500 0 0 0.500 a6 1 0.667 0 0 0.667 1 0.500 a7 0 0 0.667 0.500 0.333 0.333 0 following to that normalized benefit and total benefit values are computed according to the eqs. (8) and (9) respectively. matrix containing total benefit values is seen as table 8. rankıng value-creatıng green approach practıces ın logıstıcs companıes operatıng ın the tr a1 regıon and choosıng ıdeal green marketıng strategy 31 table 8. matrix for normalized total benefit value alternatives c1 c2 c3 c4 c5 c6 c7 a1 0.139 0.128 0.108 0.136 0.151 0.130 0.154 a2 0.139 0.128 0.108 0.068 0.151 0.087 0.077 a3 0.070 0.085 0.162 0.136 0.101 0.087 0.154 a4 0.139 0.043 0.108 0 0.050 0 0.077 a5 0.070 0.085 0.054 0.068 0 0 0.077 a6 0.139 0.085 0 0 0.101 0.130 0.077 a7 0 0 0.108 0.068 0.050 0.043 0 after that the ranking of the alternatives in this context is given in table 9 as below. table 9. ranking of alternatives according to table 9, where the alternatives are listed, the most ideal green marketing strategy in logistics companies has been "green innovation". other important green marketing strategies were “green pricing”, “green logistics” and “green communication”, respectively. the least important green marketing strategy has been the “green alliance”. the other least important green marketing strategies were determined to be the "green design and positioning" and the "green segmentation and targeting", respectively. in this framework, the general ranking of green marketing strategies selection is a1> a3> a2> a6> a4> a5> a7. 5. sensitivity analysis it is important to review the results of the model according to the demands of decision makers and different conditions. an essential component of the review is the detection of alternative ranking sensitivity in terms of varying decision makers’ judgments. for this study, a sensitivity analysis was done to present the alternative ranking according to the changes in criteria weight as per the judgments of the decision-makers (korucuk, 2019). if this level of rationality is demanded from an individual decision-maker, then mcdm methods used as a support to rational decision making should also satisfy the condition (pamučar et al., 2017) several scenarios are formed for examining the alternative rankings for sensitivity analysis. while the first scenario assigns equal criteria weights, others allow for the interchange of weights between criteria. the obtained criteria weights for six scenarios are given in the appendix a. the results for the alternative ranking of the six different scenarios are presented in table 10. alternativ es a1 a2 a3 a4 a5 a6 a7 u(ai) 0.9 46 0.75 8 0.79 5 0.41 7 0.354 0.532 0.269 ranking 1 3 2 5 6 4 7 karamaşa et al./oper. res. eng. sci. theor. appl. 4 (3) (2021) 21-38 32 table 10. sensitivity analysis results alternatives a1 a2 a3 a4 a5 a6 a7 ranking 1 3 2 5 6 4 7 scenario 1. assigning equal weights to all criteria ranking 1 3 2 5 6 4 7 scenario 2. the interchange between criteria having the highest weight and the lowest weight ranking 1 3 2 5 6 4 7 scenario 3. the interchange between criteria having the second highest weight and the second lowest weight ranking 1 3 2 5 6 4 7 scenario 4. the interchange between criteria having the third highest weight and the third lowest weight ranking 1 3 2 5 6 4 7 the results of the sensitivity analysis show a similar alternative ranking for the four different scenarios, an indication of the strength of the study in terms of significance and validity. 6. discussion studies related to value-creating green aprroaches in terms of firms have gained importance in the recent years. in this study, the criteria for value-creating green approach practices in logistics companies operating in the tr a1 region were determined and the most ideal green marketing strategy was chosen. according to the entropy results, environmental focused strategic decisions (c3) was found as the most important criterion regarding green value creation practices with the opinions of 17 people in total in the field of logistics and companies operating in the tr a1 region (erzurum, erzincan and bayburt). this result is similar to the studies of van hoek (1999); sarkis (2003); zhu et al. (2007). in the entropy method, the least significant criteria were obtained as environmental life cycle analysis (c2), decision making and tracking for environmentally friendly products (c6) and designing recyclable and reusable products (c4). besides, green innovation (a1) was obtained as the most ideal green marketing strategy and that is similar to the studies of kemp and pearson (2007); lin et al. (2009); zailani et al. (2011); weng et al. (2015); chu et al. (2019). on the other hand this result does not correspond to the studies of crane (1998); solvalier (2010); fargnoli et al. (2012); yılmazsoy and schmidbauer (2015). it is important to integrate the concepts of corporate reputation, green image, green marketing strategies and green marketing applications with the functions of firms in competitive environment. in this context, this study that aims to prioritize the value-creating green approach practices and select the most ideal green marketing strategy differs from others with respect to considered methodology and obtained results. rankıng value-creatıng green approach practıces ın logıstıcs companıes operatıng ın the tr a1 regıon and choosıng ıdeal green marketıng strategy 33 7. conclusion and future suggestions industrialization and consumption culture directly harm the nature to which human is bound by an organic bond and with the realization of the irreversible consequences of this damage, “green activities” are rapidly gaining importance with the realization that the human race will directly affect both the present and future generations. in order to reduce the harm to nature, human based approaches have been abandoned and environmental based approaches have gained importance. in this direction, efforts have been started in order to minimize the harm caused by human beings to the environment in a wide range ranging from individuals on a global scale to the state and even to international organizations. especially in the world, considering that raw material and energy costs are increasing and will continue to increase and these items will constitute the biggest item of production costs, businesses should use sustainability and therefore green marketing strategies. green marketing strategies create a better working environment in businesses and feed lean practices by improving corporate performance, and although lean management does not focus on pollution, it has a positive effect on green management by ending activities that reduce environmental and productive inefficiencies. in this study, experts who were thought to be parties to the subject were interviewed, but due to time constraints, the study was conducted in the tr a1 region. so it is difficult to generalize results for other regions of turkey. with a similar study that will cover wider regions in the future, it may be possible to compare the results of green practices in logistics between regions. on the other hand, the problem addressed in this study can be applied to enterprises or producers operating in different fields on a sectoral basis. similarly, the impact of different combinations of criteria affecting green logistics activities can be examined in future studies. in addition, this study can be developed in the future by adding fuzzy logic with other multi-criteria decision making and/or other parametric or non-parametric methods, and the results can be discussed by comparing them. references abdullah, l. & otheman, a. 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(2007). green supply chains management implications for closing the loop, transportation research part e, 44, 1 -18. © 2021 by the authors. submitted for possible open access publication under the terms and conditions of the creative commons attribution (cc by) license (http://creativecommons.org/licenses/by/4.0/). appendıx: scenarios for alternative ranking table a1. scenario 1 alternative ranking table a2. scenario 2 alternative ranking table a3. scenario 3 alternative ranking c1 c2 c3 c4 c5 c6 c7 wj 0.143 0.143 0.143 0.143 0.143 0.143 0.143 a1 a2 a3 a4 a5 a6 a7 u(ai) ranking 0.953 1 0.763 3 0.786 2 0.406 5 0.359 6 0.548 4 0.263 7 c1 c2 c3 c4 c5 c6 c7 wj 0.139 0.162 0.128 0.136 0.151 0.130 0.154 a1 a2 a3 a4 a5 a6 a7 u(ai) ranking 0.957 1 0.769 3 0.784 2 0.405 5 0.366 6 0.555 4 0.246 7 c1 c2 c3 c4 c5 c6 c7 wj 0.139 0.162 0.128 0.136 0.151 0.154 0.130 a1 a2 a3 a4 a5 a6 a7 u(ai) ranking 0.946 1 0.751 3 0.795 2 0.410 5 0.354 6 0.539 4 0.269 7 karamaşa et al./oper. res. eng. sci. theor. appl. 4 (3) (2021) 21-38 38 table a4. scenario 4 alternative ranking c1 c2 c3 c4 c5 c6 c7 wj 0.139 0.162 0.128 0.151 0.136 0.130 0.154 a1 a2 a3 a4 a5 a6 a7 u(ai) ranking 0.946 1 0.751 3 0.800 2 0.412 5 0.362 6 0.522 4 0.272 7 ranking value-creating green approach practices and choosing ideal green marketing strategy for logistics companies çağlar karamaşa 1*, mustafa ergün 2, bayezid gülcan 3, selçuk korucuk 2, salih memiş 2, dragan vojinović 4 1. introduction 2. literature review 3. methodology 3.1. entropy 3.2. maut 4. findings 4.1. weighting criteria 4.2. ranking alternatives 5. sensitivity analysis 6. discussion 7. conclusion and future suggestions references operational research in engineering sciences: theory and applications vol. 5, issue 3, 2022, pp. 40-67 issn: 2620-1607 eissn: 2620-1747 doi: https://doi.org/10.31181/oresta110722105k * corresponding author. sunilnits18@gmail.com (s. kumar), saikat.jumtech@gmail.com (s.r. maity), lokeswar.nits@gmail.com (l. patnaik) optimization of wear parameters for duplextialn coated mdc-k tool steel using fuzzy mcdm techniques sunil kumar 1, 2, saikat ranjan maity 1*, lokeswar patnaik 3 1 department of mechanical engineering, national institute of technology silchar, india 2 department of mechanical engineering, amrita school of engineering, india 3 school of mechanical engineering, sathyabama institute of science and technology (deemed to be university), india received: 06 april 2022 accepted: 07 july 2022 first online: 11 july 2022 research paper abstract: the present work evaluates the effects of different tribological process parameters on the measured responses such as hardness, coefficient of friction, surface roughness, wear mass loss and wear depth of duplex-tialn coated mdc-k tool steel material. the considered tribological process parameters are load, sliding velocity, and sliding distance. a full factorial design with 27 experimental runs is employed and based on the response values, an optimal combination of the tribological process parameters is subsequently determined. different multi-objective optimization techniques, like overall evaluation criteria and fuzzy-based multi-criteria decisionmaking methods (fuzzy evaluation based on distance from the average solution, fuzzy technique for order of preference by similarity to ideal solution, and fuzzy complex proportional assessment) are utilized to identify the optimal intermixes of the considered tribological process parameters. sensitivity analysis with respect to changing weights of the responses is performed to validate the derived rankings of the trials, whereas the results of analysis of variance revealed the most significant parameters were influencing the responses. in addition to this, two different published problems related to optimization of wear parameters were solved using the proposed method to check its capability. keywords: mdc-k tool steel, duplex-tialn coating, fuzzy mcdm, sensitivity analysis, optimization. 1. introduction mdc-k hot work tool steel contains a high percentage of chromium along with tungsten, molybdenum, and vanadium, which substantially enhances its mechanical and wear properties required for its application in the manufacturing of extrusion optimization of wear parameters for duplex-tialn coated mdc-k tool steel using fuzzy mcdm techniques 41 dies, die casting dies, hot stamping dies, and forging dies. untreated tool steel is commercially available with a hardness of ~22 hrc, constraining its application in die manufacturing. therefore, heat treatment of tool steel becomes mandatory using different hardening processes to attain the desired levels of hardness and toughness. these properties of tool steel mainly depend on its chemical composition, alloying elements, and secondary carbides formation during the hardening processes (joshy et al. 2019, kumar et al. 2021a, and soleimany et al. 2019). the alloying elements can be divided into two classes, i.e., one is responsible for carbide formation and the other is accountable for changing the tempering kinetics during the heat treatment process (podgornik et al. 2018a and podgornik et al. 2016b). further, the hardened tool steel requires surface modifications, such as nitriding (gas nitriding, salt bath nitriding or plasma nitriding) and deposition of ceramicbased hard coatings. plasma nitriding has broader advantages over salt bath nitriding and gas nitriding. it allows much closer control of the microstructure during nitriding and is able to provide a surface without the formation of a compound layer. when plasma nitriding is integrated with the physical vapor deposition (pvd) process, it is known as duplex surface treatment. during plasma nitriding, nitrogen diffuses to the surface and forms two different zones, i.e., the compound zone and diffusion zone. the compound zone is made up of fe4n and fe2-3n, whereas, the diffusion zone is formed by diffused nitrogen atoms making the surface harder (aghajani et al. 2017 and kumar et al. 2020a, 2022a). in addition to the application on nitride surfaces, ceramic coatings, such as tin, crn, tialn, ticn, alcrn, craln, etc. have widely been employed in the manufacturing, tooling, and biomedical industries due to their high resistance to wear, oxidation, corrosion, chemical stability and biocompatibility (chaliampalias et al. 2017, prabhu et al. 2018, kumar et al. 2020b, 2021b, 2022b, 2021c and patnaik et al. 2021a, 2021b, 2021c, 2021d, 2020a, 2022). many researchers have observed excellent mechanical, wear, and corrosion properties of tialn film coatings (fu et al. 2019 and ozkan et al. 2020). various experimental works have already been conducted to study the tribological, frictional, and wear behaviors of tialn coated surfaces under different conditions of normal load, sliding velocity, and sliding distance (sen et al. 2020, chowdhury et al. 2017, m’saoubi et al. 2013, kumar et al. 2021d, 2022c and kuo et al. 2018). however, investigations to study the influences of various tribological process parameters on the wear behavior of tialn coated surfaces remain unexplored. in addition to this, saravanan et al. (2015 and 2016) and patnaik et al. (2021e and 2021f) adopted the box-behnken experimental design plan (l15 orthogonal array) and conducted 15 experiments to derive a suitable combination of process parameters for tin coated ss 316l steel. out of those 15 experimental runs, one experiment was repeated three times, resulting in performing only 13 actual experiments. similar studies have been performed by kumar et al. (2022d & 2022e), where l16 orthogonal array was adopted to perform the wear experiment for crn/tialn coating. according to the authors, the use of a small set of experimental runs may not always be sufficient to determine the most suitable parameters for a specific process, and there should be sufficient experimental observations to study the process behavior. moreover, in the earlier investigations, there has been limited participation of the decision makers and equal weights (relative importance) have usually been assigned to the considered responses. thus, there is a huge opportunity to adopt different multi-criteria decision-making (mcdm) techniques allowing the kumar et al./oper. res. eng. sci. theor. appl. 5(3)2022 40-67 42 involvement of a group of decision makers in deciding the relative importance of various responses under a fuzzy environment. these mcdm techniques are very popular in the material selection for various applications (maity and chakraborty 2013 and prasad et al. 2014). to the best of the authors’ knowledge, the application of any of the fuzzy mcdm tools in studying the tribological properties of duplex-tialn coated mdc-k tool steel is really limited. thus, this paper proposes a simultaneous application of three other fuzzy mcdm techniques, in the form of fuzzy technique for order of preference by similarity to ideal solution (f-topsis), fuzzy evaluation based on distance from the average solution (f-edas) and fuzzy complex proportional assessment (f-copras) methods, to investigate effects of different tribological process parameters, like load, sliding velocity and sliding distance on different responses, i.e. hardness, coefficient of friction, surface roughness, wear mass loss and wear depth of duplex-tialn coated mdc-k tool steel material. based on the experimental observations, the most appropriate combination of those tribological process parameters is also singled out using each of the multi-objective optimization methods under consideration. all these fuzzy mcdm techniques are easy to comprehend, robust and mathematically sound. the fuzzy-topsis method endeavors to identify the best alternative based on its minimum distance from the positive ideal solution and maximum distance from the negative ideal solution (yu and pan 2021; de lima silva et al. 2020 and petrović et al. 2019). on the other hand, the fuzzy-edas method assigns a ranking order to the candidate alternatives based on the positive and negative distances from the average solution (keshavarz ghorabaee et al. 2017). the fuzzy-copras method selects the most apposite alternative considering both the positive ideal and negative ideal solutions while taking into account the performance of the alternatives with respect to different criteria and the corresponding criteria weights (zhan et al. 2020). it adopts a step-wise ranking and evaluating procedure of the alternatives in terms of their significance and utility degree. it is worthwhile to mention here that as the considered multi-objective optimization techniques have different mathematical treatments and have their own advantages and disadvantages, the ranking lists of the alternatives derived using these methods are supposed to vary, and it would be interesting to identify the best performing mathematical tool that would lead to the attainment of the most desired responses for duplex-tialn coated mdc-k tool steel. 2. methodology 2.1. preparation of the specimen in this paper, chromium-rich mdc-k tool steel is used as the substrate material and its composition is provided in table 1. the dimension of the sample (ø55 mm and thickness 5 mm) is attained using a tool room lathe (mysore kirloskar, model: ep-2215) and high precision hydraulic surface grinding machine (kingston, model: kg-cl 3060 ah). the turned substrate is then heat-treated, followed by plasma nitriding. vacuum hardening is performed at ~1080°c temperature in the absence of oxygen, whereas, quenching is performed in the same chamber in a nitrogen environment under a pressure of ~2 mpa. application of tempering (at ~0.14 mpa gas pressure and cooled to ~92°c) helps to reduce extra hardness and brittleness while imparting enough toughness to the treated material. hardness is measured using a wilson holbert micro-hardness testing machine, i.e., 460 hv. furthermore, to optimization of wear parameters for duplex-tialn coated mdc-k tool steel using fuzzy mcdm techniques 43 increase the corresponding surface hardness, plasma nitriding is performed in presence of hydrogen (75%) and nitrogen (25%) at ~0.8 kv potential. table 1. composition of mdc-k tool steel element cr w v mn c si wt% 4.4 2 1.7 0.5 0.4 0.3 the tialn coating is deposited on the plasma nitrided mdc-k tool steel surface using the magnetron sputtering method. before the deposition process, the substrates are cleaned ultrasonically using an alkaline solution, followed by ethanol for 10-15 minutes. later, distilled water is used to re-clean the substrate and is dried with ethanol. the substrate surface is then etched using titanium (ti) ions under a pulse bias of -1000v with an 80% duty cycle for four minutes. the tialn film is finally deposited using titanium (ti) and aluminum (al) cathode (50:50) under a nitrogen gas pressure of 2.5 pa. the dc bias is -40v and the temperature is maintained at ~315oc for 30 min to attain a film thickness of 3.5 µm. 2.2. selection of process parameters based on the full-factorial design plan, 27 experiments are conducted using ducom tr20le tribometer (astm: g99 standard) to investigate the effects of various tribological process parameters, like load, sliding velocity, and sliding distance on the considered responses, i.e., hardness, coefficient of friction, surface roughness, wear mass loss and wear depth of duplex-tialn coated mdc-k tool steel material. the past literature (łępicka et al. 2017 & 2019, ramezani et al. 2018, and patnaik et al. 2020b, 2021g) suggests that load, sliding velocity, and sliding distance are the most influential parameters influencing the wear properties of tialn coated materials. during the experiments, the range of each of these parameters is decided based on pilot experiment runs. when the experiments are conducted at a load less than 10 n load, sliding velocity less than 0.1 m/s, and sliding distance less than 1000 m, no significant effect on the wear properties is noticed due to the lower contact period between the pin and disc surfaces. at 20 n load, 0.3 m/s sliding velocity and 2000 m sliding distance, a wider and deeper wear track is observed on the surface with heavy abrasion and erosion of the coating. high sliding velocity provides sufficient time to repeat the same contact point, and its combined effect with high load increases the interface temperature leading to deformation and erosion of the coating. based on these results, the corresponding levels and ranges of the considered tribological parameters are determined, as exhibited in table 2. table 2. experimental conditions process parameters and their levels process parameter level value load (l) (in n) 3 10, 15, 20 sliding velocity (sv) (in m/s) 3 0.1, 0.2, 0.3 sliding distance (sd) (in m) 3 1000, 1500, 2000 uncontrollable parameters parameter description disc size 60 mm diameter × 8 mm thickness pin size 8 mm diameter × 30 mm length temperature ambient humidity ambient kumar et al./oper. res. eng. sci. theor. appl. 5(3)2022 40-67 44 2.3. fuzzy-topsis method three different fuzzy-based mcdm techniques viz. f-topsis, f-copras, and fedas are also employed for optimization of different tribological parameters to attain the most desired wear properties of duplex-tialn coated mdc-k tool steel. the topsis method selects the most apposite alternative which is nearest to the positiveideal solution and farthest from the negative ideal solution. based on the negativeideal solution, non-beneficial attributes get maximized and the beneficial attributes are minimized. on the other hand, based on the positive-ideal solution, beneficial attributes are maximized and non-beneficial attributes get minimized. furthermore, the integration of fuzzy set theory with topsis helps in dealing with ambiguity and subjectivity in the decision-making process. usually, in a multi-objective parametric optimization problem involving a single decision maker/process engineer, equal importance is assigned to all the considered responses that also ease out the calculation steps. however, in a real-time machining environment, more than one decision maker participates in assigning importance to the varying responses. the ratings allotted to the responses are usually subjective and vary from one decision to the other. in this paper, in order to assign weight to each of the responses, the triangular linguistic fuzzy numbers of table 3 is incorporated. in table 4, the linguistic fuzzy weights allotted to the five responses by a panel of three decision makers are presented, which are finally aggregated in table 5 to provide the corresponding fuzzy weights for all the responses. table 3. triangular linguistic fuzzy numbers lowest lt (0, 0, 0.1) lower lr (0, 0.1, 0.3) low l (0.1, 0.3, 0.5) medium m (0.3, 0.5, 0.7) high h (0.5, 0.7, 0.9) higher hr (0.7, 0.9, 1) highest ht (0.9, 1, 1) table 4. decision makers’ panel table 5. aggregated fuzzy weight response group of decision makers dm1 dm2 dm3 ra l m lr cof m l lr wml l m l wd m m l hv hr h ht response fuzzy weight ra (0.133, 0.3, 0.5) cof (0.133, 0.3, 0.5) wml (0.17, 0.37, 0.57) wd (0.23, 0.43, 0.63) hv (0.7, 0.87, 0.97) the procedural steps of the f-topsis method are elucidated below (shivakoti et al. 2017): step 1: based on the experimental dataset consisting of 27 observations and five responses, develop the initial decision/evaluation matrix u = [uij]27×5, where uij is the observed value of jth response (j = 1, 2, 3, 4, 5) at ith experimental trial (i = 1, 2...,27). step 2: in order to make the performance criteria values of the above decision matrix dimensionless and comparable, normalize all the elements using the vector normalization procedure. optimization of wear parameters for duplex-tialn coated mdc-k tool steel using fuzzy mcdm techniques 45 0.5 27 2 1 i =1, 2, ....., 27 ij ij ij i u x u          (1) where xij is the normalized value of uij. step 3: developed the fuzzy weighted normalized decision matrix ( ijn ~ ) while multiplying all the elements of the normalized decision matrix by the corresponding fuzzy weights of the considered responses. step 4: the fuzzy positive ideal solution  m  and fuzzy negative ideal solution  m  is needed to be calculated using eq. (2) and eq. (3) respectively.     max min , i =1, 2, ...., 27ij ijm m j j or m j j where           1 2 3 4 5, , , ,m m m m m       (2)     min max , i =1, 2, ...., 27ij ijm m j j or m j j where           1 2 3 4 5, , , ,m m m m m       (3) where,  1, 2, 3, 4, 5j  and  1, 2, 3, 4, 5j   j and j  associated with higher the better type and lower the better type respectively. in this paper, ra, cof, wml, wd are considered as lower the better and hv was considered as higher the better type. step 5: the fuzzy euclidean distance for each experimental result from the fuzzy positive ideal solution  id  and fuzzy negative ideal solution  id  is needed to be calculated using eq. (4) and eq. (5) respectively.   5 1 , m i = 1, 2, ....., 27; j = 1, 2, 3, 4 ,5 i ij i i d d m      (4)   5 1 , m i = 1, 2, ....., 27; j = 1, 2, 3, 4 ,5 i ij i i d d m      (5) where, d is the distance between two fuzzy numbers. step 6: defuzzified the positive ideal solution and negative ideal solution. step 7: calculate the closeness coefficient (coci) for each experimental run as its proximity to the ideal solution. i i i i d coc d d      (6) kumar et al./oper. res. eng. sci. theor. appl. 5(3)2022 40-67 46 step 8: rank all the experimental runs based on the descending values of coci. thus, the experimental run having the maximum coci value would be the best alternative, whereas, the worst alternative should have the minimum coci value. 2.4. fuzzy-copras method the copras method usually deals with quantitative information and the candidate alternatives are ranked based on the relative weights of various criteria. however, while solving real-time decision-making problems with incomplete or vague information, this method fails to provide an accurate ranking of the alternatives under consideration. to avoid this deficiency, the copras method is combined with the fuzzy set theory in this paper use the fuzzy technique to calculate the relative priority of responses/criteria using a fuzzy number rather than the precise number (sun 2010). in this way, the fuzzy-copras technique was proposed to deal with the insufficiency in the conventional copras method. the weight of the responses/criteria and ranking of the alternatives are evaluated using linguistic terms denoted by a fuzzy number. the following steps are used to perform the fuzzycopras decision-making albayrak 2020). step 1: construct the normalized decision matrix using eq. (1). step 2: construct the fuzzy weighted normalized matrix  x̂ using eq. (7) and eq. (8). ˆ ij j ij x w x  (7) j w is the fuzzy weight of criteria. 11 12 1 21 22 2 1 2 ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ 1, 2,3...., ; 1, 2,3,...., ˆ ˆ ˆ n n ij m m mn x x x x x x x x i m j n x x x                   (8) step 3: calculate the sum of fuzzy beneficial and non-fuzzy beneficial responses values using eq. (9) and eq. (10) respectively. 1 ˆ 1, 2,3...., ; 1, 2,3,......, k i ij j s x i m j n       (9)  1 ˆ 1, 2,3...., ; 1, 2, 3,......, k i ij j k s x i m j k k k n           (10) where, k denotes number of beneficial criteria and (n-k) denotes non-beneficial criteria. step 4: defuzzified the sum of beneficial and non-beneficial responses. step 5: determine the relative significance values (qi) for each alternative using eq. (11). optimization of wear parameters for duplex-tialn coated mdc-k tool steel using fuzzy mcdm techniques 47 1 1 1, 2,3,...., 1 m i i i i m i i i s q s i n s s             (11) step 6: determine the performance score of each alternative (pi) using eq. (12) and eq. (13). respectively.  max max 1, 2,3,..., miq q i  (12) max 100%i i q p q   (13) based on the performance score (pi), ranking of alternative was determined. higher performance score was attributed to best alternative whereas, lowest performance score was attributed to the worst alternative. 2.5. fuzzy-edas method this method was developed by ghorabaee et al. (2016), it needs a few computational steps to evaluate the process with good efficiency in comparison with other mcdm methods. furthermore, it evaluates the alternatives based on the average solution for each response (criterion). in the present study, the edas method was integrated with the fuzzy numbers. the edas method is elaborated in fuzzy linguistic terms, which are further defined by the triangular fuzzy number (table 3). in this method, the first step was to determine the average solution of each criterion. from the average solution, the positive and negative distance was calculated. the fuzzy weight of criteria was multiplied with positive and negative distance and then this value was normalized. finally, an appraisal score was calculated for each alternative, and based on this score, a ranking of alternatives was derived. the following steps were used to determine the ranking using fuzzy-edas (polat and bayhan 2020 and stević et al. 2018; vukasović et al. 2021). step 1: construct the average decision matrix (x) using following equation: ij n m x x      (14) 1 1 k p ij p ij x x k    (15) where, the performance value of alternative  1ia i n  is represented by corresponding to the criteria  1ic j n  which assigned by the pth expert  1 p k  . step 2: determine the average solutions and form their corresponding matrix. 1 j m av av        (16) kumar et al./oper. res. eng. sci. theor. appl. 5(3)2022 40-67 48 1 1 n j i ij av x n    (17) where, jav denotes the average solution corresponding to each criterion. step 3: calculate the fuzzy positive and fuzzy negative distances from the average for beneficial and non-beneficial criteria. ij n m pda pda        (18) ij n m nda nda        (19) ij j j ij ij j j x av if j b k av pda x av if j n k av                                   (20) j ij j ij j ij j av x if j b k av pda av x if j n k av                                   (21) where fuzzy positive and fuzzy negative distances are denoted by ij pda and ij nda respectively for ith alternative from the average solution in term of jth criterion. step 4: calculate the fuzzy weighted sum of positive and negative distances for each alternative using following equations. 1 m i i j ij sp w pda          (22) 1 m i i j ij sn w nda          (23) optimization of wear parameters for duplex-tialn coated mdc-k tool steel using fuzzy mcdm techniques 49 step 5: normalize the value of fuzzy spi and fuzzy sni for each alternative as follows: max i i i i sp nsp k sp           (24) 1 max i i i i sn nsn k sn            (25) step 6: defuzzified the fuzzy normalized value of ij pda and ij nda for each alternative. step 7: determine appraisal score ( ) for each alternative using eq. (26)   1 2 i i i as nsp nsn  (26) step 8: finally, rank the alternatives based on their appraisal score. the highest score corresponds to the best alternative, while the lowest score corresponds to the worst alternatives. to understand the proposed mcdm methods, a combined procedural flow diagram is presented in figure 1, where each step is connected to the other denoting process involved in the mcdm methods. kumar et al./oper. res. eng. sci. theor. appl. 5(3)2022 40-67 50 define a tribological process parameter and responses (criteria) determine experimental run (alternatives) construct the decision matrix construct the normalized decision matrix construct fuzzy weighted normalized decision matrix determine fuzzy positive and negative ideal solution determine fuzzy euclidean distance from fuzzy positive and negative ideal solution determine ranking of the experimental run calculate the sum value of fuzzy beneficial and non-beneficial response defuzzified the sum value of beneficial and non-beneficial response calculate average value of responses determine ranking of the experimental run select best experimental run is the best experiment number identical for fuzzy mcdm method? perform sensitivity analysis by changing the weight select the most suitable mcdm method no f u z z y t o p s is f u z z y c o p r a s f u z z y e d a s calculate closeness coefficient determine the performance score construct the matrices of positive and negative distance from average solution calculate fuzzy normalized weighted sum of positive and negative distance determine appraisal score form a group comprises of three members formulate the assessment conversion of fuzzy linguistic term to crisp value determine the fuzzy weight for the responses f u z z y w e ig h ta g e determine ranking of the experimental run calculate fuzzy weighted sum of positive and negative distance yes determine the relative significance value defuzzified the euclidean distance from positive and negative ideal solution defuzzified the normalized weighted sum of positive and negative distance figure 1. combined procedural flow diagram for solving multi-objective problems optimization of wear parameters for duplex-tialn coated mdc-k tool steel using fuzzy mcdm techniques 51 3. results and discussion the tribological experiments were performed according to the full factorial design. each test was repeated three times to ensure more accuracy in the measured response value. the average value of the responses is tabulated in table 6. the performance characteristics of the duplex-tialn coating were analysed by obtaining ra, cof, wml, wd, and hv. the experimental data were analysed to understand the effect of the tribological parameters on the measured responses. table 6. experimental design matrix with measured responses experiment number (alternative, en) tribological process parameters responses (criteria, c) l sv sd ra, c1 cof, c2 wml, c3 wd, c4 hv, c5 en1 20 0.1 1000 2.4 0.39 40.28 4.12 1227 en2 15 0.1 2000 5.3 0.63 32.38 3.92 1213 en3 10 0.3 2000 8.3 0.92 21.08 2.92 1147 en4 20 0.2 1500 4.9 0.49 59.58 5.02 954 en5 15 0.3 1000 6.2 0.79 54.68 4.42 1201 en6 15 0.2 1000 5.5 0.68 30.08 3.82 1137 en7 20 0.2 1000 4.6 0.47 51.98 4.52 1126 en8 15 0.2 2000 5.9 0.74 27.08 4.12 1130 en9 10 0.1 2000 6.7 0.74 16.08 2.42 1798 en10 10 0.2 1000 6.6 0.75 11.68 1.92 1894 en11 20 0.3 1500 5.2 0.61 63.68 5.52 798 en12 10 0.1 1500 6.4 0.7 12.78 2.12 1911 en13 10 0.3 1500 8.1 0.89 16.08 2.42 1498 en14 20 0.3 2000 6.1 0.64 74.38 6.72 739 en15 15 0.1 1000 4.9 0.58 17.98 2.82 1405 en16 15 0.2 1500 5.7 0.71 41.18 4.22 1171 en17 10 0.1 1000 6.3 0.75 10.14 1.18 1917 en18 20 0.1 1500 3.1 0.41 46.68 4.32 1187 en19 15 0.3 2000 6.9 0.87 49.38 5.42 878 en20 10 0.3 1000 7.8 0.84 9.58 2.22 1471 en21 20 0.3 1000 4.3 0.58 57.08 4.82 1031 en22 10 0.2 2000 7.2 0.81 18.48 2.12 1784 en23 20 0.1 2000 3.7 0.43 50.58 4.82 992 en24 20 0.2 2000 5.4 0.52 62.28 5.42 912 en25 15 0.1 1500 5.1 0.61 22.18 3.42 1415 en26 15 0.3 1500 6.6 0.84 46.58 5.12 1115 en27 10 0.2 1500 6.7 0.79 9.67 1.14 1983 3.1. ranking of the alternatives using fuzzy mcdm methods the selection of the optimum conditions of the tribological process parameters was considered to reveal the applicability of fuzzy-topsis, fuzzy-copras, and fuzzyedas method. previously, the applicable steps of the techniques were discussed. after obtaining the weightage of the responses in accordance with the decision of the decision-maker, different mcdm techniques were used to rank the alternatives. kumar et al./oper. res. eng. sci. theor. appl. 5(3)2022 40-67 52 3.1.1. ranking of the alternatives using fuzzy-topsis method value of each response was normalized using eq. 1 to obtain the normalized matrix (supplementary table 1) and this value was further multiplied with fuzzy weight of responses (table 5) to construct the fuzzy normalized weighted matrix (supplementary table 2). with the help of positive and negative ideal solutions closeness coefficient value was determined for each alternative (table 7) and based on this coefficient value ranking of the alternative was obtained. experiment number en27 (l = 10 n, sv = 0.2 m/s, and sd = 1500 m) secured first rank with highest closeness coefficient value (0.843) whereas experiment number en14 (l = 20 n, sv = 0.3 m/s, and sd = 2000 m) secured last rank with lowest closeness coefficient value (0.217) among all 27 number of experiments. table 7. coefficient of closeness and ranking of the alternatives experiment number positive ideal solution ( ) negative ideal solution ( ) closeness coefficient ( ) rank en1 0.178 0.300 0.628 11 en2 0.215 0.310 0.591 13 en3 0.237 0.285 0.546 16 en4 0.291 0.224 0.435 22 en5 0.295 0.229 0.438 21 en6 0.220 0.301 0.578 14 en7 0.248 0.273 0.524 17 en8 0.232 0.289 0.555 15 en9 0.137 0.415 0.752 5 en10 0.111 0.446 0.801 4 en11 0.335 0.176 0.344 25 en12 0.109 0.449 0.804 3 en13 0.187 0.350 0.651 10 en14 0.399 0.111 0.217 27 en15 0.140 0.393 0.737 6 en16 0.253 0.270 0.516 19 en17 0.088 0.473 0.843 2 en18 0.207 0.317 0.605 12 en19 0.344 0.168 0.328 26 en20 0.164 0.372 0.694 8 en21 0.278 0.239 0.462 20 en22 0.148 0.403 0.731 7 en23 0.247 0.269 0.521 18 en24 0.316 0.197 0.385 24 en25 0.166 0.368 0.689 9 en26 0.310 0.211 0.405 23 en27 0.088 0.473 0.843 1* *most preferable setting of tribological process parameters 3.1.2. ranking of the alternatives using fuzzy-copras method in this method normalization of response value was similar to the fuzzy topsis method. hence, the same normalized decision matrix (supplementary table 1) and fuzzy normalized weighted matrix (supplementary table 2) were used for the fuzzy copras method. the next step was to calculate the relative significance value for optimization of wear parameters for duplex-tialn coated mdc-k tool steel using fuzzy mcdm techniques 53 each alternative using eq. 11 and the calculated value tabulated in table 8. the relative significance value performance score was obtained using eq. 13 and with the help of this value ranking of alternatives was determined (table 10). the highest performance score (100) was determined for experiment number en27 (l = 10 n, sv = 0.2 m/s, and sd = 1500 m) and lowest performance score (41.359) was determined for the experiment number en14 (l = 20 n, sv = 0.3 m/s, and sd = 2000 m). table 8. performance score and ranking of the alternatives experiment number relative significance value (qi) performance score (ui) rank en1 0.089 72.557 11 en2 0.081 66.523 13 en3 0.077 63.328 16 en4 0.065 53.273 23 en5 0.069 56.402 20 en6 0.080 65.073 14 en7 0.074 60.319 18 en8 0.078 63.344 15 en9 0.105 86.033 5 en10 0.114 92.962 4 en11 0.058 47.014 26 en12 0.114 93.270 3 en13 0.091 74.459 10 en14 0.051 41.359 27 en15 0.102 83.410 7 en16 0.074 60.617 17 en17 0.122 99.546 2 en18 0.082 66.837 12 en19 0.058 47.734 25 en20 0.097 78.944 8 en21 0.068 55.616 21 en22 0.102 83.656 6 en23 0.072 58.895 19 en24 0.061 50.247 24 en25 0.094 77.123 9 en26 0.066 53.966 22 en27 0.122 100.000 1* *most preferable setting of tribological process parameters 3.1.3. ranking of the alternatives using the fuzzy-edas method in this method, initially, the average value of each response was calculated (table 6). in the next step, positive (pdaij) and negative (ndaij) distances from the average solution were calculated (supplementary table 3 and supplementary table 4 respectively). further, the fuzzy weight of the criterion was multiple with the value of positive and negative distances respectively, to obtain the fuzzy weighted sum of positive ( ) and negative distance ( ) from the average solution (supplementary table 5 and supplementary table 6 respectively). the next step is to calculate the normalized weighted sum of positive ( ) and negative ( ) distance from the kumar et al./oper. res. eng. sci. theor. appl. 5(3)2022 40-67 54 average solution (table 9). finally, the appraisal score was calculated using eq. 21 for each alternative, and based on the appraisal score, a ranking of alternatives was derived (table 9). experiment number en27 (l = 10 n, sv = 0.2 m/s, and sd = 1500 m) was obtained first rank with the highest appraisal value (0.549) whereas experiment number en14 (l = 20 n, sv = 0.3 m/s, and sd = 2000 m) was obtained last rank with the lowest appraisal value (0.070) among all 27 number of experiments. table 9. normalized weighted sum of positive and negative distance, appraisal score and ranking of the alternatives experiment number normalized weighted sum of normalized weighted sum of appraisal value ( ) rank en1 0.266 0.126 0.196 21 en2 0.932 0.016 0.474 3 en3 0.212 0.319 0.265 16 en4 0.136 0.579 0.358 10 en5 0.000 0.390 0.195 22 en6 0.065 0.129 0.097 26 en7 0.157 0.344 0.250 17 en8 0.090 0.190 0.140 24 en9 0.692 0.063 0.377 9 en10 0.849 0.066 0.458 4 en11 0.053 0.766 0.410 6 en12 0.837 0.032 0.435 5 en13 0.456 0.184 0.320 14 en14 0.070 0.073 0.072 27 en15 0.416 0.000 0.208 20 en16 0.002 0.205 0.104 25 en17 0.019 1.000 0.509 2 en18 0.235 0.233 0.234 18 en19 0.000 0.699 0.349 11 en20 0.520 0.148 0.334 12 en21 0.096 0.484 0.290 15 en22 0.675 0.116 0.395 7 en23 0.206 0.447 0.326 13 en24 0.104 0.662 0.383 8 en25 0.314 0.000 0.157 23 en26 0.000 0.452 0.226 19 en27 1.000 0.091 0.546 1* *most preferable setting of tribological process parameters thus, according to all the proposed mcdm methods, experiment number en27 (l = 10 n, sv = 0.2 m/s, and sd = 1500 m) was the most suitable parametric setting for the tribological test of duplex tialn coating. with this parametric setting, the desirable value of wear responses was obtained whereas, the undesirable value was obtained with the parametric setting of l = 20 n, sv = 0.3 m/s, and sd = 2000 m (experiment number en14) and this parametric setting was the worst parametric seating suggested by all the proposed mcdm methods. optimization of wear parameters for duplex-tialn coated mdc-k tool steel using fuzzy mcdm techniques 55 3.2. sensitivity analysis sensitivity analysis was conducted to understand the stability of the rankings under different sets of response weights (table 10). based on these weights, a ranking of alternatives was obtained using all the proposed mcdm methods (fig. 2). there are four scenarios of a group of three decision makers (table 10 (a-d)), and based on their opinion criteria weights were calculated (table 10(a’-d’)). table 10. group of decision makers and fuzzy criteria weights (a) opinion of the decision maker for scenario 1 responses scenario 1 dm1 dm2 dm3 ra m m lr cof l lr l wml l m m wd m m lr hv ht ht h (a’) fuzzy criteria weight of scenario 1 responses fuzzy criteria weight ra (0.200, 0.367, 0.567) cof (0.067, 0.233, 0.433) wml (0.233, 0.433, 0.633) wd (0.200, 0.367, 0.567) hv (0.767, 0.900, 0.967) (b) opinion of the decision maker for scenario 2 responses scenario 2 dm1 dm2 dm3 ra lr l m cof m m l wml lt l m wd l l lr hv h hr hr (b’) fuzzy criteria weight of scenario 2 responses fuzzy criteria weight ra (0.033, 0.167, 0.367) cof (0.233, 0.433, 0.633) wml (0.133, 0.267, 0.433) wd (0.067, 0.233, 0.433) hv (0.567, 0.767, 0.933) (c) opinion of the decision maker for scenario 3 responses scenario 3 dm1 dm2 dm3 ra l lt l cof lr m l wml m lr m wd m l m hv ht h hr (c’) fuzzy criteria weight of scenario 3 responses fuzzy criteria weight ra (0.067, 0.200, 0.367) cof (0.133, 0.300, 0.500) wml (0.200, 0.367, 0.567) wd (0.233, 0.433, 0.633) hv (0.700, 0.867, 0.967) (d) opinion of the decision maker for scenario 4 responses scenario 4 dm1 dm2 dm3 ra lt l lr cof m lr m wml lt m m wd lr l l hv hr ht h (d’) fuzzy criteria weight of scenario 4 responses fuzzy criteria weight ra (0.033, 0.133, 0.300) cof (0.200, 0.367, 0.567) wml (0.200, 0.333, 0.500) wd (0.067, 0.233, 0.433) hv (0.700, 0.867, 0.967) the finding of sensitivity analysis for the f-topsis method is represented in figure 2(a). there are no changes observed in the ranking of experiment numbers en6, en9, en10, en11, en12, en14, en19, and en21 when the value of fuzzy weight was changed. but there were few changes observed in the ranking of experiment numbers en1, en2, en13, en15, en17, en20, en22, en24, en25, en26, and en27. the ranking of the remaining experiment numbers was changed frequently and it was not stable at all. the sensitivity results of the f-copras method (figure 2(b)) showed that there was no effect of criteria weight change observed on the ranking of experiment numbers en4, en6, en9, en10, en12, en14, en24, and en26. unlike the remaining experiment, numbers could not hold their actual ranking and there were changes observed with kumar et al./oper. res. eng. sci. theor. appl. 5(3)2022 40-67 56 criteria weight change. the f-edas method (figure 2(c)) shows more consistent in their ranking of the experiment numbers against criteria weight change and the experiments are en2, en3, en6, en8, en10, en11, en12, en14, en16, en17, en21, en22, en25, and en27. but there were few experiments (en5, en7, en9, and en15) whose ranking slightly changed with criteria weight change. the rest of the experiment number changes its ranking frequently against criteria weight change. optimization of wear parameters for duplex-tialn coated mdc-k tool steel using fuzzy mcdm techniques 57 figure 2. result of the sensitivity analysis for different ranking methods viz; (a) ftopsis, (b) f-copras, and (c) f-edas. from sensitivity analysis, it was noted that the f-edas method was less sensitive to criteria weight change compared to f-topsis and f-copras methods. moreover was, it noticed that ranking of the best alternative (experiment number en27) was changed with criteria weight change in f-topsis and f-copras methods. thus, it can be said that the stability of the ranking given by the f-edas was the highest compared to f-topsis and f-copras methods. thus, f-edas was the more robust method to solve this kind of multi-attributed problem. these obtained results were further validated by a comparative study, where spearman’s rank correlation coefficient was calculated for each scenario of mcdm methods. 3.2.1. comparison of mcdm methods spearman’s rank correlation coefficient for f-topsis methods is shown in table 11(a). the correlation coefficient value of each scenario shows that there is a lack of inconsistency in the ranking of the f-topsis method according to different fuzzy criteria weights. from table 11(a), it can be seen that the correlation coefficient value for scenario-(1-2), scenario-(1-3), scenario-(1-4), scenario-(2-3), scenario-(2-4) and scenario-(3-4) are 0.989, 0.996, 0.998, 0.985, 0.989 and 0.996 respectively. it can be said that coefficient values are varying from 0.985 to 0.996. similarly, for f-copras method (table 11(b)) the correlation coefficient is obtained for scenario-(1-2), scenario-(1-3), scenario-(1-4), scenario-(2-3), scenario-(2-4) and scenario-(3-4) are 0.992, 0.998, 0.997, 0.989, 0.993 and 1.000 respectively. here the coefficient values are varying from 0.989 to 1.000 and this range is higher than the f-topsis range of spearman coefficient value. for the f-edas method (table 11(c)), the value of correlation coefficient value for all the scenarios is higher than 0.990. in other words, it can be said that the spearman correlation coefficient for the scenario the of f-edas method is higher than the f-topsis and f-copras methods. based on the overall kumar et al./oper. res. eng. sci. theor. appl. 5(3)2022 40-67 58 results of sensitivity analysis and correlation coefficient the f-edas method is the most robust method to solve the multi-attribute decision-making problem. table 11. spearman’s rank correlation coefficient (a) coefficient values for f-topsis scenarios s2 s3 s4 s1 0.989 0.996 0.998 s2 0.985 0.989 s3 0.996 (b) coefficient values for f-copras scenarios s2 s3 s4 s1 0.992 0.998 0.997 s2 0.989 0.993 s3 1.000 (c) coefficient values for f-edas scenarios s2 s3 s4 s1 0.990 0.995 0.994 s2 0.993 0.999 s3 0.996 3.3. other wear parameter optimization problems solved by the proposed methodology in this section, the proposed methodology solves two wear optimization problems, which have already been solved and published elsewhere. the first problem is the optimization of wear parameters for composite coating, while the second problem is to optimize the wear parameters for heat-insulated ceramic coating. 3.3.1. optimization of wear parameter for composite coating this optimization problem was solved using the gray relation analysis (gra) method (raghavendra et al. 2021). table 12 presents the alternatives for wear parameters and their criteria, based on which alternatives were ranked. each criterion presented in table 12 was identified as non-beneficial criteria, and the criteria weight (table 14) was derived using the opinion of decision-makers as mentioned in table 13. table 12. list of alternatives and their criteria (initial decision matrix) method (raghavendra et al. 2021) alternative (specific wear rate, ws) c1 (pin temperature, pt) c2 (friction coefficient, cof) c3 en1 0.3330 91.990 0.123 en2 0.3470 92.140 0.038 en3 0.8750 98.340 0.144 en4 0.2520 90.760 0.089 en5 1.1900 94.840 0.153 en6 0.4000 73.960 0.089 en7 1.5550 105.990 0.116 en8 0.4770 78.660 0.011 optimization of wear parameters for duplex-tialn coated mdc-k tool steel using fuzzy mcdm techniques 59 en9 0.4750 88.760 0.065 en10 0.8530 87.810 0.627 en11 0.2920 86.910 0.046 en12 0.6411 80.120 0.103 en13 0.7020 93.690 0.112 en14 1.2400 90.160 0.035 en15 1.1710 111.780 0.119 en16 0.7840 91.920 0.459 en17 2.1320 110.380 0.104 en18 1.4450 95.910 0.099 en19 1.5500 88.480 0.119 en20 1.3700 117.190 0.016 table 13. opinion of the decision maker for problem 1 table 14. fuzzy criteria weight for problem 1 response dm1 dm2 dm3 ws lr lr l pt l m m cof l l m responses fuzzy criteria weight ws (0.033, 0.100, 0.233) pt (0.233, 0.433, 0.633) cof (0.167, 0.367, 0.567) one by one, each mcdm method (f-topsis, f-copras, and f-edas) was employed to derive the ranking of alternatives (table 15). from the obtained results (table 15), it was noticed that the ranking of the best alternative (en6) remains similar to it obtained in the past study method (raghavendra et al. 2021) [36]. further, the correlation between rankings was studied by calculating spearman’s rank correlation coefficient. it found these rankings have a good correlation as their coefficient value lies above 0.767, in the acceptable range. table 15. coefficient of closeness, performance score, appraisal score of alternatives, and its ranking alternative f-topsis f-copras f-edas rank method (raghavendra et al. 2021) closeness coefficient (coci) rank performance score (ui) rank appraisal value ( ) rank en1 0.643 10 8.878 10 0.623 10 8 en2 0.640 11 8.854 11 0.871 3 4 en3 0.499 16 7.762 16 0.485 17 12 en4 0.670 9 9.123 9 0.740 8 5 en5 0.579 14 8.338 14 0.463 18 15 en6 1.000 1 13.734 1 1.000 1 1 en7 0.313 17 6.676 17 0.499 14 18 en8 0.915 2 12.147 2 0.804 4 2 en9 0.713 7 9.539 7 0.789 6 7 en10 0.718 6 9.553 6 0.036 20 19 en11 0.752 4 9.952 4 0.883 2 3 en12 0.886 3 11.698 3 0.695 9 6 en13 0.605 13 8.556 13 0.593 11 10 kumar et al./oper. res. eng. sci. theor. appl. 5(3)2022 40-67 60 en14 0.683 8 9.232 8 0.792 5 9 en15 0.162 19 6.009 19 0.497 16 16 en16 0.637 12 8.807 12 0.196 19 17 en17 0.199 18 6.147 18 0.498 15 20 en18 0.555 15 8.153 15 0.571 12 14 en19 0.718 5 9.569 5 0.534 13 13 en20 0.018 20 5.468 20 0.786 7 11 3.3.1. optimization of wear parameter for heat-insulated ceramic coating the waspas method was used to solve this optimization problem by sahoo et al. in the past study (sahoo et al. 2021). the evaluating criteria and alternative wear parameters are listed in table 16. there are two criteria, namely weight loss, and friction coefficient, which are identified as non-beneficial criteria. the weights (table 18) of these criteria were obtained based on the decision of the expert panel (table 17). table 16. list of criteria and alternatives (sahoo et al. 2021) alternative (weight loss (wl), mg) c1 (friction coefficient (cof), µ) c2 en1 0.19 0.077 en2 0.60 0.084 en3 4.70 0.026 en4 5.10 0.040 en5 3.50 0.079 en6 9.20 0.064 en7 14.20 0.080 en8 9.30 0.080 en9 9.90 0.067 en10 20.20 0.090 en11 11.20 0.087 en12 17.00 0.057 en13 19.20 0.078 en14 13.50 0.070 en15 9.20 0.170 en16 9.20 0.063 table 17. opinion of the decision maker for problem 2 table 18. fuzzy criteria weight for problem 2 response dm1 dm2 dm3 wl lt lr l cof l l m response fuzzy criteria weight wl (0.033, 0.133, 0.300) cof (0.167, 0.367, 0.567) the obtained criteria weights were integrated with mcdm methods as described in sections 2.4, 2.5, and 2.6 to derive the ranking of alternatives. the derived rankings are listed in table 19, and a minor deviation can be observed in the ranking of alternatives. but this deviation does not affect the overall results. the ranking of the best alternative remains the same for each mcdm method, which exactly matches the past result (sahoo et al. 2021). although, these rankings have an excellent correlation among them as spearman’s rank correlation coefficient values are equal and more than 0.85. optimization of wear parameters for duplex-tialn coated mdc-k tool steel using fuzzy mcdm techniques 61 table 19. final preference values of alternatives and its ranking alternative f-topsis f-copras f-edas rank (sahoo et al. 2021) closeness coefficient (coci) rank performance score (ui) rank appraisal value ( ) rank en1 0.988 1 246.310 1 0.731 1 1 en2 0.985 2 199.395 2 0.683 4 3 en3 0.948 4 75.490 4 1.000 3 2 en4 0.938 5 61.938 5 0.885 2 4 en5 0.962 3 88.167 3 0.638 5 5 en6 0.797 7 19.312 7 0.602 7 7 en7 0.520 13 8.259 13 0.400 13 12 en8 0.789 8 18.375 8 0.489 10 11 en9 0.765 9 16.726 9 0.563 8 9 en10 0.049 16 4.137 16 0.242 15 15 en11 0.696 11 12.859 11 0.415 12 13 en12 0.321 14 5.900 14 0.515 9 8 en13 0.131 15 4.597 15 0.323 14 14 en14 0.567 12 9.189 12 0.478 11 10 en15 0.755 10 14.560 10 0.014 16 16 en16 0.797 6 19.344 6 0.610 6 6 3. conclusions this study focuses on the optimization of the wear parameters for duplex-tialn coated mdc-k tool steel. three different fuzzy mcdm methods were proposed to solve this optimization problem. a total of five wear responses, namely surface roughness, friction coefficient, wear mass loss, wear depth, and hardness, were identified as the criteria to evaluate the alternatives, which consist of different combinations of wear parameters such as applied load, sliding velocity, and sliding distance. the criteria weight was determined using triangular fuzzy numbers that are integrated into fuzzy mcdm methods to solve the problem. the following conclusions are drawn from the results:  the obtained results showed that alternative en27 (l = 10 n, sv = 0.2 m/s, and sd = 1500 m) to be the best alternative whereas en14 (l = 20 n, sv = 0.3 m/s, and sd = 2000 m) as the worst alternative parameters for duplex-tialn coated mdc-k tool steel.  these results were tested and validated by performing a comprehensive sensitivity analysis. additionally, two sets of wear parameters from the literature were also solved using the proposed methodology to substantiate its capability. the result obtained from the proposed methodology was found similar to the result obtained in the literature.  the validation result proved that the f-edas method is more robust and less sensitive to the criteria weight change. hence, it can be further used to solve kumar et al./oper. res. eng. sci. theor. appl. 5(3)2022 40-67 62 this type of multi-decision-making problem with some modifications (either addition or removal of new alternatives or criteria). the proposed methodology is designed to solve the multi-criteria such as the selection of optimal parameters for duplex-tialn coating, where three wear parameters (load, sliding velocity, and sliding distance) and five wear responses (ra, cof, wml, wd, and hv) were considered to solve the above problem. further, it was noticed that if some new 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(m) fe fuzzy-edas ra average surface roughness (µm) topsis technique for order of preference by similarity to ideal solution cof coefficient of friction copras complex proportional assessment wml wear mass loss (mg) edas evaluation based on distance from the average solution wd wear depth (µm) s1 scenario 1 hv vickers hardness s2 scenario 2 en experiment number s3 scenario 3 mcdm multi-criteria decision making s4 scenario 4 optimization of wear parameters for duplex-tialn coated mdc-k tool steel using fuzzy mcdm techniques sunil kumar 1, 2, saikat ranjan maity 1*, lokeswar patnaik 3 1. introduction 2. methodology 2.1. preparation of the specimen 2.2. selection of process parameters 2.3. fuzzy-topsis method 2.4. fuzzy-copras method 2.5. fuzzy-edas method 3. results and discussion 3.1. ranking of the alternatives using fuzzy mcdm methods 3.1.1. ranking of the alternatives using fuzzy-topsis method 3.1.2. ranking of the alternatives using fuzzy-copras method 3.1.3. ranking of the alternatives using the fuzzy-edas method 3.2. sensitivity analysis 3.2.1. comparison of mcdm methods 3.3. other wear parameter optimization problems solved by the proposed methodology 3.3.1. optimization of wear parameter for composite coating 3.3.1. optimization of wear parameter for heat-insulated ceramic coating 3. conclusions references operational research in engineering sciences: theory and applications vol. 4, issue 3, 2021, pp. 1-20 issn: 2620-1607 eissn: 2620-1747 doi: https://doi.org/10.31181/oresta20403001s * corresponding author. amalinashadrina@gmail.com (a. shadrina), zulfa.fitri@mercubuana.ac.id (z. f. ikatrinasari) quality improvement of the e-commerce website using integration of kano model-ipa with qfd approach amalina shadrina*, zulfa fitri ikatrinasari departement of industrial engineering, mercu buana university, jakarta, indonesia received: 22 march 2021 accepted: 07 june 2021 first online: 22 september 2021 research paper abstract: this study was conducted to analyze the quality of e-commerce websites, find out which items need improvement, and make improvement design e-commerce websites. this study uses the kano model and importance performance analysis approach based on 7 dimensions with 39 attributes. this study used the survey results from 103 respondents who regularly use the e-commerce website tokopedia.com. the results of the questionnaire through the validity and reliability tests were used to analyze the reliability of items and the feasibility of the results of the questionnaire. after that, the results of the questionnaire through the corellation and hypothesis tests were used to know the relationship between variables. the findings show that 7 attributes influence customer satisfaction. however, the findings are still nowhere near the expectations. thus, it requires being the focus of improvement. improvements in design of 7 attributes in the form of house of quality with 6 technical features needed to improve the quality of e-commerce website tokopedia.com. therefore, effective management strategies can be applied to overcome the intense competition in the ecommerce industry. key words: website quality, kano model, importance performance analysis, ecommerce, qfd, customer satisfaction 1. introduction technology has rapidly developed along with the times, which allows people to be able to work more easily and effectively (wilson & keni, 2018). one of the examples is the increase in internet development. the internet is a global network system that allows people to communicate globally, get information easily, as well as buy and sell products and services online. the internet has a big influence on how people work, shop, make payments, travel, and socializes (kaur, 2011). the development of the internet in recent years has changed the way people do business for they are starting to do it in a digital manner rather than the traditional way. https://doi.org/10.31181/oresta20403001s shadrina & ikatrinasari /oper. res. eng. sci. theor. appl. 4 (3) (2021) 1-20 2 technological advances and developments make life easier for human beings by making online business as well as buying and selling a trend in the future. in traditional trade, the seller and buyer have to meet each other in the same place, negotiate, and conduct transactions, which require both parties to agree on the prices. meanwhile, in e-commerce or online trading, there is no need for buyers and sellers to meet each other. instead, they meet through a website that acts as an intermediary that connects the two parties and facilitates the transaction. therefore, buyers can buy products or services from sellers, while sellers can do business even if they do not have a place or shop (wilson et al. 2019). e-commerce can be defined as a commercial transaction between two parties, organizations, and individuals which is carried out through a network or website (psaila & wagner, 2007). ecommerce covers several types of activities, such as retail shopping, banking, ordering food, ticketing, and others. most people use the website as e-mail, looking for information, social media, and a place for online transactions. this makes buying and selling things online a trend in the future. buying and selling online in the ecommerce industry is defined as the efforts made to market a product or service as well as to rebuild relationships between sellers and buyers through internet media (kotler & amstrong, 2014). hence, a website quality assessment is needed based on several criteria and items to describe things expected of a website (rondovic et al, 2017). website quality can affect repurchase intentions. on e-commerce sites, repurchase intentions have been underlined by several researchers or actors (wilson et al. 2019; wilson & keni 2018; wilson 2018; wilson & christella 2019). in this case, the quality of website appearance is known as a factor that can build repurchase intentions to consumers. it is an advantage for the company when a consumer or customer has the intention to rebuy things from the same e-commerce company. there is a possibility that customers will buy products or services from other companies in the same industry. moreover, some researchers have underlined that the relationship between customer loyalty and the success of e-commerce companies is the key to achieving success in the e-commerce industry since it can indirectly retain customers (lee et al, 2009). one of the important things in repurchase in e-commerce is the website user interface features that are well designed that enable a positive impression on customers who will do a repurchase (fan & tsai, 2010). the quality of the website’s appearance has a considerable effect in influencing customer trust to shop on the site (gregg & walczak 2010). the quality of website design is related to the customer’s initial online buying behavior (zhou et al., 2009). online shopping websites are very important for businesses, retailers, and consumers where the features on the website are designed innovatively. for that reason, the e-commerce industry has to develop high-quality websites that provide a better online experience to attract and retain their customers in e-commerce (stuart, 2003). the main challenges for e-commerce organizations are understanding the users' needs and developing them. e-commerce companies with websites that are difficult to use will protect a bad image on the internet and weaken the company’s position in the e-commerce business (barnes & vidgen, 2002). this study aims to find out the extent of the satisfaction level of tokopedia.com e-commerce web users through measurement between the current level of quality (perception) and the desired quality (expectations). the next goal is to be able to describe the position of the tokopedia.com e-commerce website quality items to enable seeing which items are by the user's expectations and which ones need improvement. therefore, it can be designed to propose improvements on the quality improvement of the e-commerce website using integration of kano model-ipa with qfd approach 3 tokopedia.com e-commerce website. this study differs from previous studies. previous studies only reached the stage of e-commerce website quality analysis, while this study proposed improvements on the results of e-commerce website quality analysis based on kano model and importance performance analysis methods using improvement scales quality function deployment (qfd). kang et al (2016) studied the evaluation of e-commerce websites based on the e-s-qual method. a study conducted by ilbahar and cebi (2017) analyzed and classified design parameters according to customer expectations for evaluating the usefulness of ecommerce websites. mohd and zaaba (2019) argue on usability and security factor analysis on e-commerce websites. 2. literature review in general, quality is a characteristic of a product or service that reflects how well the product or service meets customer satisfaction (negash et al. 2003). according to a study, customer perceptions on the quality of a website are based on features on the website that meet customer needs and impress the total excellence of the website. the previous researchers also mentioned that various dimensions of website quality which can be categorized as security, information quality, ease of use, and service quality. customer perceptions of the quality of the website are based on features on the website that meet the needs and impressions of customers towards the website (mona et al., 2013). attractive website designs on e-commerce websites motivate consumers to engage in online shopping (ganesh et al., 2010). according to some researchers, the features on the website have an important influence on online purchase intentions (mansori et al., 2012). another study argues that informative websites allow customers to compare and evaluate product alternatives thereby increasing customer satisfaction and thus influencing online purchase intentions (hausman & siekpe, 2009). the quality of information offered by a brand on online shopping sites is also an important factor. a specific study revealed that information quality has the highest influence on customer satisfaction among all dimensions of website quality (kim & jones, 2009). 2.1. kano model kano model is used to determine how effective an indicator plays a role in improving service quality. the kano’s attributes are divided into several categories. the first category is must be (m) or basic needs, the customer simply accepts when it is fulfilled. however, if the product or service fails to satisfy the customer's basic needs, the customer will be very dissatisfied. for instance, although having unfriendly waiters causes customer dissatisfaction, having friendly service does not increase customer satisfaction since having a friendly waiters is a basic need (garibay et al, 2010). the second category is one dimensional (o) or performance needs. the level of customer satisfaction is related to one-dimensional performance; thus, the higher the perceived service quality, the higher the customer satisfaction, and vice versa. when attributes are fulfilled, customers are satisfied; if they are not fulfilled, customers are dissatisfied. the level of customer satisfaction increases in accordance with the level of such attributes. therefore, the categories of must be and one dimensional are conditions needed to achieve customer satisfaction (basfirinci shadrina & ikatrinasari /oper. res. eng. sci. theor. appl. 4 (3) (2021) 1-20 4 et al, 2015). the third category is attractive (a) or excitement needs, which shows a high level of customer satisfaction when fulfilled, but does not cause dissatisfaction when it is not fulfilled because it is not expected by the customer who may not know the product features. the fourth category is reserve (r), which indicates that if an indicator in this category exists, the customer is dissatisfied, while if the opposite is true, the customer is highly satisfied. the fifth category is indifferent (i), which indicates that the existence of indicators in this category seems to have no impact on customer satisfaction. the sixth category is questionable (q), which involves indicators that are still questionable since the possibility of customers being satisfied or dissatisfied is unclear (dewi et al, 2018). the next step is determining the kano’s category for each indicator. if (m + o + a)> (i + r), then the kano’s category for the xindicator is max {m, o, a), otherwise (m + o + a) <(i + r) then the kano’s category for the x-indicator is max {i, r} (kuo et al, 2012). the researcher will then use importance performance analysis to process the attributes that fall into the m, o, and a categories. 2.2. importance performance analysis (ipa) importance performance analysis (ipa) has been one of the most extensively acknowledged systematic methods for measuring which items demand improvement. the research focused on the importance performance analysis (ipa), evans and chon (1989) examined the capability of the ipa to control tourism strategies in two different places in the us. the investigation showed that local business workers were not content with the company’s performance. the next researcher used ipa to compare business competitiveness in hong kong with its main competitors in the asia pacific region. in analyzing the data, they used ipa for it can provide a basis for their business development strategies (enright & newton, 2004). sorensson’s (2013) research results comparing national and international tourists using ipa revealed that national tourists place a higher level of importance on sustainable tourism than international tourists. meanwhile, there are significant differences between national and international tourists in subsequent tourism. the results from the ipa consist of four quadrants. quadrant i included the high importance but low performance. the items included in this quadrant represent the main items that need to be improved with top priority. quadrant ii involved high importance with a high level of performance. thus, it does not need enhancement and the items recorded on this quadrant are meet expectations. quadrant iii is of low importance with low performance as well labeled as a low priority. therefore, the items included in this quadrant are unimportant and do not pose a threat to the company. quadrant iv means low importance with a high level of performance. quadrant iv is labeled as possibly excessive. this shows items that are too much emphasized by the organization. hence, organizations have to minimize these items. however, rather than focus in this quadrant, companies are obliged to allocate more resources to focus on items that are in quadrant i (wong et al., 2011). 2.3. quality function deployment (qfd) quality function deployment is a way to make the needs and desires of customers as part of the design and production of a product or service. qfd is used by companies to identify customer needs in technical languages (goetsch & davis, 2014). qfd originated from japan in 1972. it has been successful as a tool to help quality improvement of the e-commerce website using integration of kano model-ipa with qfd approach 5 systematic quality improvement teams translate market research and customer needs into technical characteristics to satisfy customer desires. in qfd, customer needs are reflected in the planning matrix or so-called 'quality home' or hoq (cohen, 1995). 3. methodology this study is a survey study that used a quantitative approach by involving samples directly from the existing population. the purpose of this study was to determine the extent of user satisfaction on the quality of e-commerce tokopedia.com websites, items that need to be improved and also suggestions for improvements on the quality of tokopedia.com e-commerce websites. variables measured to determine the quality of the website was to use seven dimensions including website design (wd), product quality (pq), security quality (sq), delivery quality (dq), delivery accuracy (da), customer service (cs), customer perception and satisfaction (ps). each dimension consisted of several question items as the basis for compiling the questionnaire. the sampling technique used in this study was simple random sampling where sampling was done randomly from the existing population. in general, based on the theory that sampling for factor analysis requires a minimum of 100 respondents (kline, 1994). thus, this study used a 90% confidence level with a 10% error margin where the sample size was 103 respondents. the e-commerce website used as a sample of this study was the tokopedia.com e-commerce website. the data collection technique used was a questionnaire with a likert scale and kano scale. likert scale consisting of 5 points, from strongly disagree (score 1) to strongly agree (score 5). kano scale consisting of 5 points, that is m (must be), o (one dimensional), a (atractive), i (indifferent), r (reserve) dan q (questionable). after the questionnaire was distributed, validity and reliability tests were performed to determine whether the results of the questionnaire were suitable for analysis. an item that had a positive correlation with criteria (total score) and a high correlation showed that the item had high validity as well. based on this, if the calculated r count value was smaller than the r table value, then then the question item became unvalid. moreover, it was said to be valid if the calculated value was greater than the r table value. after testing the validity of the questions used in the study, the reliability test was then performed. the reliability test was carried out to find out whether the data collection tool showed the level of accuracy, stability or consistency. thus, the data can be used for further analysis. an item is considered to be reliable if the value of cronbach alpha is bigger than the critical value. the specified critical value is 0.6. if the alpha value is greater than 0.6 then it is reliable and if the alpha value is less than 0.6 then it is not reliable (sugiyono, 2016). after that, the results of the questionnaire through the corellation and hypothesis tests were used to know the relationship between variables. after the correlation and hypothesis testing, the data can be processed using the kano model and also the importance performance analysis for further analysis. variabel and attribut of the questionnaire is presented in appendix 1. after the questionnaire data had been obtained, validity and reliability tests were performed to test the eligibility of the items and the accuracy of the questionnaire shadrina & ikatrinasari /oper. res. eng. sci. theor. appl. 4 (3) (2021) 1-20 6 results. after that, the results of the questionnaire through the corellation and hypothesis tests were used to know the relationship between variables. after being declared valid, reliable and passed hyphotesis, the result of questionnaire quality of the tokopedia website was analyzed using kano model and importance performance analysis. after getting the results from the kano model, then performed data processing importance performance analysis which showed which indicators need improvement, the design of the improvement of the tokopedia.com e-commerce website was improved by using the quality function deployment. the design of the improvement was described in the house of quality where there were several technical characteristics needed for improvement. 4. results based on the result of the questionnaire, the user of the tokopedia.com website who became the respondents by gender involved in this study were 63% or 65 respondents were female, and the remaining 37% or 38 respondents were male. meanwhile, seen from the age of respondents, 78% or 81 respondents were 20-30year-old, 15% or 15 respondents were 31-40-year-old, and 7% or 7 respondents were 41-50-year-old. the types of work of the respondents were private employees 83% or 86 respondents, civil servants 9% or 10 respondents, students 4% or 4 respondents, and housewives 4% or 3 respondents. based on the frequency of use of e-commerce websites, 19% or 20 respondents regularly used e-commerce website, 50% or 52 respondents frequently used e-commerce websites, and 31% or 31 respondents quite often used e-commerce websites. 4.1. validity and reliability analysis the following are the results of the validity and reliability tests of the questionnaire results from 103 respondents involved in this study. table 1. validity test questions r count value r table value decision r count > r table wd1 0.437 0.1638 valid wd2 0.716 0.1638 valid wd3 0.511 0.1638 valid wd4 0.536 0.1638 valid wd5 0.320 0.1638 valid wd6 0.616 0.1638 valid pq1 0.637 0.1638 valid pq2 0.652 0.1638 valid pq3 0.726 0.1638 valid pq4 0.491 0.1638 valid pq5 0.272 0.1638 valid sq1 0.633 0.1638 valid sq2 0.579 0.1638 valid sq3 0.632 0.1638 valid sq4 0.524 0.1638 valid sq5 0.738 0.1638 valid dq1 0.615 0.1638 valid dq2 0.342 0.1638 valid quality improvement of the e-commerce website using integration of kano model-ipa with qfd approach 7 table 1. validity test (continue) questions r count value r table value decision r count > r table dq3 0.731 0.1638 valid dq4 0.726 0.1638 valid da5 0.387 0.1638 valid dq6 0.208 0.1638 valid dq7 0.487 0.1638 valid da1 0.544 0.1638 valid da2 0.632 0.1638 valid da3 0.404 0.1638 valid da4 0.685 0.1638 valid da5 0.466 0.1638 valid cs1 0.251 0.1638 valid cs2 0.210 0.1638 valid cs3 0.265 0.1638 valid cs4 0.251 0.1638 valid cs5 0.716 0.1638 valid cs6 0.670 0.1638 valid ps1 0.618 0.1638 valid ps2 0.526 0.1638 valid ps3 0.620 0.1638 valid ps4 0.684 0.1638 valid ps5 0.562 0.1638 valid table 1 presents the results of the spss 25.0 calculation regarding the overall value of r count which is greater than the r table value of 0.1638 for 103 questionnaires. consequently, it can be concluded that the whole question items in the questionnaire are valid. after that, a reliability test was made to measure the reliability of respondents' responses to the general items of the questions asked. according to santoso (2010), the questionnaire is deemed to be reliable if the value of the cronbach alpha is above 0.60. the following are the results of the reliability test of 39 question items in the questionnaire. table 2. reliability test question items alpha cronbach description 39 0.931 reliable based on the calculation using spss 25.0 presented in table 2 above, it can be inferred that the cronbach alpha coefficient value is 0.931. thus, it can be concluded that the question items in the tokopedia.com e-commerce website quality questionnaire had a good level of consistency. therefore, the findings of this study can be accounted for and can be used for further data processing to provide solutions for improving the quality of e-commerce websites. 4.2. corelation analysis the relationship between each variable is referred to as correlation. correlation refers to how a change in one variable causes a change in the direction of another shadrina & ikatrinasari /oper. res. eng. sci. theor. appl. 4 (3) (2021) 1-20 8 variable. the higher the correlation, the closer the absolute value is to one. as a result, "+" indicates a positive change direction, while "-" indicates a negative change direction. the following is a correlation test between variables where all the dimensions of the tested variables are correlated or have a relationship between variables, since the value of the correlation test results is <0.05 or there are ** and * signs appeared in table 3. table 3. correlations test wd pq sq dq da cs ps 1 wd 103 103 .680** 1 pq 0 103 103 103 .529** .577** 1 sq 0 0 103 103 103 103 .608** .705** .707** 1 dq 0 0 0 103 103 103 103 103 .487** .588** .858** .683** 1 da 0 0 0 0 103 103 103 103 103 .200* .228* 0.19 .233* .249* 1 cs 0.043 0.021 0.055 0.018 0.011 103 103 103 103 103 103 .739** .637** .748** .718** .743** .294** 1 ps 0 0 0 0 0 0.003 103 103 103 103 103 103 103 ** correlation is significant at the 0.01 (2-tailed). * correlation is significant at the 0.05 level (2-tailed). 4.3. hypothesis analysis hypothesis testing aims to test the effect of the quality of the tokopedia.com website on customer satisfaction. the hypothesis was tested using regression analysis by determining seven sub-factors as independent variables, with customer satisfaction as the dependent variable. the regression analysis hypothesis test results, which are attached in table 4, are as follows. quality improvement of the e-commerce website using integration of kano model-ipa with qfd approach 9 table 4. hypothesis test unstandardized coefficients standardized coefficients t sig. adj r2 b std. error beta (constant) -2.156 1.141 -1.889 0.062 0.996 wd 1.193 0.056 0.226 21.435 0.000 pq 1.034 0.060 0.173 17.128 0.000 sq 0.933 0.078 0.160 12.029 0.000 dq 1.144 0.055 0.225 20.968 0.000 da 1.185 0.082 0.191 14.398 0.000 cs 1.235 0.071 0.115 17.329 0.000 ps 0.957 0.078 0.159 12.250 0.000 hypothesis 1 predicts that the website design (wd) positively influences consumen satisfaction. the regression analysis of hypothesis 1 has p=0.000<0.05, indicating a statistically significant correlation. thus, hypothesis 1 is accepted. hypothesis 2 predicts that the product quality (pq) positively influences consumen satisfaction. the regression analysis of hypothesis 2 has p=0.000<0.05, indicating a statistically significant correlation. thus, hypothesis 2 is accepted. hypothesis 3 predicts that the security quality (sq) positively influences consumen satisfaction. the regression analysis of hypothesis 3 has p=0.000<0.05, indicating a statistically significant correlation. thus, hypothesis 3 is accepted. hypothesis 4 predicts that the delivery quality (dq) positively influences consumen satisfaction. the regression analysis of hypothesis 4 has p=0.000<0.05, indicating a statistically significant correlation. thus, hypothesis 4 is accepted. hypothesis 5 predicts that the delivery accuracy (da) positively influences consumen satisfaction. the regression analysis of hypothesis 5 has p=0.000<0.05, indicating a statistically significant correlation. thus, hypothesis 5 is accepted. hypothesis 6 predicts that the customer service (cs) positively influences consumen satisfaction. the regression analysis of hypothesis 6 has p= 0.000<0.05, indicating a statistically significant correlation. thus, hypothesis 6 is accepted. hypothesis 7 predicts that the customer perception and satisfaction (ps) positively influences consumen satisfaction. the regression analysis of hypothesis 7 has p=0.000<0.05, indicating a statistically significant correlation. thus, hypothesis 7 is accepted. 4.4. kano model and importance performance analysis the kano model was analyzed to determine the attributes that customers need as well as those that have the potential to become a source of innovation for the tokopedia.com website. each respondent's questionnaire was categorized into m (must be), o (one dimensional), a (attractive), i (indifferent), r (reserve), and q (questionable). after collecting 103 respondents, then the results of the number of each service attribute are calculated. data processing in the kano model for each attribute is determined by the following rules, namely if (m+o+a)>(i+r), then the service attribute category is max (o, a, m) and if (m+o+a)<(i+r), then the kano’s category for the service attribute is max (i, r). table 5 summarizes the results of the kano model calculation. shadrina & ikatrinasari /oper. res. eng. sci. theor. appl. 4 (3) (2021) 1-20 10 table 5. kano model no code m o a i r q m+o+a i+r kano category 1 wd1 61 29 12 0 0 1 102 0 m 2 wd2 73 18 10 2 0 0 101 2 m 3 wd3 41 7 52 1 0 2 100 1 a 4 wd4 37 45 21 0 0 0 103 0 o 5 wd5 42 50 9 1 0 1 101 1 o 6 wd6 28 59 16 0 0 0 103 0 o 7 pq1 51 37 12 2 0 1 100 2 m 8 pq2 59 33 11 0 0 0 103 0 m 9 pq3 40 18 44 1 0 0 102 1 a 10 pq4 32 31 39 0 0 1 102 0 a 11 pq5 37 25 41 0 0 0 103 0 a 12 sq1 46 53 4 0 0 0 103 0 o 13 sq2 35 67 1 0 0 0 103 0 o 14 sq3 31 48 15 2 0 7 94 2 o 15 sq4 20 52 31 0 0 0 103 0 o 16 sq5 48 41 6 4 1 3 95 5 m 17 dq1 62 37 4 0 0 0 103 0 m 18 dq2 59 12 30 1 0 1 101 1 m 19 dq3 47 50 6 0 0 0 103 0 o 20 dq4 36 21 39 3 0 4 96 3 a 21 dq5 42 39 19 2 0 1 100 2 m 22 dq6 38 55 10 0 0 0 103 0 o 23 dq7 49 31 22 1 0 0 102 1 m 24 da1 41 58 4 0 0 0 103 0 o 25 da2 40 43 19 0 0 1 102 0 o 26 da3 28 47 26 0 0 2 101 0 o 27 da4 55 38 10 0 0 0 103 0 m 28 da5 59 41 3 0 0 0 103 0 m 29 cs1 51 26 25 1 0 0 102 1 m 30 cs2 63 19 21 0 0 0 103 0 m 31 cs3 57 28 17 0 0 1 102 0 m 32 cs4 40 53 10 0 0 0 103 0 o 33 cs5 31 49 23 0 0 0 103 0 o 34 cs6 34 52 17 0 0 0 103 0 o 35 ps1 59 40 4 0 0 0 103 0 m 36 ps2 41 11 43 5 0 3 95 5 a 37 ps3 38 9 51 5 0 0 98 5 a 38 ps4 42 31 19 11 0 0 92 11 m 39 ps5 35 20 33 12 1 2 88 13 m according to table 5, there are 17 attributes that are categorized as must be (m), 15 attributes are categorized as one dimensional (o), and 7 attributes are categorized as attractive (a) which means that all attributes are included in the categories m, o, and a which are tested, affect consumer satisfaction of e-commerce website users, while there are no attributes that fall into category i or r, which means that there is not a single attribute that does not affect customer satisfaction. quality improvement of the e-commerce website using integration of kano model-ipa with qfd approach 11 therefore, in the next ipa processing, all attributes will be analyzed. the results of the ipa analysis, as shown in figure 1, are as follows. figure 1. importance-performance analysis the items included in quadrant i were item wd2 with indicator the information on the website is effective, item pq3 with indicator all products on the website are available, item dq4 with indicator the websites offers discount or free shipping, item da4 with indicator delivers products in accordance with the set conditions, item cs4 with indicator it provides me with convenient options for returning items, item cs5 with indicator this site handles products returns well, and item cs6 with indicator return policy is simple. after analyzing the questionnaire using the kano model and importance-performance analysis (ipa) so that it is known which items need to be repaired (quadrant i), an improvement design using quality function deployment (qfd) by arranging house of quality. 4.5. quality function deployment the first phase in preparing qfd was the matrix of consumer needs or voice of customer which was a list of items that were important to consumers. in this study, the results of importance performance analysis (ipa) were used in determining the voice of customer by placing the items in quadrant i like the focus of improvement. phase 2 was determining the ratio of improvement of each quality indicator on the tokopedia.com website. to achieve desirable and measurable results, targets were measured as well. the following is the formula for calculating the value of the improvement ratio. (1) quadrant i quadrant iii quadrant iv quadrant ii shadrina & ikatrinasari /oper. res. eng. sci. theor. appl. 4 (3) (2021) 1-20 12 using this formula, the determination of the improvement ratio was done by comparing the expected value with the perception obtained from the results of the questionnaire. the calculation of the improvement ratio in quadrant i items was as follows. table 6. improvement ratio code indicator expectation perception improvement ratio (ir) wd2 the information on the website is effective 4.73 3.78 1.25 pq3 all products on the website are available 4.76 3.79 1.26 dq4 the website offers discount or free shipping 4.75 3.79 1.25 da4 delivers products in accordance with the set conditions 4.78 3.81 1.25 cs4 it provides me with convenient options for returning items 4.72 3.93 1.20 cs5 this site handles product returns well 4.81 3.78 1.27 cs6 return policy is simple 4.66 3.70 1.26 the third phase was determining the technical characteristics. technical characteristics are the response given by the company to user desires that need to be revised. determination of the technical characteristics was conducted by benchmarking, discussion, and interviews with interested parties. determination of technical characteristics included various features of the website, standards for completeness of information, consistency in implementing sops, refund policies, labor qualifications, and availability of assurance products. the fourth phase was the benchmarking stage which was conducted by comparing tokopedia.com ecommerce with similar companies. the fifth phase was the relationship analysis of what’s and how’s matrixes. in this section, the researchers described the relationship between customer needs and the technical characteristics needed to meet customer needs. this section was marked with number 3 which means it had a positive correlation and number 9 which means strong positive. the analysis of the relationship between what and how matric is presented in appendix 2. the sixth phase was determining the correlation of technical characteristics drawn on the roof of the house of quality. characteristic correlations were described by four symbols, including the black circle symbol that represented a strong positive relationship and the white symbol that represents a positive relationship. additionally, a negative relationship was depicted by a black triangle symbol which means strong negative and white triangle which means negative. further, the seventh phase was setting goals or targets for each technical characteristic which means the steps or strategies needed for the organization to achieve the specified technical features. the following were the targets or stages that have to be carried out to achieve the required technical characteristics. quality improvement of the e-commerce website using integration of kano model-ipa with qfd approach 13 table 7. target or limit value technical characteristic target variety of website features there are features about product info, shipping refunds, payment, and expedition tracking features completeness of information providing direction to the seller in the procedure of providing information in marketing their product consistency in sop implementation providing strict standards and consequences for parties related to customer sevice or the seller in carrying out duties or regulations in selling products refund policy the website provides a good refund policy labor qualification providing training to customer service websites assurance availability providing a guarantee of products purchased by customers if something goes wrong next, the final phase was determining the priority level. the priority level was used to determine which target or limit value had the highest priority level and the lowest priority level. technical priorities is the result of multiplying the values contained in the technical characteristics with the value of importance to customer. the results of the technical characteristic values can be used to calculate the percentage value for total priorities. the greater the value, the greater the priority for improvement. the results of the house of quality (hoq) design to improve the quality of e-commerce websites, in the tokopedia company is presented in appendix 3. 5. discussions value of technical priorities is obtained by multiplication between the values of the technical characteristics with the value of importance to customer. example for calculate technical priorities of variety of websites features =(9×5)+(9×5)+(9×5)+ (9×5)+(9×5)+(9×5)+(9×5)=315. example for calculate percent total priorities of variety of websites features=(315/(315+315+315+285+225+285)=18%. others technical priorities and percent total priorities can be calculated as above formula. based on appendix 3, determining the top priority in improving website quality based on the value technical priorities became the technical focus of improving the quality of e-commerce websites that have to be done immediately. the technical characteristic with the highest weight was variety of website features, completeness of information and consistency in the implementation of sop. a variety of website features is various features found on a website designed for marketing needs. thus, the intended website can meet the desires of the user. variety of website features where the website must provides features that can accommodate all information related to the product with all its policies. this includes features of the information that is accurate, reliable, timely, and also detailed. the website must provide tracking features for product shipments as well as by phone interaction with the customer service website. the standard of completeness of information in which the seller is most responsible for these characteristics. the standard of completeness of information including websites must provides accurate, reliable, timely, and also detailed information. additionally, the website has to provide information on shadrina & ikatrinasari /oper. res. eng. sci. theor. appl. 4 (3) (2021) 1-20 14 product return policies, information on compensation in the event of an internal problem, and also information about the customer service website telephone number. in case sop implementation, sop must was made with strict standards. moreover, there were consequences if the sop was not carried out according to the standard. the strict standard was to give obligations to related parties both customer service and seller in complying with the rules in the applicable sop. sop on customer service including the ability of customer service website as a good mediator in the event of the return of goods between the seller and buyer, the ability of customer service in resolving the problem immediately, the ability of customer service in providing a solution in the form of compensation in the event of an internal problem, and interacting directly with the users. meanwhile, according to the sop, the seller is required to provide accurate, reliable, up to date, and detailed information. the second-highest weighted technical characteristic was refund policy and assurance availability. refund policy was in effect for the product received which was not following the expectation of the buyer, such as a product in a defective condition, inadequate quantity, wrong color, and so on. the indicators included in the refund policy were product returns according to applicable regulations, immediately handled by the customer service, the existence of compensation, and the ease of communication between the user and the customer service website. the indicator required to be reviewed to prevent refunds was the website. in this case, the seller has to provide accurate and reliable information to minimize product returns. an assurance on the website is a guarantee given by the tokopedia.com website when things go wrong. the indicators included in this regard are the website handling product returns well, as well as being able to provide compensation in the event of an internal problem. indicators that also need to be reviewed were if the website does not provide accurate, reliable, and timely information, in addition to that if the customer service does not resolve the problem immediately and is also difficult to contact. the third-highest weighted technical characteristic was labor qualifications. employees were the spearhead of the website quality delivery system. for employees to be able to meet the expectations of website users effectively, it requires support from the main management functions. this support can be in the form of equipment, information, and training in service standards. indicators included in terms of workforce qualifications were handling product returns properly, addressing problems immediately, and also the ease of communicating with customer service websites wither through chat or by phone features. 6. conclusion based on the results of the integration of the kano and ipa models, it has been proven effective in knowing which attributes need to be improved in enhancing the quality of the e-commerce website tokopedia.com. furthermore, there are seven attributes that need to be improved out of the 39 attribute studied. the kano and ipa models' results for these seven attributes have a significant effect on customer satisfaction, but they are not as expected. quality improvement of the e-commerce website using integration of kano model-ipa with qfd approach 15 the seven attributes are the information on the website is effective, all products on the website are available, the website offers discount or free shipping, delivers products in accordance with the set conditions, it provides me with convenient options for returning items, this site handles product return well, and return policy is simple. the seven attributes that do not meet customer expectations are then evaluated with qfd, which results 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(2009). the relative importance of website design quality and service quality in determining consumers’ online repurchase behavior. information systems management, 26(4), 327–337. © 2021 by the authors. submitted for possible open access publication under the terms and conditions of the creative commons attribution (cc by) license (http://creativecommons.org/licenses/by/4.0/). https://doi.org/10.1080/09537325.2020.1849610 https://doi.org/10.19166/derema.v14i1.1108 https://doi.org/10.22146/gamaijb.33665 shadrina & ikatrinasari /oper. res. eng. sci. theor. appl. 4 (3) (2021) 1-20 18 appendix 1. dimensions & items dimension code attributes reference website design (wd) wd1 the website adequately meets my information needs blut, m. (2016) wd2 the information on the website is effective blut, m. (2016) wd3 the website is visually pleasing blut, m. (2016) wd4 the display pages within the website are easy to read blut, m. (2016) wd5 the text on the website is easy to read. blut, m. (2016) wd6 the website loads quickly blut, m. (2016) product quality (pq) pq1 this website has a good selection products blut, m. (2016) pq2 the site has a wide variety of products that interest me blut, m. (2016) pq3 all products on the website are available blut, m. (2016) pq4 the website offers discount product blut, m. (2016) pq5 the website has lower prices than offline stores blut, m. (2016) security quality (sq) sq1 i feel safe in my transactions with the website blut, m. (2016) sq2 the website has adequate security features blut, m. (2016) sq3 this site protects information about my credit card blut, m. (2016) sq4 i trust the website to keep my personal information safe blut, m. (2016) sq5 it protects information about my web-shopping behavior blut, m. (2016) delivery quality (dq) dq1 the product is delivered by the time promised by the seller blut, m. (2016) dq2 this website makes items available for delivery within a suitable time frame blut, m. (2016) dq3 it quickly delivers what i order blut, m. (2016) dq4 the website offers discount or free shipping blut, m. (2016) dq5 seller provides delivery at low cost vasic, et al. (2020) dq6 seller delivers products in accordance with the set conditions vasic, et al. (2020) dq7 the website offers the shipment tracking option vasic, et al. (2020) delivery accuracy (da) da1 you get what you ordered from this website blut, m. (2016) da2 the website is truthful about its offerings blut, m. (2016) da3 the ordered products arrived in a good condition blut, m. (2016) da4 delivers products in accordance with the set conditions vasic, et al. (2020) da5 shipment content is seldom liable to complaints vasic, et al. (2020) customer service (cs) cs1 this site provides a telephone number to reach the company blut, m. (2016) cs2 this site has customer service representatives available online blut, m. (2016) cs3 it offers the ability to speak to a live person if there is a problem blut, m. (2016) cs4 it provides me with convenient options for returning items blut, m. (2016) cs5 this site handles product returns well blut, m. (2016) cs6 return policy is simple vasic, et al. (2020) quality improvement of the e-commerce website using integration of kano model-ipa with qfd approach 19 appendix 1. dimensions & items (continue) dimension code attributes reference customer perception ps1 i am satisfied with this online retailer blut, m. (2016) and satisfaction (ps) ps2 the online retailer always meets my needs blut, m. (2016) ps3 i consider this online retailer to be my first choice for next transactions blut, m. (2016) ps4 i say positive things about this online retailer to other people blut, m. (2016) ps5 i recommend this online retailer to someone who seeks my advice blut, m. (2016) appendix 2. how and what matrix shadrina & ikatrinasari /oper. res. eng. sci. theor. appl. 4 (3) (2021) 1-20 20 appendix 3. house of quality quality improvement of the e-commerce website using integration of kano model-ipa with qfd approach amalina shadrina*, zulfa fitri ikatrinasari 1. introduction 2. literature review 2.1. kano model 2.2. importance performance analysis (ipa) 2.3. quality function deployment (qfd) 3. methodology 4. results 4.1. validity and reliability analysis 4.2. corelation analysis 4.3. hypothesis analysis 4.4. kano model and importance performance analysis 4.5. quality function deployment 5. discussions 6. conclusion reference plane thermoelastic waves in infinite half-space caused operational research in engineering sciences: theory and applications vol. 5, issue 2, 2022, pp. 61-84 issn: 2620-1607 eissn: 2620-1747 doi: https://doi.org/10.31181/oresta300622045k * corresponding author. predrag@telrad.biz (p. katanic), srdjan.damjanovic@fpe.unssa.rs.ba (s. damjanovic) correlation of human mobility in the capitals of seven european countries during the covid19 pandemic predrag katanić 1, srđan damjanović 1* 1 faculty of business economics bijeljina, university of east sarajevo, bosnia and herzegovina received: 15 march 2022 accepted: 20 may 2022 first online: 30 june 2022 reseacrh paper abstract: we monitored and compared human mobility for six discrete categories during two year the covid-19 pandemic in seven european countries: austria, france, italy, united kingdom, serbia, spain, and sweden, and their capitals: vienna, paris, rome, london, belgrade, madrid and stockholm. we have chosen countries whose capitals have more than a million inhabitants and which are located in various parts of europe. we chose sweden because it had a policy with the mildest restrictions on population movement during the pandemic. the collected data for the time period from february 15, 2020 until february 11, 2022. using basic statistical methods, we found that there is a high degree of correlation between the data, which represent the mobility of people across the countries and the mobility of people in the capital of all seven observed european countries for six discrete categories. based on this, it can be concluded that the mobility of people during the covid-19 pandemic differs a lot from country to country, because the policies of governments in restricting the movement of people in the past two years have also differed significantly. through this we want to show that data from google community mobility reports can be combined with many other data from various areas of human life and work and that various statistical processing of these data can be done to show various types of correlations with human mobility during the covid-19 pandemic and how it affects the lives and economies of people around the world. key words: covid-19 pandemic, mobility, data, country, correlation. 1. introduction at the end of 2019, the first cases of human coronavirus appeared at the end of 2019 in the chinese province of wuhan, precipitating the appearance of the disease termed covid-19 (tamagusko and ferreira 2020). in europe, the first cases of this dangerous disease that spread rapidly among humans were recorded in of january katanić and damjanović/oper. res. eng. sci. theor. appl. 5(2) 2022 61-84 62 2020. as the virus began to spread rapidly among the population of european countries, the governments of most countries have begun to apply various special measures to stop the spread of the virus. some countries have implemented very drastic measures banning people from leaving the house, gathering and moving people, as well as banning the work of schools and colleges. in contrast, only a few european countries have not decided on a strict ban on leaving the house and all cultural and sporting events (examples sweden and belarus). the world health organization has recommended to all countries in the world that the best strategy to fight the covid-19 disease is to prevent the transmission of the virus by social distancing. this has been a major problem for most countries, as most social and economic activities are based on direct interaction between people (damjanovic, katanic & drakul 2021). google company 2020 began public publishing data on global mobility daily through a report named community mobility reports (further in the work cmr). this document in csv format contains data collected from 135 countries of the world. the first data on human mobility began to be published from february 15, 2020. from then until today, this data has been updated every working day. this report in addition to the data collected for each country, its regions and cities, it also presents certain statistics for this data. in this way, google wanted to promote various studies and works on the topic the fight against covid-19 disease. through this work we want to show how these are very useful data and how they can be statistically processed and based on that various conclusions and comparisons of human mobility for certain locations between countries can be made in each of the observed countries. in our opinion, it is especially interesting to compare the collected data within one country and between countries, in order to conclude which country had a better policy towards its citizens during the covid-19 pandemic. we hope that governments around the world will use this information to act differently in the event of a new pandemic, because we believe that a total ban on leaving the house and going even to parks has not fully contributed to preventing the spread of the virus in all countries. google's cmr is based on the data that google collects from individuals who use smartphones or handheld devices in the google app. the only necessary condition for this is that the option to record "location history" be enabled on mobile devices, which almost all users of mobile devices have accepted today. most smartphones users are not even aware that their movements are constantly monitored and that google later uses this data for various studies of human behavior. each day, google compares the physical locations of each mobile device observed throughout the all day and how much time it spends in those locations. all data collected are sorted into six discrete categories locations, which can be summarized as follows: retail and recreation (restaurants, cafes, shopping malls, museums, libraries, theaters, cinemas, gyms); pharmacies and grocery stores (pharmacies, grocery stores, agricultural markets); parks (city parks, national parks, public beaches, marinas, camps, dog parks); transit stations (public transport hubs such as metro, bus and train stations, seaports, taxi stands, motorway rest areas); workplaces; correlation of human mobility in capitals of seven european countries during the covid-19 pandemic 63 and places of residence (houses and residential buildings). the numbers in the cmr represent a percentage change in human activity for each of the six observed category locations. each day of the week, the data collected are compared with the data collected for that day a month before the pandemic covid-19 (from january 3, 2020 to february 6, 2020). google has collected data for each wednesday and compared it only with the data for wednesdays before the pandemic covid-19. this comparison of the collected data has one significant limitation, because the mobility of people at some of the six observed locations in january is quite different from the mobility of people at other times of the year, especially in the summer months and during the holidays. by showing a relative percentage change in human activity, google ensured that it was not possible to determine the exact number of people who were present at the observed locations. if there were not enough people at a location during the day to ensure the anonymity of each of the visitors, then the cmr lacks data for that location that day. in this work, we have monitored and analyzed the dynamics of human mobility during the covid-19 pandemic in seven european countries: austria, france, italy, united kingdom, serbia, spain, and sweden, and their capitals: vienna, paris, rome, london, belgrade, madrid and stockholm. we have chosen countries whose capitals have more than a million inhabitants and which are located in various parts of europe. we chose sweden because it is the country that had the mildest restrictions on population movements during the pandemic. in this paper, we used the data collected over time from february 15, 2020 until february 11, 2022. the main aim of this paper is to use basic statistical functions to determine whether there is a correlation between the data, which represent the mobility of people across the country and the mobility of people in the capital of that country for seven countries in europe for six discrete categories. for discrete categories for which a high degree of correlation is found, we can say that the mobility of people in other cities of that country behaves in a similar way. another aim of the paper is to use student's t-test to determine whether there are significant differences between two arithmetic means for two data sets. one set of data is data for the whole country, and the other set of data is for the capital. first, the data for the entire observed period were analyzed, and then especially for the first two months of the 2020 pandemic. in all the analyzes we did in this paper, we left out the data for weekends, because we noticed that there are large differences in the behavior of human mobility on weekends compared to the mobility of people for five working days for all six observed locations. based on the obtained results, we want to draw a conclusion whether on the basis of these data it is possible to predict the data in some future period. the third idea of the paper is to check the correlation between the data for the list of selected countries and england. we chose england because it has the largest population among the selected countries and it had less strict measures taken by the state to restrict the movement of people compared to continental europe, but still stricter measures compared to sweden. in this way, we want to show how the many different measures on the restriction of movement in individual observed countries had different effects on human mobility for the six discrete categories. by comparing katanić and damjanović/oper. res. eng. sci. theor. appl. 5(2) 2022 61-84 64 the data between the seven observed countries, we hope that the positive effects of sweden's policy towards its citizens will be noticed. 2. related literature since the beginning of the covid-19 pandemic, a lot of scientific and professional papers have been written, which deal with the influences that this pandemic had on people's behavior. a number of papers deal with topics dealing with political decisions made by governments and parliaments around the world, which imposed various restrictions primarily on gathering people in public places. some papers highlight the positive effects of the measures taken, and some papers show that some political decisions were wrong. possibly current works describing work from home, as well as online teaching in schools and colleges. now that the pandemic has mostly passed, pupils and students have returned to schools, but a large number of people are still working from home and we can consider this to be one of the great legacies of the covid-19 pandemic. in this paper, we aim to compare the mobility of people in capitals and across the country in seven european countries by using a data from google community mobility reports. we are in this literature review presented briefly the works of some authors who statistically processed the data that google publishes daily for 135 countries around the world. we want to show only a part of their research and the conclusions they came to. the study by tamagusko and ferreira (2020) is one of the first presents several statistics and aims to promote studies that can help combat covid-19. most european countries face with a problem falling gross national product. this provoked demands for re-opening of services, public communal areas, and public transport. the paper monitors how citizens has adopted the lockdown measures. in this paper finds relationships between the mobility patterns, the social distancing measures adopted, and the spread of the disease in portugal. during the first lockdown in portugal, some cities imposed restrictions on parks. some measures were completely different in a second wave. studies show the impact of restrictive policies on physical and mental health people. the authors believe that similar research should be conducted in other countries. as the main result of this study, we can single out the conclusion that people are in portugal reacted quickly, adopting social distancing, and changing their mobility pattern, even before the government decreed restrictive measures. it was also observed that people significantly reduced the use of public transport during the pandemic, and that the use of their own transport vehicles increased. the authors found that after the initial lockdown, there was a significant increase in the number of people visiting the parks. lapatinas, athanasios (2020) have researched the causal impact of different covid-19 confinement policies on how mobility trends have changed after the spread of the epidemic has not been studied for the european union member states. an attempt was made in the paper answering the question when and how the confinement measures can be relaxed, to possible new wave increasing the number of sick citizens and introduction of new measures if needed. the authors are empirical findings indicate that reductions in out-of-home social interactions and visits to public and private places are driven by a combination of restrictive measures introduced by member states. in this paper suggests that partial and full lockdowns have the strongest causal impact on increasing presence at home and correlation of human mobility in capitals of seven european countries during the covid-19 pandemic 65 reducing visits to workplaces, public transport hubs, grocery, pharmacies, open public spaces, restaurants, cafes, shopping centers, theme parks, museums, libraries, and movie theatres. the rapid spread expansion of covid-19 pandemic in early 2020 has elicited several distinct policy responses from national governments aimed at decreasing the degree of social interactions to slow down the spread of the virus in the affected populations mendolia, stavrunova and yerokhin (2020). these government policies were aimed at the main goal to reduce human mobility. the results imply that selfimposed mobility restrictions in response to the arrival of the pandemic account for up to 14 percentage points of the total observed reduction in mobility across the countries in this paper. the authors determined that government-mandated measures account for a much larger part (up to 50 percentage points) of the reduction of human mobility. it is discussed in the paper cross-country and crossregion dependence on geographical proximity and the spread of covid-19 disease due to population movements between two regions in two neighboring countries on the example of two regions in italy and switzerland. sulyok and walker (2020) paper was thus to examine the relationship between mobility and confirmed case numbers for covid-19 globally. they tried to prove whether they were whether cross-country events in this relationship were apparent. such patterns could reflect the range of people movement restrictions implemented, but could also be due to other cultural or socio-economic differences of each particular state. they linked the collected data on sick people with cmr data into disease models, to assess whether it could enhance model quality and enable prediction of data for the next period. for calculations, correlations between the analyzed data were used by the authors kendall’s τ due to the nonparametric nature of the data. kendall’s τ correlations were calculated with a time delay of plus or minus 28 day. multiple group comparisons were done in study with the kruskal– wallis test, pairwise comparisons with the dunn test on the continent-level data. the authors have proven that there is a high degree correlations between covid-19 case incidence and changes in people’s mobility shown by google’s cmr. of particular interest are the correlations calculated for large geographical areas north america, western europe, russia and australia. mobility of people in locations "parks" and "housing" increased in line with covid-19 incidence, suggesting increased time spent in a location close to home as case numbers rose. in the united states, such orders have been implemented on a state-by-state basis with considerable variations in compliance paez (2020). concurrently, numerous initiatives have been developed to track the progress and the impact of the pandemic. as a result, there are new sources of data such as the recently-released google community mobility reports, as well as the new york times repository of covid-19 data2. these two open data sets offer novel opportunities to investigate in quasi-real time the relationship between mobility patterns and transmission of covid-19. these results suggest the potential of google community mobility reports to investigate the potential effects of mobility on the incidence of covid-19. in particular, growth appears to be more strongly driven by parks-related mobility. in terms of the use of these mobility indicators, there are some limitations that must be acknowledged. the baseline level is not defined in a metric that is amenable to policy development. without a clearer understanding of the absolute levels of these katanić and damjanović/oper. res. eng. sci. theor. appl. 5(2) 2022 61-84 66 variables, these indicators are useful for inference and perhaps short-term forecasting, but their potential for applied policy analysis appears to be more limited. li et al. (2020) assessed six different mobility metrics rather than a single composite mobility metric. this approach could help refine the components of nonpharmaceutical interventions by restricting certain activities that are shown to increase r substantially or relaxing activities that have a smaller effect on transmission. the research was conducted on data collected at 330 locations across the united kingdom. in the case study of france iacus et al. (2020) have found that mobility can explain from 52% up to 92% of the excess deaths reasonably linked to the covid-19 outbreak. they have found similar results for italy to 91%, but with great differences between the various provinces. for data of people collected in spain, a high degree of correlation was found up to 75% between the number of patients with the human mobility. ramadhan and syakurah (2021) in indonesia used normality test with kolmogorov-smirnov has indicated that the community mobility in retail and recreation, transit station, daily cases were normally distributed (p>0.05), while other locations were abnormally distributed (p<0.05). they are at work correlations analysis were utilized to find the correlations between community mobility and covid-19 daily cases. based on the presented results, the authors determined that it exists very strong positively correlations between community mobility and daily covid-19 cases were found in locations retail and recreation, parks, and transit stations on the same day to the next three days. on the other side of the location housing were negatively strong correlations between community mobility and daily cases on the same day to the next three days. a weak level of correlation was found at the locations the grocery, pharmacy and workplaces. still the highest correlation of each of six locations were found for retail and recreation. we believe that our review of papers will interest many authors to process data on the mobility of people in different countries of the world, in order to draw conclusions that may be useful for the emergence of a new pandemic in the future. 3. data and methodology in this paper, we have processed and presented data of human mobility movements during the covid-19 pandemic in seven european countries: austria, france, italy, united kingdom, serbia, spain, and sweden, and their capitals: vienna, paris, rome, london, belgrade, madrid and stockholm. data were processed for a time period from february 15, 2020 until february 11, 2022 for six available categories of locations. we have chosen countries from different parts of europe. one of the criteria for selecting the observed countries was that the countries have had different policies to control the movement of citizens since the beginning of the covid-19 pandemic. another criterion for selecting countries was that the capitals of the selected countries have more than a million inhabitants. we used data from google’s cmr, which has over seven million rows over the time period of two years, with data on country, regions, cities, and percentage changes in people’s mobility in six different locations. from this data, we first extracted data for each country individually, and then separately extracted data for the entire country and its capital. correlation of human mobility in capitals of seven european countries during the covid-19 pandemic 67 to more easily describe the process of our research, we show the flow diagram of our study in figure 1. aim: check whether there is a correlation in human mobility for six different location categories during the covid-19 pandemic between capitals and the whole country in 7 european countries.  1. description of the research problem: identify the countries to be analyzed. identify statistical methods that are to be applied in data processing.  2. find data on human mobility: find on the internet a csv file which containing data on human mobility for 135 countries worldwide. extract data on human mobility for 7 european countries. for each individual country, separate data on changes in people's mobility for the entire country and its capital. extract data on changes in people's mobility only for working days of the week. make graphs that represent the mobility of people for 4 locations.  3. statistical data processing: calculation of mean values. calculation of standard deviations. calculation of correlations student's ttest  4. analysis of the resulting data: comparison of data obtained from different countries. discussion on the existence of correlation between the observed data. figure 1. general flow diagram of the study for each seven observed country at excel, we have created attendance change charts for four categories of locations: parks, transit stations, workplaces, and housing facilities. due to the clarity of the charts, we omitted data on two categories of human mobility: retail and recreation and pharmacies and grocery stores, but we also statistically processed this data. the x-axis of the chart shows the months from february 2020 to february 2022. the y-axis of the chart shows the percentage of changes in human attendance of the observed locations. looking at the constructed charts for seven country, we have determined that on weekends day, on public holidays and religious holidays, there are big peaks in changes in attendance. in order to reduce the noise on the charts that appeared in all countries on weekends, we excluded data for all saturdays and sundays from the statistical processing and charts in the observed time period of two years. however, we have left data for nonworking days of christmas, new year’s day, may day and individual non-working days for public holidays in individual countries, so that we can correlate data katanić and damjanović/oper. res. eng. sci. theor. appl. 5(2) 2022 61-84 68 between the whole country and the respective capital, as well as correlate data between the countries and students t-test for individual locations. figure 2 shows graphs of changes mobility of people for 2020, 2021 and 2022 year at four locations in france and paris. for france, but also for all other countries, it is immediately noticeable a big drop in the movement of people in march 2020, and the biggest drop is noticed in the location of transport and work. on the other side in the same period, we notice a sudden jump in the number of people, who started spending a lot more time at home, than they did before the covid-19 pandemic. this is precisely the time when the first period of increased numbers of infected people in europe and around the world began. following the “work” curve, we can notice that in july and august 2020 there is a second drop in the number of people visiting the location of their jobs. figure 2. france and paris mobility of people for 2020, 2021 and 2022 year but looking at other curves in the graph 2, we can conclude that this decline in attendance is not caused by an increase in the number of sick people or closure measures taken by the french state, but that this decline can be attributed to the holiday season in france. this is confirmed especially by the "park" curve, because people during the summer, when the holiday season, massively changed their place of residence, spending much more time outside the cities in nature, the coast and places of rest. following the “work” curve, it can be seen that the third period of correlation of human mobility in capitals of seven european countries during the covid-19 pandemic 69 declining job attendance occurred in november and december 2020, then in april and may 2021, and finally again in the summer months of 2021, but this can again be more attributed to annual vacation leaves that employees took. comparing the graphs for paris, as the capital, and for the whole of france, at first glance, we can see very large differences in the number of visits to the parks site, while the number of visits to the other three sites behaves in approximately the same way. based on this, it can be concluded that the citizens of paris spent much less time in parks than the rest of the country, or that a large number of parisians left their stay in paris and worked from home outside the capital. figure 3 shows graphs of changes mobility of people for 2020, 2021 and 2022 year at four locations in serbia and belgrade. following the line “workpl.” it can be seen that the first major wave of the pandemic began in march 2020, the second in november 2020, and the third in march 2021. the decline in workplace site visits in the summer months can be attributed more to vacations during this period. we confirm this by the fact that in the summer months there is a sharp increase in attendance at parks. figure 3. serbia and belgrade mobility of people for 2020, 2021 and 2022 year comparing the graphs for belgrade, as the capital, and for the whole of serbia, we can see very large differences in the number of visits to the parks site. based on this, katanić and damjanović/oper. res. eng. sci. theor. appl. 5(2) 2022 61-84 70 it can be concluded that the citizens of belgrade spent much less time in parks than the rest of the country, or that a large number of citizens left their stay in belgrade and worked from home outside the capital. in the first two months of the pandemic, it can be seen that in the capital, compared to the whole country, there was a slightly higher percentage of declining job attendance, and that on the other hand people were more likely to stay at home. figure 4 shows graphs of changes mobility of people for 2020, 2021 and 2022 year at four locations in austria and vienna. following the line “workpl.” it can be seen that the first major wave of the pandemic began in march 2020, the second in november 2020, and the third in march 2021. the decline in workplace site visits in the summer months can be attributed more to vacations during this period. comparing the curves for the whole country and the capital, one can notice a great coincidence of the shapes of all the curves. only at the "park" location it can be noticed that the citizens of the capital stayed about 50% less at this location compared to the whole country. occurrence of individual narrow peaks at the site "workpl." which represent a large drop in job attendance of 90% is a consequence of non-working days for public or religious holidays in austria. figure 4. austria and vienna mobility of people for 2020, 2021 and 2022 year correlation of human mobility in capitals of seven european countries during the covid-19 pandemic 71 figure 5 shows graphs of changes mobility of people for 2020, 2021 and 2022 year at four locations in italy and rome. following the line “workpl.” it can be seen that the first major wave of the pandemic began in march 2020, the second in november 2020, and the third in march 2021. the decline in workplace site visits in the summer months can be attributed more to vacations during this period. comparing the curves for the whole country and the capital, one can notice a great coincidence of the shapes of all the curves. only at the "park" location it can be noticed that the citizens of the capital stayed about 50% less at this location compared to the whole country. we explain this by saying that during the summer tourist season 2020 and 2021, italy had an increase in the number of tourists visiting coastal cities, and that there was no increase in the number of tourists visiting rome as the capital and as one of the most visited tourist locations in the whole world. occurrence of individual narrow peaks at the site "workpl." which represent a large drop in job attendance of 90% is a consequence of non-working days for public or religious holidays in italy. figure 5. italy and rome mobility of people for 2020, 2021 and 2022 year figure 6 shows graphs of changes mobility of people for 2020, 2021 and 2022 year at four locations in united kingdom and london. when comparing the graphs for all seven observed countries, we can say that for the location "workplace" and "housing" the least oscillations occur in united kingdom. following the line “housing” it can be seen that in united kingdom to this day the highest percentage of katanić and damjanović/oper. res. eng. sci. theor. appl. 5(2) 2022 61-84 72 work from home remains after the first wave of the 2020 pandemic. comparing the curves for the whole country and the capital, one can notice a great coincidence of the shapes of all the curves. compared to the other six countries, we can see that the united kingdom is the country with the lowest percentage difference in the mobility of people between the whole country and the mobility of people in the capital. the united kingdom also has the largest overlap between the curve "workplace" and the curve "transp.". we explain this by saying that with the beginning of the covid-19 pandemic, people in united kingdom did not increase the use of their own vehicles for transport to work, i.e. that they continued to use public transport, which is not the case in the other six observed countries. figure 6. united kingdom and london mobility of people for 2020, 2021 and 2022 year figure 7 shows graphs of changes mobility of people for 2020, 2021 and 2022 year at four locations in spain and madrid. following the line “workpl.” it can be seen that the first major wave of the pandemic began in march 2020, the second in october 2020, and the third in january 2021. the decline in workplace site visits in the summer months can be attributed more to vacations during this period. comparing the curves for the whole country and the capital, one can notice a great coincidence of the shapes of all the curves. only at the "park" location it can be noticed that the citizens of the capital during the summer months, especially 2021, stayed about 100% less at this location compared to the whole country. we explain this by saying that during the summer tourist season 2021, spain had an increase in correlation of human mobility in capitals of seven european countries during the covid-19 pandemic 73 the number of tourists visiting coastal cities, and that there was no increase in the number of tourists visiting madrid as the capital. figure 7. spain and madrid mobility of people for 2020, 2021 and 2022 year figure 8 shows graphs of changes mobility of people for 2020, 2021 and 2022 year at four locations in sweden and stockholm. despite the fact that in sweden there was no classic ban on gathering of people or visiting sporting events, the diagram shows that at the time of the pandemic there was a reduction in time spent at work. the large narrow peaks representing the decline in going to work probably stem from some public holidays in sweden, and similar peaks exist in all other countries and their capitals whose graphs are not shown in this paper. of particular interest to sweden is the curve representing the mobility of people at park locations. from the graphs it can be seen that people in sweden started spending more time in parks immediately with the first signs of a pandemic in march 2020, unlike other countries, where in march 2020 there is a sharp decline in human mobility at the parks , and that only after a few months the number of people at this location begins to increase. we would also like to point out that people in sweden in the summer months had by far the highest percentage of increased visits to the parks site compared to all other observed countries. this confirms the thesis that the policy of the swedish government towards restrictions on the movement of people was completely different from the rest of the countries on the european continent. all katanić and damjanović/oper. res. eng. sci. theor. appl. 5(2) 2022 61-84 74 these conclusions are confirmed by the statistical data presented in the following tables. comparing the graphs for stockholm, as the capital, and for the whole of sweden, at first glance, we can see very large differences in the number of visits to the parks site more than 250% during the summer months. based on this, it can be concluded that the citizens of stockholm spent much less time in parks than the rest of the country, or that a large number of citizens of the capital during the summer months left their stay in the capital and that they went on vacation or even worked outside the capital much more than all the other six countries observed. it can also be noticed that the drop in job attendance and the increase in work from home percentage was the largest difference between the whole country and the capital in sweden in relation to all other six observed countries. figure 8. sweden and stockholm mobility of people for 2020, 2021 and 2022 year 4. discussion we have statistically processed google's cmr data for seven european countries and their capitals. we processed data for all six available locations on human mobility, but first we removed data for all saturdays and sundays for all observed countries and all six locations. data for weekends were omitted because for the observed period of two years we noticed the existence of a large noise in these data, during the statistical processing of these data. this noise that exists on weekends correlation of human mobility in capitals of seven european countries during the covid-19 pandemic 75 disturbs the appearance of graphs, but also and the calculated statistical parameters shown in the following tables. that is the reason why we decided to exclude data for weekends from our analysis in the entire observed period, but we kept the data for national and religious holidays, so that we could correlate the data between countries. table 1, table 2 and table 3 show twelve statistical parameters of human mobility data for serbia, france and sweden. we calculated all these statistical parameters for the other four observed european countries, but due to the large number of data we did not show them in the work in the tables. part of that the statistical data is graphically shown in figures 9 to figure 17. abbreviated labels in the tables and graphs have the following meaning: avg allaverage value of percentage change of human mobility from february 15, 2020 until february 11, 2022; avg 2020average value of percentage change of human mobility for 2020; avg 2021average value of percentage change of human mobility for 2021; avg 2022average value of percentage change of human mobility for 2022; avg 2 monthaverage percentage change of human mobility from march 20, 2020 to may 20,2020 (first wave of the covid-19 pandemic); sd allstandard deviation of the percentage change of human mobility from february 15, 2020 until february 11, 2022; sd 2020standard deviation of the percentage change of human mobility for 2020; sd 2021standard deviation of the percentage change of human mobility for 2021; sd 2022standard deviation of the percentage change of human mobility for 2022; sd 2 monthstandard deviation of percentage change of human mobility from march 20, 2020 to may 20,2020 (first wave of the covid-19 pandemic); cor coun-cap correlation of the percentage change of human mobility between the whole country and the capital in country from february 15, 2020 until february 11, 2022; cor coun-gb correlation of the percentage change of human mobility between the whole country data and united kingdom from february 15, 2020 until february 11, 2022. table 1. changes in attendance for 6 location in serbia. retail pharmacy park transport work place housing av all -6 18 14 -8 -21 2 av 2020 -17 1 7 -23 -28 6 av 2021 1 28 20 2 -17 -2 katanić and damjanović/oper. res. eng. sci. theor. appl. 5(2) 2022 61-84 76 av 2022 4 39 3 3 -14 4 av 2 month -50 -22 -26 -57 -53 17 sd all 22 23 31 23 17 7 sd 2020 23 17 34 22 18 8 sd 2021 18 18 28 17 14 4 sd 2022 15 23 21 13 19 3 sd 2 month 21 21 28 15 14 8 cor coun-cap 0.97 0.97 0.83 0.99 0.99 0.98 cor coun-gb 0.64 0.61 0.50 0.63 0.51 0.59 table 2. changes in attendance for 6 location in france. retail pharmacy park transport work place housing av all -24 4 39 -25 -32 9 av 2020 -31 -7 30 -35 -38 12 av 2021 -19 12 51 -17 -28 7 av 2022 -16 17 6 -18 -20 7 av 2 month -74 -32 -51 -74 -65 29 sd all 24 19 70 21 17 8 sd 2020 28 19 78 24 20 10 sd 2021 19 16 65 14 14 4 sd 2022 3 4 11 4 2 1 sd 2 month 15 19 22 12 12 7 cor coun-cap 0.90 0.79 0.67 0.98 0.93 0.96 cor coun-gb 0.81 0.76 0.81 0.78 0.70 0.77 analyzing the statistical data presented for serbia in table 1, france in table 2, sweden in table 3, but also data for the other four analyzed countries (due to the volume, not all data are presented in the paper) we can conclude that there is a very high degree of correlation between the percentage change in attendance between the whole country and the capital for all processed countries. because for the approximate limits of correlations when the value is from 0.75 to 1 (analogously -1 to -0.75) there is a close functional connection between two variables, and when the value is from 0.50 to 0.75 (analogously -0.75 to -0.50) there is a significant degree of connection between two variables (damjanovic, katanic & krsmanovic, 2020). based on this, it can be concluded that there is a high degree of correlation between data for the whole country and other cities or regions, whose data is collected and published by google in its crm. in all analyzed countries, the lowest degree of correlation occurs at the park location. at parks only in france and spain, the correlation coefficient between the percentage change in attendance between the whole country and the capital is in the range of 0.50 to 0.75, while in all other observed countries for all observed locations the correlation coefficient is in the range of 0.75 to 1. correlation of human mobility in capitals of seven european countries during the covid-19 pandemic 77 table 3. changes in attendance for 6 location in sweden. retail pharmacy park transport work place housing av all -9 1 83 -33 -32 8 av 2020 -9 0 92 -30 -31 8 av 2021 -7 3 85 -35 -32 8 av 2022 -20 -4 2 -44 -34 12 av 2 month -18 -3 55 -36 -32 11 sd all 14 10 99 10 15 4 sd 2020 13 8 96 12 17 4 sd 2021 16 12 103 8 14 4 sd 2022 5 4 14 5 11 3 sd 2 month 9 8 35 7 14 4 cor coun-cap 0.81 0.68 0.81 0.91 0.95 0.92 cor coun-bg 0.55 0.52 0.71 0.66 0.51 0.63 we used the student’s t-test to test whether there were significant differences between the two arithmetic means for the two data sets, one of which was for six locations across the country and the other data sets for the capital. based on the calculated t-value and the limit table for the appropriate number of degrees of freedom, the rules for deciding whether there is a significant difference between two sets of data (i.e. whether the hypothesis is accepted as correct or rejected) are defined (damjanovic, katanic & krsmanovic, 2020). based on the calculated t-value for the student's t-test, we can say that the difference between the data is statistically significant, because the risk is less than 1% (p> 0.01), i.e. the level of safety is greater than 99%. the graphs in figure 9 to figure 17 shows a comparison of attendance changes for 7 countries and capitals between the first two months of the pandemic and the entire 2-year period for the workplace, housing and park location. abbreviated labels in the graphs have the following meaning: rs serbia; at austria; it italy; fr france; gr united kingdom; es spain; sw sweden; avg 2 month average percentage change of human mobility for whole country from march 20, 2020 to may 20,2020 (first wave of the covid-19 pandemic); avg all average percentage change of human mobility for whole country from february 15, 2020 until february 11, 2022; avg 2 m cap average percentage change of human mobility for capital from march 20, 2020 to may 20,2020 (first wave of the covid-19 pandemic); avg all cap average percentage change of human mobility for capital from february 15, 2020 until february 11, 2022; coun cap comparison of the correlation of changes in attendance between the whole country and the capital; coun gb comparison of the correlation of changes in attendance between six country and united kingdom. katanić and damjanović/oper. res. eng. sci. theor. appl. 5(2) 2022 61-84 78 the graph in figure 9 shows a comparison of attendance changes between the whole country and the capital of 7 countries for the first two months of the pandemic and the whole period of 2 years for the location of workplaces. we note that the largest decline in attendance in the first two months of the pandemic was observed in: france, united kingdom and spain. it can also be noticed that in relation to other observed countries in sweden, the decline in the number of visits to workplaces is completely different and that it is approximately the same in the first two months of the pandemic as for the entire observed period of two years. figure 9. comparison of attendance changes between the whole country and the capital of 7 countries for the first two months of the pandemic and the whole period of 2 years for the location of workplaces figure 10. comparison of changes in attendance between the whole country and the capital of 7 countries for the first two months of the pandemic and the whole period of 2 years for the location of housing the graph in figure 10 shows a comparison of attendance between the whole country and the capital of 7 countries for the first two months of the pandemic and the whole period of 2 years for the location of housing. we note the increase in traffic to this site in almost all countries is similar to the corresponding decline in work place site traffic. the graph in figure 11 shows a comparison in attendance between the whole country and the capital of 7 countries for the first two months of the pandemic and correlation of human mobility in capitals of seven european countries during the covid-19 pandemic 79 the whole period of 2 years for the location of park. we notice that the biggest drop in attendance in the first two months of the pandemic was in italy and spain, and these are the countries where the strictest lockdown policy was put in place. attendance at the park's location in sweden is the highest compared to all other observed countries, especially in the first two months of the pandemic. sweden was one of the few countries in europe that did not ban its citizens from park visits in the first two months of the pandemic. figure 11. comparison of changes in attendance between the whole country and the capital of 7 countries for the first two months of the pandemic and the whole period of 2 years for the location of park the graphs 12 shows a comparison of the difference in attendance changes between the whole country and the capital of 7 countries for the first two months of the pandemic and the whole period of 2 years for the location of workplaces. the biggest difference in the mobility of people at the location of workplaces appears in serbia and sweden, and the smallest in france and spain. graphs 14 and graphs 15 show that france is the country with the largest difference in the mobility of people between the capital and the whole country at the three locations shown. based on this, it can be concluded that a large number of parisian citizens left the city and moved to live and work somewhere outside the city or in other cities. figure 12. comparison of the difference in attendance changes between the whole country and the capital of 7 countries for the first two months of the pandemic and the whole period of 2 years for the location of workplaces katanić and damjanović/oper. res. eng. sci. theor. appl. 5(2) 2022 61-84 80 the graphs 13 shows a comparison of the difference in attendance changes between the whole country and the capital of 7 countries for the first two months of the pandemic and the whole period of 2 years for the location of home. the biggest difference in the mobility of people at the location of home appears in france, united kingdom, spain and sweden, and the smallest in serbia. figure 13. comparison of the difference in attendance changes between the whole country and the capital of 7 countries for the first two months of the pandemic and the entire period of 2 years for the housing location the graphs 14 shows a comparison of the difference in attendance changes between the whole country and the capital of 7 countries for the first two months of the pandemic and the whole period of 2 years for the location of park. the biggest difference in the mobility of people at the location of home appears in austria, italy, france and united kingdom, and the smallest in serbia. figure 14. comparison of the difference in attendance changes between the whole country and the capital of 7 countries for the first two months of the pandemic and the entire period of 2 years for the park location the graphs 15 show comparison of the correlation of changes in attendance between the capital and the whole country, and observed country and united kingdom for the location workplace. united kingdom was chosen as the reference country for statistical comparison with other six countries, because it has the biggest correlation of human mobility in capitals of seven european countries during the covid-19 pandemic 81 population of all observed countries. it can be noticed that in all observed countries there is a very high degree of correlation of the data between the capital and the whole country at the location workplace. these graphs can also show the degree of correlation of each observed country in relation to england the smallest in serbia and sweden. figure 15. comparison of the correlation of changes in attendance between the capital and the whole country, and observed country and united kingdom for the location workplace the graphs 16 show comparison of the correlation of changes in attendance between the capital and the whole country, and observed country and united kingdom for the location housing. it can be noticed that in all observed countries there is a very high degree of correlation of the data between the capital and the whole country at the location housing. these graphs can also show the degree of correlation of each observed country in relation to england the smallest in serbia and sweden. figure 16. comparison of the correlation of changes in attendance between the capital and the whole country, and observed country and united kingdom for the location housing katanić and damjanović/oper. res. eng. sci. theor. appl. 5(2) 2022 61-84 82 the graphs 17 show comparison of the correlation of changes in attendance between the capital and the whole country, and observed country and united kingdom for the location park. it can be noticed that in all observed countries there is a very high degree of correlation of the data between the capital and the whole country at the location park, but still a lower degree of correlation compared to the other two locations shown. this can be explained by the fact that in the summer months parks were visited much less in the capitals than in the whole country, i.e. that people spent a lot more time outside the capitals in the summer months. these graphs can also show the degree of correlation of each observed country in relation to england the smallest in serbia. figure 17. comparison of the correlation of changes in attendance between the capital and the whole country, and observed country and united kingdom for the location park 5. conclusion in the past two years, most european countries have taken policies aimed at reducing the mobility of people and increasing their presence in their homes. state governments believed that the reduced number of people outside homes caused lower rates of transmission of covid-19 disease and mortality. these political measures have produced a high social and economic cost. in this paper, we wanted to show how the mobility of people has changed in the last two years in seven european countries and their capitals. the main contribution of the paper is reflected in the fact that we have shown for which locations and which countries there is a high degree of correlation between the mobility of people in the capitals and the whole country. as a result of this, we believe that based on the data on the mobility of people throughout the country, we can predict how the mobility of people behaved in individual cities in that country. especially in this paper, we want to highlight the data presented the mobility of people in sweden in the last two years. we chose sweden because it had a policy with the mildest restrictions on population movement during the pandemic. of all the countries observed, only sweden has never banned citizens from visiting parks. we believe that it was the right decision of their government, because it did not lead to an increase in the number of patients in that country, but on the contrary, it had a positive effect on people's health. i think that all other european countries should accept this policy if there is another correlation of human mobility in capitals of seven european countries during the covid-19 pandemic 83 pandemic in the future. based on a comparison of data on the mobility of people from individual countries with the mobility of people in england, it can be concluded that the mobility of people during the covid-19 pandemic varies greatly from country to country in the 2 years. the set of observed data in this paper has a several limitations. first, data for only seven european countries are presented. second, persons who do not use in any way smartphones or handheld devices or person who do not carry their smart device when visiting one of the six observed locations are not included in google crm. third, google crm only includes persons who on your smart device have google accounts and with the location history option activated. we believe that the results and conclusions presented in this paper can serve as a basis for many future research. the social distancing of people in the last two years in european countries has caused a great decline in many economic, social, cultural, sporting and social events. we believe that data from google crm can be combined with many other data sets from diverse areas of human life and work and that various statistical processing techniques of these data can be done to show various types of correlations with human mobility during the covid-19 pandemic. all future research related to preventing the mobility of people during the covid-19 pandemic, should give us various recommendations on how to behave governments and citizens themselves, if in the future there is a new pandemic around the world. the main goal of this research is to recommend ways to control the spread of disease, reduce the number of patients, reduce the number of deaths and to minimize the economic consequences in the economy. references carlos s., francesco s., spyridon s., stefano m. i., alessandro a., dario t., & michelev. 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(2021). assessing country performances during the covid-19 pandemic: a standard deviation based range of value method. journal operational research in engineering sciences: theory and applications, vol. 4, issue 3, pp. 59-81. doi: https://doi.org/10.31181/oresta081221059t © 2022 by the authors. submitted for possible open access publication under the terms and conditions of the creative commons attribution (cc by) license (http://creativecommons.org/licenses/by/4.0/). https://dx.doi.org/10.1126/science.abb4218 plane thermoelastic waves in infinite half-space caused operational research in engineering sciences: theory and applications vol. 2, issue 1, 2019, pp. 51-71 issn: 2620-1607 eissn: 2620-1747 doi:_https://doi.org/10.31181/oresta1901036r * corresponding author. ran@magtu.ru (a. rakhmangulov), osintsev@magtu.ru (n. osintsev), dmitri_muravev@sjtu.edu.cn (d. muravev) an optimal management model for empty freight railcars in transport nodes aleksandr rakhmangulov 1*, nikita osintsev 1, dmitri muravev 2, alexander legusov2 1 nosov magnitogorsk state technical university, magnitogorsk, russia 2 shanghai jiao tong university, china received: 12 february 2019 accepted: 04 april 2019 first online: 13 april 2019 original scientific paper abstract. the paper presents the actual problem of increasing the efficiency of empty railcars management in rail nodes. the problem lies in need to consider the several constraints. firstly, railcars’ owners are willing to load their rolling stock by specific goods for the given directions (consumers). secondly, it is necessary to consider schedule and formation of trains between railway stations of the node when we developing the routes for movement of the empty railcars. final constraint is based on compliance with the schedule of the railcars loading in the transport node. we propose the minimum of total time costs that railcar has spent in the specific transport node as the objective function. this problem is being sophisticated in terms of increased irregularity of railcar traffic flows, and as a result, it increases the loading factor of the individual railway stations in the transport node. hence, it creates an uneven loading factor of railway stations in the node. in order to optimally manage empty railcars at rail nodes, both the mathematical model and its solving method are presented. one of the distinctive features of the developed model lies in the application of a fuzzy logic method to evaluate online the loading factor of railway stations in the rail node. moreover, this model takes into account these evaluations by optimizing the distribution of empty railcars at the loading points. the present study puts forward the method and algorithm of the developed mathematical model for empty railcars management. they could additionally take into account the possibility to include empty railcars groups in the composition of trains moving on schedule within large railway nodes or in systems of railway transport at large industrial enterprises. the proposed model significantly reduces the complexity of operational planning of dispatchers for distributing the empty railcar traffic volumes. furthermore, the developed model minimizes the total handling time of railcars in rail nodes and ensures the timely supply of empty railcars to the loading points. key words: rail transport, railcar traffic volume, empty railcars, station loading, train schedule, mathematical model, linear programming, fuzzy-logic. rakhmangulov et al./oper. res. eng. sci. theor. appl. 2 (1) (2019) 51-71 52 1 introduction the railways in the countries of the former soviet union heritage the complex railway transport systems of large industrial enterprises, whose width of the rail gauge equals 1520 mm. currently, the transport system is faced with a dramatic increase in railcar handling costs. as a result of the uncoordinated interaction between the mainline and the industrial rail transport, the total annual losses of a single metallurgical enterprise could reach up to 1.5 billion rubles ($45 million us dollars) (osintsev and rakhmangulov, 2013; rakhmangulov et al. 2016). an increase in these losses mainly occurs due to the increased complexity of the operational planning and management of railcar traffic in the railway transport node. the following factors might be the source of this intricacy: • the growth and multiplicity of rail freight traffic in russia and the cis; • a plenty of new private railcar owners; • an increase in uneven railcar traffic; • frequent and significant workload changes in railway stations and spans (rakhmangulov, 2014). according to these conditions, a possible way to solve this issue might be linked to the modernization of the freight traffic flow system in order to reduce the total railcar dead time in the transport nodes. moreover, a lack of promptness with respect to the delivery of railcars is the main concern the railcar owner is faced with, which significantly raises their overpayment. this issue should, therefore, be considered as well. the changes caused by the structural reform of the federal railway transport have a significant impact on the functioning of the transport service systems (rakhmangulov et al. 2014). the main factor of this reform is the transfer of freight railcars to the operating companies’ properties. as a result, by the beginning of 2015, the proportion of private railcars increased up to 100%. at the same time, there is an outstripping growth of the value of the freight traffic flow in relation to the rail transport volume. this correlation indicates the irrational use of railcars. the disadvantages of such a type of changes are as follows: • a rise in empty railcar transit; • a decrease in the reserves of the throughput and the capacity of railway stations and the span because of the enlargement of the effective railcar time usage; • an increase in the new rolling stock necessity (borodin and sotnikov, 2011; rakhmangulov et al. 2014). the rail transport analysis of industrial enterprises depicts an increase in the railcar dead time by 20% on average during the last seven years (kornilov and varzhina, 2015). as is shown in the russian and foreign experience, a reduction in railcar dead time in industrial transport systems (itss) is achieved as a result of the variety of the accounting parameters of railcar volumes based on the methods for managing railcar traffic volumes in intelligent transport systems. these methods include linear and nonlinear optimization, dynamic optimization, simulation modelling (lind, 2000; berezhnaya and berezhnoy, 2006; lesin, 2011). an optimal management model for empty freight railcars in transport nodes 53 based on the operational control methods for railcar exploitation, the problem of the acceleration of the railcar transit time in transport systems has been discussed in north america and in europe (clausen and voll, 2013; clausen and rotmann, 2014). european researchers emphasized the mathematical and heuristic approaches to solving the optimization problems of the railcar traffic flow in rail transport nodes. the discrete mathematical models and algorithms, their implementation and the development strategy of the railcar traffic flow planning within various speeds for a small transport network are proposed in the late 1990s (carey and lockwood, 1995; dorfman and medanic, 2004). different ways were proposed at that time: • the adjustment of the train traffic route on the basis of increasing the accuracy of a reaction to the high dynamics of the train schedule parameters (pellegrini et al., 2014); • the heuristic approaches to the railcar traffic flow management while simultaneously optimizing the solving of the problems of their movement in the railway transport node (fugenschuh et al. 2008); • an analysis of the empty railcar management methods (spieckermann and vosz, 1995). the previous studies (jha et al. 2008) are focused on the practical application of the modern heuristic methods based on the solution to the multi-product transportation problem. later, these techniques were developed (kauppi et al. 2006; d'ariano, 2008) and, consequently, the optimization of the transport issue was described. the result of solving this issue implies the minimization of the costs of the private railcar movement in transport systems. the practical application of the operative management methods for industrial transport reflects in the implementation of the automated systems of the management of the railway transportation process. the researcher (hailes, 2006; kozlov, 2007) described how the methods were formed and how computerized systems were developed for the management of the railcar traffic flow in rail transport nodes and the its. however, the mathematical models currently used in intelligent rail transport systems do not sufficiently take into account the complex and variable structure of railcar traffic volumes. furthermore, these models do not consider the uneven workload of railway stations in the railway transport node. it can be explained that, due to the railcar owners’ decisions, restrictions on their use of railcars often change. as a rule, such changes occur once at the beginning of the day (an estimated period). this feature allows us to consider the problem of the optimal empty railcar distribution in transport nodes as a static linear programming problem and also to modify it to the transport problem with additional constraints (rakhmangulov et al. 2016). according to the well-known models (spieckermann and vosz, 1995; shenfeld et al. 2012), constraints on the supply of certain empty railcars by certain consignors in the railway transport node were previously implemented. however, delays in the supply of empty railcars for the workload associated with the inclusion of these railcars in the size of the trains moving between railway transport node stations according to the fixed or flexible schedule are not taken into account by these rakhmangulov et al./oper. res. eng. sci. theor. appl. 2 (1) (2019) 51-71 54 models. such a flexible schedule can be formed in an operational mode by changing the train routes in the railway transport node and by choosing the stations with a low level of workload (a large amount of the capacity reserve) for the transportation of these types of trains. the solution to the problem of the optimal control of empty railcars in the railway transport node, together with the abovementioned limitations, requires that operational data should be used by means of modern intelligent transport systems in railway transport (kozlov et al. 2011; crainic and laporte, 1997). 2 a mathematical model of the optimal distribution of empty railcars in the railway transport node 2.1. the statement of the operating problem of empty railcar flows the effectiveness of the distribution of empty railroad cars in the railway transport node was deeply discussed in a previous study (rakhmangulov et al. 2014). however, the disadvantage of this paper is the absence of real station workload data. hence, the current research study presents a promising model combining the operating work level of railway stations and the allocation of empty railcars. the objective function of the model minimizes the railcar-hours cost during the period of the storage of empty railroad cars in the railway transport node to the loading places. 1 1 1 min, l m n kij kij k i j c x = = =  → (1) where c is the amount of the transit time from the railway station i to the railway station j of the empty railcars belonging to the group k (depending on their type and/or their belonging to a certain railcar owner); x is the number of the railcars belonging to the group k and included in the freight railcars flow (a block of railcars) between the stations i and j; l is the number of the empty railcar groups in the railway node at the beginning of the base period; m is the number of the railway stations in the railway node; n is the number of the loading points of the empty railcars in the railway node. the following constraints should be satisfied during the planning of the distribution of empty railcars in the railway transport node: the distribution of all empty railcars situated in the railway node at the beginning of the base period: 1 1 , 1, 2, , , m n ki kj k i j a b a k l = = = = =  (2) an optimal management model for empty freight railcars in transport nodes 55 where , ki kj a b are the number of the railcars belonging to the group k and, respectively, located at the departure stations (i) and at the empty railcar loading points (j). taking into consideration all of the empty railcars belonging to a certain group with respect to the railcar traffic flows in the railway transport node: 1 1 , 1, 2, . m n kij k i j x a k l = = = = (3) always a positive value of the railcar traffic flows in the railway transport node: 0, 1, 2, ; 1, 2, ; 1, 2, . kij x k l i m j n = = = (4) taking into consideration the empty railcar block with respect to their addition to the train size departing from the railway station soon: 1 ( ) , ir i i i ir t p t t −  +  (5) where r is the sequence train number in the train departure schedule of the railway station i. in this case, the index i denotes any station of the railway transport node where at the current moment of time the empty railcars included in the train r are located; ir t is the departure time of the train r from the railway station i; i p is the potential of the ith tor (table of an optimal route) of the transport network describing the scheme of the railway transport node tracks, or the total time of railcar transit on their route from the starting route station to the ith station; ir t is the dead time of the railcars at the station i; i  is the station workload factor (the calculation approach is presented in section 2.2). taking into consideration the minimum transit time of the empty railcars inside the railway transport node (according to formula (5), the dead time of the empty railcars before they can be added to the soonest train and the transit delay due to the operating work level of the railroad station should be taken into account) , 1, 2, ; 1, 2, , ij i ij p p p i m j n−  = = (6) where j p is the potential of the jth tor of the transport network, for which the ith peak is the preceding one of the empty railcar route; ij p is the potential of the transport network arc connecting the peaks i and j, or the amount of the transit time of the empty railcars on the railway track which directly connects the stations i and j. an equilibrium between the potential (estimation) of the tor peak of the transport network (j) and the summation of the potential of the preceding tor peak (i) and the potential of the transport network arc connecting these peaks: rakhmangulov et al./oper. res. eng. sci. theor. appl. 2 (1) (2019) 51-71 56 ijij ppp i += (7) the interconnection of the transport network peaks – this condition is used to implement formula (6) for the purpose of the verification of all the transport network peaks for which the station i is the preceding station. transport network peaks might be checked via the algorithm presented in the third section of this study. , 1, 2, ; 1, 2, , j i i m j n= = = (8) where j  is the index of the tor peak (the railway station) which precedes the jth station on the way of the empty railcars in the railway transport node, i.e.:  , , ,ij ii s i j = . a constraint on the number of the railcars in the train r to which the empty railcars belonging to the railcar flow kij х and being at the station i can be added: , kij ir х q (9) where ir q is the maximum train r size. in chapter 3, both the approach to and the example of solving a transport problem, specifically being the issue of the optimization of the distribution of empty railcars in the railway transport node. 2.2 the assessment of the throughput and the handling capacity of the railway station – a fuzzy logic approach basically, the statement of the problem of the evaluation of the effectiveness of the throughput and the handling capacity of a railway station might be described as follows. there are many technological railway stations, each characterized by a reserve of the throughput and the handling capacity  mi aaaaа ,...,,..., 21= . in turn, each station is characterized by a set of the indicators that on their own part exert an influence on the throughput and the handling capacity reserves   nj kkkkk ,...,,...,, 21 = . thus, the station with the largest throughput and the handling capacity reserve should be chosen, i.e. the variant ia from the set а . table 1 indicates the four-factor groups (rakhmangulov et al. 2016) used in order to estimate the work of the railway station k . in the previous study (rakhmangulov and osintsev, 2011), each factor was found to have its own functions, qualitatively determining the influence of the ratio on the amount of the throughput and the handling capacity reserve at the railway station. an optimal management model for empty freight railcars in transport nodes 57 table 1. the factors and indicators of the operational assessment of the railway station workload factor groups id factor groups feature assessment indices of the railway station technical factors group the characterization of the technical equipment of the station – railway tracks development, shunting and cargo facilities the number of the automatic switches the number of the train locomotives type of the shunting locomotives the blocking type in the railway spans the incline of the station railway tracks the presence of the technical inspection points of the railcars at the station the number of the railroad spans at the station the number of the loading areas the presence of the weighing facilities at the station the presence of the weighing facilities in the loading areas technolog ical factors group the characterization of the amount and complexity of the technological operations currently being performed at the station; the characterization of the availability of the railway track elements the presence of shunting work in the railway span the presence of shunting work in the loading areas exceeding the limit of the dead time during the loading operations uneven goods arrival from the external network uneven products loading the reconstruction of the railway station the reconstruction of the workshop the time of the day visibility air temperature the number of the railcars the availability of shunting locomotives subjective factors group the characterization of the complexity of the operational management of the railway station under certain conditions: depending on the level of organization, informatization, automatization, the weather and climatic conditions, the time of the day, etc. the sufficiency of the shunting facilities at the station the sufficiency of the receiving/shipping railway tracks at the station the sufficiency of the receiving/shipping railway tracks capacity at the station a sufficient number of the exits at the station the actual capacity of each railway span the level of the technical development and capacity of the loading areas the professional competence of the operating personnel the presence of unfavorable routes at the station the presence of the corner railway tracks at the station employees factors group the characterization of the professional competence of the railway station management the years of age of the railway station managers the railway station managers’ education the railway station managers’ work experience rakhmangulov et al./oper. res. eng. sci. theor. appl. 2 (1) (2019) 51-71 58 as is shown in figure 1 below, in order to estimate the reserve of the throughput and the handling capacity of the station, the methods of the fuzzy set theory can be applied (andreichikov and andreichikova, 2000; harris, 2006; rakhmangulov and osintsev, 2011). preparing a list of indicators in order to evaluate the railway station кi, i=1…n determining the number of the railway stations aj, j=1…m determining the actual values of the evaluation indicators for the railway station ni(fact) i=1…n are the actual values of all the indicators determined (i=n)? next indicator (i=i+1) determining the membership function values for each indicator зi,j i=1…n, j=1…m are all the values of the membership functions defined (i=n, j=m)? next function (i=i+1; j=j+1) forming fuzzy set methods in order to estimate the reserve of the throughput and the handling capacity of the station μki (a) selecting the methods of the fuzzy sets theory (the method of the maximin convolution; absolute solutions; the main parameter; a compromise solution; the benchmark test comparison б, etc.) no no yes yes selecting the station with the maximum reserve of the throughput and the handling capacity ia from the set а determining the weight indicators i figure 1. the algorithm for the estimation of the reserve of the throughput and the handling capacity of the station. the numerical values of the reserve of the throughput and the handling capacity of stations are evaluated by the load factor of the station ( i ) (rakhmangulov and osintsev, 2011). these values can be used to calculate the cost of the railcar hours during the passing of empty railcar flows on their routes. an optimal management model for empty freight railcars in transport nodes 59 3 the calculation of the plan for the optimal distribution of empty railcars in the railway transport node. the method, the algorithm and an example. in previous studies (rakhmangulov et al. 2014), several methods for the optimal distribution of empty railcars in the railway transport node were discussed. the practical implementation of the proposed model consists of the seven stages. stage 1 is associated with the preparation of the initial data characterizing the technical and technological indicators of the conditions of the transport network, the number of different railcar groups at the stations (figure 2) and the train timetable inside the railway transport node (table 2). the railcar handling time at the stations ii t  is calculated based on the reserves of the throughput and the handling capacity of each station and the railcar handling time at a single station. peaks of the transport network (stations, loading areas) which are conventionally numbered with prime numbers; ki a is the number of the railcars of each group k which are located at each railway station i of the railway transport node, railcars; kj b is the exigency of the empty railcars at each j th station or at the loading point, railcars; i t is the average handling time of transit railcars at the j th station, min.; i  is the coefficient of the station workload; ij t is the train movement time between the neighboring stations of the railway transport node, min.; ir t is the train timetable inside the railway transport node. the moments of the train departures for each r th train at the railway station, min.; ir q is the maximum number of the railcars that can be included in the train size r which is supposed to be sent according to the schedule from the station i at a moment of time irt , railcars. ki a kj b it i  ijt figure 2. an example of a transport network scheme with the initial data in order to calculate the optimal plan for the distribution of empty railcars in the railway transport node rakhmangulov et al./oper. res. eng. sci. theor. appl. 2 (1) (2019) 51-71 60 table 2. the train timetable between the stations inside the railway transport node j 1it 1iq 2it 2iq 3it 3iq 4it 4iq 5it 5iq 1 2 2 3 2 4 1 8 8 4 4 3 3 5 4 9 8 9 5 9 3 6 3 7 9 6 6 7 6 10 9 10 7 10 2 1 3 2 4 2 8 1 4 8 3 4 5 3 9 4 9 8 9 5 6 3 7 3 6 9 7 6 10 6 10 9 10 7 60 30 90 120 30 360 100 80 70 60 40 50 90 80 45 60 90 120 140 300 200 120 300 30 15 10 60 70 90 80 120 100 30 20 26 15 16 16 9 28 27 24 7 14 12 6 14 20 10 8 10 28 10 22 12 28 8 27 21 15 13 25 10 25 14 7 7 25 282 203 223 417 146 528 191 435 393 340 212 131 206 425 373 154 400 227 492 508 346 474 564 265 233 340 211 321 428 225 471 394 180 253 17 16 11 14 29 20 17 26 24 10 7 24 11 25 13 11 16 17 9 21 7 10 15 16 5 21 7 5 28 5 16 27 8 6 465 472 437 658 300 762 493 578 635 566 364 385 531 769 452 262 700 467 623 797 490 818 836 381 535 468 549 525 572 386 580 685 471 389 26 23 17 29 20 19 11 29 28 11 26 5 16 21 21 10 15 18 7 11 13 10 24 25 6 15 12 26 5 10 21 25 15 21 696 758 758 997 615 1073 662 746 834 816 469 586 616 1006 657 493 837 731 790 1030 718 1096 1032 451 711 560 838 870 666 635 712 752 626 577 12 13 24 9 19 23 8 13 28 28 5 15 30 24 22 18 15 16 26 8 14 7 27 9 29 28 20 29 16 18 26 28 27 6 865 1115 1047 1062 865 1213 940 853 1129 1161 740 912 937 1360 929 576 1098 1060 1111 1302 784 1260 1145 692 812 896 1024 1065 736 950 999 961 918 654 6 10 23 8 17 5 23 8 21 17 15 29 17 28 9 16 21 17 5 19 9 30 12 9 6 16 18 16 13 26 30 27 15 24 stage 2 is linked to the construction of an optimal route set for all the stations which have empty railcars ki a . for example, as is shown in figure 2, the stations №1, №2, №3 and №6 are considered to be these types of stations. the formation of an optimal route set is made by the constructing method of the table of an optimal route (tor) in the transport network (rakhmangulov, 1999). the table of an optimal route consists of three columns (figure 3). the first column contains the number of the stations i (the transport network peaks). the second column has the numbers of the preceding peaks i . the third consists of the potentials of the peaks ip . the shortest route to the i th peak is determined by the an optimal management model for empty freight railcars in transport nodes 61 numbers of the preceding peaks. in the tor constructing process, it is possible to repeatedly adjust the peak potentials and the numbers of the previous peaks. thus, it is common to build several tables and transfer the results of the previous constructions to a new table. the tor constructing algorithm consists of the following actions: 1. the first and the second columns of tor are filled in with the peak numbers of the transport network in ascending order. in the second column, the starting peaks are marked as the negative values. the third column is filled in by the starting potentials of the peaks. the initial potentials of the starting peaks are equal to zero. the initial potentials of all other peaks are taken as the number m – the largest possible number. 2. for each arc from the marked peak, the optimal arc condition ijij ppp i − is checked. it means that a potential difference between the starting and the final arc peaks needs to be greater than the assessment value of the arc in-between these peaks. if this condition is satisfied, the usage of this arc is favorable. then, as the preceding peak for the final arc peak (the second column is tor) the peak number i (marked) is specified. the final peak potential is defined as the sum of the starting arc peak potential and the estimation of that arc, i.e. ijij ppp i += . 3. if the optimal arc condition fails, the next arc from the marked peak is checked. 4. if the optimal arc condition is checked for all the arcs from the marked peak, then the label from this peak is removed and the arcs from any next marked peaks are considered. after that, all calculations are repeated, starting with the second. the optimal route constructions are repeated as long as there is at least one marked peak in tor. figure 3 shows the results of the tor construction for the station №1. stage 3 is associated with the determination of the transportation time kij с of the empty railcars delivered from the starting station of each route i to the final stations j , where there is an empty railcar exigency kj b . in this case, the value kij с might be equal to the final peak potential value of the corresponding route, i.e. jkij pс = . for example, since there are empty railcars of the groups №1 and №2 at the station №1, the transportation cost is only determined for those stations where there is the railcar exigency of this group. rakhmangulov et al./oper. res. eng. sci. theor. appl. 2 (1) (2019) 51-71 62 i λi pi λi pi λi pi λi pi λi pi λi pi λi pi 1 -1 0 1 0 1 0 1 0 1 0 1 0 1 0 2 2 m -1 70 1 70 1 70 1 70 1 70 1 70 3 3 m 3 m -2 102 2 102 2 102 2 102 2 102 4 4 m 4 m -2 154 -3 136 3 136 3 136 3 136 5 5 m 5 m 5 m -3 209 -3 209 3 209 3 209 6 6 m 6 m 6 m -3 215 -3 215 3 215 3 215 7 7 m 7 m 7 m -3 325 -3 325 -3 325 3 325 8 8 m -1 100 -1 100 -1 100 -1 100 -1 100 1 100 9 9 m 9 m 9 m 9 m -4 379 -6 347 6 347 10 10 m 10 m 10 m 10 m 10 m -6 453 6 453 starting table the first iteration the second iteration the third iteration the forth iteration the fifth iteration the sixth iteration figure 3. the example of the calculation of the optimal routes for the station i=1 there is demand of the first railcars group at the stations № 7 and №10. с1,1,7 = 325 min.; с1,1,10 = 453 min.; there is demand of the second railcars group at the stations № 7 and №10. с2,1,7 = 325 min.; с2,1,10 = 453 min. similarly, the values kij с are defined for another railway starting station and for another railcar group. as a result, the transportation time matrix for the empty railcars k of each group belonging to the contact schedule (table 3) is formulated. an optimal management model for empty freight railcars in transport nodes 63 table 3. the transportation time matrix of the empty railcars as a part of the trains inside the railway transport node the railcar group the number of the railcars at the station ki a the number of the railcars at the station kij с and the exigency of the empty railcars kj b at the station k =1 b17=170 b1,10=10 а11=30 325 453 а12=50 288 150 а13=100 325 453 k =2 b27=160 b2,10=10 а21=10 325 453 а22=20 288 150 а23=60 325 453 а26=80 90 150 k =3 b31=80 а32=40 40 а33=20 213 а36=20 438 stage 4 is related to the calculation of the optimal values of the empty railcar flow kij x (formula 1) and is based on the solution to the static transport problem of linear programming in the matrix formulation (rakhmangulov, 1999; rakhmangulov et al., 2014) (table 4). the standard excel macros “solution search” was used to solve this example. however, in order to implement the developed algorithm as a part of the intelligent transport system of railway transport, it is recommended that specialized programs for solving transport problems or linear programming libraries, e.g. the linear programming library (gipals32), should be used. table 4. the results of the calculation of the optimal size of the empty railcar flow inside the railway transport node the railcar group the number of the railcars at the station ki a the sizes of the empty railcar traffic flow kij x k =1 b17=170 b1,10=10 а11=30 30 0 а12=50 40 10 а13=100 100 0 k =2 b27=160 b2,10=10 а21=10 10 0 а22=20 10 10 а23=60 60 0 а26=80 80 0 k =3 b31=80 а32=40 40 а33=20 213 а36=20 438 rakhmangulov et al./oper. res. eng. sci. theor. appl. 2 (1) (2019) 51-71 64 stage 5 is relevant to the preparation of the initial data in order to check the limit (formula 9) of the number of the empty railcars in the train size (table 5). table 5. initial data to check the limit of the number of the empty railcars in the train size the railcar group, k the startin g statio n, i the final stati on, j the optimal size of the railcar block, kij x , the railcar the size of the undistribute d empty railcar block, kij x , the railcar the size of the distribute d empty railcar block, kij x , the railcar transportati on time, kij с min. 3 2 1 40 25 15 40 2 6 7 80 67 13 90 1 2 10 10 1 9 150 2 2 10 10 10 0 150 3 3 1 20 4 16 213 1 2 7 40 40 0 288 2 2 7 10 10 0 288 1 1 7 30 22 8 325 1 3 7 100 100 0 325 2 1 7 10 10 0 325 2 3 7 60 60 0 325 3 6 1 20 5 15 438 if the condition irkij qх  fails for the train r on any of the route peaks, then the railcar block size kij x is taken as the minimum value ijirkij siforqx = min , and the difference irkijkij qxx min−= is stored as an undistributed block. if the condition irkij qх  is satisfied, the values ir q for all the route peaks are reduced by the block size kijirir хqq −= . consequently, the block kij x is stored as distributed. if the value ir q becomes zero for the train r , then the train is excluded from further calculations (table 6). an optimal management model for empty freight railcars in transport nodes 65 table 6. the check results of the limit of the number of the empty railcars in the train size no.1 r irq no. 2 r irq no. 3 r irq no.4 r irq no.5 r irq 2 1 15 1 6 1 13 7 2 1 9 4 1 10 9 1 14 10 2 1 0 4 1 1 9 1 5 10 3 1 16 2 2 16 1 2 1 0 4 1 1 9 1 5 10 2 6 7 2 1 0 4 1 1 9 1 5 10 2 6 7 1 1 26 2 1 16 3 1 8 7 3 1 0 7 1 1 18 2 1 8 3 1 0 7 3 1 0 7 6 1 15 9 1 28 8 2 26 1 as a result of the distribution of the railcar block 321 x for the stations no. 2 and no. 1, the following consequences occur: • the size of the block 321 x decreases by 15 cars; • the size of the block 267 x decreases by 13 cars, and so on. tables 7, 8 present the maximum possible number of empty railcars as a part of train size (initial data). also, these tables include the distribution result of the railcar blocks 321 x , 267 x , 10,12 x , 10,22 x , 331x , 127x , 227x , 117x , 137x , 217x , 237x , 361x . table 7. the maximum possible number of the empty railcars in the train size (the initial data) i j 1iq 2iq 3iq 4iq 5iq 1 2 2 3 2 4 1 8 8 4 4 3 3 5 4 9 8 9 5 9 2 1 3 2 4 2 8 1 4 8 3 4 5 3 9 4 9 8 9 5 26 15 16 16 9 28 27 24 7 14 12 6 14 20 10 8 10 28 10 22 17 16 11 14 29 20 17 26 24 10 7 24 11 25 13 11 16 17 9 21 26 23 17 29 20 19 11 29 28 11 26 5 16 21 21 10 15 18 7 11 12 13 24 9 19 23 8 13 28 28 5 15 30 24 22 18 15 16 26 8 6 10 23 8 17 5 23 8 21 17 15 29 17 28 9 16 21 17 5 19 rakhmangulov et al./oper. res. eng. sci. theor. appl. 2 (1) (2019) 51-71 66 3 6 3 7 9 6 6 7 6 10 9 10 7 10 6 3 7 3 6 9 7 6 10 6 10 9 10 7 12 28 8 27 21 15 13 25 10 25 14 7 7 25 7 10 15 16 5 21 7 5 28 5 16 27 8 6 13 10 24 25 6 15 12 26 5 10 21 25 15 21 14 7 27 9 29 28 20 29 16 18 26 28 27 6 9 30 12 9 6 16 18 16 13 26 30 27 15 24 table 8. the number of the empty railcars in the train size (after the distribution of the railcar blocks) i j 1iq 2iq 3iq 4iq 5iq 1 2 2 3 2 4 1 8 8 4 4 3 3 5 4 9 8 9 5 9 3 6 3 7 9 6 6 7 6 10 9 10 7 10 2 1 3 2 4 2 8 1 4 8 3 4 5 3 9 4 9 8 9 5 6 3 7 3 6 9 7 6 10 6 10 9 10 7 18 0 8 0 0 28 27 24 7 14 12 6 14 20 1 8 10 13 10 22 12 28 0 27 21 0 0 25 10 25 5 7 7 25 17 0 11 14 29 20 17 11 24 10 7 24 11 25 13 11 16 17 9 21 7 10 15 16 5 21 7 5 28 5 16 27 8 6 26 23 17 29 20 19 11 29 28 11 26 5 16 21 21 10 15 18 7 11 13 10 24 25 6 15 12 26 5 10 21 25 15 21 12 13 24 9 19 23 8 13 28 28 5 15 30 24 22 18 15 16 26 8 14 7 27 9 29 28 20 29 16 18 26 28 27 6 6 10 23 8 17 5 23 8 21 17 15 29 17 28 9 16 21 17 5 19 9 30 12 9 6 16 18 16 13 26 30 27 15 24 an optimal management model for empty freight railcars in transport nodes 67 stage 6 is related to the correction of leftover empty railcars at the stations (table 9). table 9. the effect of the adjustment of the leftover empty railcars. undistributed railcar blocks distributed railcar blocks k i kijx k j kijx 1 1 1 1 2 2 2 2 2 3 3 3 1 2 2 3 1 2 2 3 6 2 3 6 22 1 40 100 10 10 10 60 67 25 4 5 1 1 1 1 2 2 2 2 2 3 3 3 7 7 7 10 7 7 7 7 10 1 1 1 0 8 0 9 13 0 0 0 0 15 16 15 a11=22; a12=41; a13=100; a21=10; a22=20; a23=60; a26=67; a32=25; a33=4; a36=5; total: 354 railcars b17=162; b1,10=1; b27=147; b2,10=10; b31=34 total: 354 railcars thus, according to the adjustment, the following intermediate results are formed: • a set of the distributed railcar blocks kij x ; • the routes of their transit ij s ; • the train numbers r which have distributed railcar groups in their train size (table 10). table 10. the intermediate results of the optimal distribution of the empty railcars k i j kij x kij с no.1 r no.2 r no.3 r no.4 r no.5 r 1 1 7 8 325 1 1 2 1 3 1 7 1 2 10 9 150 2 1 4 1 9 1 10 2 6 7 13 90 6 1 7 3 2 1 15 40 2 1 1 3 3 1 16 213 3 1 2 2 1 3 6 1 15 438 6 1 9 1 8 2 1 stage 7 is related to the correction of the initial data for the next iteration, and it includes: 1. the adjustment of the number of the empty railcars at the stations (figure 4, the new values are marked in red). rakhmangulov et al./oper. res. eng. sci. theor. appl. 2 (1) (2019) 51-71 68 2. the adjustment of the train schedule according to the contact itinerary. as a result of this adjustment, the trains that can no longer include empty railcars are removed from the train schedule (table 11). figure 4. the results of the adjustment of the initial data for the second iteration (the correction of the transport network) table 11. the result of the train schedule adjustment inside the railway transport node i j 1it 1iq 2it 2iq 3it 3iq 4it 4iq 5it 5iq 1 2 2 3 2 4 1 8 8 4 4 3 3 5 4 9 8 9 5 9 3 6 3 7 9 6 6 7 6 10 9 10 7 10 2 1 3 2 4 2 8 1 4 8 3 4 5 3 9 4 9 8 9 5 6 3 7 3 6 9 7 6 10 6 10 9 10 7 60 90 360 100 80 70 60 40 50 90 80 45 60 90 120 140 300 200 120 30 15 70 90 80 120 100 30 20 26 15 16 16 9 28 27 24 7 14 12 6 14 20 10 8 10 28 10 22 12 28 8 27 21 15 13 25 10 25 14 7 7 25 282 203 223 417 146 528 191 435 393 340 212 131 206 425 373 154 400 227 492 508 346 474 564 265 233 340 211 321 428 225 471 394 180 253 17 0 11 14 29 20 17 11 24 10 7 24 11 25 13 11 16 17 9 21 7 10 15 16 5 21 7 5 28 5 16 27 8 6 465 472 437 658 300 762 493 578 635 566 364 385 531 769 452 262 700 467 623 797 490 818 836 381 535 468 549 525 572 386 580 685 471 389 26 23 17 29 20 19 11 29 28 11 26 5 16 21 21 10 15 18 7 11 13 10 24 25 6 15 12 26 5 10 21 25 15 21 696 758 758 997 615 1073 662 746 834 816 469 586 616 1006 657 493 837 731 790 1030 718 1096 1032 451 711 560 838 870 666 635 712 752 626 577 12 13 24 9 19 23 8 13 28 28 5 15 30 24 22 18 15 16 26 8 14 7 27 9 29 28 20 29 16 18 26 28 27 6 865 1115 1047 1062 865 1213 940 853 1129 1161 740 912 937 1360 929 576 1098 1060 1111 1302 784 1260 1145 692 812 896 1024 1065 736 950 999 961 918 654 6 10 23 8 17 5 23 8 21 17 15 29 17 28 9 16 21 17 5 19 9 30 12 9 6 16 18 16 13 26 30 27 15 24 an optimal management model for empty freight railcars in transport nodes 69 stages 2-7 of the described algorithm must be repeated until the very occurrence of undistributed railcar blocks. if there are such railcar blocks at the end of the estimated period, they are the leftover empty railcars carried forward to the next estimated period. this leftover can be eliminated by increasing the values ir q for the trains. after that, a full recalculation of the plan for the distribution of the empty railcars is required and should start with the first step of the algorithm. 4 conclusion the results of the present model are: • a considerable cluster of the values kij x that determines the optimal number of the railcars of each group in the blocks. these railcars are supposed to be delivered to the specific loading points (stations) during the estimated period (within one day); • the optimal transit routes of the railcar blocks ij s ; • the scheduled number of the trains r for each station. the train size should include empty railcar blocks. as a result, the proposed model, associated with the rational use of empty railcars, might lead to an around 15-20% decline in the dead time of empty railcars in the railway transport node. the developed model, the method and the algorithm of its implementation can easily be integrated into the existing intelligent control systems of railway transport hubs. current railway transport systems are ready and contain all the data necessary for the implementation of the present model. at the same time, the disadvantage of this algorithm is the relatively low accuracy of compliance with the train schedule in the railway transport node and in the railway transport systems of industrial enterprises. in most cases, this type of schedule is not in place due to the fact that internal railway traffic is moderated by dispatchers and depends on the availability of specific railcars at the railway station, as well as on the current loading situation at this and closely located stations. owing to the solid internal scheduled train flows in the railway transport node, there are still some stable freight traffic flows. however, it is worth noting that even for these trains frequent schedule breaches were observed due to uneven railway stations and the railway track workload. future studies are expected to bring about a solution to this problem. the prediction of the time of the train departure from the railway transport node stations by using bigdata tools might be a possible way to carry it out. a promising approach to the improvement of the accuracy of train traffic forecasts inside the railway transport node implies using the simulation method in the operational mode. based on the data of the availability and transit status of railcars, the modern simulation models of railway stations can enable an operational assessment of the possible scenarios of the operating workload of railway stations. rakhmangulov et al./oper. res. eng. sci. theor. appl. 2 (1) (2019) 51-71 70 to sum it up, the current research study, specifically the promising tools and methods, might be helpful in improving the accuracy of the result of optimization during the distribution of empty railcars in the railway transport node. acknowledgements this work is supported by the pjsc magnitogorsk iron and steel works (contract «mathematical support of the intelligent control module of the railcar traffic flow as part of the automated dispatching system of railway transport control» pjsc magnitogorsk iron and steel works, no. 01201274221). references andreichikov, a.v. & andreichikova, o.n. 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(1995). a case study in empty railcar distribution. european journal of operational research, 3, 586-598. http://www.optimalon.com/product_gipals32.htm operational research in engineering sciences: theory and applications vol. 4, issue 2, 2021, pp. 55-78 issn: 2620-1607 eissn: 2620-1747 doi: https://doi.org/10.31181/oresta20402055a * corresponding author. taliparsu@aksaray.edu.tr (t. arsu), ejder.aycin@kocaeli.edu.tr (e. ayçin) evaluation of oecd countries with multicriteria decision-making methods in terms of economic, social and environmental aspects talip arsu 1*, ejder ayçin 2 1 aksaray university, vocational school of social sciences, department of tourism and hotel management, turkey 2 kocaeli university, faculty of economics and administrative sciences, department of business administration, turkey received: 23 march 2021 accepted: 11 may 2021 first online: 25 june 2021 research paper abstract: exhausted natural resources and deteriorating ecological balance, together with the social privileges that people expect to have, are proof that the development of countries cannot be reduced to economic development alone. in this respect, this study aimed to evaluate the economic, social and environmental aspects of organization for economic co-operation and development (oecd) countries. within this scope, the countries were firstly divided into two groups by performing cluster analysis in order to create more homogeneous country groups. then, 12 criteria, consisting of four economic, four social and four environmental criteria, were determined by considering the literature and expert opinions. the criteria importance through intercriteria correlation (critic) method was used to weight the determined criteria and using the calculated criterion weights, the countries in each cluster were then evaluated with the measurement of alternatives and ranking according to compromise solution (marcos) method. as a result, the most successful countries in the first cluster were determined as switzerland, denmark and ireland with 68.8%, 62.7% and 62.5% performance scores, respectively. whereas, the most unsuccessful countries were usa, canada and australia with 49.8%, 50.0% and 50.1% performance scores, respectively. the most successful countries in the second cluster were found as slovenia, spain and portugal with 65.9%, 65.5% and 64.5% performance scores, while the most unsuccessful countries were turkey, chile and colombia with 45.9%, 55.4% and 55.9% performance scores, respectively. finally, in order to test the sensitivity of the marcos method, the solution was repeated with the mairca, waspas, mabac and cocoso methods using the weights obtained by the critic method. a high correlation (greater than 80%) was found between the rankings acquired using the other methods and the rankings obtained by the marcos method. key words: oecd countries, economicsocialenvironmental development, critic, marcos arsu & ayçin /oper. res. eng. sci. theor. appl. 4 (2) (2021) 55-78 56 1. introduction the continuous increase of the world population and the inequality in resource sharing drive countries into a constant growth war. this is because countries that strive to get the highest share of limited natural resources, especially oil, are aware that the primary way to achieve this is economic growth. however, the socioenvironmental effects created by the economic growth of countries have brought forth increasing concerns in society. as developing countries begin to consume resources at the same level as developed countries, the planet is constantly being dragged into a disastrous situation. economic growth is often accompanied by adverse environmental and social impacts such as excessive use of natural resources, income inequality, exploitation of manual labor and toxic gas emissions. therefore, in order to evaluate the socio-economic performance of nations, economists have gradually started to address issues related to social welfare and environment as well as economic growth (santana et al., 2014). however, it is still widely accepted to rank countries or regions by evaluating their performance and growth levels in terms of their gross domestic product (gdp). gdp is useful for measuring and comparing market activity, as its intended purpose is to measure crude economic activity. however, in the last few decades gdp has been given a role that goes beyond its intended purpose. it has started to be used as a proxy indicator of economic competence as well as human progress and general social and economic well-being. today, gdp is characterized as the most widely used indicator of a country's overall performance, even though it was never designed for such a purpose (charles & d'alessio, 2020). this is because societies with strong economic backgrounds are considered to be highly developed. however, obtaining and comparing the development level of societies only according to economic indicators can yield unrealistic and unreliable results. in fact, economic indicators cannot fully reflect the performance of countries in areas such as environment, public health, public education, etc. (omrani et al., 2020). in any case, evaluating a country's performance should not be limited to only economic data or only non-economic data. countries should be considered from both aspects simultaneously and in a coherent framework. more specifically, a country’s gdp level of is seen as its ability to provide its citizens with the appropriate opportunities to take advantage of their economic, social and environmental conditions. increase in per capita gdp can only be considered as a basic precondition for improving the living standards of a population (cracolici et al., 2010). therefore, in recent years, many indexes including the social progress index (spi), human development index (hdi), environmental performance index (epi), life satisfaction index (lsi), have been created in order to evaluate countries especially in terms of environmental and social aspects. however, although such indexes have been put forward by many different organizations, none of the indexes alone are sufficient for the social and environmental evaluation of countries. although economic growth, social development and environmental quality seem to be completely independent from each other, there are meaningful relationships between them. for instance, environmental constraints can lead to a decrease in regional growth, which is necessary for demographic development, and subsequently increased levels of unemployment (fakher & abedi, 2017), while population explosion and the struggle to improve economic growth can lead to more pollution and waste from industrial, agricultural and construction activities (iram et al., 2020). in addition, healthy economic growth can be used as a social welfare tool for the citizens of that evaluation of oecd countries with multi-criteria decision-making methods in terms of economic, social and environmental aspects 57 country. as can be understood from the examples, there are tight ties between the economic, social and environmental development of countries. therefore, this study aimed to evaluate the organization for economic co-operation and development (oecd) countries in terms of economic, social and environmental aspects. it does not seem possible for a country to develop only economically or socially or environmentally. economic development in a country means that a person living in that country earns more income. people who earn more income will want to have various social rights and privileges after their basic physiological needs are met. in addition, only people who can meet their basic physiological needs will be able to concern themselves with environmental issues. therefore, all economic, social and environmental data should be taken into account when evaluating a country properly. from this point of view, as this study used economic, social and environmental data it yielded important results. in recent years, there have been studies conducted with a tendency to evaluate the sustainability performance of countries. using multiple-criteria decision-making methods, tajbakhsh & shamsi (2019) evaluated the sustainability performance of 133 countries while antanasijevic et al. (2017) evaluated that of european countries, ecer et al. (2019) evaluated that of 41 opec countries and costa et al. (2019) evaluated that of 34 oecd countries. in this direction, the aim of contributing to the studies in the literature and evaluating the sustainability performances of oecd countries with regard to economic, environmental and social criteria constituted the main motivation of the present study. differently from other studies in the literature, a cluster analysis was first performed in order to evaluate countries in more homogeneous groups. following the cluster analysis, the sustainability performances of the countries were evaluated with a hybrid model using the critic-marcos methods. the particular goals of the present study specified to fill the gaps in the literature are listed below. • carrying out a performance evaluation for oecd countries with regard to the three main criteria of the concept of sustainability, • performing a cluster analysis in order to obtain homogeneous groups of countries prior to the performance evaluation, • comparatively presenting the outcomes of potential multiple-criteria decision-making methods that can be used for sustainable performance evaluation, • proposing an applicable methodology for the determination of the oecd country with the highest sustainability performance. the criteria importance through intercriteria correlation (critic) method was used to determine the importance weights of the criteria used to evaluate the countries in the study. since the critic method reaches outcomes by performing processes that are based on real data, it eliminates the impact of decision-makers on the decision. due to the inclusion of real data related to three main criteria and subcriteria for the oecd countries in the present study and the importance of the correlations between these criteria, the critic method was used for weighting criteria. then, the criterion weights calculated with the critic method were used in the measurement of alternatives and ranking according to compromise solution (marcos) method and the countries were ranked according to their performances. in arsu & ayçin /oper. res. eng. sci. theor. appl. 4 (2) (2021) 55-78 58 the marcos method, the utility functions of decision alternatives are obtained and the performances of alternatives are revealed with compromise rankings based on reference values (ideal and anti-ideal solution values). it is a flexible method and the fact that it allows for the evaluation of a large number of criteria with compromise solution, that it can be used in the solution of complex problems despite being a simple solution algorithm and that it is a strong and reliable decision-making tool for the optimization of multiple purposes can be listed as its advantages in comparison with other similar methods. finally, in order to test the sensitivity of the solution obtained by the critic-marcos methods, solution values were obtained by using different mcdm methods and the obtained results were compared. 2. literature review studies in the literature have examined countries economically, socially and environmentally many times using different methods. although methods such as structural equation modelling (cracolici et al., 2010), fuzzy logic (phillis et al., 2011) and multiple regression (kaklauskas et al., 2020) have been used for the economic, social and environmental evaluation of countries, multi criteria decision making (mcdm) methods are often preferred for this assessment. table 1. mcdm studies in which economic, social and environmental criteria was used writer criteria methods* countries/areas eco. soc. env. charles & d’alessio (2020) √ √ √ dea 28 areas of peru giannakitsidou et al. (2020) √ √ dea 26 european countries iram et al. (2020) √ √ dea 26 oecd countries iqbal et al. (2019) √ √ dea 20 industrial countries ecer et al. (2019) √ √ √ cocoso 41 opec countries costa et al. (2019) √ √ electre tri-c 34 oecd countries tajbakhsh & shamsi (2019) √ √ √ dea 133 countries kılıç depren & bağdatlı kalkan (2018) √ √ √ entropy ve multimoora 37 oecd countries moutinho et al. (2018) √ √ dea 16 latin american countries antanasijevic et al. (2017) √ √ √ promethee 30 european countries skare & rabar (2017) √ √ √ dea 30 oecd countries şahin & öztel (2017) √ √ copras brics countries and turkey santana et al. (2014) √ √ √ dea brics countries shmelev & rodríguezlabajos (2009) √ √ √ naiade austria malul et al. (2008) √ √ √ dea 38 developed, 53 developing countries *mcdm methods name, multimoora: full multiplicative form of multi-objective optimization by ratio analysis, electre: elimination et choix traduisant la realité, dea: data envelopment analysis naiade: novel approach to imprecise assessment and decision environments, copras: complex proportional assessment, promethee: preference ranking organization method for enrichment evaluations), cocoso: combined compromise solution among these studies, there are studies that have examined countries using economic, social and environmental criteria as well as studies that have examined only evaluation of oecd countries with multi-criteria decision-making methods in terms of economic, social and environmental aspects 59 economic and social or only economic and environmental criteria. table 1 shows the criteria and methods used in the literature to examine countries. most decisions made in the real world have many criteria that often conflict. therefore, mcdm methods have become an extremely necessary tool for decision makers (benítez & liern, 2020). in recent years, mcdm methods have been used in many decision problems. panchal et al. (2017) used fuzzy ahp, fuzzy codas methods to evaluate maintenance decisions in the urea fertilizer industry; panchal et al. (2019) used fuzzy fmea, fuzzy topsis, fuzzy edas, fuzzy vikor methods to analyze the performance problems of the chemical process plant; chatterjee et al. (2020) used edas in biomaterial selection; gopal & panchal (2020) used fuzzy copras, fuzzy topsis methods for risk analysis and reliability assessment of the milk processing industry; das et al. (2021) used pfmea, topsis, vikor methods for risk analysis in the milk industry. in this study, mcdm methods were preferred as there were many criteria, most of which were conflicting. first of all, the critic method recommended by diakoulaki et al. (1995) and used in many decision problems such as air conditioning selection (vujicic et al., 2017), risk assessment (ayrım & can, 2017), third party logistics service provider selection (keshavarz ghorabaee et al., 2017), construction equipment evaluation (keshavarz ghorabaee et al., 2018), financial performance evaluation (şenol & ulutaş, 2018), bank performance evaluation (akbulut, 2019), cargo company assessment (ulutaş & karaköy, 2019), corporate sustainability performance analysis (yalçın & karakaş, 2019), venture capital investment trusts assessment (apan & öztel, 2020), personnel selection process (ayçin, 2020), r&d performance assessment of countries (orhan & aytekin, 2020) and 5g industry assessment (peng et al., 2020) was preferred to weigh the selected criteria. then, using these weights, the countries were evaluated with the marcos method developed by stević et al. (2020) and used in decision problems such as project management software evaluation (puška et al., 2020), human resources assessment in the transportation sector (stević & brković, 2020), supplier selection (stević et al., 2020; badi & pamucar, 2020; chattopadhyay et al., 2020; madenoğlu, 2020), risk assessment of railway infrastructure (simić et al., 2020), distribution channel selection (dalić et al., 2020), stacker selection for logistics systems (ulutaş et al., 2020), traffic risk analysis (stanković et al., 2020), sanitary landfill selection for medical waste (torkayesh et al., 2021), healthcare performance assessment of insurance companies (ecer & pamucar, 2021) and e-service quality assessment in the airline industry (bakır & atalık, 2021). as seen in the detailed literature review, the critic and marcos methods were not used in studies conducted to evaluate countries. in this respect, the present study is the first of its kind in the literature. 3. method 3.1. critic diakoulaki et al. (1995) proposed the critic method to overcome the problems of subjective weighting methods such as reliability and consistency (diakoulaki et al., 1995). the procedure of the critic method consists in the following steps: step 1: forming the decision matrix arsu & ayçin /oper. res. eng. sci. theor. appl. 4 (2) (2021) 55-78 60 in the first step, the decision matrix includes a set of n criteria and m alternatives are constructed by using equation (1). 𝑋 = 𝐴1 𝐴2 ⋮ 𝐴𝑚 [𝑥11 𝑥12 … 𝑥1𝑛 𝑥21 𝑥22 … 𝑥2𝑛 ⋮ ⋮ … ⋮ 𝑥𝑚1 𝑥𝑚2 … 𝑥𝑚𝑛 ] (1) step 2: normalization the values of the criteria with different units in decision problems should be standardized to take a value in the range of [0,1] by the normalization process. the normalized decision-making matrix is calculated using equations (2) and (3): 𝑟𝑖𝑗 = 𝑥𝑖𝑗−𝑥𝑗 𝑚𝑖𝑛 𝑥𝑗 𝑚𝑎𝑥−𝑥𝑗 𝑚𝑖𝑛 𝑗 = 1,2, … , 𝑛 𝑖𝑓 𝑗 ∈ 𝐵 (2) 𝑟𝑖𝑗 = 𝑥𝑗 𝑚𝑎𝑥 − 𝑥𝑖𝑗 𝑥𝑗 𝑚𝑎𝑥 − 𝑥𝑗 𝑚𝑖𝑛 𝑗 = 1,2, … , 𝑛 𝑖𝑓 𝑗 ∈ 𝐶 (3) where b is a group of benefit criteria and c is a group of cost criteria. step 3: constructing the correlation coefficient matrix the correlation coefficient matrix consisting of linear relationship coefficients is created to measure the degree of the relationships between the criteria. the correlation coefficient is calculated by using equation (4). 𝜌𝑗𝑘 = ∑(𝑟𝑖𝑗 − 𝑟�̅� ). (𝑟𝑖𝑘 − 𝑟�̅� ) 𝑚 𝑖=1 √∑(𝑟𝑖𝑗 − 𝑟�̅� ) 2 𝑚 𝑖=1 . ∑(𝑟𝑖𝑘 − 𝑟�̅� ) 2 𝑚 𝑖=1 ⁄ 𝑗, 𝑘 = 1,2, … , 𝑛 (4) step 4: calculating the 𝐶𝑗 values information contained in mcdm problems is related to both the contrast intensity and conflict of the decision criteria. hence, the amount of information c j, emitted by the jth criterion can be determined by composing the measures that quantify the two notions using equations (5) and (6). 𝐶𝑗 = 𝜎𝑗 ∑(1 − 𝜌𝑗𝑘 ) 𝑛 𝑘=1 𝑗 = 1,2, … , 𝑛 (5) 𝜎𝑗 = √∑(𝑟𝑖𝑗 − 𝑟�̅� ) 2 𝑚 𝑖=1 /(𝑚 − 1) (6) step 5: calculating the final criteria weights in the last step of the critic method, the objective weights are calculated by using equation (7). evaluation of oecd countries with multi-criteria decision-making methods in terms of economic, social and environmental aspects 61 𝑤𝑗 = 𝑐𝑗 ∑ 𝑐𝑘 𝑛 𝑘=1 ⁄ (7) 3.2. marcos stevic et.al presented the main ideas of the marcos method, which is based on defining the relationship between alternatives and reference values (ideal and antiideal alternatives). on the basis of the defined relationships, the utility functions of the alternatives are determined and compromise ranking is made in relation to ideal and anti-ideal solutions. decision preferences are defined on the basis of utility functions. utility functions represent the position of an alternative with regards to an ideal and anti-ideal solution. the best alternative is the one that is closest to the ideal and furthest from the anti-ideal reference point (stevic et al., 2020). the procedure of the marcos method consists of the following steps (stevic et al., 2020, ecer, 2020; đalić et al. 2021): step 1: forming the initial decision matrix. the initial decision matrix includes a set of n criteria and m alternatives. in the case of group decision-making, expert evaluation matrices are aggregated into an initial group decision-making matrix. step 2: forming the extended initial decision matrix. the extended initial decision matrix is created by defining ideal (ai) and anti-ideal (aai) solutions as shown in equation (8). 𝐶1 𝐶2 … 𝐶𝑛 𝑋 = 𝐴1 𝐴2 ⋮ 𝐴𝑚 𝐴𝐴𝐴𝐼 𝐴𝐴𝐼 [𝑥11 𝑥12 … 𝑥1𝑛 𝑥21 𝑥22 … 𝑥2𝑛 ⋮ ⋮ ⋮ ⋮ 𝑥𝑚1 𝑥𝑚2 … 𝑥𝑚𝑛 𝑥𝑎𝑎1 𝑥𝑎𝑎2 ⋯ 𝑥𝑎𝑎𝑛 𝑥𝑎𝑖1 𝑥𝑎𝑖2 ⋯ 𝑥𝑎𝑖𝑛 ] (8) ai and aai are calculated by using equations (9) and (10) depending on the nature of the criteria. 𝐴𝐼 = 𝑥𝑖𝑗 𝑖𝑓 𝑗 ∈ 𝐵 𝑎𝑛𝑑 𝑥𝑖𝑗 𝑖𝑓 𝑗 ∈ 𝐶 (9) 𝐴𝐴𝐼 = 𝑥𝑖𝑗 𝑖𝑓 𝑗 ∈ 𝐵 𝑎𝑛𝑑 𝑥𝑖𝑗 𝑖𝑓 𝑗 ∈ 𝐶 (10) where b is the benefit-based criteria and c is the cost-based criteria. step 3: normalizing the extended initial decision matrix. the normalized matrix n is calculated by using equations (11) and (12). 𝑛𝑖𝑗 = 𝑥𝑖𝑗 𝑥𝑎𝑖 𝑖𝑓 𝑗 ∈ 𝐵 (11) 𝑛𝑖𝑗 = 𝑥𝑎𝑖 𝑥𝑖𝑗 𝑖𝑓 𝑗 ∈ 𝐶 (12) arsu & ayçin /oper. res. eng. sci. theor. appl. 4 (2) (2021) 55-78 62 where 𝑥𝑖𝑗 and 𝑥𝑎𝑖 are the elements of the extended initial decision matrix (x). step 4: determining the weighted decision matrix (v). the weighted matrix, v, is obtained by multiplying the normalized matrix elements with the weight coefficients of the criterion 𝑤𝑗 as shown in equation (13). 𝑣𝑖𝑗 = 𝑛𝑖𝑗 × 𝑤𝑗 (13) step 5: forming the utility degrees of the alternatives (𝐾𝑖 ). the utility degrees of alternatives are calculated by using equations (14) and (15). 𝐾𝑖 + = 𝑆𝑖 𝑆𝑎𝑖 (14) 𝐾𝑖 − = 𝑆𝑖 𝑆𝑎𝑎𝑖 (15) 𝑆𝑖 represents the sum of the elements of the weighted decision matrix (v) as shown in equation (16). 𝑆𝑖 = ∑ 𝑣𝑖𝑗 𝑛 𝑖=1 (16) step 6: forming the utility function of the alternatives f(𝐾𝑖 ). the utility function is the compromise of the observed alternative in relation to the ideal and anti-ideal solution. this function is calculated by using equation (17). 𝑓(𝐾𝑖 ) = 𝐾𝑖 + + 𝐾𝑖 − 1 + 1 − 𝑓(𝐾𝑖 +) 𝑓(𝐾𝑖 +) + 1 − 𝑓(𝐾𝑖 −) 𝑓(𝐾𝑖 −) (17) utility functions in relation to the ideal and anti-ideal solution are calculated by using equations (18) and (19). 𝑓(𝐾𝑖 +) = 𝐾𝑖 − 𝐾𝑖 + + 𝐾𝑖 − (18) 𝑓(𝐾𝑖 −) = 𝐾𝑖 + 𝐾𝑖 + + 𝐾𝑖 − (19) step 7: ranking the alternatives. the final values of the utility function allow for a comparison between the alternatives. the best alternative has the highest rank in terms of the value of the utility function. evaluation of oecd countries with multi-criteria decision-making methods in terms of economic, social and environmental aspects 63 4. data when determining the criteria used in this study, the criteria used in previous studies that evaluated countries in terms of economic, social and environmental aspects were taken into consideration. among these, the most used 12 criteria based on a comprehensive literature review, namely four economic, four social and four environmental criteria, were selected to evaluate the oecd countries. information regarding the direction and unit of the selected criteria, in which study they are used and where they were obtained from are presented in table 2. table 2. criteria used in the study criteria (abbreviation) aspect unit source data e co n o m ic a l gdp per capita (gdp) max $ antanasijevic et al., 2017; ecer et al., 2019; malul et al., 2008; moutinho et al., 2018 ; santana et al., 2014; shmelev & labajos, 2009; chattopadhyay & bose, 2015; fare et al., 1994; skare & rabar, 2017; karakış & göktolga, 2016; özbek & demirkol, 2019 worldbank, 2019 unemployment rate (ur) min % antanasijevic et al., 2017; cracolici et al., 2010; phillis et al., 2011; shmelev & labajos, 2009; chattopadhyay & bose, 2015; ela & kurt, 2019; eyüboğlu, 2016; skare & rabar, 2017; podvezko, 2011; karakış & göktolga, 2016; özbek & demirkol, 2019 international labor organization (ilo), 2019 inflation rate (ir) min % ecer et al., 2019; chattopadhyay & bose, 2015; ela & kurt, 2019; eyüboğlu, 2016 ; skare & rabar, 2017; karakış & göktolga, 2016; özbek & demirkol, 2019 worldbank, 2019 growth rate (gr) max % ela & kurt, 2019; eyüboğlu, 2016; podvezko, 2011; karakış & göktolga, 2016; özbek & demirkol, 2019 worldbank, 2019 s o ci a l social progress index (spi) max 0-100 kaklauskas et al., 2020; benitez & liern, 2020; giannakitsidou et al., 2020; charles & d’alessio, 2020 social progress imperative, 2020 gini coefficient (gini) min 0-1 ecer et al., 2019; malul et al., 2008; shmelev & labajos, 2009; costa et al., 2019; eren et al., 2017; cravioto et al., 2011 worldbank, oecd, 20152018 human development index (hdi) max 0-1 malul et al., 2008; krylovas et al., 2019; şahin & öztel, 2017; eren & kaynak, 2017; eren et al., 2017; bilbao-terol et al., 2014; cravioto et al., 2011 united nations development programme (undp), 2020 life satisfaction index (lsi) max 0-10 shmelev & labajos, 2009; kılıç depren & bağdatlı kalkan, 2018; cravioto et al., 2011 oecd better life index , 2019 e n v ir o n m e n ta l share of renewable energy in gross final energy consumption (sre) max % antanasijevic et al., 2017; moutinho et al., 2018; phillis et al., 2011 worldbank, 2015 arsu & ayçin /oper. res. eng. sci. theor. appl. 4 (2) (2021) 55-78 64 co2 emissions per capita (co2) min tones cracolici et al., 2010; ecer et al., 2019; moutinho et al., 2018; phillis et al., 2011; santana et al., 2014; shmelev & labajos, 2009 our world in data, 2019 environmental performance index (epi) max 0-100 malul et al., 2008; olafsson et al., 2014; bilbao-terol et al., 2014; fakher & abedi, 2017 epi, 2020 ecological footprint per capita (ea) min hectar olafsson et al., 2014; bilbao-terol et al., 2014; blancard & hoarau, 2013 global footprint network 2019 the criteria used in the study consist of various economic, social and environmental indicators and indices. definitions regarding these indicators and indices are given below. gross domestic product per capita (gdp): gdp per capita, which is used as a criterion in many economic performance studies, is obtained by dividing the gdp by the mid-year population. the data published annually by the world bank are given in current us dollars. unemployment rate (ur): the indicator obtained by proportioning the nonworking people in the working population over the age of 15 to the total workforce is used in many studies to measure economic performance. the labor force rate is calculated annually by the international labor organization (ilo) using national estimates. inflation rate (ir): inflation, which is measured by the consumer price index, reflects the annual percentage change in the average cost of purchasing a basket of goods and services that can be fixed or changed at certain intervals such as every year. the inflation rate, which is frequently used in economic performance reviews and calculated annually by the international monetary fund (imf), is published by the world bank. growth rate (gr): this is the annual gdp growth rate at constant local currencybased market prices. the indicator, calculated on the basis of constant 2010 usd, is shared annually by the world bank. social progress index (spi): it is an index calculated using basic indicators (access to food, personal security, etc.), welfare indicators (access to information, health rights, etc.) and opportunity indicators (personal freedoms, human rights, etc.). it is calculated by “the social progress imperative” using 12 different indicators in three main headings. gini coefficient (gini): it measures the extent to which the distribution of income (or, in some cases, consumption expenditures) deviates from an exactly even distribution among individuals or households in an economy. a gini coefficient of 0 represents perfect equality while a coefficient of 1 indicates perfect inequality. the most up-to-date data on the gini coefficient, which is not calculated for each year, varies between 2015 and 2018 according to country. human development index (hdi): this index is published annually by the united nations development program and includes indicators related to income, life expectancy and educational opportunities. the hdi consists of three dimensions: the long and healthy life dimension, which is measured by life expectancy at birth; the evaluation of oecd countries with multi-criteria decision-making methods in terms of economic, social and environmental aspects 65 knowledge dimension, which is measured by schooling times for adults aged 25 and over, and the expected education period for children at school starting age, and the decent standard of living dimension, which is measured by gross national income per capita. life satisfaction index (lsi): this index is based on the results of a survey that measures how people evaluate their lives as a whole rather than their current emotions. it is based on the average of the answers given to the question "how happy are you?", which is asked to the participants to determine the better life index. it is calculated annually for all oecd member countries. share of renewable energy in gross final energy consumption (sre): this is the share of renewable energy in the total energy consumption in the country where the data is provided. this indicator is frequently used to measure environmental performance, as it is thought that the increase in renewable energy consumption will have positive environmental consequences. co2 emission per capita (co2): the contribution of the citizens of each country to the co2 emission can be obtained by dividing the total emissions of that country by the total population. the achieved value is called co2 emissions per capita. co2 emission per capita is one of the most frequently used indicators in environmental performance measurements. environmental performance index (epi): this index is calculated using 32 performance indicators under 11 dimensions and ranks countries in terms of environmental health and ecosystem vitality. the epi provides a national scale indicator of how close countries are to setting environmental policy goals. due to the large number of performance indicators it contains, it can be used on its own in many environmental performance evaluation studies. ecological footprint (ef): ecological footprint per person is obtained by dividing a nation's total ecological footprint by the nation's total population. to live within the resources of our planet, the earth's ecological footprint must equal the available biocapacity per person on our planet, currently 1.7 global hectares. thus, if a country's ef is 6.8 global hectares per person, it means that the citizens of that country demand four times the resources and waste that our planet can regenerate and absorb in the atmosphere. oecd members consist of countries that are economically, socially and environmentally different from each other. these differences can reduce the quality of the evaluations made. in the present study, the countries were grouped in order to prevent this and to reveal more homogeneous country groups. accordingly, cluster analysis was performed using the two-step cluster method. the silhouette, which was examined in order to test the consistency and accuracy within the data sets in the clustering analysis, revealed that the grouping was at a "fair" level. the country groups formed as a result of the cluster analysis are shown in table 3. arsu & ayçin /oper. res. eng. sci. theor. appl. 4 (2) (2021) 55-78 66 table 3. oecd country clusters first cluster countries second cluster countries usa sweden estonia germany switzerland spain australia japan italy austria canada colombia belgium luxemburg latvia czech republic norway lithuania denmark hungary finland poland france portugal south korea slovakia holland slovenia england chile ireland turkey israel greece when conducting the cluster analysis, 12 criteria were taken into account to evaluate oecd countries economically, socially and environmentally. as mexico's growth rate was negative, it was excluded from the analysis and only 34 countries were included in the cluster. of these 34 countries, 20 were in the first cluster and 14 were in the second cluster. 5. results when evaluating the countries, the criteria were weighted with the critic method. then, using the obtained weights, the countries were evaluated using the marcos method. in this section, the solution values calculated with the critic and marcos methods are shown respectively. 5.1. critic results the decision matrix used in both the critic method and the marcos method was created as shown in equation (1). as a result of the clustering analysis, the decision matrices created with the values taken by the oecd countries, which were divided into two clusters, according to the criteria shown in table 2 are presented in table 4. the normalization process was implemented primarily to the maximization and minimization criteria by using the values in the decision matrix given in table 4. then, the correlation coefficient matrix was created by using the criterion values in the normalized decision matrix. finally, the criterion weights were calculated using the 𝐶𝑗 values representing the amount of information of the criteria. the criteria weights for each cluster of countries obtained after the operations seen in equations (2)-(7) were carried out are shown in table 5. evaluation of oecd countries with multi-criteria decision-making methods in terms of economic, social and environmental aspects 67 table 4. decision matrix of the clusters countries economic criteria social criteria environmental criteria g d p u r ir g r s p i g in i h d i l s i s r e c o 2 e p i e f m a x m in m in m a x m a x m in m a x m a x m a x m in m a x m in f ir st c lu st e r usa 65118 3.7 1.8 2.3 85.7 0.39 0.92 6.9 8.72 16.2 69.3 8 germany 46258 3.1 1.4 0.6 90.5 0.28 0.93 7 14.21 9.6 77.2 4.7 australia 54907 5.2 1.6 1.9 91.2 0.32 0.93 7.3 9.18 16.9 74.9 7.3 austria 50277 4.5 1.5 1.6 89.5 0.27 0.91 7.1 34.39 7.9 79.6 6 belgium 46116 5.4 1.4 1.4 89.4 0.26 0.91 6.9 9.2 8.5 73.3 6.6 czech republic 23101 2 2.8 2.6 86.6 0.24 0.89 6.7 14.83 9.9 71 5.5 denmark 59822 5 0.8 2.4 92.1 0.26 0.93 7.6 33.17 6.0 82.5 6.9 finland 48685 6.7 1 1 91.8 0.26 0.92 7.6 43.24 8.1 78.9 5.8 france 40493 8.4 1.1 1.5 88.7 0.29 0.89 6.5 13.5 5.3 80 4.6 south korea 31762 3.7 0.4 2 89.0 0.35 0.90 5.9 2.71 12.5 66.5 6.2 holland 52447 3.4 2.6 1.8 91.0 0.28 0.93 7.4 5.89 9.6 75.3 5 england 42300 3.7 1.7 1.4 88.5 0.36 0.92 6.8 8.71 5.8 81.3 4.2 ireland 78661 4.9 0.9 5.5 90.3 0.29 0.94 7 9.08 8.1 72.8 5 israel 43641 3.8 0.8 3.5 83.6 0.34 0.90 7.2 3.71 7.8 65.8 5.5 sweden 51610 6.8 1.8 1.2 91.6 0.27 0.93 7.3 53.25 4.2 78.7 6.1 switzerland 81993 4.4 0.4 0.9 91.4 0.29 0.94 7.5 25.29 4.5 81.5 4.5 japan 40246 2.4 0.5 0.7 90.1 0.33 0.91 5.9 6.3 9.3 75.1 4.7 canada 46194 5.7 1.9 1.7 91.4 0.31 0.92 7.4 22.03 15.5 71 8.1 luxemburg 114704 5.6 1.7 2.3 89.5 0.32 0.90 6.9 9.03 15.6 82.3 12.8 norway 75419 3.7 2.2 1.2 92.7 0.26 0.95 7.6 57.77 8.2 77.7 5.8 s e co n d c lu st e r estonia 23659 4.4 2.3 4.3 87.2 0.30 0.88 5.7 27.48 14.1 65.3 7.2 spain 29613 14.1 0.7 2 88.7 0.33 0.89 6.3 16.25 5.8 74.3 4 italy 33189 10 0.6 0.3 87.3 0.33 0.88 6 16.52 5.7 71 4.4 colombia 6432 10 3.5 3.3 74 0.50 0.76 6.3 23.56 1.9 52.9 1.9 latvia 17836 6.3 2.8 2.2 83.1 0.35 0.85 5.9 38.1 3.7 61.6 6.1 lithuania 19455 6.3 2.3 3.9 83.9 0.37 0.86 5.9 28.96 4.7 62.9 5.9 hungary 16475 3.4 3.3 4.9 81.0 0.28 0.84 5.6 15.56 5.1 63.7 3.7 poland 15595 3.3 2.2 4.1 84.3 0.27 0.87 6.1 11.91 8.8 60.9 4.7 portugal 23145 6.5 0.3 2.2 87.7 0.32 0.85 5.4 27.16 5.3 67 4.4 slovakia 19329 5.8 2.7 2.4 83.1 0.22 0.85 6.2 13.41 6.6 68.3 4.4 slovenia 25739 4.4 1.6 2.4 87.7 0.24 0.90 5.9 20.88 6.8 72 4.9 chile 14896 7.3 2.6 1.1 83.3 0.46 0.84 6.5 24.88 4.5 55.3 4.3 turkey 9042 13.7 15.2 0.9 68.2 0.40 0.80 5.5 13.37 5.2 42.6 3.5 greece 19582 17.3 0.3 1.9 85.7 0.31 0.87 5.4 17.17 7.0 69.1 4.1 arsu & ayçin /oper. res. eng. sci. theor. appl. 4 (2) (2021) 55-78 68 table 5. criteria weights of the clusters determined using the critic method first cluster 𝑤𝑗 economic criteria gdp ur ir gr 0.072 0.099 0.103 0.089 social criteria spi gini hdi lsi 0.069 0.081 0.072 0.082 environmental criteria sre co2 epi ef 0.083 0.087 0.088 0.075 second cluster 𝑤𝑗 economic criteria gdp ur ir gr 0.071 0.094 0.058 0.099 social criteria spi gini hdi lsi 0.065 0.079 0.068 0.107 environmental criteria sre co2 epi ef 0.100 0.093 0.063 0.104 when the criteria weights in table 5 are examined, it can be seen that the most important criteria for the first cluster were inflation rate (ir), unemployment rate (ur) and growth rate (gr), while the most important criteria for the second cluster were the life satisfaction index (lsi), ecological footprint (ef) and the share of renewable energy in gross final energy consumption (sre). 5.2. marcos results in the next step, the marcos method was used to evaluate the economic, social and environmental performance of the oecd countries. the mathematical steps of the marcos method as shown in equations (8)-(19) were followed respectively and the results are shown in table 6. table 6. results of the marcos method for the clusters country 𝑆𝑖 𝐾𝑖 𝐾𝑖 + 𝑓(𝐾𝑖 -) 𝑓(𝐾𝑖 +) 𝑓(𝐾𝑖 ) rank f ir st c lu st e r usa 0.5620 1.3157 0.5620 0.2993 0.7007 0.4983 20 germany 0.6230 1.4585 0.6230 0.2993 0.7007 0.5524 13 australia 0.5659 1.3249 0.5659 0.2993 0.7007 0.5018 18 austria 0.6472 1.5152 0.6472 0.2993 0.7007 0.5738 8 belgium 0.5862 1.3724 0.5862 0.2993 0.7007 0.5198 17 czech republic 0.6462 1.5129 0.6462 0.2993 0.7007 0.5730 9 denmark 0.7072 1.6557 0.7072 0.2993 0.7007 0.6270 2 finland 0.6581 1.5407 0.6581 0.2993 0.7007 0.5835 6 france 0.6250 1.4633 0.6250 0.2993 0.7007 0.5542 12 south korea 0.6187 1.4483 0.6187 0.2993 0.7007 0.5485 14 holland 0.6143 1.4381 0.6143 0.2993 0.7007 0.5446 15 england 0.6280 1.4703 0.6280 0.2993 0.7007 0.5568 11 ireland 0.7054 1.6514 0.7054 0.2993 0.7007 0.6254 3 israel 0.6334 1.4828 0.6334 0.2993 0.7007 0.5616 10 sweden 0.6933 1.6232 0.6933 0.2993 0.7007 0.6148 5 evaluation of oecd countries with multi-criteria decision-making methods in terms of economic, social and environmental aspects 69 switzerland 0.7769 1.8188 0.7769 0.2993 0.7007 0.6888 1 japan 0.6562 1.5362 0.6562 0.2993 0.7007 0.5818 7 canada 0.5647 1.3221 0.5647 0.2993 0.7007 0.5007 19 luxemburg 0.5888 1.3785 0.5888 0.2993 0.7007 0.5221 16 norway 0.7033 1.6465 0.7033 0.2993 0.7007 0.6236 4 s e co n d c lu st e r estonia 0.6807 1.7267 0.6807 0.2828 0.7172 0.6125 8 spain 0.7289 1.8489 0.7289 0.2828 0.7172 0.6558 2 italy 0.6358 1.6126 0.6358 0.2828 0.7172 0.5720 11 colombia 0.6220 1.5776 0.6220 0.2828 0.7172 0.5596 12 latvia 0.6932 1.7582 0.6932 0.2828 0.7172 0.6236 5 lithuania 0.6904 1.7512 0.6904 0.2828 0.7172 0.6211 6 hungary 0.7170 1.8187 0.7170 0.2828 0.7172 0.6451 4 poland 0.6815 1.7287 0.6815 0.2828 0.7172 0.6132 7 portugal 0.7179 1.8208 0.7179 0.2828 0.7172 0.6459 3 slovakia 0.6555 1.6628 0.6555 0.2828 0.7172 0.5898 9 slovenia 0.7329 1.8591 0.7329 0.2828 0.7172 0.6594 1 chile 0.6164 1.5636 0.6164 0.2828 0.7172 0.5546 13 turkey 0.5106 1.2950 0.5106 0.2828 0.7172 0.4593 14 greece 0.6381 1.6185 0.6381 0.2828 0.7172 0.5741 10 results were obtained for each cluster with the marcos model. when table 6 is examined it can be observed that for the first cluster switzerland, denmark and ireland had the highest performance score, while usa, canada and australia had the lowest performance score and for the second cluster slovenia, spain and portugal had the highest performance score, while turkey, chile and colombia had the lowest performance score. 6. examination of results in this section, the sensitivity analysis of the critic-marcos methodology is presented. for this purpose, the reliability and validity of the proposed model were analyzed by using the multi-attribute ideal-real comparative analysis (mairca), attributive border approximation area comparison (mabac), weighted aggregated sum product assessment (waspas) and combined compromised solution (cocoso) methods. the comparative results of these mcdm methodologies for the first and second cluster are shown in figures 1 and 2, respectively. arsu & ayçin /oper. res. eng. sci. theor. appl. 4 (2) (2021) 55-78 70 figure 1. sensitivity results of the first cluster figure 2. sensitivity results of the second cluster spearman’s correlation coefficient was used to determine the ranking position of the difference between the results of the critic-marcos methodology and the all other mentioned mcdm methods. the spearman correlation coefficients for both clusters are shown in table 7. 0 5 10 15 20 25 marcos mairca mabac waspas cocoso 0 2 4 6 8 10 12 14 16 marcos mairca mabac waspas cocoso evaluation of oecd countries with multi-criteria decision-making methods in terms of economic, social and environmental aspects 71 table 7. spearman correlation results cluster/method mairca mabac waspas cocoso average value cluster-1 (critic-marcos) 0.782* 0.782* 0.991* 0.690* 0.811 cluster-2 (critic-marcos) 0.785* 0.785* 0.978* 0.723* 0.818 according to table 10, the correlation coefficients of each cluster was above 80.0%. these results show a significant correlation between the ranks of the proposed critic-marcos methodology and all other mentioned mcdm methods in both clusters. this confirms that the ranking results suggested by the critic-marcos methodology were valid and credible. 7. discussion firstly, the countries were divided into two clusters using cluster analysis in order to make the heterogeneous structure of the countries homogeneous and evaluate the countries with similar characteristics together. there were 20 developed countries including usa, germany, denmark and switzerland in the first cluster, while there were 14 relatively less developed countries including estonia, lithuania, slovenia and colombia included in the second cluster. after the countries were clustered, 12 criteria used for the economic, social and environmental evaluation of each cluster were weighted using the critic method. the most important criteria for the first cluster were determined as inflation rate (ir: 0.103), unemployment rate (ur: 0.099) and growth rate (gr: 0.089), while the most important criteria for the second cluster were found as the life satisfaction index (lsi: 0.107), ecological footprint (ef: 0.104) and the share of renewable energy in gross final energy consumption (sre: 0.100), respectively. kılıç depren & bağdatlı kalkan (2018) used both unemployment rate and the life satisfaction index criteria to evaluate oecd countries. in the study where 24 criteria were weighted using the entropy method, the life satisfaction index was determined as the ninth most important criterion while unemployment rate was determined as the twentieth most important criterion. in the present study, unemployment rate was determined as the second most important criterion for the countries in the first cluster while the life satisfaction index was determined as the most important criterion for the second cluster. this result is proof that different combinations of criteria produce different results in the evaluation of countries. the countries were evaluated using the criterion weights obtained by the critic method in the marcos method. among the countries in the first cluster, switzerland, denmark and ireland had the best performances, respectively, while australia, canada and usa had the worst performances. it is noteworthy that the economic data of countries with good performance in particular were higher than the other countries in the first cluster. even though the economic data of the poor performing countries were similar to the other countries in the first cluster, the gini coefficient representing the income equity and the co2 emissions representing the air quality were worse than the other countries in the cluster. therefore, these countries should focus on policies that will ensure income justice and take steps to improve air quality. arsu & ayçin /oper. res. eng. sci. theor. appl. 4 (2) (2021) 55-78 72 among the countries in the second cluster, slovenia, spain and portugal performed the best, while colombia, chile and turkey performed the worst. the gdp values of the most successful countries in the second cluster were relatively better than the other countries in the cluster. likewise, the social progress and human development index values of these countries were higher than the other countries in the cluster. the economic data of the most unsuccessful countries were noticeably worse than the other countries in the cluster. in previous studies in the literature, similar results emerged although countries were not evaluated in two different clusters. in many recent studies, switzerland and denmark, which are at the top of the first cluster, demonstrated the highest performance while chile and turkey, which are at the bottom of the second cluster, were among the countries with the lowest performance (skare & rabar, 2017; kılıç depren & bağdatlı kalkan, 2018; costa et al., 2019; iram et al., 2020). australia, canada and usa, which are among the countries in the first cluster with the lowest performance, demonstrated high performance in some studies (kılıç depren & bağdatlı kalkan, 2018; costa et al., 2019; iram et al., 2020) and lower performance in others (skare & rabar, 2017). therefore, the findings obtained in the present study support the current literature. the country rankings obtained using the critic and marcos methods were rankings belonging to this combination of criteria. it is possible to reach different rankings under different criteria. in order to test the accuracy and consistency of the criteria used in this study and the rankings acquired, a sensitivity analysis was performed. by using the criterion weights obtained by the critic method, the model was re-solved using mairca, mabac, waspas and cocoso methods and country rankings were achieved. the spearman rank correlations between the country rankings obtained with the marcos method and those acquired with the other methods were calculated. the calculated correlation values revealed that there were significant relationships between the rankings. an average of over 80% similarity was found between the rankings obtained with marcos and the rankings acquired by the other methods. this shows that the analysis made was a consistent and accurate analysis. 8. conclusion in general, when trying to determine the development levels of countries economic data are taken into consideration. however, economic development alone is not often sufficient for the people of a country to live in tranquility and prosperity. income increase resulting from economic development can be considered as a tool to support the social development of people. moreover, socially developed individuals are also more likely to be more interested in the environment. these meaningful connections between economic, social and environmental development were the main motivation for the present study. therefore, oecd member countries with heterogeneous characteristics in terms of economic, social and environmental aspects were evaluated in this study. the findings obtained include those that policymakers of countries will refer to when developing economic, social and environmental policies. based on these findings, certain managerial implications were proposed for policymakers to utilize. evaluation of oecd countries with multi-criteria decision-making methods in terms of economic, social and environmental aspects 73 for many years, decision-makers tend to rank countries based on their gdp. however, the results of the present study serve as proof that countries should not be ranked based on gdp only. for example, although the gdp of the usa, which ranks last in the first cluster, is approximately three times that of the czech republic, czech republic ranked ninth. therefore, gdp alone is not enough to reflect national welfare. furthermore, in the findings of the present study, economic criteria were determined as the most important criteria for the first cluster, which consists of countries that completed their social and environmental development, while social and environmental criteria stood out for countries in the second cluster. based on this, it is necessary for particularly the countries in the second cluster to develop economic policies towards increasing their gdp while focusing on developing policies to improve their social and environmental performance by increasing medical and educational expenditures. both the data on the countries and the results of the present study indicate that countries that were regarded as the greatest global forces in the past are beginning to lose importance against countries that were previously ineffective. the great powers of the past such as the usa, england, france and germany are unable to provide their citizens with the opportunities that countries such as switzerland, sweden, denmark and ireland offer to their citizens. this situation cannot be explained by the difference in population between the countries or the richness of national resources alone. in addition to economic data, national welfare depends on a number of non-economic factors such as income equality, freedom of speech, gender equality and co2 emissions, as well. therefore, countries that are unable to demonstrate high performance in economic, social and environmental terms should use benchmarking processes based on successful countries while developing policies. although the present study produced original results in terms of the criteria, methodology 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(2019). https://data.worldbank.org/ accessed 19 december 2020 yalçın, n., & karakaş, e. kurumsal sürdürülebilirlik performans analizinde criticedas yaklaşımı. çukurova üniversitesi mühendislik-mimarlık fakültesi dergisi, 34(4), 147-162. https://doi.org/10.21605/cukurovaummfd.704167 © 2021 by the authors. submitted for possible open access publication under the terms and conditions of the creative commons attribution (cc by) license (http://creativecommons.org/licenses/by/4.0/). evaluation of oecd countries with multi-criteria decision-making methods in terms of economic, social and environmental aspects talip arsu 1*, ejder ayçin 2 1. introduction 2. literature review 3. method 3.1. critic 3.2. marcos 4. data 5. results 5.1. critic results 5.2. marcos results 6. examination of results 7. discussion 8. conclusion references plane thermoelastic waves in infinite half-space caused operational research in engineering sciences: theory and applications vol. 5, issue 1, 2022, pp. 69-89 issn: 2620-1607 eissn: 2620-1747 doi: https://doi.org/10.31181/oresta210322091b * corresponding author. yousafkhan@giki.edu.pk (y.a. khan), u2017206@giki.edu.pk (m.u. baig), gem1971@giki.edu.p (o.u. rehman) enhancing resilience of oil supply chains in the context of developing countries mirza muhammad usama baig, yousaf ali*, obaid ur rehman* school of management sciences ghulam ishaq khan institute of engineering sciences & technology topi, swabi, kpk, pakistan received: 20 october 2021 accepted: 31 january 2022 first online: 21 march 2022 research paper abstract: oil supply chains play a vital role in the day-to-day functioning of national economies and obstruction in its services can lead to dire consequences. for this purpose, it is imperative for oil supply chains to be on guard against all probable vulnerabilities and develop adequate protection mechanisms. this research study aims to identify the most important vulnerabilities for oil supply chains in the context of pakistan, a developing country. subsequently, these identified vulnerabilities were used to design a protection framework, embodying different supply chain capabilities. for this purpose, this study employs a hybrid multi-criteria decision making approach. full consistency method (fucom) has been used to prioritise vulnerabilities and fuzzy quality function deployment (qfd) has been used to identify those capabilities that can ensure protection against these vulnerabilities. this study utilizes secondary data for the identification of vulnerabilities and capabilities through a comprehensive literature review. in addition, primary data has been incorporated as relevant experts were asked to rate the importance of these identified vulnerabilities and capabilities. results indicate that crude oil price instability, fuel price shocks, unpredictable demand, and information and communication disruptions are the most important and catastrophic vulnerabilities in the context of pakistan’s oil industry. for mitigation of these vulnerabilities, oil supply chains need to incorporate real-time information sharing, visibility, e-procurement, traceability, and transparency as resilience measures. these recommendations are of considerable importance to pakistan’s oil industry and policymaking authorities. moreover, this study fulfils the research gap by focusing on enhancing the resilience of pakistan’s oil supply chains, with the aid of mcdm techniques. key words: oil industry, supply chain, resilience, fuzzy set theory, fucom, qfd baig et al./oper. res. eng. sci. theor. appl. 5(1) (2022) 69-89 70 1. introduction the oil industry is one of the key contributors to the global and national economies, as it is one of the most significant and commonly dealt products. the worth of the oil development, production, and distribution have a handsome share in a country’s economy. numerous economic sectors count on petroleum products as it drives the generation of electrical energy, transport sector, heating in homes, industrial operations, and fulfils residential needs. globally, in 2016, it was estimated that global annual and daily consumption of oil stood at 35,442,913,090 and 97,103,871 barrels respectively (worldometers, 2021). the economic worth of a country can be estimated by its production, refinement, transportation, as well as consumption of petroleum products. pakistan is a developing country, and like other countries, its economic advent also relies on the active role of the oil industry. its petroleum sector faces frequent disruptions due to various policy, administrative, market-based, and financial issues. the effect of these disruptions is realized in the form of losses to national gdp and deterioration of the quality of life of citizens. the effective and smooth operations of oil supply chains are often threatened on account of their vulnerabilities, which are exploited by potential disasters. thus, huge losses to revenue, operations, quality, and other attributes are caused (ponomarov & holcomb, 2009). these vulnerabilities are both intrinsic and extrinsic in nature. the disruptions can be realized due to the occurrence of natural disasters, pandemics, epidemics, and internal forces such as failure to incorporate different functions of the supply chain. moreover, the modern day’s turbulent and uncertain business environment has also rendered supply chains more prone to looming disasters. the traditional mechanisms to become profitable supply chains is also exposing companies to new vulnerabilities (tarei, et al., 2020). the increased number of threats and risks associated with the vulnerabilities can destabilize the entire supply chain. the cascading effect of this destabilization drives the company to a greater extent, and the economic sector to a lesser extent, into chaos (sheffi, 2005). recently, the coronavirus pandemic (covid-19) has posed a serious threat to the sales and market share of each industry. these increased disruptions and vulnerabilities ask for the inclusion of supply chain capabilities (sccs) to become resilient (christopher & lee, 2004). because if vulnerabilities are not timely mitigated, the consequences could halt the supply chain operations which would, in turn, result in loss of revenue (ponomarov & holcomb, 2009). the dilemma of vulnerabilities and disruptions is also existent in oil supply chains. however, due to the crucial role of petroleum products in national and global economies, the implications of these disruptions are more execrable in nature. the sccs have the potential to act as resilient features and either prevent disruptions or help the supply chain resume normal operations right after disruptions (pettit, et al., 2011). the concept of resilient supply chains is a universally accepted and recognized agenda due to the prevalent vulnerabilities and complexities of the global supply chains. the sccs should be organized in such a way that they not only mitigate risks but also deliver a sufficient amount of petroleum products in a reasonable, reliable, effective, environmentally friendly, proactively administered and socially acceptable manner (sovacool, et al., 2011). a real-world application of mitigating supply chain vulnerabilities (scvs) through sccs enhances not only the financial performance of the oil industry (fan, et al., 2017) but also the overall performance of the established supply chains (thun & hoenig, 2011). enhancing resilience of oil supply chains in context of developing countries 71 there are numerous sccs and it is usually difficult and costly for supply chains to adopt all sccs. there is a need for a mechanism that can be employed to determine which sccs are most pertinent and relevant for respective supply chains. thus, supply chains would be able to identify the important sccs and incorporate a limited number of these sccs or focus on these sccs in order of their impact. this study proposes that sccs can be viewed as a tool to combat vulnerabilities. therefore, scvs can be used to prioritise sccs and thus supply chains can focus on these prioritised ccs according to their importance. this research study aims to identify and prioritize the supply chain vulnerabilities with regard to pakistan’s oil industry. furthermore, these prioritized vulnerabilities have then been employed to design a resilience framework, comprising supply chain capabilities. these capabilities are also prioritized on the basis of their effectiveness against vulnerabilities. thus, the study’s primary hypothesis is to determine the rank of sccs for oil supply chains of developing countries. for this purpose, a hybrid combination of two mcdm techniques has been used. full consistency method (fucom), a rather recent technique, has been used to assign relative importance weights to supply chain vulnerabilities. furthermore, fuzzy quality function deployment (qfd), has been used to prioritize supply chain capabilities as per their ability to combat the previously prioritized vulnerabilities and reinforce other capabilities. the full consistency method has been employed because it is an improved method for the relative comparison of criteria. it embodies the advantages of qualitative decision making and non-linear programming, thus assigning a reasonably fair value for relative comparison of attributes. in this study, initially, scvs have been compared relative to each other and assigned with numerical values with the aid of the fucom method. moreover, the fuzzy quality function deployment tool was primarily developed to incorporate customer preferences into product design. it prioritises product design features that can ensure adherence to customer preferences. lately, its scope has been diversified and has been widely adopted in research studies. in this study, it has been used to incorporate resilience against scvs through sccs. the rest of this research study is structured as follows. the introduction is followed by literature review, where research studies relevant to the topic and methodology have been discussed. data collection and methodology elaborates the data collection process and the analysis. subsequently, the result and discussions describe the results and policy recommendations. finally, the conclusion section concludes the study. 2. literature review crude oil is considered one of the key sources of energy. it plays a significant role in the day-to-day functioning of the world’s economy. the oil supply companies (oscs) have multifarious structures with regards to the choice of products, consumer markets, and operations (ahmad, de brito m, rezaei, & tavasszy, 2017; saad, elsaghier, & ezaga, 2018). due to the complexity prevailing in the upstream, midstream, and downstream functions, the oil supply chains are quite vulnerable to disruptions. a research study emphasized and assessed safety risks and the overall vulnerability in the oil industry by establishing a risk matrix. the study analyzed the baig et al./oper. res. eng. sci. theor. appl. 5(1) (2022) 69-89 72 consequences of the indicators such as accidents’ proportions, economic loss, reputation loss, and environmental pollution (tian, et al., 2018). the most dangerous risk associated with oscs is the financial risk. high price fluctuation within the global energy market is one of the key threats to the financial stability of the oil industry (chikunov, et al., 2019). the recent shock due to the covid-19 pandemic has also severely destabilized the energy sector, global economic growth, and geopolitics (mcnally, 2020; đukić et al. 2021). similarly, a study addressed vulnerabilities within remote operations of the oil industry including technical information and communications-based risks, organizational risks, and risks associated with human factors (johnsen, et al., 2007). from the perspective of developing countries, the nigerian oil industry was assessed with political risks (frynas & mellahi, 2003). the researchers concluded that it has varying effects on transnational firms. in some cases, firms underperform while in other cases, firms can get benefits under certain circumstances. in addition, (bimha, et al., 2020) analyzed the zimbabwean petroleum industry with respect to the uninterrupted flow of quality products at reasonable prices. the top fifteen oilimporting south asian countries were assessed on the indicators like geopolitical risk, transportation risk, oil price unpredictability, and us dollar instability (iqbal, et al., 2020). these risks result in poor performance and competitiveness at both micro and macro levels. in past decades, supply chains have been challenged by vulnerabilities in the shape of disasters and have thus left an impact on society and ecosystems (sodhi, et al., 2012). resilient supply chains are required in order to tackle the frequently occurring and severe vulnerabilities. numerous research studies have been conducted on resilient supply chains which focus on capabilities that help to confront such vulnerabilities. the pseudo-resilient supply chain concept was introduced in a study where the supply chain performs much better with the inclusion of risk management capabilities (rajesh, 2018). a decision support system (dss) was developed keeping in view the indian petroleum supply chain. managers can select a suitable risk management strategy and accelerate the execution of risk management enablers (tarei, et al., 2020). sccs sum up all such resilient measures to cope up with the vulnerabilities prevailing in any business. a study identified the problem of low visibility and integration in the supply chain and proposed three top resilient measures which include contingency plan, monitoring and maintenance, and the supply chain relationship management (lam & bai, 2016). the complexity of oil supply chains requires effective supplier selection and close relationships to overcome the uncertainty. researchers developed an integrated approach for supplier selection within iran’s oil industry to ensure a continuous supply stream (kaviani, et al., 2019). the logistics network of oscs is also exposed to vulnerabilities. a study discussed the uniform commercial code related to oscs management issues and developed several strategies to improve the supply chain (chima, 2007). another research focused on european union’s oil supply chains and observed that there is a robust resiliencmechanismsm in place, however, it needs to be synchronized (urciuoli, et al., 2014). (hossain, et al., 2019) employed a bayesianetwork-based approach to explore resilience in oil and gas supply chains. in addition, (alfaqiri, et al., 2019) focused on africa as a case study and investigated the existence and applicability of the complex system governance in the context of risks in oil supply chains. however, the demand side of oil supply chains, especially in the enhancing resilience of oil supply chains in context of developing countries 73 context of developing countries, has not been adequately addressed from the perspective of oil supply chains. the adoption of blockchain in supply chains is a modern trend and has gained widespread popularity. blockchain can enhance oscs performance with unique features like real-time information sharing, cybersecurity, transparency, reliability, traceability, and visibility (aslam, et al., 2021). the important and essential technologies of blockchain implementation in osc has been discussed in a study with four features including trading, management and decision-making, supervision, and cybersecurity (lu, et al., 2019). traceability was ranked as the highest core innovation technology to exploit existing sccs and resources (hald & kinra, 2019). blockchain features including information transparency, information immutability, and effective contracts have a positive impact on partnership growth (kim & shin, 2019). a research study identified the disrupted vulnerabilities like piracy in oscs by providing a holistic complex system of governance (alfaqiri & pinto, 2019). furthermore, issues related to poor governance including weak regulatory system, poor policy regarding oil industry operations, logistics and communication challenges weaken the existing sccs and industry competitiveness (bimha, et al., 2020). fucom is a multi-criteria decision-making (mcdm) technique, and it was developed by (pamučar, et al., 2018). it has found several applications in determining the weight coefficients of the relative importance of attributes in consideration. (pamucar & ecer, 2020) presented the fuzzy fucom approach and applied it to the evaluation of green suppliers. the authors compared the results of fuzzy fucom with fuzzy analytical hierarchy process and fuzzy best worst method and thus confirmed its vitality. a research study combined fucom approach with d numbers and the fuzzy rafsi method for the development of a hybrid decision-making model (božanić, et al., 2021). similarly, (durmić, et al., 2020) used fucom in addition with rough saw approach. another research used fucom with the mabac model in a decision making research scenario (bozanic, et al., 2020). thus, there is evidence from the literature that fucom has been used in addition with other decision-making techniques. the quality function deployment (qfd) technique was developed in the 1970s by akao in japan. qfd, being a comprehensive and extensively recognized quality management tool, was developed to translate customer requirements into characteristics of process or product (akao & mazur, 2003). this is achieved by building a house of quality (hoq). the needs can be identified through the help of past literature and questionnaire survey from managers and employees. qfd has proven to be a systematic process to resolve the key issues involved in any process. lately, qfd has been widely used for the selection of strategies, risks, supplier selection while using the weight derived from decision-making tools (lima-junior & carpinetti, 2016; chen, ko, & yeh, 2017). fuzzy set theory was developed for the mitigation of uncertainty in qualitative judgments (zadeh, 1965). fuzzy qfd has been used in a variety of studies. (wang, et al., 2020) used fuzzy qfd for developing a system collaborative framework for designing quality products. (deveci, et al., 2019) employed fuzzy qfd and developed a framework for quantitative assessment with regards to customer satisfaction in public transportation. similarly, a study designed a safety methodology with the aid of fuzzy qfd (fargnoli, et al., 2018). this research study contributes to the literature and addresses the research gap from two perspectives. firstly, it focuses on mitigating vulnerabilities in oil supply baig et al./oper. res. eng. sci. theor. appl. 5(1) (2022) 69-89 74 chains in the context of developing countries. oil supply chains in developing countries lie on the demand side in the supply chain spectrum have not been given adequate attention in the literature. thus, the results of this study would be of considerable significance to developing countries and aid them in enhancing the resilience of oil supply chains. secondly, this study has used a novel combination of research techniques for addressing supply chain vulnerabilities with supply chain capabilities. the proposed combination of research tools i.e., fucom in association with fuzzy qfd has rarely been used to address the vulnerabilities and design a resilience framework. thus, the results of this study would not only add a unique perspective to the existing literature regarding risks in oil supply chains but also propose a research framework that can be adopted for enhancing resilience in other sectors. 3. data collection & methodology this research study is focused on the evaluation of adequate supply chain resilience capabilities against the most important and common vulnerabilities, in the context of pakistan’s oil industry. the study utilizes a unique combination of fucom and fuzzy qfd methods to conduct the analysis. the finalized vulnerabilities and capabilities are presented in table 1 and 2, respectively. table 1. supply chain vulnerabilities categories vulnerabilities references demand and supply vulnerabilities resource unavailability (sovacool, et al., 2011); (feygin & satkin, 2004) oil dependence risks (zhang, et al., 2013); (yang, et al., 2014); (li, et al., 2014) supplier disruptions (sun, et al., 2017); (alfaqiri, et al., 2019) financial vulnerabilities crude prices instability (kaufmann, 2016); (alfaqiri, et al., 2019) economic recession (hanabusa, 2010); (blos, et al., 2009) refined fuel prices shocks (blos, et al., 2009) social and political vulnerabilities geopolitical risks (blos, et al., 2009); (iqbal, et al., 2020) transportation risks (sun, et al., 2014); (wu, et al., 2009) pandemic/epidemics (mhalla, 2020) natural hazards (badida, et al., 2019) political instability (blos, et al., 2009); (block, et al., 2015) operational vulnerabilities demand fluctuations (davis, 2018); (zhu, et al., 2020); (berget, 2020) information & communication disruptions (giri & sarker, 2017); (aslam, et al., 2021); (kshetri, 2018) lack of research & development (kraal, 2019) inadequate government policies (imbun, 2019); (aung, 2017); (akrofi & antwi, 2020) the proposed combination is novel as it integrates the two techniques, by utilizing the relative importance weights deducted from the fucom analysis in the fuzzy qfd analysis. in the first step, an extensive literature review was conducted to identify supply chain vulnerabilities and capabilities. it resulted in the identification of several factors, and for maintaining relevancy and reduction of redundancy, a total of fifteen enhancing resilience of oil supply chains in context of developing countries 75 capabilities and vulnerabilities were shortlisted. in addition, a panel of experts was also consulted for shortlisting these factors. table 2. supply chain vulnerabilities s. no. sc capabilities references 1. minimization of shutdown period (machado, et al., 2020) 2. compliance with regulatory developments (myasnikova, et al., 2019); (sanchez, et al., 2019) 3. improved reliability (aslam, et al., 2021); (hasan, et al., 2020) 4. real-time information sharing system (aslam, et al., 2021); (hald & kinra, 2019); (queiroz, et al., 2019) 5. transparency (aslam, et al., 2021); (cole, et al., 2019); (kim & shin, 2019) 6. traceability (aslam, et al., 2021); (hasan, et al., 2020); (kshetri, 2018); (song, et al., 2019) 7. visibility (aslam, et al., 2021); (kim & shin, 2019); (kshetri, 2018) ; (rogerson & parry, 2020) 8. e-procurement (aslam, et al., 2021); (tie & cheng, 2015) 9. risk management culture (ahmad, et al., 2016); (pagell & wu, 2009) 10. improved forecast reliability (chima, 2007); (vonderembse, et al., 2006) 11. timely and effective delivery (ako, 2012); (ablo, 2015); (chang, et al., 2011) 12. continuous supply stream of products (neiro & pinto, 2003) 13. product quality in compliance with specifications (wei, et al., 2019) 14. unbundling/decentralization of authority in petroleum industry (agrell & bogetoft, 2017) 15. managing bullwhip (rajesh, 2018); (mackelprang & malhotra, 2015) the techniques used in this study are reliant on expert opinion for assigning importance and adequacy weights to attributes. therefore, a questionnaire was developed which comprised of three major parts. in the first part, the experts were asked to gauge the relative importance of each attribute, and in the second part, the experts were asked to rate the effectiveness of each capability against vulnerabilities. the third part focused on the nature of bolstering or undermining the relationship between capabilities. the experts’ panel was comprised of reputable managers in the oil industry. these experts, as shown in figure 1, were serving in refineries, exploratory firms, omcs, and the ministry of petroleum. a total of eleven responses were gathered which are sufficient, considering the detailed nature of the questionnaire and the usual sample size used in mcdm techniques. the baig et al./oper. res. eng. sci. theor. appl. 5(1) (2022) 69-89 76 questionnaires were filled after a detailed briefing to experts and their queries regarding various aspects of questionnaires were addressed. figure 1. experts' panel 3.1. fully consistency method (fucom) fully consistency method (fucom) is a multi-criteria decision making (mcdm) technique, developed by (pamučar, et al., 2018). fucom has been employed to gauge the relative effectiveness of supply chain vulnerabilities, as each vulnerability has a different level of importance owing to its probability, severity, costs, and other aspects. the various steps involved in the fucom method are explained below. step 1: the set of factors, whose relative importance is to be gauged, is identified. a questionnaire is formed, and the experts are asked to respond on a likert scale, determining the importance of each factor. step 2: the average importance weight for each factor is determined and the factors are ranked in the decreasing order of their weights. scv j (1) > scv j (2) > scv j (3) > ……. > scv j (k) (1) where scv represents the supply chain vulnerabilities, and j represents the ranks of criteria when arranged in an order. step 3: comparative priorities of criteria, which represent the advantage of criteria over other criteria, are determined with the aid of equations 2 and 3. 𝛼𝑗 𝑗+1⁄ = scv𝑗 scv𝑗+1 (2) φ = α1/2 , α2/3 , … , αk/k+1 (3) step 4: a non-linear programming model is constructed, which essentially comprises of two conditions. the ratio of final weight coefficients of criteria equals the respective comparative priority. 𝑊𝑗 𝑊𝑗+2 = α𝑗 α𝑗+1 (4) the condition of mathematical transitivity is fulfilled by the weight coefficients. enhancing resilience of oil supply chains in context of developing countries 77 𝑊𝑗 𝑊𝑗+1 = α𝑗 α𝑗+1 ∗ α𝑗+1 α𝑗+2 (5) step 5: the final weight coefficients are determined by forming and solving a nonlinear programming model. the standard format of the model is given below. these weight coefficients are later used in the fuzzy qfd analysis, explained in the next section. min χ s.t. | 𝑊𝑗 𝑊𝑗+1 − ϕ𝑗 𝑗+1⁄ | ≤ χ, ɐj | 𝑊𝑗 𝑊𝑗+2 − ϕ𝑗 𝑗+1⁄ ∗ ϕ𝑗+! 𝑗+2⁄ | ≤ χ, ɐj ∑ wj = 1, n j=1 𝑤𝑗 ≥ 0, ɐj (6) 3.2. fuzzy quality function deployment (qfd) quality function deployment alternatively knows as, house of quality is a tool developed by akao, a japanese researcher (akao, 1990). originally, it was designed to translate customer requirements into product design. however, its scope has lately been diversified and it’s widely used in scenarios where there are sets of clearly defined challenges and solution strategies. the challenges and strategies are referred to as whats and hows respectively. in this study, the supply chain vulnerabilities and capabilities constitute whats and hows. qfd analysis is also dependent upon the experts’ response, which inherently contains vagueness or uncertainty up to a certain degree. in order to mitigate this uncertainty, fuzzy set theory developed by (zadeh, 1965) has been incorporated in the qfd. the fuzzy set theory considers the relative importance of attributes instead of absolute judgments. the various steps involved in fuzzy qfd analysis are explained below. step 1: the whats and hows for the qfd model are identified and expert opinion is gathered. experts’ panel is asked to respond on a likert scale, regarding the effectiveness of each strategy against a challenge, and the supporting or diminishing role with respect to other strategies. step 2: the final weights derived from the fucom analysis for scvs are used as the importance weights of strategies or whats in the qfd model. this step embodies the methodolgoial contribution of the study as it incorporates the relative importance weights derived from the fucom analysis, instead of absolute weightages given by experts. thus, the relative importance weights increase the authencity of the weights and improve the overall analysis. baig et al./oper. res. eng. sci. theor. appl. 5(1) (2022) 69-89 78 step 3: the relationship matrix is constructed, between whats and hows. the (i,j) entry in the matrix shows the strength of jth how in achieving ith what. in this case, it represents the ability of jth capability to mitigate ith vulnerability. the matrix is developed, based on the average value of expert responses. the experts are asked to rate the effectiveness of each strategy against each challenge on the likert scale given in table 3. table 3. linguistic scale for relationship matrix degree of relationship degree of relationship fuzzy number strong 0.7 1 1 medium 0.3 0.5 0.7 weak 0 0 0.3 step 4: the correlation matrix is constructed between hows. it represents the nature of the relationship between various hows. the (i,j) entry in the matrix shows the relationship of ith how and jth how. in this case, it represents the relationship between supply chain capabilities. the matrix is developed, based on the average value of expert responses. the positive values show supporting relationships while negative values show a damaging relationship between strategies. the experts are asked to rate the effectiveness of each strategy against each challenge on the likert scale given in table 4. table 4. linguistic scale for relationship matrix step 5: the relative importance weights of each how are calculated from the relationship matrix, with the aid of equation 7. rij = ∑ wi n i=1 ∗ rij (7) where j = 1,2,..,m and (rj = rju, rjm, rju) here wi refers to the weight coefficients calculated from fucom analysis, while rij represents the entries of the relationship matrix. step 6: the priority weights are calculated with equation 8. rij ∗ = rij + ∑ tkjk=j ∗ rik (8) where j = 1,2,.., m and (rij ∗ = rijl ∗, rijm ∗, riju ∗) here, t refer to the entries of the correlation matrix. step 7: the priority weights are normalized by the division of each value by the maximum value of priority wights. subsequently, the priority weights are de-fuzzified degree of correlation degree of relationship fuzzy number strong positive 0.3 0.5 0.7 positive 0 0.3 0.5 negative -0.5 -0.3 0 strong negative -0.7 -0.5 -0.3 enhancing resilience of oil supply chains in context of developing countries 79 via geometric mean. the hows are then ranked in the descending order of the defuzzified weights. 4. results and discussion the results and discussion section is divided into two parts. the first part focuses on the results of the fucom analysis while the second part elaborates on the results of the fuzzy qfd analysis. 4.1. fucom analysis – supply chain vulnerabilities the non-linear programming model of fucom analysis resulted in final weight coefficients given in table 5. table 5. rankings of scvs derived from fucom rankings supply chain vulnerabilities weight 1 scv 4 crude prices instability 0.096 2 scv 6 refined fuel prices shocks 0.093 3 scv 12 demand fluctuations 0.083 4 scv 13 information & communication disruptions 0.083 5 scv 15 inadequate government policies 0.080 6 scv 3 supplier disruptions 0.069 7 scv 1 resource unavailability 0.067 8 scv 2 oil dependence risks 0.065 9 scv 9 pandemic/epidemics 0.065 10 scv 14 lack of research & development 0.065 11 scv 5 economic recession 0.056 12 scv 8 transportation risks 0.049 13 scv 11 political instability 0.048 14 scv 7 geopolitical risks 0.046 15 scv 10 natural hazards 0.035 the weights coloumn of the anlysis indicate the final relative weights assigned to scvs. each of the scvs have been assigned with a weight between 0 and 1, and the sum of all these weights equal 1. these weights indicate the priority of each vulnerability with respect to other vulnerabilities, and the higher weights indicate increased priority. the fucom analysis indicates that crude oil price instability is a top-ranked vulnerability, which can jeopardize the steady operations of oil supply chains. crude oil price instability is directly associated with stock returns of oil companies, production costs, diminished profit margins, inability to meet consumer demand, inventory costs, and policy fluctuations (apergis & miller, 2009; arouri & nguyen, 2010). however, this vulnerability is inherently extrinsic in nature as crude oil prices are primarily determined by the organization of petroleum exporting countries (opec). moreover, fuel price shock occupied second place in ranked vulnerabilities. in pakistan, usually, fuel prices are revised on a fortnightly basis. thus, there are constant speculations about expected trends or policy decisions, and omcs respond respectively. in case of lower expected prices, these companies try to delay baig et al./oper. res. eng. sci. theor. appl. 5(1) (2022) 69-89 80 procurement and in case of higher prices, the ignominious practise of hoarding takes place. unpredictable demand proved to be yet another vital risk in the petroleum sector. the recent covid-19 pandemic exhibited a strong and unpreceded fluctuation in consumer demands. opec asked its petroleum sector to cut oil production by a record of 10 million barrels per day in may 2020, which was still not sufficient to minimize the gap between demand and supply (iea, 2020). since the lockdowns are expected to happen routinely in a near future due to the ravaging nature of the pandemic, and other reasons, consumer demand would remain unpredictable and would thus adversely affect oil supply chains. information and communication disruptions are also prevalent in the petroleum industry of pakistan. these disruptions have severe disastrous impacts on the functioning and operations of oil supply chains. these disruptions cause supply-demand imbalance, financial mismanagement, and increased operational costs. thus, the ranking derived from fucom analysis is justifiable and there is a need to design preemptive strategies which should help in overcoming these vulnerabilities. 4.2. fuzzy qfd analysis – supply chain capabilities the results of the fuzzy qfd analysis are presented in the table 6. the ri coloumn lists the relative importance weights of sccs. these weights indicate the strength of each scc with respect to combating scvs as per their importance, and the capacity of each scc to withhold/support other sccs. table 6. rankings of sccs derived from qfd rankings supply chain capabilities ri 1 scc4 real-time information sharing system 0.38 2 scc7 visibility 0.37 3 scc8 e-procurement 0.37 4 scc6 traceability 0.36 5 scc5 transparency 0.36 6 scc15 managing bullwhip 0.33 7 scc9 risk management culture 0.30 8 scc3 improved reliability 0.29 9 scc11 timely and effective delivery 0.28 10 scc12 continuous supply stream of products 0.28 11 scc10 improved forecast reliability 0.27 12 scc1 minimization of shutdown period 0.24 13 scc13 product quality in compliance with specifications 0.08 14 scc 2 compliance with regulatory developments -0.06 15 scc14 unbundling/decentralization of authority in petroleum industry -0.12 the results of the fuzzy qfd analysis are presented in the table 6. the ri column lists the relative importance weights of sccs. these weights indicate the strength of each scc with respect to combating scvs as per their importance, and the capacity of each scc to withhold/support other sccs. the results of the fuzzy qfd analysis present strong evidence for the need for the incorporation of blockchain features in pakistan’s petroleum supply chains. the top enhancing resilience of oil supply chains in context of developing countries 81 five capabilities, prioritized as a result of fuzzy qfd analysis are associated with blockchain features and practices. the top-ranked strategy that would mitigate most vulnerabilities and play a supporting role with regards to other capabilities, is the realtime information sharing system. its incorporation would lead to the smooth functioning of the business activities and effective communication within and between business entities (wanga, et al., 2020). it would also aid in improved forecasts as the varying trend of demand and supply can be instantaneously accommodated in the forecasting mechanisms (zhoua & benton, 2007). the information system would provide accurate information regarding the status of availability of crude, demand at the downstream end, and the transportation associated with oscs. thus, its incorporation would lead to mitigation of vulnerabilities as respective authorities would be better able to track down instabilities and interruptions, conduct effective planning, design preemptive strategies. similarly, the adoption of visibility as a vulnerabilities mitigation mechanism would serve in a variety of ways. it would enhance focus, monitoring, and control of the entire operations of oil supply chains (bartlett, et al., 2007). there are several products involved in the oscs and each product has a distinct route, source, and destination. in addition, there are supporting roles for ensuring the smooth delivery of products. visibility would maintain coordination between all these segments of operations. furthermore, e-procurement is another rapidly growing modern trend that enables purchasing via digital means. it reduces delivery time, provides better bargaining options, increases accountability and transparency, and minimizes communication disruptions (jelassi & martínez-lópez, 2020). e-procurement can also reduce severity or impact in case of occurrence of disruptions. it also reduces significant costs through reduction of lead time, effective resource planning, and reduction of inventory levels. traceability has also proven to be a dominant feature with regard to resilience in supply chains. it helps in mapping down the processes and the complete journey of petroleum products in the oil industry. petroleum products require adequate and well-designed safety and quality measures, which can be improved with traceability mechanisms as companies are in knowledge of where, when, and how their products are coming (malik, et al., 2021). it also aids in protective mechanisms against physical thefts in vulnerable areas. supply chain transparency is another feature that increases acceptibilty and success of supply chains (jabbar, et al., 2021). transparancy refers to the practice of communicating information, functional status, operationa; standards, and impact within supply chains, to upstream and downstream linkages and customers (gardnera, et al., 2019). trasnparancy in supply chains assure customers and other associated entities that supply chain’s practices align with their ethical, functional, and busuiness values. thus, it increases confidence in supply chains and associated entities are able to positively engage with the supply chain. ensuring transaparancy is also a blockchain feature, and with the use of digitial communication, artificial intelligence, and industry 4.0, the information can be gathered, analysed and broadcasted to respective audience (saberi, et al., 2019). in addition to the five discussed sccs, all the other sccs with positive ri values are viable strategies and should be incorporated in oil supply chains of pakistan. however, baig et al./oper. res. eng. sci. theor. appl. 5(1) (2022) 69-89 82 in case of time, cost, or other constraints, priority should be given to the top five ranked strategies. the incorporation of top five sccs would enable pakistan’s oil supply chains to track demand, disruptions, variations and respond proactively to these challanges. it would also aid in effective monitoring of market and operational status, effective planning, and optimized distribution of resources. these benefits would lead to stability in the overall oil industry and government authorities would be able to design and implement improved policies. companies operating the in upstream and downstream of oscs would also be able to gain functional insights. thus, the supply chain data management support system, if integrated with the products, materials, suppliers, and governmental bodies, would provide numerous benefits. 5. conclusion the oil industry is one of the key determinants of the effective functioning of national economies. its smooth, timely, and efficient supply reinforces other sectors of the economy while interruptions in its services lead to deleterious effects on the overall economy. therefore, it is pertinent for government authorities and private sectors to design preemptive strategies that could identify and minimize the impact of vulnerabilities. this research study aimed to identify and prioritize various supply chain vulnerabilities that could occur within pakistan’s oil industry. subsequently, it identified and prioritized supply chain capabilities that can improve the risk mitigation profile of pakistan’s oil industry. this study employed a combination of fucom and fuzzy qfd, mcdm techniques, for analysis. fucom was used to rank the supply chain vulnerabilities while fuzzy qfd aided in prioritizing supply chain capabilities in order to preemptively deal with the vulnerabilities. a total of ten supply chain vulnerabilities and ten supply chain capabilities were identified from the literature and analyzed. results indicated that crude price instability, fuel price shocks, unpredictable demand, and information and communication disruptions are amongst the most important vulnerabilities. in order to reduce the impact of these vulnerabilities, oil supply chains should incorporate realtime information sharing systems, visibility, e-procurement, traceability, and transparency practices in every aspect of their operations. these strategies are associated with the blockchain technologies, that are gaining popularity day by day. pakistan is a developing country whose oil industry and its intermediaries are lagging in terms of financial performance. the mitigation of vulnerabilities would lead to relative stability, increase the confidence of investors, boost economic activities and thus improve the quality of life of citizens besides bolstering economic activities. this research study has few limitations as it relied only on qualitative judgements of experts and first hand numerical data was not incorporated. moreover, the experts panel was limited in geographical context, as all the experts had professional experience in a common country. in future studies the analysis can be improved by feasibility analysis of the recommended features, pilot studies relying on firsthand data, geographical expansion of experts’ panel, and the factors considered in this study can be further diversified. in addition, the comparative analysis with the 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multiple-case study, international journal of production economics, 224, 107548. https://doi.org/10.1016/j.ijpe.2019.107548 © 2022 by the authors. submitted for possible open access publication under the terms and conditions of the creative commons attribution (cc by) license (http://creativecommons.org/licenses/by/4.0/). https://doi.org/10.1016/j.enpol.2009.04.031 https://doi.org/10.1016/j.energy.2014.02.091 https://doi.org/10.1016/j.eneco.2013.03.014 https://doi.org/10.1016/j.jom.2007.01.009 https://doi.org/10.1016/j.ijpe.2019.107548 operational research in engineering sciences: theory and applications vol. 5, issue 2, 2022, pp. 28-60 issn: 2620-1607 eissn: 2620-1747 doi: https://doi.org/10.31181/oresta300622015b * corresponding author. unesbahalke@gmail.com (u. bahalke), n.hamta@arakut.ac.ir (n. hamta), amirreza.shojaeifard@studio.unibo.it (a.r. shojaeifard), m.alimoradi@autlook.de (m. alimoradi), kavosh2007ra@yahoo.com (s. rabiee) a new heuristic algorithm for multi vehicle routing problem with and/or-type precedence constraints and hard time windows unes bahalke 1, nima hamta 2*, amir reza shojaeifard 3, maryam alimoradi 4, samira rabiee 5 1 department of industrial engineering, iran university of science and technology, tehran, iran 2 department of mechanical engineering, arak university of technology, arak, iran 3 department of statistical sciences, school of economics and management, università di bologna, italy 4 baumann bildung und qualifizierung gmbh, daten­analyse und prozess­analyse, berlin, germany 5 department of industrial engineering, university of eyvanekey, eyvanekey, iran received: 18 february 2022 accepted: 14 march 2022 first online: 30 june 2022 research paper abstract: in this paper the classic known multi vehicle routing problem (vrp) is studied where classically several vehicles are set in a central depot, depending on the allocation strategy, each vehicle starts traveling to visit a set of nodes one after another to provide a service of gathering or delivering commodities with the aim of minimizing total traveling distances and costs. in the current paper, this classic problem is extended by new approach of and/or precedence constraints (pc) which have not been considered so far in the related literature. traditionally, pc have been considered in vrps as the 'and' type, where the immediate successor of a node cannot be visited until its predecessor nodes have reached their end of services. however by additional or-type precedence constraints, there are some interconnected nodes through the concept of or, therein no mandatory need to visit all predecessors of a successor node is acquired before it can be met, and only finishing a part of them can let to that particular node to get visited. this fact is widely observed in pickup and routing and distribution real cases where requisites for some specific products can be fulfilled via various potential suppliers. implementation of this type of pc graph in vrp is considered as the first introduction and application in the category of this problem. so, initially, the problem is mathematically formulated, then, due to problem’s np-hard complexity and allocationrouting characteristics, a decomposition-based technique is utilized to solve the a new heuristic algorithm for multi vehicle routing problem with and/or-type precedence constraints and hard time windows 29 problem. the procedure is based on recently enhanced benders’ decomposition approach named as branch and search algorithm, partitioning the original main problem into allocation and routing parts. unlike the previous version of benders algorithm, logic based, this newly promoted method acts in a way that at the allocation level, it generates partition of nodes with feasible solutions in lower routing level. the routing part itself has been enhanced by heuristics to cover and/or pc graphs. furthermore, the efficiency of the proposed solution procedure is tested and verified by running on several generated problems in different sizes and in the larger scale it is implemented on the real case of a distribution company in iran. key words: multi vehicle routing problem, and/or precedence constraints, hard time windows, branch and search algorithm 1. introduction the vehicle routing problem (vrp) is one of the most studied optimization problems and is considered with the optimal routes to be designed by a fleet of vehicles to serve a set of customers (final users) (golden, 2008). since many papers have been devoted to the development of vrp, many variants of this problem have been presented by now. for example, the capacitated vrp (cvrp), in which there is a homogeneous fleet of vehicles where the only constraint is the vehicle capacity, or the vrp with time windows (vrptw), where customers are served in a specified time interval and the schedule of the vehicle trips should be determined. in this paper the new approach of and/or precedence relation type has implemented in the body of the classic routing problem. this new implementation will have effects on the traveling schedules and sequences which will lead to changes in processing times and consequently will affect on total time and cost of the whole task assignment and scheduling of travels. the rest of the paper will provide the literature of the previous studies in vrp that will clarify the changes and the effects of this new contribution of and/or precedence relationships on the classic routing problems which is the first time introduced in vrps. recently, much attention has been paid to more complicated variants of vrp, which are closer to the practical distribution problems in the real world. particularly, these variants are characterized by multiple vehicle types, multiple trips, multiple depots or other operational concerns such as loading constraints (toth & vigo, 2002). for typical applications of this problem can mention to solid waste collection, school bus routing, dial-a-ride systems, street cleaning, transportation of handicapped persons/workers, routing of sellers/maintenance units. among the various surveys on the vrp in the book by toth and vigo (toth & vigo, 2002). in vrp, the obtained routes must meet operational constraints based on the nature of the transported goods, the quality of service level, and the characteristics of customers and vehicles. some typical operational constraints are the following: the load of each vehicle cannot exceed the vehicle capacity along each route; the customers can serve as delivery or collection of goods in a route, or both possibilities can exist; and customers can be served only in their time windows and the working times of associated vehicles’ drivers (coelho, 2016). bahalke et al./oper. res. eng. sci. theor. appl. 5(2) 2022 28-60 30 precedence constraints determines the order in which the customers should be served in a route. one type of precedence constraint needs that a given customer be served in the same route serving a given subset of other customers and that the customer must be visited before (or after) the customers belonging to the associated subset. this case is called pickup and delivery problems, wherein the routes can perform both the collection and delivery of goods, and the goods collected from the pickup customers must be carried to the corresponding delivery customers by the same vehicle. another type of precedence constraint imposes that if different types of customers are served in the same route, the order in which the customers are visited is fixed. this situation is called vrp with backhauls, wherein again, the routes can perform both the collection and delivery of goods (zhang, 2017). this paper considers an important variant of the vrp, in which a fleet of vehicles with different capacities and costs distributes the goods between depots and customers. the problem is known as the mixed fleet vrp or as the heterogeneous fleet vrp, firstly considered in a structured way in golden et al. (golden, 1984). vrp is one of the major problems in transportation systems that arose from traveling salesman problem (tsp). the goal of tsp is to find the shortest tour among a given set of cities which salesman visited them based on the traveling costs. the solution of feasible assembly sequence of tsp based on the and/or precedence can be found by restricting the next city visited by the salesman. this condition was called the constrained tsp (chen, 1990). then, all feasible assembly sequences can be generated based on this concept of the constrained tsp (chen, 1990, 1989, 1990). de fazio et al. considered a simplified model and generated the precedence knowledge based on a series of and/or rules (de fazio & whitney, 1987). möhring et al. presented efficient algorithms to solve the general model of and/or precedence constraints (möhring, 2004). donald et al. applied and/or precedence constraints to assign scheduling tasks according to minimal length schedules (gillies, 1995). and/or precedence constraints have been utilized for scheduling jobs by donald et al. then two heuristic algorithms were applied to schedule and/or task systems and minimize completion time. finally, the worst-case performance of these algorithms was analyzed by them (gillies, & liu, 1990). möhring applied a linear-time algorithm to deduce additional and/or precedence constraints (möhring, 2004). sanghyup et al. considered a flexible job-shop scheduling problems with and/or precedence constraints and developed genetic and tabu search algorithms to solve it (lee, 2012). one type of the most important problems in variant of the vrp is multi vehicle routing problem with time windows (mvrptw) that has been noticed by many researchers and distribution company managers, due to its wide application in urban transportation. in this area, dong et al. consider a multi-objective vrp with time windows and used a tissue p system based on evolutionary algorithm (dong, 2018). anggodo et al. used a genetic algorithm to optimize a multi-trip vrp with time windows on the problems of the tourist routes in banyuwangi (anggodo, 2017). ghoseiri et al. presented a new model and solution for multi-objective vrp with time windows. they used goal programming and genetic algorithm to solve it (ghoseiri & ghannadpour, 2010). chungyu et al. used a hybrid heuristic algorithm to solve multivehicle and multi-depot vehicle routing problem with time windows (chunyu & xiaobo, 2010). ariyani et al. used a hybrid method called ga-sa to solve a multi-trip vehicle routing problem with time windows (ariyani, 2018). https://www.sciencedirect.com/topics/engineering/genetic-algorithm a new heuristic algorithm for multi vehicle routing problem with and/or-type precedence constraints and hard time windows 31 the literature of exact method shows that the usage of exact method has been scarce. mvrptw with exact solution approaches can be found in the related literature rarely. for example, the branch and price algorithm was one of exact methods which hernandeza et al. used to solve multi-trip vrp with time windows. the presented method was the first exact solution approaches for this important problem (hernandeza, 2016). goel et al. considered a multi-objective vrp and solved it by improved multi ant colony algorithm (goel & maini, 2021). this method isn’t an exact solution approach. cӧmert et al. used a hierarchical approach consisting of two stages as cluster-first route-second to solve a vehicle routing problem with soft time window (cӧmert ,2017). cetin et al. surveyed a vrp with hard time windows wherein pickup and delivery is simultaneous (cetin & gencer, 2010). the branch and price algorithm was presented for multi-trip vrptw by hernandez et al. (hernandez, 2016). also, an exact hybrid method as combining a branch-price-and-cut (bpc) algorithm was used to solve the vrptw by alvarez et al. wherein deliverymen had been considered multiple (alvarez & munari, 2017). parragh et al. considered the truck and trailer vrptw and used a branch and price and adaptive large neighborhood search. a vehicle routing problem with a heterogeneous fleet and time windows was introduced by jiang et al. they used the tabu search algorithm to solve it. presented vrptw by miranda et al. considered stochastic travel and service time (jiang, 2014). a meta-heuristic method was applied to solve the vehicle routing problem with time windows by bouthillier et al. (le bouthillier & crainic,2005). nazif et al. applied a genetic algorithm to solve vehicle routing problem with time windows (nazif & lee, 2010). a multi objective vehicle routing problem with time windows has been considered by chiang & et al. they used an evolutionary algorithm to solve it (chiang & hsu, 2014). bae et al. surveyed a multidepot vehicle routing problem with time windows wherein delivery and installation vehicles was considered (bae & moon, 2016). wang considered a hybrid swarm optimization genetic algorithm to solve vehicle routing problem (wang, 2015). kumar et al. considered a time-dependent vrp with time windows and solved it using a genetic algorithm as one of meta-heuristic methods (kumar & panneerselvam, 2015). pierre et al. solved a vrp with time windows using a genetic algorithm (pierre & zakaria, 2016). koc et al. developed heterogeneous fleet vehicle routing problems with time windows then utilized a hybrid evolutionary algorithm to solve it (koc, 2015). dabia applied a branch and price as an exact method to solve a vehicle routing problem with time windows (dabia, 2013). azi et al. applied an exact algorithm and solved the vrptm wherein multiple use of vehicles had been considered (azi, 2010). mingozzi et al. presented an exact method to solve the multi-trip vehicle routing problem. their computational results indicated that the proposed exact algorithm can solve mtvrp (mingozzi, 2013). hernandez et al. solved the multi-trip vehicle routing problem with time windows by presentation a branch and price algorithm (hernandez, 2016). hernandez et al. presented an exact two-phase algorithm to solve the multi-trip vehicle routing problem with time windows and limited duration, wherein first phase considered possible ordered lists of clients based on the maximum trip duration criterion. and the second phase utilize a branch and price algorithm to generate and choose a best set of trips so that all customers are visited (hernandez, 2014). bahalke et al./oper. res. eng. sci. theor. appl. 5(2) 2022 28-60 32 the previous researches are summarized in table 1. by examining the frequency of methods presented in previous researches and the tendency to achieve an accurate and optimal solution, conducting research using exact methods will be felt. since recently several studies have focused on exact method, in this paper will apply a branch and search algorithm to solve mvrptw. table 1. a classification of vrp in the recent literature title of articles s in g le -t ri p v r p m u lt itr ip v r p solution method e x a ct m e th o d m e ta / h e u ri st ic m e th o d a new exact algorithm to solve the multi-trip vehicle routing problem with time windows and limited duration (hernandez, 2014)   branch-and-price algorithms for the solution of the multitrip vehicle routing problem with time windows (hernandez, 2016)   an exact algorithm for the multi-trip vehicle routing problem (mingozzi, 2013)   an exact algorithm for a vehicle routing problem with time windows and multiple use of vehicles (azi, 2010)   branch and price for the time-dependent vehicle routing problem with time windows (dabia, 2013)   a hybrid evolutionary algorithm for heterogeneous fleet vehicle routing problems with time windows (koc, 2015)   a knowledge-based evolutionary algorithm for the multi objective vehicle routing problem with time windows (chiang & hsu, 2014)   optimized crossover genetic algorithm for vehicle routing problem with time windows (nazif & lee, 2010)   a cooperative parallel meta-heuristic for the vehicle routing problem with time windows (le bouthillier & crainic, 2005)   the vehicle routing problem with hard time windows and stochastic travel and service time (miranda & conceição, 2016)   an exact hybrid method for the vehicle routing problem with time windows and multiple deliverymen (alvarez & munari, 2017)    vehicle routing problem with a heterogeneous fleet and time windows (jiang, 2014)   branch-and-price and adaptive large neighborhood search for the truck and trailer routing problem with time windows (2017)   branch-and-price algorithms for the solution of the multitrip vehicle routing problem with time windows (hernandez, 2016)   a new approach for solution of vehicle routing problem with hard time window (cӧmert ,2017)   a new heuristic algorithm for multi vehicle routing problem with and/or-type precedence constraints and hard time windows 33 title of articles s in g le -t ri p v r p m u lt itr ip v r p solution method e x a ct m e th o d m e ta / h e u ri st ic m e th o d improved multi-ant-colony algorithm for solving multiobjective vehicle routing problems (goel & maini, 2021)   branch-and-price algorithms for the solution of the multitrip vehicle routing problem with time windows (hernandeza, 2016)   hybrid genetic algorithms and simulated annealing for multi-trip vehicle routing problem with time windows (ariyani, 2018)   research on multi-vehicle and multi-depot vehicle routing problem with time windows electronic commerce (chunyu & xiaobo, 2010)   multi-objective vehicle routing problem with time windows using goal programming and genetic algorithm (ghoseiri & ghannadpour, 2010)   optimization of multi-trip vehicle routing problem with time windows using genetic algorithm (anggodo, 2017)   a tissue p system based evolutionary algorithm for multiobjective vrp with time windows (dong, 2018)   a time-dependent vehicle routing problem with time windows for e-commerce supplier site pickups using genetic algorithm (kumar & panneerselvam, 2015)   as we can see and study in the literature of vrp, we could not find any paper referring to implementation of and/or precedence constraints in the problem structure. however, we can see this type of relationships in the real situations and industries in which ignoring this fact will result in not optimized assignments and sequences that will lead to more costs to industry owners. in this study, this approach is introduced and it is tried to clarify these costs. due to the huge complexity of the problem, a hybrid general algorithm is designed and proposed to handle the problem. this paper is structured as follows. multi-trip vehicle routing problem with hard time windows (mvrptw) problem with and/or-type precedence constraints is explained in section 2. in section 3, developed algorithms to solve the considered problem is described in detail. section 4 presents the computational experiments in which the results obtained by proposed algorithm. finally, section 5 is devoted to conclusions and recommendations for future research. 2. problem description and mathematical formulation 2.1. and/or-mtvrptw in this section, the and/or multi-trip vehicle routing problem with hard time windows (and/or-mtvrptw) problem is described and formulated in a mixedbahalke et al./oper. res. eng. sci. theor. appl. 5(2) 2022 28-60 34 integer linear programming model. the problem is generally based on the well-known vehicle routing problem with hard time windows with more similarity to very familiar pickup and delivery type which has got many attentions in last recent years and there are huge numbers of accomplished and running competing studies, focusing on optimum node visit scheduling and permutations in the routes. one of the contributions of this paper is to applying a new form of pc arc into vrps, as an important factor in scheduling, which has resulted in more complex problems but with the better cost-oriented outcome. to the best of authors’ knowledge, this issue has not been considered so far in the history of vrps. this type of synchronization has existed in the real vrp problems, but in most cases, it’s denied or simplified by forcing it to change into an and-type pc arc. so, in order to make the benefit of considering and/or pc arcs, the main and the first point is to identify the synchronizations with or-type characteristics and making them group together with linked or-arcs. finally, implementing the developed mathematical model and algorithms would lead to time and cost benefits for companies to deal with this kind of problem. when the details of the problem are clarified as following, more details will be illustrated that how it will end up with better results. as mentioned before, the problem deals with traveling of a limited number of vehicles along with the geographically scattered nodes/customers in order to deliver products or serve a service. according to li & lim benchmark web page (li & lim, 2008), the first priority goal is to minimize the number of used vehicles and the second priority is to minimize the total traveled distances of vehicles. the position of each node is declared as a point on the xy − 𝑝𝑙𝑎𝑛𝑒 and the distances between nodes are calculated by using cartesian coordinates 𝐴(𝑥1, 𝑦1) and 𝐵(𝑥2, 𝑦2). all vehicles start their travels at the time zero on the first trip (𝑝1) from the depot (𝑛0) and are allowed to have several trips. each trip starts from the depot and ends to the depot. all vehicles are the same and are limited by maximum capacity restrictions which must not be exceeded in every trip of the particular vehicle. the program of traveling should be planned in a way that at the end of the travels, all nodes/customers must be visited once, not more, not less. each customer has its own time window for taking service, declared as [earlytime𝑖, latetime𝑖] which means that it would not accept service/delivery before or after its determined window. thus, if a vehicle reaches a node at a time before earlytime, it must wait until that time window opens. also, it is clear that received after 𝐿𝑎𝑡𝑒𝑇𝑖𝑚𝑒 is prohibited. the above descriptions are the basic conditions of a vrptw problem, except for the multi-trip part. the maximum allowed trip number for every vehicle had been fixed at one. but in this paper, in order to get more harmony with our considered problem, vehicles are allowed to do multi trips in which maximum of trip numbers are bounded. in the following, the considered and/or synchronization constraints are clarified. by application of and/or synchronization constraints, permutations would lead to change, consequently, every cost function which is derived by or dependent on sequences will be affected. there are two types of pc arcs that are assumed as and-type and or-type. the first type refers to classic precedence relationships defined as linked arc from 𝑖 to 𝑗 (𝑖 → 𝑗), in which 𝑖 is the precedence of 𝑗 that must be completely processed prior to 𝑗. a new heuristic algorithm for multi vehicle routing problem with and/or-type precedence constraints and hard time windows 35 in some new versions, the restriction on completely has been changed and limitations on finishing precedence task have been reduced. in general, in the literature of the vrps, only the first type has been considered. as it was mentioned, in some cases, various types of network graphs with different levels of restrictions have extended and formed. the most well-known type of pc is found in pickup and delivery vrps where nodes are linked as a pair by an and-type arc. the pickup node has the precedence role and the delivery node has the successor role in which the pickup one must be completely processed before reach the delivery one. in this paper, this type of synchronization is considered as an and-type pc arc where there is no restriction to put an and-type pair into a single same vehicle anymore. to better illustrate this difference, according to our considered problems, there are no pickup and delivery services, but still, there are a kind of limitations in which some specific nodes in the same route, should have been visited before their pairs. so, there is no obligation to put an and-type pair into a single same vehicle and they are free to be serviced individually by any vehicle. but if both paired nodes determined to be visited by the same vehicle, pc must be implemented and it would make them met the precedence relationship constraint. this approach would lead to higher complexity of the problem. in fact, when the problem consists of n nodes and k vehicles, where all nodes are paired, it deals with the allocation of 𝑁 ⁄ 2 nodes into 𝐾 vehicles. however, by eliminating the same vehicle restriction of paired nodes, by allocating n nodes into k vehicles, the complexity of the problem will be doubled. furthermore, the second or-type pc arc has also considered in this study where it is counted as the first implementation of or-type arc in vrps. this pc arc is implemented when starting a process is dependent to other processes. it is defined for tasks with multiple predecessors where finishing of only one predecessor would let the successor could start its process. in many real industrial cases, because of the simplicity or due to lack of knowledge and awareness of the subject, they were mistakenly considered as and-type arcs. forcing and restricting a set of processes into limited options which were led to detrimental consequences, losing potential better scheduling alternatives. for an example, consider a subset of nodes 𝐴, 𝐵 and 𝐶 in a routing problem with 𝑁 nodes and node 𝐶 as a successor linked to nodes 𝐴 and 𝐵 by and-type arcs. assume that in a practical condition, visitation of node 𝐶 could start its process by either completion of service to 𝐴 or 𝐵. besides, assume that the distance between 𝐵 and 𝐶 is relatively large compared to the distance between 𝐴 and 𝐶. so, according to the classic formation of and arcs, both nodes of 𝐴 and 𝐵 must be visited prior to 𝐶 even if its final permutation lead to worse traveling costs. but if both of them were initially defined as or-type, the order of serving node 𝐵 could be moved to any further sequence after visiting node 𝐶. thus, by these newly opened alternatives they could have resulted in at least better outcomes in terms of traveling costs. with all the above interpretations, it is now easier to understand that how would consider the or-type pc arcs in a vehicle routing problem could bring benefit to a company. it can widen the alternatives by providing more open space with possible better options for the decision makers. this can lead to more efficient plans with better outcomes. in the following, the introduced problem is mathematically modeled used notations are declared. bahalke et al./oper. res. eng. sci. theor. appl. 5(2) 2022 28-60 36 2.2. mixed-integer mathematical model in this section the problem is mathematically formulated and the used notations and variables are declared. further assumptions of the problem are assumed as following: • there are 𝑁 customer nodes plus the node depot as node 0. • each customer has a demand that must be supplied by the unique vehicle. • each customer must be visited only once. • either and or or-type arcs are implemented when linked pairs assigned to be visited by the same vehicle. • each node has a fixed value of service time. • no stochastic parameter or input data is considered. • preemption or interruption is not allowed • vehicles’ speeds are equal to one unit. • every route is traveled with single vehicle and includes multi trips each starting from the depot and ending to the depot. following introduces notations and their corresponding definitions: 𝑖, 𝑗, 𝑡 indexes for all nodes 𝑘, 𝑠, 𝑟 index of vehicle 𝐾 maximum number of available vehicles 𝑝, 𝑛 index of a trip in a route 𝑁 number of all nodes 𝐷𝑖𝑠𝑖 𝑗 distance between node 𝑖 and 𝑗 𝐷𝑖 demand of node 𝑖 𝐶𝑜𝑠𝑡 cost of using a vehicle 𝐶𝑎𝑝𝑎𝑐𝑖𝑡𝑦 maximum capacity of a vehicle 𝑃 maximum number of allowed trips service𝑖 service time on node 𝑖 earlytime𝑖 lower bound for time window of node 𝑖. latetime𝑖 upper bound for time window of node 𝑖. 𝑉𝑘 a binary variable indicating use of vehicle 𝑘. 𝑥𝑖 𝑗 𝑛 𝑘 a binary decision variable indicates visit of node 𝑗 immediately after node 𝑖 at trip 𝑛 by vehicle 𝑘. 𝑧𝑖 𝑛 𝑘 a binary variable indicating assignment of node 𝑖 on trip 𝑛 by vehicle 𝑘. 𝑆𝑡𝑖 𝑘 start time of servicing to node 𝑖 by vehicle 𝑘. 𝐶𝑜𝑛 𝑘 reach time to node depot after finishing trip 𝑛 by vehicle 𝑘. 𝑦𝑖 𝑗 𝑘 a binary variable that indicates if visiting of node 𝑖 occurred earlier than node 𝑗 by vehicle 𝑘. the mathematical model is developed as follows: a new heuristic algorithm for multi vehicle routing problem with and/or-type precedence constraints and hard time windows 37 minimize 𝑂𝑏𝑗 = ∑ 𝑥𝑖 𝑗 𝑛 𝑘 ∙ 𝑑𝑖𝑠𝑖 𝑗 𝑖 𝑗 𝑛 𝑘 + ∑ 𝑉𝑘 ∙ 𝑐𝑜𝑠𝑡 𝐾 𝑘=1 (1) 𝑉𝑘 ≥ 𝑧0 1 𝑘 (2) 𝑉𝑘 ≥ 𝑉𝑘+1 (3) 𝑧𝑖 𝑛 𝑘 = ∑ 𝑥𝑖 𝑗 𝑛 𝑘 𝑗 = 1 𝑓𝑜𝑟 𝑎𝑙𝑙 𝑖 , 𝑛, 𝑘 (4) 𝑧𝑗 𝑛 𝑘 = ∑ 𝑥𝑖 𝑗 𝑛 𝑘 𝑖 = 1 𝑓𝑜𝑟 𝑎𝑙𝑙 𝑗, 𝑛, 𝑘 (5) 𝑦𝑖 𝑗 𝑘 + 𝑦𝑗 𝑖 𝑘 ≥ [(∑ 𝑧𝑖 𝑛 𝑘 𝑛 + ∑ 𝑧𝑗 𝑛 𝑘 𝑛 ) − 2] ∙ bigm + 1 𝑖 ≠ 𝑗 ≠ 0 (6) 𝑦𝑖 𝑗 𝑘 + 𝑦𝑗 𝑖 𝑘 ≤ 1 𝑓𝑜𝑟 𝑎𝑙𝑙 𝑖 ≠ 0, 𝑗 ≠ 0, 𝑘 (7) ∑ 𝑦𝑖 𝑗 𝑟 + 𝑦𝑗 𝑖 𝑟 𝑟 ≤ [2 − (∑ 𝑧𝑖 𝑛 𝑘 𝑛 + ∑ 𝑧𝑗 𝑛 𝑠 𝑛 )] ∙ bigm 𝑖 ≠ 𝑗 ≠ 0 (8) 𝑆𝑡𝑗 𝑘 ≥ 𝑆𝑡𝑖 𝑘 + servic𝑖 + (𝑦𝑖 𝑗 𝑘 − 1) ∙ bigm (9) ∑ 𝑦𝑖 𝑗 𝑘 𝑖 ∈ 𝑜𝑟⃗⃗⃗⃗ 𝑗 ≥ [∑(𝑧𝑡 𝑛 𝑘 + 𝑧𝑗 𝑛 𝑘) 𝑛 ] − 1 𝑓𝑜𝑟 𝑎𝑙𝑙 𝑡 𝑂𝑅⃗⃗⃗⃗ ⃗ 𝑗, (10) ∑ 𝐷𝑖 ∙ 𝑧𝑖 𝑛 𝑘 𝑖 ≤ 𝐶𝑎𝑝𝑎𝑐𝑖𝑡𝑦 (11) 𝑆𝑡𝑗 𝑘 ≥ 𝑆𝑡𝑖 𝑘 + servic𝑖 + 𝐷𝑖𝑠𝑖 𝑗 + (𝑥𝑖 𝑗 𝑛 𝑘 − 1) ∙ bigm (12) ∑ 𝑥𝑖 𝑗 𝑛 𝑘 𝑗 − ∑ 𝑥𝑗 𝑖 𝑛 𝑘 𝑗 = 0 𝑓𝑜𝑟 𝑖 = {0,1,2, . . , 𝑁} (13) 𝑆𝑡𝑗 𝑘 ≥ 𝑆𝑡𝑖 𝑘 + service𝑖 𝑓𝑜𝑟 𝑖 ∈ 𝑖 𝐴𝑁𝐷⃗⃗⃗⃗⃗⃗⃗⃗ ⃗ 𝑗 (14) 𝐶𝑜𝑛 𝑘 ≥ 𝑆𝑡𝑗 𝑘 + service𝑗 + 𝑑𝑖𝑠𝑗 0 + (𝑥𝑗 0 𝑛 𝑘 − 1) ∙ bigm (15) 𝑆𝑡𝑗 𝑘 ≥ 𝐶𝑜𝑛 𝑘 + 𝑑𝑖𝑠0 𝑗 + (𝑥0 𝑗 𝑛+1 𝑘 − 1) ∙ bigm (16) bahalke et al./oper. res. eng. sci. theor. appl. 5(2) 2022 28-60 38 𝑆𝑡𝑖 𝑘 ≥ earlytime𝑖 (17) 𝑆𝑡𝑖 𝑘 ≤ latetime𝑖 (18) equation (1) presents the objective function of minimizing travel cost which includes traveling distance related costs and vehicles using costs. by giving a very big positive value to 𝑐𝑜𝑠𝑡, model gives a first priority to minimize the total number of used vehicles. constraints (2) and (3) show the usage of vehicle 𝑘. equations (4) and (5) indicate assignment of nodes 𝑖 and 𝑗 to route 𝑘. constraints (6), (7) and (8) indicate that if two nodes are in the same route of a vehicle, variable 𝑦 will take value and one node will be serviced sooner and one another, later. in other words, if two individual nodes are assigned to two different routes, no sequence relationship is defined between those two. constraint (9) synchs starting times to visiting orders. constraint (10) is developed in order to declare or-type precedence relationship. it defines that if node 𝑗 is linked by a set of or-type predecessors, servicing of only one member of them, those who are in the same route with node 𝑗, is adequate to let the successor 𝑗 to be visited. constraint (11) limits the vehicle’s capacity. constraint (12) assigns starting times for nodes in a route which are visited consecutively. equation (13) declares that every node in a route has one input and one output. constraint (14) shows and-type relationships. it is clear that every node 𝑖 which is paired with a successor node 𝑗 in a route 𝑘 must be visited prior to 𝑗. constraints (15) and (16) make a link between completion time of a trip in a route and start time of the first customer in next trip. at the end, constraints (17) and (18) implement the hard time window restrictions. 3. developed algorithms 3.1. general scheme in this section, our developed algorithm is introduced. the applied algorithm’s general scheme is completely new and it is based on the integration of rules, random search and a new intelligent large neighborhood searching technique which is entirely fit to vrp problems. also, in the inner layers of the algorithm, the latest heuristic algorithms’ key implementations, well-known meta-heuristics like simulated annealing and tabu search are also considered. moreover, in order to make use of genetic algorithms’ wide diversity characteristics, some solution pools are created to avoid losing elite solutions. the challenging part in the vrp problems with hard time windows is the feasibility check. in many studies of the literature, the complexity of problem makes researchers to use mathematical models to check the feasibility of every generated solution. since it consumes the most part of computational time and it will become more complex by adding and/or precedence arcs, the performance of any presented algorithm will be affected. therefore to overcome this challenge, a new solution has been proposed in this paper, and the use of mathematical models has been greatly limited, and rulebased techniques have been used instead. entire process of the developed algorithm is presented as follows. the general procedure of the algorithm starts by a heuristic rule or_enh_heu which generates a feasible solution, considering two main factors of using maximum a new heuristic algorithm for multi vehicle routing problem with and/or-type precedence constraints and hard time windows 39 capacity and minimum traveling costs. then, the obtained solution goes through two different techniques called parent and child in order to eliminate vehicles those are recognized as bad allocations. next, the remained bad allocations’ routes and their belonging nodes are eliminated from the solution and are transferred to stack. afterwards, some techniques are applied along the algorithm in order to add stacked nodes as rule-based adding, randomly adding and randomly substitutions with the aim of reconstructing a complete solution with minimum cost. hence, according to the strategy beyond the minimizing vehicles, it is called drop and add. furthermore, the algorithm deals with two searching techniques, the local search and the intelligent large neighborhood search called intlllns from now on. the local search itself includes two different perturbation methods mov_perturb and rep_perturb where tabu movements and simulated annealing approaches are implemented there. the intlllns procedure is completely novel and acts based on the characteristics of the nodes in the same route. it evaluates their geographical positions and also creates time zones according to same routed nodes’ early and late times. then the large numbers of intelligent movements or replacements are done based on the initial evaluations. one of the useful advantages of the developed algorithm is its solution pool which is active any time a solution is generated. it determines whether a new feasible solution be admitted to the pool or not. this option helps to avoid losing diversity and also keep holding elite solutions. another advantage of this algorithm is that vehicles can always be removed along the local search and intlllns. this is possible due to the elimination approach that is embedded in all stages of the algorithm. by means of this approach while a feasible solution with fewer vehicles is produced, then there is no chance to get back to former worse allocations. this obligation is implemented due to the high priority of minimizing number of vehicles. additionally, at the end of every iteration, the child procedure is performed to be certain about the minimum possible number of vehicles. it is clear that child would not guarantee optimum number of vehicles but it does some attempts to minimize it as much as possible based on the rules, allocations and sequences provided by the whole process. the proposed algorithm is named as hybrid and/or intelligent large neighborhood search algorithm called as haor_intlnsa. its’ general scheme is interpreted in the following flowchart in figure 1. bahalke et al./oper. res. eng. sci. theor. appl. 5(2) 2022 28-60 40 read_data calculate_node_distances format or_arcs format and_arcs or_enh_heu parent child add_nodes_to_stack eliminate_empty_vehicles local_search (ls) is_stack_empty? add_to_solution _pool yes rand_add_from_stack rand_subs_by_stack is_stack_empty? no end_ls? yes intlllns yes no is_stack_empty? rand_add_from_stack rand_subs_by_stack yes add_vehicle no add_to_solution_pool is_stack_empty? add_stack _all no child yes child no figure 1. haor_intlnsa flowchart the pseudocode of the main function of the haor_intlnsa is presented in figure 2. a new heuristic algorithm for multi vehicle routing problem with and/or-type precedence constraints and hard time windows 41 main () { read_data(); calculate_distances(); format_arcs(); or_enh_heu(); parent(); child(); add_to_stack(); new_cycle: local_search(){ int ls_iteration = 0; do { int rand_number = rand (); if (rand_number < perturb_orient_percentage) { type_1_perturb(); } else { type_2_perturb(); } if (is_stack_empty) { sort_pool(); consider_new_solution(); } else{ rand_add_from_stack(); rand_subs_by_stack(); } ls_iteration++; } while (ls_iteration < max_ls_iter); } //local search end; intlllns () { int lns_iteration = 0; do () { int lns_rand_number = rand (); if (lns_rand_number < intlllns_orient_percentage) { type_1_intlllns(); } else { type_2_intlllns(); } if (is_stack_empty) { sort_pool(); consider_new_solution(); } else { rand_add_from_stack(); rand_subs_by_stack(); } lns_iteration++; }while (lns_iteration < max_ls_iter); } // intlllns end; if (is_stack_empty) { if (is_terminal_condition_met){ sort_pool(); choose_best_pool_member(); } //algorithm finishes here else { goto new_cycle; } } else { add_vehicle(); //try to add all stacks into all available routes add_stack_to_all() { one_by_one_add(); if (succeed_adding) { sort_pool(); consider_new_solution(); goto new_cycle; } } } //end of else; } //main end; figure 2. haor_intlnsa pseudocode bahalke et al./oper. res. eng. sci. theor. appl. 5(2) 2022 28-60 42 3.2. or_enh_heu haor_intlnsa starts by a heuristic rule which at the end of its process, it generates one feasible solution. this solution is constructed with focus on late times as first priority and then traveling distance as second priority. or_enh_heu starts assignments of nodes to routes through a step-by-step procedure. at each step a set of candidates (𝐶𝑎𝑛𝑑𝑖𝑑𝑎𝑡𝑒𝑆𝑒𝑡) is setup, and then every individual node from this set is tested by adding to current solution which its feasibility is evaluated through a rulebased feasibility checking process. candidates who successfully pass the evaluation stage will be included in the final set of candidates called as 𝑁𝑜𝑚𝑖𝑛𝑒𝑒𝑆𝑒𝑡. at final step, the nearest node to the last positioned node in the current solution is admitted as new assignment. finally, the 𝐶𝑎𝑛𝑑𝑖𝑑𝑒𝑆𝑒𝑡 are updated and all members in 𝑁𝑜𝑚𝑖𝑛𝑒𝑒𝑆𝑒𝑡 are eliminated. this procedure continues until all nodes have been assigned to routes. at the beginning of the rule, number of input or-type arcs of each node 𝑖 (if any) is held in variable 𝑂𝑅𝑝𝑟𝑒[𝑖]. then the 𝐶𝑎𝑛𝑑𝑖𝑑𝑎𝑡𝑒𝑆𝑒𝑡 is reconstructed at the beginning of assignment for every new route, considering 𝑂𝑅𝑝𝑟𝑒[𝑖] in which all nodes with no input or arc (𝑂𝑅𝑝𝑟𝑒[𝑖] == 0) will be included in the candidateset. the reason beyond this action is to give more option and chance for or-predecessor nodes to assign. because fixing an or-type successor node before any of its predecessors in a route would not let any of its predecessors to assign to that route. step 1: declare variables for all 𝑖 𝑂𝑅𝑝𝑟𝑒[𝑖] = 0; declare variable ℎ𝑜𝑙𝑑𝑒𝑟 = 0 ; declare 𝑉𝑒ℎ𝑖𝑐𝑙𝑒𝑁𝑢𝑚𝑏𝑒𝑟 = 0 ; for all 𝑖 ≠ 0 declare 𝑖𝑠𝑉𝑖𝑠𝑖𝑡𝑒𝑑[𝑖] = 0 ; step 2: for all 𝑖, if (𝑂𝑅𝑝𝑟𝑒[𝑖] == 0 &&𝑖𝑠𝑉𝑖𝑠𝑖𝑡𝑒𝑑[𝑖] == 0) 𝑇ℎ𝑒𝑛 add 𝑖 to candidateset ; step 3: 𝐢𝐟 ( 𝐹𝑒𝑎𝑠𝑖𝑏𝑖𝑙𝑖𝑡𝑦𝐶ℎ𝑒𝑐𝑘 (𝐶𝑎𝑛𝑑𝑖𝑑𝑎𝑡𝑒𝑆𝑒𝑡(𝑖) ) == 𝐭𝐫𝐮𝐞 )𝑡ℎ𝑒𝑛 add 𝑖 to nomineeset ; 𝐢𝐟 (𝐶𝑎𝑛𝑑𝑖𝑑𝑎𝑡𝑒𝑆𝑒𝑡 == ∅) 𝑡ℎ𝑒𝑛 𝐠𝐨𝐭𝐨 step 6; step 4: 𝐢𝐟 (𝐶𝑎𝑛𝑑𝑖𝑑𝑎𝑡𝑒𝑆𝑒𝑡 ≠ ∅ &&𝑁𝑜𝑚𝑖𝑛𝑒𝑒𝑆𝑒𝑡 == ∅) 𝑡ℎ𝑒𝑛 {𝑉𝑒ℎ𝑖𝑐𝑙𝑒𝑁𝑢𝑚𝑏𝑒𝑟 + +; ℎ𝑜𝑙𝑑𝑒𝑟 = 0; 𝐶𝑎𝑛𝑑𝑖𝑑𝑎𝑡𝑒𝑆𝑒𝑡 = ∅ ; 𝐠𝐨𝐭𝐨 step 2; } step 5: 𝐢𝐟 ( min distance == 𝑑𝑖𝑠[ℎ𝑜𝑙𝑑𝑒𝑟][𝑁𝑜𝑚𝑖𝑛𝑒𝑒𝑆𝑒𝑡(𝑖)]) 𝑡ℎ𝑒𝑛 {ℎ𝑜𝑙𝑑𝑒𝑟 = 𝑖 ; 𝑖𝑠𝑉𝑖𝑠𝑖𝑡𝑒𝑑[𝑖] = 1; } for all 𝑖 𝐢𝐟 (𝑝𝑐 (ℎ𝑜𝑙𝑑𝑒𝑟 → 𝑖) == 𝑂𝑅𝑇𝑦𝑝𝑒) 𝑡ℎ𝑒𝑛 { 𝑂𝑅𝑝𝑟𝑒[𝑖] − −; 𝐢𝐟 (𝑖𝑠𝑉𝑖𝑠𝑖𝑡𝑒𝑑[𝑖] == 0)add 𝑖 to 𝐶𝑎𝑛𝑑𝑖𝑑𝑎𝑡𝑒𝑆𝑒𝑡 ; } for all 𝑖 𝐢𝐟 (𝑝𝑐 (𝑖 → ℎ𝑜𝑙𝑑𝑒𝑟 ) == 𝐴𝑁𝐷𝑇𝑦𝑝𝑒) 𝑡ℎ𝑒𝑛 {remove 𝑖 from 𝑁𝑜𝑚𝑖𝑛𝑒𝑒𝑆𝑒𝑡 ; 𝐠𝐨𝐭𝐨 step 2; } step 6: end; figure 3. pseudocode of or_enh_heu after each successful assignment, 𝐶𝑎𝑛𝑑𝑖𝑑𝑎𝑡𝑒𝑆𝑒𝑡 should be updated where newly assigned node will be eliminated. then it will be checked that whether the assigned node is an and-type successor or not. if it is and-type successor, then its paired predecessor will be removed from 𝐶𝑎𝑛𝑑𝑖𝑑𝑎𝑡𝑒𝑆𝑒𝑡. also, if assigned node is an or-type predecessor of node 𝑖, then 𝑂𝑅𝑝𝑟𝑒[𝑖] = 𝑂𝑅𝑝𝑟𝑒[𝑖] − 1. also, node 𝑖 will be added to a new heuristic algorithm for multi vehicle routing problem with and/or-type precedence constraints and hard time windows 43 𝐶𝑎𝑛𝑑𝑖𝑑𝑎𝑡𝑒𝑆𝑒𝑡 for the current route since one of its predecessors has been finished already in that route. finally, the general procedure of or_enh_heu rule is interpreted as pseudocode in figure 3. one of the advantages of haor_intlnsa is the application of a rule-based feasibility check since it takes much less computational time than the used application of mathematical models. the procedure of this rule is declared in following section. 3.3. rule-based feasibility check according to the described procedure of generating feasible solutions, the rule is doing core job of creating complete route. whenever the feasibility of a node is checked, the rule determines the visiting order of all allocated nodes in the route. then, it checks feasibility in the aspects of and/or precedence relationships, number of trips and time windows. next, it returns constructed route along with a true or false value in the case of feasibility or infeasibility. the core logic of this rule is based on the giving priority to nodes with earlier late times. this simple but efficient rule is implemented repeatedly in classic vrp and single machine scheduling problems dealing with due dates (hu, 2018),( gordon, 1997) and its efficiency is proved already. due to the extended aspects of the inhanded problem and its high complexity, simple sorting of nodes would not be a costefficient work, because it might be losing a high number of feasible solutions due to its weak created order of visits in the route. so, all assigned nodes in a specific route are determined in a permutation of visiting order one by one where in each step, noted constraints are tested. since the rule checks all aspects of feasibility, it will not lead to return a true feasible feedback in contrast with mathematical model, but it is still possible to lose some mathematically feasible solutions. regarding this issue, two conditions are defined that if rule falls the route into the following two categories, it will not return directly a decision on feasibility. the first one is a condition in which all nodes are visited in their time windows and all precedence constraints are met but the number of trips exceeds the predetermined upper bound. in this case, the considered assignment is sent to check by mathematical model and the model’s feedback is referred as feasibility status. the second one refers to a condition in which the number of trips is in bound and precedence relations are met but time window restrictions are violated. in this situation, first, feasibility of time window restrictions is checked under a completely hypothetical condition without capacity constraints with one trip. if an assignment successfully passes feasibility check, then a shifting method is applied in order to check possible feasibility of initial formed route. it acts in a way that if forward trip consists of lower capacity usage than former trip, shifting replaces last ordered node from former trip into forward trip and then it checks if this action lead to feasible route. shifting iterates until find a feasible route but if all possible shifting replacements are done and no feasible route is found, then rule returns final false decision of feasibility. the initial application of the simple rule-based feasibility check was led to weak results where it was losing lots of feasible solutions. but by evaluations of differences between mathematical and rule’s created routes, it’s found that embedding of above introduced novel revising methods could bring a significant improvement. so, one of bahalke et al./oper. res. eng. sci. theor. appl. 5(2) 2022 28-60 44 the most important weaknesses in the application of rule-based feasibility check has been largely eliminated. since computational time of an algorithm is one of the most prominent factors on deciding an algorithm, using rule-based methods will considerably reduce computational time. 3.4. removing inefficient routes after creating a feasible solution, haor_intlnsa sets up the routes in order to drop those vehicles with low consisting nodes. by dropping the vehicles, their belonging nodes are transferred to stack and they remain there until find a good assignment to re-enter them into the solution. before this elimination occurs, the algorithm does some attempts to move the nodes which are belonged to the targeted routes, into the rest. it should be noted that the targeted routes are diagnosed by means of an input parameter, 𝑚𝑒𝑎𝑛𝑇ℎ𝑟𝑒𝑠ℎ𝑜𝑙𝑑, indicating a level for the number of nodes in a route. thus, all routes under the 𝑚𝑒𝑎𝑛𝑇ℎ𝑟𝑒𝑠ℎ𝑜𝑙𝑑 are included in the target set. the algorithm continues with two steps before that elimination happens. the first step is called 𝑃𝑎𝑟𝑒𝑛𝑡 in which for all nodes in targeted routes, their chances of assignment in the rest routes are tested. this checking for possible movement starts from the nearest route and ends to the farthest one and in the meantime anywhere it leads to a feasible solution, checking for that node ends and the movement is done. after ending 𝑃𝑎𝑟𝑒𝑛𝑡, there might still some nodes remain in the targeted routes, so, the algorithm continues with a uniting approach in step 2 called 𝐶ℎ𝑖𝑙𝑑. it tries to unite sporadic nodes. for this aim, the 𝐶ℎ𝑖𝑙𝑑 iteratively moves nodes into other feasible routes among the targeted routes. these movements repeat until no better movements are possible in the aspect of the number of empty routes. after the above steps, the targeted routes will be updated since it might some changes in the number of nodes in routes have occurred during 𝑃𝑎𝑟𝑒𝑛𝑡 and 𝐶ℎ𝑖𝑙𝑑. then, newly diagnosed targeted routes are eliminated and their belonging nodes are transferred to stack in a process called 𝐴𝑑𝑑𝑇𝑜𝑆𝑡𝑎𝑐𝑘. by ending the process of elimination and 𝐴𝑑𝑑𝑇𝑜𝑆𝑡𝑎𝑐𝑘, the algorithm enters into the cycle part, starting with a local search approach to find neighbors with possible better solutions. in this paper, two types of perturbation strategies are applied which are defined and described in the following section. 3.5. local search in this paper, two types of perturbation approaches are implemented as local search. the first type is a well-known perturbation method which has used consecutively in the literature. in this type, two randomly selected nodes from the randomly selected route are marked in order to be replaced by two randomly selected nodes of the randomly destined route. if this replacement ends up with an acceptable result, it will be done but if not, then the action is considered tabu. this tabu consideration might use memory, however it avoids wasting computational time by blocking repetition. furthermore, in order to widen the search space, the same strategy as simulated annealing is implemented. the sum of travel cost of the route of origin and the destination route, before replacement, is compared a new heuristic algorithm for multi vehicle routing problem with and/or-type precedence constraints and hard time windows 45 to the sum of costs for both after replacement. by setting up an acceptable range, the resulted replacements might be done even though the latter costs are worse than the initial ones. this range has determined by an input parameter called 𝑆𝑎𝑅𝑎𝑡𝑒, by a value bigger than 1. the second type of perturbation is a novel movement approach that moves nodes instead of replacement. the logic of this perturbation is to consider the elimination of vehicles as much as possible. when a movement perturbation occurs, that selected node might be the last member of that route, so by transferring it, the origin vehicle will be useless and automatically will be removed from the solution. it should be noted that all movements during the algorithm proceeding have arranged in a way that only occurs between routes that are not empty. in order to move a single node to another active route, the feasibility of this movement and also the resulted cost difference between the former and after movement, will be considered. although the route of origin is selected randomly, the destination route is not. the movement of that particular selected node goes through a complete test in all other active routes. at last, the elite route which has led to the highest improvement in cost will be selected to transfer. the same tabu and 𝑆𝑎𝑅𝑎𝑡𝑒 related strategies, which are used in the first type, are considered in this type of perturbation, too. every time a perturbation occurs and a complete feasible solution is produced, it is checked for entering into the provided solution pool. the pool is embedded with the aim of storing elite solutions. it is limited in the size which is determined by a 𝑝𝑜𝑜𝑙𝑆𝑖𝑧𝑒 parameter. a solution should meet two conditions to get into the pool. first, its cost should be different from those solutions which are already stored in the pool. besides, its cost should be less than the last member of the pool. next, if this admission process is successful, then the whole pool will be re-sorted based on solutions’ cost values. this whole procedure is called 𝐶𝑜𝑛𝑠𝑖𝑑𝑒𝑟𝑁𝑒𝑤𝐴𝑙𝑙𝑜𝑐𝑎𝑡𝑖𝑜𝑛. finally, because there are probabilities of resulting with some empty vehicles, the final solution of this step is reconstructed and all routes are rearranged, with a new label of numbers, in order to completely remove those empty routes which are remained between active ones. 3.6. add from stack there are three kinds of methods, which are developed in order to pick nodes from the stack and add them into solutions, or to replace them. these picking efforts are embedded at different parts of the algorithm, during, and after perturbing, during, before, and after intelligent lns and after adding a new vehicle. the first type iteratively selects a random node from the stack and tries to embed it into a randomly selected route. this type is called 𝑎𝑑𝑑𝐹𝑟𝑜𝑚𝑆𝑡𝑎𝑐𝑘. the second type which is called 𝑆𝑢𝑏𝑆𝑡𝑎𝑐𝑘 , attempts to substitute a random node of a random route with a random node of the stack. it does this replacement if that substitution leads to a better cost function. at last, the type 𝑆𝑡𝑎𝑐𝑘𝑇𝑜𝐴𝑙𝑙 tries to vacate the stack pool, by testing every individual member of the stack into all routes. these three methods are partially embedded inside the local search as well as intlllns. bahalke et al./oper. res. eng. sci. theor. appl. 5(2) 2022 28-60 46 in search-based optimization algorithms, it is logical to design some techniques to diversify the search space due to avoiding trapping in local optima. in this paper, a novel procedure is developed which its details are clarified in the next section. 3.7. intelligent large neighborhood search in many of large neighborhood search algorithms, it is usual to see big changes at once since a large group of individuals are decided randomly to alteration. in the and/or mtvrptw there are restrictions in which group random alterations would lead to high number of infeasibilities due to two types of precedence relationships, decisive time windows and capacity of the vehicles in trips. although this type of lns has seen in the literature of pdptw, decision to do randomly large perturbations would not be an adroit action. for this reason, in this paper, two approaches are developed to perform lns. both of them are designed based on the problem’s main characteristics. they will remove a bunch of infeasible or inefficient moves. instead, they will act in an intelligent way by setting up an elite group. this group consists of nodes that have a high probability to fit in destined routes, which might lead to better solutions. the approach focuses on the geographical position of nodes in a route on xy-plane. at the first step, it gathers information of each route’s traveling costs and defines an index as 𝑐𝑜𝑠𝑡𝐼𝑛𝑑𝑒𝑥 = 𝑡𝑟𝑎𝑣𝑒𝑙𝐶𝑜𝑠𝑡𝑘 𝑁𝑢𝑚𝑏𝑒𝑟𝑂𝑓𝑁𝑜𝑑𝑒𝑠𝑘 for all routes of a solution. lower values of this index, indicates that the corresponding vehicle of the route travels reasonable distance compared to the number of customers it must visit. consequently, the higher of this index, shows inappropriate allocation, in which the vehicle might be able to carry out more customer visitations along that traveled distance. according to this defined index, all routes of a solution are sorted from high values to low. next, random nodes from a set of candidates are selected to transfer to those routes which are at the top of the sorted list with high values of index. for setting a group of candidates, the proposed lns acts in an intelligent way by finding a set of nodes which are seem to be appropriate choices to transfer to specific routes. due to this action, many of the random choices and vain attempts with low probability of success perturbation will be eliminated. in order to clarify this action, see figure 4. it is a sample of a route for a vehicle which should visit 6 customers in two trips. in this figure, it is clear that nodes a and b would not be appropriate choices for entering to route 𝑘 concerning the aspect of traveling costs. on the other side, nodes c and d seems to be more fit. in order to discern and distinguishing these set of appropriate and inappropriate nodes, intlllns performs a rule. based on this rule, for each route a center point in xy-plane is calculated as 𝑋𝑐𝑒𝑛𝑡𝑒𝑟𝑘= ∑ 𝑋𝑖 𝑖∈𝑘 𝑁𝑢𝑚𝑏𝑒𝑟𝑂𝑓𝑁𝑜𝑑𝑒𝑠𝑘 , 𝑌𝑐𝑒𝑛𝑡𝑒𝑟𝑘= ∑ 𝑌𝑖 𝑖∈𝑘 𝑁𝑢𝑚𝑏𝑒𝑟𝑂𝑓𝑁𝑜𝑑𝑒𝑠𝑘 , then by means of this center point and the radius equal to 𝑑𝑖𝑠[𝑐𝑒𝑛𝑡𝑒𝑟][𝑓𝑎𝑟𝑡ℎ𝑒𝑠𝑡 𝑛𝑜𝑑𝑒 𝑖𝑛 𝑘], a circular zone is determined. every node inside this zone is included in the candidate set of that particular route, as seen in figure 4. a new heuristic algorithm for multi vehicle routing problem with and/or-type precedence constraints and hard time windows 47 as aforementioned, first approach of intlllns considers cost indexes and it tries to add nodes from other routes or stack into targeted route. as explained, this set of targeted routes are marked from the top part of the list which this part is determined by a ratio between [0, 1] where it is fixed as an input parameter called 𝑖𝑛𝑡𝑙𝑙𝑅𝑎𝑡𝑒. the second approach of intlllns considers idle times in a route. idle time is defined as the time between actual reaching time of a vehicle to a node and the early time of that node. in fact, when a vehicle reaches a node at a time before the time window, it should wait until that time window opens. this time gap is considered as idle time. in this approach, all gaps of a route are cumulated and considered as idle time index and the maximum occurred gap along with its starting and ending points are considered as a label on that route. then, the routes in a solution are sorted according to this index from top to down. all routes in the top part of the list have more idle times. same as the first approach, a set of candidate nodes is created. in this case, those nodes in which their time windows are inside the duration of the maximum gap of the route are included in the candidate set of that route. finally, as same as first approach, intlllns iteratively runs and repeats above operations until the maximum number of allowed iterations are met. according to above explanations, the pseudo code of the intlllns is proposed as following in figure 5. finally, after the intlllns and adding from stack operations, the algorithm checks if the stack is empty or not. if stack is still not empty, then a new vehicle is added to the solution. a full procedure of or_enh_heu rule for a single vehicle is implemented, in order to construct a complete feasible route, considering nodes in the stack. after this final step of the cycle, another attempt is done called 𝐴𝑑𝑑𝑇𝑜𝐴𝑙𝑙, which as mentioned before, tries to vacate the stack pool by testing all individual nodes in all active routes. y-axis c d a b center radius depot figure 4. intlllns circular zoning farthest node x-axis bahalke et al./oper. res. eng. sci. theor. appl. 5(2) 2022 28-60 48 step 1: for all routes calculate costindex(𝑘); ciorder = sortroutes (𝐶𝑜𝑠𝑡𝐼𝑛𝑑𝑒𝑥); step 2: for all routes calculate idletimeindex(𝑘); itorder = sortroutes (𝐼𝑑𝑙𝑒𝑇𝑖𝑚𝑒); step 3: if (rand < pintllorient) { for all routes in top of ciorder setcandid(𝐶𝑖𝑟𝑐𝑙𝑒𝑍𝑜𝑛𝑒(𝑘)); selectrandnode(𝑆𝑒𝑡𝐶𝑎𝑛𝑑𝑖𝑑(𝑖)); checkmove(𝑖, 𝑘); 𝑖𝑛𝑡𝐼𝑡𝑒𝑟 + +; } step 4: if (rand ≥ pintllorient) { for all routes in top of itorder setcandid(𝑀𝑎𝑥𝐺𝑎𝑝(𝑘)); selectrandnode(𝑆𝑒𝑡𝐶𝑎𝑛𝑑𝑖𝑑(𝑖)); checkmove(𝑖, 𝑘); 𝑖𝑛𝑡𝐼𝑡𝑒𝑟 + +; } step 5: if (𝑖𝑛𝑡𝐼𝑡𝑒𝑟 < maxlnsiteration) { if(isstackempty){ addfromstack (𝑗, 𝑘); subsstack(𝑗, (𝑖, 𝑘)); } goto step 1; } else end; figure 5. intlllns pseudocode 4. computational experiments in this chapter of the paper, the performance of both developed mathematical model and haor_intlnsa heuristic algorithm is tested through experiments on wellknown benchmark instances of li and lim(li & lim, 2008). since the exact implementation of these instances would not fit to our introduced problem, some modifications have been made to them. besides, minimum size of the instances found in the literature begins with the size of 100 nodes. due to the resulted high complexity of and/or-mtvrptw, proposed milp model would not be able to optimally solve these instance sizes in a reasonable computational time. our experiments using milp model show no optimal solution even after 3 days for an instance with 100 sizes in which at the best case, it could reach to 39% gap from the lower bound. therefor these limitations make us to do some modifications on standard set of benchmarks of li and lim in the aspect of problem characteristics as well as problem sizes (li & lim, 2008). the details are clarified in following sub-section. 4.1. data generation as it was mentioned, the minimum size found in standard pdptw begins with 100 nodes, and we should note that in the pdptw nodes are paired in a way that they cannot be served by separate vehicles. this fact itself reduces the complexity of the problem where it practically solves allocation of 𝑁/2 sets into 𝑘 vehicles however in and/or-mtvrptw the allocation of 𝑁 sets into 𝑘 vehicles are considered. besides, dealing with multiple trips adds to the complexity of the base pdptw problem. so, in order to evaluate the proposed model’s efficiency, set of small sized instances are derived, using standard instances with 100 nodes from all categories of lc_type_i, lc_type_ii, lr_type_i, lr_type_ii, lrc_type_i and lrc_type_ii. a new heuristic algorithm for multi vehicle routing problem with and/or-type precedence constraints and hard time windows 49 at the first step of this operation, all pickup nodes which have same position with their delivery pairs are eliminated. for better understanding of this action, if we pay more attention to the instances of li and lim (li & lim, 2008), we will find that in the existing examples, there are pairs of nodes that practically both pickup and delivery have occurred at the same node. so, the purpose of elimination here is related to this kind of pairs and it is implemented on the pickup parts. as a result of this operation, some nodes will be left alone, without any precedence connection. then, a set of random nodes with their belonging pairs will be selected until the number of nodes in the set reaches to the targeted size. afterwards, in order to build feasible or arcs, for every and designated arc from 𝑖 to 𝑗 (𝑖 → 𝑗) we give a 50 percent chance to change into or arc. then, all resulted or candidates (if any) are partitioned into sets in which the maximum number of included pairs in a set is determined by an input parameter called 𝑀𝑎𝑥𝑃𝑎𝑟𝑡. finally, from all delivery part of the paired nodes in a set, a single one is randomly selected as or arc successor which all pickup nodes will be connected to that selected successor as its or predecessors. and the remained other delivery nodes got relief with none precedence connection. consequently, by means of above described four step procedure, small sized instances are generated. also, in order to generate larger sized instances, the first, third and the last steps of the proposed procedure are carried out. the entire trend of the used procedure is summarized in four steps as in figure 6 and all generated instances are available in an attachment to this paper. step 1: for all pickup 𝑖 and delivery 𝑗, if (𝑋(𝑖) == 𝑋(𝑗)&& 𝑌(𝑖) == 𝑌(𝑗)){ eliminate(𝑖); } step 2: size = 0; pickrand(𝑖, 𝑗); size = size + 2; if (𝑠𝑖𝑧𝑒 < 𝑆𝐼𝑍𝐸) goto step 2; step 3: for all 𝑖 𝐴𝑁𝐷⃗⃗⃗⃗⃗⃗⃗⃗ ⃗ 𝑗 , if (rand(t) < 50%) 𝑂𝑅𝑠𝑒𝑡𝐶𝑎𝑛𝑑𝑖𝑑 = (𝑖 → 𝑗); step 4: for 𝑡 from 1 to 𝑇, { partition(𝑂𝑅𝑠𝑒𝑡𝐶𝑎𝑛𝑑𝑖𝑑, 𝑀𝑎𝑥𝑃𝑎𝑟𝑡); destinor(t) = rand (𝑑𝑒𝑙𝑖𝑣𝑒𝑟𝑦(𝑗)); for 1 to maxpart if (is_and_arc_exist 𝑖 to 𝑗 ) creator (𝑖 𝑂𝑅⃗⃗⃗⃗ ⃗ destinor(t)) ; } figure 6. instance generating rule in the following section, all results of the experiments are provided that begins with a small sample example with complete explanation for the problem and the optimal result. 4.2. results and discussions the introduced problem of and/or-mtvrptw is new, so, any exact coincide could be found neither in the aspect of problem structure nor in the aspect of solution algorithms. therefore, the performance of the haor_intlnsa is evaluated via comparisons against optimal solution of the proposed mathematical model for the small sized instances. six categories of problems are considered in which in total, 24 instances are derived by means of the rule explained in previous section. furthermore, since there is not any gauge for testing the developed algorithm, it is decided to test bahalke et al./oper. res. eng. sci. theor. appl. 5(2) 2022 28-60 50 our algorithm by making some modification on li and lim (li & lim, 2008) wellknown set of instances. the instances and the proposed algorithm’s input parameters and conditions are arranged in a way that the final results could be compared in some aspects under the determined conditions. for this aim, at the first step, the demand requests are all set to a same positive unit number of 1. because, there is no pickup and delivery services are considered in the introduced problem. moreover, because the positive and negative values of the nodes’ demands in a vehicle neutralize each other, practically, the capacities of vehicles are ineffective. thus, in the generated large instances, the maximum capacity is set to a value equal to the maximum number of nodes allocated in a vehicle according to the best solution found in the pdptw benchmark. since the demands are all set to 1 that’s why the number of nodes value is considered as the maximum capacity. the rest of information regarding the input parameters and conditions are provided along the tables of results. in the following it is tried to more clarify the introduced problem’s details and features by solving a small-sized sample instance. then, the efficacy of the haor_intlnsa in small scales is testified through a set of comparisons against mathematical model’s optimal results. furthermore, the performance of algorithm is checked by setting a set of comparisons including instances with 100, 200 and 400 nodes in size. then the obtained results are interpreted and the efficiency of the proposed methodology is discussed. suppose the following scattered nodes in 𝑋𝑌 − 𝑝𝑙𝑎𝑛𝑒 with 10 customer nodes and one depot in figure 7 and with input data presented in table 2. table 2. sample example data node x y demand earlytime latetime servicetime depot 5 5 0 0 1000 0 a 5 6 1 1 5 1 b 6 6 1 3 7 1 c 4 4 2 1 3 1 d 8 8 2 8 13 1 e 3 3 3 10 20 1 f 12 12 1 10 20 1 g 4 3 1 3 7 1 h 7 6 1 5 8 1 i 8 9 1 13 20 1 j 10 10 2 7 15 1 positions of nodes and corresponding precedence constraints arcs are depicted in figure 7. for this sample instance maximum number of allowed trips is 3 and the capacity of all vehicles is assumed 3. according to optimum solution achieved by mathematical model, the example is solved in total 5 trips. three vehicles are used and all start their travels at the time zero. the first trip of first vehicle begins from depot, then the vehicle visits node a, b and h, next it returns to depot and then starts a further trip by visiting d, i and ends in depot. the second vehicle starts its first trip by visiting node c, then g and back to depot and continues its service by traveling to node j and f and finally ends travel in depot. the third vehicle carries out a single visitation of node e. a new heuristic algorithm for multi vehicle routing problem with and/or-type precedence constraints and hard time windows 51 in this sample the concept of or precedence relationship is clearly seen in v1_t1. first vehicle starts its trip by visiting a, then b, then node h, even though both nodes of a and h are the or-type predecessors of node b. but since in the concept of or-pc, the completion of only one of the predecessors are adequate to start the successor, this fact is implemented and node b is allowed to be visited after giving service to node a. in v1_t2 we see that the node d is visited prior to node i as designated by an andtype pc arc. the rest of precedence constraints have not met, because pairs have not assigned in the same vehicles. in the following the generated small sized instances are solved by mathematical model and the haor_intlnsa. all six categories of the bench-mark are considered and in total, 24 instances are generated. because of the high complexity of the problem, the most cases of these small instances could not be solved optimally by math model in reasonable time. so, beside of these instances a set of so smaller feasible instances are also created by authors that their optimality are solved and proved by the solver. table 3 presents the detailed results of these experiments. it should be noted that the mixed integer linear model is written in c++ using cplex 12.8 ilog concert technology. experiments have done on a core i7 pc with 3.34 ghz cpu speed and 8 mb of ram. 4.2.1. parameters setting according to the descriptions given about the procedure of the developed algorithm, there is a set of parameters that their values should be determined before the execution of the program. due to this determination action, a full factorial design is implemented to extract the most effective and efficient parameter values. so, for each parameter a set of values are predetermined, evoked through initial test experiences. it is clear that we should take an instance(s) in order to apply the all figure 7. solution of sample example precedence arcs: 𝑪 𝑨𝑵𝑫⃗⃗⃗⃗⃗⃗⃗⃗⃗⃗ 𝑬 𝑮 𝑨𝑵𝑫⃗⃗⃗⃗⃗⃗⃗⃗⃗⃗ 𝑬 𝑫 𝑨𝑵𝑫⃗⃗⃗⃗⃗⃗⃗⃗⃗⃗ 𝑰 𝑭 𝑨𝑵𝑫⃗⃗⃗⃗⃗⃗⃗⃗⃗⃗ 𝑰 𝑱 𝑨𝑵𝑫⃗⃗⃗⃗⃗⃗⃗⃗⃗⃗ 𝑰 𝑨 𝑶𝑹⃗⃗⃗⃗⃗⃗ 𝑩 𝑯 𝑶𝑹⃗⃗⃗⃗⃗⃗ 𝑩 customer ------ depot ---------- x-axis y-axis 5 5 bahalke et al./oper. res. eng. sci. theor. appl. 5(2) 2022 28-60 52 design of experiments to decide of the parameters’ values. for this aim, we took two sample instances, one for small-size and the other as the representative for big-size instances. the size of the instances should be selected in such a way that their solving times are taken into account due to the high number of tests (3 × 2 × 1 × 3 × 3 × 2 × 1 × 1 × 1 × 2 = 216). so, considering above mentioned conditions two instances with 16 and 100 nodes are selected for small and big size instances, respectively. table 3 has given the set of parameters and their relevant values. the last two columns of table 3 indicate decided value for each parameter for each group of instances. table 3. parameters setting of the developed algorithm parameter description alternatives smallsize bigsize pop_size population size {1,20,50} 20 1 total_iteration total iteration of the algorithm {100,500} 100 500 lns_iteration total iteration of lns procedure {100} 100 100 intllrate a portion of the targeted vehicles {0.3, 0.5, 0.8} 0.3 0.3 perturb_orient a percentage to go to move or replace perturb {30%, 50%, 80%} 50% 50% perturb_iter total iteration of perturbation {100,500} 100 500 lns_orient a percentage to go to or replace perturb {50%} 50% 50% sub_stack number of add from stack with substitute target {100} 100 100 r_add_stack number of iterations to randomly add from stack {100} 100 100 acc_rate simulated annealing rate in which solutions with this difference from earlier solution would be accepted {1.2,1.5} 1.2 1.2 making use of above arrangements the algorithm and the mathematical models are executed and obtained results are concluded in tables 4 to 8. table 4. small-size instances results s iz e m a x _v e h icl e m a x _trip c a p a city n o .o r -a rcs n o .a n d a rcs o b j_cp le x t im e (s) v e h icle t rip s o b j_h a o r _ in tl n s a n o .v e h icle n o .trip t im e (s) g a p 7 6 3 4 2 2 28.2843 1 2 2 28.2843 2 2 10 0% 8 6 3 4 3 2 36.0328 1 2 2 36.0328 2 2 7 0% 9 6 3 4 2 3 53.8195 1 2 3 53.8195 2 3 15 0% 10 6 3 4 4 2 48.3182 2 2 3 48.3182 2 3 12 0% 11 6 3 4 2 5 39.7498 6 3 5 39.7498 3 5 10 0% 12 6 3 4 2 5 82.0936 5 3 5 82.0936 3 5 11 0% 13 6 3 4 2 5 127.327 55 4 6 127.327 4 6 20 0% 14 6 3 4 4 5 193.604 239 4 7 193.604 4 7 18 0% 15 6 3 4 5 5 196.379 212 4 6 196.379 4 6 20 0% 16 6 3 4 6 5 346.967 225 5 8 346.967 5 8 24 0% a new heuristic algorithm for multi vehicle routing problem with and/or-type precedence constraints and hard time windows 53 instances in table 4 are generated in a complete random manner with aim of producing feasible problems by authors. as shown in table 4, mathematical model could reach to optimum solutions for all of these 10 instances. as seen the computational times have started to grow from the instance with size of 13. the efficiency of the proposed algorithm is clearly proved due to its performance on capability to optimum results in a small amount of computational time. once the size of the problems grows to 21 nodes, it has come out that the mathematical model solver got in trouble and could not reach to optimality for a considerable portion of the instances, however, the proposed algorithm has resulted in reliable results. table 5. results for instances with medium size in sta n ce _siz e m a x _v e h icle m a x _trip c a p a city n o .o r -a rcs n o .a n d a rcs b e st_fo u n d _ o b j o p t_g a p t im e (s) v e h icle t rip s o b j_h a o r _i n tl n s a n o .v e h icle n o .trip t im e (s) g a p lc101_21 6 3 4 6 4 375.17 0% 41 3 6 375.17 3 6 64 0 lc102_27 6 3 4 7 5 603.50 40% 14430 5 483.23 4 8 70 19.9% lc103_23 6 3 4 3 7 622.83 24.99% 68262 4 602.4 4 6 56 -3.2% lc104_21 6 3 4 3 6 524.30 33.34% 4078 3 408.68 3 5 57 22.1% lc201_21 6 3 4 5 5 501.40 0% 21 2 6 503.04 2 6 69 0.3% lc202_21 6 3 4 5 5 436.35 33.29% 3836 3 477.54 2 6 54 9.4% lc203_21 6 3 4 7 3 450.54 0.5% 10493 2 458.21 2 6 68 1.7% lc204_21 6 3 4 6 4 457.74 0% 22324 2 5 457.74 2 5 40 0% lr101_21 6 3 4 3 7 459.84 0% 7 6 6 459.84 6 6 58 0% lr102_21 6 3 4 5 4 474.95 0% 892 4 6 474.95 4 6 24 0% lr103_21 6 3 4 3 7 4309 532.77 3 7 65 ** lr104_21 6 3 4 3 7 4440 520.21 3 8 37 ** lr201_21 6 3 4 3 7 417.43 0% 447 2 5 417.43 2 5 70 0% lr202_21 6 3 4 4 6 510 0.06% 4986 2 516.78 2 6 26 1.3% lr203_21 6 3 4 4 6 557.4 0.1% 3662 2 558.82 2 6 34 0.2% lr204_21 6 3 4 5 5 488.91 0.07% 4637 2 486.41 2 6 69 -0.5% lrc101_21 6 3 4 5 5 472.23 0% 259 5 5 472.23 5 5 43 0% lrc102_21 6 3 4 6 4 3673 468.88 5 5 48 ** lrc103_21 6 3 4 6 4 677.50 33.36% 3646 3 492.14 3 7 61 27.3% lrc104_21 6 3 4 5 5 440.87 59.96% 57041 5 467.32 3 8 38 5.9% lrc201_21 6 3 4 3 7 507.53 0% 1895 2 5 507.53 2 5 53 0 lrc202_21 6 3 4 2 8 600.05 0.1% 3666 2 600.05 2 6 116 0 lrc203_21 6 3 4 5 5 672.23 33.36% 4807 3 605.56 2 6 32 -9.9 lrc204_21 6 3 4 4 6 586.91 0.12% 8840 2 589.73 2 6 59 0.4 results in table 5 show a complete superiority of the developed algorithm in comparison with exact mathematical model since it obtained better results for majority part of the instances. three rows of table 5 are in grey color. it should be noted that the mathematical results show difference from lower bound considering a bahalke et al./oper. res. eng. sci. theor. appl. 5(2) 2022 28-60 54 cost value for every vehicle used. for an example in case lc_202_21 it seems that the best found traveling cost function of mathematical model is better than the result of algorithm, however, we should note that the solution found by the algorithm resulted in lower number of vehicles. so to better evaluate the outcome, the numbers of the resulted used vehicles are also should be taking into account while evaluating the efficiency of the algorithm. table 6. haor_intlnsa results for instances with size 100 in sta n ce _s iz e n o . a rcs m a x _v e h icle m a x _trip c a p a city o b j_h a o r _i n tl n s a n o .v e h icle t im e (s) lc101_100 47 10 3 14 881.65 6 148 lc102_100 47 10 3 14 893.19 7 93 lc103_100 48 9 3 14 1022.56 4 119 lc104_100 47 9 3 14 780.77 4 80 lc201_100 49 3 2 36 525.84 2 76 lc202_100 49 3 2 36 568.47 2 104 lc203_100 49 3 2 36 608.74 2 118 lc204_100 49 3 2 36 545.37 2 97 lr101_100 47 19 3 8 1576.68 13 140 lr102_100 45 17 3 8 1203.11 11 78 lr103_100 48 13 3 8 1375.58 6 92 lr104_100 48 9 3 8 890.75 4 121 lr201_100 49 4 2 28 1430.57 3 126 lr202_100 50 3 2 38 1078 2 122 lr203_100 49 3 2 47 899.46 2 80 lr204_100 50 2 2 51 906.82 2 66 as described before three instance groups are generated in order to evaluate the performance of proposed algorithm. the results of all three are gathered in tables 68. as described before, the arcs are produced and implemented in the problems. the total number of all and and or arcs are noted in the tables in front of each instance case. the maximum vehicle number for each instance is determined considering the best minimum found so far in the literature for the classic form of the problem. and the total maximum allowed trips are considered randomly from the set of {2,3} giving more chance to value 3 (80%) for instances with max_vehicle more than 10 and giving more chance for value 2 for instances with max_vehicle number lower than 10. for each instance, best traveling cost objective value with obtained minimum number of vehicles are noted. also, the computational time for each instance is also calculated in seconds and depicted in a separate column. a new heuristic algorithm for multi vehicle routing problem with and/or-type precedence constraints and hard time windows 55 table 7. haor_intlnsa results for instances with size 200 in sta n ce _siz e n o . a rcs m a x _v e h icle m a x _trip c a p a city o b j_ h a o r _in tl n s a n o .v e h icle t im e (s) lc101_200 94 20 3 14 2456.98 14 296 lc102_200 95 19 3 14 2555.21 14 240 lc103_200 97 17 3 14 2870.66 12 223 lc201_200 98 6 2 36 1796.59 5 299 lc202_200 98 6 2 36 1840.47 5 266 lc203_200 99 6 2 36 1867.14 5 226 lr101_200 95 20 3 12 4400.31 16 232 lr102_200 95 17 3 16 4733.81 13 214 lr103_200 96 14 3 18 4179.17 11 264 lr201_200 99 5 2 30 4101.25 5 223 lr202_200 99 4 2 54 3711.68 4 238 lr203_200 99 4 2 54 2846.28 4 238 lrc1_301_200 94 19 3 12 3369.57 16 248 lrc1_302_200 97 15 3 20 3559.85 12 284 lrc1_303_200 95 13 3 24 3325.64 11 219 since the problem in its current form is accounted as a novel class of problem, so making comparisons with other authors proposed algorithms seems to be not suite for this case. even re-coding of the algorithms developed in the history of vrp problems would not be a good choice to show the capability of the proposed algorithm. in this research authors did their best to make use of the methodologies which are derived from the most recent achievements in literature of the problem. looking the body of the algorithm shows this fact that in the perturb process or simple lns or simple feasibility check process we first applied the most used and claimed functions, then we did improvements and made considerable enhancements in each part. also by introducing the new procedure for lns we could obtain better results by eliminating time consuming recent procedures. considering all of these there is one way to show the capability and efficiency of our proposed algorithm. by using predetermined values for capacity and maximum number of vehicles considering the bench mark and the data given in the li and lim (li & lim, 2008). the resulted traveling costs show a much about the performance of the algorithm. for example we took a look for the traveling costs of the instances in their classic form of the third group of instances with size 400. as it is seen, obtained traveling costs by haor_intlnsa for the major part of instances are better than what were resulted before. actually this is not a fair comparison since the form of precedence relations are changed and also trips options are added in these new instances which all lead to more alternatives. but it can at least show that haor_intlnsa is reliable algorithm for the introduced class of problem since it could reach to results as they are anticipated by widening the feasible space. this problem is new and very attractive with challengeable several aspects from developing exact algorithms to constructing search based fast solution techniques. and also it has resulted in a set of problems with very high complexity. thus, authors bahalke et al./oper. res. eng. sci. theor. appl. 5(2) 2022 28-60 56 invite researchers and authors to do studies on this problem since it has lot to grow and progress. table 8. haor_intlnsa results for instances with size 400 in sta n ce _siz e n o . a rcs m a x _v e h icle m a x _trip c a p a city o b j_ h a o r _in tl n s a n o .v e h icle t im e (s) t ra v e l_co st(p d p t w ) lc101_400 189 40 3 14 6805.55 29 370 7152.06 lc102_400 189 38 3 14 8148.32 26 310 8007.79 lc103_400 190 32 3 14 8264.86 25 345 8678.23 lc201_400 197 12 3 38 4213.38 8 253 4116.33 lc202_400 198 12 3 38 4071.44 8 340 4144.29 lc203_400 197 12 3 38 4024.43 8 239 4401.08 lr101_400 192 40 3 14 11032.72 32 396 10639.75 lr102_400 191 30 3 17 10800.66 24 251 11009.51 lr103_400 192 22 3 28 8763.18 17 245 9251.13 lr201_400 199 8 3 50 8601.78 8 298 9726.88 lr202_400 199 7 3 50 9233.86 7 246 9405.40 lr203_400 198 5 3 50 9687.67 5 275 10282.01 lrc1_301_400 192 36 3 15 8902.64 28 359 9124.52 lrc1_302_400 191 31 3 15 8222.36 29 299 8346.06 lrc1_303_400 194 24 3 18 7736.29 23 327 7805.16 5. conclusions and future research in this paper, and/or precedence constraints have introduced in the field of vehicle routing problems with the aim of minimizing total traveling distances and costs. this type of precedence relations has not been considered so far in the literature of vrps. although the nature of this type of precedence relations exists in the body of problem but in the real cases, it has ignored by the researchers. therefore, this paper introduces this extension to that former problem for the first time as well as proposing a practical general hybrid optimization algorithm which is able to solve the medium and large size problems. by this additional or-type precedence constraints to the classical 'and' type pc, it is not needed to visit all predecessors of a successor node before it can be met, and finishing one of them can let to that particular successor to get started. this paper implemented this type of pc graph in vrp for the first time in the related literature. the problem was mathematically formulated. since vrps are known as np-hard, even in simple versions, our more complicated problem was also np-hard. therefore, a decomposition based heuristic method was employed to solve the problem. indeed, the routing part was enhanced by heuristics to cover and/or pc graphs. the computational experiments on several problem instances with different sizes demonstrated the efficiency of proposed solution method in terms of solution quality. because of the novel nature of the problem, it is recommended two future research guidelines: on one hand, this work can be proceeded with other types of vrps such as a new heuristic algorithm for multi vehicle routing problem with and/or-type precedence constraints and hard time windows 57 vrp with backhauls and open vrp; on the other hand, the application of other 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(2017). a hybrid algorithm for a vehicle routing problem with realistic constraints. information sciences, 394, 167-182. https://doi.org/10.1016/j.ins.2017.02.028 © 2022 by the authors. submitted for possible open access publication under the terms and conditions of the creative commons attribution (cc by) license (http://creativecommons.org/licenses/by/4.0/). https://doi.org/10.1016/j.asoc.2016.09.039 https://doi.org/10.1016/s0166-218x(01)00316-x https://doi.org/10.1016/s0166-218x(01)00351-1 https://doi.org/10.1016/j.eswa.2015.02.058 https://doi.org/10.1016/j.ins.2017.02.028 operational research in engineering sciences: theory and applications vol. 4, issue 3, 2021, pp. 39-58 issn: 2620-1607 eissn: 2620-1747 doi: https://doi.org/10.31181/oresta20402039w * corresponding author. swidjajanto@gmail.com (s. widjajanto), erry.rimawan@mercubuana.ac.id (e. rimawan) modified failure mode and effect analysis approaching to improve organization performance based on baldrige criteriaa case study of an electro-medic industry sugiri widjajanto, erry rimawan industrial engineering department, universitas mercu buana, jakarta, indonesia received: 27 may 2021 accepted: 06 july 2021 first online: 23 september 2021 research paper abstract: full attention is paid to quality in manufacturing; however, less effort is made to develop the organizational performance, which drives overall manufacturing quality. this research measures performance of one manufacturing company that in 2020 experienced surging in demand and experiencing barriers to social activities due to the pandemic. the evaluation was carried out using seven variables from the malcolm baldrige criteria for performance excellence (mbcfpe) which were elaborated into 43 indicators of organizational performance. weaknesses and strengths of organizational performance were sharpened through focus group discussions with experts and ended with a performance improvement solution with a priority rank based on risk priority numbers (rpn) of the fmea method. the highest rpn is 567 and 432, respectively, for national standard implementation in a particular product and operational scheme during emergency conditions like the cov-19 pandemic. this study contributes to indonesian research that combines questionnaires and fmea improvement analysis based on the us baldrige criterion. keywords: performance excellence, baldrige criteria, mbcfpe, fmea. 1. introduction the industrial governance crisis due to covid-19 has hit almost all countries, regardless of technological reliability, the sophistication of health services, or economic independence. (ranggajati et al., 2020). according to various studies in the past year, the external aspects of the organization have greatly influenced the organization's performance, be it business in general or specifically in the industrial sector throughout 2020. (yap, 2020), (ahlstrom et al., 2020). external aspects that affect organizational performance include socio-economic shocks, political policies, and the environment (amarkhil, 2019). according to the 2020 undp report on the actions of asia pacific business people, it was stated that in the period of the cov-19 widjajanto and rimawan/oper. res. eng. sci. theor. appl. 4 (3) (2021) 39-58 40 pandemic, 35% of businesses had to lay off staff, 25% postponed orders, 25% had to delay investment, 24% had to decrease wages, 18% reduce service (united nations development programme, 2020). the report from mckinsey released in early 2021 (zurich et al., 2021) shows that the companies that have managed to survive are the companies that have succeeded in responding to changes to the challenges of the pandemic during 2020. for example, operational efficiency has decreased, and the company has taken action to cut the budget. likewise, the use of technology has increased with better technology. however, those reports did not provide basis of evaluation other than questionnaire. there is research gap between what had been done by the companies in respond to pandemic situation and what was background or reason for chosen actions. this gap requires approaching that put an existing or previous condition as base-line and find improvement in another way using tools that commonly being used by industries. hence, this phenomenon is developed in this research by conducting studies and evaluating a manufacturing organization's performance during challenging periods. this research selected one organization as the research object, pt-emb, which is a local industry that focuses on the fabrication and manufacturing of electromedical devices located in the serpong industrial area, banten province of indonesia. this organization has iso-13485 as the standard for the production quality of several types of medical devices. the company produces oxygen generators, which are in high demand during 2020, and the locally made ventilator. this research is carried out for all organization sections about production, including leadership criteria, strategic planning, customer handling, operational processes, labor factors, knowledge management, and performance measurement. the method chosen is the baldrige criteria issued by the united states, which is commonly called the malcolm baldrige criteria for performance excellence (mbcfpe), containing seven primary variables (nist, 2020). large companies typically recognize baldrige performance measurement because the criteria or variables evaluated represent the overall indicators of organizational performance. baldrige criteria can be applied to government institutions (h. anggara & hasibuan, 2020; widjajanto et al., 2020), hospitals (sintari, 2020), education (thompson & blazey, 2017), and industries. the research question in this paper is how to evaluate local business performance during the 2020 pandemic period and what to be improved. thus, this study's objectives are described as assessing the organization's performance during the 2020 pandemic period using seven baldrige variables and determining activities that must be improved to increase organizational performance. the baseline is baldrige criteria version 2019-2020, but this research is intended to find performance improvement instead of performance scoring for award ranking. data collection, interviews, and discussions were carried out from november 2020 to january 2021. modified failure mode and effect analysis approaching to improve organization performance based on baldrige criteria a case study of an electro-medic industry 41 2. literature study 2.1 baldrige criteria for performance measurement baldrige method is a quality management application formally enforced in its home country, i.e., the united states. the us-congress initiated it in 1987 as a request to malcolm baldrige, commerce department secretary. this system was approved by the us president and outlined in the "malcolm baldrige national quality award improvement act of 1987" on august 20, 1987 (vinyard, 2015). tens of thousands of companies have adopted the baldrige method in more than 70 countries in the world. indonesia also adopted mbnqa and made the indonesian quality award (iqa) an award for corporate performance (widjajanto et al., 2020). baldrige criteria consist of seven variables and are elaborated for this research into forty-three (43) indicators below table 1. table 1. baldrige variable and indicators criteria no. indicator c ri te ri a 1 l e a d e rs h ip 1 management must evaluate the company's vision and mission 2 evaluate consistency in vision and mission 3 evaluate the organization's code of ethics 4 improved work environment 5 dissemination of new regulations and policies 6 evaluate all work according to rules and policies c ri te ri a 2 s tr a te g ic p la n n in g 7 quality planning 8 innovative proposals 9 evaluation of strategic planning in day-to-day work 10 evaluation of the success/achievement of strategic planning 11 flexibility of planning changes c ri te ri a 3 c u st o m e r f o cu s 12 evaluate the end-user / customer group 13 identify the needs of the customer 14 identify customer satisfaction and dissatisfaction 15 making decisions related to customer satisfaction 16 staff knowledge of the company's main customers c ri te ri a 4 m e a su re m e n t, a n a ly si s, k n o w le d g e m a n a g e m e n t 17 application of performance measurement methods (kpi) 18 performance results as the basis for improvement or change 19 alignment of employee and company performance 20 job information for all employees 21 monitoring, controlling, and recording in the workplace 22 use of working procedures and instructions in operating equipment and tools. 23 all employees know about the company's achievements c ri te ri a 5 w o rk fo rc e 24 teamwork 25 support for employee career advancement 26 employee performance appreciation 27 job security 28 evaluate employee commitment c ri te ri a 6 o p e r a ti o n a l / p ro c e ss 29 availability of materials, spare parts, and tools 30 evaluate the work process according to instructions widjajanto and rimawan/oper. res. eng. sci. theor. appl. 4 (3) (2021) 39-58 42 criteria no. indicator 31 all equipment is operated using approved instructions 32 equipment operated by authorized personnel 33 evaluate the use of methods and sops 34 preparation of operational schemes to deal with emergencies such as the covid-19 pandemic c ri te ri a 7 r e su lt s 35 production targets are met 36 customer satisfaction is met 37 financial condition is maintained 38 compatibility of competencies with the final product 39 efforts to overcome obstacles 40 compliance with local industry regulations 41 application of national standard for ventilator production 42 csr support for the surrounding community 43 workplace comfort and safety many organizational performance appraisals have been carried out using various methods (abdollahbeigi & salehi, 2020). several countries developed their version of the way by referring to standards or practices that are already popular internationally. for example, the thai government has tools for performance measurement in their agencies and organizations that adopt iso and mbnqa (pengsuwan & choonhaklai, 2019). then there is the siq, namely the swedish institute for quality which was developed by adopting the mbnqa (raharjo & eriksson, 2017). specifically, in several asian countries, several articles describe the performance assessment of public service organizations such as the batu pahat city government office, malaysia (kaliannan et al., 2014), four government institution (custom, immigration, land transport, and mining) in malaysia (ali et al., 2017), indonesian jakarta government licensing services (h. anggara & hasibuan, 2020) and a performance appraisal in the local government of the united arab emirates written by a us researcher (furst bowe, 2019) as well as an article on saudi arabia public service organization written by uk researchers (alhaqbani, 2017). another study originating from europe outlines the performance appraisal of public services, namely the lithuanian public sector, using mbnqa, efqm & bsc. (balabonienė & večerskienė, 2015), organizations in sweden (eriksson et al., 2016), public and private organizations in sweden use siq (raharjo & eriksson, 2017) and the mayor's office in greece (tasiou, 2017). efqm is the european foundation for quality management which emerged recently after the popular mbnqa (balabonienė & večerskienė, 2015) and sweden (eriksson et al., 2016). 2.2 fmea method for evaluating organizational performance failure mode and effect analysis (fmea) was first developed in the aerospace industry in the 1960s as a systematic methodology for identifying known and unknown modes of failure, including causes and consequences on the system and verifying risks associated with priority scales for corrective action. (liu, 2016). the fmea used in this research is classified as modified fmea, which is developed according to a particular business organization (huang et al., 2020). one example is a modified fmea approach that combines multiple criteria decision making, adding a cost component to the risk priority number (rpn) calculation (lo & liou, 2018). modified failure mode and effect analysis approaching to improve organization performance based on baldrige criteria a case study of an electro-medic industry 43 another example is the management of waste management in health institutions that also use modified fmea (ouyang et al., 2021) and fmea modifications for health services (shi et al., 2019). a study proving the relationship between risk management and organizational performance found the most important reasons for decreased performance in administrative implementation items through using the fmea method by looking at cost and time losses (hezla et al., 2020). the fmea stages are briefly described:  describes all operational activities,  compiling potential problems that could arise,  give the list of severity, occurrence, and detectability levels.  calculating the risk priority number (rpn).  rpn = severity (s) x occurrence (o) x detectability (d)  compile a list of actions or actions to reduce risk according to the rpn. the fmea method is commonly used in industry, including electronic and medical devices. several previous studies have shown significant results related to the use of this method. the use of fmea is commonly used in the industry to identify possible failures in the production process. it aims to improve product quality and reliability (hasbullah et al., 2017). alternative repairs for each failure are priority improvements shown in the risk priority number (rpn) values (budi puspitasari et al., 2017). fmea can also be combined with the statistical process control (spc) method, as carried out in a study that analyzed defects in the pulp and paper industry (putra et al., 2020). many practitioners use fmea in the application of total productive maintenance (tpm). a study to optimize machine maintenance using reliability centered maintenance (rcm) and fmea was conducted to evaluate the highest failures on a single type of machine with deficient availability & reliability values and did not meet production standards. the fmea method is used to find six engine components with a high failure rate so that improvements can be made that increase the reliability value of the machine (nugroho et al., 2020). fmea in the electronics industry, as practiced in mobile phone manufacturing, can trace essential steps in improving the manufacturing process, resulting in reduced failures, reduced industrial costs and improved quality index, and satisfying customers. (oliveira et al., 2019). 3. research method the stages of this research were started from determining the problem, aim and objectives, develop a methodology, and identifying the organization's profile of the research object. the collection of the profile information was carried out through initial interviews. if the information regarding the profile is sufficient, then placing the performance criteria is carried out through a questionnaire. the questionnaire results will be tested to see the level of correlation and the level of reliability. in figure 1, a research flow diagram is presented that explains the steps of this research. widjajanto and rimawan/oper. res. eng. sci. theor. appl. 4 (3) (2021) 39-58 44 current organization performance baldrige criterias (43 indicators in 7 variables) theory, standard, previous research modified fmea severity, detectability, occurrence performance improvement suggestion with risk priority number (rpn) figure 1. research framework this paper's research aims to evaluate the organizational performance of a local indonesian electro-medical equipment manufacturing company, which during the covid-19 pandemic period received a high demand for ventilator and oxygen generator products. the challenges faced, such as social restrictions, logistical difficulties, and other obstacles, will be analyzed in depth. evaluating the organization's performance is continued by looking for improvement opportunities to improve its organizational capabilities that can compete globally based on the baldrige criteria used by multinational companies. this study uses a descriptive exploratory approach using surveys, interviews, and discussions. based on the baldrige criteria, organizational performance appraisal produces a scoring used as a baseline as a brief description of the organization's profile. a focus group discussion (fgd) was used with experts selected based on their capabilities. that was part of the brainstorming with the fmea approach through many performance indicators mapping the organization's condition. the empirical mapping was ranked under the severity, occurrence, and detectability category of the fmea. the fmea method makes it easy to adapt to actual situations and presents direct interactions between researcher, respondents, and related experts (mzougui & el felsoufi, 2019). a list of questions was adopted from baldrige examiner edition 2019/2020 (nist, 2020) and practical samples (yusuf, 2017) (vinyard, 2015). secondary data is taken from the company in log data related to fabrication activities during the cov-19 regulation in the form of records and reports obtained that will be helpful in the analysis and determination of corrective steps. the stages in the design of modified failure mode and effect analysis approaching to improve organization performance based on baldrige criteria a case study of an electro-medic industry 45 performance improvement are carried out using a modified fmea approach with the following steps:  using the data obtained from baldrige indicator list.  discuss fmea to find solutions for performance by ranking priorities. the tables for severity, occurrence, and detectability modified by reference are shown in the table below.  evaluate and develop potential problems on severity, occurrence, detectability and calculate for respective indicators of baldrige variables. 4. data result and analysis 4.1 baldrige scoring based on questionaire the research questionnaire was distributed to all employees, where the characteristics of the respondents were collected as well age, gender, work experience, education level, and the job position of the respondent. item analysis is used to check the validity and reliability of items in measuring variables. these measuring use a likert scale as the degree of approval of a statement. the questions in the questionnaire used the baldrige for examiner edition 2019/2020 reference (nist, 2020). minitab's item analysis yields the pearson correlation and cronbach's alpha values. the pearson value obtained by minitab is then compared with the value from the pearson r critical value table, with a significance of 0.05 and df = 24; the figure is 0.388. if the calculated pearson correlation value shows a value greater than 0.388, the data is declared valid. item analysis was carried out to all baldrige variables and concluded that all survey data is valid and reliable. baldrige score on each questionnaire variable, according to h. anggara & hasibuan (2020) obtained through the formula: x (standard score for each baldrige variable) (1) ni = number of respondent for the answer i wi = weight of answer i n = total number of respondents w = largest answer weight = 5 (likert scale) y = total number of questions for each categorical variable calculation and recapitulation of performance scores uses common excel spreadsheets. its summary is presented in table 2 as a summary of total scoring. the baldrige score for the company performance is 463.09 shown in the table. that is equal to 45.86% compared to the ideal baldrige excellence performance. obtained a total score of 463.09 is in the early improvement achievement according to mbnqa award criteria. criteria 1 until 7 description is available in table 1 including all relevant question poin. widjajanto and rimawan/oper. res. eng. sci. theor. appl. 4 (3) (2021) 39-58 46 table 2 total score baldrige criteria criteria score ideal mbnqa comparison (score/ideal) gap remarks 1 leadership 58.00 120 48.33% 2.47% strength 2 strategic plan 39.44 85 46.40% 0.54% strength 3 customer focus 39.78 85 46.80% 0.94% strength 4 makm 39.10 90 43.44% -2.41% weakness 5 workforce 39.10 85 46.00% 0.14% strength 6 operation 36.67 85 43.14% -2.72% weakness 7 bussines result 211.00 450 46.89% 1.03% strength total 463,09 1000 45,86% the table also states the gap value obtained from subtraction the obtained score against the average. the negative score on the gap column is classified as weakness, while the positive as strength. the lowest minus value is in criteria no.6 or the baldrige criteria for operations. that has been labeled as weakness and will be the primary target for corrective action. in that summary, the performance that is considered weak falls also to criteria no.4 measurement, analysis and knowledge management (makm). the leadership or criteria no.1 is superior to the most robust criteria in this company. 4.2 fmea fgd result the next step in finding a performance improvement solution is to quantify the baldrige performance items by looking at the potential failures of this company. the qualitative performance items are evaluated using a modified fmea by analyzing the effect of the loss on the schedule, costs, and outputs that impact either major or minor (harman, 2020; hezla et al., 2020). the fmea working paper produced in this research can be classified as a preventive risk assessment method. the results are finding, prioritizing, and removing potential problems as material for improvement and lessons learned in future company activities. (hezla et al., 2020). table 3 (a). severity level effect severity level rank schedule huge impact, exceeding tolerable limits 9 ~ 10 total cost additional expenses are very significant technical problem useless output, discarded schedule impact on schedule 10-20% of the target 7 ~ 8 total cost additional expenses up to 20% of budget technical problem output is impacted and cannot be used by the client schedule schedule affected up to 10% of target 5 ~ 6 total cost total expenditure costs increased up to 10% technical problem outputs are impacted and require client approval schedule schedule affected, still within tolerance 3 ~ 4 total cost total expenses have increased within tolerance limits technical problem minor impact and requires internal company approval no effect for all 1~ 2 modified failure mode and effect analysis approaching to improve organization performance based on baldrige criteria a case study of an electro-medic industry 47 table 3 (b). occurrence level possible poor performance probability (occurrence) rank very high >1 in 2 10 1 in 3 9 high (repeatedly) 1 in 8 8 1 in 20 7 table 3 (c). detectability level detectability assessment rank no detection (of performance measurement) method is available that can alert enough time for corrective action 9 ~ 10 the detection method (of performance measurement) is unreliable or untested. the effectiveness of detection methods is not known for identifying poor performance 7 ~ 8 performance detection / measurement methods are quite effective in some units / divisions / departments 5 ~ 6 the performance detection/measurement method has been effectively implemented in all work units 3 ~ 4 the performance detection method is very effective, and it is almost certain that poor performance will be detected in a sufficient time 1 ~ 2 in compiling the fmea, three people were selected as an expert, the first resource person from government representative (x1 or expert no.1), the second is an academic lecturer (x2 or expert no.2), and the third expert is person-in-charge general manager of the company (x3 or expert no.3). some references have been used to determine severity level by looking at the effects of the schedule, total costs and technical problems (liu, 2016) (hezla et al., 2020) elaborated in table 3 (a). the level of occurrence and detectability is consecutively in table 3 (b) and table 3 (c). the assessment begins with the information obtained from the baldrige criteria as the basis for performance items. the points of failure are developed, which can be extracted from the situation in the company that is the object of research and evaluated for possible losses that can reduce the company's organizational performance. focus on the three main variables of the fgd results that show weak performance. each item in the variable is assessed severity, occurrence, and detection and calculates risk priority number (rpn). the evaluation results are in table 4 below and sorted by rpn ranking. indicator desciprion is available in table 1 in previous section. rpn = sxoxd (2) rpn: risk priority number s: severity rank o: occurrence rank d: detectability rank widjajanto and rimawan/oper. res. eng. sci. theor. appl. 4 (3) (2021) 39-58 48 table 4. fmea result with rpn ranking indicator id no. x1 x2 x3 s x1 x2 x3 o x1 x2 x3 d rpn rank 41 9 9 9 9.00 9 9 9 9.00 7 7 7 7.00 567.0 1 34 9 9 9 9.00 8 8 8 8.00 6 6 6 6.00 432.0 2 29 8 8 8 8.00 8 9 9 8.67 6 6 6 6.00 416.0 3 22 7 7 8 7.33 7 8 8 7.67 8 7 7 7.33 412.3 4 32 7 7 8 7.33 8 8 8 8.00 5 6 6 5.67 332.4 5 31 7 8 8 7.67 8 8 8 8.00 5 5 6 5.33 327.1 6 20 7 7 8 7.33 7 7 8 7.33 5 5 6 5.33 286.8 7 33 7 8 8 7.67 7 7 8 7.33 5 5 5 5.00 281.1 8 36 7 7 8 7.33 7 8 8 7.67 5 5 5 5.00 281.1 9 35 7 8 8 7.67 7 7 7 7.00 5 5 5 5.00 268.3 10 37 7 8 8 7.67 7 7 7 7.00 5 5 5 5.00 268.3 11 40 7 7 8 7.33 7 7 7 7.00 5 5 5 5.00 256.7 12 the results obtained in the table show that the priority which has the potential to become a significant problem is the absence of a reference standard, in this case, the specific indonesian national standard (sni) for ventilator products, getting the highest rpn score of 567. that is confirmed by other experts who work in certification bodies that currently, indonesia does not have it yet. hence, the prototype built during the 2020 pandemic uses open-source references from research institutions (fkui, 2020). the subsequent finding that becomes the second priority is the availability of material needs, spare parts, and work tools with an rpn score of 416.7. the root of the problem that was successfully explored was the finding of non-standard components so that for each unit produced, different tunings and adjustments had to be done. the company confirmed the failure because the materials and parts they received were from research institutions without an independent purchasing process to find a better supply source. the potential for performance failure, which is ranked third with an rpn score of 396, is related to the readiness of the operational scheme to face the covid-19 pandemic emergency. the informant confirmed that the challenges faced during the pandemic were the limitation on the number of workers due to social distancing, difficulties in mobilizing to testing agencies, and logistical constraints on sensor components that still have to be imported from abroad. potential failure in the subsequent rpn ranking is regarding teamwork cooperation, equipment operated by authorized personnel, approved work instructions and sops, customer satisfaction, information on work implementation for all employees, sharing information on production targets, and stable company financial performance condition, and the comfort of the working place. the availability of work guidelines is emphasized in table 6 under several indicators, i.e., all equipment operated using approved instructions with an rpn score of 327.1 and is ranked sixth. the seventh and eighth ranks were also related to work instructions, with an rpn score of 299.9. evaluation of the use of the method & sop has an rpn score of 281.1. modified failure mode and effect analysis approaching to improve organization performance based on baldrige criteria a case study of an electro-medic industry 49 5. result and discussion 5.1 company performance evaluation compare with other researches this study presents two empirical studies, the first on assessing baldrige variables in organizations using questionnaire data, which according to the literature, is a selfassessment. the second is to evaluate baldrige performance indicators according to independent reviewers with selected sources. as such, it provides a deeper level of reliability and validity regarding assessment, perception, and reporting. the second important aspect of these studies is improving and improving the quality of performance in organizations that can be developed over time. this research results obtained the highest baldrige score on leadership performance, as shown in table 5 (a) and (b). the lowest score is received on the operational and process performance variables. that is consistent with the results of previous research in the application of quality management in industry (anastasiadou & taraza, 2019; fatima & mahaboob, 2018; mellat-parast, 2015; parast & golmohammadi, 2019; savov et al., 2017; thompson & blazey, 2017). this research found that the leadership factor is the primary driver of the quality performance of the organization. these results confirm the baldrige concept that organization system is driven by leadership as well as senior staff, and this is the primary key to improving quality performance (ahuja et al., 2019; asif et al., 2019; parast & golmohammadi, 2019; savov et al., 2017). table 5 (a) performance criteria that needs to be improved priority based on baldrige scoring 1st operational (criteria 6) 2nd measurement, analysis, and knowledge management (criteria 4) 3rd workforce (criteria 5) table 5 (b) dominant performance criteria dominant criteria actual / ideal score (%) gap the highest score leadership 58.00 / 120 48.33% 2.47 % the lowest score operational 36.67 / 85 43.14% -2.72 % table 6 below is compiled from various references related to the development of organizational performance and its significant factors. these essential factors affect organizational performance, either directly or indirectly, and positively encourage or hinder organizational performance improvement. the leadership factor is a significant factor affecting organizational performance, both positive and negative (nandasinghe, 2020), (parast & golmohammadi, 2019), (asif et al., 2019), (ahuja et al., 2019), (anastasiadou & taraza, 2019), (savov et al., 2017). widjajanto and rimawan/oper. res. eng. sci. theor. appl. 4 (3) (2021) 39-58 50 table 6. significant factors for organizational performance in previous research description previous researches leadership factor (nandasinghe, 2020), (parast & golmohammadi, 2019), (asif et al., 2019), (ahuja et al., 2019), (anastasiadou & taraza, 2019), (savov et al., 2017). training and sharing of knowledge and attention to employee intellectual property (kanapathipillai & azam, 2020), (ahmed et al., 2020), (muwardi et al., 2020), (mahmud et al., 2020), (abdul rauf et al., 2020), (abbas et al., 2018), (abualoush et al., 2018), (chaudhry et al., 2017), (puška et al., 2018) strategic planning (kasushik & guleria, 2020), (chioke & mbamalu, 2020), (ahuja et al., 2019), (anastasiadou & taraza, 2019), (dobrosavljević & urošević, 2019) external organization factor (social, politic, environment) (yap, 2020), (ahlstrom et al., 2020), (amarkhil, 2019) one literature shows the importance of the causal relationship from the leadership factor to the information factor. the analysis is quantitatively demonstrated, proving that leadership has a vital role in information analysis and knowledge management variables. (parast & golmohammadi, 2019). another study examined the relationship between leadership, quality of administration, quality of medical services, and patient satisfaction using the mbnqa criteria. further research in hundreds of pakistan hospitals investigated the effect of interventions on quality of medical service with relation to patient satisfaction and leadership. it obtained a positive relationship between leadership, administrative quality, medical quality, and patient satisfaction. in addition, administrative quality and medical quality were found as potential mediators in the relationship between leadership and customer satisfaction (asif et al., 2019). the second factor is by improving the internal work system of the organization, which is manifested by training actions, sharing knowledge between members of the organization and between departments so that the main objectives of the organization are achieved with the best collective performance and also job rotation (sebt & ghasemi, 2021), (kanapathipillai & azam, 2020), (ahmed et al., 2020), (muwardi et al., 2020), (mahmud et al., 2020), (abdul rauf et al., 2020), (abbas et al., 2018), (abualoush et al., 2018), (chaudhry et al., 2017), (puška et al., 2018). the third significant factor, according to the previous literature, is strategy and planning (khan et al., 2021), (kasushik & guleria, 2020), (chioke & mbamalu, 2020), (ahuja et al., 2019), (anastasiadou & taraza, 2019), (dobrosavljević & urošević, 2019), which in this research, it is included in the baldrige variable number 2. however, this study did not find that variable is the dominant performance. however, strategic planning is still needed, especially the redesign of the roles and functions of each employee to adapt to the post-pandemic new normal conditions. according to the literature, the fourth significant factor is the external influence of the organization, namely the social, environmental, or political policies imposed by the government. there are challenges in the form of social restrictions policies that limit the industry's movement both organizationally and in employee activities. working conditions under pressure, restrictions on job access, and decreased employee motivation will affect organizational performance (s. a. anggara et al., 2019). however, other research shows that managing the risks that may arise will improve the performance of the company organization (najib et al., 2019). modified failure mode and effect analysis approaching to improve organization performance based on baldrige criteria a case study of an electro-medic industry 51 the literature review also shows the importance of customer relationship management, leadership, communication, and strategic alignment as a very significant causal in implementing efficient continuous performance improvement. (ahuja et al., 2019). as a comparison, researchers also reviewed research on evaluating organizational performance in education using the baldrige criteria in greece. the results of these studies prove that the main factor in their tertiary education system is leadership. the following variable that must be taken into account is strategic planning, which also has a significant effect on the successful implementation of quality (anastasiadou & taraza, 2019). the last article used as a reference shows that using a performance measurement system will affect organizational performance, especially helping organizations monitor performance, which ultimately leads to target achievement and gathering information and activity records that are useful for improving its performance. this system will affect various aspects of the organization, including financial and non-financial performance, employee behavior, and overall performance (owais & kiss, 2020). 5.2 research contribution to the company this research provides several contributions to the companies related to evaluating their performance, including leadership, strategic planning, knowledge management, customer handling, employment, operations, and production. first, this research evaluates the companies' performance using a baldrige model, which is theoretically robust and has been widely applied in the business world. it is the first empirical performance evaluation to pt-emb uses this kind of performance measurement. one of the critical implications of this finding is that the pt-emb will use the baldrige model as a self-assessment tool to improve the quality of performance further. table 7. list of performance indicator to be improved by pt-emb no performance variable performance indicator to be modified/improved indicator id 1 operational and process availability of materials, spare parts, and tools 29 preparation of operational schemes to deal with emergencies such as the covid-19 pandemic 34 equipment operated by authorized personnel 32 all equipment is operated using approved instructions 31 evaluate the use of methods and sops 33 2 measurement, analysis, and knowledge management use of working procedures and instructions in operating tools 22 information and socialization of job task to all employees 20 3 business results implementation of the national standard for ventilator product 41 customer satisfaction is met 36 production targets are met without defect 35 organizational financial condition is maintained 37 compliance with local industry regulations 40 4 workforce teamwork enhancement 24 widjajanto and rimawan/oper. res. eng. sci. theor. appl. 4 (3) (2021) 39-58 52 previous research has used the baldrige model to improve performance quality using cross-sectional surveys (parast & golmohammadi, 2019), and it usually follows up with swot analysis. thus, the second contribution of our research is the novelty that brings up baldrige indicator assessment via fmea to produces suggestions for performance improvements on a priority scale. this is a contribution to academic theory as well that combines baldrige with fmea approach. the third contribution of this research is to understand how to carry out comprehensive organizational performance measurements regardless of the business model and looking for loopholes to improve the quality of performance using the baldrige approach. the improvement suggestions to the company are listed out relevant with each main criterion in table 7. one of the critical points of the discussion above is the absence of a specific indonesian national standard (sni) for the production of ventilators. although this sni is the government's responsibility through the national standardization agency for indonesia, this does not escape its responsibility in ensuring the quality of its products. in general, the production process at this company has met the iso-13485 quality standard (the quality standard for the medical device industry) except for the local ventilator production line, which specifically mass-produced prototypes made in indonesia. in addition, it is recommended that the pt-emb involves the quality team from the planning stage, the purchasing process stage, and the material receiving stage. at the planning stage, selecting materials and determining specifications that guarantee quality should be considered. in the purchasing stage, the supplier selection must be reviewed and the technical quality specifications offered by the supplier. when receiving goods, the quality team must verify all materials are per the desired quality. 5.3 research limitation this study has limitations related to social and activity restrictions due to the pandemic in the company, which causes questionnaire data collection, interviews, and discussions to be carried out in stages repeatedly—some using a paper questionnaire form and some using an online application. the same thing was done when fgd discussions with experts were conducted online using the video call facility and the online google-form application. the time limitation possessed by the five experts can be overcome by partially discussing several stages until all the results are collected, which can be made a consensus with the confirmation of the experts as a resource. organizational performance appraisal using the baldrige variable in this company has never been carried out other than a performance appraisal for employees as a requirement for calculating the annual bonus and iso13485 assessment for administrative production areas. thus, the result cannot be compared to the previous comprehensive company performance evaluation. other industries in indonesia that use the baldrige variable are only government-owned companies, hospitals, and educational institutions; hence, benchmarking cannot be carried out. the performance evaluation was in the cov-19 pandemic period so that company activities were only prioritized for the production of equipment for covid-19 handling, which was carried out urgently, i.e., oxygen generators and local prototype modified failure mode and effect analysis approaching to improve organization performance based on baldrige criteria a case study of an electro-medic industry 53 ventilators, and might be different from activities in normal conditions either before or after the pandemic. 6. conclusion and suggestion 6.1 conclusion the results showed that the performance of this company, when analyzed using the baldrige variable, was at the early improvement level of achievement, with the best value performance in the leadership variable and the lowest value performance in the operational variable. it is in line with the expert's evaluation that the priority performance should be improved is the operational variables. apart from these variables, other variables also show weak performance indicator items, namely in the knowledge management variable, performance analysis, and measurement and outcome variables. weak performance in the labor variable is only found in the indicator of co-worker cooperation. this study produces solutions to improve company performance in the order of priority. in practical terms, the performance items that involve the internal company will be easily corrected. what will be difficult to implement is the availability of national standards for ventilator products. until the time this research was compiled has not been issued by the national standardization agency for indonesia. 6.2 suggestion for future research  evaluating organizational performance using the baldrige variable for manufacturing electro-medical devices can be a role model for similar industries, particularly in indonesia and south east asia. the obstacles encountered can be used as lessons learned by other researchers.  organizational evaluation using the baldrige model combined with fmea was not found in previous literature. thus, further research is expected to be followed that will strengthen the 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(2021). will productivity and growth return after the covid ‑ 19 crisis ? in mckinsey global institute executive summary (issue march). https://www.mckinsey.com/industries/public-and-socialsector/our-insights/will-productivity-and-growth-return-after-the-covid-19-crisis © 2021 by the authors. submitted for possible open access publication under the terms and conditions of the creative commons attribution (cc by) license (http://creativecommons.org/licenses/by/4.0/). modified failure mode and effect analysis approaching to improve organization performance based on baldrige criteriaa case study of an electro-medic industry sugiri widjajanto, erry rimawan 1. introduction 2. literature study 2.1 baldrige criteria for performance measurement 2.2 fmea method for evaluating organizational performance 3. research method 4. data result and analysis 4.1 baldrige scoring based on questionaire 4.2 fmea fgd result 5. result and discussion 5.1 company performance evaluation compare with other researches 5.2 research contribution to the company 5.3 research limitation 6. conclusion and suggestion 6.1 conclusion 6.2 suggestion for future research references plane thermoelastic waves in infinite half-space caused operational research in engineering sciences: theory and applications first online issn: 2620-1607 eissn: 2620-1747 doi: https://doi.org/10.31181/oresta280922001k * corresponding author. brajkar@gmail.com (b. kar), bapibiswa86@gmail.com (b. mohapatra), kar_satya@yahoo.com (s. kar), sushant.tripathy@gmail.com(s. tripathy). small and medium enterprise debt decision: a best-worst method framework brajaballav kar 1, biswajit mohapatra 2, satyaballav kar 3, sushanta tripathy 2* 1 school of management, kiit university, bhubaneswar, india 2 school of mechanical engineering, kiit university, bhubaneswar, india 3 giet university, rayagada, india received: 16 april 2022 accepted: 07 june 2022 first online: 28 september 2022 research paper abstract: lack of resources among small and medium enterprises (smes) but a lower level of debt, despite policy incentives, is perplexing. the level of debt in smes has four influencers such as the business owner, firm, bank, and government. primarily, business owners would like to increase wealth and retain control, banks would lend and cover the risk of debt, and the government would promote smes for employment and growth. thus, the decision for debt and subsequent growth and performance appears simple. but, the reserve of bank of india observes that the level of debt in smes remains below the expected level, over the years, despite policy incentives. though the factors leading to debt decisions are known, how the priorities of such factors explain the contradiction are lacking. this research identifies various factors leading to debt decisions from the literature, uses the best worst methodology (bwm) to find their relative importance, and corroborates it with the qualitative data gathered from experts. we find that banks at 34 percent weight in debt decision (highest), 6 percent more compared to the firm. the government has the least importance, at around 10 percent. however, the firm performance, trust in the bank, compliance, firm growth, and bank-firm relationship are the top five decision variables for debt. given the stronghold of banks, their actions and decision-making must be suitable for the sme business context. operationalization of the qualitative criteria of bank’s trust in sme, digitalization, improvement in bank transaction documentation, and the possibility of digital gateway organizations emerging as institutional sme lenders are some future research scopes. keywords: sme, india, debt, bank, entrepreneur, best worst method. 1. introduction new venture formation within resource constraints is the hallmark of entrepreneurship. given the importance of entrepreneurship, government, banks and mailto:brajkar@gmail.com mailto:bapibiswa86@gmail.com mailto:kar_satya@yahoo.com mailto:sushant.tripathy@gmail.com f. kar et al./oper. res. eng. sci. theor. appl. first online other entities try to mitigate resource constraints especially, finance. often, policymakers try to estimate the credit gap to micro, small, and medium enterprises (msme in india or smes in general) and address the issue of access to credit. therefore, it is surprising when smes in a country like india do not consume enough credit, despite an ongoing policy focus. the reserve bank of india (rbi) reported on the weak growth of msme credit as “years of mandated lending have not produced enough progress and new approaches are needed (reserve bank of india, 2019).”the sme credit shrank in 2020 despite government incentives fueling concern of widening of the credit gap and subsequent adverse impact on economic growth and wage (sen, 2020). the covid-19 crisis fueled serious concerns about credit availability, and the government tried to match the crisis through various policy measures and support. however, the rbi observation was for extended periods, suggesting the issue is not limited to the policy or banks alone. entrepreneurs, firms, banks, and governments are four entities responsible for the outcomes of the institutional financing mechanism. apparently, debt aversion is a personal attitude; a negative disposition of entrepreneurs towards the debt that affect the financing decision of their businesses. the personal characteristics of an entrepreneur are independent variables. secondly, the firm has characteristics such as growth, performance, and tangible assets among other factors influencing the eligibility for an institutional debt. banks, on the other hand, evaluate different firm and entrepreneurial factors, match the demand and supply of funds for loans. the government with its policies and incentives can influence the entrepreneur, firm, and the bank for the desired outcome of a loan decision. institutional finance helps smes to improve their productivity and growth but simultaneously expose them to various debt risks. this research responds to the question why policy incentives do not prompt smes to take adequate loans. in general, we try to understand the importance of different factors in institutional debt decisions. we approach this question though the best worst method (bmw) of multi criteria decision making. this method for the debt decision frame work is novel and not applied in earlier research. the results contribute to the pecking order theory, trade-off theory, and agency theory applicable to the capital structure of firms. as the subsequent review indicates, the capital structure decision framework in the case of smes is an understudied area. the interplay of various factors necessitates a purposive review of literature, presented in the next section. subsequent sections include literature review, factors affecting debt decision in smes, theoretical framework, research gap, methodology, analysis discussion, limitation, and future scope. 2. literature review typically, an entrepreneur finances a new venture from his own funds or bootstrapping. initial funds deployed are usually equity. according to the pecking order theory (pot), entrepreneurs do not accept external equity due to the accompanying threat of wealth dilution (sapienza et al., 2003). a formal debt infusion to the capital structure takes place subsequently. debt sources can be informal, from individuals and known sources. banks are institutional sources of finance and such finances are known as sme finance. there is a supply and demand side of sme finance but the rbi report indicates that the demand side of sme finance is lacking small and medium enterprise debt decision: a best-worst method framework consistently. sme finance influences capital investment, firm performance, and employment, but its influence on profitability and wages is not apparent (kersten et al., 2017). this finding is debatable. another study contested that debt funding is not beneficial for sme performance (cheong et al., 2020). the relationship between finance on performance and employment makes policymakers focus on it. secondly, improvements in firm performance and resource constraints presuppose the need for debt. in an ideal situation, the demand and supply for sme financing should match but this is not the case. an optimal level of debt helps improve sme performance (jadoua & mostapha, 2020) but it is also argued that the book value of equity is an adjustable accounting number and does not play a significant role in financing decisions (kieschnick & moussawi, 2018). the capital structure of smes is not a country-specific issue. recent research on debt and capital structure spread across countries such as ethiopia (melesse, 2020), europe (li et al., 2019), japan (cui, 2020), argentina (briozzo et al., 2016), portugal (pacheco & tavares, 2017; serrasqueiro et al., 2016), sweden (heshmati, 2001; öhman & yazdanfar, 2017), india (bhama et al., 2018; kent baker et al., 2020; kumar & rao, 2016), spain (acedo-ramírez et al., 2013), lebanon (jadoua & mostapha, 2019, 2020), srilanka (kuruppu & azeez, 2016), france (adair & adaskou, 2018)], and united states (coleman et al., 2016). the geographical spread indicates the commonality and seriousness of the issue. the following section groups the findings of the review based on stakeholder of debt decisions such as entrepreneur/ sme owners, firms, banks, and government. 2.1. e: entrepreneur attributes the personal characteristics of the entrepreneur determine the level of debt (chaganti et al., 1996). personal perspectives, life events, future outlook, and future funding options influencing decisions in the sme context, indicate that smes are an extension of the owners’ personal objectives (wong et al., 2018). uncertainty avoidance and individuality characteristics are negatively related to the long-term debt of smes (kearney et al., 2012). similarly, entrepreneurial optimism based on earnings forecasts is associated with debt decisions. more optimistic entrepreneurs prefer equity (fourati & attitalah, 2018). firms run by debt-averse entrepreneurs are less likely to use debt, even if guaranteed by the government during the covid-19 crisis; interestingly, the debt policies reduce interest significantly (paaso et al., 2021). even the socio-emotional wealth of the entrepreneur influences debt decisions (rajamani, 2021). 2.1.1. e1: expertise entrepreneurial expertise is related to decision-making, responsiveness to situations, performance, recognize patterns and situations, detecting unpredictable situations, decisiveness to take action, and having a non-predictive approach (dew et al., 2015). abilities of owner-managers influence the capital structure in the sme context (eniola, 2018). many times, entrepreneurial optimism is not adequate to convince the banks of the prospect of business and loans (fourati & attitalah, 2018). f. kar et al./oper. res. eng. sci. theor. appl. first online 2.1.2. e2: experience risk perception and experience have a curvilinear relation (sitkin & pablo, 1992). the confidence of an inexperienced and very experienced business owner is likely to be different. dependence on information and perception of the ability to control may vary due to the level of experience. the nature of entrepreneurial experience influences entrepreneurial optimism and thereby the financing choices; serial entrepreneurs are more likely to use debt (fourati & attitalah, 2018). the threat rigidity hypothesis also suggests that individuals with prior experience of failure may be more conservative (van gelder et al., 2007). the business sector, asset size, and demography factors of owner such as education and experience are also major determinants of debt (kuruppu & azeez, 2016). lack of experience and immigrant status implies more personal sources of debt (coleman et al., 2016). 2.1.3. e3: risk appetite risk appetite is the amount of risk one is willing to accept to pursue one’s objective. risk propensity is the general tendency to take risks but risk perception is the assessment of risk in a situation (eniola, 2018). the risk propensity is influenced by a habit (inertia) or by the outcomes of past successful attempts (outcome).risk appetite influences financial and non-financial performance (fang & an, 2016). though the perception of risk is related to the opportunities, it is not only about economic risk, the risk of conceding self-determination or control over business is also an important factor (sapienza et al., 2003). avoidance of uncertainty and business risk are negatively associated with long-term debt of smes (kearney et al., 2012). 2.1.4. e4: social status debt attitude is determined by education, risk-taking, and financial literacy, and it has a cultural element that passes through generations (almenberg et al., 2019). the risk of bankruptcy negatively affects the self-esteem of sme owner (khan et al., 2020). the loss of income, personal debt, a decline in social status, low self-esteem, feeling of being stigmatized, blaming others, feeling of remorse, and regret are major costs of business failure (rasekhi et al., 2017). 2.1.5. e5: ability to manage risk smes do not consider debt as a business risk leading to failure thus, the risk of debt is considered insignificant (kramoliš & dobeš, 2020). but, interest to sales ratio is one of variables that predict the financial failure of smes (zizi et al., 2020). non-firmspecific factors influence the mix of funds for a firm. financial flexibility, limited selfliability, business risk, financial risk, interest rate risk, transaction cost, and tax benefits among other factors influence the debt level of a firm. however, business owners have a neutral attitude towards the 'debt level of other industries' and 'innovative schemes of banks' while considering debt decisions (dogra & gupta, 2009). in addition to the business risk, sme owners also desire to reduce interference from debt providers and maintain independence and autonomy (kearney et al., 2012). the ability of the entrepreneur to manage financial risk influences the competitiveness of smes (kozubíková et al., 2017). small and medium enterprise debt decision: a best-worst method framework 2.1.6. e6: control over business almost all forms of external financing require business owners to sacrifice some decision control (winborg & landström, 2001). thus, the degree of control on the business and external financing contradicts each other. authors have proposed that the choice of the financing source is determined by the drive for self-determination, emotion may also limit the rational-economic decision (sapienza et al., 2003). a firm’s debt level depends on a businessperson's attitude toward debt, need for control, risk propensity, experience, social norms, and personal net worth (matthews et al., 2016). 2.2. f: firm attributes several firm attributes are evaluated for a loan. the firm size is one such attribute that encompasses assets, sales, or market value of equity. smes prefer internal funds followed by bank financing (long-term loans from government and financial institutions). for smes. the trade credit, funds from family and friends, and money lenders remain informal sources in order (kent baker et al., 2020). major sources of short term debt are the trade credit and bank loan which is associated with firm characteristics (size, age, ownership, sector, and region), the capital structure of smes are determined by the age, profitability, tangibility, and liquidity (kumar & rao, 2016). the financing decision of smes depended on firm characteristics (firm age, size, and legal form) and owner characteristics (age, education, and perceived emotional bankruptcy costs (briozzo et al., 2016). the firm age did not significantly impact the pecking order of debt usage. however, debt redemption behavior was different for different firm sizes. larger firms redeem more debt compared to small and medium firms, which was explained as a need to retain funds for future financing needs of young firms (bhama et al., 2018). the level of debt in an sme is likely to be higher if the initial start-up capital included debt (melesse, 2020). in the hospitality sector, the debt is influenced by profitability, assets tangibility, firm dimension, total liquidity, and risk (pacheco & tavares, 2017). a firm’s debt was found to be influenced by profitability, firm age, the structure of ownership, and government support (melesse, 2020). sme access to debt depended on firm size, firm age, type of industry, type of ownership, tangibility, and profitability where firm age, type of industry and profitability have a positive effect but firm size and type of ownership have a negative effect on access to debt (jadoua & mostapha, 2019). firm characteristics (growth opportunity, firm size, assets, and selling products) and owner characteristics (net worth, experience, education, and ethnicity), and personal sources were preferred by small but growing firms (coleman et al., 2016). information asymmetry, agency problems, and collateral requirements are important for small firms to access long-term debt (jadoua & mostapha, 2019; serrasqueiro & caetano, 2014). a contradictory finding was that the firm size, gender of the owner, and education did not show a correlation with debt level (melesse, 2020). firms try to maintain a target level of debt and if the target is exceeded considerable time is required to bring it back to the level (heshmati, 2001). 2.2.1. f1: firm growth the level of debt is influenced by growth opportunities, credit risk, and control over ownership (adair & adaskou, 2018). along with growth, variables such as size, f. kar et al./oper. res. eng. sci. theor. appl. first online age, profitability, liquidity, asset tangibility, non-debt tax shields, and industry affiliation explained the debt policy (öhman & yazdanfar, 2017). however, there are sector-specific variations. in the hospitality sector, the firm growth and tax benefits were not related to the debt (pacheco & tavares, 2017). japanese smes, which are small, profitable, and older, pursue the strategy of ‘non-positive net debt’ (cui, 2020). such firms are likely to have few growth opportunities, and higher tangibility. it is also known that young firms tend to focus on growth rather than profitability (epure & guasch, 2020). debt has a positive association with growth opportunity but a negative relationship with the cost of debt, age, and cash flows (acedo-ramírez et al., 2013). 2.2.2. f2: collateral collateral is one of the most common criteria of evaluation for debt. as per the rbi guideline, banks are forbidden to ask for collateral security for loans up to inr 1 million to units in the micro and small enterprises (reserve bank of india, 2021). the availability of collateral security enables businesses to secure debt. the availability of pledgeable short-term assets enables export-intensive smes (maes et al., 2019). researchers did not find a significant effect of tangibility on access to debt (jadoua & mostapha, 2019). 2.2.3. f3: performance profitability and firm size are negatively associated with the leverage for smes in manufacturing, and large firms with stable earnings do not prefer debt (rao et al., 2019). the adverse impact of short-term and long-term debt has been reported in a panel data study (franquesa & vera, 2021). debt has a significant negative effect on firm performance for smes, and the effect reduces when the firm size exceeds a threshold level (ibhagui & olokoyo, 2018). the credit risk moderates the debt level and firm performance but the debt ratio is negatively related to firm performance in low credit risk smes (li et al., 2019). a lower level of debt is related to a higher level of profitability (serrasqueiro et al., 2016). 2.2.4. f4: age arguing that the small firms have information opacity influencing the credit risk, authors have suggested that the firm age is a better predictor of risk than size (nitani & riding, 2015). even among small businesses, the financing pattern varies. typically, newer firms depend more on debt compared to older firms (auken & doran, 1989). independently, the firm age, is negatively related to the use of debt however, there is an interaction effect of firm age with corporate governance features in older firms where managers can adequately exercise their risk preferences to change the capital structure (kieschnick & moussawi, 2018). 2.3. b: bank attributes loan decision-making is influenced by bank characteristics, as well as the loan officer’s decision‐making biases, and deliberate and intuitive reasoning style (trönnberg & hemlin, 2012). banker’s behavior significantly influences banking products awareness and outcomes (kar, 2019). bank officers use deliberative and intuitive analysis for lending decisions which includes soft information and situational factors (trönnberg & hemlin, 2014). in the absence of the performance history of the firm and verified skill of the entrepreneurs, banks perceive incompetence and small and medium enterprise debt decision: a best-worst method framework opportunism and collateral reduces the risk of debt (sapienza et al., 2003). research has indicated a negative relationship between power distance and debt implying a consultative role of financial institutions to be more appropriate (kearney et al., 2012). the more complex horizontal and vertical structure of the bank forces entrepreneurs to choose costlier alternatives (samuel baixauli-soler et al., 2021). 2.3.1. b1: relationship some argue that the bank debt has a governance role based on bank-firm relationship and can act as a signal to outside investors (serrasqueiro & caetano, 2014). the bank-firm relationship does not depend on transactions but on trustrelated factors for which smes choose local banks and maintain a long-term relationship (jackowicz et al., 2020). a relationship grounded on trust is better for smes access to debt (hernández-cánovas & martínez-solano, 2010). however, banks typically attempt to reduce the risk on the bank and shift it to the smes while taking a loan decision (bruns & fletcher, 2008). 2.3.2. b2: trust trust-related factors influence sme lending decisions (jackowicz et al., 2020). literature proposes that trust reduces agency costs. the trust of the bank manager in smes increases the credit availability (moro & fink, 2013). public sector and private sector banks deploy different uncertainty strategies for sme lending and the trust development mechanism varies between them (nguyen et al., 2007). a longitudinal study confirms a robust positive relationship between trust and credit access (kautonen et al., 2020). however, trust matters only when formal information to assess the sme’s creditworthiness is insufficient further, banks try to avoid uncertainty and depend on trust while lending to private business clients (nguyen et al., 2007). 2.3.3. b3: interest rate the cost of debt is more but the access to debt increases, if smes have long relationship with a single bank, suggesting that the relationship should be with at least two banks (hernández-cánovas & martínez-solano, 2010). the cost of debt is influenced by macro-economic factors and firm-specific factors (size) (yazdanfar & öhman, 2020). further, the quality of financial statements is inversely related to the effective interest cost for smes (vander bauwhede et al., 2015). banks also charge differentially based on innovation and location, even for publicly guaranteed loans, which the authors have called the ‘innovation debt penalty’ (cowling et al., 2018). 2.3.4. b4: compliance lenders can impose ‘covenants’ or restrictions on the firms’ operations (sapienza et al., 2003). debt contracts have been observed to be less strict if asset tangibility is higher and the firm is family-owned (hillier et al., 2018). however, ‘shareholdercreditor agency conflict’ is a well-acknowledged phenomenon. covenants affected access to loans by smes, banks formulate strict loan extension procedures to reduce loan defaults (sansa, 2019). f. kar et al./oper. res. eng. sci. theor. appl. first online 2.4. g: government attributes the government tries to promote the cause of smes through various policy measures. salient measured are indicated below as factors. 2.4.1. g1: policy incentives the level of debt and policy incentive has been difficult to ascertain (reserve bank of india, 2019). start-ups depend on access to capital during the initial stages and government funding or grants are important sources for high-technology entrepreneurs (elston & audretsch, 2011). a nigerian study indicated a significant relationship between government policy and the business growth of smes (alabi fa et al., 2019). 2.4.2. g2: subsidy/ tax benefit subheading the role of subsidy or tax-benefit declared by the policy of the government on firm debt and performance is ambiguous at best. smes, supported by the government programs recorded negligible financial performance (chen et al., 2020). the financial support policies were not found effective in addressing cash constraints or reopening of smes, possibly due to complications in access to policy-oriented loans or a misallocation (chen et al., 2020). however, debt was found inversely related to nondebt tax shields and directly to fixed assets (acedo-ramírez et al., 2013). 2.4.3. g3: loan guarantee credit guarantee to smes is an international phenomenon, and such schemes are in operation in india since 1981 (levitsky, 1997). the ministry of msme, india, and small industries development bank of india (sidbi), established the credit guarantee fund trust for micro and small enterprises (cgtmse) in the year 2000 to ensure credit guarantee. the government and sidbi contribute to the fund in the ratio of 4:1 respectively. while some suggest that such assistance beyond conventional financing improves sme performance (xiang & worthington, 2017), others argue that the effect is difficult to measure due to lack of clarity in operations, irregular monitoring, and nontransparent accounting among other factors (honohan, 2010). guaranteed access to credit and trade credit influenced the level of debt in the case of french smes (adair & adaskou, 2018). 2.5. theoretical background literature suggests three theories, the pecking order theory (pot), tradeoff theory (tot), and agency theory related to the capital structure of the smes (acedo-ramírez et al., 2013; kumar et al., 2019; serrasqueiro & caetano, 2014). the pecking order theory (pot) argues that the financing preference is internally generated funds, debt, and external equity in the order. this preference for source and performance is not unequivocal. for start-ups, research reported a small positive impact of internal funding on start-up growth, debt funding did not have any whereas, external equity obtained from private equity or venture capital has a weak role. whereas, it is known that financial constraints limit the growth of startups (corsi & prencipe, 2018). on the other hand, the trade-off theory suggests that firms decide on their optimum level of debt taking into account the net debt benefits. it is found that profitable and small and medium enterprise debt decision: a best-worst method framework old smes choose less debt but larger smes choose more debt thereby indicating that these theories are not exclusive to each other (serrasqueiro & caetano, 2014). it is also known that the information asymmetry and uncertainty associated with a new firm make the external finance scarce and costly. the agency cost theory (agency theory) suggests that the debt holder of firms restricts the use of capital through covenants if they believe that the agents (managers) are likely to favor equity holders. another corollary is that the managers are self-serving agents to be disciplined by debt. thus, debt plays a balancing role between agency cost of equity and agency cost of debt. the debt level was influenced by three different characteristics such as trade-off behavior, pecking order, and an extreme aversion to debt (briozzo et al., 2016). the wealth maximizing explanation of financing decisions in smes is argued to be inadequate. wealth maximization and self-determination are two primary motives that drives entrepreneurial financing, but the trade-off between them is complex and dynamic (sapienza et al., 2003). the decision on the level of debt can change with the change in contexts, it is not expected to be static. further, the term (short or long) of debt has different explanations. the applicability of tot is more to the long term debt and pot is more applicable for short term debt (nunes & serrasqueiro, 2017). 3. research gap sme capital structuring does not follow traditional finance theory. in addition, there are bootstrapping mechanisms to generate various combinations of financing mechanisms suitable for entrepreneurial organizations (winborg & landström, 2001). capital structuring choices of entrepreneurial firms are open to investigation and debate (sapienza et al., 2003). the uniqueness of cultural, legal, and institutional characteristics in the emerging markets makes the debt decision in smes more important compared to others (vo, 2017). researchers acknowledge that how smes decide their financial structures are not known but agree that there are a series of factors including personal perspectives, life events, and future outlook, and future funding options, thereby reinforcing the view that smes are an extension of the owners’ personal objectives (wong et al., 2018). literature does suggest the factors responsible for capital structure decision and to some extent the interaction among factors. however, the relative importance of banks, entrepreneurs, governments, and firms as different criteria, in the decision is not investigated adequately. each of these criteria has various sub-criteria and their relative importance are also not adequately understood. thus, the objectives of this research are to understand the relative importance of criteria and sub-criteria in the sme debt decision. 4. methodology the multi criteria decision making (mcdm) method best-worst method (bwm) was used due to its advantages of higher reliability compared to ahp and fewer data requirements for comparison (rezaei, 2015). bwm is also used in combination with balanced scorecard for business performance evaluation (dwivedi et al., 2021), supplier selection decision (fazlollahtabar & kazemitash, 2021), service provider selection in the supply chain (muravev & mijic, 2020), and off-road vehicle selection f. kar et al./oper. res. eng. sci. theor. appl. first online (d. s. pamučar & savin, 2020). literature indicates increased usage of bmw method in research. the steps involved in bwm are as follows: step 1: determine a set of decision criteria the decision criteria are identified in this stage. step 2: determine the best (b) (most desirable or most important) and the worst (w) (least desirable or least important) decision criteria based on experts’ opinion. step 3: determine the preference of the best decision criterion (b) over all the other decision criteria, using a 9-point scale (1: b is equally important to j; 9: b is extremely more important than j; where j are the other criteria under consideration). the result is a best-to-others (bo) vector as follows: zb = (zb1, zb2… zbn) (1) where zbj represents the preference of b over j and zbb = 1. step 4: determine the preference of all the decision criteria over the worst criterion (w), using a 9-point scale (1: j is equally important to w; 9: j is extremely more important than w). it results in a others-to-worst (ow) vector as follows: zw = (z1w, z2w… znw)t (2) where zjw represents the preference of j over w and zww = 1. step 5: find the optimal weights (𝑤1 ∗,𝑤2 ∗,………. ,𝑤𝑛 ∗). the optimal weights should be determined such that the maximum absolute differences { |𝑤𝐵 − 𝑧𝐵𝑗.𝑤𝑗|, |𝑤𝑗 − 𝑧𝑗𝑤.𝑤𝑤| } ⩝ j is minimized i.e. min𝑚𝑎𝑥⏟ 𝑗 { |𝑤𝐵 − 𝑧𝐵𝑗.𝑤𝑗|, |𝑤𝑗 − 𝑧𝑗𝑤.𝑤𝑤| } (3) s.t. ∑ 𝑤𝑗𝑗 = 1 wj ≥ 0, ⩝ j problem (1) is equivalent to the following linear problem: min ȇ s.t. |𝑤𝐵 − 𝑧𝐵𝑗.𝑤𝑗|≤ ȇ, ⩝ j |𝑤𝑗 − 𝑧𝑗𝑤.𝑤𝑤| ≤ ȇ, ⩝ j (4) ∑ 𝑤𝑗𝑗 = 1; wj ≥ 0, ⩝ j. solving problem (2), the optimal weights ( 𝑤1 ∗,𝑤2 ∗,……….,𝑤𝑛 ∗) are determined alongwith the optimal objective function value ȇ* (consistency index or ksi*). the closer the value of ksi* to zero, the more higher level of consistency of the pairwise comparisons provided by the expert(s). if the mcdm has more than one level, each levels’ weights are obtained through the bwm (steps 1 to 5), which is then multiplied with all level weights to obtain the global weights of each criteria. based on the value of global weights of criteria, the ranks were assigned to them which fulfils the objective of the concerned research. small and medium enterprise debt decision: a best-worst method framework the 17 identified sub-factors/criteria were evaluated by experts (9 in number; r1 to r9) who quantified and ranked the factors based on contributions toward the debt decision smes from banks. a scale of 1-9 was used for the best and worst factors separately for each criterion. at the initial level, the factors such as entrepreneur, firm, bank, and government role were ranked and subsequently, the sub-factors of each factor were ranked. the analysis was done by the use of bwm solver2021 version (excel file) developed by zafar rezaei, the contributor of the bwm method. the factors and sub-factors are shown in figure-1. the experts were qualified by their profession, experience in the profession, education, and awareness about the topic under investigation (msme, bank, and government policy). figure 1. proposed model for debt decision in smes during the ranking process, experts chose to comment on the issue and it was noted down as additional qualitative feedback. the feedback is presented in a separate section, as corroboration to the findings. table 1. expert profiles (r1 to r9 are experts) q1 q2 q3 q4 q5 q6 q7 r1 banker 41 14 m.com. 8 8 8 r2 banker/ academician 65 36 ph.d. 6 8 7 r3 banker 51 23 m.sc.(ag) 7 9 8 r4 entrepreneur (hotel, govt. supplier/ contractor) 51 25 b.e. 8 7 7 r5 academic/ entrepreneur 52 29 ph.d. 6 6 6 r6 govt., industry promotion officer 46 23 l.l.b. 9 7 9 r7 retail 33 10 b.com 6 7 6 r8 entrepreneur 51 25 b. tech. 6 7 6 r9 academician 51 25 ph.d. 5 6 5 entrepreneur firm bank government sme debt decision g1: policy incentive g2: subsidy/ tax benefit, g3: loan guarantee b1: relationship b2: trust b3: interest rate b4: compliance f1: growth, f2: collateral f3: performance, f4: age e1: expertise e2: experience e3: risk appetite e4: social status e5: ability to manage risk e6: control on business f. kar et al./oper. res. eng. sci. theor. appl. first online note: r1-9: respondent, q1: profession, q2: age, q3: experience, q4: highest education, q5: awareness of msme, q6: awareness of bank, q7: awareness of govt. policy on msme, the scale for q5 to q7 is 1-least, 9best experts chosen for the study belonged to relevant actors in the loan decision (business owners, bankers, industry promotion officer, and academicians. the academicians chosen had different roles as academicians and bankers and entrepreneurs. anonymity was maintained to ensure response accuracy and validity. the demography and awareness levels of experts were as follows, age (mean= 49, sd=8.73), experience (mean=23.3, sd=7.63), msme awareness (mean=6.8, sd1.30), awareness about banks (mean=7.2, sd=0.97), awareness about government policy (mean=6.9, sd=1.27). 5. research results responses from the experts were converted to weights and are presented in table2 to table-6. table 2 showcases the main criteria weightage (e, f, b, g) by each of the 9 experts (r). the average of each gives the local weightage of the main criteria. similarly, for each sub-criterion within each main criterion the weightage were calculated from experts’ opinions (table 3 to table 6). table 2. general attributes {e, f, b, and g} weightage by individual experts respondent/ attributes e f b g ksi* r1 0.1558 0.2597 0.4870 0.0975 0.2922 r2 0.5000 0.2858 0.1428 0.0714 0.0714 r3 0.4545 0.1818 0.2727 0.0910 0.0909 r4 0.1490 0.4964 0.2978 0.0568 0.0992 r5 0.1571 0.4429 0.3142 0.0858 0.1857 r6 0.1617 0.0598 0.6437 0.1348 0.1646 r7 0.4333 0.2000 0.3000 0.0667 0.1666 r8 0.1615 0.0665 0.5701 0.2019 0.2375 r9 0.1966 0.6103 0.0621 0.1310 0.1758 e: entrepreneurs; f: firm; b: bank; g: government table 3. entrepreneurship sub-criteria weightage {e1 to e6} respondents/ sub-factors e1 e2 e3 e4 e5 e6 ksi* r1 0.4391 0.1822 0.1368 0.0514 0.1094 0.0911 0.1077 r2 0.1034 0.1292 0.3899 0.0428 0.2585 0.0862 0.1268 r3 0.0941 0.1176 0.2351 0.0561 0.3504 0.1567 0.1198 r4 0.0885 0.1106 0.1475 0.0627 0.3794 0.2213 0.0632 r5 0.1106 0.1475 0.3794 0.0627 0.2213 0.0885 0.0632 r6 0.3794 0.2213 0.1475 0.0627 0.1106 0.0885 0.0632 r7 0.3794 0.1475 0.1106 0.0985 0.2213 0.0527 0.0632 r8 0.2222 0.1482 0.1111 0.0470 0.1111 0.3704 0.0740 r9 0.0781 0.0936 0.1560 0.0471 0.2340 0.4012 0.0668 e1: expertise; e2: experience; e3: risk appetite; e4: social status; e5: ability to manage risk; e6: control over business small and medium enterprise debt decision: a best-worst method framework table 4. firm sub-criteria weightage {f1 to f4} respondent/ sub-factors f1 f2 f3 f4 ksi* r1 0.5824 0.1477 0.1847 0.0852 0.1562 r2 0.2353 0.0588 0.5294 0.1765 0.1764 r3 0.3000 0.2000 0.4333 0.0667 0.1667 r4 0.4545 0.1818 0.2727 0.0909 0.0909 r5 0.2586 0.1724 0.4655 0.1035 0.0517 r6 0.1603 0.5496 0.0764 0.2137 0.0916 r7 0.2586 0.1724 0.4655 0.1035 0.0510 r8 0.2222 0.0777 0.5667 0.1334 0.1000 r9 0.2951 0.1475 0.4918 0.0656 0.0983 f1: firm growth; f2: collateral (firm); f3: firm performance; f4: firm age table 5. bank sub-criteria weightage {b1 to b4} respondent/ sub-factors b1 b2 b3 b4 ksi* r1 0.4848 0.1818 0.2727 0.0607 0.0606 r2 0.0578 0.2480 0.5454 0.1488 0.1983 r3 0.2040 0.4286 0.0612 0.3062 0.1836 r4 0.1724 0.2586 0.1034 0.4656 0.0517 r5 0.2586 0.1724 0.1034 0.4656 0.0517 r6 0.2586 0.4656 0.1034 0.1724 0.0517 r7 0.4656 0.2586 0.1724 0.1034 0.0517 r8 0.1632 0.2176 0.0836 0.5356 0.1171 r9 0.0680 0.5272 0.1156 0.2892 0.0510 b1: bank relationship; b2: trust in bank; b3: interest rate; b4: reporting compliance table 6. government sub-criteria weightage {g1 to g3} respondent/ sub-factors g1 g2 g3 ksi* r1 0.5416 0.1667 0.2917 0.0416 r2 0.0910 0.2272 0.6818 0.2272 r3 0.0588 0.8059 0.1353 0.2764 r4 0.6444 0.2445 0.1111 0.0888 r5 0.1667 0.5417 0.2916 0.0416 r6 0.5417 0.2916 0.1667 0.0416 r7 0.1667 0.5417 0.2916 0.0416 r8 0.2444 0.6444 0.1112 0.0888 r9 0.6444 0.2444 0.1112 0.0888 g1: policy incentive; g2: subsidy/tax benefit; g3: government loan guarantee table-7 represents the weightage of criteria, which was evaluated by taking the mean of each factor (column) for e, f, b, and g respectively. the weights for e, f, b, and g are 0.2633, 0.2892, 0.3434, and 0.1041 respectively. similarly, the local weights for sub-criteria are evaluated from tables (3, 4, 5, and 6) to find the local weights of each sub-factor. the global weights are calculated by multiplying the factor weights corresponding to the sub-factors and the local weights of sub-factors. the summation of all 17 global weights should be 1. f. kar et al./oper. res. eng. sci. theor. appl. first online table 7. local and global weights of criteria and sub-criteria and ranking criteria weight sub-criteria local weight global weight (%) ranks entrepreneurs 0.2633 e1: expertise 0.2105 5.54 8 e2: experience 0.1442 3.84 13 e3: risk appetite 0.2015 5.30 10 e4: social status 0.059 1.55 17 e5: ability to manage risk 0.2217 5.84 7 e6: control over business 0.1631 4.29 11 firm 0.2892 f1: firm growth 0.3074 8.89 4 f2: collateral (firm) 0.1898 5.49 9 f3: firm performance 0.3873 11.20 1 f4: firm age 0.1155 3.34 15 bank 0.3434 b1: bank relationship 0.237 8.14 5 b2: trust on bank 0.3065 10.52 2 b3: interest rate 0.1735 5.94 6 b4: reporting compliance 0.283 9.72 3 government 0.1041 g1: policy incentive 0.3444 3.58 14 g2: subsidy/tax benefit 0.412 4.28 12 g3: govt. loan guarantee 0.2436 2.54 16 the global weights converted into percentages indicate firm performance, trust in the bank, report compliance to banks, firm growth, and the relationship with banks to be the first five important factors. the impact of loan decision on social status is the least important factor. 5. qualitative feedback during the response collection eight of the nine experts (except r1) chose to share additional feedback about the research question and their opinion is discussed in this section, the parenthesis mentions the expert’s identification. the feedback is arranged by actors in the loan decision. entrepreneur: entrepreneurial expertise of business owners are low, they do not even maintain a basic accounting process and completely depend on chartered accountants for a loan application, indicating a need for the basic accounting education of business owners, and continual handholding (r2). entrepreneur’s often lack awareness or clarity on the policy but, insist on granting the loan (r3). the populist nature of government policy prompts a lax attitude towards the loan, and entrepreneurs assume the loan as a consumable credit, not to be repaid (r3). at times, entrepreneurs do not even meet the ‘know your customer’ (kyc) requirement of a bank and fit into the policy guidelines (r3). a genuine businessperson will not take small and medium enterprise debt decision: a best-worst method framework loan with low interest (r4). the expert r5 opined businesspersons have a financial plan; the loan decisions are relevant and important within a time frame only. bank: banks are security-oriented and demand organized documents for loan appraisal, a new policy cannot change the behavior overnight (r2). banks as business organizations check the businesspersons as potential candidates for evaluation through documented track record (r4). banks don’t take the risk (r4, r8). however, banks do not ask for records if a sufficient down payment is given which, indicates an absence of fixed policy or procedure (r4). some bank managers take risk grant loans, others can ask for many other documents which the businessperson does not have (r4). smes do not get a loan from banks, even with policy, because of stricter criteria of banks (r8). collateral is not a sufficient condition, the current performance and history of the business are more important than the projected growth, so, the decisionmaking is regressive (r8). loan to large businesses are more likely to become nonperforming assets than the loan to smes (r8). banks check net worth, and paying capacity, but do not check the feasibility of the project (r6). if there is a loan guarantee, banks adjust the mortgage amount while granting and grant the rest amount (r6). many business owners borrow from private banks because nationalized banks ask for many compliance terms (r6). banks demands security even for mudra loan (r7). a bank is an obstacle in asking for surety in repayment (r7). it is better to go for crowdfunding than a bank loan because of the over-demand of information by the bank and compliance (r5). government: the government role is limited to the level of policy (r2). often, the government policy is populist (r3). the government policy is for voters and is localized; to access a loan guarantee policy businesspersons have to offer bribes (r4). government policies are on sympathetic grounds (e.g. natural calamity) rather than on business grounds (r8). often, business owners take the subsidy for purposes other than business (r4). in the case of the prime minister’s rojgar yojana (pmry), the government is only a sponsoring agency with the role identify firms, banks are the final arbitrator on loans (r6). policy is important because of its specific terms (r6). the government policies are for the upper or lowest level of business, there is nothing for mid-level business (r7). government should promote the schemes regularly to create awareness and associated incentives can bring competitive spirit among businesspersons (r9). 6. sensitivity of factor ratings since the scores are sensitive to individual expert’s opinions, we conducted a sensitivity analysis to understand the robustness of ranks identified in this study. the sensitivity analysis of different multi-criteria decision making has been suggested in various studies (božani´cbožani´c et al., 2022; durmić et al., 2020; d. pamučar et al., 2021). for the sensitivity analysis, the score of the factors was changed, and the score of the sub-factors was not changed. thus, this sensitivity test considered the factors (entrepreneur, firm, bank, and government). secondly, in each scenario, the score of one factor was increased by 30 percent from the survey scenario and a corresponding reduction of 10 percent from the other three factors to keep the sum of factor scores as 1. for four factors in this study, a variation of 30 percent was considered as maximum. in another situation, each factor was considered to have the same weight (25 percent each). thus, we arrived at the following scenarios. survey factor score f. kar et al./oper. res. eng. sci. theor. appl. first online (s0), all factor weights equal (s1), entrepreneur factor score 30 percent more than survey (s2), firm factor score 30 percent more than survey (s3), bank factor more than 30 percent (s4), and government factor more than 30 percent more (s5) than the survey score (table 8). table 8. sensitivity test of factor and change of global rank sub-factors e1: e2: e3: e4: e5: e6: f1: f2: f3: f4: b1: b2: b3: b4: g1: g2: g3: s0 8 13 10 17 7 11 4 9 1 15 5 2 6 3 14 12 16 s1 10 15 11 17 9 14 4 12 2 16 8 5 13 6 3 1 7 s2 7 12 8 17 5 9 4 11 1 15 6 2 10 3 14 13 16 s3 9 14 10 17 8 12 2 6 1 11 5 3 7 4 15 13 16 s4 8 13 10 17 7 11 5 9 4 15 3 1 6 2 14 12 16 s5 9 14 11 17 8 13 4 10 1 16 5 2 7 3 12 6 15 figure 2. rank variation at sub-factor level due to variation in factor weights note: the numbers indicate the sub-factor for entrepreneur (e), firm (f), bank (b), and government (g) table 8 and figure 2 indicate that the ranks of sub-factors do not vary even with a 30 percent increment except when all factors have equal weight. if all factors have equal weight, then the primary sub-factor is to avail subsidy/ tax benefit in a loan decision. also, in all the scenarios considered, the social status remains the least important sub-factor. thus, the sub-factor scores are found stable in different scenarios. 6. discussion and conclusion table 7 indicates that banks have substantially more weight in the debt decision compared to other factors. firm, entrepreneur, and government play subsequent important roles in that order. the importance of the first six factors combined (f3: s0 s3 s5 0 5 10 15 20 e1: e2: e3: e4: e5: e6: f1: f2: f3: f4: b1: b2: b3: b4: g1: g2: g3: small and medium enterprise debt decision: a best-worst method framework firm performance, b2: trust in bank, b4: reporting compliance, f1: firm growth, b1: bank relationship, and b3: interest rate) account for 54 percent of the score. however, the lowest score of social status indicates that smes are not debt averse. a six percent more importance of banks than the importance of firms indicates a pervasive role of banks. the relative importance of sub-factors under the bank includes trust, reporting compliance, relationship, and interest rate, in that order. the first three factors are difficult to achieve for an sme without long past, transaction history, or personal rapport. the objective factor of interest rate is the last, indicating the importance of subjective rather than objective criteria of debt decision by smes. the second important factor ‘firm’ has firm performance, growth, and collateral as three most important criteria in that order. this order indicates that the current performance is more important than future growth. thus, the debt decision for future expansion or operation is regressive, indicating a contradiction and bank’s inclination to pass on the risk. in such a scenario, the credit offtake is expected to less during pessimistic economic growth, even with policy incentive. the ability to manage risk, expertise, and risk appetite are the three most important entrepreneurial characteristics determining the debt decision. control over the business and social status factors are last two important factors indicating the pragmatic nature of entrepreneurs. the subsidy or tax benefit and policy incentives are two most important criteria within government as a factor. the sequence indicates that debt decision partly anchors with some immediate to a medium term benefit to smes. the banking process deserves more scrutiny in light of this finding. the documentation or transaction-related opacity is likely to be mitigated partially due to recent digitalization practices (unified payment interface, upi) adopted and enhanced during the pandemic. digital transactions may also improve the creditworthiness assessment leading to improved sme lending. the findings support statements of the experts presented earlier. corruption significantly affects the choice of sources of financing, increases the use of informal debt and reduces the use of formal debt, owner's equity, and retained earnings (phan & archer, 2020). the pecking order theory indicates the use of internal fund, optimal debt, and then equity whereas, the tradeoff theory indicates the debt level is up to the tax-saving benefit. however, we find that the weight of ‘tax benefit’ factor is only 4.28 percent in the debt decision. thus, the debt is likely to be sub-optimal in case of smes. the agency theory perspective that the owners are likely to infuse debt to discipline managers is also debatable because sme owners are the managers of their businesses. 7. limitations and future scope many entrepreneurship attributes such as ethnicity were not explicitly incorporated in this research (coleman et al., 2016). similarly, the ownership structure, location, and crises were not explicit in the questions. firms with different ownership structures and legal forms such as family firms have a different levels of medium-term debt (migliori et al., 2018). the financial crisis of 2008 also influenced debt decisions (ramalho et al., 2018). this study asked the experts about the trust of entrepreneurs in the banker, but apparently, the banker’s trust in sme owners is more important in the decision context, and both trusts are not symmetric. research suggests bankers use qualitative criteria of trust for lending decisions however, it is not known how (kautonen et al., 2020). others have suggested the non-bank credit f. kar et al./oper. res. eng. 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(2020). determinants and predictors of smes’ financial failure: a logistic regression approach. risks, 8(4), 107. https://doi.org/10.3390/risks8040107 © 2022 by the authors. submitted for possible open access publication under the terms and conditions of the creative commons attribution (cc by) license (http://creativecommons.org/licenses/by/4.0/). plane thermoelastic waves in infinite half-space caused operational research in engineering sciences: theory and applications vol. 5, issue 2, 2022, pp. 206-221 issn: 2620-1607 eissn: 2620-1747 doi: https://doi.org/10.31181/oresta190822150b * corresponding author. mouba121286@yahoo.fr (m.b. bouraima), chelalclement@yahoo.com (c. k. kiptum), marakakevin@yahoo.com (k. m. ndiema), publicqiu@vip.163.com (y. qiu), ilijat@uns.ac.rs (i. tanackov) prioritization road safety strategies towards zero road traffic injury using ordinal priority approach mouhamed bayane bouraima 1, 2, 3, clement kiprotich kiptum 4, kevin maraka ndiema 4, yanjun qiu 1, 2*, ilija tanackov 5 1 school of civil engineering, southwest jiaotong university, china 2 highway engineering key laboratory of sichuan province, southwest jiaotong university, china 3 organization of african academic doctors (oaad), nairobi, kenya 4 department of civil and structural engineering, school of engineering, university of eldoret, kenya 5 university of novi sad, faculty of technical sciences, novi sad, serbia received: 21 june 2022 accepted: 11 august 2022 research paper abstract: road traffic safety has emerged as an urban mobility and development issue for african cities throughout time. to establish a comprehensive road safety reform within cities, one needed to be familiar with the political and legal environment, institutional responsibilities, and stakeholders. road safety reform, though, is not without its issues. this study aims to prioritize nairobi's road safety strategies to achieve zero traffic injuries. four road safety reform challenges were examined based on the opinions of three experts. the ordinal priority approach (opa) was used to calculate the weights and ranks of experts, alternatives, and criteria, simultaneously. the findings of the study indicated that lack of political priority given to road safety reform is the most significant challenge, while the lack of coordination among different government agencies is the least challenge. the findings of the study also indicated that the top three strategies for successfully enacting a road safety reform are to take advantage of broad institutional and governance reform, reframe the road safety in political and public debate, and bundle the road safety with other important public issues. key words: prioritization, road safety strategy, zero traffic injury, ordinal priority approach mailto:mouba121286@yahoo.fr mailto:chelalclement@yahoo.com mailto:marakakevin@yahoo.com prioritization road safety strategies towards zero road traffic injury using ordinal priority approach 207 1. introduction every year, approximately 1.3 million people are murdered and 50 million are injured in road traffic accidents (gopalakrishnan, 2012). over 90% of road traffic accidents (rtas) occur in the low and middle-income countries (lmics), with africa having the highest death rate (alimo, agyeman, sumo, bouraima, & lartey-young, 2022; das, 2022), and an indicator ranging from 25 to 34 per million people (mohammed, ambak, mosa, & syamsunur, 2019). in the recent decade, road safety has also become a major international concern. two road safety targets are included in the 2030 agenda for sustainable development: target 3.6 by 2020 and target 11.2 by 2030. according to current projections, neither target is likely to be met. in terms of tackling road safety issues, some countries have been significantly more effective than others. in locations where significant progress has been made, the importance of a comprehensive approach to road safety cannot be overstated (welle et al., 2018). road safety is considered as a public healthy lifestyle that emerges from the interaction of all transportation system elements, including habitat usage, vehicle standards, emergency services, law, roadside design, modes of transportation, and other variables. despite all of the acquired knowledge about what such a "safe system" appears like, establishing and adopting it continues to be a major challenge for many countries, particularly lmics. as the number of deaths in developing countries continues to rise (bener, abuzidan, bensiali, al-mulla, & jadaan, 2003), and road traffic collisions continue taking an incredibly huge social and financial cost burden, it is crucial to assess and fully comprehend what is adversely obstructing progress and what might be done to prevent these statistics. sharpin, harris, dempster, and menocal (2018) have conducted a study project to assess the obstacles to road safety improvement in lmics, as well as to develop a set of strategies to assist policy-makers and practicians working on road safety improvement. the initiative started with the research of wales (2017) that looked at the broad scope of the problem, the main aspects of the global response, and the current state of evidence on interventions to respond to the challenges. the study found a lack of particular emphasis on the challenges linked with road safety reform, as well as a knowledge gap about how improvement strategies should be prioritized for an effective implementation. nairobi, among other cities, was chosen for a more extensive case study examination to close this gap. a thorough assessment was carried out in partnership with local partners, based on a review of the city's injuries, fatalities, and collisions, the major actors involved in handling road safety, as well as the challenges and prospects for development. the outcomes of this study report revealed both road safety challenges and strategies for eradicating them. past studies related to road safety challenges and remedial strategies are presented in table 1. as can be seen from the table 1, very few researchers have identified the road safety challenges and remedial strategies in africa (bezabeh, 2013; khayesi & peden, 2005; martin & tawia, 2020). additionally, only one study has discussed kenya's road safety strategies and challenges without providing any proposals for the most efficient strategies to use to address these challenges (sharpin et al., 2018). moreover, these studies have not applied the multi-attribute decision making (madm). without a relevant exceptional system, an accurate pinpointing and classification of challenges and remedial strategies for road safety could not be bouraima et al./oper. res. eng. sci. theor. appl. 5 (2) (2022) 206-221 208 reached. so, the findings of these previous incomplete investigations could not give the required details for policy-makers to ameliorate road safety reform for zero road traffic injuries. based on the previous studies, an acute shortage of documentation exists about the uncertain prioritization of remedial strategies. a research gap remains in handling extensive research by taking into account both qualitative and madm methodologies. by integrating the madm method and qualitative investigation, this study intends to answer this research gap accurately. in this study, a methodology for an extensive examination of road safety challenges and prioritization of remedial strategies in nairobi is presented based on the ordinal priority approach. in this study, we will prioritize the road safety improvement strategies for nairobi according to the decision criteria for experts to have an implementation scheme. six strategies (alternatives) are taken into consideration for this reason. these strategies are evaluated based on four main criteria. the criteria are established based on the report of sharpin et al. (2018) titled: “securing safe roads: the politics of change” and confirmed with the assistance of professionals in the field. the strategies are also displayed in the same report. this study uses the ordinal priority approach (opa) recently developed by ataei, mahmoudi, feylizadeh, and li (2020). opa method gives a new multiple attribute decision-making (madm) scheme for dealing with road safety improvement based on prioritization strategies towards zero road traffic injuries. as a result, the following are the study's main contributions and novelty: (1) the opa can define the weights of experts, attributes, and alternatives concurrently without the need for normalization, pairwise comparisons, or information perfectness (pamucar, deveci, gokasar, tavana, & koppen, 2022); (2) to address the issue of a limited selection of specified scales in traditional techniques for a similar evaluation of criteria (alosta, elmansuri, & badi, 2021; badi & abdulshahed, 2019; bouraima, qiu, yusupov, & ndjegwes, 2020; bouraima, stević, tanackov, & qiu, 2021; kovač, tadić, krstić, & bouraima, 2021; stevic, badi, tanackov, & milicic, 2017; stević et al., 2022); (3) this is the first study to look at the prioritization of road safety improvement strategies in nairobi, to achieve zero road traffic injuries. in addition, four main criteria are defined to provide a feasible framework for effective prioritization of relevant strategies; (4) this research offers recommendations for choosing the best strategy for achieving zero road traffic injuries as part of the road safety improvement; (5) the opa enables policymakers to choose the most appropriate road safety improvement strategy, successfully respond to road safety challenges in nairobi. the research goals of this study are as follows: (i) to give an implementation framework for road safety improvement towards zero traffic injuries (ii) to examine the ordinal priority approach in the prioritization of road safety improvement strategies (iii) to use an example of road safety improvement strategies for zero traffic injuries in nairobi for the applied method. by doing so, the study will answer three subsequent questions: (*) what is the framework to be implemented for road safety improvement towards zero traffic injuries? (**) what is the most challenging factor impeding the road safety reform? (***) what are the best strategies to be implemented for an effective of road safety reform? prioritization road safety strategies towards zero road traffic injury using ordinal priority approach 209 table 1. an overview of available research works in the field of road safety challenges and remedial strategies prioritization the rest of the paper is structured into the following sections. section 2 presents the antecedent works on the applied method and the multi-criteria decision making (mcdm) usage for road safety evaluation. section 3 introduced the steps of the suggested method. section 4 deals with the methodology of the study based on data collection technique, collected data, and the framework of the prioritization of road authors location discussion on challenges/ risks discussion on strategies prioritization of safety reform strategies odonkor, mitsotsoumakanga, and dei (2020) sub-saharan africa agerholm and andersen (2015) denmark martensen et al. (2019) europe bliss and breen (2012) developing countries oster jr and strong (2013) united states deme (2019) africa hasson (1999) oecd countries bertin-jones (2010) global morgan (1999) america khayesi and peden (2005) africa martin and tawia (2020) africa dhliwayo (2000) southern african development community dhliwayo (2007) africa yannis et al. (2018) africa bezabeh (2013) africa mzee and chen (2012) dar es salaam raynor and mirzoev (2014) kenya lamont and lee (2015) kenya sharpin et al. (2018) columbia, india, kenya our study nairobi (kenya) bouraima et al./oper. res. eng. sci. theor. appl. 5 (2) (2022) 206-221 210 safety improvement strategies. in section 5, the results and discussion are shown. lastly, the conclusions with further research directions and limitations are provided in section 6. 2. literature review two parts have characterized the literature section as shown bellows. 2.1. studies applied the ordinal priority approach the ordinal priority approach (opa) is firstly introduced by ataei et al. (2020). after that, the benefits of their method have emerged in numerous studies such as the assessment of construction sub-contractors (mahmoudi & javed, 2022), suppliers for healthcare center assessment (quartey-papafio, islam, & dehaghani, 2021), agriculture sector (islam, 2021), robot selection (abdel-basset, mohamed, abdelmonem, & elfattah, 2022), risk assessment (sadeghi, mahmoudi, & deng, 2022), postpandemic strategies (le & nhieu, 2022), and planning strategies prioritization (pamucar, deveci, gokasar, martínez, & köppen, 2022). 2.2. mcdm on the road safety evaluation in the context of road safety performance, a wide range of mcdm strategies has been suggested. table 2 indicates various mcdm techniques that have been used in the road safety assessment. table 2. recapitulation of road safety studies with application of mcdm authors country methods research topic ghram and frikha (2020) tunisia aras-h classifying the tunisian governments based on road safety problem assessment farooq and moslem (2020) hungary anp assessing driver behavior parameters concerning road safety chen, zhu, zu, lyu, and yang (2022) southeast asia criticelectrefcm evaluating road safety achievement omrani, amini, and alizadeh (2020) iran dea, bwm assessment of road safety farooq et al. (2021) hungary ahp-bwm evaluation of considerable factors impacting frequent lane-changing zhu, chen, li, and shuai (2021) china cem, regret theory, waspas assessment of road safety performance m. khorasani et al. (2013) european countries ahp road safety performance evaluation sudha and rajarajeswari india ahp road safety management analysis prioritization road safety strategies towards zero road traffic injury using ordinal priority approach 211 (2012) bao, ruan, shen, hermans, and janssens (2012) european countries fuzzy topsis road safety performance assessment zu, peng, and chen (2022) european union member states cv, promethee supervision of road safety progress moslem, farooq, ghorbanzadeh, and blaschke (2020) hungary ahp, bwm assessment of driver’s behavior factors based on road safety rosić, pešić, kukić, antić, and božović (2017) serbia dea, topsis selection of optimal road safety composite g. khorasani et al. (2013) european countries saw, ahp, fuzzy topsis assessment of road safety performance damjanović, stević, stanimirović, tanackov, and marinković (2022) montenegro dea, imf swara, marcos traffic safety evaluation mitrović simić et al. (2020) bosnia and herzegovina critic, fuzzy fucom, dea, fuzzy marcos road section evaluation stević, das, and kopić (2021) south africa critic, dea, marcos traffic safety assessment our study kenya opa prioritization road safety strategies note: analytical hierarchy process: ahp; analytical network process: anp; additive ratio assessment: aras; best–worst method: bwm; cross efficiency method: cem; criteria importance through intercriteria correlation: critic; coefficient of variation: cv; data envelopment analysis: dea; élimination et choix traduisant la realité: electre; fuzzy c-means: fcm; improved fuzzy step-wise weight assessment ratio analysis: imf swara; preference ranking organization method for enrichment of evaluations: promethee; technique for order preference by similarity to ideal solution: topsis; weighted aggregated sum product assessment: waspas; measurement of alternatives and ranking according to compromise solution: marcos; technique for order preference by similarity to the ideal solution: topsis. 3. ordinal priority approach method in the present study, the opa method is applied to evaluate the weights of the experts, and criteria, and to prioritize road safety improvement strategies for nairobi bouraima et al./oper. res. eng. sci. theor. appl. 5 (2) (2022) 206-221 212 city towards zero road traffic injuries. this section briefly described the calculation steps of the opa. table 3 indicates the fundamental parameters of the method. table 3. sets, indexes, and variables for opa sets i set of experts j set of criteria k set of alternatives ∀ indexes i index of the experts (1,….,p) j index of preference of the criteria (1,……n) k index of the alternatives (1,…..,m) variables z objective function weight (importance) of k th alternative based on jth criterion by ith expert at k th rank parameters i the rank of expert i j the rank of criterion j r the rank of alternative k following the subsequent studies of mahmoudi, deng, javed, and zhang (2021), and ataei et al. (2020), the applicable steps of the opa are presented below. step 1: examining the challenging factors to the road safety reform. step 2: definition of the ordinal preference of challenging factors. step 3: formation of the linear model (1) according to the data collected from steps 1 and 2, and then solving of the model via an adequate software, excel in our case. (1) max z s.t: where z: unrestricted in sign prioritization road safety strategies towards zero road traffic injury using ordinal priority approach 213 after solving the model, eqs. (2) to (4) are used to find out the weights of the alternatives, criteria, and expert (s). eq. (2) must be used to find out the weights of alternatives, which are road safety strategies in the present study. (2) eq. (3) should be applied for the determination of the weights of the criteria, which are challenges in the present study. (3) eq. (4) should be applied for the determination of the weights of experts. (4) uncomplicated steps are necessitated in the opa method to find out necessary weights without the assistance of other techniques. 4. research methodology based on the hierarchical framework in figure 1, the data collection was obtained from three different experts. six strategies were suggested to grasp sound technical reforms. these strategies were prioritized based on their impact on the remediation of the key challenges to road safety reform. figure 1. prioritization of road safety improvement strategies based on key challenges bouraima et al./oper. res. eng. sci. theor. appl. 5 (2) (2022) 206-221 214 the three respondents were working at the nairobi metropolitan area transport authority (namata), the national transport safety authority (ntsa), and at university, respectively. they have 10, 8, and 5 years of experience in road safety, respectively. decisions by the experts were based on four criteria, namely road safety is not a political priority (c1), road safety is seen as an issue of personal responsibility (c2), there is little coordination between relevant government bodies (c3), and data is lacking (c4), where all the criteria are of beneficial criteria. criteria have been ranked based on their degree of severity. first priority is given to the criteria that is more critical or that mostly challenge the road safety reform. for instance, in table 4, expert 1 has given the first priority to c3. this means that c3 is the most challenging factor to the road safety reform according to his opinion. meanwhile, c2 is the last priority for e1 (p4), this explains that c2 is the least challenging factor for road safety reform. the collection of data is presented in tables 4 and 5. in these tables, p1, p2, p3, p4, p5, and p6 signify priorities with p1 as the highest priority and p6 as the lowest priority. the prioritization of strategies will be done through the ordinal priority approach. the advantage of utilizing the model is that one can prevent the normalization of data, for instance, one can disregard which criteria were the higher-the-greater and which the lower-the-greater as the constituents are assessed according to their respective choice (mahmoudi & javed, 2022). table 4. classification of criteria according to the judgment of three experts p1 p2 p3 p4 e1 c3 c1 c4 c2 e2 c1 c3 c2 c4 e3 c2 c1 c4 c3 table 5. classification of strategies based on the criteria by the three experts p1 p2 p3 p4 p5 p6 e1 c3 s4 s5 s3 s1 s6 s2 c1 s2 s1 s3 s5 s4 s6 c4 s6 s4 s3 s2 s5 s1 c2 s1 s5 s6 s3 s2 s4 e2 c3 s4 s1 s2 s3 s5 s6 c1 s2 s1 s4 s3 s5 s6 c4 s6 s2 s1 s3 s4 s5 c2 s2 s5 s4 s1 s3 s6 e3 c3 s3 s5 s4 s1 s2 s6 c1 s2 s4 s5 s3 s1 s6 c4 s6 s1 s2 s3 s5 s4 c2 s6 s2 s1 s3 s4 s5 note: “e” indicates expert. in this study, we have three experts: e1, e2, and e3. 5. results and discussion in this section, the weights of the three elements of the model namely experts, criteria (challenges), and alternatives (road safety strategies) were got using eqs (2)prioritization road safety strategies towards zero road traffic injury using ordinal priority approach 215 (4). then, they were classified in descending order, where lower weight indicates lower rank. the weights and ranking of the experts and criteria are shown in table 6. table 6. the weights and classification of experts and criteria using the opa weight rank experts e1 0.545454 1 e2 0.272727 2 e3 0.181818 3 criteria c1 0.349090 1 c2 0.305454 2 c3 0.149090 4 c4 0.196363 3 as shown in table 6, the most challenging factor remains the first criterion c1 (road safety is not a political priority) with a value of 0.349. our findings are in accordance with the previous studies of small (2014) and odonkor et al. (2020) which indicate that the absence of political concern, interest, and priority is the main shortcoming of road safety management in africa. the least significant criterion remains the third criterion c3 (little coordination between relevant government bodies). when considering the alternatives (strategies), exploiting broad institutional and governance reform strategy (s4) emerges as the best one followed by reframing road safety in the public and political debate (s2), and the strategy to bundle road safety with more important popular issues (s1), as indicated in figure 2. figure 2. proposal prioritization of road safety improvement strategies 7. conclusion in this study, the ordinal priority approach is utilized to prioritize strategies for zero traffic injury based on challenges to road safety reform. as a result of the literature review, four criteria were used: road safety as not being a political priority, road safety being seen as an issue of personal responsibility, little coordination between relevant government bodies, and data lacking. the survey includes the opinions of three experts. the study's findings revealed that the road safety reform bouraima et al./oper. res. eng. sci. theor. appl. 5 (2) (2022) 206-221 216 as not being a political priority is the most challenging factor to road safety reform, followed by road safety as an issue of personal responsibility. the least challenging factor is the lack of coordination amongst various government bodies. according to the significance weights of the criteria and expert’s opinions, exploiting broad institutional and governance reform is chosen as the best strategy, even though the improvement of road safety in nairobi was proven to be difficult because of disintegrated responsibility or absence of ownership (sharpin et al., 2018). given the negative effects of these challenges on road safety reform, it is first advised that nairobi should improve its institutional cooperativeness and responsibility so that the public confidence in local institutions will be increased and a disposition to follow local regulations will be built. in addition, typical reforms to the transport department, city finances, police, and public transport should be implemented to boost nairobi’s city capacity to impact, administer and surveil the mobility and safety of people. finally, the population should have the right to use the courts to mandate weakly coordinated institutions to take action on road safety. these recommendations can be implemented by the government ministries, departments and agencies (mdas) in the road safety policy guidelines in nairobi city. this study is practical for academicians, security agencies and the national transport and safety authority (ntsa) officials and permits full and effective analysis of road safety reform. this is the first study of its sort in nairobi city, incorporating the use of multiattribute decision-making to assess the most challenging factors to road safety reform and find out the best strategies to be implemented toward a zero-traffic injury goal. the implemented technique demonstrated how the criteria were reviewed without the need for a decision-making matrix or a pairwise comparison matrix, as well as the decision-maker's ability to only judge alternatives and attributes for which they have sufficient information and competence. based on the application results, it can be said that the applied methodology is an efficient assessment procedure that policymakers and managers can use to make valuable inferences, proactive behavior for the challenging factor evaluation of road safety reform. as a result, the methodology presented here has the potential to be applied in a variety of circumstances. the approach's most significant drawback is that it fails to account for situations in which experts have doubts about their judgment. because of the more dynamic environmental conditions and the procedure requirement of incomplete and unclear information, the method can be extended in future studies by incorporating additional demands on mathematical approaches for multi-criteria optimization. the fact that only four criteria were considered, as well as the opinions of only three experts, is another shortcoming in this paper. future research for in-depth analysis may take more criteria divided into political, institutional, legal, social, and economic groupings. in addition, the number of professionals with various backgrounds should be increased. additionally, national research that considers other counties rather than just nairobi city is required prioritization road safety strategies towards zero road traffic injury using ordinal priority approach 217 acknowledgment we like to pay special thanks to all survey participants for the data collection. the authors would also like to extend their gratitude to the three anonymous reviewers. references abdel-basset, m., mohamed, m., abdel-monem, a., & elfattah, m. a. 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(2022). overseeing road safety progress using cvpromethee ⅱ-jss: a case study in the eu context. expert systems with applications, 195, 116623. doi: https://doi.org/10.1016/j.eswa.2022.116623 © 2022 by the authors. submitted for possible open access publication under the terms and conditions of the creative commons attribution (cc by) license (http://creativecommons.org/licenses/by/4.0/). https://doi.org/10.7763/ijfcc.2012.v1.66 https://doi.org/10.1016/j.aap.2021.106395 https://doi.org/10.1016/j.eswa.2022.116623 plane thermoelastic waves in infinite half-space caused operational research in engineering sciences: theory and applications vol. 5, issue 1, 2022, pp. 20-40 issn: 2620-1607 eissn: 2620-1747 doi: https://doi.org/10.31181/oresta190222046c * corresponding author. sohinirits@gmail.com (r. chattopadhyay), partha.d@smit.smu.edu.in (p.p. das) s_chakraborty00@yahoo.co.in (s. chakraborty) development of a rough-mabac-doe-based metamodel for supplier selection in an iron and steel industry ritwika chattopadhyay1, partha protim das2, shankar chakraborty1* 1 department of production engineering, jadavpur university, kolkata, india 2 department of mechanical engineering, sikkim manipal institute of technology, sikkim manipal university, majitar, sikkim, india received: 26 september 2021 accepted: 09 december 2021 first online: 19 february 2022 research paper abstract: in the context of supply chain management, supplier selection can be defined as the process by which organizations score and evaluate a range of alternative suppliers to choose the best possible one who can provide superior quality of raw materials at cheaper rate and lesser lead time. it is a decision making process with multiple trade-offs between various conflicting criteria which in turn helps the organizations identify the suitable suppliers that would establish a robust supply chain assisting in maintaining a competitive edge. the main objective of supplier selection is thus focused on reducing purchase risk, maximizing overall value to the organization, and developing closeness and long-term relationships between the suppliers and the organization. in this paper, while selecting the most suitable supplier for gearboxes in an indian iron and steel industry, assessments of three decision makers on the performance of five candidate suppliers with respect to five evaluation criteria are first aggregated using rough numbers. the definitive distances of those rough numbers are then treated as the inputs to a 25 full-factorial design plan with the corresponding multi-attributivec border approximation area comparison (mabac) scores as the output variables. finally, a design of experiments (doe)-based metamodel is formulated to interlink the computed mabac scores with the considered criteria. the competing suppliers are ranked based on this rough-mabac-doe-based metamodel, which also easies out the computational steps when new suppliers are included in the decision making process. key words: supplier selection; rough numbers; mabac; doe; metamodel development of a rough-mabac-doe-based metamodel for supplier selection in an iron and steel industry 21 1. introduction in the light of present day covid-19 pandemic situation, the importance of a robust supply chain management system has been reasserted. the goals of a supply chain have been newly oriented opting for a fair balance between the global and local networks. this has made industries in diverse sectors to reconsider their existing choices and identify the most reliable suppliers to keep their raw material supplies uninterrupted without compromising on quality, specially under uncertain environment. this problem has intensely been pronounced in the manufacturing sector which needs to keep up with its production to meet the global requirements irrespective of the prevailing situation (vonderembse and tracey, 1999). iron and steel industry is one such important manufacturing sector that needs regular supplies of raw materials; therefore, a critical analysis is demanding while selecting an appropriate set of suppliers. it involves a well informed and rigorous research regarding the possible parameters based on which the candidate suppliers for a particular item should be evaluated to single out the most appropriate supplier while scraping out the unsuitable ones (verma and pullman, 1998). in this direction, application of any of the existing multi-criteria decision making (mcdm) techniques would be quite helpful as it has the ability to identify the most apposite supplier to provide the right quantity of material with right quality at right time and right price based on a set of conflicting evaluation criteria (mukherjee, 2017). the mcdm is the science which takes into account different criteria with varying degrees of importance to search out the most suitable option/course of action. the first step involves in development of the initial decision matrix exhibiting the relative performance of each of the candidate alternatives with respect to the considered criteria. in this step, there may be participation of a group of experts/decision makers, each opining and assigning performance scores to the available alternatives based on each criterion. in the second step, again based on the judgments of the decision makers, relative weights are allocated to all the criteria depending on their importance to the decision making problem under consideration. the final step involves in ranking of the set of alternatives from the best to the worst. the application potentiality of mcdm methodologies in solving complex manufacturingrelated decision making problems has attracted attention of the researchers leading to the development of different innovative ranking techniques, like analytic hierarchy process (ahp) (saaty, 1988), technique for order of preference by similarity to ideal solution (topsis) (behzadian et al., 2012), grey relational analysis (gra) (abdulshahed et al., 2017), multi-attributive border approximation area comparison (mabac) (pamučar and ćirović, 2015), measurement of alternatives and ranking according to compromise solution (marcos) (stević et al., 2020; mahmutagić et al. 2021) etc. while all these methods have their unique mathematical foundations, their implementation in a manufacturing industry largely depends on the ease of implementation and ability to generate accurate ranking results. the mabac is one such methodology which can provide a detailed analysis of the alternatives while partitioning them into upper, lower and border approximation areas along with identification of their relative strengths and weaknesses with respect to each of the criteria. however, there is a major challenge associated with formulation of the decision matrix due to uncertainty/vagueness involved in human judgment. usually, the chattopadhyay et al./oper. res. eng. sci. theor. appl. 5(1) (2022) 20-40 22 criteria set based on which the candidate alternatives are assessed consists of both quantitative and qualitative attributes. for qualitative criteria, it becomes difficult for the team of decision makers to assign exact deterministic values. in these cases, performance scores of the alternatives with respect to the qualitative criteria are assigned based on imprecise linguistic judgments which greatly vary from one decision maker to the other. although, it is remarkably important to account for this vagueness while solving critical decision making problems, like supplier selection, it cannot be denied that implementation of fuzzy mcdm techniques is more mathematically complex, involving choice of appropriate fuzzy membership functions affecting the final selection decision. in this direction, a lot of methodologies have already been proposed to aggregate the subjective performance scores of the alternatives. it has been noticed that application of rough numbers with uncomplicated mathematical steps can effectively resolve the problem of dealing with qualitative criteria in a decision making problem (zhai et al., 2009). rough numbers have efficiently been integrated with other mcdm tools, like analytic network process (anp) and topsis (li et al., 2018), complex proportional assessment (copras) (matić et al., 2019), additive ratio assessment (aras) (radović et al., 2018), ahp and mabac (roy et al., 2018; pamučar et al., 2018a), best worst method (bwm) and weighted aggregated sum product assessment (waspas) (stević et al., 2018; stojić et al., 2018), bwm and simple additive weighting (saw) (stević et al., 2017), step-wise weight assessment ration analysis (swara) and waspas (sremac et al., 2018), ahp and topsis (shojaei and bolvardizadeh, 2020) etc. in most of the mcdm techniques, the corresponding ranking results are derived based on pair-wise or relative comparisons between the candidate alternatives, which make the decision making process more tedious and time consuming. whenever a new alternative enters into the decision making process or an existing alternative leaves the process, the entire computational procedure needs to be reinitiated from the scratch. in most of the practical situations, the set of alternatives always keeps on changing. for example, in an iron and steel industry, it has often been noticed that a new supplier may reach out, while an existing supplier may fall off the list due to poor/failing standards. learning from the recent times of vulnerability and uncertainty, it is recommended to keep the list of participating suppliers always dynamic. in this paper, an mcdm methodology integrating rough numbers, mabac method and design of experiments (doe) is proposed to account for the vagueness involved in the group decision making process while providing detailed analysis of the derived results at the same time. in an iron and steel industry, the relative performance of five participating suppliers is appraised by three decision makers with respect to five evaluation criteria based on a 1-9 scale. these subjective judgments of the decision makers are then aggregated to form the initial decision matrix using rough numbers. with five evaluation criteria, a 25 full-factorial experimental design plan is formulated along with determination of the corresponding mabac score for each of the experimental trials. in this methodology, different evaluation criteria and mabac scores are respectively treated as the design parameters and responses in the doe to develop a metamodel. based on this metamodel, the composite score of any supplier can easily be calculated in a single step, thus relieving the decision maker from complex and time-consuming computational steps. in other mcdm techniques, the concerned decision maker development of a rough-mabac-doe-based metamodel for supplier selection in an iron and steel industry 23 needs to reinitiate the entire calculation steps when a new supplier enters into or leaves out the existing list of candidate alternatives. but, in this developed metamodel, the respective score along with the rank of a new supplier can easily be estimated while putting the corresponding performance values into the model. similarly, the relative ranking of the suppliers can quickly be updated when an existing supplier leaves the appraisal process. simply, the computational burden would be remarkably reduced using this metamodel in the supplier selection process. the rest of this paper is organized as follows. section 2 reviews the recent literature dealing with the application of different mcdm techniques in solving diverse supplier selection problems. in section 3, mathematical details of rough numbers, mabac method and doe are presented. section 4 deals with a case study where the proposed rough-mabac-doe method is adopted for identifying the most appropriate supplier in an indian iron and steel industry. conclusions are drawn in section 5 along with the future directions. 2. literature review the present literature is flooded with the applications of various mathematical techniques, especially mcdm tools, for identification of the suitable suppliers to fulfill the requirements of a diverse range of organizations. the supplier selection process generally starts with listing the right set of criteria based on which the competing suppliers are appraised. this criteria set obviously varies from one industry to the other depending on the requirements and end products. the process terminates with the application of a suitable methodology to single out the most appropriate supplier for a given organization. zimmer et al. (2016) conducted an exhaustive literature survey to list down all the possible criteria that can be accounted for selection of sustainable suppliers along with diverse methodologies implemented to rank them. luzon and el-sayegh (2016) adopted delphi method along with ahp to select suppliers for oil and gas projects, while classifying the considered criteria into techno-commercial and organizational aspects. kumar et al. (2018) designed a capital procurement decision making model by integrating fuzzy-delphi and ahpdecision making trial and evaluation laboratory (dematel) methods for selecting suppliers for a given organization. yazdani et al. (2017) proposed an integrated quality function deployment (qfd)-mcdm-based approach for green supplier selection while considering several important evaluation criteria, like quality adaptation, price, energy and natural resource consumption, and delivery speed. while treating cost of products, quality of products, service provided, capability of delivering on time, technology level, environmental management system and green packaging as the evaluation criteria, abdullah et al. (2018) applied preference ranking organization method for enrichment of evaluations (promethee) for solving a green supplier selection problem. badi et al. (2018) proposed the application of combinative distance-based assessment (codas) method for solving a supplier selection problem for a steel making industry in libya, which considering quality, direct cost, lead time and logistics services as the main evaluation criteria. in a group decision making environment, badi and ballem (2018) integrated roughbwm with multi-attribute ideal real comparative analysis (mairca) to assess the chattopadhyay et al./oper. res. eng. sci. theor. appl. 5(1) (2022) 20-40 24 performance of pharmaceutical suppliers based on cost, quality, supplier profile, delivery and flexibility criteria. a study was conducted by banaeian et al. (2018) to evaluate and select green suppliers for an agri-food industry while combining fuzzy set theory with vikor (vlsekriterijumska optimizacija i kompromisno resenje), gra and topsis methods, and considering service level, quality, price and environmental management system as the evaluation criteria. akcan and güldeş (2019) applied several integrated mcdm methodologies, like ahp-topsis, ahpsaw, ahp-gra and ahp-elimination et choice translating reality (electre) to rank suppliers based on logistics, cost, quality, flexibility and reliability criteria. while accounting for the uncertainties involved in a group decision making process, chattopadhyay et al. (2020) proposed the application of d-marcos method for solving a supplier selection problem in a steel industry with product quality, delivery compliance, price, technical capability, production capability, financial strength and electronic transaction capability as the evaluation criteria. in order to deal with both weighting of the criteria and uncertainty in group decision making, javad et al. (2020) combined bwm with fuzzy topsis to rank green suppliers in a steel company considering collaborations, environmental investments and economic benefits, resource availability, green competencies, environmental management initiatives, research and design initiatives, green purchasing capabilities, regulatory obligations, pressures and market demand as the major selection criteria. stević et al. (2020) endeavored to prove the application potentiality of a new mcdm methodology in the form of marcos to assess and rank sustainable suppliers in healthcare sector with an exhaustive set of 21 criteria. wang et al. (2020) first employed fuzzy-ahp method to determine weights of reliability, responsiveness, flexibility, cost and assets criteria, and later adopted promethee to rank the competing suppliers in a textile industry. it has been revealed from the above-cited literature that selection of suppliers for varying organizations based on a set of conflicting evaluation criteria is really a complicated problem to solve, especially in group decision making environment involving a degree of uncertainty with respect to human judgments. to resolve this issue, several hybridized models have already been proposed. however, most of those models are computationally expensive which hinders their applications in realtime manufacturing scenario. in all those models, with the addition of a new alternative or deletion of an existing alternative from the set disrupts the entire calculation process and it needs to be reinitiated from the scratch in each occasion. taking these drawbacks of the existing hybridized mcdm tools in solving supplier selection problems, this paper proposes to develop a doe-based metamodel in the form of an regression equation while integrating rough numbers with the advantageous features of mabac method. the performance scores of the alternative suppliers with respect to the evaluation criteria are aggregated using rough numbers in a group decision making environment having three participating decision makers and the competing suppliers are finally ranked from the best to the worst using the computed mabac scores. based on the developed metamodel, the performance score of a new supplier can easily be computed, thus relieving the concerned decision maker from lengthy repetitive calculation steps. keeping in mind the requirements and importance of selection of suppliers, the applicability of this integrated rough-mabac-doe method is demonstrated here to appraise and rank development of a rough-mabac-doe-based metamodel for supplier selection in an iron and steel industry 25 five different suppliers in a leading steel manufacturer in india based on five pivotal criteria in a group decision making environment. 3. methods 3.1. rough numbers one of the biggest challenges associated with group decision making is the uncertainty and vagueness involved in determining the relative weights of different criteria and performance appraisal of the candidate suppliers with respect to those criteria. in this direction, various methodologies, like fuzzy set theory, intuitionistic fuzzy set, d numbers etc. have been proposed. in this paper, the application potentiality of rough numbers in assessing the performance of the considered alternatives with regard to five evaluation criteria while solving a supplier selection problem is explored. rough numbers have become popular due to their simplicity and adaptability while taking into account linguistic judgments of different decision makers based on boundary intervals using lower and upper limits (zhai et al., 2008). zhai et al. (2009) further introduced interval arithmetic to analyze and operate rough numbers. let u be the universal set comprising all the objects, x is an arbitrary object of u, and r is a set of n clases r = {c1,c2,…,cn} covering all the objects in u. if these n classes are ordered as {c1 < c2 <…< cn}, then ,, rcux q  1 ≤ q ≤ n, where r(x) denotes the class to which the object belongs. the lower approximation ))(( q capr , upper approximation ))(( qcapr and boundary region ))(( qcbnd of class cq are given as below:   qq cxruxcapr = )(/)( (1)   qq cxruxcapr = )(/)( (2)     qqq cxruxcxruxcbnd = )(/)(/)( (3) thus, the class cq can be expressed as rough number )( qcrn with upper limit ( ))( qclim and lower limit ( ),)( qclim defined as below (chakraborty et al., 2020): )(|)( 1 )( q u q caprxxr m clim =  (4) )(|)( 1 )( q l q caprxxr m clim =  (5)    u ij l ijqqq xxclimclimcrn ,)(),()( == (6) where um and lm are the number of objects in the upper and lower approximations respectively, and l ijx and u ijx are the lower and upper evaluation chattopadhyay et al./oper. res. eng. sci. theor. appl. 5(1) (2022) 20-40 26 limits of jth criterion with respect to ith alternative respectively. the rough boundary interval (rbnd) can now be expressed as the difference between the upper and lower evaluation limits. )()( qq climclimrbnd −= (7) a large value of rbnd symbolizes more vagueness, while, a small value represents more preciseness. it is often important to rank rough numbers to attain definitive results. zhai et al. (2008) proposed a methodology for ranking of rough numbers. let rn(a) and rn(b) be two rough numbers. if one rough boundary interval is not strictly bounded by the other, there may be two possibilities: a) if )()( blimalim  and )()( blimalim  or )()( blimalim  and ),()( blimalim  then ).()( brnarn  b) if )()( blimalim = and ),()( blimalim = then ).()( brnarn = however, if they are strictly bounded, they can be ranked based on their median values. hence, the following three cases may be observed: a) if m(a) > m(b), then rn(a) > rn(b) b) if m(a) < m(b), then rn(a) < rn(b) c) if m(a) = m(b), then rn(a) = rn(b) where m(a) and m(b) are the median values of rough numbers rn(a) and rn(b) respectively. let us assume rn(α) = [lα, uα] and rn(β) = [lβ, uβ] where lα and lβ are the lower limits, and uα and uβ are the upper limits of the respective rough numbers. the following arithmetic rules can then be applied for interval analysis: rnα + rnβ = [lα + lβ, uα + uβ] (8) rnα × rnβ = [lα × lβ, uα × uβ] (9) rnα × k = [klα, kuα], where k is a non-zero constant. (10) in order to determine the distance between two rough numbers, the euclidian distance equation is employed. thus, d(a,b) represents the euclidian distance between two rough numbers rn(a) and rn(b) such that rn(a) = [a-, a+] and rn(b) = [b-, b+]. ( ) ( )( )22 2 1 ),( ++−− −+−= bababad (11) this property of rough numbers is employed to calculate the distance between the considered alternative for a given criterion and geometric aggregation value for that criterion. an illustration of the same can improve the understanding. let us assume a decision matrix x having n alternatives (a1, a2,…,ai,…,an) and m criteria (c1, c2,…,cj,…,cm) such that using rough numbers, the performance score for ith alternative against the considered set of criteria can be expressed as        ( )+−+−+−+−= imimijijiiiii xxxxxxxxa ,,,,,,,,, 2211  . the geometric aggregation value for jth criterion is given by  +−= jjj fffrn ,)( , where development of a rough-mabac-doe-based metamodel for supplier selection in an iron and steel industry 27 n n i ijj xf /1 1       =  = −− (12) n n i ijj xf /1 1       =  = ++ (13) this helps in formation of the distance matrix y = [yij]n×m from the initial matrix x such that: criterion benificialfor )()( if ),( )()( if ),( jijjij jijjij ij frnxrnfxd frnxrnfxd y −  = (14.a) criterioncost for )()( if ),( )()( if ),( jijjij jijjij ij frnxrnfxd frnxrnfxd y  − = (14.b) where ( ) ( )( )22 2 1 ),( ++−− −+−= jijjijjij fxfxfxd (15) 3.2. rough mabac mabac is a newly developed and widely accepted mcdm technique (pamučar and ćirović, 2015) which primarily ranks a set of alternatives based on their distances from the border approximation area for each criterion. however, it has been modified from time to time to develop more purposeful hybrid models. in this paper, mabac is integrated with rough numbers which is further fed into a doe model to provide a generalized metamodel for evaluation and ranking of a set of suppliers. considering a decision problem having n alternatives (a1, a2,…,ai,…,an) and m criteria (c1, c2,…,cj,…,cm), the procedural steps of rough mabac method are enumerated as below (chakraborty et al., 2020): step 1: the decision matrix x is constructed using rough numbers while taking into account the judgments of a team of experts/decision makers in assessing the relative performance of the suppliers with regard to the evaluation criteria:               =             = +−+−+− +−+−+− +−+−+− ],[],[],[ ],[],[],[ ],[],[],[ )()()( )()()( )()()( 1111 2222222121 1112121111 2 1 21 22221 11211 2 1 nmnmnnnn mm mm n nmnn m m n xxxxxx xxxxxx xxxxxx a a a xrnxrnxrn xrnxrnxrn xrnxrnxrn a a a x           (16) where rn(xij) = ].,[ +− ijij xx chattopadhyay et al./oper. res. eng. sci. theor. appl. 5(1) (2022) 20-40 28 step 2: depending on the type of the criterion, the initial decision matrix x is normalized to obtain the corersponding normalized decision matrix   ., mnijij nnn  +− =                        − − − −          − − − − = +− +− +− ++ −+ −+ −+ −− , if ;, , if ;, )( cj xx xx xx xx bj xx xx xx xx nrn jj jij jj jij jj jij jj jij ij (17) where ),(min),(max −−++ == ij i jij i j xxxx b is the set of beneficial criteria and c is the set of cost criteria. step 3: determine the weight assigned to each criterion w = (w1, w2,…,wj,…,wm) such that 1 1 = = m j j w . the weighted normalized decision matrix   mnijij yyy  +− = , is now calculated using eq. (18). ( ) jijij wny 1+= −− ; ( ) jijij wny 1+= ++ , mjni ,...,2,1 ; ,...2,1 == (18) step 4: the border approximation area (baa) matrix is derived based on geometric aggregation of the rough numbers.  )()()( 21 m qrnqrnqrnq = mjyq mjyq n n i ijj n n i ijj ,...,2,1 , ,...,2,1 , 1/ 1 1/ 1 =      = =      =   = ++ = −− (19) step 5: the eucledian distance of an alternative from the baa is evaluated based on the difference between the border approximation area and the weighted normalized matrix, and is represented by the matrix   mnij krnk  = )( . ( ) ( )( ) )()(if 2 1 ),( 22 jijjijjijjijij qrnyrnqyqyqydk −+−== ++−− (20) ( ) ( )( ) )()(if 2 1 ),( 22 jijjijjijjijij qrnyrnqyqyqydk −+−−=−= ++−− step 6: the considered alternatives are finally ranked in descending order of si values.  = == m j iji niks 1 ),,2,1(  (21) 3.3 design of experiments the doe is a statistical methodology to help in determining the influence of independent factors/variables as well as effect of their interactions on the system development of a rough-mabac-doe-based metamodel for supplier selection in an iron and steel industry 29 response (dependent variable). each of these factors can operate at different levels and hence, several experiments need to be performed to study the effects of factor level variations on the system under consideration. it has already established itself as a helpful tool for engineers and decision makers to develop strong mathematical metamodels based on experimental results. a full-factorial design proves to be exhaustive as it includes all the possible combinations for the factors at each of their corresponding levels. however, implementation of a full-factorial design plan is computationally expensive and time consuming. in these cases, a suitable subset of factor level combinations is selected resulting in a fractional factorial experiment design plan. in this paper, a two-level full-factorial experimental design plan is adopted to visualize how the considered evaluation criteria influence the mabac scores for alternative suppliers. the metamodel linking the dependant variable (mabac score) with m independent variables (criteria) is expressed as below:  +++++= immii xxxy  22110 (22) where y is the response variable (mabac score), β0 is the y-intercept coefficient, β1-βm are the effect coefficients for m criteria, x1-xm are the input variables and ε is the error term. the main effect of each input variable is presumed to be independent of the other variables. in this metamodel, interaction effects can also be considered to explore the presence of interactions between the input variables. in this paper, a two-level full-factorial design plan is adopted with 25 combinations, where only the minimum and maximum intervals for each factor (criterion) are considered to develop the corresponding factorial design. the related distance values of these intervals are subsequently treated as the inputs and mabac scores as the outputs to the doe for development of the required metamodel. 4. development of a rough-mabac-doe-based metamodel it has already been noticed that the manufacturing industries often face problems while indentifying the best alternative/course of action amid a set of conflicting criteria. this paper proposes a new methodology for evaluation and ranking of competing suppliers based on a developed metamodel in an indian iron and steel industry. the existing mcdm techniques suffer from a major drawback, i.e. when a new alternative is introduced in the decision making problem, the entire computational process needs to be reinitiated from the scratch to derive the ranking of the candidate alternatives, which often constrains their applications in real-time situations. in the proposed method, once the rough-mabac-doe-based metamodel is formulated, the concerned decision maker can easily estimate the corresponding mabac score for a new supplier based on its performance and position it in the revised ranking list. the application potentiality of this method is illustrated as a case study in an indian iron and steel industry with an annual production of around 2.4 million tonnes of crude steel. like any other industry operating at such a large scale, it also houses a large number of machineries which need to be maintained from time to time for uninterrupted production. this creates requirement for large varieties of gearboxes to be procured from the suppliers across the globe. at this stage, it becomes essential to choose the most apposite supplier who can deliver the right quality of gearboxes at right quantity, right price and right time. it is chattopadhyay et al./oper. res. eng. sci. theor. appl. 5(1) (2022) 20-40 30 worthwhile to mention here that while selecting the most suitable supplier for a manufacturing industry, the set of evaluation criteria usually varies depending on the item/product to be purchased. in a group decision making environment, assessment of the candidate suppliers with respect to the considered criteria also varies from one decision maker to the other depending on the experience and expertise of each of the participating decision makers. to deal with this problem, i.e. selection of suppliers for providing gearboxes in the iron and steel industry, the opinions of three decision makers (dm1, dm2 and dm3) are sought. these decision makers have been respectively selected from the finance, materials management and mechanical technical bureau of the organization having 15, 20 and 15 years of job experience. tables 1 and 2 exhibit the list of evaluation criteria and candidate suppliers considered for this supplier selection problem. for having replications in the experimental design plan while developing the corresponding metamodel, two sets of criteria weights are chosen based on the judgments of the decision makers. in this direction, other subjective techniques for criteria weight measurement, like bwm (rezaei, 2015), full consistency method (fucom) (pamučar et al., 2018b; durmić et al. 2020), level based weight assessment (lbwa) (žižović and pamučar, 2019) etc. can also be applied. these criteria weights are so selected that their summation must be always one. amongst these criteria, delivery compliance and price are nonbeneficial (cost) attributes requiring their lower values, whereas, higher values are desired for the remaining three beneficial criteria. table 1. description of the evaluation criteria criterion description weight product quality (c1) it accounts for credibility of the product with respect to its expected performance and quality. 0.318 0.300 delivery compliance (c2) it considers the time taken to fulfill an order once it has been placed even in uncertain situations. meeting the delivery schedule is extremely important to maintain uninterrupted production of the end products. 0.226 0.240 price (c3) it is the monetary value of an item that the organization has to pay to the supplier against its delivery. 0.206 0.200 technological capability (c4) it deals with the capability of a supplier to remain updated with the state-of-the-art technologies to fulfil the requirements of the modern day manufacturing organizations. 0.132 0.138 production capability (c5) it focuses on the competence of a supplier to provide the required quality and quantity of products, especially in times of fluctuating demands. 0.118 0.122 in order to single out the most suitable supplier for the identified product, the decision makers now appraise the performance of each of the candidate suppliers with respect to five evaluation criteria, while assigning scores based on a 1-9 scale, where 1-2 indicate poor performance, 3-7 denote moderate performance and 8-9 signify satisfactory performance. this performance appraisal process by the three development of a rough-mabac-doe-based metamodel for supplier selection in an iron and steel industry 31 participating suppliers is exhibited through tables 3-5 in the form of evaluation matrixes. from table 3, it can be revealed that dm1 assesses the performance of supplier s1 with respect to criteria c1 = 4 (moderate), c2 = 3 (moderate), c3 = 2 (poor), c4 = 6 (moderate) and c5 = 8 (satisfactory). rough numbers are now employed to aggregate the individual judgments of the three decision makers. for example, the set of performance ratings for supplier s1 with respect to criterion c1 as evaluated by the three decision makers is expressed as x11 = {4, 6, 7}. based on eqs. (4)-(6), this set of subjective linguistic information is converted into the corresponding rough numbers as below: for element x11 = {4, 6, 7} ,67.5)764( 3 1 )4(,00.4)4( =++== limlim 50.6)76( 2 1 )6(,00.5)64( 2 1 )6( =+==+= limlim 00.7)7(,67.5)764( 3 1 )7( ==++= limlim ]00.7,67.5[)(],50.6,00.5[)(],67.5,00.4[)( 3 11 2 11 1 11 === xrnxrnxrn ,88.4 3 67.500.500.4 11 = ++ = l x 39.6 3 00.750.667.5 11 = ++ = u x table 2. list of the candidate suppliers supplier description s1 while this supplier proves to be a cheaper alternative with reputable delivery compliance, it does not appear to be the most suitable option under emergency situations. s2 it is a public sector organization situated in the eastern india. while it is reputed for its technological strength and reliability, there are situations when it fails to meet the supply deadlines. s3 this organization manufacturing premium gearboxes has customers all over the country. however, there is a substantial tradeoff with respect to robustness of its supply chains and adaption to changing technological scenario. s4 it is a reputed organization established in the southern india, always adhering to the specified delivery schedules while supplying gearboxes of perfect quality. however, it offers higher price for its products as compared to other suppliers. s5 it is a relatively new organization, yet to capture its reputation in the market and stabilize its delivery modes. in this way, all the performance assessment scores assigned by the three decision makers are aggregated using rough numbers to formulate the corresponding combined evaluation matrix, as shown in table 6. in this table, the beneficial and cost criteria are also identified along with their best and worst rough intervals. for example, with respect to product quality, s3 performs the best, s1 ensures the best delivery compliance at the lowest price, s2 has the highest technological capability and 4s exhibits the highest production capability. chattopadhyay et al./oper. res. eng. sci. theor. appl. 5(1) (2022) 20-40 32 table 3. evaluation matrix by dm1 criteria c1 c2 c3 c4 c5 supplier s1 4 3 2 6 8 s2 7 2 4 7 4 s3 8 3 2 5 6 s4 6 4 4 8 9 s5 7 5 3 6 5 table 4. evaluation matrix by dm2 criteria c1 c2 c3 c4 c5 supplier s1 6 2 3 7 5 s2 7 3 3 8 6 s3 8 4 2 6 7 s4 7 2 4 5 8 s5 7 4 2 6 7 table 5. evaluation matrix by dm3 criteria c1 c2 c3 c4 c5 supplier s1 7 2 3 8 6 s2 8 4 2 7 7 s3 7 3 4 6 6 s4 8 2 3 7 8 s5 6 3 4 5 5 table 6. aggregated evaluation matrix criteria c1 c2 c3 c4 c5 supplier s1 [4.88,6.39] [2.11,2.55] [2.44,2.88] [6.50,7.50] [5.61,7.11] s2 [7.11,7.55] [2.5,3.50] [2.5,3.5] [7.11.7.55] [4.88,6.39] s3 [7.44,7.88] [3.11,3.55] [2.22,3.11] [5.44,5.88] [6.11,6.55] s4 [6.50,7.50] [2.22,3.11] [3.44,3.88] [5.88,7.38] [8.11,8.55] s5 [6.44,6.88] [3.50,4.50] [2.50,3.50] [5.44,5.88] [5.22,6.11] min/max max min min max max best [7.44,7.88] [2.11,2.55] [2.44,2.88] [7.11,7.55] [8.11,8.55] worst [4.88,6.39] [3.50,4.50] [3.44,3.88] [5.44,5.88] [4.88,6.39] in order to develop the corresponding metamodel, five supplier selection criteria are treated as the input variables, whereas, the computed mabac score is the output variable. to represent the two-level combinations for these five input variables, a 25 full-factorial design plan having 32 experiments is proposed in table 7 while considering only the worst and best rough intervals of each input variable in the experiment plan. now, employing eqs. (12)-(15), the corresponding value of definitive distance for each of the rough intervals is computed, as shown in table 8. development of a rough-mabac-doe-based metamodel for supplier selection in an iron and steel industry 33 for example, in case of criterion c1, the geometric aggregation is given as:  +−= 111 ,)( fffrn where 41.6)44.650.644.711.788.4( 5/1 1 == − f and .22.7)88.650.788.755.739.6( 5/1 1 == + f table 7. 25 full factorial design plan with rough intervals of the considered criteria experiment no. factor level c1 c2 c3 c4 c5 1 [7.44,7.88] [2.11,2.55] [2.44,2.88] [7.11,7.55] [8.11,8.55] 2 [4.88,6.39] [2.11,2.55] [2.44,2.88] [7.11,7.55] [8.11,8.55] 3 [7.44,7.88] [3.50,4.50] [2.44,2.88] [7.11,7.55] [8.11,8.55] 4 [4.88,6.39] [3.50,4.50] [2.44,2.88] [7.11,7.55] [8.11,8.55] 5 [7.44,7.88] [2.11,2.55] [3.44,3.88] [7.11,7.55] [8.11,8.55] 6 [4.88,6.39] [2.11,2.55] [3.44,3.88] [7.11,7.55] [8.11,8.55] 7 [7.44,7.88] [3.50,4.50] [3.44,3.88] [7.11,7.55] [8.11,8.55] 8 [4.88,6.39] [3.50,4.50] [3.44,3.88] [7.11,7.55] [8.11,8.55] 9 [7.44,7.88] [2.11,2.55] [2.44,2.88] [5.44,5.88] [8.11,8.55] 10 [4.88,6.39] [2.11,2.55] [2.44,2.88] [5.44,5.88] [8.11,8.55] 11 [7.44,7.88] [3.50,4.50] [2.44,2.88] [5.44,5.88] [8.11,8.55] 12 [4.88,6.39] [3.50,4.50] [2.44,2.88] [5.44,5.88] [8.11,8.55] 13 [7.44,7.88] [2.11,2.55] [3.44,3.88] [5.44,5.88] [8.11,8.55] 14 [4.88,6.39] [2.11,2.55] [3.44,3.88] [5.44,5.88] [8.11,8.55] 15 [7.44,7.88] [3.50,4.50] [3.44,3.88] [5.44,5.88] [8.11,8.55] 16 [4.88,6.39] [3.50,4.50] [3.44,3.88] [5.44,5.88] [8.11,8.55] 17 [7.44,7.88] [2.11,2.55] [2.44,2.88] [7.11,7.55] [4.88,6.39] 18 [4.88,6.39] [2.11,2.55] [2.44,2.88] [7.11,7.55] [4.88,6.39] 19 [7.44,7.88] [3.50,4.50] [2.44,2.88] [7.11,7.55] [4.88,6.39] 20 [4.88,6.39] [3.50,4.50] [2.44,2.88] [7.11,7.55] [4.88,6.39] 21 [7.44,7.88] [2.11,2.55] [3.44,3.88] [7.11,7.55] [4.88,6.39] 22 [4.88,6.39] [2.11,2.55] [3.44,3.88] [7.11,7.55] [4.88,6.39] 23 [7.44,7.88] [3.50,4.50] [3.44,3.88] [7.11,7.55] [4.88,6.39] 24 [4.88,6.39] [3.50,4.50] [3.44,3.88] [7.11,7.55] [4.88,6.39] 25 [7.44,7.88] [2.11,2.55] [2.44,2.88] [5.44,5.88] [4.88,6.39] 26 [4.88,6.39] [2.11,2.55] [2.44,2.88] [5.44,5.88] [4.88,6.39] 27 [7.44,7.88] [3.50,4.50] [2.44,2.88] [5.44,5.88]] [4.88,6.39] 28 [4.88,6.39] [3.50,4.50] [2.44,2.88] [5.44,5.88] [4.88,6.39] 29 [7.44,7.88] [2.11,2.55] [3.44,3.88] [5.44,5.88] [4.88,6.39] 30 [4.88,6.39] [2.11,2.55] [3.44,3.88] [5.44,5.88] [4.88,6.39] 31 [7.44,7.88] [3.50,4.50] [3.44,3.88] [5.44,5.88] [4.88,6.39] 32 [4.88,6.39] [3.50,4.50] [3.44,3.88] [5.44,5.88] [4.88,6.39] based on eq. (14), as [7.44,7.88] > [6.41,7.22], the definitive distance for the best interval of c1 can be estimated as ( ) ( )( ) 865.022.788.741.644.7 2 1 22 =−+−=d . similarly, as [4.88,6.39] < [6.41,7.22], the definitive distance for the worst interval of c1 can be calculated as ( ) ( )( ) .231.122.739.641.688.4 2 1 22 −=−+−−=d chattopadhyay et al./oper. res. eng. sci. theor. appl. 5(1) (2022) 20-40 34 table 8. definitive distance matrix along with the mabac scores experiment no. c1 c2 c3 c4 c5 mabac score 1 2 1 0.865 0.696 0.355 0.928 1.960 0.345 0.345 2 -1.231 0.696 0.355 0.928 1.960 0.124 0.135 3 0.865 -0.998 0.355 0.928 1.960 0.184 0.174 4 -1.231 -0.998 0.355 0.928 1.960 -0.037 -0.036 5 0.865 0.696 -0.704 0.928 1.960 0.215 0.220 6 -1.231 0.696 -0.704 0.928 1.960 -0.006 0.010 7 0.865 -0.998 -0.704 0.928 1.960 0.054 0.049 8 -1.231 -0.998 -0.704 0.928 1.960 -0.167 -0.161 9 0.865 0.696 0.355 -0.771 1.960 0.239 0.235 10 -1.231 0.696 0.355 -0.771 1.960 0.018 0.025 11 0.865 -0.998 0.355 -0.771 1.960 0.078 0.064 12 -1.231 -0.998 0.355 -0.771 1.960 -0.143 -0.146 13 0.865 0.696 -0.704 -0.771 1.960 0.109 0.110 14 -1.231 0.696 -0.704 -0.771 1.960 -0.112 -0.100 15 0.865 -0.998 -0.704 -0.771 1.960 -0.052 -0.061 16 -1.231 -0.998 -0.704 -0.771 1.960 -0.273 -0.271 17 0.865 0.696 0.355 0.928 -0.797 0.256 0.254 18 -1.231 0.696 0.355 0.928 -0.797 0.035 0.044 19 0.865 -0.998 0.355 0.928 -0.797 0.095 0.083 20 -1.231 -0.998 0.355 0.928 -0.797 -0.126 -0.127 21 0.865 0.696 -0.704 0.928 -0.797 0.126 0.129 22 -1.231 0.696 -0.704 0.928 -0.797 -0.095 -0.081 23 0.865 -0.998 -0.704 0.928 -0.797 -0.035 -0.042 24 -1.231 -0.998 -0.704 0.928 -0.797 -0.256 -0.252 25 0.865 0.696 0.355 -0.771 -0.797 0.150 0.144 26 -1.231 0.696 0.355 -0.771 -0.797 -0.071 -0.066 27 0.865 -0.998 0.355 -0.771 -0.797 -0.011 -0.027 28 -1.231 -0.998 0.355 -0.771 -0.797 -0.232 -0.237 29 0.865 0.696 -0.704 -0.771 -0.797 0.020 0.019 30 -1.231 0.696 -0.704 -0.771 -0.797 -0.201 -0.191 31 0.865 -0.998 -0.704 -0.771 -0.797 -0.141 -0.152 32 -1.231 -0.998 -0.704 -0.771 -0.797 -0.362 -0.362 based on the procedural steps of mabac method, the corresponding scores are computed for all the experimental trials using two different criteria weight sets. thus, for each combination of factor levels, two mabac scores are calculated at two replications. assignment of different criteria weight sets results in different mabac scores. this experimental design plan with definitive distance values as the inputs and mabac scores as the responses is now analyzed using minitab (r17) software which results in subsequent development of the corresponding metamodal and analysis of variance (anova) table. this metamodel in the following form can not only account for the main effects of different factors, but can also highlight the existent interactions among them. development of a rough-mabac-doe-based metamodel for supplier selection in an iron and steel industry 35 5432112345 5 1 0 , xxxxxxxxx xxxxxxy i j k l lkjiijkl i j k kjiijk i j jiij i ii lkji kjiji       ++ +++= =   (23) where y is the mabac score, β0 is the intercept coefficient or overall mean response, βi is the main or first-order effect of factor i, βij is the two-factor interaction between factors i and j (i ≠ j), βijk is the three-factor interaction between i, j and k (i ≠ j ≠ k), βijkl is the four-factor interaction between i, j, k and l (i ≠ j ≠ k ≠ l), and β12345 is the fivefactor interaction between all the factors. table 9. estimated effects and coefficients term effect coefficient se of coefficient t-value p-value constant -0.00597 0.00283 -2.11 0.043 c1 0.21044 0.10522 0.00283 37.12 0.000 c2 0.17106 0.08553 0.00283 30.18 0.000 c3 0.12244 0.06122 0.00283 21.60 0.000 c4 0.11306 0.05653 0.00283 19.94 0.000 c5 0.08494 0.04247 0.00283 14.98 0.000 c1×c2 -0.00506 -0.00253 0.00283 -0.89 0.379 c1×c3 0.00506 0.00253 0.00283 0.89 0.379 c1×c4 -0.00506 -0.00253 0.00283 -0.89 0.379 c1×c5 0.00506 0.00253 0.00283 0.89 0.379 c2×c3 -0.00506 -0.00253 0.00283 -0.89 0.379 c2×c4 0.00506 0.00253 0.00283 0.89 0.379 c2×c5 -0.00506 -0.00253 0.00283 -0.89 0.379 c3×c4 -0.00506 -0.00253 0.00283 -0.89 0.379 c3×c5 0.00506 0.00253 0.00283 0.89 0.379 c4×c5 -0.0×0506 -0.00253 0.00283 -0.89 0.379 c1×c2×c3 0.00506 0.00253 0.00283 0.89 0.379 c1×c2×c4 -0.00506 -0.00253 0.00283 -0.89 0.379 c1×c2×c5 0.00506 0.00253 0.00283 0.89 0.379 c1×c3×c4 0.00506 0.00253 0.00283 0.89 0.379 c1×c3×c5 -0.00506 -0.00253 0.00283 -0.89 0.379 c1×c4×c5 0.00506 0.00253 0.00283 0.89 0.379 c2×c3×c4 -0.00506 -0.00253 0.00283 -0.89 0.379 c2×c3×c5 0.00506 0.00253 0.00283 0.89 0.379 c2×c4×c5 -0.00506 -0.00253 0.00283 -0.89 0.379 c3×c4×c5 0.00506 0.00253 0.00283 0.89 0.379 c1×c2×c3×c4 0.00506 0.00253 0.00283 0.89 0.379 c1×c2×c3×c5 -0.00506 -0.00253 0.00283 -0.89 0.379 c1×c2×c4×c5 0.00506 0.00253 0.00283 0.89 0.379 c1×c3×c4×c5 -0.00506 -0.00253 0.00283 -0.89 0.379 c2×c3×c4×c5 0.00506 0.00253 0.00283 0.89 0.379 c1×c2×c3×c4×c5 -0.00506 -0.00253 0.00283 -0.89 0.379 chattopadhyay et al./oper. res. eng. sci. theor. appl. 5(1) (2022) 20-40 36 table 9 shows the effects and coefficients of different factors along with their varied levels of interactions, while table 10 exhibits the derived anova results based on the calculated mabac scores. these anova results provide a summary of the main effects and interactions between various factors. in table 9, the p-values help in identifying statistically significant factors and interaction effects. terms with p-value less than or equal to 0.05 are considered to be statistically significant, whereas, those with p-value greater than 0.05 can be neglected while developing the corresponding metamodeal. in this table, the column ‘term’ depicts the main effects and all the possible interactions among the factors. the ‘effect’ column shows the relative strength of a particular factor or interaction. the β coefficients and their standard errors (se) are provided in the third and fourth columns respectively. the last two columns highlight the calculated tand p-values. in tables 9-10, the rows of all the significant factors (p ≤ 0.05) are shown in bold face. based on the derived results, it can be concluded that all the two-way, three-way, four-way and five-way interactions are statistically insignificant, whereas, all the main effects due to criteria c1, c2, c3, c4 and c5 have independently significant contributions in calculating the mabac score. thus, the metamodel for obtaining the mabac score for a given supplier based on the evaluation criteria can be expressed as below: y = -0.00597 + 0.10522×c1 + 0.08553×c2 + 0.06122×c3 + 0.05653×c4 + 0.04247×c5 (24) in table 10, the r2 value is the square of correlation coefficient indicating the percentage of variation explained by the developed metamodel out of the total variation. on the other hand, the value of r2(adj) represents the proportion of variation in the target variable contributed by the statistically significant terms. it can be concluded that 99.07% of the variation in the dependant variable y (mabac score) can be explained by the variation of the independent variables in this metamodel. extremely high values of both r2 and r2(adj) as 99.07% and 98.16% respectively thus confirm the acceptance of the developed metamodel in exhibiting the relationship between mabac score and supplier selection criteria. table 10. anova results source dof adj. ss adj. ms t-value p-value linear 5 1.73656 0.347311 675.46 0.000 2-way interaction 10 0.00410 0.000410 0.80 0.632 3-way interaction 10 0.00410 0.000410 0.80 0.632 4-way interaction 5 0.00205 0.000410 0.80 0.560 5-way interaction 1 0.00041 0.000410 0.80 0.379 error 32 0.01645 0.000514 total 63 1.76367 r2 = 99.07%, r2(adj) = 98.16% now, based on this model, the corresponding mabac scores for the five alternative suppliers are determined as y1 = -0.0301, y2 = 0.0746, y3 = 0.0175, y4 = 0.1100 and y5 = -0.1990 (where yi is the mabac score for ith supplier). when these mabac scores are arranged in descending order, a complete ranking of the development of a rough-mabac-doe-based metamodel for supplier selection in an iron and steel industry 37 competing suppliers from the best to the worst can be derived. thus, s4 emerges out as the most competent supplier for providing gearboxes to the iron and steel industry under consideration, followed by suppliers s2 and s3. in the derived ranking list of the suppliers, s5 performs the worst. in table 11, the rankings of the considered suppliers derived using rough-mabac-doe-based metamodel are contrasted with those obtained using rough-topsis, rough-edas, rough-aras and rough-waspas-doe-based metamodels. it can be revealed that except rough-edas, the ranking of the most favoured supplier (s4) matches for all the remaining roughmcdm-doe-based metamodels. high spearman’s rank correlation coefficients (rs) prove the application potentiality of rough-mabac-doe-based metamodel in solving supplier selection problems. table 11. comparison of rankings of the suppliers using different rough mcdm methods supplier mabac topsis edas aras waspas s1 4 5 5 5 5 s2 2 2 1 2 2 s3 3 3 3 3 3 s4 1 1 2 1 1 s5 5 4 4 4 4 rs 0.90 0.80 0.90 0.90 4. conclusions this paper proposes a novel approach to solve a supplier selection problem in an indian iron and steel industry while integrating rough numbers with mabac method and doe leading to the development of a metamodel. its application starts with aggregation of the relative performance scores of five competing suppliers using rough numbers considering the uncertainty involved in the decision making process. based on the worst and best rough number intervals, a 25 full-factorial experimental design plan is formulated with subsequent conversion of those rough intervals into the corresponding definitive distances. using two different criteria weight sets as the replications, the related mabac scores are computed for all the experiment trials. finally, a metamodel is developed interlinking the mabac scores and supplier evaluation criteria, which is finally employed to rank the competing suppliers. its main advantage lies on easy computation of the performance score (in terms of mabac score) for a new supplier to be included in the decision making process, thus relieving the decision maker from reinitiating the entire calculation from the scratch. besides its application in iron and steel industry, it can also be efficiently employed in other sectors, like healthcare, tourism, food, textile etc. the possibility of similar hybridization with other mcdm techniques, like marica, marcos, combined compromise solution (cocoso) etc. for solving supplier selection problems can be explored as the future scope of this paper. two sets of criteria weights are considered here based on the opinions of the decision makers, helping in replication of the mabac scores. other subjective methods, like bwm, fucom or lbwa can also be applied for estimating the corresponding 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applications vol. 5, issue 3, 2022, pp. 1-16 issn: 2620-1607 eissn: 2620-1747 doi: https://doi.org/10.31181/oresta0310220016d * corresponding author. serif.demirdag@giresun.edu.tr (ş. a. demirdağ) ranking the recreational leadership factors in the behavioral dimension and selection of the most ideal organizational citizenship model şerif ahmet demirdağ department of tourism management, bulancak kadir karabaş vocational school, giresun university, turkey received: 20 june 2022 accepted: 28 september 2022 first online: 03 october 2022 research paper abstract: the concepts of management and organization are concepts that have existed throughout human history and are necessary for regular human life. since people live in groups, management is needed to ensure the order of these groups, to establish a hierarchical structure, and to achieve goals and objectives. in order for these groups to reach their goals and objectives, someone (from within the group or outside of the group) needs to take a managing and guiding role. it is possible to state that these guides are leaders who can gather people around certain goals and objectives with their own beliefs and opinions, rather than being appointed by someone, who can influence and mobilize them. therefore, the concept of leadership also emerges as a phenomenon that has existed in every period of history. for this reason, leadership styles and behaviors are important issues that need to be focused on, regardless of any field such as production, management, marketing, tourism, engineering. in this study, it is aimed to rank the recreational leadership factors of tourist guides in behavioral dimension according to their importance and to determine the most ideal organizational citizenship behavior model at this point. according to the results of the study, in which entropy and grey incidence analysis (gia) methods were used, it was determined that the most important criterion in behavioral recreational leadership factors was “paternalistic leadership”, and the most ideal organizational citizenship model alternative criterion was "altruism". therefore, it can be said that it would be more beneficial for the tourist guides, who constitute the sample group of the study, to exhibit leadership behavior at the paternalistic level and organizational citizenship behavior in the altruism dimension. key words: recreational leadership, organizational citizenship, tourist guides, entropy, gia. ş. a. demirdağ /oper. res. eng. sci. theor. appl. 5(3)2022 1-16 2 1. introduction a personnel policy built on the principle of merit and managed correctly/honestly is very important and necessary in every field or type of work. in particular, the success of the activities carried out in an organized manner depends more on the leader who will manage and direct the organization compared to other activities (meyer, 1942). the success of these organizations is closely related to the fact that the leader, who will manage and direct the group members, is someone who is believed, trusted and respected. because when people trust someone, they assume that they will act honestly and correctly and will not abuse their trust (robbins, 2002). therefore, trust is the essence of leadership and it is impossible for a person to lead those who do not trust him. leaders try to create an organizational culture that will create trust, progress and growth in people with the actions, behaviors and management style they exhibit. allowing others to develop and mature is also the essence and result of leadership (fairholm and fairholm, 2009). leadership is an interpersonal interaction applied in certain situations and conditions, and leaders lead people to achieve a certain goal or goals throughout the communication process (tannenbaum and massarik, 1957). moreover, it can be said that organizational citizenship behavior (ocb), which is related to the voluntary individual behavior above and beyond what people can do in order to support the organization and its functioning (organ, 1988; 1997), is one of the characteristics of most leaders. it is possible to say that ocb and the concepts of commitment, devotion and loyalty are closely related. therefore, leaders dedicate themselves to the goals and objectives they set. leadership and ocb also play an important role in recreational activities that enable people to regain their energy, renew themselves, and thus be more efficient and productive. regardless of the business line, leisure and recreation activities are important and necessary for people to be more productive, reproduce and find themselves. because leisure activities pave the way for people to renew, rest, recuperate, get away from busy, stressful and routine work life, find themselves, establish or strengthen social relationships with other people, be free, make life as rich and full as possible, and manage their daily plans, schedules and time (kelly, 1990). people often participate in such activities individually or in groups. as with all activities carried out as a group, a leader who creates, directs and leads this group is needed in leisure or recreation activities. tour guides, who lead tourist groups participating in touristic trips as a leisure and recreational activity, also strive for the welfare of their group members. in this study, it is aimed to rank the recreational leadership attitudes in behavioral dimension of the tourist guides examined within the scope of the recreational leader and to determine the best organizational citizenship model in this direction. the criterion weights were determined by the entropy method and the gia was used in the selection of the most ideal organizational citizenship model. in the following parts of the study, there is a detailed literature review on recreational leadership and ocb; entropy and gia methods were applied and explained in detail in the part of methodology, and the study was completed with the conclusionsuggestions. ranking the recreational leadership factors in the behavioral dimension and selection of the most ideal organizational citizenship model 3 2. literature review in group activities, management and leadership are very important. here, the behaviors exhibited by the manager or leader and some organizational behaviors such as organizational citizenship have a key role. morale can be built through recreation, and on the other hand, behaviors learned through recreation can help in facing and coping with problems. for this reason, workers for recreation area should realize that they are both leaders and educators (lindeman, 1941). in particular, the success of organized recreational activities is more dependent on the leader who will direct the organization than any other factor (meyer, 1942). leadership styles should be modified to reflect situational factors. most leadership is based on either a directive or a supporting force (robbins, 2002). it can be said that recreational leadership is a leadership attitude in which different leadership characteristics can be exhibited according to situational conditions in terms of some basic responsibilities. recreational leadership encompasses different functions, in various forms and to a large extent, for various purposes. recreational leaders manage many different types of recreational activities and engage with leisure/recreation agencies. they help organize and manage programs that display a wide variety of activities, and even take on these functions (demirdağ, 2019; tezcan, 1977). from this point of view, in this study, it is aimed to rank the recreational leadership factors of tourist guides in the behavioral dimension and to determine the most ideal organizational citizenship model. no academic study examining the relationship/effect between recreational leadership and organizational citizenship behaviors has been found. this situation shows that this study on related subjects is original. a detailed literature review is presented below, along with the examination of some notable academic studies on recreational leadership and organizational citizenship in the tourism sector; karaküçük and yetim (1996), who conducted research on leadership and its functions in recreational activities, underlined that the effect of leadership behavior types can change according to the type of activity and application conditions in a wide variety of recreational activities. gubersky et al (1955), who studied the subject of recreation for the elderly, reached the conclusion that a mature leader must have certain characteristics. gubersky et al listed these characteristics (commands) that a leader should have such as “know and follow topics related to field”, “give professional guidance”, “be open to learning, try to learn from leaders in own group and other groups”, “know yourself”, “be confident but be prepared to make mistakes”, “have the tools for a particular job and the know-how”, “use a top-down communication system for good communication”, “don't spread yourself too much by taking on too much responsibility”, “develop good human relations with people” and “think”. according to the results of a study (demirdağ and güçer, 2019) examining the relationship between business ethics and recreational leadership, it has been determined that there were significant relationships between recreational leadership behavior and business ethics. according to the results of a study conducted by hambrick et al (2018) on cohesion and leadership in individual sports in running groups, it was concluded that individuals who run for recreational purposes adapt, and informal leaders emerge alongside formal leaders. ş. a. demirdağ /oper. res. eng. sci. theor. appl. 5(3)2022 1-16 4 in the study of basoglu (2013a), in which he examined the relationship between participation in recreational activities and leadership behaviors of secondary school students, it was determined that students engaged in sports activities showed transformational leadership characteristics, while students who did not engage in sports activities showed more interactional leadership characteristics. in another study, basoglu (2013b) examined the relationship between leadership and participation in recreational activities on citizens, he concluded that the behaviors of recreational leaders who carry out recreational activities directly affect the participation of citizens in activities. therefore, it can be interpreted that the role and importance of the leaders who organize and manage the recreational activities in participation and implementation of activities is quite high. when the above studies on recreational leadership are examined, it is seen that the evaluation of recreational leadership in terms of participants or its relationship with different variables has been examined. in this study, the relationship between organizational citizenship behavior and recreational leadership of tourist guides has been tried to be revealed. however, the absence of any academic study on the relationship between organizational citizenship and recreational leadership reveals the importance and originality of this study. in order to better understand the organizational citizenship behavior of tourist guides, the following paragraphs of the research include a literature review on organizational citizenship behavior in the tourism sector. tuan and ngan (2021), who conducted research on ethical leadership to shape the service-oriented organizational citizenship behavior of tourism salespeople who have almost the same purpose as tourist guides, concluded that there is a significant relationship between ethical sales leadership and organizational citizenship behavior. according to the results of an academic study (buil et al, 2016) investigating the relationship between internal brand management and organizational citizenship, it was found that work engagement is an important predictor of organizational citizenship, and that identification also affects organizational citizenship behavior. as a result of a study on promoting service-oriented organizational citizenship behaviors in hotel establishments (tang and tang, 2012), it was revealed that highperformance human resources practices affect employees' cognitions about how they are treated by hotels and what service behaviors are expected. in addition, it has been determined that high-performance human resources practices positively affect collective service-oriented organizational citizenship behaviors. in the another study conducted by kim et al (2020) on the environmental leadership of hotels and the organizational citizenship behaviors of employees, it was concluded that the environmental belief of the employees, both environmental transformational leadership and environmental policies, have an effect on the organizational citizenship behavior towards the environment, and that the organizational support perception of the employees is related to the environmental belief and organizational citizenship behavior towards the environment. in the study by dewi et al (2021), in which the predictions about the relationship between psychological ownership and job satisfaction and organizational citizenship behavior were examined, it was predicted that the personality traits of the employees affected the organizational citizenship behavior positively. ranking the recreational leadership factors in the behavioral dimension and selection of the most ideal organizational citizenship model 5 in general, there are numerous academic studies on organizational citizenship behavior, which is a positive organizational variable for businesses, employees and managers. organizational citizenship behavior, which is associated with different dimensions, in which the relationship/effect between different variables is investigated or compared with the personality traits of the employees, is also a very important behavior for tourist guides who guide and lead tourists. from this point of view, the aim of this research is to rank the recreational leadership factors of tourist guides in behavioral dimension and to determine the most ideal organizational citizenship behavior model by using entropy and gia methods. in the following part of the paper, information about the method used in the study, the universe-sample and the scales are presented. 3. methodology in this study, it is aimed to rank the recreational leadership factors of tourist guides in behavioral dimension according to their importance and to determine the most ideal organizational citizenship model. in line with the aforementioned purpose, the data set of the research was created by applying the survey technique to a total of 12 licensed guides operating in ankara, turkey. the recreational leadership scale developed by demirdağ (2019) was used regarding the recreational leadership expressions in the behavioral dimension. in this scale, there are a total of 7 factors as “democratic (participatory)”, “paternalist”, “transformer”, “charismatic”, “authoritarian”, “libertarian” and “innovative”, and the participants were asked to rate these factors from 1 to 5 according to themselves. in the scale used to determine the ideal organizational citizenship behavior model, there are 5 dimensions in total, which are determined by organ (1997), consisting of “altruism”, “compliance”, “sportsmanship”, “courtesy”, and “civic virtue”. in the aforementioned scale, the guides were asked to rate from 1 to 5 according to the leadership dimensions in order to determine the most ideal organizational citizenship behavior model. on the back page of the questionnaire, which is applied to the tourist guides and consists of two parts, there are explanations about the concepts. the analysis of the data collected in accordance with the purpose of the study was carried out using entropy and gia methods. entropy-based gia methods were chosen in the study, and fuzzy methods were not preferred. because the main problem of fuzzy logic is that there is no definite method to prove in the analysis of stability, observability and controllability in fuzzy methods. in addition, nowadays this is only possible with expensive experiences (elmas, 2003). in other hand, according to menteş (2000), fuzzy methods do not have a definite formal design and do not have good metrics, and it is not possible to predict how well they will yield compared to traditional methods and when they should be used. fuzzy methods are not preferred due to the issues mentioned above. the entropy method, which is a multi-criteria decision making (mcdm) method, was used to determine the importance levels of recreational leadership factors in the behavioral dimension of tourist guides in ankara. because mcdm methods are applied differently from statistical analysis techniques, that is, they are methods in which objective and non-objective factors are evaluated together. analyzes are carried out within the framework of expert opinions, and at the same time, the study can be shaped according to the opinion of a single expert or the opinion of a group of ş. a. demirdağ /oper. res. eng. sci. theor. appl. 5(3)2022 1-16 6 experts. on the other hand, mcdm methods are not among the methods used to generalize from a sample mass to the main mass as in statistical analysis. so, these methods are methods in which subjective and objective criteria can be evaluated together and analysis is carried out according to expert opinions (korucuk, 2021). in this section, the entropy method, which is used to evaluate the criteria determined for the factors affecting the recreational leadership process of tourist guides in the behavioral dimension, is explained. 3.1. entropy entropy is one of the weighting methods that reflect reality. entropy, an effective method used to explain the maximum uncertainty or minimum certainty of the problem, also eliminates human-induced errors. in practice, the smaller the value in the method, the smaller the degree of irregularity (wu et al, 2011; çiçek, 2013). according to bouraima et al (2021), entropy method is a means of ambiguity in information produced regarding the hypothesis of the probability. moreover, the nature of the criteria marked as inputs allows objective determination of the weights of criteria and the entropy method is applied. (blagojević et al, 2020). in decision-making problems involving many criteria, the entropy method is evaluated in the category of objective weight calculation methods in the literature for calculating criterion weights. in the entropy method, the data in the decision matrix is used to calculate the weights of the criteria in the decision problem. the applicability of the method is quite easy since there is no need for any other subjective evaluation (ayçin and güçlü, 2020). unlike other multi-criteria decision making methods (such as swara, ahp and analytical network process) used for weight finding, the method does not require a separate data set for criteria (ulutaş, 2019). ecer (2020) states that the entropy method yields very good results in different evaluation events in different decisionmaking processes. because with this method, by calculating the irregularities between the criteria, decision makers can draw uncomplicated results. due to the above-mentioned benefits and advantages of the entropy method, this method was preferred in the study. the application steps of entropy weight method are given below (abdullah and otheman, 2013; mishra et al, 2020); step 1. creating the initial decision matrix for a multi-criteria decision problem with m decision alternatives and n evaluation criteria, an initial decision matrix is created as follows. (1) step 2. normalization of the initial decision matrix in the normalization process, the following formulas are applied depending on whether the criteria are benefit (2) or cost (3) (memiş and korucuk, 2021): ranking the recreational leadership factors in the behavioral dimension and selection of the most ideal organizational citizenship model 7 pij = i = 1,…..,m; j = 1,…..,n (2) pij = i = 1,…..,m; j = 1,…..,n (3) in the equation below, the 𝑡𝑖𝑗 value is the normalized version of the 𝑟𝑖𝑗 value. the mentioned equation is presented in the equation (4). tij = (4) step 3. calculation of entropy value the entropy value (ej) is calculated with the help of the following equation (5): ej = -k (5) here, the value of “k” is calculated with the formula k = (ln(m))-1. step 4. calculation of degree of differentiation and weight of entropy the degree of variation (dj) of the entropy value is calculated with the help of equation (6): dj = 1-ej ; ɐj (6) the objective weight (wj) of each criterion is defined according to equation (7): wj = , ɐj (7) 3.2. gia the gia method developed by deng (1989) is defined as a system that includes unknown information represented by gray numbers and gray variables (chou and tsai, 2009). the gia method, which is based on number theory, can be easily used in decision problems that do not create certainty and where there is not enough information about alternatives (chan and tong, 2007). according to huang and lee (2003), the gia also provides a clear and precise definition of all the relationships within a system of all existing situations in certain study subjects. it is known that the gia method has advantages such as allowing many criteria to be handled together, being able to evaluate even when the number of data is small, lack of strict rules for the sample size, and allowing ranking according to the degree of relationship in cases where the distribution is unknown or not normal (liu and forrest, 2007). according to atan et al (2020), the gia method provides a great advantage against deviations and distortions that may occur in some assumptions compared to other mcdm methods and statistical techniques. some of these advantages can be stated as the need for a small number of samples for the process, effective results with uncertain data, no need for any probability distribution of the data, and the calculation of the gray relational coefficient with a very simple and few operations. in addition, if the ş. a. demirdağ /oper. res. eng. sci. theor. appl. 5(3)2022 1-16 8 decision makers do not have sufficient expertise, the gia method gives very successful results in mcdm problems. due to the benefits and advantages of the gia method, this method was preferred in the study. the application stages of the gia method are presented below in detail (zhai et al, 2009; korucuk, 2018): step 1. establishment of alternatives (i=1,...,m) and criteria (j=1,...,n). xi=(xi (1), xi (2), xi (3), ……xi (n)), (8) step 2. generation of reference series based on the lowest or highest values of the comparable series xo=(xo (1), x0 (2), xo (3), ……xo (n)), (9) step 3. performing the normalization activity that allows the values to be freed from the unit effect. this step can be done in three ways as outlined below: lower is better: (10) higher is better: (11) ideal value is better: (12) step 4. calculation of gray incidence coefficient values as an indicator of similarity between reference series and alternative series (13) step 5. calculation of gray incidence degrees to use in ranking alternatives according to similarity of reference series    n 1k ioi0 ))k(),k(( n 1 ),( (14)    n 1k ioii0 ))k(),k(()k(w),( (15) 4. findings in this study, a two-stage multi-criteria decision model was created for the evaluation of the recreational leadership factors in the behavioral dimension of the tourist guides in ankara and for the selection of the most ideal organizational citizenship model. in this regard, primarily behavioral recreational leadership factors ranking the recreational leadership factors in the behavioral dimension and selection of the most ideal organizational citizenship model 9 and organizational citizenship model issues were determined by using the literature review with expert opinions (see methodology section). since the determined criteria were not of equal importance, it was necessary to weight the criteria. in this framework, with the entropy method, the recreational leadership factors of the tourist guides in ankara were weighted in the behavioral dimension. by using weighted criteria, the most ideal organizational citizenship model was listed with the gia method. a limited number of studies in the literature were used while selecting criteria and alternatives. at this point, the relevant alternatives and criteria were determined by 2 experts with the preliminary study. while determining the expert group, an experience-based selection was made as a tourist guide. the study was applied to tourist guides who have 10 years or more of working experience. while determining the criteria, the following table 1. was created by using the recreational leadership scale developed by demirdağ (2019) together with expert opinions. table 1. recreational leadership decision criteria recreational leadership factors in the behavioral dimension democratic (participatory) leadership (c1) paternalist leadership (c2) transformer leadership (c3) charismatic leadership (c4) authoritarian leadership (c5) libertarian leadership (c6) innovative leadership (c7) while determining the alternatives, the following table 2. was created by using the dimensions introduced by organ (1997) together with expert opinions. table 2. organizational citizenship alternatives organizational citizenship model altruism (a1) compliance (a2) sportsmanship (a3) courtesy (a4) civic virtue (a5) 4.1. weighting criteria at this stage, where the entropy method is used, a questionnaire was created to evaluate the criteria. the aforementioned questionnaire was applied to the tourist guides, that is, a total of 12 experts, who are the stakeholders of the study. in this context, the application steps of the entropy method are presented in the tables below. in table 3., the decision matrix of the study is given. ş. a. demirdağ /oper. res. eng. sci. theor. appl. 5(3)2022 1-16 10 table 3. decision matrix c1 c2 c3 c4 c5 c6 c7 a1 3 2.33 3 3.50 4 3.50 4.50 a2 4 2.50 3 3.50 3.50 4 2.50 a3 4 4.50 2 3.50 3.50 4 4.50 a4 4 4 1.50 3 3 3.63 4.50 a5 4.50 3 2.50 3.75 2 3.50 3.50 table 4. presents the normalized decision matrix. table 4. normalized decision matrix c1 c2 c3 c4 c5 c6 c7 a1 0.154 0.143 0.250 0.215 0.250 0.188 0.231 a2 0.205 0.153 0.250 0.215 0.219 0.215 0.127 a3 0.205 0.276 0.167 0.215 0.219 0.215 0.231 a4 0.205 0.244 0.125 0.186 0.187 0.194 0.231 a5 0.231 0.184 0.208 0.169 0.125 0.188 0.180 in this context, the results of the analysis are presented in detail in table 5. below. table 5. criterion weights table c1 c2 c3 c4 c5 c6 c7 weight 0.142 0.149 0.147 0.137 0.145 0.136 0.144 ranking 5 1 2 6 3 7 4 when the values in table 5 are examined, the factor that has the highest weight in the behavioral dimension of the recreational leadership criteria of the tourist guides according to the entropy method is the “paternalistic leadership” criterion. other important factors were determined as “transformer leadership”, “authoritarian leadership”, “innovative leadership” and, “democratic (participatory) leadership”, respectively. on the other hand, it has been determined that the factor with the least weight among the recreational leadership criteria in the behavioral dimension for tourist guides is “charismatic leadership” and “libertarian leadership”. 4.2. ranking of alternatives in this section, the gia method was used to rank the alternatives. by using the weights of the criteria obtained by the entropy method, the alternatives were ranked by the gia method. evaluation of each alternative in the previously determined decision criteria was made with the gia questionnaire. during the evaluation phase, the participants were asked to rate each alternative between 1 and 5 (1-worst, 5best). in this direction, the decision matrix was created, then the decision matrix was normalized and table 6. was created and presented below. table 6. grey incidence analysis method decision matrix c1 c2 c3 c4 c5 c6 c7 a1 3.50 4 4.5 4 2 3 3.50 a2 3 4.75 3.75 4 3 3 3.25 a3 1.50 3 3 3 2.50 2.50 2.50 a4 3 4 2 3 2.25 3.50 4 a5 2 2 4 3 2 2 2.50 ranking the recreational leadership factors in the behavioral dimension and selection of the most ideal organizational citizenship model 11 making use of equation 9, the total of the decision matrix reference series is shown in table 7. below. on other hand, table 8. normalized decision matrix was calculated by using equations 10, 11 and 12. table 7. decision matrix reference series c1 c2 c3 c4 c5 c6 c7 max max max max min min max reference series 3.50 4.75 4.50 4 2 2 4 a1 3.50 4 4.5 4 2 3 3.50 a2 3 4.75 3.75 4 3 3 3.25 a3 1.50 3 3 3 2.50 2.50 2.50 a4 3 4 2 3 2.25 3.50 4 a5 2 2 4 3 2 2 2,50 table 8. gia normalized decision matrix c1 c2 c3 c4 c5 c6 c7 a1 1.000 0.273 1.000 1.000 1.000 0.333 0.333 a2 0.250 1.000 0.300 1.000 0.000 0.333 0.500 a3 0.000 0.636 0.600 0.000 0.500 0.667 0.000 a4 0.250 0.273 0.000 0.000 0.750 0.000 1.000 a5 0.750 0.000 0.200 0.000 1.000 1.000 0.000 in the last stage, the weights determined by the entropy method were prioritized and the result is shown in detail in table 9. below. table 9. gray incidence degrees and ranking with the entropy method a1 a2 a3 a4 a5 γ0i 0.752 0.613 0.464 0.460 0.577 ranking 1 2 4 5 3 according to the values in table 9., “altruism (a1)” was found to be the best alternative in the order of choosing the most ideal organizational citizenship behavior. other criteria in the order of choosing the most ideal organizational citizenship behavior were realized as “compliance (a2)”> “civic virtue (a5)”> “sportsmanship (a3)”> “courtesy (a4)”. 5. conclusion and future suggestions as in every type of sector, leadership has a very important place in the activities and in the realization of these activities in the tourism sector. especially in tours served by tourist guides, the tour guide's management abilities and leadership skills come into play in the successful and effective conclusion of the tours. tourist consumers, who allocate a significant amount of time and money for the holidays and tours, want to get back the full value of their money and time. at this point, the leadership behaviors that tourist guides will exhibit or adopt may differ from other business lines. because here, factors such as the money/time spent, the purpose of the tour, and the satisfaction of the tourists come to the fore. from this point of view, ş. a. demirdağ /oper. res. eng. sci. theor. appl. 5(3)2022 1-16 12 it can be thought that authoritarian leadership, which is a strong leadership style in general, cannot be very valid in such works (except when necessary, of course). therefore, it will be beneficial to adopt and implement the most ideal and most appropriate leadership style, taking into account all of these factors for tourist guides. in this study, the criteria for recreational leadership factors in behavioral dimension of tourist guides operating in ankara were determined and the most ideal organizational citizenship model was chosen. according to entropy results, “paternalistic leadership” is the most important criterion regarding the behavioral dimension of the recreational leadership criteria with the opinions of 12 tourist guides who operating in ankara. this result is similar to the result of another academic study (demirdağ, 2019) conducted with animation workers examined within the scope of recreational leaders. likewise, it can be expected that tourist guides can adopt a parental attitude (paternalistic leadership) or a leadership style that allows a little more freedom (laissez-faire/liberal), being aware of their responsibilities towards tourists who spend money/time for tours or holidays. other important factors were determined as “transformer leadership”, “authoritarian leadership”, “innovative leadership”, “democratic (participatory) leadership”, “charismatic leadership” and “libertarian leadership”, respectively. transformer leadership, which contributes to gaining vision, enabling participants to realize what and why they are doing, creating meaning for the participants, helping them achieve success, helping them develop and developing a sense of creativity, was also found to be of secondary importance for tourist guides. in some cases, the irresponsible behavior or personality traits of the tourists participating in the tours cause the tourist guides to exhibit an authoritarian leadership attitude, although it is not preferred. therefore, the criterion for authoritarian leadership behavior was found to be third important for tourist guides. although the tours led by the tourist guides are classic and they tell and show the same places, they still think that it is necessary to be innovative. so, the criterion for innovative leadership behavior was found to be fourth important criteria for tourist guides. according to the tourist guides, since the tours were planned in advance and acted in accordance with this plan, the degree of importance for democratic leadership was found to be fifth. because, especially when leading large tourist groups, there may be a risk of different voices from each head, and therefore it can be thought that democratic leadership may not be appropriate in these situations. similarly, the charismatic leadership and libertarian leadership criteria for tourist guides were also underestimated. it can be interpreted that this can be explained by the relationship between the work that the tourist guides will do and the lines of this work and their sense of responsibility. according to the results of the analysis carried out with the gia method, the most ideal organizational citizenship model in tourist guides was found to be “altruism (a1)”. it can be said that such a result can be expected in relation to tourist guides in the organizational citizenship dimension. because, in recreational touristic trips, tourist guides may make sacrifices under certain conditions for the satisfaction of the participants and sometimes they may give up their own interests for the interests of the participants. other criteria in the most ideal organizational citizenship model for tourist guides were found as “compliance (a2)”, “civic virtue (a5)”, “sportsmanship (a3)”, and “courtesy (a4)”, respectively. compliance, the second highest criterion presented in the model, is important in terms of efficient tours with tourist guides and participants. the third criterion, "civic virtue (a5)," is important both professionally and in terms of the sustainability of tours, as it describes qualities such ranking the recreational leadership factors in the behavioral dimension and selection of the most ideal organizational citizenship model 13 as morality, truthfulness, helpfulness, valor, wisdom, humility, good-heartedness, and temperance. “sportsmanship (a3)”, which is the fourth criterion in the model, is one of the factors found in the politeness and civility dimension of tourist guides. although this criterion is also very important, it was found to be slightly lower than other criteria in the ranking. according to the perception of tourist guides who contributed directly to creating the model, the lowest organizational citizenship criterion was found to be “courtesy (a4)”. as stated above, all of the criteria in the organizational citizenship dimension are very important for the tourist guiding profession, and they are sorted in this way in line with the opinions they give. in this direction, the ranking of the most ideal organizational citizenship model of tourist guides was as follows; a1>a2>a5>a3>a4. according to the findings obtained from this study, it is possible to state that the research results show consistency and stability. the results of some studies (biswas et al, 2021a; biswas et al, 2021b, biswas et al, 2022 etc.), which were used as a reference in justifying the study and determining the methods used, also show consistency and stability. in addition to its theoretical contributions, the study has very important implications for decision makers and practitioners in the tourism sector and those who are interested in this subject. one of them also offers the opportunity to evaluate organizational citizenship models in terms of leadership and business. on the other hand, in organizational citizenship models, the business leads a basic model to choose the optimal alternative to participants and recreational leadership. it provides a flexible and structured decision-making environment, and a decision-making environment and opportunity that takes into account different and separate views. another valuable contribution of the study is that it helps decision makers make a new route and planning that takes into account the existing market conditions for the criteria and alternatives determined using the proposed model. in this study, 12 tourist guides with cockades operating in ankara province of turkey and who are experts in the subject for this study were interviewed. in the future, it will be possible to compare the recreational leadership behaviors of tourist guides in behavioral dimension and organizational citizenship dimensions with a similar study that will cover other provinces of turkey and maybe other countries. in addition, other leadership types can be applied to other professional groups in future academic studies instead of recreational leadership discussed in this study. finally, this study can be developed and results can be compared by using other multicriteria decision 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(2009). design concept evaluation in product development using rough sets and grey relational analysis. expert systems with applications, 36(3), 7072-7079. https://doi.org/10.1016/j.eswa.2008.08.068 © 2022 by the authors. submitted for possible open access publication under the terms and conditions of the creative commons attribution (cc by) license (http://creativecommons.org/licenses/by/4.0/). ranking the recreational leadership factors in the behavioral dimension and selection of the most ideal organizational citizenship model şerif ahmet demirdağ 1. introduction 2. literature review 3. methodology 3.1. entropy 3.2. gia 4. findings 4.1. weighting criteria 4.2. ranking of alternatives 5. conclusion and future suggestions references plane thermoelastic waves in infinite half-space caused operational research in engineering sciences: theory and applications vol. 5, issue 2, 2022, pp. 152-175 issn: 2620-1607 eissn: 2620-1747 doi: https://doi.org/10.31181/oresta110722120g * corresponding author. gyenge.balazs@uni-mate.hu (g. balázs), meszaros.zoltan.gabor@gmail.com (z. mészáros), peterfi.csaba.attila@gmail.com (c. a. péterfi) process measurement and analysis in a retail chain to improve reverse logistics efficiency gyenge balázs 1, zoltán mészáros 2, csaba attila péterfi 3* 1 hungarian university of agricultural and life sciences, hungary 2 faculty of finance and accountancy, budapest business school, hungary 3 doctoral school of economics and regional sciences, hungarian university of agriculture and life sciences, hungary received: 12 april 2022 accepted: 11 july 2022 first online: 11 july 2022 research paper abstract: the concept of logistics efficiency, especially reverse logistics efficiency measuring has become one of the key factors in our modern society as business and transportation become increasingly complex and networked. however, reverse logistics involves a high degree of uncertainty, which affects and makes evaluation more difficult. our motivation and purpose is to present the efforts of one of the world’s leading retail companies to improve overall efficiency with a new supplementary measurement and analysis tool. our initial hypothesis was that unladen logistics returns are inefficient and improvements in this area are more sustainable, so in our design and methodology approach we try to analyze logged data. according to our goals, this study is meant to demonstrate the significance of the reasons and the way to customize data analysis to formulate more adequate suggestions. through a live practical example, a presentation is given how we can identify and highlight the hotspots to improve reverse logistics. the main results and originality of the paper are to develop a practical scalable model framework which can be customized by companies having a similar problem. contrary with the well-known dea models the presented model a system thinking method that provides (up-to-date) information which enables better flexibility and highlights areas of interdependency for development projects. key words: logistics processes, reverse logistics, efficiency improvement, cost reduction, freight transport 1. introduction the importance of reverse logistics has a massive impact in the companies’ life and has a noticeable large influence on their costs as well. wang et al. (2017) and bajor et al. (2014) also confirm this idea, saying that reverse logistics is a critical part process measurement and analysis in a retail chain to improve reverse logistics efficiency 153 of supply chain management, and its scope has expanded significantly since its early introduction. first of all, the concept of activity needs to be clarified, which several people have tried to define: one approach is the task of reverse logistics, by definition, to costeffectively return products, raw materials, and related information from the place of consumption to the place of origin for the return, repair, remanufacturing, and recycling of products. inverse logistics thus allows environmental considerations to be met throughout the product life cycle. supply chains that combine traditional forward logistics with reverse (also known as inverse) logistics are called closedloop supply chains. such supply chains cover all value-creating processes from the creation of a product to its cessation (szász & demeter, 2017). in another formulation, reverse logistics is the flow of goods back into the sales channel, that is, the flow of goods from the consumer to the retail store, from the store to the distribution center, and then from the distribution center to the manufacturer. the tasks of reverse logistics also include the storage and transport of packaging (pallets, crates, recyclable glass) and recyclable waste. the packaging is reused as packaging material and the waste must be stored or disposed in accordance with regulations (agárdi, 2017, vöröskői et al., 2020; gyenge et al., 2021). whereas, according to the third wording, return logistics is the material flow from the customer to the company, where the purpose of returning the product is to use some kind of service, most often for environmental purposes (chikán, 2020). based on the definitions, the main tasks of reverse logistics include the return of unused products and materials from the consumer to the producer, as well as the removal of generated waste and packaging for destruction, recycling and reuse. according to bajor et al. (2014), the study of reverse logistics issues, even in advanced logistics systems, remains an area that needs to be continuously researched in order to optimize the entire supply chain. bajor et al.'s (2014) idea is fully consistent with our present research. huscroft et al. (2013), guide and van wassenhove (2009), and hazen (2011) believe that this increase in research and practitioner focus reinforces reverse logistics as a key strategic capability appearance within the supply chain. to define the role of reverse logistics for the company, a few words about the role of logistics must be told first, which is to create and maintain a proper flow of raw materials, semi-finished and finished products, either within a company or across company boundaries. logistics was originally created to optimize transportation and warehousing tasks, but today it has a broader meaning. all flow processes are controlled by logistics in a way that minimizes total cost and maximizes customer satisfaction (see figure 1). (kopcsay, 2016) figure 1: the role of logistics and marketing (own editing based on kopcsay, 2016) b. gyenge, et al./oper. res. eng. sci. theor. appl. 5(2) 2022 152-175 154 so it has a big impact on costs and maximizing customer satisfaction (see figure 1), as evidenced by porter’s value chain theory, where logistics has been ranked among the primary activities, also known as value-creating activities. through inbound and outbound logistics, it has an impact on the company’s operations, capacity utilization, and cost developments through value-creating processes (see processes of the corporate value chain by m.e. porter 1985). supply chains are formed through the interconnection of logistics processes and value chains across the borders of companies, which provide many benefits to chain members and require much closer collaboration (see figure 2). figure 2: extending the value chain concept to the supply chain level (szász & demeter, 2017) with the development of supply chains, the chain members coordinated their purchasing, production, sales and information activities, so in the narrower sense, logistics and, more widely supply chain management has got and concentrated particular responsibility. it no longer only affects the profitability of a company through costs and value-creating activities, but also regulates the operations and not just one but all companies are involved in the supply chain efficiency. therefore, we want to develop a new plug-in tool to deepen the analysis of the problem, and to lay the foundations for the development of reverse logistics integration with our logistics partners. the second section briefly presents the relationship between reverse logistics and efficiency by comparing the main sources of the topic and the evolution of approach over the years. in the third section, the research method and model background will be presented. the fourth section discusses the results of the analysis in parallel with practical and theoretical aspects, without conclusions in case studylike form. in the fifth section is followed by conclusions and suggestions, in which the paper presents the company’s specific results and generalized considerations, as well as the resulting recommendations. process measurement and analysis in a retail chain to improve reverse logistics efficiency 155 2 reverse logistics and its efficiency in literature reverse logistics also contributes to consumer satisfaction, as the supply chain does not end at the same time as purchase / consumption. the collection and proper processing of non-purchased products, waste generated during consumption and packaging is an essential part of the process. today, supply chain management cannot be analyzed without considering reverse logistics (guide & van wassenhove, 2009). according to rubio and jiménez-parra (2014), the origins of reverse logistics date back to the 1970s, where raw material recycling was published in some publications. de brito and dekker (2004) define reverse logistics as the process of planning, implementing, and controlling the return of materials, process inventory, packaging, and finished products, from the point of manufacture, distribution, or use to recovery or proper disposal. many discussions have been generated by reverse logistics operations due to the complexity of decision-making and planning (kumar & saravanan, 2014). process difficulties and hardly measurable stochastic behavior situations frequently emerge when residual material and return products collection is planned by enterprises (costa-salas et al., 2017). eventually, a holistic and strategic approach became prevalent in the 21st century, explicitly acknowledging the coexistence of the forward (from producer to consumer) and the reverse (from consumer to producer) (dowlatshahi, 2000). this is the source of the closed loop supply chain (clsc) concept, which can be defined as a ‘supply chain’ or ‘supply network’ where, in addition to typical material flows from suppliers to end users, there are also reverse flows (ferguson & souza, 2010). the interest in introducing reverse logistics systems is generally attributed to three factors that drive companies: (1) gaining competitiveness advantage, (2) environmental legislation, and (3) pressure from various stakeholders, also known as profit, environment, and people (subramoniam et al., 2009). the task of reverse logistics can be divided into two parts: • return management: which performs the task of returning expired products and packaging, and the failure of any 7r element can cause a return flow without quality issues. • waste management: in the concept of consumption and supply chain, it deals with the collection and recycling of waste generated during closer cooperation than before. costa-salas et al. (2017) presents the challenges of waste management through the collection of tires. the main task of reverse logistics is to promote waste recovery and active participation in integrated waste management. it should be noted, however, that reverse logistics is not only the recovery of waste, but also the efficient organization of all return logistics tasks, material and information flows, similar to logistics (rogers et al., 1999). supply chains, from the extraction or production of raw materials to the sale of final products and the processing of waste from final products, are in fact the link between the natural environment and economic activities. thus, managers responsible for operating value-creating processes in a supply chain cannot circumvent environmental considerations (szász & demeter, 2017; agárdi 2017). b. gyenge, et al./oper. res. eng. sci. theor. appl. 5(2) 2022 152-175 156 based on the previously mentioned topics, the organization of return logistics must also take into account environmental goals, and in several cases a parallel can be drawn with better utilization of capacities. for the sake of example after a truck or transport vehicle has completed its primary transport task, it is allowed to perform various valuable logistical tasks instead of returning empty loads to its point of departure: • collection of return goods, packaging, waste. • to carry out a new (raw) material supply. • or the return capacity may be sold as a service. each is an environmentally conscious activity on the one hand and a cost-effective activity for the company on the other hand. figure 3: conceptual framework of the traditional and reverse logistics process (own edited) the traditional logistics processes can be seen in figure 3 in which the product reaches the consumer through value-creating processes, while in contrast, reverse logistics is used to collect, process and recycle waste. meanwhile, information and packaging flow back in the opposite direction in the supply chain. although reverse logistics obviously contribute to the smooth operation of the company, usually it cannot be classified as a value-creating activity, so less attention is paid to it. it must not be ignored in any way because, it can dramatically influence the expenditures and can cause imbalances in transportation flows. although there is great potential in reverse logistics to increase performance and improve customer relationships, the potential value of its efficiency is often underestimated (kaynak et al., 2013). as kaynak et al. (2013) declares ‘lack of awareness of the benefits of reverse logistics, both economically and environmentally, is one of the main factors that provokes resistance to complementing logistics activities with reverse logistics’. there are various quantitative and qualitative methods and techniques in literature for measuring performance of logistics and reverse logistics at different levels of the supply chain or company (strategic, tactical and operational) (andrejić, pajić & kilibarda, 2021). it is not an easy question at all, as we can estimate efficiency process measurement and analysis in a retail chain to improve reverse logistics efficiency 157 or effectiveness based on a wide variety of concepts. efficiency can be defined quite differently depending on what we consider to be a task or a strategic goal. there are various indicators and methods in the literature for optimizing transport efficiency, fleet allocation targets, utilization of vehicle capacity, coordination of transport and pickup-delivery planning, cost-benefit concepts, environmental aspects, legislative concerns, customer service level maximization etc., according to the initial objectives. one of the best known data envelopment analysis (dea) methods is a nonparametric linear programming technique that enables mutual comparison of systems, i.e. it determines whether each decision-making unit (dmu, see the introduction of the dmu concept charnes, cooper, & rhodes, 1978), based on input and output data, is relatively efficient compared to other units that are part of the analysis and homogenous enough as well. the dea method is widely used in logistics to compare different homogeneous decision-making units (min & joo, 2006; momeni et al. 2015; andrejić, kilibarda & popović, 2017; mitrović et al., 2022). ‘the traditional models for dea type performance measurement are based on thinking about production as a black box’ (momeni, azadi, & farzipoor, 2015). these models successfully compare different logistics units, distribution centers, transportation capacities, warehouse operations, and can successfully determine which groups of indicators represent efficiency better. dea model can be used to estimate the effectiveness of 3pl efficiency from a provider’s perspective (min & joo, 2006) and from a user’s perspective (ding, zang & jiang, 2008). some articles analyze the efficiency of reverse logistics (haas, murphy & lancioni, 2003; ratković, andrejić & vidović, 2012, yoon, & le, 2013), distribution centers’ (dcs) efficiency as a part of complex supply chains (ross, & droge, 2002) and sometimes the dea models are combined with other models. (andrejić, pajić & kilibarda, 2021; sharma et al., 2021) other researchers have tried to combine indicators from field experts and delphi, ahp, and topsis methods to determine their relevance, weight, and ranking (kumar et al., 2021) and ranking the success factor according to expert opinions in the literature (tyagi et al., 2019) or failure mode effect analysis (fmea) method with intuitionistic fuzzy concept (kushwaha et al., 2020; gopal & panchal 2021). on the other hand, the latest publications approach the topic of reverse logistic from the side of technological developments, such as industry 4.0 (krstic at al., 2022). industry 4.0 sets the stage for creating a smart framework based on technologies and applications that enable easy communication and connections between various objects (bahrin at al. 2016). krstic and his colleagues used industry 4.0 as a decision support device with a unique method cobra (comprehensive distance based ranking). cobra was compared with multi-criteria decision making (mcdm) techniques to several methods as topsis, vikor, waspas and so on, and it is stated, that cobra could be used to solve any mcdm problem in various fields including reverse logistic. according to ray (ray et al. 2021), in the field of transportation and logistics, the internet of things can make the company more efficient. it shows the connection between companies using iot and the benefits associated with the technology. despite great results of these papers, it is still a question of what efficiency or effectiveness means technically, because it ultimately depends on the opinion of managers. for example, higher profit rate performance, higher capacity utilization rate or a higher level of a complex indicator is not equal to higher effectiveness or efficiency (which is more closely related to financial considerations) because it could b. gyenge, et al./oper. res. eng. sci. theor. appl. 5(2) 2022 152-175 158 ruin the flexibility expectation of managers or customers. thus, one of the drawbacks of the above mentioned models is the neglect of harmonizing possibilities of activities. in this chain-like thinking, the outputs from one stage become the inputs to the next stage without a combination of resources (although momeni et al. 2015 use a multi objective additive network approach). most of these models focus only on operational efficiency and most of them are trying to measure efficiency with operational performance indicators i.e. working hours of the drivers, duration of the route, distance travelled, number of employees, number of delivers, utilization of a resource, inversion value transport error, inversion value emission of harmful gases. the most of the existing literature focuses on efficiency as an operational issue and measures it using a bunch of different indicators but sometimes results fluctuate wieldy due to the many stochastic factors, such as the partner does not have time to prepare materials, the hand pallet truck not working in the rain, or the truck drivers do not have enough time for more action etc. these decision units are not homogeneous enough and even the repetitions of individual activities are not homogeneous in order to use dea method. to the best of our knowledge, this paper will try to investigate the problem in a more strategic way and use a holistic approach to highlight the root causes and suggest or develop a modest but relevant number of kpis for the leaders to monitor and improve collaboration with our partners. that is our originality and motives to provide practical value for the logistics managers by supporting decision-making process and it also represents a good basis for further research. 3. research method and model background in a functioning supply chain, efficiency and cost-effectiveness is a key focus, especially nowadays when transportation costs can have a decisive impact on a company’s profitability or provide a competitive advantage through additional services that is embodied in the efficiency and flexibility of the entire supply chain. market competition is extremely fierce, so every opportunity must be seized to help maintaining market position. in our research, the reverse logistics of the supply chain will be analyzed in case of a multinational retail company. according to our research method, the measured data is inserted into a basic framework in which they can be combined by two-dimensional, step-by-step cross-comparison, and the conclusion can be drawn hierarchically at each stage, thus proposing a root cause failure approximation analysis (rcfaa) step-by-step method to support decision. (see the original rca concept by carol, 1989.) the four steps of empirical model are built on each other hierarchically. in our opinion, the presented model is suitable for the application of the method by other company managers with similar problems, as well as for the modification and supplementation of their own industry. we did not aim to create a universal method, but the dilemma that arose during the research made the creation of an assessment method necessary that could answer the following questions. theoretical rcfaa model of the analysis: 1. determine the types of problems that occur. root cause analysis (rca) is a combined approach that represents the methodology and tools for investigating events (carroll, 1998). rca is based on the assumption that causes, causal chains and occurrence can be identified by accurate and analytical processes. although the actual methods (facts vs. belief; 5 why; is/is not) are simple, but it is very difficult to process measurement and analysis in a retail chain to improve reverse logistics efficiency 159 formulate assumptions and apply ideas. to identify and capture the root causes of problems that appear in our research, the first step is to follow the causal chain of the current problem to determine the causes in the background that lead to their development. with the help of the actors actively involved in the process (e.g. driver, administrator; shop employee), recurrent causes were coded that cover deviations from normal operation. according to the classification, the most important thing is that the event receives the same code if the root cause (trigger) was very similar. 2. the second step is to examine occurrence and importance. (which partnerships show more common problems?) in general, most researchers believe that there is a relationship between frequency and importance, especially in the case of failures. although this is not entirely true, we can make a pareto distribution, a percentage distribution, or any other classification technique. in our method, the simple distribution percentage by day will show relevant pattern to analyze. the database was extracted directly by the administrator colleagues from the data entry process according to the query formula defined for this purpose. 3. periodicity analysis. thirdly, to find out what is the periodic characteristic (pattern or cyclicality) of the emergence of problem types in shortand long-term? analysis can be used to characterize the causes of the problem, observations can be made by processing the data and by using different distributional indices. in the paper the daily periodicity was exanimated by distributions and reason analysis. 4. cross-correlations (causal analysis). by projecting the variables (factors) on each other and examining cross-correlations, can key areas be identified (relationships) or ‘hotspots’ that must be taken into account in management decisions and the management of reverse logistics, as well as the need for adequate efficiency? according to the analysis, independent impact factor pairs were used to construct cross-combinations, especially days and partners by failure types. the levels of the model described below are as follows: 1. descriptive statistical analysis of the failure types, e.g.: frequency of occurrence, distribution of error causes, distribution of errors by destinations. 2. search for correlations between failure causes and occurrence times (days) and for correlations between failure causes and destinations using a categorized intensity cross-tabulation method. 3. combined examination of impact factor pairs (aka independent variables) for failure or error rates. to define these particularly critical relationships. 4. time series studies to examine whether there are trend-like correlations in relation to the examined factors and to what extent. model framework. the examined data was measured in the period 20.07.07.27-2021.09.03, under average operating conditions. apart from the pandemic in the industry, under investigation there were no significant environmental distorting effects during the period considered. it is worth knowing that the surveyed company delivers to its nearly 200 stores every day of the week. this extremely large-scale logistics task is based on a fleet of nearly 100 trailers, with an average of 120-140 routes per day. of b. gyenge, et al./oper. res. eng. sci. theor. appl. 5(2) 2022 152-175 160 course, this means that there is a theoretical possibility for the same number of return journeys per day. trucks usually perform back freight transporting (backhauling), which can be: • waste, packaging, return collection. • participation in procurement transport by selling backhaul capacity. of these, procurement service, or in other words ‘delivery’ is primary because it is easier to monetize through close collaboration with other participants of the supply chain. the company has contracted with some other suppliers in the supply chain to take over some freight tasks, generating beneficial effects on both sides. • the supplier does not have to maintain its own fleet. • some of the return trip capacities has been sold. nevertheless, the focus of this study is more on the first return logistics task related to waste, packaging and returns, which, while not generating direct added value and revenue in the supply chain, has a major impact on operations and stores. for example, packaging (empties) / waste / and returns accumulated in stores makes their day-to-day operations more difficult or even disruptive, so proper and regular collection is essential. at this point, however, delivery and collection are also linked, because the more accurate the collection, the more deliveries can be made to the company, and in addition to facilitating the work of the stores, it is also possible to increase the company's revenue. overall, rotation time improves and flexibility increases. hereinafter, thus satisfactory data management is not considered a goal but an indispensable tool and has been developed below. the apparatus for supporting value creation consists of the following: • the staff who handle it. • the technical environment in which the data is stored and processed. • needs, i.e. the partly constant and partly changing needs of the economic and logistical processes served. in general, when we talk about data management, perhaps our first thought is the corporate management information systems itself (like, erps enterprise resource planning systems) or (eis executive information systems) which appears to us as a kind of super integrated entity. it is a well-documented area, and it is also a fact that the examined logistics system that provides the day-to-day supply of goods to more than 200 stores cannot exist without prosperous automation and robust technical orientation for trouble-free operation. however, robustness also means limitations, so it is worth implementing project-based methods that give opportunities for new ideas, which, if necessary, further expand the scope of corporate management information systems by using engineering work. what does this look like in reality and what is the main obstacle of the implementation? experience has shown that in many cases, in addition to corporate management information systems, the semi-operative network of excel spreadsheets, which usually serve tangible business needs and even implement online teamwork, provide information to management and so on. briefly, their value in use far exceeds the process measurement and analysis in a retail chain to improve reverse logistics efficiency 161 requirements imposed on them. the main problem is that over time, this jungle that initially seems customized goes beyond users to such an extent that it becomes almost a corporate standard. but as long as the modules of a corporate management information system meet the required engineering standards, this not to be expected from ad-hoc generated tables, which are often unsuitable for making a validated business decision and it is even more annoying that over time the original idea and ‘domain’ knowledge begins to fade. our experience is that after a short period of usefulness, these tables and functions are lost, the original motivation has been eroded, they reappear later at new users increasing redundancy, the technical concept and the cooperation are often lost with the creator colleague himself. there is always only one thing left, the decision situation and the different concepts associated with it. in our study, we attempt to provide insight into the process of using an easily accessible software tool, data analysis and project management methodologies to develop an analytical environment or model concept that can serve as a specification for further development of a ‘large’ system to develop new plug-in modules. currently, each process necessarily involves several administrative processes, which on one hand ensure the operation and monitoring of legal regulations and on the other hand provide an opportunity to collect measurement data that can be used to increase the efficiency of tasks. as a first step, since measurability can provide an opportunity for improvement, we established a database in which all unrealized return transport tasks have been collected (usually interpreted as “failure” or resource underutilization). in an initial step, the following data have been collected based on excel to distinguish destinations: date; route number; store count; store name; reason for obstruction i.e. p – packaging (empties) / w – waste; driver; company. the recording and processing is illustrated in the following figure (see figure 4): figure 4: data acquisition and processing process used for decision support, practical process survey model, source: own editing b. gyenge, et al./oper. res. eng. sci. theor. appl. 5(2) 2022 152-175 162 phases of the process (practical process survey model): • create: in our case, the information is recorded by the administrator after the completed return trip. in consultation with the delivery team leader the reason of the unladen status will be recorded from predefined categorized codes in an excel spreadsheet. • store (storage, data acquisition): in order for error-free recording and smart data entry, the recorder stores the data in a table with a vba macros assigned to a button and predefined selection lists (i.e. automatic store and subcontractor check, cause selection with poka-yoke tools etc.) • process validation & preparation (data, processing, enrichment, verification): data saved by the vba macro in tabular form are loaded into the excel power query module. using the built-in functions, each record gets new fields e.g. day name, calendar week number, anonymization to avoid recording errors. in this case, it is also possible to receive an additional report on data that may have been incorrectly modified (e.g. subsequent irregular corrections, etc.) raw data is validated, extended and verified. • analyze preprocess & analyze: from the records that have undergone power query processing, pivot tables are created according to the analysis criteria: which can be one-dimensional or two-dimensional matrices and time series. after the update, the new data is loaded and the information from the data becomes available. • share: a visual and textual summary is created from the cross-tables to identify intervention points, track trends, and detect deviations from goals. the summaries or reports prepared this way are sent in separate files to the project stakeholders, thus passing on the representative and pragmatic inputs to the ‘application’ section. • archive: the power query processing interface also provides a data storage function and backs up the processed data. finally, a saved copy of the analysis result is made to ensure traceability or detection of any progress in the application phase. 4. survey model and results in this section, the results of data analysis in parallel with practical and theoretical aspects are presented from the first step to the end. the company under study places great emphasis on warehousing and transportation logistics indicators, but this is not the case for reverse logistics, so we assume that the whole scale operation would be more satisfactory for both owners and customers by developing an analysis and a secondary indicator, that does not override the main logistics indicators but can help the developing of reverse logistics. in the next section, the new analysis (practical process survey model) for reverse transport in practice and how the indicators were formulated in collaboration with management board will be presented as a case study. the data was collected from 27.07.2021 to 03.09.2021, 138, data sets were added to our database. sampling is not very large yet but maybe suitable for monitoring trends. analyzing the data, the following trends can be observed about backhauling: step 1: when trucks are primarily booked to deliver process measurement and analysis in a retail chain to improve reverse logistics efficiency 163 goods and the truck returns to its base with no goods are carried on its back, describes a failure in backhauling and unperformed reverse transport tasks. in the first step, the analysis assesses the failure rate with a standard time-dimensional distribution by every causes. table 1. distribution of unperformed transport tasks by calendar days (as part of the reverse logistics) source: data analysis in 2021 breakdown by calendar day days distribution sunday 22% wednesday 20% thursday 18% friday 15% saturday 14% tuesday 7% monday 4% total 100% table 2 shows the distribution of unperformed transport tasks by calendar days (which means the percentage of the failed return task by day). the average ratio between failed tours and days of the week is 14%. so, sundays, wednesdays, thursdays and fridays are worse than average. at this stage the theoretical reasoning (reason analysis) is much more important than the numbers. so the deviations can be explained by the fact that there is a ‘truck stop’ on sundays in hungary, which means that only fresh goods can be delivered and the adhesive packaging can be returned from the destinations (constrain 1). if there is not enough quantity in the store to load the truck (constrain 2), there is no possibility to redirect it to another store. the other reason that can generate a high rate on sundays is that the waste processing warehouse (constrain 3) is closed on sundays, so trucks can only bring packaging, return goods or take delivery freight, but not waste. table 2. distribution of unperformed reverse transport tasks by causes source: data analysis in 2021 distribution by cause reason distribution quantity 1st shop (store) did not give (not given) 44% 61 2nd there was no p – packaging (empties) / w – waste on the last station and the next shipment followed (no p/w & next shipment followed) 27% 37 3rd there was not a forklift truck (no forklift) 9% 13 4th there was no p / w on the last station and could not be diverted due to expiring working time (no p/w & expiring working time) 8% 11 5th the driver make a call too late / did not make a call, so he did not receive p / w (later or missing call) 7% 9 6th shop did not give because of the rain (weather conditions) 4% 6 7th there was nowhere to redirect (nowhere to redirect) 1% 1 total 100% 138 the higher values on wednesdays, thursdays and fridays are explained by the fact that the volume delivered is also higher on these days, so more routes release to b. gyenge, et al./oper. res. eng. sci. theor. appl. 5(2) 2022 152-175 164 the shops, as a result of which a vehicle has to deliver more freight. in this case, any diversion is also more difficult due to the limited working hours of drivers. to better understand the specifics and constraint background of reverse logistics, the following table can help to analyze the main causes. examining the distribution by causes (see table 3), it can be seen that 80% of all failed tours were caused by three causes, in order: ‘the store did not give’; ‘there was no p / w on the last station and the next shipment followed’; ‘there was not a forklift’ numerically, 111 of the 138 were caused by the above three types. it can be observed that despite the relatively small population, the values converge according to the pareto principle. the case study-like processing also reveals that the most common reasoné for unperformed reverse transport tasks is ‘the store did not give’. this may be due to e.g. a shortage of consignees, congested trucks at the store, or no quantity to be returned. this is followed by ‘there is no p / w at the last station, but there is another shipment’, so there is no time to redirect the truck to another store because it needs to hurry back to the warehouse to deliver the next shipment. the 4th most common reason is also related here, with the difference that the driver’s ‘…working time expires’ and therefore cannot be redirected. as it can be observed in the deeper analysis, the latent correlation may be 1; 4 and 3 because the lack of a tool generates overtime that participants (drivers; employee) cannot always afford. this is a good example of how records and numeric data can conceal the real causes and many aspects that can be improved by cooperation. in our approximation method (rcfaa), it means another repetition of the analysis with different codes. another critical lesson is that unloading takes place on a ramp, but packaging and waste are usually stored in the backyard outside the store, so in the absence of a forklift, only unloading is possible, but loading is not possible. furthermore, it cannot be loaded during raining with an electric forklift or in the case of uncovered storage. at this point, a key question arises as how much the quality of the partners or the suitability of the partners, can affect the efficiency of reverse logistics. the following business-by-business analysis helps to analyze this issue (see table 4). table 3. distribution of unperformed reverse transport tasks by stores source: data analysis in 2021 distribution by stores store code distribution 1st 9 7% 2nd 5 6% 3rd 7 5% 4th 3 4% 5th 19 4% 6th 6 4% 7th 8 4% 8th 35 3% 9th 10 3% … … … examining the distribution by store, it turned out that the value of 1% is very common, from which it was concluded that this was due to fluctuations in the ‘normal’ business, so we did not deal with them. in our study from all business process measurement and analysis in a retail chain to improve reverse logistics efficiency 165 destinations only the 9 highest values highlighted that visibly stands out from random effects (see elimination of random effects). the affected stores, which have been coded for proper data management, are as follows: 9; 5; 7; 3; 19; 6; 8; 35, 10. in the present case, these 9 stores have generated 40% of all failed tours. at this point in our study, it can be said that one of the primary goals has been achieved, which was to narrow the analysis horizon by focusing on ‘hotspots’ of relationships. step 2: two-dimensional relationship studies using categorized intensity coefficients in cross sections and edge frequencies. our goal is to further refine the assumed impact factors. in our study, two factors were examined and intensity categories were defined, which were represented by colors for easier evaluation. table 4. distribution of unperformed reverse transport tasks by days and causes source: data analysis in 2021 the combined effect of days and causes on the distribution of unperformed tasks (%) days sh o p d id n o t g iv e w e a th e r co n d it io n s la te r o r m is si n g c a ll n o w h e re t o re d ir e ct n o f o rk li ft n o p / w & e x p ir in g w o rk in g ti m e n o p / w & n e x t sh ip m e n t fo ll o w e d d is tr ib u ti o n wednesday 9% 1% 3% 0% 1% 4% 9% 26% thursday 12% 1% 1% 0% 2% 0% 9% 24% friday 6% 0% 2% 1% 4% 2% 6% 20% sunday 18% 1% 1% 0% 4% 0% 5% 29% distribution 45% 3% 7% 1% 11% 6% 28% 100% according to the distribution table (see table 5: days & causes), it can be observed that the relationship between sunday and thursday 'shop did not give' has a significant effect, while in the case of wednesdays and thursdays was more typical as the reason was marked ‘there was no p / w on the last station and the next shipment followed’. the code of ‘there was not a forklift truck’ was also more common on fridays and sundays. table 5. distribution of unperformed reverse transport tasks by stores and causes source: data analysis in 2021 effect of shops and causes on the distribution of default (%) days sh o p d id n o t g iv e w e a th e r co n d it io n s la te r o r m is si n g c a ll n o w h e re t o re d ir e ct n o f o rk li ft n o p / w & e x p ir in g w o rk in g t im e n o p / w & n e x t sh ip m e n t fo ll o w e d d is tr ib u ti o n 9 7% 2% 0% 0% 5% 0% 4% 18% 5 7% 0% 2% 0% 0% 2% 4% 15% 7 5% 0% 0% 0% 0% 2% 5% 13% 3 7% 0% 0% 0% 0% 0% 4% 11% 19 5% 2% 0% 0% 0% 0% 4% 11% 6 5% 0% 2% 0% 0% 0% 2% 9% 8 5% 0% 0% 0% 0% 0% 4% 9% 35 5% 0% 0% 0% 0% 0% 2% 7% 10 0% 2% 2% 0% 0% 0% 4% 7% distribution 49% 5% 5% 0% 5% 4% 31% 100% b. gyenge, et al./oper. res. eng. sci. theor. appl. 5(2) 2022 152-175 166 one of the prominent values of the 6th two-dimensional cross table above for store 9 shows ‘there was not a forklift truck’. it can be observed that almost everywhere the highlighted combinations are either ‘store did not give’ or ‘there was no p / w on the last station and the next shipment followed’ and store 7 is an outlier from the others. based on the above, it is worth paying less attention to information gaps, as indicated by the distribution of the code ‘make a call too late / did not make a call’. overall, the first and last codes ‘store did not give’ and ‘there was no p / w on the last station and the next shipment followed’ could be subdivided because half of the cases are related to them in some ways. according to the research, our second result concerns the importance of redesigning the current code system. step 3: the next step is also a two-dimensional relationship study, but between the independent impact factor pairs, which can reveal particularly important critical combinations as ‘hotspots’. examining the co-occurrence of ‘store code’ and ‘days’ in table 7 below, it can be seen that 9 is the most affected. for store 9, three days are the most valid, and for other stores, there are usually only two key days. most problems emerged in case of 9;5;7;3 stores, from which the store 3 is affected by 'truck stop' and 5 and 7 generate the most problems on wednesday (see table 6). table 6. distribution of unperformed reverse transport tasks by stores and days source: data analysis in 2021 the combined effect of shops and days on the distribution of default (%) shop code m o n d a y t u e sd a y w e d n e sd a y t h u rs d a y f ri d a y s a tu rd a y s u n d a y d is tr ib u ti o n 9 0% 2% 2% 5% 4% 5% 0% 18% 5 0% 4% 4% 2% 2% 2% 2% 15% 7 2% 0% 4% 2% 2% 2% 2% 13% 3 0% 0% 0% 4% 2% 0% 5% 11% 19 2% 2% 0% 2% 4% 2% 0% 11% 6 0% 0% 2% 0% 4% 4% 0% 9% 8 0% 0% 0% 4% 0% 2% 4% 9% 35 0% 0% 2% 0% 2% 0% 4% 7% 10 0% 2% 0% 2% 4% 0% 0% 7% distribution 4% 9% 13% 20% 22% 16% 16% 100% based on the above, the potential impact of the days can be examined on a storeby-store basis. no trend-like regularity can be detected yet, which is likely to be better reflected in the larger sample. presumably, after a few months of performing the same analysis, a clearer picture may be obtained (see table 6). step 4: time series studies to examine whether there are trend-like correlations in relation to the factors examined and to what extent. our goal is to reveal trends. we also start with simple time-series statistics in the fourth step and examine the results in several steps (see table 7). process measurement and analysis in a retail chain to improve reverse logistics efficiency 167 table 7. weekly distribution of unperformed reverse transport tasks source: data analysis in 2021 time series number of causes calendar week quantity 30 27 31 25 32 30 33 28 34 23 total 133 examining the selected five weeks, after a significant fluctuation there is a slight downward trend in the number of unperformed reverse transport tasks (see table 7). putting the non-compliance data in context and comparing it with the total number of shipments gives the following result (see figure 5): figure 5. relationship between unperformed reverse transport tasks ratio (%) and total number of routes by week, source: data analysis in 2021 it can be assumed that there is a negative, non-coherent relationship between the total number of tours and the proportion of unperformed reverse transport tasks. it can be seen that we encounter some weeks where the number of unperformed reverse transport tasks are higher than the average, but the total number of tours are also outstanding, so the proportion of unfulfilled transport tasks will remain low. a more thorough examination of the issue has revealed to us that the efficiency and effectiveness of unperformed reverse transport tasks from the perspective of the entire logistics process requires a time-sensitive approach and cannot be marked with static indicators. if we want to measure and know the effectiveness (and later efficiency) it is necessary to develop a dynamic measurement and active fine-tuning 749 795 820 658 757 3.6% 3.1% 3.7% 4.3% 3.0% 0 100 200 300 400 500 600 700 800 900 0.0% 0.5% 1.0% 1.5% 2.0% 2.5% 3.0% 3.5% 4.0% 4.5% 30 31 32 33 34 unperformed reverse transport tasks (%) and total number of routes (pcs) b. gyenge, et al./oper. res. eng. sci. theor. appl. 5(2) 2022 152-175 168 in time with more accurate cooperation and continuous redirection based on current (on-time) data. the method presented above and its resilience allows for any continuous fine-tuning as well as the development of resource and it integration of our partners. certainly, a temporary metric (over a certain time horizon) will help us decide how to evaluate the performance for a given week. however, a well-designed metric or indicator also provides a kind of default target value for continuous monitoring of deviations, which is also advantageous from a control point of view. examining the chosen 5 weeks, it can be seen that the average is around 3.5% in terms of the ratio between the total number of tours and the number of unperformed reverse transport tasks. as we can see 31;34 weeks are better than the average only. comparing the 32nd and 33rd values (see figure 5) by unperformed reverse transport tasks and total number of tours, the week 32(3.7%) which corresponds to 30.3 occasions or urtts (unperformed reverse transport task) and week 33(4.3%) 28.3 urtts. according to the ratio the 32nd is better than the 33rd if we take into account the much smaller number of transports in the 33rd week. based on the average value of 3.54%, the management board (as the stakeholders) temporarily set the target value of urtt as 2% for all tours. for the confirmed target value, a visual management method was used to visualize the monitoring system (see figure 6). in the figure the target value, shown in green, is 2% of the planned number of tours, which is around 15 at week 30, and the current value is 3.6% (urtt ratio), which corresponds to 27 and the deviation of 12 can be seen easily. figure 6. deviation from target values unperformed reverse transport tasks source: data analysis in 2021 process measurement and analysis in a retail chain to improve reverse logistics efficiency 169 in the fourth step of our model study, another result is obtained, which can also be expressed in the form of a management support indicator. as we can see, the resulting indicator is very easy to calculate and use, meaning that at the current level of strategic requirements, 2% of the total number of tours should be targeted. looking back at this calculation, we can also estimate the magnitude of significant deviations from the previous goal. to sum it up, with the present methodology, we have successfully investigated the fulfillment and non-fulfillment of the examined segment of reverse logistics processes, the root causes, and we have been able to formulate new, forward-looking results in each phase of the proposed rcfaa application, in order to make effective progress. the results and conclusions obtained by generalizing the model are summarized below. 5. conclusions and recommendations the importance of return logistics is becoming increasingly important in the competition of our globalized world, where companies must do everything they can to create a competitive advantage. first of all, the topicality of the present study is, to move forward and go beyond the classic concept of the corporate value chain in order to move closer to the concept of the supply chain management and a more sustainable value flow in practice. this study is the real evidence that the examined company has taken a significant step in the direction of that not only economic aspects can control and measure the complex system of value flows, but also the degree of cooperation with partners especially, in the field of reverse logistics. the first steps were taken to map and learn about the reverse logistics of a large international company, while a practical methodology for creating a customized database was developed to examine the effectiveness of reverse logistics processes in the field of freight transport. in the framework of the present study, two practical methodologies have been developed with the aim of standardizing the previously separated measurement processes and the method of analysis itself. it was presented in a case study through a live practical example of how these models were developed and work in practice. theoretical (or logical) model of root cause failure approximation analysis (rcfaa) which is a scalable model framework, is flexible enough for customization to other companies or other economic conditions and to apply different methods. according to our research method, the measured data is inserted into the framework in which they can be examined with cross-comparisons step by step, and the conclusion can be drawn hierarchically at each stage. the process survey model is a practical model for standardizing the data collection and processes used for decision support. this model is a simple guide for colleagues to involve and empower them to conduct the survey. these standards help integrate results into the enterprise knowledge system, and is an ideal way to analyze data and highlight critical ‘hotspots’ (root causes) regardless of the company’s specifics. the method presented above has enough resilience to allow any continuous fine-tuning in time, and the development of resource and it integrations with our partners. b. gyenge, et al./oper. res. eng. sci. theor. appl. 5(2) 2022 152-175 170 we hope that our method presented here for the first time can be applied by others and, after some customization, they will be able to successfully measure their own reverse logistics performance. from the above case study, it can be clearly seen that with conceptual data collection we can create an opportunity to measure processes, resources, efficiency, and even to determine the basis of effective countermeasures. by analyzing the data collected in the database and using the simple methodology presented, i.e. the rcfaa 4-step model and intensity crosstabulations, the main impact factors and hotspots were successfully identified. using the model in the case study, the following observations were made in connection with the reverse logistics transportation tasks as conclusions: when a recorded data tries to support a measured indicator or connected to different causes then lot of mix can be observed between the root cause and the coded cause. especially in the case of reverse logistics, because the factors are connected more complex ways (comparing to the manufacturing processes). it requires constant code updating. a more thorough examination of the data patterns has revealed that the efficiency or effectiveness of unperformed reverse transport tasks (urtt) from the perspective of the entire logistics process requires a time-sensitive approach and cannot be marked with static indicators. if we want to measure and know the efficiency it is necessary to develop a dynamic measurement. in the case of reverse logistics, there are more participants (as stakeholders) in the material flow (e.g. waste processing companies; disposers; state and municipal authorities; institutions; logistics service providers) and in addition, more constraints (e.g. increased weather exposure; ‘truck stop’; partner duty; any restrictions; lack of information; working time constraints etc.) which causes high degree of uncertainty and greater imbalances in time; making the reverse logistics assessment significantly more difficult, and as a result it is not enough to examine or apply direct indicators. with the presented model study methodology a new practical result was obtained, relevant hotspots were identified for the unperformed reverse transport tasks (urtt) and their root causes. we have successfully investigated noncompliance causes, and with the consent of the management board, were able to formulate a general default target value between 2%-3.5% urtt for all tours. a visual management method has been developed to control transport processes with a confirmed target value to easily monitor deviations. at the current level of strategic requirements, it works better than a static kpi. it should also be kept in mind that these indicators are not carved in stone. they need to be constantly monitored in the light of processes and partnerships. the main problem with static indicators or kpis is the ability to reduce the corporate interests behind the processes to the individual effectiveness of peers (individual efficiency of the members), thereby eliminating the entire supply chain concept and perspectives. instead, this study identified a need that is more important than a kpi and the balanced and smooth operation of the stores can increase revenue more than focusing on separate efficiencies. using the methods presented, the following observations were made and the following complex analytical results were obtained in our own example. the process measurement and analysis in a retail chain to improve reverse logistics efficiency 171 distribution by days of the week revealed that on higher-traffic days (wednesday, thursday, and friday), in addition to the sunday (which is classified as a critical day and inferior in efficiency and effectiveness) there are more tours that do not perform their reverse tasks. we found that in many cases the main reasons behind the failed return logistics tasks were. the store does not return packaging / waste on the last station. there is not enough packaging / waste in the last station and the driver cannot switch to another shop due to the next transport task or the end of working hours. in the absence of a forklift truck, there is no one to carry out the loading. in addition, there are outstanding differences among our store partners, which can be traced back to certain typical reasons, such as labor shortages (e.g. lack of forklift driver, receiving clerk). these shortages represent an opportunity for cooperation. after plotting and examining the variables leading to failed tasks, it can be shown that correlations can be observed between the days of the week, the causes, and the stores, e.g.: thursday, sunday – ‘shop did not give’. wednesday, thursday – ‘there was no p / w on the last station and the next shipment followed’. for stores 9 and 5, we have identified the typical disincentives that could serve as a basis for development proposals. from the weekly representation of failed tasks, a higher control resulting from measurability can be observed, as we can see a slightly decreasing trend. (the proverb says we can only improve on what we measure.) finally, in agreement with stakeholders, a metric was determined against which the company’s reverse logistics could be assessed and was proportional to outbound shipments. recommendations: after a systematic and conceptual examination of the processes and the resulting knowledge, a number of focus points came to the fore, on which we formulate development proposals in order to increase efficiency, which are the following: in case of reverse logistics tasks, the first and foremost is the continuous provision of measurability based on the implemented model and the databases already used. with the help of the information obtained, it is necessary to standardize the data processing, which must be evaluated and checked at least weekly. this is also important because our studies show that the performance of reverse logistics is more sensitive and hectic than forward logistics due to the greater uncertainty. according to our studies, the secondary indicators were used to measure and evaluate reverse logistics, which means that the primary efficiency was controlled by transportation tasks of forward logistics and the hierarchically subordinate target values of the reverse tasks can take place if they are not inconsistent with them. the analysis shows that in most cases it is not possible to pick up the packaging / waste at the last shops on the tours for various reasons. our proposal was to further development a system with the help of the partners, which allows for the preliminary measurement and monitoring of exact quantities (e.g. formerly transported, estimated by habits etc.) and the lack of adequate manpower can also be indicated, even due to shifts. this would prevent most of the unperformed transportation tasks. in most cases, in the spirit of the supply chain concept, it means it development and information sharing. b. gyenge, et al./oper. res. eng. sci. theor. appl. 5(2) 2022 152-175 172 certainly, the data presented and collected in its current state reflects only five weeks of data collection. our future goal is to continue the survey toward a broader time horizon, which will certainly lead to the discovery of new correlations, trends and patterns over time. the perspectives and possible future research directions include extending the time horizon, extending the scope of survey to other reverse logistics tasks such as warehousing and different materials, aspects of cooperation with our partners and developing mutual it systems and their information sharing concepts for better redirection (e.g. predicting information). the data will be reviewed regularly in the future. nevertheless, in our present study, we have succeeded in highlighting some important focal points that increase the profitability and efficiency of the company with our proposals and have a positive impact on the operation of our partners in the spirit of supply chain management. by further structuring the research, it seeks to encourage the use of analytical methodologies that analyze performance from root causes through the entire supply chain, highlighting a number of points that would not be possible with other methods. references agárdi i. 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(gajic, 2013). end-user expectations for software services are increasing. it is common knowledge that today's society is developing into an information society. this technology becomes an instrument in the service of information, so information is knowledge, power, and money. application solution to the stage of aggregation method for assessing the quality of service provided 87 the speed and success of the application of information technology will become the basic factor of the strength and usability of today's managers (ilić et al. 2017). managers who decide on a day-to-day basis determine and choose ways to solve the problems they face, which will be in line with the set aims of the organization, but also taking into account the circumstances in which the business takes place. on that case, managers use all available sources of information and quality-processed data on the problem or the conditions in which they need to be addressed, while in the absence of the necessary information they rely on intuition and experience. professor oldcorn in his book states that "managers must make decisions that is their responsibility", according to which the decision-making phases are the following (oldcorn, 1998): 1. identify the problem that needs to be solved 2. discover the facts and find the cause 3. develop some of the possible solutions to the problem 4. narrow the choice of the alternative direction of action 5. make a decision 6. implement the decision made 7. analyze the consequences of this solution. the rapid development of information systems and computer technology, introducing the decision making in the presence of a larger number of the most often conflicting criteria. the specific approach to the application of information systems in decision-making has imposed a decision support system that, together with expert systems, provides support for decision-making. practical managerial problems set different and diverse requirements, often with different relative significance, differently sensitive to changes in input and output sizes. therefore, managerial decision-making requires the application of multicriteria decision-making methods. a number of different and diverse criteria provide a more comprehensive and objective picture in accordance with the requirements that the decision-maker sets. criteria can appear in different units, often with different relative significance and different requirements for maximizing or minimizing. this method makes it possible to better understand the underlying causes of specific service behavior. understanding the behavior of service is a key prerequisite for improving services. the method encapsulates a systematic approach in a comparative analysis of the defined parameters of each service, with the same parameters of other services that belong to the same ranking. in order to remain competitive, it is very important to constantly improve the quality of software services and be able to meet new needs faster (to be more agile) (tomašević, 2017). below is proposed a software solution fam4qs that can be used in continuous improvement of quality. 2. the method formed fam4qs (fuzzy aggregation method for quality service (software), fam4qs), has been created with modification of lsp (logical scoring of preferences) methods (dujmović and dujmović, 2016; dujmović, 2018) and sssi (six-step service improvement method used lsp (logical scoring of preferences) algoritama (marković and maksimović, 2012). this had imposed a need for the support of the appropriate software (tomaseivć et al. 2018). the fam4qs mathematical model for tomašević/oper. res. eng. sci. theor. appl. 2 (2) (2019) 86-100 88 assessing the quality of the service provided is based on operations with fuzzy numbers (tomašević, 2017; tomaseivć et al. 2018). by formulating the fam4qs method, a more accurate assessment of the quality of the service is done, choosing different values for degrees in the aggregation used to estimate the parameters, or groups of system parameters, and the service itself. also contributing to a better assessment, which is conditioned by the different nature of the parameters. that difference implies more or less disjunctively, that is, the conjugacy of the form of the chosen aggregation function (greater r disjunctive form, less r more conjunctive form). instead of standard real numbers, the model looks at fuzzy numbers and corresponding operations defined over them shown in (stević, 2017; puška et al. 2018; stević et al. 2018; stević et al. 2019; chatterjee et al. 2019). justification for the introduction, i.e. replacing crisp numbers with fuzzy numbers consists of the fact that the estimates of the parameters considered in the system are either vague (imprecise) or can range in a range. below is a shown in detail of how to calculate the quality of service using fam4qs. in experimental data processing, the use of the fuzzy method includes the following steps: • • data fuzzification; • • processing the fuzzy data; • • defuzzification the results. the first step shows that data which is vague, for example, about 20% fuzzification, i.e. we present the fuzzy set (fuzzy number) (klement et al. 2000). the second step is to work with these fuzzy objects, for example, the addition of two fuzzy numbers (klir et al. 1995). the result of the second step is the fuzzy number, and it is usually required to answer to the solution of problem be a crisp number, and in the third step, it is performed defuzzification of that number, that is, assigned a crisp value. depending on the nature of the data, i.e. professional assessments (whether precisely determined or not) are applied fuzzy numbers and the fuzzy operations of them, for imprecisely determined or not accurately estimated weights i w on the following way: r r nn r ewewe 1 11 )(...)(       ++=  . (1) the parameter estimation is first calculated mjp j ...1, = using equation (2): j j rrk q jqjqj ewe 1 1               =  =  . (2) application solution to the stage of aggregation method for assessing the quality of service provided 89 by each of the fuzzy numbers ),,( jqjqjq www jq rmlw =  joins its  section according to (tomašević, 2017):  *** , jqjq ww , and each of fuzzy number ),,( jqjqjq eee jq rmle =  joins its section according to (tomašević, 2017):  *** , jqjq ee . now  section of je  can be calculated by the following way:     jj rr jqjq k q jqjqj eewwe 1 *** 1 *** ),,( =  =  , (3) after that we using equation (4):           ==  ==  j j j j r rk q jqjq r rk q jqjqjjj eweweee 1 1 **** 1 1 ***** ))(,,))(,(,  . (4) by applying previous equations formule (1) assessment of service is calculated as fuzzy value, so the final assessment of service in form of section is:     rr jj k j jj eewwe 1 *** 1 *** ),,( =  =  (5) in analogy to the previous use of the rules for working with intervals, we get:   ( ) ( )       ==  ==  r k j r jj r k j r jj eweweee 1 1 **** 1 1 ***** )(,)(,  . (6) especially if j e  is crisp value equal to j e :         ==  ==  r k j r jj r k j r jj eweweee 1 1 ** 1 1 **** )(,)(,  . (7) with the fam4qs method, the ranking of the service from the lowest c, middle b and highest rank a was done according to the following criterion: observing the mean value interval   niee ,...1,, *** = :       =  == n i i n i i e n e n e 1 ** 1 * 1 , 1 , (8) adding for example. %10 or %5 (ucl 1.05, lcl 0.95) on left and right border of interval: tomašević/oper. res. eng. sci. theor. appl. 2 (2) (2019) 86-100 90 , 1 1.1, 1 1.1 1 ** 1 *       =  == n i i n i i e n e n ucl , 1 9.0, 1 9.0 1 ** 1 *       =  == n i i n i i e n e n lcl (9) getting the criterion of choosing whether a service belongs to the highest-ranking (a) or the lowest (c) is obtained. those services that have a core (dots) (ie  section for 1= ) higher than the right border ucl have the highest-ranking (a), and those services that have a core less than the left-hand lcl have the lowest ranking (c). services with a core within the left-hand lcl and right-hand side of ucl are middlelevel services (b). 3. fam4qs implementation fam4qs is written in the programming language c#. defined operators facilitate basic operations with fuzzy numbers and alpha cross-sections (figure 1). figure 1. basic operations with alpha sections and fuzzy numbers basic operations include: addition, subtraction and multiplication. for example, the addition of an alpha cross-section with a fuzzy number is done by converting the application solution to the stage of aggregation method for assessing the quality of service provided 91 first fuzzy number into an alpha cross-section, and then the operation of the addition of two alpha cross-sections is performed, which collects the initial boundaries of the interval with the initial, that is shown in figure 2. figure 2. complex operations with alpha cross-sections and fuzzy numbers figure 3. calculation of fam4qs method tomašević/oper. res. eng. sci. theor. appl. 2 (2) (2019) 86-100 92 method calculate fam4qs () calculating imprecise data in a way that collectscores () collecting the values of the ratings entered by the user in the rating table (figure 3). var subgroups = groups.keys.where(x => !x.equals(const.maingroupname)). tolist(); is a code that filters all the groups and only names the subgroups. with these names, for loops, it goes through all subgroups. first, check whether the user has selected r values for each subgroup. if not, the error message is printed and the code execution is stopping. if the check r value is passed, the code continues by going through all the services, using the other for the loops. first, all previous calculations are canceled. then, the third for loop goes through all the selected r values. depending on the selected weight type (crisp or fuzzy), the estimation of each subgroup is calculated. by calling the cartesianproduct method (), combinations of selected r values are obtained for all groups. figure 4. save and loading data application solution to the stage of aggregation method for assessing the quality of service provided 93 the standard way of storing objects in a file in the c # programming language is specified in the windows forms environment, as well as loading them from files (figure 4). the first step defines the number of services that are evaluated and the percentage accuracy of the results is entered (figure 5). figure 5. entering initial data in the example, it is shown case for three services and a probability of accuracy of 90% (figure 6). figure 6. example of entering data tomašević/oper. res. eng. sci. theor. appl. 2 (2) (2019) 86-100 94 in step 2 (figure 7) we enter the names of the services we want to compare. figure 7. entering the names of the services in step 3 (figure 8), the parameter values for the groups are selected, whether the correct value or the fuzzy number. figure 8. selection of the parameter type in step 4 (figure 9), group parameters are entered. application solution to the stage of aggregation method for assessing the quality of service provided 95 figure 9. entering parameters for groups in step 5 (figure 10), values for the parameters are entered. figure 10. entering values for parameters in step 6 (figure 11), a parameter is selected for entering data into subgroups. figure 11. selection a parameter for entering data into subgroups tomašević/oper. res. eng. sci. theor. appl. 2 (2) (2019) 86-100 96 in the seventh step (figure 12), the selection of the type of parameter in the subgroup is made. figure 12. selection the type of parameters in the subgroup in the eighth step (figure 13) subgroup parameters and assign values are entered (figure 14): • • weight coefficients for parameters, • • each service is evaluated by this parameter and • • values for r are selecting. the values for r are taken from the nature of the data, which is explained in more detail in the previous section. figure 13. entering parameters in a subgroup application solution to the stage of aggregation method for assessing the quality of service provided 97 figure 14. assigning values to parameters from a subgroup this process (step seven and eight) is repeated for other groups of parameters. when finished, click the calculate button. in the ninth step, results are obtained as all combinations of selected values for r. in relation to the data type, results, fuzzy numbers (figure 15) or intervals are obtained (figure 16). the mean value of the fuzzy number is the mean value crisp. figure 15. results – fuzzy number figure 16. results interval tomašević/oper. res. eng. sci. theor. appl. 2 (2) (2019) 86-100 98 in step ten: • • ranking services by quality, showing them graphically, • • services are evaluated and • • analyze the best and the worst. 4. discussion unlike lsp (logical scoring of preferences), in the newly introduced model here, instead of the standard real numbers, the fuzzy numbers and the corresponding operations defined over them are observed. justification for the introduction, i.e. replacing crisp numbers with fuzzy numbers consists of the fact that the estimates of the parameters considered in the system are either vague (imprecise) or can range in a range. similar to the lsp, where individual parameters are evaluated, as well as the entire service, and here it is taken into account that each of the individual parameters does not participate equally in the overall assessment, and therefore assign different weights which are in this model triangular fuzzy numbers. and for the estimates for individual parameters, the triangular fuzzy numbers are taken, which finally gives the assessment of the service that is the fuzzy number (it does not have to be necessarily triangular). for the purpose of this calculation, the apparatus fuzzy arithmetic was used, ie the display of the results as an alpha cross-section (closed interval), rather than a crisp number. by selecting an alpha the degree of confidence in the assessment of the experts for a particular parameter is chosen, and depending on this, the result obtained is vague. the final result is mainly corrected by 5% (or 10% depends on the nature of the parameters themselves) and the obtained interval values (ucl and lcl) that determine the rank (quality) of the service. the nature of the results determines the choice of the rank of the service, that is, if the core is the fuzzy number corresponding to the estimated service, less than the left limit ucl is assigned the worst rank, and if it is higher than the right limit, the lcl is the highest ranking. all observed values of service ranges that are between these borders are of the middle rank. number r which occurs in the formula for estimating parameters as well as the entire service and determines whether the given rating is more or less pessimistic or optimistic, which is determined by the nature of the parameters. in a model developed for parameter estimation, a fuzzy-aggregation function is actually used, which in its nature works with imprecise data and generates a new average value from more than one value. therefore, this apparatus can be used to model a decision that represents some sort of averaged value from several individual imprecision decisions made, in any similar decision making where imprecise data enters. the disadvantage of this model is that the result is not precise, but it is also a result of the imprecision of the experts judgment. 5. conclusions forming fam4qs, imposed a need for the implementation of the appropriate software for its support, which was the goal of the software application of this work as well as the improvement of the support system for multi-criteria decision-making. application solution to the stage of aggregation method for assessing the quality of service provided 99 the software developed in this paper had the basic goal of automating the fam4qsbased calculation based on aggregation functions. in this way, a qualitatively new approach to the fam4qs budget is provided, and at the same time an analysis of the solutions obtained by this software solution. in addition to the calculation, the software provides a display of comparative results obtained by changing the parameters r over certain groups and subgroups of the given service. this enables the analysis obtained based on different parameter values r (whether the given rating of a particular service is more or less pessimistic or optimistic, which is also determined by the nature of the parameters). the contribution of this application solution is reflected in a more faithful reflection of reality and increasing the quality of decisions made, making this process faster and more efficient. also, the software solution is reflected in the possibility of direct application of the developed software and providing new information for the scientific and professional public, which can represent a quality basis for further development of the model for decision making. the presented solution is general and with certain settings and a higher level of integration can be applied in different decision areas. research has shown that there are certain constraints that require attention and should be the subject of further research in the future: 1) extension and testing of methods with a larger number of parameters 2) application of neural networks 3) developing a web system that would make it easier to make a decision, or whose result would not be a number, but a clear report based on a large projection of parameters and knowledge base (the current state the standard). in a mathematical view, the given model can be changed in several directions: • by changing the aggregation function one can observe a function that depends not only on one parameter r , but more than that of which we can adjust the criteria for evaluating the service. • presenting values not as triangular but as trapezoidal fuzzy numbers. acknowledgement: the investment co-financed by the republic of slovenia and the european union, european regional development fund, implemented under the operational programme for the implementation of the eu cohesion policy in the period 2014 – 2020. references chatterjee, p., & stević, ž. 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(2018). assessment of conditions for implementing information technology in a warehouse system: a novel fuzzy piprecia method. symmetry, 10(11), 586. tehnike donošenja odluka, https://www.link-elearning.com (accessed 10 april 2019). tomašević m., (2017). adaptivni model za upravljanje lancima snabdevanja u malim i srednjim preduzećima, doktorska disertacija, univerzitet u novom sadu fakultet tehnickih nauka tomašević, m., ralević, n., stević, ž., marković, v., & tešić, z. (2018). adaptive fuzzy model for determining quality assessment services in the supply chain. tehnički vjesnik, 25(6), 1690-1698. https://www.link-elearning.com/ plane thermoelastic waves in infinite half-space caused operational research in engineering sciences: theory and applications vol. 2, issue 2, 2019, pp. 72-85 issn: 2620-1607 eissn: 2620-1747 doi:_ https://doi.org/10.31181/oresta190247m * corresponding author. jelena.mihajlovic@masfak.ni.ac.rs (j. mihajlović), pedja.rajk@gmail.com (p. rajković), pgoran1102@gmail.com (g. petrović), dusan.ciric@hotmail.com (d. ćirić) the selection of the logistics distribution fruit center location based on mcdm methodology in southern and eastern region in serbia jelena mihajlović*, predrag rajković, goran petrović, dušan ćirić faculty of mechanical engineering, university of niš, serbia received: 15 june 2019 accepted: 09 august 2019 first online: 18 august 2019 original scientific paper abstract. location selection for the logistics distribution center is often one of the most critical elements in a supply chain’s management success. decision making in location selection domain is a complex process due to the fact that a wide range of diverse criteria, stakeholders and possible solutions are embedded into this process. this paper focuses on the application of some multi-criteria decision-making (mcdm) approaches for the logistics distribution fruit center location selection in the southern and eastern serbia region. an analytic hierarchy process (ahp) and a weighted aggregated sumproduct assessment (waspas) have been implemented in this process for evaluation and location selection. key words: location selection problem, logistics distribution center, mcdm, ahp, waspas. 1. introduction the location selection problem (owen & daskin, 1998; farahani & hekmatfar, 2009; zak & weglinski, 2014) consists in determining proper placement of an infrastructural component (ground, site, facility, etc.) in a considered area, taking into account the decision maker’s preferences and existing constraints. it has a universal character and may refer to different categories of sites (farahani & hekmatfar, 2009; farahani, et al, 2010; zak & weglinski, 2014). the location selection problem plays a crucial role in logistics, where it refers to find the most desirable location for logistics facilities. the main goal of this paper is to show the usage of multi-criteria decision-making (mcdm) methodology on the location selection problem which refers to an installment of the logistics center for storing and distribution of fruits on the territory of southern and eastern region in serbia. mailto:jelena.mihajlovic@masfak.ni.ac.rs the selection of the logistics distribution fruit center location based on mcdm methodology in southern and eastern region in serbia 73 as a key component in a supply chain, the distribution center, plays the vital role of obtaining materials from different suppliers, performing value-added activities, and assembling (or sorting) products to fulfil customer orders and offer a high level of service (baker, 2007, 2008; parkih & meller, 2008; vieira et al., 2017). to improve every aspect of the supply chain and satisfy all relevant involved factors for the most suitable logistics center location, a multi-criteria decisionmaking problem (mcdm) methodology has been used. to solve problems related to decision-making, ćojbašić et al. (2018) say that several optimization methods are used in practice. but, in the case where decision activities are based on similar options, it becomes critical to analyze various factors, alternatives with similar category, involving a set of different and opposite criteria. when mcdm methods are applied for solving the location selection problem, they can help decision-maker with objective and systematic evaluation of alternatives on multiple criteria. two mcdm methods, which are applied on the practical example (the location selection of the logistics distribution center), are classical mcdm method analytic hierarchy process (ahp) method and hybrid mcdm method weighted aggregated sum product assessment (waspas) method. the first method, the ahp method, was used for the determination of the criteria weights, and, furthermore, for the evaluation of the alternatives. the second method, the waspas method, was only used for the evaluation of the alternatives while using the criteria weights determined by the ahp method. the location selection of the logistics distribution fruit center is being determined inside the southern and eastern serbia region (alternative solutions are region’s districts with their govern cities). by the defined criteria set, alternatives are evaluated with the help of the mentioned mcdm methods (section 4). the final result of this paper should be, respectively to the previously emphasized distribution center importance, the best possible location for its installment. this location will be proposed to the responsible authorities of the southern and eastern region, as well as the ministry of agriculture, forestry and water management. 2. the location selection problem – literature preview the location selection problem is a worldwide “phenomenon”, which is widely discussed in transportation and logistics circles. this problem (owen & daskin, 1998; chen, et al., 2007; daganzo, 1996; ozcan, et al., 2011) refers to the selection of specific locations of such facilities as: warehouses, distribution centers, transportation hubs, passenger and cargo terminals, material inventory, parking lots and many others (van thai & grewal, 2005; drezner & hamacher, 2002; fierek, et al, 2007; zak & weglinski, 2014). the focus of this paper is location selection for the logistics distribution center and gutjahr & dzubur (2015) said that in the literature on facility location, much attention has been devoted to the optimal choice of facilities or distribution centers where customers are supplied with products, commodities or services of a different kind. logistics distribution centers have evolved from traditional warehouses. the main difference between distribution centers and warehouses is in the fact that a warehouse is designed to store goods for longer periods. distribution centers are mihajlović et al./oper. res. eng. sci. theor. appl. 2 (2) (2019) 72-85 74 facilities with the primary purpose of logistic coordination. beside manipulative activities (loading, unloading, load transfer), constantly adapting to new market demands, continuous automation and computerization, there is a development in trade, delivery and transport functions in logistics systems on all levels (pupavac et al., 2014). choosing the most suitable location for the logistics distribution center is a complex decision which involves the consideration of multiple factors including: politics, economics, infrastructure, environment, competition, development strategy, product features, logistic costs, and customers service levels (rao et al., 2015). the complexity of the problem increases with the increase of the possible solutions and number of the criterion which affects them. choosing the most suitable location for the logistics distribution center becomes the mcdm problem. mcdm methods can help decision-maker with objective and systematic evaluation of possible solutions-locations, on multiple criteria involved. to find the best alternative the location selection models have been designed. over the past decades, those models have increased significantly (kazemi & amiri, 2017). these models are principally mathematical models that can be categorized into two groups: static and deterministic and dynamic and stochastic (cheng at al., 2005). but, the most recent models contain both quantitative and qualitative values with the concentration on decision-makers’ behavior (hashemkhani et al., 2013). some classical and hybrid models are included in mcdm methodology, as presented in this research. multiple criteria facility location problems were presented by farahani et al. (2010), while the study on location selection started more than a century ago when researchers were trying to find the most suitable location of the warehouse in order to have minimum distance with the customer (cheng et al., 2005). chou et al. (2008) utilized mathematical programming in order to process the facility model for a distribution center. stevic et al. (2015) and bagum & rashed (2014) used classical ahp method on the selection of the logistics distribution center location. the same method was used by tomić et al. (2014) in order to find the best locations for the distributive center on the balkan peninsula. burnaz et al., (2006) applied the mcdm approach for the evaluation of retail locations. ozcan et al. (2011) proposed a comparative analysis of mcdm methods (topsis, electre and grey theory) on a warehouse location selection problem. selection of a similar problem was done combining ahp and dea methodology (korpela et al., 2007). the selection of the logistics center location based on the electre iii/iv method was carried away in poland (zak & weglinski, 2014). electre methods were also used by wang & triantaphyllou (2008) for ranking irregularities while evaluating alternatives. nowadays, more and more popular are fuzzy variants of mcdm methods and he et al., (2017) used fuzzy topsis and fuzzy ew+ahp for sustainable decision making for joint distribution center location selection. fuzzy optimization has been applied for locating and distributing centers in a supply chain network (chen et al., 2007). sanayei et al. (2010) proposed vikor mcdm method under the fuzzy environment in the selection process. steep-fuzzy ahp+topsis method has been developed for evaluation and selection of thermal power plant location (choudhary et al., 2012). the selection of the logistics distribution fruit center location based on mcdm methodology in southern and eastern region in serbia 75 3. multi-criteria decision-making (mcdm) methods multi-criteria analysis methods have been developed as mathematical tools to support decision-makers involved in the decision-making process (madić et al., 2015). those methods are gaining importance as potential tools for analyzing and solving complex real-time problems due to their inherent ability to evaluate different alternatives concerning various criteria for possible selection of the best alternative (chakraborty et al., 2015). they are based on scientific principles that enable an effective and efficient way of determining the “optimal” solution. some methods have many common features or a similar application procedure, while others are different, but most of them, are based on quantitative calculations. each method has some of its unique characteristics, logic, advantages, and disadvantages, depending on a decisionmaking problem (madić et al., 2015; petrović et al., 2018). the choice of the method which will be in use for solving the specific multicriteria analysis problem depends on: the nature of the problem, the availability of information concerning a problem, the number of alternatives, as well as the knowledge, previous experience and preferences of the decision-maker. when a particular mcdm method is finally chosen for a specific application, it is observed that its solution accuracy and ranking performance are seriously influenced by the value of its control parameter (chakraborty et al., 2015). proposed mcdm methods for solving this paper’s decision-making problem, the location selection problem, are: analytic hierarchy process (ahp) and weighted aggregated sum-product assessment (waspas). in order to evaluate the overall effectiveness of the candidate alternatives (locations), rank and select the most suitable location, the primary objective of an mcdm methodology is to identify the relevant location selection criteria, assess the alternatives information relating to those criteria and develop methodologies for evaluating the significance of criteria (ćojbašić et al., 2018). the weights of relevant location selection criteria are calculated by the ahp method, while, the same method and waspas method are furthermore used for evaluation of alternatives (locations). 3.1. analytic hierarchy process (ahp) method the analytic hierarchy process (ahp) method was originally proposed by thomas saaty (1977, 1980). it represents one of the best known and the most commonly used mcdm method. the ahp can be implemented in a few simple consecutive steps: step 1: computing the vector of criteria weights. the vector of criteria weights can be computed by creating a pairwise comparison matrix a where each element aij of the matrix a represents the importance of the ith criterion relative to the jth criterion. the comparisons between two elements are assembled, using the values from 1 to 9 from fundamental saaty scale. final determination of criteria weights wj is based on the geometric mean method as shown by the following equation: , /1 1 n n i iji agm       = = , 1 = = n i i i i gm gm w (1) mihajlović et al./oper. res. eng. sci. theor. appl. 2 (2) (2019) 72-85 76 where gmi is geometric means of each row and n is the number of considered criteria. step 2: testing the consistency of results. the pairwise comparisons made by ahp method are subjective and this method tolerates inconsistency through the amount of redundancy in the approach. the value that measures the consistency of the subjective comparisons is consistency index ci: 1 max − − = n n ci  (2) where 𝜆max is the maximum eigenvalue of the pairwise comparison matrix a. finally, the ratio ci/ri, that is termed the consistency ratio cr, should be less than 0.1. in eq. 3 ri is the random index (table 1), i.e. the consistency index when the entries of matrix a are completely random. ri ci cr = (3) table 1. values of a random index (ri) depending on the number of criteria number of criteria 3 4 5 6 7 8 9 10 ri 0.52 0.89 1.11 1.25 1.35 1.4 1.45 1.49 step 3: comparison of alternatives concerning each criterion. this step implies the determination of pairwise alternative comparison matrix bj, where elements of this matrix bkl represent the preference of the kth alternative relative to the lth alternative according to criterion j. the comparisons have to be done using the values from 1 to 9 from saaty scale in the same way as described in step 1. step 4: synthesize global ratings. the final step is the multiplication of local priorities by the weight of the respective criterion and the results are summed up to produce the overall priority of each alternative (global ratings). 3.2. weighted aggregated sum product assessment (waspas) method weighted aggregated sum product assessment (waspas) method was proposed by zavadskas et al. (2012). the waspas method is a unique combination of two well-known mcdm approaches, i.e. weighted sum model (wsm) and weighted product model (wpm) (chakraborty et al., 2015). the waspas can be implemented in a few simple consecutive steps: step 1: determine the decision matrix:               == m nmm n n ij xxx xxx xxx xx     21 22221 11211 (4) where xij represents the performance of i-th alternative with respect to j-th criteria; m is the number of alternatives and n is the number of the criteria. step 2: determine the normalized decision matrix computing its elements by one of the formulas: the selection of the logistics distribution fruit center location based on mcdm methodology in southern and eastern region in serbia 77 iji ij ij x x x max = , for maximal criterion, (5) ij iji ij x x x min = , for minimal criterion, (6) where ijx is the normalized value of ijx . step 3: the first criterion of optimality is similar to wsm method. the total relative importance of the i-th alternatives is determined by the formula:  = = n j jiji wxq 1 )1( , (7) where wj is the weighted coefficient of the j-th criteria. step 4: the second criterion of optimality is similar to wpm method. the total relative importance of the i-th alternatives is determined by the formula:  = = n j iji jw xq 1 )2( . (8) step 5: a joint importance is based on the contribution of wsm and wpm: 2 )2()1( ii i qq q + = . (9) to increase ranking accuracy and effectiveness of the decision-making process, in waspas method, a more generalized equation for determining the total relative importance of i-th alternative is developed as below (saparauskas et al., 2011; zavadskas et al., 2012):  == −+=−+= n j w ijj n j ijiii j xwxqqq 11 )2()1( )1()1(  , 1,...,1.0,0= . (10) now, the candidate alternatives are ranked based on the q values, i.e. the best alternative would be that one having the highest q value. 4. case study – the selection of the logistics distribution fruit center location the southern and eastern serbia is one of five statistical regions of the republic of serbia. this region covers the area of 26 255 km2, which makes 29.71% out of the whole country’s area. in this region live 1 559 281 citizens, this makes 21.5% out of the entire population (by the 2011 census, statistical office of the republic of serbia). mihajlović et al./oper. res. eng. sci. theor. appl. 2 (2) (2019) 72-85 78 southern and eastern serbia consists of 9 districts (every district has administrative center): bor district (bor), braničevo district (požarevac), jablanica district (leskovac), nišava district (niš), pčinja district (vranje), pirot district (pirot), podunavlje district (smederevo), toplica district (prokuplje), zaječar district (zaječar) (figure 1). alternatives (locations) are administrative centers form a1 to a9 respectively ordered by districts, as in the previous passage, and shown in figure 1 and 2, and in decision matrix in table 2. figure 1. southern and eastern serbia region’s districts. by the agricultural census from 2012 (statistical office of the republic of serbia), there are 187 744 registered agricultural holdings in the southern and eastern region, this makes 29.75% out of all registered agricultural holdings. 97 401 registered agricultural holdings are registered as the fruit growing holdings, on the total area of 43 372 ha. mentioned number of agricultural holdings grow a wide selection of fruits, such as apples, pears, peaches, apricots, plums, quinces, different sorts of nuts (walnuts, the selection of the logistics distribution fruit center location based on mcdm methodology in southern and eastern region in serbia 79 hazelnuts, almonds, etc.), as well as the berry fruits (raspberry, strawberry, blackberry, blueberry, etc.). this paper shows the usage of mcdm methodology as a reliable tool in the decision-making process, and that the result of this process should be a proposal for construction of logistics distribution fruit center in one of the 9 districts inside the southern and eastern serbia region. designed logistic distribution center should be used to store fruit products, as well as their further distribution inside the region, inside the country and abroad. the selection of the location for the logistics distribution center has become a key concern in logistics and supply chain management practice and design. the proposed mcdm methods from section 3 have been used for logistics distribution fruit center location evaluation and selection. the working model for location selection of the logistics distribution fruit center in southern and eastern serbia region is presented in the figure 2. figure 2. a model for the location selection problem. a well-considered logistic distribution center will reduce the logistics cost, improve the efficiency of transport flows, improve a citizen’s living condition, sustain the city’s economic vitality and can contribute to the harmonious development of the economy, environment, and society. however, a poorly designed logistic distribution center can cause a series of negative externalities and external costs, such as greater traffic congestion, increased emission, road safety, and damaged urban image (rao et al., 2015). this paper’s criteria set consist of 7 criterions. those criteria have been based on the factors that affect the problem, of the location selection, the most. the criteria set have been chosen on the previous authors’ experience – literature preview, type of the problem (location selection problem), as well as the current fruit growing situation in the region. c1 – land price is the minimization criterion defined on the basis of grades. land price is a very important factor for logistics distribution center construction because mihajlović et al./oper. res. eng. sci. theor. appl. 2 (2) (2019) 72-85 80 it directly affects the increase of the investment costs. besides the required amount of land which is necessary for the logistics distribution center, there must be enough additional surrounding space available for future development. c2 – infrastructure access is the maximization criterion defined on the basis of grades. transportation is the essence of logistics distribution, and logistics distribution center must have a variety of possible means of transport (highways, railroads, river ports, airports) in order to facilitate transit. c3 – a number of the registered agricultural holdings is also the maximization criterion which represents the total number of the agricultural holdings which are oriented in growing fruits by the district (agricultural census 2012, statistical office of the republic of serbia). c4 – a number of the citizens is the maximization criterion which represents the total number of the citizens by the district (by the 2011 census, statistical office of the republic of serbia). the number of citizens dictates the number of customers and available label workers. c5 – delivery time is the minimization criterion, and it is very important that delivery must be on time, especially, because of the product’s type. this criterion is in relation to criterion c2 – infrastructure access, and it also depends on the delivery destination. c6 – presence of competitors is the minimization criterion defined on the basis of grades. this criterion refers to the level of competitors’ presence in the districts. the less competitive environment, the better the result is. c7 – orchards and soil under the berry fruits is maximization criterion which represents the total amount of soil under fruits by the district (agricultural census 2012, statistical office of the republic of serbia). criteria c1, c2, c5, and c6 are evaluated by the group of experts on the basis of the saaty’s scale for pair-wise comparison of 9 numerical values. after the evaluation of the criteria, mean values were taken into account. on the other hand, for the criteria c3, c4 and c7, real values were taken. decision matrix has been formed and presented in table 2 and based on the described alternatives (locations) and defined criteria. table 2. location’s performance ratings – decision matrix criteria c1 c2 c3 c4 c5 c6 c7 alternative min max max max min min max a1 4.8 5.0 12609 158717 5.6 7.4 3874.6 a2 7.4 7.2 16669 216304 2.4 7.0 6819.08 a3 4.0 4.6 12625 90600 2.4 3.6 9828.69 a4 8.2 8.8 15400 373404 1.4 6.8 5527.7 a5 3.0 4.4 7519 92277 2.8 6.4 1874.85 a6 4.0 3.6 8501 119967 4.0 4.4 3603.94 a7 2.6 4.0 4804 124992 5.8 2.6 1529.34 a8 4.2 5.0 12461 183625 3.4 5.0 4019.88 a9 8.4 7.4 6813 199395 2.2 7.8 6294.35 the team of experts has also evaluated the significance of the defined criteria by creating a pairwise comparison matrix (table 3). the selection of the logistics distribution fruit center location based on mcdm methodology in southern and eastern region in serbia 81 table 3. evaluation of criteria – pairwise comparison matrix criteria c1 c2 c3 c4 c5 c6 c7 c1 1.000 0.294 0.263 5.200 0.278 7.200 2.200 c2 3.400 1.000 2.200 7.400 0.417 8.600 3.400 c3 3.800 0.455 1.000 5.200 0.313 7.600 2.600 c4 0.192 0.135 0.192 1.000 0.122 3.600 0.455 c5 3.600 2.400 3.200 8.200 1.000 8.800 5.200 c6 0.139 0.116 0.132 0.278 0.114 1.000 0.238 c7 0.455 0.294 0.385 2.200 0.192 4.200 1.000 table 4. criteria weights obtained using ahp mcdm method criteria weights c1 c2 c3 c4 c5 c6 c7 ahp 0.113 0.234 0.171 0.039 0.354 0.021 0.068 to ensure the objectivity of the calculated criteria weights the consistency index (cr) has been calculated and its value is 0.087, while the maximal allowed value of this index is 0.1. ahp method and hybrid combination of the mcdm method (ahp+waspas) were used for the complete assessment for the logistics distribution fruit center location in southern and eastern serbia region. the application of the proposed methods gives a complete range of location selection, as shown in table 5 and figure 3. table 5. complete rankings of the locations according to different mcmd approaches log. distr. center location a1 a2 a3 a4 a5 a6 a7 a8 a9 ahp 0.082 (7) 0.123 (2) 0.108 (4) 0.164 (1) 0.095 (6) 0.079 (8) 0.075 (9) 0.097 (5) 0.109 (3) ahp+waspas 0.443 (7) 0.671 (2) 0.615 (3) 0.842 (1) 0.487 (6) 0.425 (8) 0.371 (9) 0.528 (5) 0.584 (4) 0 0.2 0.4 0.6 0.8 1 a1 a2 a3 a4 a5 a6 a7 a8 a9 r a n k o f a lt e r n a ti v e s alternatives (locations) ahp ahp+waspas figure 3. complete rankings of the locations according to different mcdm approaches. mihajlović et al./oper. res. eng. sci. theor. appl. 2 (2) (2019) 72-85 82 in accordance with those table and figure, it can be seen that ranks are of the same importance in both methods. in both cases (ahp and ahp+waspas) the best alternative solution is the alternative a4, i.e. the best location for the logistics distribution fruit center is the administrative center, the city of niš (nišava district). on the other hand, in both cases too, the worst alternative solution is the alternative a7, i.e. the worst location for the logistics distribution center is the administrative center, the city of bor (borski district). the only difference in the results of those two mcdm approaches is for the alternative a3 (administrative center of prokuplje – toplica district) and a9 (administrative center of smederevo – podunavlje district). in the case of classic mcdm approach (ahp method), alternative a3 has a rank 4, while alternative a9 has a rank 3. in the case of hybrid mcdm approach (ahp+waspas), alternative a3 has a rank 3, while alternative a9 has a rank 4. 5. conclusion this research has demonstrated the applicability of classic mcdm approach (ahp method) and a hybrid mcdm approach (ahp+waspas) in the location selection for logistics distribution fruit center in southern and eastern serbia region. in the case of logistics center location both considered approaches give insignificant variation in the final ranking scores. both approaches selected alternative a3 (administrative center, the city of niš (nišava district)) as the best choice. the authors of this paper belong to a narrow group of researches (e.g. daganzo, 1996; zak & weglinski, 2014) who have realized that the logistics distribution center must be considered as a hierarchical problem, a two-level problem. the first level represents a macro analysis of the one wider area, which has been described in this paper. the selection of the best location for the logistic distribution fruit center was done by observing the whole southern and eastern serbia region. in the macro-region analysis potentials and advantages of the districts was observed to construct a logistics center of this type. the second level represents a microanalysis for described logistics center inside the previously chosen location in the first level of study. 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mcdm/a methodology, transportation research procedia, 3, 555–564. zavadskas e.k., turskis z., antucheviciene j., zakarevicius a., (2012), optimization of weighted aggregated sum product assessment, electronics and electrical engineering, 122(6), 3–6. http://www.lokalnirazvoj.org/sr/books/details/23, figure 1. southern and eastern serbia region’s districts, accessed on 12.06.2019. http://www.lokalnirazvoj.org/sr/books/details/23 operational research in engineering sciences: theory and applications vol. 4, issue 2, 2021, pp. 102-123 issn: 2620-1607 eissn: 2620-1747 doi: https://doi.org/10.31181/oresta20402102y * corresponding author. yorulmaz@istanbul.edu.tr (ö. yorulmaz), sultan.kuzu@istanbul.edu.tr (s. kuzu yıldırım), bahadirf.yildirim@istanbul.edu.tr (b. f. yıldırım) robust mahalanobis distance based topsis to evaluate the economic development of provinces özlem yorulmaz 1, sultan kuzu yıldırım 2, bahadır fatih yıldırım 3* 1 department of econometrics, faculty of economics, istanbul university, turkey 2 department of quantitative methods, school of business, istanbul university, turkey 3 department of logistics, faculty of transportation and logistics, istanbul university, turkey received: 07 april 2021 accepted: 07 june 2021 first online: 01 july 2021 research paper abstract: in this paper, 81 turkish provinces with different development levels were ranked using the topsis method. to evaluate the ranking with topsis, we presented an improvement to mahalanobis distances, by considering a robust mm estimator of the covariance matrix to deal with the presence of outliers in the dataset. additionally, the homogenous subsets, which were obtained from the robust mahalanobis distancebased topsis were compared with robust cluster analysis. according to our findings, robust topsis-m scores reflect the inter-class differences in economic developments of provinces spanning from the extremely low to the extremely high level of economic developments. considering indicators of economic development, which are often used in the literature, i̇stanbul ranked first, ankara second, and i̇zmir third according to the robust topsis-m method. moreover, with the robust cluster analysis, these provinces were diagnosed as outliers and it was seen that obtained clusters were compatible with the ranking of robust topsis-m. keywords: economic development, mahalanobis distance, robust clustering, robust topsis-m, outliers. 1. introduction in today's world where globalization and competition are rapidly increasing, countries are trying to gain an advantage with both their economic activities and social policies. to increase the international competitiveness of the countries, it is aimed to keep the economic indicators in the national context. because it has been observed that regional and local economies also affect the global economy and increase competition (kılıç et al., 2011). economic development has generally been robust mahalanobis distance based topsis to evaluate the economic development of provinces 103 conceptualized as a balance increase in per capita income (ascani et al., 2012). however, studies draw attention to the importance of determining the factors affecting per capita income. for regional development, the necessity of both increasing exports and following import substitution strategies have been put forward (shaffer, 1989; blair and carroll, 2008; cooke and watson, 2011). exports are generally considered in two dimensions as the export of goods and services. advanced technology and advanced industrial facilities used in developed countries increase the sales potential for the foreign market by enabling these countries to produce fast and high quality (contractor and mudambi, 2008). on the other hand, developing countries, follow a policy that will increase exports by utilizing their raw materials and underground resources. the service sector has been identified as a new growth engine for both developed and developing countries (noland et al., 2012, akın and özsağır, 2012). regions and provinces in the country carry out export activities according to the characteristics of their geographical location, production, and service types. according to these characteristics, there are important differences between the export capacities of the provinces and the development levels accordingly. economic development, in another definition, focuses on increasing wealth (mathur, 1999). according to this view, domestic savings are one of the most important sources of development. the positive relationship between saving and growth has been noted in studies of many countries (room, 2002; carroll and weil, 1994). in recent years a decline was observed in domestic savings in turkey. this decline causes a negative impact on the economy through a deficit and it has led to the emergence of domestic savings again. (peace and space, 2015). another factor that is thought to have an impact on economic development is population. however, the direction and strength of the relationship between economic development and population are still under debate. while some argue that rapid population growth has a negative effect on economic development (srinivasan, 1988; kentor, 2001), there are also studies showing that the relationship between them is not significant (easterlin, 1967). the population-oriented economic growth hypothesis, which states that population growth supports economic development, also maintains its validity. it is seen that population growth has positive effects on economic development, especially in developing countries (furuoka, 2009). increasing population brings some needs with it. the most important of these is the need for housing. with the sale of housing, not only the construction sector but also many sub-sectors such as cement, ready-mixed concrete, iron, and steel are affected. specifically, when the economic contraction begins in developing countries, a way out of this bottleneck is sought by increasing investment expenditures in the construction sector. thus, economic recovery is provided. topsis (technique for order preference by similarity to solution) method makes it possible to assess the objects concerning multidimensional economic phenomena based on the group of economic variables (yoon and hwang, 1995; balcerzak and pietrzak, 2016). most economists think that international comparisons of the level of sustainable development must be done with an application of quantitative methods (balcerzak and pietrzak, 2016). topsis is referred to be a very useful and informative technique for ranking and selecting variables (shih et al., 2007; bhutia and phipon, 2012, kizielewicz et al. 2021). for this reason, topsis is widely used in studies that yorulmaz et al./oper. res. eng. sci. theor. appl. 4 (2) (2021) 102-123 104 are based on the comparisons of economic and financial performances and realworld problems. eyüboğlu (2016) compared the developing countries considering macro performances as economic growth, inflation rate, unemployment rate, and the current account balance/gdp using analytic hierarchy process (ahp) and topsis methods. using similar variables, dinçer (2011) ranked both european union members and candidate countries using topsis and similarly, kuncova (2012) made the comparisons of european countries in terms of e-commerce. topsis method was also preferred to evaluate economic performances of countries during the financial crisis period (mangır and erdoğan, 2011) and used to examine the development achievement by european countries in the field of implementing the concept of sustainable development (balcerzak and pietrzak, 2016). topsis method was employed to evaluate the good governance development in the european union countries for the years of 2007-2017 (ardielli, 2019). to assess the e-government in the countries topsis was used (ardielli and halaskova, 2015). besides the comparisons of countries, municipalities were evaluated considering environmental sustainability using dematel based topsis (kiliç and yalçın, 2020). slovak municipalities were assessed according to management criteria using topsis (vavrek, et al, 2015). different from the listed studies here, topsis was also used to identify suitable health indicators to evaluate the efficiency of slovak municipalities (vavrek et al., 2021). in this study, it was aimed to evaluate the level of economic competition of 81 turkish provinces considering the economic indicators using topsis-m (mahalanobis distance-based topsis) which is based on the robust covariance matrix. the topsis method is used to construct the ranking of items considering many variables and it is based on euclidean distance that assumes the criteria of monotonically increasing or decreasing and this approach disregards the dependence among variables. conversely, topsis-m uses dependencies between variables considering the correlation matrix. however, in the presence of outliers, the use of methods based on covariance matrix should be approached with attention. because the covariance matrix can be manipulated by outliers and give misleading results. topsis method is based on the distances from the model values (“positive ideal solution” and “negative ideal solution”) and in case of the existence of outliers in a dataset, the maximum and minimum values of the variables affect the model values inevitably and this leads to excessive remoteness from typical values of the considered variables that narrow the range of variability of the constructed synthetic measure (luczak and just, 2020). several studies in the literature suggested limiting the effect of outliers on the topsis method. khalif, et al. (2017) proposed the spearman correlation matrix to handle outlier effects in the topsis method. luczak and just (2020) used robust standardization and spatial median to make the topsis method resistant against outliers. de andrede, et al. (2020) used singular value decomposition (svd) topsis approach to decrease the impacts of outliers while evaluating the performance of tv programs. in this study, different from the previous approaches we presented an improvement to topsis-m by using robust mahalanobis distances which are resistant to outliers. to make mahalanobis distances resistant to outliers, a robust covariance matrix was used. the covariance matrix employed in this study is based on the mm estimator. however, mcd, ogk, and s estimators were also evaluated, but robust mahalanobis distance based topsis to evaluate the economic development of provinces 105 since the results were very similar, only the results based on the mm estimator are included here. to evaluate the level of economic competition of provinces in this study, per capita gdp, the trade deficit (import-export), the population, the total housing sales numbers, and the total bank deposit accounts were determined as variables. since this dataset includes socioeconomic variables belonging to the provinces, due to the provinces with different development levels, the existence of outliers and dependency between variables are expected. therefore, in the first stage of the application, descriptive statistics and correlation matrices were used to evaluate the dataset and outliers were diagnosed. in the next stage, the findings obtained from topsis, topsis-m, and robust mm covariance matrix based topsis-m were evaluated. in addition to rank the provinces by taking into account the economic indicators, it was also included to classify provinces with robust cluster analysis. at the final stage, findings of robust cluster analysis were compared homogenous subsets obtained from robust mahalanobis distance-based topsis. 2. methodology topsis method, originally developed by hwang and yoon (1981), is a simple and efficient multi-criteria decision-making (mcdm) method to identify solutions from a finite set of alternatives. the main idea is based on determining the best alternative which should have the closest geometric distance from the ideal solution. however, there are some main disadvantages in the traditional topsis model: (i) correlations between criteria, (ii) uncertainty in obtaining the weights only by objective and subjective methods, finally, (iii) possibility of alternative closed to positive and negative ideal points concurrently (li et al., 2011). additionally, when the data set does not only include regular observations, outliers may have effects on the definition of ideal solutions and the calculation of distances it is important to consider robust estimators to deal with outliers. because of the listed disadvantages, traditional topsis can lead to biased estimation of relative significances of alternatives and can cause inaccurate ranking results. to overcome the deficiency of correlation between criteria in the topsis model, mahalanobis distance-based topsis was preferred. mahalanobis distance is a measure that takes into consideration the correlation in the data by using the covariance matrix. however, outliers have a major influence on the covariance matrix. because covariance matrix is known as a low breakdown estimator. outliers attract mean and inflate variance towards its direction (becker and gather, 1999). to make mahalanobis distances resistant against outliers, robust estimates of the covariance matrix are preferred to use (rocke and woodruff, 1996). robust estimators are used to reducing and limiting the effect of outliers and strong asymmetry when calculating mahalanobis distance. the robustness of an estimator can be evaluated by considering breakdown points and influence function properties (huber, 1981; maronna et. al., 2006). minimum covariance determinant (mcd) estimator, s-estimators, orthogonalized gnanadesikan-kettenring (ogk) estimator, and mm-estimators are well-known high-breakdown robust estimator of mean and covariance matrix. the covariance matrix employed in this study is based on the mm estimator. yorulmaz et al./oper. res. eng. sci. theor. appl. 4 (2) (2021) 102-123 106 2.1. mahalanobis distance-based topsis (topsis-m) the euclidean distance approach used by the topsis method is insufficient in terms of investigating the relationship between the criteria in the mcdm problem and including it in the decision process. therefore, it is more appropriate to use mahalanobis distance in calculating the deviations from the ideal solutions. topsis-m method is a type of analysis in which deviations are computed using mahalanobis distance in traditional topsis algorithm. mahalanobis distance measurement also takes into account the correlation between variables in measuring the distance between two points. this measurement was proposed by mahalanobis in 1936 and is used under his name. mahalanobis distance between 1 x and 2 x points is calculated with the help of the following equation:      11 2 1 2 1 2, t d x x x x c x x     (1) c in eq. (1) shows the variance-covariance matrix of the x set consisting of x values. (xiang et al., 2008). analysis of the decision problem with the topsis-m method consists of the following steps. step 1. as in all mcdm problems, the analysis process in the topsis method starts with generating a decision matrix in which is the performance score of the alternative according to the criterion is expressed together. the a matrix created by the decision-maker is shown as below: 11 12 1 21 22 2 1 ij n n m mn a a a a a a a a a              (2) step 2. since the performance values created in the decision matrix represent different units or sizes according to different criteria, the evaluation process is continued by standardizing the decision matrix. standardized performance scores to standardize the decision matrix, represented by ij r , are obtained as follows: 2 1 1, 2, , 1, 2, , ij ij m kj k a r i m j n a      (3) r standardized decision matrix is obtained by making use of eq. (3). step 3. as mentioned in the definition of the topsis-m method, it is based on the principle of proximity calculation to ideal solutions. in this step of the topsis-m method, in which the ideal solution is handled in two directions, the ideal positive solution and the ideal negative solution sets are created, and the process continues. while creating the ideal solution clusters, the attributes of the criteria included in the decision problem are taken into account, considering the benefits and cost conditions. robust mahalanobis distance based topsis to evaluate the economic development of provinces 107 in the topsis-m method, the positive ideal solution set is calculated with eq. (4), and the negative ideal solution set is calculated with the help of eq. (5).  * '(max ), (minij ijiia v j j v j j   (4)  '(min ), (maxij ij ii a v j j v j j     (5) in the equations, j refers to benefit index and j’ refers to cost index. step 4. in the topsis-m method, the mahalanobis distance approach is used to calculate deviations from ideal solution sets. as a result of the process, ideal separation values are calculated for each solution set. the positive ideal discrimination measure * i s is calculated using eq. (6) and the negative ideal discrimination measure i s  is calculated using eq. (7).      * * * 1 *, t t i i i i s d x a a x c a x        (6)      1, t t i i i i s d x a x a c x a            (7) the c value in the equations represents the variance-covariance matrix of the x decision matrix of mxn, and  represents the square root of the elements of the weight vector on the diagonal matrix. the diagonal matrix  is obtained using eq. (8).  1 2, , , ndiag w w w  (8) step 5. in the calculation of the * i c value, which expresses the relative proximity of each alternative to the ideal solution, the ideal separation measures obtained in step 5 are used. * * * , 0 1i i i i i s c c s s       (9) as the * i c values that take values between 0 and 1 grow, it expresses the absolute proximity to the positive ideal solution. the * i c value obtained as a result of the analysis steps is ranked in descending order and a ranking based on the closeness of the alternatives to the ideal is obtained (wang and elhag, 2006). 2.2. robust mm estimator the mm-estimator is a high breakdown value estimator, and it is an extension of the s-estimator (maronna et. al., 2006). s-estimator was proposed by rousseeuw and leroy (1987). s-estimators of location μ and covariance s are defined such that the yorulmaz et al./oper. res. eng. sci. theor. appl. 4 (2) (2021) 102-123 108 determinant of the matrix s is minimized under the constraint (maronna et. al., 2016):     ' 1 1 1 n i i i x s x b n         (10) where b is a constant and ( )x is the loss function. a popular choice loss is tukey’s bi-weight function (hubert and rousseuw, 2013): 3 22 2 1 1 , 6 ( ) , 6 k x x k k x k x k                   (11) for the estimation of the mm estimator the following steps should be considered (maronna et. al., 2006.): a) define a loss function ρ to compute the s-estimators of location and covariance, (  and  ). b) calculate 1/ 2 ˆ p    c) find the mm-estimator of the location and the shape parameter, ˆˆ( , )  , that minimize: ' 1 1/ 2 1 1 1 ˆ(( ) ( )) / ) n i i i x x n          (12) d) compute the mm-estimator of the covariance matrix ˆ ˆ̂   2.3. robust cluster cluster analysis is based on identifying homogeneous clusters with large heterogeneity among them. many studies emphasize outliers may impair clustering ability and clustering methods need to be robust if they are to be useful in applications (garcía-escudero et al. 2010, ruwet et al. 2012). for handling outliers, robustness in cluster analysis is needed because outliers appear many times joined together (garcia-escudero et.al. 2011). to refrain from the outlier effects garcíaescudero et al. (2008) introduced the tclust approach. the tclust approach performs robust clustering to find clusters with different distribution structures and weights (ruwet et al. 2012). the tclust algorithm allows for eigenvalue rate restriction and trimming of a specific observation rate determined by the researchers to eliminate the effect of outliers. the t-clust method is known as the trimmed kmeans technique. in this study, tclust was used to identify clusters with trimming a rate of 5%. the flowchart in figure 1 summarizes the steps followed throughout the methodology. as can be seen from the flow chart in the first stage, mahalanobis distances based on the solid mm covariance matrix were calculated using the first robust mahalanobis distance based topsis to evaluate the economic development of provinces 109 decision matrix and these distances were used for ranking in the topsis process. similarly, based on this decision matrix, topsis scores, and topsis-m scores based on the classical covariance matrix were obtained. in the last step, provinces were classified using robust cluster analysis and the findings were evaluated considering the mm covariance-based topsis-m, topsis-m, and topsis rankings. normalized decision matrix robust mahalanobis distances initial decision matrix robust clustering determine the positive and negative ideal solutions sets calculation of the similarity distances obtain c* values rank provinces calculation of the similarity distances obtain c* values rank provinces calculation of the similarity distances obtain c* values rank provinces topsis robust top sis-m topsis-m c o m p a re r e su lt s robust mm covariance matrix figure 1. flowchart of the evaluation methodology used. 3. dataset and results in this study, the variables of gdp per capita, the trade deficit of the provinces (import-export), the population of the provinces, the total housing sales figures in the provinces, and the total bank deposit accounts of the provinces are used for the years 2019 and 2020. datasets have been created through the official web page of the turkish statistical institute and the banking supervision and regulatory agencies. the reason why the topsis method based on mahalanobis distance was preferred in this study is the strong correlation coefficients between the variables. when the correlation values in table 1 are examined, it is seen that there is a strong relationship. however, it was observed that the relationships were slightly weaker in the mm correlation matrix. table 1. pearson correlation matrix population gdp per capita housing sales trade deficit bank deposit population 1.00 gdp per capita 0.52 1.00 housing sales 0.97 0.61 1.00 trade deficit 0.85 0.39 0.77 1.00 bank deposit 0.96 0.52 0.93 0.94 1.00 yorulmaz et al./oper. res. eng. sci. theor. appl. 4 (2) (2021) 102-123 110 descriptive statistics were presented in table 2. as can be seen from table 2, the difference between mean and median values of variables (except gdp per capita) seem significantly different. this raises the suspicion of the existence of outliers. as a matter of fact, in a way to confirm this situation, outlying observations can be seen in figure 2. figure 2 corresponds to the distance-distance plot defined by rousseeuw and van zomeren (1991). this plot is based on classical mahalanobis distances versus robust mahalanobis distances (based on mm covariance estimator), it enables the classification of regular observations and outliers. the dashed line depicts the points where both distances are equal. the vertical and horizontal lines were drawn at the points ( 2  df=5, 0.975). observations beyond these lines (istanbul, ankara, and izmir) are defined as outliers. table 2. descriptive statistics of development indicators variables mean std. dev. median mad bank deposit 45353637,4 171658598 9715929 8497261 housing sales 18510,07 35694,54 7625 7168,37 population 1032276,07 1872575,82 537762 419343 trade deficit -402315,83 4976466,74 35118 142794 gdp per capita 39506,76 13648,03 36820,7 10774,7 figure 2. distance-distance plot (detection of outlying provinces). robust topsis-m analysis steps and final scores of 81 provinces which obtained based on robust mm covariance matrix, are included in the appendix. however, in figure 3, provinces are divided into homogeneous groups based on these robust topsis-m scores. as can be seen from this map, the provinces with the highest scores are respectively istanbul, ankara, izmir, and antalya. the scores with the lowest provinces are ardahan, bayburt, and tunceli. these rankings are consistent with the robust mahalanobis distance based topsis to evaluate the economic development of provinces 111 actual values, considering the development levels of the provinces. robust topsis-m scores reflect the inter-class differences in the economic developments of provinces. figure 3 presents ten classes of provinces, spanning from the extremely low to the extremely high levels of economic development. figure 3. classification of provinces according to robust topsis-m scores. figure 4. classification of provinces according to robust clustering. in figure 4, robust clustering results were given. according to the tclust algorithm, four clusters and an outlier group were obtained. cluster 0 consists of the outlying provinces. the map in figure 4 also includes rank values of provinces according to robust topsis-m scores. as can be seen, provinces were divided into four groups according to the robust clustering. following the "distance-distance plot" in figure1, istanbul, ankara, and izmir have been determined as outliers here as well, and these provinces are in the top three with the robust topsis-m ranking. it is seen that the homogeneous groups defined based on robust topsis-m scores in figure 3 are compatible with the clusters in figure 4. although there are fewer clusters in figure 4, only four clusters, these clusters can show the inter-class differences in terms of development indicators. yorulmaz et al./oper. res. eng. sci. theor. appl. 4 (2) (2021) 102-123 112 table 3 presents the ranking of provinces according to topsis, topsis_m, and topsis-mm approaches. this table also contains information about the cluster to which each province belongs. rankings of provinces in the same cluster in table 3 are expected to be close to each other. although the order of provinces falling into clusters with 0 and 4 codes is close to each other in all three approaches, the order of provinces in clusters with codes 1-2 and 3 seems compatible only in topsis-mm. denizli, kocaeli, şırnak, hatay, and çorum are not compatible in the clusters in which they are ranked according to topsis and topsis-m approaches. table 3. ranking of provinces based on topsis, topsis-m, and topsis-mm approaches province t o p s is t o p s is -m r o b u st t o p s is -m r o b u st c lu st e r province t o p s is t o p s is -m r o b u st t o p s is -m r o b u st c lu st e r i̇stanbul 1 1 1 0 adıyaman 47 50 42 1 ankara 2 2 2 0 kırklareli 35 39 43 1 i̇zmir 3 3 3 0 kastamonu 42 38 44 1 antalya 5 5 4 4 giresun 40 42 45 1 bursa 4 4 5 4 uşak 45 36 46 1 gaziantep 6 9 6 3 isparta 37 35 47 1 kocaeli 12 6 7 3 düzce 41 52 48 1 konya 7 8 8 3 aksaray 44 37 49 1 adana 10 7 9 3 yalova 38 40 50 1 denizli 14 15 10 3 yozgat 57 46 51 1 mersin 8 10 11 2 siirt 64 75 52 1 hatay 24 13 12 2 batman 54 54 53 1 muğla 17 11 13 2 bolu 46 51 54 1 kayseri 9 12 14 2 amasya 55 60 55 1 manisa 19 16 15 2 niğde 53 59 56 1 balıkesir 16 14 16 2 bilecik 49 65 57 1 tekirdağ 13 19 17 2 karabük 68 49 58 1 aydın 15 17 18 2 nevşehir 59 44 59 1 samsun 21 20 19 2 kırşehir 63 57 60 1 kahramanmaraş 25 25 20 2 karaman 52 55 61 1 diyarbakır 20 23 21 2 burdur 51 56 62 1 sakarya 11 22 22 2 şırnak 39 73 63 1 eskişehir 22 18 23 2 ağrı 67 70 64 1 şanlıurfa 18 27 24 2 kırıkkale 56 64 65 1 trabzon 23 21 25 2 çankırı 62 67 66 1 erzurum 36 43 26 1 bitlis 74 76 67 1 elazığ 32 34 27 1 kars 72 69 68 1 ordu 30 30 28 1 muş 65 72 69 1 afyonkarahisar 27 28 29 1 erzincan 58 61 70 1 malatya 28 29 30 1 sinop 66 63 71 1 van 31 45 31 1 bartın 70 62 72 1 mardin 26 58 32 1 artvin 60 66 73 1 çanakkale 29 26 33 1 hakkari 77 78 74 1 sivas 33 31 34 1 bingöl 73 68 75 1 çorum 81 32 35 1 iğdır 71 74 76 1 kütahya 34 41 36 1 gümüşhane 78 77 77 1 zonguldak 75 24 37 1 kilis 76 79 78 1 rize 50 47 38 1 ardahan 79 80 79 1 edirne 43 33 39 1 tunceli 69 71 80 1 osmaniye 61 53 40 1 bayburt 80 81 81 1 robust mahalanobis distance based topsis to evaluate the economic development of provinces 113 figure 5. comparision of topsis, topsis-m, and robust topsis-m results the provinces that exists in cluster 0 and cluster 4 are also consistent in terms of rankings. while denizli and kocaeli should be in the third cluster, they are in the second cluster according to topsis and topsis-m rankings. the province of zonguldak, which should be in the first cluster, falls in the second cluster according to the topsis and topsis-m rankings, and şanlıurfa, which should be in the second yorulmaz et al./oper. res. eng. sci. theor. appl. 4 (2) (2021) 102-123 114 cluster, falls into the first cluster. however, as can be seen in figure 5, there is no inconsistency between robust topsis-m and clusters. 4. conclusion the topsis method is an mcdm method that is frequently used to sort the observations and divide them into homogeneous groups, considering various variables. however, the topsis method is calculated based on the euclidean distance and ignores the relationship between variables. the topsis-m method calculated based on the mahalanobis distance takes into account the dependency structure between variables. however, since mahalanobis distances are calculated based on the covariance matrix, these distances calculated when there are outliers in the data set give misleading results. in this study, it was proposed to make the topsis-m method resistant with the use of the mm covariance matrix, which is resistant to outliers. robust mahalanobis distances are used frequently in the literature by using robust covariance matrix. however, to the best of our knowledge, this approach has not been applied to the topsis-m method in studies conducted so far. in this study, it was aimed to rank 81 turkish provinces by taking into account the variables of per capita gdp, foreign trade deficit (import-export), population, total housing sales, and total bank deposit accounts. the limitation of this study is that the most up-to-date values of statistics collected by provinces are 2019. the fact that the provinces have quite different levels of economic development inevitably made it necessary to consider the effect of outlying observations in the data. for this reason, since the topsis-m method is based on the classical covariance estimator and this estimator is a low breakdown estimator, the covariance matrix was made resistant to outliers using the robust mm estimator. in addition, provinces were classified using the robust clustering method. according to the robust cluster analysis, istanbul, ankara, and izmir, which are obtained as outliers were found to be the top 3 provinces with the robust topsis-m method. antalya and bursa, which are in the first cluster, are ranked as the fourth and fifth provinces in the ranking. gaziantep, kocaeli, konya, adana, and denizli, which are in the second cluster, were ranked from 6 to 10 in the robust topsis-m ranking, again producing consistent results. the last 3 provinces in the ranking for economic development are ardahan, tunceli, and bayburt. the top provinces in the robust topsis-m ranking and observations in clusters number three and four (including outliers) correspond to important industrial and trade centers. likewise, it is seen that the population density is concentrated in these provinces. for this reason, housing sales are also high in these provinces. when the provinces that are the last in the ranking are examined, it is known that these provinces have some disadvantages such as natural disasters and terrorism due to their geographical location, and therefore economic development is lower. this situation both accelerates migration and prevents investment in these regions. according to our findings, obtained robust clusters and homogenous groups that are based on mm estimator based topsis-m and the actual situation seem compatible. this research presents that robust mm estimator based topsis-m performs correct rankings and partitions homogeneous groups in case of variables with outliers. the ranking of the provinces taking into account the socio-economic robust mahalanobis distance based topsis to evaluate the economic development of provinces 115 indicators are included in various studies. however, while ranking in these studies, the dependency between indicators and the potential effects of outliers were not taken into account. the topsis approach based on robust mahalanobis distance, which is resistant to outliers, was used because the data used in this study consisted of provinces with different development levels and correlated variables. to make mahalanobis distances resistant to outliers, a robust covariance matrix was used. the covariance matrix employed in this study is based on the mm estimator. the findings obtained in this study are consistent with the real situation. for this reason, we recommend using robust mm estimator based topsis-m for the evaluation of the economic development of provinces described by variables with outliers. in this study, the importance of the criteria was accepted as equal and the ranking was made accordingly. the importance of criteria can also be determined by subjective methods such as ahp, anp, dematel or objective weighting methods such as critic and entropy-based on expert opinion. in addition, the results can be compared by considering the vikor, aras, copras methods. another suggestion is that robust estimators can be used when analyzing data sets containing outliers. acknowledgement: the authors would like to thank the editor and two anonymous referees who kindly reviewed the earlier version of this manuscript and provided valuable suggestions and comments. appendix appendix 1. initial decision matrix opt. direction max max max min max provinces c1 c2 c3 c4 c5 adana 55967796.32 28014.82016 1877332.698 -311514.1 2250.26969 adıyaman 1863197.32 2070.82016 251073.698 -31357.12 -12116.15031 afyonkarahisar 6888921.32 4691.82016 355526.698 234945.9 1539.61969 ağrı -2645137.68 -2840.17984 154049.698 -87890.12 -17843.02031 aksaray 713663.32 1693.82016 41625.698 19646.88 2482.87969 amasya -295349.68 150.82016 -45891.302 427.8769 1172.38969 ankara 492294499.3 151783.8202 5281936.698 -3483295 36456.87969 antalya 132877245.3 58586.82016 2166922.698 780921.9 26061.19969 ardahan -5284044.68 -5119.17984 -285224.302 -49309.12 74.52969 artvin -3411236.68 -3236.17984 -211884.302 -15058.12 16262.21969 aydın 23029583.32 28466.82016 737698.698 511716.9 3318.19969 balıkesir 25442739.32 26952.82016 858899.698 149926.9 9731.58969 bartın -3302268.68 -2577.17984 -182406.302 -31205.12 -2380.33031 batman -675291.68 -32.17984 238892.698 -58419.12 -11171.71031 bayburt -5952091.68 -4568.17984 -299475.302 -52799.12 -588.14031 bilecik 24778.32 -1558.17984 -162668.302 2948.877 22498.06969 bingöl -4503701.68 -2761.17984 -99617.302 -50850.12 -7248.06031 bitlis -3181196.68 -3062.17984 -30391.302 -49285.12 -12390.60031 bolu 203256.32 1250.82016 -66583.302 -106321.1 19585.19969 burdur -950198.68 -1557.17984 -114293.302 144657.9 7718.20969 bursa 103889557.3 49910.82016 2720447.698 1892625 24386.28969 çanakkale 5925653.32 7541.82016 160162.698 7834.877 19109.07969 çankırı -2747841.68 -2633.17984 -188957.302 46700.88 3018.99969 çorum 6674460.32 3493.82016 148740.698 -1790497 -2984.09031 yorulmaz et al./oper. res. eng. sci. theor. appl. 4 (2) (2021) 102-123 116 opt. direction max max max min max provinces c1 c2 c3 c4 c5 denizli 53935630.32 12770.82016 659529.698 1355305 11958.85969 diyarbakır 15438764.32 14021.82016 1402045.698 97005.88 -10925.07031 düzce 1390404.32 2540.82016 14293.698 37837.88 9178.98969 edirne 3728462.32 2354.82016 26377.698 -93268.12 9517.71969 elazığ 7909597.32 5613.82016 206574.698 69351.88 -2341.99031 erzincan -3181739.68 -2104.17984 -146954.302 -33907.12 12717.06969 erzurum 8618759.32 4625.82016 376893.698 -73632.12 -4335.33031 eskişehir 18079022.32 16869.82016 507442.698 96372.88 21037.71969 gaziantep 85062990.32 30046.82016 1719771.698 2837014 3062.58969 giresun 1361999.32 2313.82016 67335.698 183646.9 -3347.60031 gümüşhane -4913512.68 -3789.17984 -239683.302 -17616.12 -5486.51031 hakkari -4193366.68 -5115.17984 -100871.302 -51723.12 -4378.33031 hatay 35258735.32 19863.82016 1277934.698 -1128064 -3548.01031 iğdır -4458034.68 -3356.17984 -180071.302 20415.88 -3832.76031 isparta 1270343.32 1548.82016 58918.698 115079.9 6658.64969 i̇stanbul 1461674123 259786.8202 15081066.7 -44100660 52227.99969 i̇zmir 184423821.3 88145.82016 4013308.698 3085818 25983.10969 kahramanmaraş 22580684.32 10205.82016 786777.698 -173798.1 -464.72031 karabük 206223.32 -727.17984 -137771.302 -253143.1 4144.99969 karaman -772106.68 -2061.17984 -126466.302 102636.9 12431.04969 kars -3063130.68 -2282.17984 -96462.302 -52533.12 -8298.62031 kastamonu 1818376.32 1564.82016 -5008.302 98800.88 4187.53969 kayseri 30238897.32 24721.82016 1040069.698 1343356 9640.35969 kırıkkale -1904612.68 1071.82016 -102682.302 -52676.12 4675.43969 kırklareli 2668193.32 3197.82016 -19648.302 -25132.12 22464.03969 kırşehir -311130.68 -763.17984 -138343.302 -100793.1 -798.78031 kilis -5406827.68 -2276.17984 -238593.302 -35270.12 -5464.94031 kocaeli 86408382.32 31458.82016 1615872.698 -1863656 46657.65969 konya 60562975.32 31884.82016 1868634.698 1237525 6322.18969 kütahya 3786265.32 2929.82016 195302.698 50603.88 7249.71969 malatya 6182146.32 7375.82016 424770.698 120705.9 -4147.51031 manisa 31011819.32 20323.82016 1069230.698 -208845.1 14896.21969 mardin 4259936.32 3300.82016 473330.698 582686.9 -5707.20031 mersin 37674319.32 38184.82016 1487371.698 317713.9 2502.11969 muğla 33571393.32 16931.82016 619387.698 276033.9 21892.43969 muş -3682386.68 -2947.17984 29731.698 -29532.12 -11243.22031 nevşehir -435112.68 -1773.17984 -76423.302 -24949.12 2160.34969 niğde -370740.68 1959.82016 -19314.302 -50039.12 1344.10969 ordu 6967854.32 6100.82016 380014.698 159544.9 -4303.13031 osmaniye 3450177.32 1594.82016 167170.698 -342117.1 -4603.69031 rize 4066309.32 -1308.17984 -37026.302 78696.88 6147.14969 sakarya 16619602.32 17106.82016 661263.698 1655493 15186.54969 samsun 22123112.32 20644.82016 974693.698 -115775.1 229.80969 siirt 531142.32 -2521.17984 -50315.302 8529.877 -7978.65031 sinop -3238326.68 -1697.17984 -164925.302 -30873.12 -3016.23031 sivas 4712271.32 4699.82016 254503.698 2109.877 418.87969 şanlıurfa 13184870.32 20959.82016 1733870.698 -130692.1 -17105.90031 şırnak -2774068.68 -4059.17984 156376.698 528624.9 -7290.49031 tekirdağ 23358321.32 29306.82016 699679.698 256729.9 36217.16969 tokat 2076276.32 1249.82016 216475.698 -31300.12 -7668.86031 trabzon 15582031.32 6753.82016 430515.698 909257.9 2743.69969 tunceli -5448571.68 -4318.17984 -297942.302 -52940.12 13259.17969 uşak 1847229.32 680.82016 -11952.302 8509.877 9212.63969 robust mahalanobis distance based topsis to evaluate the economic development of provinces 117 opt. direction max max max min max provinces c1 c2 c3 c4 c5 van 4106565.32 2366.82016 767956.698 -45450.12 -15861.99031 yalova 1351893.32 6788.82016 -105335.302 -173924.1 20458.87969 yozgat 409397.32 136.82016 37709.698 -58432.12 -5858.70031 zonguldak 4575397.32 1537.82016 209818.698 -818261.1 2122.10969 appendix 2. normalize decision matrix provinces c1 c2 c3 c4 c5 adana 0.036 0.082 0.106 -0.007 0.017 adıyaman 0.001 0.006 0.014 -0.001 -0.093 afyonkarahisar 0.004 0.014 0.020 0.005 0.012 ağrı -0.002 -0.008 0.009 -0.002 -0.137 aksaray 0.000 0.005 0.002 0.000 0.019 amasya 0.000 0.000 -0.003 0.000 0.009 ankara 0.313 0.446 0.298 -0.078 0.281 antalya 0.084 0.172 0.122 0.017 0.201 ardahan -0.003 -0.015 -0.016 -0.001 0.001 artvin -0.002 -0.010 -0.012 0.000 0.125 aydın 0.015 0.084 0.042 0.011 0.026 balıkesir 0.016 0.079 0.048 0.003 0.075 bartın -0.002 -0.008 -0.010 -0.001 -0.018 batman 0.000 0.000 0.013 -0.001 -0.086 bayburt -0.004 -0.013 -0.017 -0.001 -0.005 bilecik 0.000 -0.005 -0.009 0.000 0.173 bingöl -0.003 -0.008 -0.006 -0.001 -0.056 bitlis -0.002 -0.009 -0.002 -0.001 -0.095 bolu 0.000 0.004 -0.004 -0.002 0.151 burdur -0.001 -0.005 -0.006 0.003 0.059 bursa 0.066 0.147 0.153 0.042 0.188 çanakkale 0.004 0.022 0.009 0.000 0.147 çankırı -0.002 -0.008 -0.011 0.001 0.023 çorum 0.004 0.010 0.008 -0.040 -0.023 denizli 0.034 0.037 0.037 0.030 0.092 diyarbakır 0.010 0.041 0.079 0.002 -0.084 düzce 0.001 0.007 0.001 0.001 0.071 edirne 0.002 0.007 0.001 -0.002 0.073 elazığ 0.005 0.016 0.012 0.002 -0.018 erzincan -0.002 -0.006 -0.008 -0.001 0.098 erzurum 0.005 0.014 0.021 -0.002 -0.033 eskişehir 0.011 0.050 0.029 0.002 0.162 gaziantep 0.054 0.088 0.097 0.063 0.024 giresun 0.001 0.007 0.004 0.004 -0.026 gümüşhane -0.003 -0.011 -0.014 0.000 -0.042 hakkari -0.003 -0.015 -0.006 -0.001 -0.034 hatay 0.022 0.058 0.072 -0.025 -0.027 iğdır -0.003 -0.010 -0.010 0.000 -0.030 isparta 0.001 0.005 0.003 0.003 0.051 i̇stanbul 0.929 0.763 0.850 -0.987 0.402 i̇zmir 0.117 0.259 0.226 0.069 0.200 kahramanmaraş 0.014 0.030 0.044 -0.004 -0.004 karabük 0.000 -0.002 -0.008 -0.006 0.032 karaman 0.000 -0.006 -0.007 0.002 0.096 yorulmaz et al./oper. res. eng. sci. theor. appl. 4 (2) (2021) 102-123 118 provinces c1 c2 c3 c4 c5 kars -0.002 -0.007 -0.005 -0.001 -0.064 kastamonu 0.001 0.005 0.000 0.002 0.032 kayseri 0.019 0.073 0.059 0.030 0.074 kırıkkale -0.001 0.003 -0.006 -0.001 0.036 kırklareli 0.002 0.009 -0.001 -0.001 0.173 kırşehir 0.000 -0.002 -0.008 -0.002 -0.006 kilis -0.003 -0.007 -0.013 -0.001 -0.042 kocaeli 0.055 0.092 0.091 -0.042 0.359 konya 0.038 0.094 0.105 0.028 0.049 kütahya 0.002 0.009 0.011 0.001 0.056 malatya 0.004 0.022 0.024 0.003 -0.032 manisa 0.020 0.060 0.060 -0.005 0.115 mardin 0.003 0.010 0.027 0.013 -0.044 mersin 0.024 0.112 0.084 0.007 0.019 muğla 0.021 0.050 0.035 0.006 0.169 muş -0.002 -0.009 0.002 -0.001 -0.087 nevşehir 0.000 -0.005 -0.004 -0.001 0.017 niğde 0.000 0.006 -0.001 -0.001 0.010 ordu 0.004 0.018 0.021 0.004 -0.033 osmaniye 0.002 0.005 0.009 -0.008 -0.035 rize 0.003 -0.004 -0.002 0.002 0.047 sakarya 0.011 0.050 0.037 0.037 0.117 samsun 0.014 0.061 0.055 -0.003 0.002 siirt 0.000 -0.007 -0.003 0.000 -0.061 sinop -0.002 -0.005 -0.009 -0.001 -0.023 sivas 0.003 0.014 0.014 0.000 0.003 şanlıurfa 0.008 0.062 0.098 -0.003 -0.132 şırnak -0.002 -0.012 0.009 0.012 -0.056 tekirdağ 0.015 0.086 0.039 0.006 0.279 tokat 0.001 0.004 0.012 -0.001 -0.059 trabzon 0.010 0.020 0.024 0.020 0.021 tunceli -0.003 -0.013 -0.017 -0.001 0.102 uşak 0.001 0.002 -0.001 0.000 0.071 van 0.003 0.007 0.043 -0.001 -0.122 yalova 0.001 0.020 -0.006 -0.004 0.157 yozgat 0.000 0.000 0.002 -0.001 -0.045 zonguldak 0.003 0.005 0.012 -0.018 0.016 appendix 3. covariance matrix c1 c2 c3 c4 c5 c1 7.76e+13 71414896520 2.90942e+12 3.62346e+11 30383494618 c2 7.14e+10 71756333 2661769030 374774730 34537249 c3 2.91e+12 2661769030 1.33093e+11 18567394308 -212823424 c4 3.62e+11 374774730 18567394308 32006766617 107912881 c5 3.04e+10 34537249 -212823424 107912881 165872410 robust mahalanobis distance based topsis to evaluate the economic development of provinces 119 appendix 4. robust topsis-m results and robust clusters provinces ss* c* rank robust cluster i̇stanbul 3806970.55 0.00 1.0000 1 0 ankara 1315344.95 2494550.68 0.3452 2 0 i̇zmir 540509.74 3274118.34 0.1417 3 0 antalya 396058.35 3419752.48 0.1038 4 4 bursa 330753.25 3487381.04 0.0866 5 4 gaziantep 277507.93 3542972.56 0.0726 6 3 kocaeli 276162.66 3541735.68 0.0723 7 3 konya 219392.06 3603602.94 0.0574 8 3 adana 207115.82 3615707.45 0.0542 9 3 denizli 194374.17 3630396.97 0.0508 10 3 mersin 163408.66 3664411.81 0.0427 11 2 hatay 154532.08 3673023.35 0.0404 12 2 muğla 147826.70 3681960.66 0.0386 13 2 kayseri 145282.08 3686437.22 0.0379 14 2 manisa 145128.76 3684833.95 0.0379 15 2 balıkesir 132516.62 3700386.28 0.0346 16 2 tekirdağ 127596.18 3706567.06 0.0333 17 2 aydın 127282.54 3707360.65 0.0332 18 2 samsun 126212.93 3708004.87 0.0329 19 2 kahramanmaraş 125600.94 3708571.90 0.0328 20 2 diyarbakır 116569.03 3721282.25 0.0304 21 2 sakarya 116280.49 3723596.74 0.0303 22 2 eskişehir 115656.03 3721757.37 0.0301 23 2 şanlıurfa 114373.51 3724234.47 0.0298 24 2 trabzon 111612.58 3728659.48 0.0291 25 2 erzurum 98085.95 3747016.37 0.0255 26 1 elazığ 96291.94 3750128.47 0.0250 27 1 ordu 96003.68 3751018.17 0.0250 28 1 afyonkarahisar 95901.64 3751339.97 0.0249 29 1 malatya 95048.94 3752610.14 0.0247 30 1 van 93597.31 3755186.68 0.0243 31 1 mardin 93352.18 3756901.33 0.0242 32 1 çanakkale 93207.95 3755240.61 0.0242 33 1 sivas 91889.38 3757735.11 0.0239 34 1 çorum 91063.00 3754443.44 0.0237 35 1 kütahya 90466.14 3760470.56 0.0235 36 1 zonguldak 90079.02 3758778.28 0.0234 37 1 rize 89697.81 3761760.02 0.0233 38 1 edirne 89321.95 3762063.33 0.0232 39 1 osmaniye 89151.99 3761846.64 0.0232 40 1 tokat 88192.13 3764793.87 0.0229 41 1 adıyaman 88081.94 3765080.11 0.0229 42 1 kırklareli 87977.97 3764919.61 0.0228 43 1 kastamonu 87144.59 3767103.59 0.0226 44 1 giresun 87058.94 3767686.80 0.0226 45 1 uşak 87010.94 3767075.77 0.0226 46 1 isparta 86840.86 3767906.40 0.0225 47 1 düzce 86662.16 3767969.21 0.0225 48 1 aksaray 85953.20 3769527.17 0.0223 49 1 yalova 85801.86 3768973.01 0.0223 50 1 yorulmaz et al./oper. res. eng. sci. theor. appl. 4 (2) (2021) 102-123 120 provinces ss* c* rank robust cluster yozgat 85421.17 3770463.34 0.0222 51 1 siirt 85271.04 3770921.94 0.0221 52 1 batman 85096.64 3771558.44 0.0221 53 1 bolu 84797.12 3771567.26 0.0220 54 1 amasya 84458.37 3772823.86 0.0219 55 1 niğde 84410.23 3772788.28 0.0219 56 1 bilecik 84407.81 3772772.88 0.0219 57 1 karabük 84164.54 3772408.90 0.0218 58 1 nevşehir 84142.10 3773447.97 0.0218 59 1 kırşehir 83876.31 3773707.63 0.0217 60 1 karaman 83874.45 3774547.24 0.0217 61 1 burdur 83803.32 3774923.73 0.0217 62 1 şırnak 83736.19 3777277.36 0.0217 63 1 ağrı 82723.75 3777316.70 0.0214 64 1 kırıkkale 82594.90 3777297.79 0.0214 65 1 çankırı 81699.87 3780150.88 0.0212 66 1 bitlis 81664.43 3780126.62 0.0211 67 1 kars 81542.53 3780329.88 0.0211 68 1 muş 81497.20 3780856.44 0.0211 69 1 erzincan 81377.80 3780799.86 0.0211 70 1 sinop 81221.97 3781266.28 0.0210 71 1 bartın 81109.97 3781574.80 0.0210 72 1 artvin 81017.96 3781881.92 0.0210 73 1 hakkari 80631.68 3783181.03 0.0209 74 1 bingöl 80405.97 3783954.88 0.0208 75 1 iğdır 80323.38 3784453.71 0.0208 76 1 gümüşhane 79753.45 3786130.63 0.0206 77 1 kilis 79407.02 3787346.82 0.0205 78 1 ardahan 79335.75 3787401.81 0.0205 79 1 tunceli 79231.01 3787762.23 0.0205 80 1 bayburt 78884.23 3789196.40 0.0204 81 1 references ardielli, e. 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(1995). quantitative applications in the social sciences, no. 07-104.multiple attribute decision making: an introduction. sage university papers series. sage publications, inc. © 2021 by the authors. submitted for possible open access publication under the terms and conditions of the creative commons attribution (cc by) license (http://creativecommons.org/licenses/by/4.0/). robust mahalanobis distance based topsis to evaluate the economic development of provinces özlem yorulmaz 1, sultan kuzu yıldırım 2, bahadır fatih yıldırım 3* 1. introduction 2. methodology 2.1. mahalanobis distance-based topsis (topsis-m) 2.2. robust mm estimator 2.3. robust cluster 3. dataset and results 4. conclusion appendix references operational research in engineering sciences: theory and applications vol. 4, issue 3, 2021, pp. 82-106 issn: 2620-1607 eissn: 2620-1747 * corresponding author. yousafkhan@giki.edu.pk (y. ali), manzoorahmed12234@gmail.com (m. ahmad), sabir.m@nbs.nust.edu.pk (m. sabir), alisajad421@gmail.com (s. a. shah) regional development through energy infrastructure: a comparison and optimization of iran-pakistan-india (ipi) & turkmenistan afghanistan-pakistan-india (tapi) gas pipelines yousaf ali 1*, manzoor ahmad2, muhammad sabir 3, sajjad ali shah2 1 school of management sciences, gik institute of engineering sciences and technology, topi, swabi, kp, pakistan 2 faculty of mechanical engineering, gik institute of engineering sciences and technology, topi, swabi, pakistan 3 nust business school (nbs), national university of sciences and technology (nust), islamabad, pakistan received: 10 september 2021 accepted: 24 november 2021 first online: 09 december 2021 research article abstract: pakistan is working on two pipeline projects, namely, iran-pakistan-india (ipi) and turkmenistan-afghanistan-pakistan-india (tapi) gas pipelines, to meet its energy supply-demand gap. this study's aims to compare these two projects and identify the most suitable option for pakistan. furthermore, as the tapi project is progressing faster than the ipi project, this study also aims to identify the critical activities associated with tapi projects. finally, a model is proposed to optimize the material and transportation costs related to the tapi project. the study's contribution by using fuzzy set theory-based multi-criteria decision-making (fuzzy mcdm) to compare two projects along with usage of the fuzzy critical path method (fcpm) for the identification of critical activities associated with the tapi project. finally, the genetic algorithm is applied to optimize the material and transportation costs of the tapi project. the results show that ipi has advantages over tapi in terms of power generation, transporta tion cost, transits fee, and gas prices. the critical path analysis of the tapi gas pipeline shows that it will take approximately 75 to 330.5 weeks to complete. the study is useful for the managers who have to work in these projects, the policymakers considering these projects at various levels, and the researcher having an interest in applying fuzzy set theory with mcdm, cpm, and in the context of the energy infrastructure. key words: optimization models, fuzzy topsis, fuzzy cpm, genetic algorithm, mcdm, tapi, ipi doi: https://doi.org/10.31181/oresta091221082a regional development through energy infrastructure: a comparison and optimization of iranpakistan-india (ipi) & turkmenistanafghanistan-pakistan-india (tapi) gas pipelines 83 1. introduction pakistan is confronted with increasing energy demand and the energy demandsupply gap (ali, et al., 2020a). pakistan's energy mix is dominated by thermal sources, mainly imported from middle east countries (mof, 2020). although pakistan has been producing oil and gas locally, it is insufficient to meet its energy demand (mof, 2020). pakistan's geographic closer locations to oil-rich middle-eastern countries and its land connection with iran and natural gas-rich central asian states (via afghanistan) give it a geographic advantage. historically, pakistan has heavily relied on oil imports from the kingdom of saudi arabia (ksa) and the united arab emirates while ignoring the neighbour iran mainly due to economic sanctions on iran. to meet its growing energy demand, pakistan has been exploring multiple options. these options include an increase in local exploration of energy sources and identifying and connecting to importing energy resources from other countries. in this regard, there has been a discussion on projects like the iran-pakistan-india (ipi) pipeline that was planned to connect these three countries for gas supply from iran. however, the ipi project could not be implemented according to the expectations and plans due to international sanctions on iran and pressure from the united states and ksa. the alternative to the ipi pipeline project that is proposed, debated, and supported by the stakeholders is turkmenistan-afghanistan-pakistan-india (tapi) gas pipeline. tapi has support from both the usa and the ksa. however, there are concerns over the safety and security of the tapi pipeline, especially across afghanistan. also, there are issues with funding for the project. however, currently, the ipi pipeline project is not progressing significantly compared to the tapi pipeline project. this study has two main objectives. first, the study does a feasibility comparison of ipi and tapi gas pipeline projects for pakistan. we consider several factors such as capacity, length, costs and other associated benefits and costs of these two projects to undertake its feasibility. secondly, given the fast progress on the tapi project, the study also identifies the critical activities being involved in the tapi pipeline project and suggests cost optimization that may help implement the tapi pipeline project. finally, the study also proposes a model to optimize the material and transportation costs related to the tapi project. to the best of our knowledge, no such analysis is undertaken for these two projects. the major contribution of this study is the first of its type comparison of the ipi and tapi pipelines project and the application of fuzzy set theory based multi-criteria decision method (mcdm) topsis (technique for order preference similarity to ideal solution) and critical path method (fcpm) along with the application of a genetic algorithm for the optimization of tapi project. these techniques are not employed in such a context in earlier literature. thus, the study contributes also in terms of the application of advanced decision-making techniques in feasibility studies. the rest of the study is organized as follows: section 2 is a literature review. section 3 consists of an overview of the ipi and tapi pipeline projects and their comparison. furthermore, section 4 presents the fuzzy topsis, fuzzy cpm, and genetic algorithm and the various steps associated with each method. this section also describes the data and the sources used in this study. section 5 presents the results of the study. finally, section 6 concludes the study. ali, y. et al./oper. res. eng. sci. theor. appl. 4 (3) (2021) 82-106 84 2 literature review the literature review section is divided into subsections. the first subsection discusses studies associated with ipi and tapi projects. the second subsection discusses the studies on the methodological aspects of these studies 2.1 the literature on ipi and tapi projects there are various aspects of scholarly studies focusing on ipi and tapi projects. for instance, several studies discuss feasibility aspects (economic or political) of tapi or ipi projects. some researchers discuss both projects together while considering a single-country perspective. the feasibility studies covering either tapi and ipi or even both are undertaken from different project partner countries. for instance, pandian (2015) studied the indian perspective for the ipi project. similarly, hudaa & ali (2017) covers the tapi project from pakistan's perspective. below we discussed scholarly studies that are explored these two projects from different member countries' perspectives. the study of pandian (2005) does discuss the ipi project from the indian perspective. the research performed a qualitative cost-benefit analysis and argued that the ipi project could work as a confidence-building between india and pakistan to create an energy partnership between the two countries and open up more possibilities for commercial businesses. sahir & qureshi (2007) examined the pakistani perspective on the region's energy security and its role as an energy corridor. the study also briefly describes pakistan's importance for pipeline projects (such as ipi and tapi) that could meet india and china's energy needs along with benefits to pakistan. similarly, abbas (2015) describes a brief history of ipi and tapi projects in pakistan's energy needs. also, pradhan (2020) described in detail the tapi project and its importance for india. the study also detailed the reasons for delays in the project and the lack of interest of international firms to finance the tapi project. the ipi project is vital for india because it will provide a four-time cheaper gas than other sources, even after paying the transit fee to pakistan (pradhan, 2020). furthermore, the project will bring earnings for pakistan and improve energy security in both india and pakistan. the project could ensure a path for energy and trade connectivity across the south-asia. however, as per pradhan (2020), pakistan and india disagree on the transits fee. furthermore, india has concerns over the continuation of supply in case of a rise in political conflict. ksa is not in favour of this project. but, china has shown interest in participating in the ipi project. in this situation, pakistan can still enjoy transits country status (pradhan, 2020). mahmood et al. (2014) studied to make assessments for pakistan's energy needs. so the study assesses the energy that pakistan can obtain from various energy sources and do discuss the energy import options from ipi and tapi gas pipelines. the study describes these projects' potential to meet pakistan's future energy needs and consider energy from other possible sources. however, mahmood et al. (2014) do not undertake direct feasibility studies of these projects or make any comparison. similarly, munir et al. (2013) is also not a full feasibility study. however, munir et al. (2013) referred to the ipi project as viable for pakistan with a net reduction of import bill by us$2.3 billion annually with generating 4000 mw of electricity. however, the international geopolitical conditions and the iran economic sanctions were considered a point of concern for this project's success for pakistan. regional development through energy infrastructure: a comparison and optimization of iranpakistan-india (ipi) & turkmenistanafghanistan-pakistan-india (tapi) gas pipelines 85 it is essential to highlight the geopolitical conditions that strongly influence both these projects in south and central asia. there are various aspects of international politics and countries like the usa, china, russia, saudi arabia, and the member countries of the project. there are abundant studies that discuss various aspects of international relations and geopolitics and their impacts on these projects. for instance, hudaa & ali (2017) emphasized increasing the number of stakeholders in mega projects (like tapi) beyond the member countries. they argue that such an approach may bring a better political consensus and earn more significant support and the shifting focus from the projects' security to inclusiveness and cooperation. lee (2014) explored the opportunities for diversification of turkmenistan gas export routes and related risks. the study also highlights the tapi project from turkmenistan's perspective, discusses the various international events and china's role, and argues that these events are causing delays in implementing the tapi project. anceschi (2017) interestingly called tapi a virtual pipeline, given its delays and misinformation around the project while no work was started on its implementation. furthermore, anceschi (2017) referred to some studies and raised concerns about the overall viability and security concerns particularly that of the 750 lengths planned to be in the afghanistan region. similarly, khan (2012) focused on the ipi pipeline project, the usa sanctions, and its resultant situation and its implementation for pakistan and other countries involved. the other aspect of the project is its safety and security. in particular, for the tapi project as passes through afghanistan. india has concerns over the project's safety and security, especially if it has not a good relationship with pakistan. for instance, pradhan (2020) highlights concerns over the pipeline's protection in afghanistan and the pakistan-afghanistan border region. the study also insisted that the gas supply should be ensured, and a proper mechanism should be placed that must be independent of the pakistan-india political relations. the study refers to the project as a win-win for all the participating member countries. the recent delays in these project implementations are also of concern for the partner countries. sadat (2015) describes five phases for the implementation of tapi phases. accordingly, the first few phrases that required signing the framework and agreements, sales, and purchases of gas agreements are already completed. however, other aspects, in particular, the implementation of the project itself is not completed. sadat (2015) referred to security, scarcity of the required funds, diplomatic relationships of the member countries, and alternative energy sources' availability as significant delays on further progress on the tapi project. joshi (2011) studied the economics and politics associated with the tapi pipeline and refer it to a plan that does not proceed beyond discussion due to afghanistan and pakistan's conditions, thus suggesting that india explore alternative options and courses of action for its energy needs. more recently, rajpoot & naeem (2020) did the feasibility of the tapi project. they emphasise the tapi project as being more valuable for meeting the energy crisis of pakistan and india. however, the study has not employed any decision making or advanced techniques instead is based on published literature and media reports. according to, khetran (2020), for successful implementation of tapi the bilateral relationship between india, pakistan, and afghanistan is important. rajmil, et al. ali, y. et al./oper. res. eng. sci. theor. appl. 4 (3) (2021) 82-106 86 (2021) debated the nature of the relationship between china, iran and pakistan in form of their common economic corridor. accordingly, they argue that despite their partnership being built through belt and road initiative investments, but future of such relations mainly depends on the mutual relationship between pakistan and india. all these developments have implications for the implementations of tapi and ipi projects. 2.2 research methods used for studying ipi and tapi projects the studies discussed above are mainly based on qualitative techniques. for instance, khetran (2020) (based on published media reports and scholarly articles), hudaa & ali (2017) (interview of policymakers), pandian (2005) (qualitative costbenefit analysis), sahir & qureshi (2007) (regional geopolitical and energy concerns), abbas (2015) (energy needs), and anceschi (2017) (qualitative analysis). furthermore, these studies are mostly focused on a single project (tapi or ipi) from a unique country perspective and with a lack of applying formal economic viability or feasibility techniques. even if some studies discussed both projects, it does not go beyond the deceptive analysis. the scholarly literature on infrastructure projects does employ several methods for analyzing the economic viability of infrastructure projects. the most popular among these techniques are traditional cost-benefit analysis (e.g., ali et al., 2020b). some other popular techniques are net present value (ali et al, 2021) and internal rate of return (ali et al 2021). another interesting application is that of mcdm based cost-benefit analysis (e.g., bilal, et al. 2021). since tapi and ipi are mega projects, going through multiple countries and have a lot of technical complications, therefore using the traditional method of feasibility (such as cost-benefit analysis) may not be useful due to the absences of the finest data details. therefore, in the absence of such information, multi-criteria-based decision-making (mcdm) techniques become more relevant for analysis. this study, therefore, has two major objectives. the study aims to compare ipi and tapi projects based on several factors (capacity, pipeline lengths, project costs, associated benefits and costs). due to the unavailability of detailed project data, the study uses mcdm based methodology namely, fuzzy topsis (technique for order preference similarity to ideal solution) (gopal and panchal, 2021). furthermore, the study aims to identify the critical activities in the implementation of the tapi project, as pakistan is currently implementing this project. for this purpose, the study uses the fuzzy critical path method (fcpm). finally, the study also aimed to optimize the resource usage in the tapi project, for which the study employed a genetic algorithm. thus, the study not only does employ advanced decision-making techniques (i.e., fuzzy mcdm) but also apply them in combination with fuzzy cpm and genetic algorithm. no previous studies (to the best of our knowledge) on the subject projects or in such context has applied such methodology earlier. thus, the study contributes to the literature not only by providing a new approach to undertake the feasibility studies of similar projects, but also providing a useful policy direction for the decision-makers associated with tapi and ipi projects. regional development through energy infrastructure: a comparison and optimization of iranpakistan-india (ipi) & turkmenistanafghanistan-pakistan-india (tapi) gas pipelines 87 3 tapi and ipi: background the turkmenistan-afghanistan-pakistan-india (tapi) and iran-pakistan-india (ipi) pipelines are important infrastructure projects for pakistan's future energy needs. these two international energy supply pipeline projects will be the first of their kind in this region. below we briefly describe these two projects and presents some relevant details about each of them. 3.1 turkmenistan-afghanistan-pakistanindia (tapi) gas pipeline project tapi project will start from gas fields in south yolotan turkmenistan (galkynysh and adjacent gas fields) and link to quetta (pakistan) through the afghanistan areas of herat, nimruz, and kandahar. in pakistan, it goes through the dera ghazi khan, multan, and then onward to fazilka (india) (hudaa & ali, 2017). figure 1 presents the approximate route of the tapi gas pipeline project. this pipeline is approximately 1680 km long, with 56-inch pipe diameter, and has a capacity to supply about 3.2 (bcfd) per day gas supply that will be shared between afghanistan (500 mcfd), pakistan (1325 mcfd), and india (1325 mcfd) (isgs, 2020). the cost of the project is estimated to be about us$ 7.74 billion (adb, 2020). figure 1. tapi and ipi project locations (source: google maps) tapi project is essential for pakistan for several reasons. the gas supply from the project can be used in power generation in pakistan (gas through the tapi pipeline can generate 6,000 megawatts cheaper electricity (naseem, 2015). this electricity is more than the current electricity generation of the largest pakistan tarbela dam). although, pakistan recently ensured lng from the central asian states, however, it will still face the shortages for its need that has been tried to manage with its domestic production (adb, 2020). furthermore, the project can ensure a consistent supply of foreign exchange for project life duration in royalty payments from india. additionally, ali, y. et al./oper. res. eng. sci. theor. appl. 4 (3) (2021) 82-106 88 project construction and operations can lead to further public and private investments and job creations, leading to more economic activities. the intangible benefits could be the improvement in india and pakistan's relationship, resulting in a peace process in this entire region. tapi project would be of equal benefits to india, afghanistan, and turkmenistan. indian economy energy demand is on the rise, and they would be able to get cheaper gas supplies at their doorstep. afghanistan will earn in royalty from both india and pakistan, along with creating jobs and employment opportunities that are almost nonexistent in their country at the moment. it will be an opportunity for turkmenistan to expand its energy market and build a more strategic relationship with its customers in the region. according to d'souza (2017), the tapi gas pipeline is a game-changer for the countries that are part of it. it will improve their economy and fulfil their energy requirements and eventually become the primary source of enhancing the people's lifestyle in south and central asia. 3.2 iran-pakistan-india (ipi) gas pipeline project the iran-pakistan-india (ipi) pipeline as a project idea can be traced back to the 1950s. however, the main proposal was placed during 1989, and the three governments agreed upon it during 1999 (baluch, 2012). the indian government has withdrawn from the project during 2009. however, the indian government can still reconsider their decision and later join the project (haq, 2010). therefore, we will be considering india as a part of this project while comparing ipi and tapi in this study. the ipi project cost is us$ 7.6 billion, with a total capacity of 5.3 billion cubic feet of gas per day, with pakistan and india share as 2.1 and 3.2 bcfd, respectively. the project was expected to provide about us$ 700 million in transit revenue to pakistan (mof, 2007). pakistan is responsible for constructing a pipeline network on its side, whereas iran has to build its part. however, currently, due to sanctions on iran, there is no major progress on the project. this project is essential for pakistan because it will provide pakistan not only, supply of gas from iran but also will provide much needed foreign exchange in the form of transit fees from india. 3.3 comparison of tapi and ipi projects it is essential to highlight that pakistan has considered both tapi and ipi projects due to its energy increasing demand. due to international geopolitical conditions and iran's position, pakistan has been under pressure to prefer the tapi gas pipeline project over the ipi gas pipeline project. some studies recommend that the tapi gas pipeline project is not feasible because of the low gas quality and the unstable situation of afghanistan (mazhar & goraya, 2013). furthermore, the tapi project will be facing significant security challenges due to its passage from afghanistan, where there are various militant and nationalist troubles, especially in the area of the project (khetran, 2017). although afghanistan will provide full security for the project, india has preferences for it (khetran, 2017). in the pakistani region, the tapi project has no significant threats as it may have in afghanistan. regional development through energy infrastructure: a comparison and optimization of iranpakistan-india (ipi) & turkmenistanafghanistan-pakistan-india (tapi) gas pipelines 89 contrary to mazhar & goraya (2013), the study from (kulkarni 2016) refers to the tapi project as feasible only if its geopolitical and commercial prospects are considered. similarly, about 99 per cent of the respondents to a survey (in afghanistan) during 2019 supported this project and viewed it as a role model project for the other national development projects (saqib, 2019). finally, the usa is also supporting the tapi project compared to the ipi project (hudaa & ali, 2017) because of sanctions on iran and its deteriorating relations since the islamic revolution in iran back in the 1970s. the ipi project is facing many challenges. perhaps the primary problem is that iran is under united nations economic sanctions that is a big hurdle for pakistan and iran to proceed on this project. not much progress has been made in more recent years. there have been renegotiations on the same clauses of the project agreement, to make it more workable for the future. there is some comparison provided in table 1 below for the two projects. table 1. basic statistics of ipi and tapi projects details ipi tapi pipeline length (kilometers) 2,775 1,735 pipeline diameter (inches) 56 56 pipeline capacity (bcfd*) 5.3 3.2 project costs (us$ billions) 7.6 7.74 global risk factors iran sanctions nil internal risk factor political conditions safety and security * billion cubic feet per day sources: (adb, 2012; mahmood, et al., 2014; hudaa & ali, 2017; adb, 2020 and pradhan, 2020) 4. research methodology and data this study has multiple objectives. it aims to perform a feasibility comparison of ipi and tapi projects. secondly, it identifies the critical activities and optimizes the tapi pipeline project's material and transportation costs. therefore, the study uses fuzzy topsis, fuzzy critical path method (cpm), and genetic algorithm. we divided this section into several subsections and described the applications of each of these methodologies. the last sub-section describes the data used in this study. 4.1. fuzzy technique for order preference by similarity to ideal solution the technique for order preference by similarity to ideal solution (topsis) is one of the well-known techniques that are used for multiple-criteria decision making (mcdm). topsis was introduced by ching & kwangsun, (1981) and later modified by tung, (2000). this technique has been extensively used in various fields, including operations (ali, et al., 2019), supply chain (ali, et al., 2020a), and economics (ali, et al., 2019). the basic idea of topsis is to help in selecting an alternative (among a set of available options) that is closest to the ideal positive solution and farthest from ali, y. et al./oper. res. eng. sci. theor. appl. 4 (3) (2021) 82-106 90 the ideal negative solution. topsis uses linguistic scales for weights.1 tung (2000) modified linguistic scales for weight by using fuzzy triangular values, i.e., a fuzzy version of the topsis environment. fuzzy topsis is also in use in scholarly literature in many applications, for instance, decision making (khan, et al., 2020), economic development (bin hameed, et al., 2020), and supply chain (ertuğrul & karakaşoğlu, 2008). figure 2 shows the typical steps involved for the topsis approach (minatour, et al., 2015) that are adopted in this study. figure 2. illustrating typical steps in the topsis approach (minatour, et al., 2015) the topsis procedure can be described as follows. assume that there are 𝑁 decision-makers with 𝑦 alternatives among which they have to choose while using 𝑦 criteria. the various steps for this decision making using fuzzy topsis will be as follows: step 1: in the first step of the fuzzy topsis procedure, 𝑁 decision-makers compare all alternatives with a given criterion and then rate each alternative with respect to each criterion. step 2: the criteria receiving the most number of selections is taken for criteria weight and fuzzy numbers rating respectively as per set weight criteria. this study adopted the following (table 2) linguistic variable weighting for each criterion. table 2. linguistic variables use for weighting each criterion linguistic variable triangular number very high (1.00,0.25,0.00) high (0.75,0.15,0.15) moderate (0.50,0.25,0.25) low (0.25,0.15,0.15) very low (0.00,0.00,0.25) source: (izadi, et al., 2013) step 3: in this step, we will select the appropriate linguistic variable from table 2 to find the importance weights of different criteria assigned by decision-makers. weights are assigned to different responses obtained from decision-makers 𝑊𝑗̅̅ ̅= 1 𝐾 [�̌�𝑗 1 + �̌�𝑗 2 +. . . +�̌�𝑗 𝑘 ] (1) where 𝑊𝑗̅̅ ̅ weight of different criteria assigned by decision-makers. 1 a linguistic scales for weights extracted from izadi, et al., (2013) is presented in table a2 in appendix. regional development through energy infrastructure: a comparison and optimization of iranpakistan-india (ipi) & turkmenistanafghanistan-pakistan-india (tapi) gas pipelines 91 step 4: in this step, we will select appropriate linguistic variables from table 1 to find the importance rating of different alternatives for criteria. �̌�𝑖𝑗 = 1 𝐾 [�̌�𝑖𝑗 1 + �̌�𝑖𝑗 2 +. . . +�̌�𝑖𝑗 𝑘 ] (2) where �̌�𝑖𝑗 𝑘 is the rating of kth decision-maker, against alternatives i and criteria j. step 5: now in this step we will convert linguistic variables evaluation into fuzzy triangular numbers to construct a fuzzy decision matrix as well as determine the fuzzy weight of each criterion. i.e. 𝐶1 𝐶2 … 𝐶𝑛. �⃐� = 𝐴1 ⋮ 𝐴𝑚 [ �̌�11 �̌�12 … �̌�21 �̌�22 … �̌�𝑚1 �̌�𝑚2 … �̌�1𝑛 �̌�2𝑛 �̌�𝑚𝑛 ] (3) similarly weight: 𝑊𝑗̅̅ ̅ = [𝑤1 𝑤2 … 𝑤𝑛], �̌�𝑖𝑗 = (𝑎𝑖𝑗 , 𝑏𝑖𝑗 , 𝑐𝑖𝑗 ) (4) where �̌�𝑖𝑗 represent a triangular fuzzy number. 𝐴1, 𝐴2 … … 𝐴𝑛 are alternatives and 𝐶1, 𝐶2, … … 𝐶𝑛 are criteria. step 6: in this step, we will construct a normalized fuzzy decision matrix from above step 5. to avoid lengthy and complex formulation we use a linear scale so �̅� gives normalized values; �̅� = [�̃�𝑖𝑗 ] 𝑚×𝑛 (5) �̃�𝑖𝑗 = ( 𝑎𝑖𝑗 𝐶𝑗 ∗ , 𝑏𝑖𝑗 𝐶𝑗 ∗ , 𝑐𝑖𝑗 𝐶𝑗 ∗ ), 𝐶𝑗 ∗= max 𝑐𝑖𝑗 (6) step 7: in this step, we will construct a weighted normalized fuzzy decision matrix. �̇� = [�̃�𝑖𝑗 ]𝑚×𝑛 i = 1, 2, 3…..m j=1, 2, 3….n (7) �̃�𝑖𝑗 = �̃�𝑖𝑗 × 𝑊𝑗 (7a) step 8: this step will determine the fuzzy positive ideal solution (fpis) as (𝐹∗) as well as fuzzy negative ideal solution (fnis) as (𝐹−) mentioned in the below equations. 𝐹∗= �̃�1 ∗ , �̃�2 ∗ , … . . �̃�𝑛 ∗ (8) 𝐹−= �̃�1 −, �̃�2 − … … �̃�𝑛 − where �̃�𝑗 ∗ = (1, 1, 1) and �̃�𝑗 − = (0, 0,0), j= (1, 2 … n) (8a) similarly, the distance between two fuzzy numbers can be calculated by vertex method i.e. if x and y are two fuzzy numbers; x= (a, b, c) y= (x, y, z) then d(x, y) = √ 1 3 [(𝑎 − 𝑥)2 + (𝑏 − 𝑦)2 + (𝑐 − 𝑧)2] (9) step 9: this step will determine the distance from a negative and positive ideal solution. ali, y. et al./oper. res. eng. sci. theor. appl. 4 (3) (2021) 82-106 92 d steric = ∑ 𝑑(�̃�𝑖𝑗 , �̃�𝑗 ∗)𝑛𝑗=1 (10) d negative = ∑ 𝑑(�̃�𝑖𝑗 , �̃�𝑗 − )𝑛𝑗=1 where d shows the distance between two fuzzy numbers step 10: this step will determine the closeness factor of each criterion. cc = d negative d steric + d negative (11) step 10: rank the given criteria on basis of the closeness factor. the criteria having more closeness factors will be chosen best in descending order. 4.2. fuzzy critical path method (fcpm) the fuzzy critical path method (fcpm) is based on fuzzy set theory. fuzzy set theory was introduced by zadeh, (1996). the fuzzy approach is useful in a decision situation when the past data are not available or relevant (liberatore & matthew, 2002). the fuzzy set theory approach is applied now in every field of technology (aziz, 2013) and has many applications in various fields, including artificial intelligence, computational intelligence, and data analysis (mares, 2006). a project manager may use the critical path method (cpm) and program evaluation and review technique (pert) to manage, monitor, and control project activities. pert is considered more realistic because it provides three-time durations (most likely, pessimistic and optimistic) of the activities (compared to only one in cpm). these time values are obtained from experts, and the beta distribution is also used (ramo, 2014). on the other hand, fuzzy cpm helps plan and control difficult projects like ipi or tapi. the basic logic behind fuzzy cpm is the same as simple cpm, but fuzzy triangular numbers or trapezoidal fuzzy numbers are used in fuzzy cpm. it helps in the identification of critical activities in the network critical path. furthermore, it can be employed for gas pipeline construction projects to identify various related activities and critical paths to complete projects without delay. an arithmetic operation can be done on any generalized trapezoidal fuzzy numbers. for example, consider two trapezoidal fuzzy numbers 𝑋 = (𝑈1, 𝑈2, 𝑈3, 𝑈4) and 𝑌 = (𝑉1, 𝑉2, 𝑉3, 𝑉4), then the summation and subtraction are (vahidi & rezvani, 2013): 𝑋 + 𝑌 = (𝑈1, 𝑈2, 𝑈3, 𝑈4) + (𝑉1, 𝑉2, 𝑉3, 𝑉4) = (𝑈1 + 𝑉1, 𝑈2 + 𝑉2, 𝑈3 + 𝑉3, 𝑈4 + 𝑉4) (12) 𝑋 − 𝑌 = (𝑈1, 𝑈2, 𝑈3, 𝑈4) − (𝑉1, 𝑉2, 𝑉3, 𝑉4) = (𝑈1 − 𝑉4, 𝑈2 + 𝑉3, 𝑈3 + 𝑉2, 𝑈4 + 𝑉1) (13) now, to describe the fuzzy critical path method (fcpm) technique following notations are used: 𝑁𝑑 : nodes in the project network diagram 𝐴𝑐𝑡𝑖𝑗 : activity between the nodes 𝐴𝐹𝑇𝑖𝑗 : activity fuzzy time of 𝐴𝑐𝑡𝑖𝑗 𝐹𝐸𝑇: fuzzy earliest time 𝐹𝐿𝑇: fuzzy latest time 𝐹𝑆𝑇𝑖𝑗 : total fuzzy slack time of 𝐴𝑐𝑡𝑖𝑗 𝐹𝐶𝑇(𝑃𝑛): fuzzy completion time 𝑁𝑢𝑚: number of activities in our project network diagram fuzzy critical path method (cpm) may be applied using the following steps: regional development through energy infrastructure: a comparison and optimization of iranpakistan-india (ipi) & turkmenistanafghanistan-pakistan-india (tapi) gas pipelines 93 step 1: consider the fuzzy earliest time (fet1) value (0, 0, 0, 0). step 2: calculate beta value using the below equation: 𝐵 = ∑ ∑ (𝑋𝑖𝑗−𝑊𝑖𝑗) (𝑋𝑖𝑗−𝑊𝑖𝑗)+(𝑍𝑖𝑗−𝑌𝑖𝑗) 𝑁𝑢𝑚 ⁄ (14) step 3: calculate fuzzy earliest time (fet) for each node with the help of the equation given below: 𝐹𝐸𝑇𝑗 = 𝐹𝐸𝑇𝑖 + 𝐴𝐹𝑇𝑖𝑗 (15) step 4: at the intersection, node compare fuzzy earliest time ( 𝐹𝐸𝑇𝑗𝑠 ) and select the maximum number for fuzzy earliest time (𝐹𝐸𝑇𝑗 ) for each node. 𝐹𝐸𝑇𝑗 = 𝑚𝑎𝑥{𝐹𝐸𝑇𝑖 + 𝐴𝐹𝑇𝑖𝑗 𝐹𝐸𝑇𝑗 = max{(𝑆𝑎 , 𝑈𝑎 , 𝑉𝑎 , 𝑊𝑎 ), (𝑆𝑏 , 𝑈𝑏 , 𝑉𝑏 , 𝑊𝑏 )} (16) step 4.1: now, find the values of 𝐴1 and 𝐴2 by using the below equations: 𝐴1 = min {𝑆𝑎 , 𝑈𝑎 , 𝑉𝑎 , 𝑊𝑎 , 𝑆𝑏 , 𝑈𝑏 , 𝑉𝑏 , 𝑊𝑏 ) (17) 𝐴2 = max {𝑆𝑎 , 𝑈𝑎 , 𝑉𝑎 , 𝑊𝑎 , 𝑆𝑏 , 𝑈𝑏 , 𝑉𝑏 , 𝑊𝑏 ) (18) step 4.2: calculate the values of r (𝑆𝑎 , 𝑈𝑎 , 𝑉𝑎 , 𝑊𝑎 ) and r (𝑆𝑏 , 𝑈𝑏 , 𝑉𝑏 , 𝑊𝑏 ) with the given below equations: 𝑅(𝑆𝑖 , 𝑈𝑖 , 𝑉𝑖 , 𝑊𝑖 , ) = 𝛽[(𝑊𝑖 − 𝐴1 (𝐴2 − 𝐴1 − 𝑉 + 𝑊) + (1 − 𝛽)[1 − 1 − (𝐴2 − 𝑆𝑖 ) (𝐴2 − 𝐴1 + 𝑉𝑖 − 𝑆𝑖 )}⁄⁄ (19) step 4.3: select the fuzzy earliest time (𝐹𝐸𝑇𝑗 ) which is more significant after comparing the results of r(𝑆𝑖 , 𝑈𝑖 , 𝑉𝑖 , 𝑊𝑖 ) step 5: find the fuzzy latest time (flt) for each node by using the equation given below: 𝐹𝐿𝑇𝑗 = 𝐹𝐸𝑇𝑘 + 𝐴𝐹𝑇𝑗𝑘 (20) step 6: intersection nodes compare the fuzzy latest time (𝐹𝐿𝑇𝑗𝑠 ) and consider the minimum number as 𝐹𝐿𝑇𝑗 for each node. 𝐹𝐿𝑇𝑗 = 𝑚𝑖𝑛{𝐹𝐸𝑇𝑘 − 𝐴𝐹𝑇𝑗𝑘 } 𝐹𝐿𝑇𝑗 = 𝑚𝑖𝑛{((𝑆𝑎 , 𝑈𝑎 , 𝑉𝑎 , 𝑊𝑎 ), (𝑆𝑏 , 𝑈𝑏 , 𝑉𝑏 , 𝑊𝑏 )} (21) consider the sub-steps of step 4 as same for step 6. step 7: calculate fuzzy slack time (𝐹𝑆𝑇) for each activity from the given equation below. 𝐹𝑆𝑇𝑖𝑗 = 𝐹𝐿𝑇𝑗 − (𝐹𝐸𝑇𝑖 + 𝐴𝐹𝑇𝑖𝑗 ) (22) step 8: from all the paths 𝐹𝐶𝑇 will be calculated for each one, and the below equation can be used to calculate the fct for the activities in the possible path node. 𝐹𝐶𝑇(𝑃𝑛) = ∑ 𝐹𝑆𝑇𝑖𝑗 (23) ali, y. et al./oper. res. eng. sci. theor. appl. 4 (3) (2021) 82-106 94 step 9: minimum number is selected after calculating the fcts, and the path which has the lowest r-value is taken as a critical path. 𝐹𝐶𝑇(𝑃𝑛) = 𝑚𝑖𝑛 {𝐹𝐶𝑇(𝑃𝑖)|𝑖 = 1,2,3,4, . . . . 𝑛 (24) activities involved in the fuzzy critical path method (fcpm): the tapi gas pipeline activities were divided into two categories, one for pipeline construction and the other for the gas compression station. in this regard, the two major types of activities are presented below in table 3 as per oilscams (2018) and stephanatos (2014): table 3. activities for gas pipelines and gas compression stations gas pipelines activities (oilscams, 2018) gas compression stations (stephanatos, 2014) a approval of tapi gas pipeline l installation of gas compression stations b survey & route design m installation of filters c order of gas pipelines n fitting of suction valves d hiring of workers o fitting of control valves e cleaning & grading of ground for gas pipeline p attachment to the gas pipeline. f trenching of the ground g stringing & bending of gas pipeline h welding i non-destructive & hydrostatic testing j commissioning k restoration 4.3. genetic algorithm genetic algorithm (g.a.) is widely used in operations research (and also in computer sciences) for optimization related problems. the main idea behind (g.a.) is based on the theory of the evolution of darwin (mitchell, 1996). the process by its nature is imperative in which a candidate solution with its properties is selected from the population, and this candidate can be "mutated" or "altered" to a new solution called generation; this process is continued till the final solution. we aim to use the g.a. solution for the optimization of the material and transportation costs of the project. it may be noted that the work on the optimization of material and transportation cost has already been performed by many researchers using other techniques like linear programming and time window constraints (yadav & kumar, 2017). however, for the construction of the gas pipeline, g.a. can quickly solve problems with vast data. furthermore, the g.a. approach has been widely applied in optimizing the gas pipelines to optimize the design cost. for instance, goldberg & richardson (1987) used the genetic algorithm to optimize the working of a steady-state gas pipeline, which had 10 compressor stations and ten pipes. each regional development through energy infrastructure: a comparison and optimization of iranpakistan-india (ipi) & turkmenistanafghanistan-pakistan-india (tapi) gas pipelines 95 compression station consisted of 4 pumps in series (goldberg & richardson, 1987). the study's target is to optimize power consumption at specified controlled and allowable pressure (goldberg & richardson, 1987). similarly, singh & nain (2012) designed a new model based on a genetic algorithm for selecting the pipe sizes. some other studies based on genetic algorithm includes goldberg, (1989) and narváez, (2003). this study's optimization model uses the non-dominated sorting genetic algorithm to minimize project costs as given by equation (25). 𝑀𝑖𝑛𝑖𝑚𝑖𝑧𝑒𝑑 𝑐𝑜𝑠𝑡 = ∑ 𝐶𝑜𝑠𝑡𝑛𝑚=1 (25) the genetic algorithm procedure is applied using the following steps. step 1: choose the type of optimization. the optimization can be single-objective optimization or multiple objective optimizations. step 2: input the population size. the population size tells us the number of times it will run the different solutions. therefore, the greater the population size, the more time the program will take to run. step 3: choose the type of algorithm. choose the type of algorithm from generational, generational elitist, and steady state. step 4: choose the respective crossover. this operator is used to connect individuals to produce new offspring’s having characteristics of their parents. these offspring may have a better solution or a worse solution. step 5: choose the selector. selector plays an essential role in a genetic algorithm, which is how the algorithm will select solutions. there are three types of selectors used: roulette, roulette by rank, and tournament. step 6: select the mutator. the mutation operator provides new genetic material during optimization. it has three types: simple, simple by gene, and adaptive mutation. step 7: defining chromosomes and linking with ms excel. all decision variables for the problem give us genes in a genetic algorithm. the genes are comprehended together to form new chromosomes. step 8: defining the objectives. one objective must be defined in a single objective and more than one for multiple-objective function. step 9: define the constraints. constraints are used to penalize variables for going out of ranges. step 10: run the program. the study used a microsoft excel add-in tool called solvexl. this tool uses a genetic algorithm to solve complex problems. the optimization and configuration of the tool are done easily by a build-in user-friendly wizard. solve is superior to other commercial products and helps in performing single and multiple objective genetic algorithmic solutions. solvexl utilizes a com interface to interact with microsoft excel. solvexl is written in the c++ programming language. ali, y. et al./oper. res. eng. sci. theor. appl. 4 (3) (2021) 82-106 96 4.4. data collection the data for this study was obtained both from primary and secondary sources. we used three questionnaires for getting the preliminary data required for analysis. these questionnaires were containing structured questions with pre-decided closeended answers (such as multiple choice and rating scales). the data was collected using google online survey tool. the data were obtained from 15 experts from the field. all the respondents were experts in the oil and gas industry. the respondents were managers and engineers working in the field for a long period. there were ten factors considered (as given in table 4), and experts were asked to assign weights to each of these criteria using the four options (very low, low, medium, high, and very high) as per their experience and knowledge. the data were obtained from all experts for both projects on all these ten factors. table 4. factors consider and the weight assigned by experts criterion ipi tapi capacity (c1) very low low medium-high very high very low low medium high very high gas price (c2) transit fee (c3) capital cost (c4) economic factors (c5) length of pipeline (c6) power generation (c7) time of completion (c8) geographical location (c9) international support (c10) the data collected through this procedure were more feasible, simpler, and timeefficient. this primary data was used in the usage of fuzzy cpm and fuzzy topsis. however, there are many limitations, as many assumptions are made while finding out optimized costs and completion times. the exact duration of activities is not always reliable or sometimes even known (rao & nowpada, 2012). but given the uncertain situation and absence of enough published information, this approach was considered appropriate. the secondary data were also used in this study. for instance, the cost of containers for different length pipes was obtained by consulting an expert field engineer in schlumberger. the criterion for fuzzy topsis was selected based on previous literature confirmed by the same field engineer. we took costing data available on the internet and from experts' opinions as the costing reports of both projects are not published. parameters can be varied to find out total costs like elevation in the setup of pipelines, temperature, and any accident happening while working as it could cause a change in our fuzzy cpm values. however, given these limitations, we still believe that it is the best approach to compare these two projects in given uncertain circumstances, where these projects have been under discussion for so long, but still, no significant progress has been made on either of them. regional development through energy infrastructure: a comparison and optimization of iranpakistan-india (ipi) & turkmenistanafghanistan-pakistan-india (tapi) gas pipelines 97 5. results and discussion the result section is divided into three sub-section. these sections represent the results of fuzzy topsis, fuzzy critical path method and the genetic algorithm, respectively. it may be noted that discussion on each of these results is also included in each of these specific sections, respectively. 5.1. results from fuzzy topsis the fuzzy topsis method was applied using the expert ratings being obtained through the steps stated in the earlier section. table 5 presents the final results of the fuzzy topsis method.2 there are several important observations from table 5. it is clear that the ipi has an advantage over the tapi in terms of power generation, transportation cost, transits fee, and gas prices. furthermore, the closeness coefficients (determined using equation (11)) for ipi and tapi projects are 0.45299 and 0.43973, respectively. this implies that ipi is better than tapi in the ranking (ipi > tapi) in the considered study settings. this implies that the ipi project is ranked higher than the tapi project. table 5. results of fuzzy topsis ipi tapi d steric d negative d steric d negative gas price 0.046 0.057 0.350 0.046 transit fee 0.499 0.367 0.310 0.498 capital cost 0.035 0.026 0.353 0.035 economic factor 0.615 0.272 0.367 0.615 length of pipeline 0.045 0.033 0.348 0.045 power generation 0.629 0.951 0.371 0.630 time completion 0.049 0.086 0.349 0.049 geographical location 1.131 0.523 0.626 1.129 international support 0.049 0.068 0.338 0.049 capacity 0.033 0.075 0.365 0.033 sum of li + sum of li sum of li + sum of li 3.130 2.457 3.777 3.128 cc (%) 43.973% 45.299% these findings are consistent with earlier studies such as hudaa & ali (2017) and munir et al. (2013). these findings may not be unexpected given that with lower cost of gas, lesser security and safety concerns, no third country for transit, and higher supplier indicates better economic choices for ipi compared to tapi. the major hurdle for ipi implementation is the iran economic sanctions and the international geopolitical conditions. 2 we do not include the detailed calculation results of this or other methods to keep the article's length to a manageable level. for interested readers, the detailed tables of the calculations can be provided on the request. ali, y. et al./oper. res. eng. sci. theor. appl. 4 (3) (2021) 82-106 98 5.2. fuzzy cpm as stated earlier, there is significant progress going on tapi compared to the ipi pipeline project. therefore, this study undertakes the fuzzy cpm analysis for identifying the critical activities associated with the tapi pipeline project. in this regard, table 6 shows various activities involved in the tapi gas pipeline, predecessor, and fuzzy time for each activity. these time estimations are based on the experts' survey (also known as trapezoidal fuzzy numbers).3 the activity on arrow (aoa) network is presented in figure 3. the fuzzy activity time is shown in the form of trapezoidal fuzzy numbers, where 𝑎 represents the minimum value, and 𝑑 represents the maximum value. the network diagram for this study is constructed based on the concept of activity on arrow. figure 3 illustrates the aoa network diagram that is built using activities and their predecessors given in table 6. each circle represents a node while the alphabets are showing the activities between the nodes. the dotted lines in figure 3 represent the dummy activities. the fuzzy time for the dummy activities is considered to be zero making the overall connection between the activities logically correct. table 7 shows all considered possible paths from the network diagram and calculated the fuzzy completion time using equation (23). subsequently, values of r are calculated for each path using equation (24) and selected. the minimum value obtained was our critical path for the tapi gas pipeline project. also, table 8 presents the fuzzy earliest time, fuzzy latest time, and fuzzy slack time (fst) for each node, respectively. the result shows the tapi gas pipeline project's critical path is (1-2-3-5-6-8-10-12-14-15-16-17-18) possible path, and the activities lying on the critical path are (a-b-d-e-f-g-h-i-j-k). this implies that the activities (ab-d-e-f-g-h-i-j-k) cannot be delayed. any delay in critical activity will automatically delay the entire tapi pipeline project. however, other activities such as (l-m-n-o-p) can be delayed, as they do not lie on a critical path. project completion time for the tapi gas pipeline was calculated by adding up the time duration of all activities on the critical path. the results show that the tapi gas pipeline will take approximately 75 to 330.5 weeks to complete. however, this time is not consistent with a project of similar nature (malaysian peninsula gas utilization that was constructed in 1984 and is 1700 km long) that was completed in 517.43 weeks. the inconsistency in completion times may be because of many reasons, for instance, the improvement in technology during all these years and not considering all factors involved in the construction of the tapi gas pipeline. furthermore, the estimated time from peninsula gas utilization is not optimized for the construction. the estimated time for the tapi pipeline project is determined by fuzzy cpm and is optimized for completion time. 3 the network diagram is the graphical representation of the project's activities, and it is constructed based on the activities predecessors. generally, two types of network diagrams can be built: activity on arrow network diagram and activity on node network diagram. regional development through energy infrastructure: a comparison and optimization of iranpakistan-india (ipi) & turkmenistanafghanistan-pakistan-india (tapi) gas pipelines 99 table 6. activity fuzzy time for each activity of the tapi gas pipeline activity predecessor activity fuzzy time aft (in weeks) a b c d a 48 52 63 70 b a 9 13 15 20 c b 2 3 4.5 6 d b 4.5 5 5.5 7 e b, d 3.5 5 6 8 f d,e 5 6 9 12 g c,f 3 7 8 8.5 h g 5 6 7.5 9 i g,h 3 4.5 8 10 j i 1 1.5 2 3 k j 1 2 2.5 3 l c 3 5 7 9 m l 4 6 8 9 n m 3 4.5 5.5 7 o n 2 3.5 5 6 p o 3 5 6.5 9 table 7. fuzzy completion time (𝐹𝐶𝑇𝑝𝑖 ) and r (𝐹𝐶𝑇𝑝𝑖 ) values for all possible critical paths of the gas pipeline possible paths fuzzy completion time fct (pi) r-value (1-2-3-4-7-9-11-13-18) -535 -160.5 270.5 652.5 0.516 (1-2-3-5-6-8-10-12-14-15-16-17-18) -877.5 -318.5 318.5 877.5 0.486 (1-2-3-6-8-10-12-15-16-17-18) -742.5 -269.5 269.5 742.5 0.488 (1-2-3-4-10-12-14-15-16-17-18) -728 -257.5 279.5 751.5 0.493 (1-2-3-5-8-10-12-14-15-16-17-18) -810 -294 294 810 0.487 x1=min(all possible paths) -877.5 𝑅𝑚𝑖𝑛 0.485955 x2=max(all possible paths) 877.5 beta risk factor 0.473 1-beta 0.528 figure 3 activity on arrow network diagram of tapi pipeline project ali, y. et al./oper. res. eng. sci. theor. appl. 4 (3) (2021) 82-106 100 table 8. fuzzy earliest time, fuzzy latest time and fuzzy slack time for each node node fuzzy earliest time (fet) fuzzy latest time (flt) fuzzy slack time (fst) a b c d a b c d a b c d 1 0 0 0 0 -68 -25 24.5 67.5 -67.5 -25 25 68 2 48 52 63 70 2.5 38.5 76.5 116 -67.5 -25 25 68 3 57 65 78 90 22.5 53.5 89.5 125 -67.5 -25 25 68 4 59 68 82.5 96 43 70 103 136 -53 -13 35 77 5 61.5 70 83.5 97 29.5 59 94.5 129 -67.5 -25 25 68 6 61.5 70 83.5 97 29.5 59 94.5 129 -67.5 -25 25 68 7 62 73 89.5 105 52 77 108 139 -53 -13 35 77 8 65 75 89.5 105 37.5 65 99.5 133 -67.5 -25 25 68 9 66 79 97.5 114 61 85 114 143 -53 -13 35 77 10 70 81 98.5 117 49.5 74 106 138 -67.5 -25 25 68 11 69 83.5 103 121 68 90.5 118 146 -53 -13 35 77 12 73 88 106.5 125.5 58 82 113 141 -67.5 -25 25 68 13 71 87 108 127 74 95.5 122 148 -53 -13 35 77 14 78 94 114 134.5 67 89.5 119 146 -67.5 -25 25 68 15 78 94 114 134.5 67 89.5 119 146 -67.5 -25 25 68 16 81 98.5 122 144.5 77 97.5 123 149 -67.5 -25 25 68 17 82 100 124 147.5 80 99.5 125 150 -67.5 -25 25 68 18 83 102 126.5 150.5 83 102 127 151 -67.5 -25 25 68 5.3. genetic algorithm (g.a.) this study also optimizes the material and transportation costs involved in the tapi project using a genetic algorithm. in the absence of any number, we will develop a model that, if adopted, the project engineers can optimize the tapi project's transportation and material costs. we used the chelpipe firm's data (a russian company responsible for supplying pipes to the tapi gas pipeline project). it is learned that chelpipe provides customers with different packages giving them discounts as customers buy more containers, as shown in table 9: table 9 different packages along with their prices for each container quantity pricing (millions) length packages # of pipeline containers 1 meter 3 meters 5 meters 7 meters 12 meters package a 3 $ 4.50 $ 4.41 $ 4.28 $ 4.19 $ 3.96 package b 5 $ 7.35 $ 7.20 $ 6.98 $ 6.83 $ 6.45 package c 12 $ 17.10 $ 16.74 $ 16.20 $ 15.84 $ 14.94 package d 15 $ 20.25 $ 19.80 $ 19.13 $ 18.68 $ 17.55 package e 20 $ 24.00 $ 23.40 $ 22.50 $ 21.90 $ 20.40 the diameter of all the pipes is 1.42 meters. the cost values are taken by consulting experts in the oil and gas sectors. the first column in table 9 shows different packages, while the second column indicates the number of containers in that package. the remaining columns show the price of one meter, 3 meters, 5 meters, 7 meters, and 12 meters containers. for example, by analysis of package a consisting of 3 pipeline containers, a 1-meter pipe container costs $4.50 million, 3 meters pipe container costs $4.41 million, and a 5 meters pipe container costs $ 4.19 million, and 12 meters regional development through energy infrastructure: a comparison and optimization of iranpakistan-india (ipi) & turkmenistanafghanistan-pakistan-india (tapi) gas pipelines 101 pipeline containers cost $ 3.69 million. the difference in prices is due to the weight secured by each container. the cost of 12 meters container is less because most of the container's space will go to waste as the 12 meters pipes are more in length, therefore weighing less and occupying more space. however, a 1-meter pipe takes more space in the container, increasing its weight as more 1-meter pipes can be brought by stacking. this increases the cost of one container of 1-meter pipeline container. the idea is to get the required number of containers at the most minimal cost. this study optimizes the cost of purchasing 512 containers, which is the value taken randomly just to illustrate our model. table 10 below discusses the number of packages needed to satisfy the requirement of 512 containers at the cost of $562.43 million. the number of times g.a. will run the program is demonstrated by the population which was configured before running the algorithm. the more the population size, the more time it takes to find an optimized solution.4 by the analysis of results, it can be determined that eight extra containers are required, which results in more cost. therefore, if the number of iterations increases, the solution moves toward global value. like the results achieved, a genetic algorithm can be used to construct models for different parameters like the pipeline material, and pipeline length can be added to further increase accuracy. table 10. optimized cost model by genetic algorithm packages number of packages total number of containers for each packages per unit cost total cost a 5 15 $4.28 $21.38 b 1 5 $7.35 $7.35 c 0 0 $0.00 $0.00 d 0 0 $0.00 $0.00 e 25 500 $20.40 $510.00 total cost=$ pkr 538.73 million; required containers= 512; total containers from calculation: 520 the results demonstrated in table 10 can act like a typical model for minimizing cost if several companies provide different packages, rather than using sophisticated techniques like the heuristic approach and integer programming approach for cost minimization. the model illustrated above can help engineers optimize the tapi gas pipeline's material and transportation cost using the above model. furthermore, the model allows engineers to achieve prices close to the global solution by increasing the number of iterations. 4 we used a population size of 20; the genetic algorithm results can be presented on request for interested readers. ali, y. et al./oper. res. eng. sci. theor. appl. 4 (3) (2021) 82-106 102 6. conclusion the study is based on the feasibility comparison of the ipi and tapi projects. as pakistan's energy demand is on the rise and there is a considerable supply-demand gap, these projects are essential for pakistan's future energy needs. the study used a fuzzy set-based topsis (a fuzzy mcdm) model to compare the two models and concluded that ipi is more beneficial to pakistan than tapi. furthermore, since more work is ongoing on tapi rather than on ipi, the study applied the fuzzy critical path method on the tapi project to identify the project's critical activities. finally, the genetic algorithm application is applied to a scenario for the tapi gas pipeline that could be easily extended to a more realistic situation to optimize the material and transportation cost. the approach can help with the reduction of the material and transportation cost significantly. there are several implications of this study. for instance, pakistan is focused on tapi mainly, whereas ipi is the project it must consider based on power generation capacity, transportation cost, transit fee and gas prices comparison of both projects. therefore, this study recommends that the decision-makers in pakistan explore the ipi project, especially in the recent geopolitical development. because china also became a significant buyer from iran. there are some reports of china showing interest in the ipi project (pradhan, 2020). pakistan may work on bringing china on board for this project; this will help meet china's energy demand for the future and make the ipi project economically more beneficial for pakistan. the participation of china can help to nullify the global pressure against this project. similarly, the study identifies the approximate time of accomplishing the tapi gas project as about 75 to 330.5 weeks. these are useful information for policymakers working on the tapi projects at the national level. furthermore, the approach of this study can be adapted by the policymakers for comparing such projects globally. the study is based on mcdm analysis and sample size does not matter much for such studies, however, it would have been better to have a sample from experts across multiple countries except only from pakistan. this would have enriched the analysis. some other factors such as consideration of afghanistan under taliban (as of 2021) may pose a big challenge for prospects of tapi. future studies on these projects must give due 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optimization of iran-pakistan-india (ipi) & turkmenistanafghanistan-pakistan-india (tapi) gas pipelines yousaf ali 1*, manzoor ahmad2, muhammad sabir 3, sajjad ali shah2 1. introduction 2 literature review 2.1 the literature on ipi and tapi projects 2.2 research methods used for studying ipi and tapi projects 3 tapi and ipi: background 3.1 turkmenistan-afghanistan-pakistanindia (tapi) gas pipeline project 3.2 iran-pakistan-india (ipi) gas pipeline project 3.3 comparison of tapi and ipi projects 4. research methodology and data 4.1. fuzzy technique for order preference by similarity to ideal solution 4.2. fuzzy critical path method (fcpm) 4.3. genetic algorithm 4.4. data collection 5. results and discussion 5.1. results from fuzzy topsis 5.2. fuzzy cpm 5.3. genetic algorithm (g.a.) 6. conclusion references plane thermoelastic waves in infinite half-space caused operational research in engineering sciences: theory and applications vol. 4, issue 3, 2021, pp. 142-175 issn: 2620-1607 eissn: 2620-1747 doi: https://doi.org/10.31181/oresta111221142c * corresponding author. cetinkaya@cankaya.edu.tr (f. c. çetinkaya), mehmet.duman@neu.edu.tr (m. duman) scheduling with lot streaming in a twomachine re-entrant flow shop ferda can çetinkaya 1*, mehmet duman 2 1 department of industrial engineering, çankaya university, ankara, turkey 2 nerita, near east university, trnc, mersin 10, turkey received: 16 august 2021 accepted: 24 november 2021 first online: 11 december 2021 research paper abstract: lot streaming is splitting a job-lot of identical items into several sublots (portions of a lot) that can be moved to the next machines upon completion so that operations on successive machines can be overlapped; hence, the overall performance of a multi-stage manufacturing environment can be improved. in this study, we consider a scheduling problem with lot streaming in a two-machine re-entrant flow shop in which each job-lot is processed first on machine 1, then goes to machine 2 for its second operation before it returns to the primary machine (either machine 1 or machine 2) for the third operation. for the two cases of the primary machine, both single-job and multi-job cases are studied independently. optimal and near-optimal solution procedures are developed. our objective is to minimize the makespan, which is the maximum completion time of the sublots and job lots in the single-job and multijob cases, respectively. we prove that the single-job problem is optimally solved in polynomial-time regardless of whether the third operation is performed on machine 1 or machine 2. the multi-job problem is also optimally solvable in polynomial time when the third operation is performed on machine 2. however, we prove that the multi-job problem is np-hard when the third operation is performed on machine 1. a global lower bound on the makespan and a simple heuristic algorithm are developed. our computational experiment results reveal that our proposed heuristic algorithm provides optimal or near-optimal solutions in a very short time. key words: scheduling, lot streaming, two-machine, re-entrant flow shop, makespan. 1. introduction manufacturing systems vary from a simple one-stage environment to more complex environments, such as a general job shop system, where jobs have different routings through multiple stages. since the well-known efficient scheduling algorithm for the basic two-machine flow shop system, in which the flow of each job scheduling with lot streaming in a two-machine re-entrant flow shop 143 is the same, was proposed by johnson (1954), scheduling problems in different and more complicated manufacturing environments have been extensively studied. the re-entrant flow shop, which is a relatively new flow shop manufacturing environment, has drawn researchers’ attention. in the re-entrant flow shop, a job has to re-visit some of the machines since the number of operations for each job is more than the number of machines (lev & adiri, 1984). we observe re-entrant re-entrant flow shops can be observed mainly in textile and high-tech industries, such as printing printed circuit boards, wafer fabrications, and signal processing. in all of the studies in the literature for the re-entrant flow shops and most of the scheduling studies for the other multi-stage manufacturing systems, it is assumed that jobs are indivisible entities. thus, an operation of a job-lot (i.e., a process batch) consisting of identical units must be finished before it this job lot is transferred to the next machine. however, in many industrial applications, a job lot can be split into several sublots (i.e., transfer batches), which are the partial batches of the process batch. transfer of the processed sublots to downstream machines without waiting for the completion of the whole job-lot on a machine gives an opportunity of allows the operations overlapping to overlap. the process of simultaneously splitting a joblot into sublots and scheduling those sublots by overlapping their operations is known as lot streaming, which was first mentioned as a scheduling technique by reither (1966). in this paper, we consider a scheduling problem with lot streaming in a twomachine re-entrant flow shop where each job-lot is processed first on machine 1, then goes to machine 2 for its second operation before it returns to the primary machine (either machine 1 or machine 2) for the third operation. we first focus on the single-job problem where a job-lot is spilt split into a given number of consistent or variable sublots. consistent sublots case is the case where the size of each sublot does not change over the machines. however, the sublot sizes may change vary over the machines when variable sublots are used. next, we extend the problem to the multi-job case in which the size of sublots and the schedule of multiple sublots and job lots need to be determined simultaneously. our objective is to minimize the makespan, equivalent to the time to complete the last sublot in the single-job case, whereas it is the time to complete the last job lot in the multi-job case. makespan aims to increase the utilization of the machines in the shop. to the best of our knowledge, our study is the only one that applies lot streaming for singleand multijob cases in the re-entrant flow shops. the organization of the remaining parts is as follows. the following section presents a literature review on lot streaming problems, especially those in twoand three-machine manufacturing shops. in section 3, the single-job problem is studied, and the optimal schedules with consistent and variable sublots are developed. section 4 considers the multi-job lot streaming problem and gives an exact algorithm that determines the optimal consistent-sublot sizes and job schedules when the primary machine is machine 2. next, the multi-job lot streaming problem, in which the primary machine is machine 1, is proved to be strongly np-hard, and a polynomial-time solvable case of the problem is provided. moreover, a heuristic algorithm is provided for the multi-job problem where the primary machine is machine 1, and its effectiveness is computationally tested. finally, our brief conclusions and some issues for future research are summarized in section 5. çetinkaya & duman /oper. res. eng. sci. theor. appl. 4 (3) (2021) 142-175 144 2. literature review although lot steaming is known and used in practice, there were no analytical studies in the literature of scheduling problems until the late ‘80s. since then, lot streaming has attracted significant interest from researchers dealing with scheduling problems. based on the number of job lots, the studies in the literature can be divided into two categories. one category is called the single-job lot problem and deals with the sublot-sizing problem in which the sublot sizes are determined when there is a single job lot. the other category is called multi-job problem and deals with the sublotsizing and job-sequencing subproblems simultaneously. here, we limit our literature review to the lot streaming studies for the singleand multi-job lot cases in twoand three-machine manufacturing shops only to expose the proper place of our study in the literature. the study by baker (1988) is the first one considering the lot streaming technique for a single-job problem in twoor three-machine flow shops to minimize the makespan. for the two-machine case, he provided a linear programming model and determined the sublot sizes optimally. he also determined the optimal sublot sizes for the three-machine case where the job-lot is split into two sublots only. potts & baker (1989) proved that optimal sublots are consistent in the two-machine flow shop and illustrated that the consistent sublots are not always optimal for the flow shops with three and more machines. glass et al. (1994) developed an algorithm that determines the optimal consistent-sublot sizes for the three-machine flow shop to minimize the makespan. this study was extended to the cases with sequenceindependent detached and attached setups by chen & steiner (1997) and chen & steiner (1998), respectively. in the attached setup case of a machine, the first sublot belonging to a job lot should be available before setting up this machine. however, in the detached setup case, no need to wait for the arrival of the job lot. in both cases, no setup is necessary between successive sublots of the same job lot. in both cases, no setup is necessary between successive sublots of the same job lot. on the other hand, variable sublots case of the single job-lot problem was first examined by trietsch (1989). the optimal solution with variable sublots in the three-machine flow shop was proposed by trietsch & baker (1993). alfieri et al. (2012) and alfieri et al. (2021) proposed exact, and heuristic solution approaches based on dynamic programming for a single-job problem to minimize the makespan and total flow time, respectively, in a two-machine flow shop with attached setup times. vickson & alfredson (1992) considered the concept of lot streaming for scheduling multiple job lots in flow shops. they demonstrated that a modified johnson’s algorithm with unit-sized sublots solves the two-machine makespan minimization problem when the number of sublots in each jot-lot is unlimited and proved that sublots in each job-lot should be processed successively without the intermingling of different job lots. vickson & alfredson’s study was extended by çetinkaya & kayalıgil (1992) to develop a unified algorithm that treats sequenceindependent attached and detached setups. çetinkaya (1994) considered the scheduling of multiple job lots in a two-machine flow shop with attached setup and removal times on the machines and proved that the optimal schedule of the job lots to minimize the makespan is obtained by determining the equal or unequal sublots sizes of each job-lot independently and sequencing the job lots by a modified scheduling with lot streaming in a two-machine re-entrant flow shop 145 johnson’s algorithm. vickson (1995) provided an optimal solution for the multi-job problem in a two-machine flow shop with sequence-independent attached or detached setups and transfer times from the first machine to the second one. pranzo (2004) extended çetinkaya’s study by considering limited buffers between machines. glass & possani (2011) considered the two-machine flow shop problem with attached setup and transportation times to minimize the makespan of the multiple job lots. their study showed that sublot-sizing and job-sequencing problems are solved independently, as in çetinkaya (1994) and vickson (1995), and provided an algorithm solvable in polynomial time. baker (1995) considered the multi-job problem with equal-sized sublots and setup times in a two-machine flow shop and proposed an algorithm using the time-lag approach. yang & chern (2000) extended baker’s study to where detached setup times, transportation times, and removal times exist. sriskandarajah & wagneur (1999) investigated the multi-job problem in a two-machine flow shop with no-wait constraint. çetinkaya (2005) considered a two-machine flow shop with a single agent transferring a completed item from machine 1 to machine 2. machine 1 is blocked while the transport agent is in transferring and returning. he provided an algorithm that determines the optimal schedule for the case with unit-sized sublots. from the early 2000s, researchers began to consider flow shops with more than three machines (stages). several metaheuristic algorithms, such as genetic algorithms (yoon & ventura, 2002; marimuthu et al., 2008; martin, 2009; defersha & chen, 2010), discrete particle swarm optimization algorithm (tseng & liao, 2008), threshold accepting and ant-colony optimization algorithms (marimuthu et al., 2009), discrete artificial bee colony algorithm (pan et al., 2011), and migrating birds optimization algorithm (devendra et al., 2014; meng et al., 2018) have been proposed to solve the multi-job lot streaming problem by considering its different aspects. all the studies mentioned above for the multi-job scheduling with lot streaming in the flow shops with more than three machines assume that sublots in each job lot should be processed successively for each operation on each machine. i.e., the intermingling of the job lots is not allowed, and the schedules are permutation schedules where the sequence of job lots on all machines is the same. however, a more realistic case is when intermingling of the job lots and non-permutation schedules are allowed. feldmann & biskup (2008) investigated the permutation flowshop scheduling problem with lot streaming and intermingling and developed a mixed-integer programming model. rossit et al. (2016) investigated this nonpermutation flowshop scheduling problem with lot streaming. they proposed a mathematical model to minimize the makespan of the multiple job lots that are not allowed to be intermingled. besides the studies mentioned above, lot streaming studies for other twoand three-machine manufacturing shops are scarce. there are studies considering open shops (şen & benli, 1999), hybrid flow shops (kim et al., 1997; zhang et al., 2003; zhang et al., 2005; liu, 2008; defersha, 2011; defersha & chen, 2012a; naderi & yazdani, 2015; cheng et al., 2016; zhang et al., 2017; wang et al., 2019; li et al., 2020), and mixed shops (çetinkaya & duman, 2010), job shops (buscher & shen, 2009; defersha & chen, 2012b), and assembly shops (sarin et al., 2011; yao & sarin, 2014; nejati et al., 2016; cheng & sarin, 2020). çetinkaya & duman /oper. res. eng. sci. theor. appl. 4 (3) (2021) 142-175 146 the comprehensive surveys by chang & chiu (2005), sarin & jaiprakash (2007), gomez-gasquet et al. (2013), and cheng et al. (2013), and salazar-moya & garcia (2021) are also available for lot streaming problems with job lots having more than one operation in multiple machines environments. as we can see from the lot streaming literature and to the best of our knowledge, there is no previous study dealing with lot streaming for singleand multi-job cases in the re-entrant flow shops. the main contributions of our study can be summarized as follows: • this study is the first one in the scheduling literature dealing with lot streaming in the re-entrant flow shops. • our study proves that the single-job problem is polynomial-time solvable regardless of whether the third operation is performed on machine 1 or machine 2 and develops optimal schedules with closed formulae for the optimal consistent and variable sublot sizes. • our study also proves that the multi-job problem is polynomial-time solvable when the third operation is performed on machine 2 and develops optimal schedules with closed formulae for the optimal sublot sizes. however, the multi-job problem is np-hard when the third operation is performed on machine 1. • a global lower bound on the makespan and a simple heuristic algorithm providing optimal or near-optimal schedules have been developed. 3. single-job case our single-job problem in the two-machine re-entrant flow shop is explained as follows: a job-lot of u identical items has three operations to be performed. each operation k )3,2,1( =k requires kp time units of processing. there are two machines 1m (machine 1) and 2m (machine 2) operating independently. the first and second operations of the job-lot are performed on 1m and 2m , respectively. a primary machine ( 1m or 2m ) is re-visited by each item of the job lot for its third operation; hence the shop is a re-entrant flow shop. the job-lot is split into s sublots, and kix , is the size of the i th sublot that completes its k th operation. sublots of a job-lot can be immediately transferred from one machine to another for their next operation without waiting to complete other sublots. the goal is to determine the size and schedule of all sublots to minimize the makespan, which is the time to complete the third operation of the sublot processed as the last. the assumptions made for the single-job problem are summarized here: • the sublots of a job lot are processed without any interruption on every machine. i.e., pre-emption is not allowed. • each machine is ready at the beginning, say time zero, of the planning horizon. i.e., machines are not batching machines. • at any time, only one item of a job lot can be processed by a machine. • an unlimited storage space exists between the machines. • an idle time on a machine may occur between processing sublots. scheduling with lot streaming in a two-machine re-entrant flow shop 147 • transfer times from one machine to another are negligibly so short and thus ignored. • setup times before processing the job-lot on a machine are negligibly so short and thus ignored. • the number of sublots is known in advance and fixed from one machine to another. • processing times are known and deterministic. 3.1. machine 2 is the primary machine we first consider that 2m is the primary machine where the third operation is performed. we investigate the problem for cases with consistent and variable sublots. 3.1.1. consistent sublots when the lot streaming is applied, sometimes there might be no advantage to change the size of the sublots after they have completed their processing on a machine. in this situation, it is reasonable to let the sublot sizes be constant (consistent) over all pairs of operations, i.e., iki xx =, for 1, 2,..., ; 1, 2, 3i s k= = where ux si i = 1 . sublot availability assumption is used when sublots are consistent. i.e., a sublot can be processed at the next machine if all items in this sublot are completed on the current machine. we start our analysis with the following lemma. lemma 1. for the single-job problem where 2m is the primary machine, it is sufficient to consider schedules of sublots where the last two operations of the sublots are processed consecutively on 2m . proof. consider any schedule of the consistent sublots. suppose that there is a pair of sublots u and v , where the second operation of sublot v is immediately processed before the third operation of sublot u on 2m . then interchanging the positions of sublots u and v on 2m is feasible and does not increase makespan. on machine 2m , when all sublots, which are immediately processed before sublot u , are pair-wise interchanged with the second operation of sublot u , then it is possible to consecutively process the second and the third operations of sublot u on 2m . similarly, it is possible to schedule consecutively the second and the third operations of all sublots on 2m . from lemma 1, the single-job problem can be illustrated by a network, as shown in figure 1. let 1 2( , ,..., )sx x x x= denote the sublot sizes, and ( , )k i be a node for the pair with operation k ( 1, 2, 3)k = and sublot i ( 1,..., )i s= where k ip x is the processing time of the k th operation of sublot i . the vertical arc from node (1, )i to node (2, )i indicates that sublot i cannot be processed on 2m unless it is completed on 1m . the horizontal arc from node (1, )i to node (1, 1)i + indicates that 1m can çetinkaya & duman /oper. res. eng. sci. theor. appl. 4 (3) (2021) 142-175 148 start to process sublot 1i+ upon the completion of sublot i on 1m . similarly, the horizontal arc from (2, )i to (3, )i represents that the third operation of sublot i can be started when its second operation is completed on 2m . figure 1. network representation for the case where 2m is the primary machine here, the goal is to determine the sublot sizes minimizing the critical path (longest path) length from node (1, 1) to (3, )s , in which the sum of the processing times of the nodes on the critical path gives the length of the critical path. the following theorem gives the optimal sublot sizes for the single-job problem where 2m is the primary machine. theorem 1. for the single-job problem where 2m is the primary machine, the optimal consistent-sublot sizes are 2 1 1 /(1 ... ) s x u    − = + + + + , 1 1 xx i i − = for si ,...,2= where ( ) 132 / ppp += , 1 ii su x =  , and the associated optimal makespan is ( )2 1max 1 1 2 3 1 2 31( ) /(1 ... ) ( ) s s ii c p x p p x p p p u   − = = + + = + + + + + + . proof. see the appendix a. ■ theorem 1 proves that the single-job problem where 2m is the primary machine is equivalent to the single-job problem in the basic two-machine flow shop with processing times 1p and 32 pp + on 1m and 2m , respectively. from theorem 1, it is clear that the optimal consistent-sublot sizes can be determined in ( )o s time. example 1. in this numerical example, we illustrate theorem 1, in which the consistent sublots are optimal. suppose that we have a job lot of 70 identical items that will be split into three sublots, and the processing times for its three operations are 2, 3, and 1 time-units, respectively. then, from theorem 1, we determine that the sublot sizes are found to be 10, 20, and 40 units for the first, second, and third sublots, respectively. that is, 2 1 3 1 1 /(1 ... ) 70/(1 2 2 ) 10 s x u    − − = + + + + = + + = , 2x = 1 12 (2)(10) 20x = = , and 2 3 1 2 (4)(10) 40x x= = = , where 2 3 1( ) / (3 1) / 2p p p = + = + 2= . the optimal makespan is max 1 1 2 3( ) (2)(10) (3 1)(70) 300c p x p p u= + + = + + = , as illustrated in figure 2. 3.1.2. variable sublots in some cases, there might be some advantages to change the size of the sublots after they have completed their processing on a machine. thus, variable sublots are 11xp 12xp 21xp 22xp sxp2 sxp3 13xp 23xp sxp1 1m 2m 31xp 32xp scheduling with lot streaming in a two-machine re-entrant flow shop 149 preferred to the consistent sublots, using the item availability assumption where an individual item in a sublot can be processed at the next machine when this item is completed on the current machine. figure 2. optimal schedule of the sublots in example 1 remark 1. there is no need to investigate the optimal solution for the single-job problem having variable sublots in the two-machine re-entrant flow shop where 2m is the primary machine. the solution of the single-job problem having consistent sublots is also optimal for the single-job problem having variable sublots since only one set of sublot transfers from 1m to 2m is needed when the second and third operations are performed on 2m . 3.2. machine 1 is the primary machine we now consider that 1m is the primary machine where the third operation is performed. we again investigate the problem for cases with consistent and variable sublots. 3.2.1. consistent sublots similar to the analysis given by wang et al. (1997) for the basic two-machine reentrant flow shop makespan minimization problem without lot streaming, we present the following lemma and theorem for finding the optimal solution to our problem having consistent sublots when 1m is the primary machine. we first give the following definitions. definition 1. a schedule is called a compact schedule if the first operations of all sublots are scheduled successively on 1m and then followed by the third operations of all sublots. definition 2. a schedule is called a permutation schedule if all sublots are processed in the same order on both machines. lemma 2. for the single-job problem where 1m is the primary machine, it is sufficient to consider only compact and permutation schedules of the sublots. proof. consider any feasible schedule  with consistent sublots. we first show that  can be transformed into a compact schedule on 1m without worsening the makespan. suppose we have a pair of two sublots, u and v , where the last (third) operation of sublot u immediately precedes the first operation of sublot v on 1m , i.e., 1,3, vu oo  . then interchanging their positions does not worsen the makespan. 60 50 300 260 140 140 120 60 2 20 20 2m 1m 1 2 3 1 1 2 3 3 çetinkaya & duman /oper. res. eng. sci. theor. appl. 4 (3) (2021) 142-175 150 when all sublots, which immediately follow sublot u , are pair-wise interchanged with sublot u , we assume that all first operations of the sublots are scheduled first on 1m . if any, we may eliminate the idle time between the first operations of any pair of successive sublots by moving the start time of the second sublot in the pair to the left. this movement does not affect the feasibility and does not change the makespan. now, assume that an idle time exists between the last operations of any pair of successive sublots. then we can eliminate it by moving all sublots except the last to the right. again, this movement does not affect the feasibility and does not change the makespan. this shows that the first and the last operations of the job-lot are performed continuously without idle time between the sublots on 1m . now, consider any optimal schedule  , which is compact on 1m but in which the processing order of the sublots on the first pair ),( 21 mm of machines is different. let sublots u and v be the first pair of sublots such that 2,1, vu oo  and ,2 ,2 v uo op . let sublots u and v be the last pair of sublots such that 1,1, vu oo  and 2,2, uv oo  . interchanging the order of 2,uo and 2,vo is possible and maintains compactness on 1m , and the makespan remains unchanged. this indicates that an optimal schedule, which is compact and the processing order of the sublots on the last pair ),( 12 mm of machines is the same, exists. theorem 2. let maxc and maxc denote the optimal makespan values of the single-job problem having consistent sublots in the two-machine re-entrant flow shop where 1m is the primary machine and the single-job problem having consistent sublots in the basic three-machine flow shop, respectively. if max 1 31 ( ) s ii c p p x =   + = 1 3( )p p u+ then maxmax cc = ; otherwise, uppc )( 31max += . proof. the single-job problem where 1m is the primary machine can be represented by a network, as illustrated in figure 3. let ),...,,( 21 sxxxx = denote the sublot sizes and ),( ik be a node for the pair with operation k )3,2,1( =k and sublot i ),...,1( si = , having a weight of ikxp that represents the sublot processing time. the vertical arc from node ) ,1( i to node ) ,2( i indicates that sublot i can be processed on 2m upon its completion on 1m . the horizontal arc from node ) ,1( i to node )1 ,1( +i indicates that 1m can start to process sublot 1i+ upon the completion of sublot i on 1m . similarly, the vertical arc from ) ,2( i to ) ,3( i represents that the third operation of a sublot can be started when the second operation is completed on 2m . in view of lemma 2, we observe that the precedence constraint of arc between ) ,1( s and )1 ,3( becomes redundant if uppc )( 31max + . thus, an idle time on 1m exists between the first operation of the last sublot and the third operation of the first sublot. however, if the arc between ) ,1( s and )1 ,3( is removed from the network )(xn , the new network then represents the lot streaming problem in the three-machine flow shop. therefore, it is clear that  max max 1 3max , ( )= +c c p p u . it is obvious that max max =c c when max 1 3 ( )  +c p p u . thus in this case, the lot streaming problems in scheduling with lot streaming in a two-machine re-entrant flow shop 151 the basic three-machine flow shop and the two-machine re-entrant flow shop are equivalent. however, max 1 3 ( )= +c p p u when max 1 3 ( )c p p u  + . ■ as a result of theorem 2, an optimal solution to the single-job problem where 1m is the primary machine can be constructed by the optimal solution proposed by glass et al. (1994) for the single-job problem having consistent sublots in the basic threemachine flow shop, as in the following corollary. figure 3. network representation for the case where 1m is the primary machine corollary 2. when the makespan is minimized, the optimal consistent-sublot sizes for the single-job problem in the basic three-machine flow shop are also optimal for the single-job problem having consistent sublots in the two-machine re-entrant flow shop where 1m is the primary machine, and they are as follows: (i) if 31 2 2 ppp  , then the optimal sublot sizes are: / )1/()1( 31 31 1         = −− = ppifsu ppifu x s  , 1 1 xx i i − =  for si 2 where 2 3 1 2( )/( )p p p p = + + . (ii) if 31 2 2 ppp  , then there exists a crossover sublot h , which can be determined by a search algorithm in )(log so time, for which the optimal sublot sizes are:           = =  −+−− −−+− −−−+−− = +− +− 3221 3221 3221 1 1 , , , })1/()1/{( )}1/()1(1/{ }1)1/()1()1/()1/{( ppppif ppppif ppppif hsu hu u x h hs hsh h    , h ih i xx − = for 11 − hi , h hi i xx − = for sih  where 21 / pp= and 23 / pp= . example 2. assume that we have a job lot of 70 identical items that will be split into three sublots, and the processing times for its three operations are 1, 4, and 2 timeunits, respectively. this case corresponds to the second case in corollary 2 since 2 2 p = 2 1 3 (4) 16 (1)(2) 2p p=  = = . the size of the crossover sublot h is determined 11xp 21xp 11 −sxp sxp1 1m 12xp 22xp sxp2 2m 12 −sxp 13xp 23xp 13 −sxp sxp3 1m çetinkaya & duman /oper. res. eng. sci. theor. appl. 4 (3) (2021) 142-175 152 by 1 /{( 1) /( 1) ( 1) /( 1) 1} h s h h x u     − + = − − + − − − where 4/1/ 21 == pp and 3p = 2 / 1/ 2p = since 1 2 3 1 4 2p p p=  =  = . when 1=h , 1 1 3 1 1 1 1 1 (1/ 4) 1 (1/ 2) 1 / 1 70 / 1 1 1 (1/ 4) 1 (1/ 2) 1 h s h x u     − + − +   − − − − = + − = + − =      − − − −    70 40 1.75 = , 20)40()2/1( 1 1 12 2 === − xx  , 10)40()2/1( 2 1 13 3 === − xx  , and 340max =c . when 2=h , 1 2 3 2 1 2 1 1 (1/ 4) 1 (1/ 2) 1 / 1 70 / 1 1 1 (1/ 4) 1 (1/ 2) 1 h s h x u     − + − +   − − − − = + − = + − =      − − − −    70 40 1.75 = , 10)40()4/1( 1 1 12 1 === − xx  , 20)40()2/1( 1 1 23 3 === − xx  , and 330max =c (see figure 4a). when 3=h , 1 3 3 3 1 3 1 1 (1/ 4) 1 (1/ 2) 1 / 1 70 / 1 1 1 (1/ 4) 1 (1/ 2) 1 h s h x u     − + − +   − − − − = + − = + −       − − − −    53.33 , 33.3)33.53()4/1( 2 1 13 1 === − xx  , 33.13)33.53()4/1( 1 1 23 2 === − xx  , and 390max =c . it is clear that the optimal sublots are achieved when 2=h , and their sizes are 101 =x , 401 =x , and 203 =x . note that the optimal makespan is 330maxmax == cc since max 1 3 330 ( ) (1 2)(70) 210 =  + = + =c p p u , and the optimal schedule is obtained by carrying the third operations of the sublots in the three-machine flow shop problem to 1m , as illustrated in figure 4b. figure 4. optimal schedules with consistent sublots for the single-job problem in example 2: (a) three-machine flow shop; (b) two-machine re-entrant flow shop. 10 50 70 50 70 210 290 330 10 50 210 290 10 50 70 190 210 290 330 1m 2m 1 2 3 1 1 2 3 2 3 10 50 210 290 2m 1m 3m 3 1 2 3 (a) (b) 2 1 1 2 3 scheduling with lot streaming in a two-machine re-entrant flow shop 153 3.2.2. variable sublots as a result of theorem 2, an optimal solution to the single-job problem having variable sublots where 1m is the primary machine can be constructed by the optimal solution proposed by trietsch & baker (1993) for the single-job problem with variable sublots in the basic three-machine flow shop, as in the following corollary. corollary 3. when the makespan is minimized, the optimal variable-sublot sizes in the single-job problem in the basic three-machine flow shop are also optimal for the singlejob problem having the variable sublots in the two-machine re-entrant flow shop where 1m is the primary machine, and they are as follows: (i) if 31 2 2 ppp  , then the consistent sublots are optimal, and they are: 1 ( 1)/x u = − ( 1)s − , 1 1 xx i i − =  for si 2 where )/()( 2132 pppp ++= . (ii) if 31 2 2 ppp  , then the variable sublots are optimal, • the optimal sublot sizes between 1m and 2m are: )1/()1(1 −−= s ux  , 1 1 xx i i − = for si 2 where 12 / pp= , and • the optimal sublot sizes between 2m and 1m are: )1/()1(1 −−= s ux  , 1 1 xx i i − =  for si 2 where 23 / pp= . from corollary 3, it is clear that the optimal variable-sublot sizes can be determined in ( )o s time. example 3. in this numerical example, we illustrate the second case of corollary 3, in which the variable sublots are optimal since 31 2 2 ppp  . assume that we have a job lot of 15 identical items that will be split into two sublots, and the processing times for its three operations are 1, 2, and 1 time-units, respectively. from corollary 2, the sublot sizes between 1m and 2m are found to be 5)12/()12(15 2 1 =−−=x and 10)5)(2( 1 2 ==x where 21/2/ 12 === pp and ).1)(1(4)2( 31 22 2 === ppp (see figure 5a). similarly, the sublot sizes between 2m and 1m are calculated as 2 1 15((1/ 2) 1) /((1/ 2) 1) 10x = − − = and 5)10)()2/1(( 1 2 ==x since 2/1/ 23 == pp . thus, the optimal makespan of the problem having variable sublots in the basic three-machine flow shop is 40, and the optimal schedule of the problem in the twomachine re-entrant flow shop is obtained by carrying the third operations of the sublots in the optimal schedule of the problem in the three-machine flow shop to 1m , as illustrated in figure 5b. 4. multi-job case in this section, we extend our problem presented to the multi-job case. the multijob problem is explained as follows: there is a job-lot set  njjj ,...,2,1== where each job-lot has ju identical items of type j . let kjp , be the processing time for çetinkaya & duman /oper. res. eng. sci. theor. appl. 4 (3) (2021) 142-175 154 k th ( )3,2,1=k operation of job-lot j . there are two machines 1m and 2m . each job-lot is processed first on 1m , on 2m for its second operation before returning to the primary machine ( 1m or 2m ) for the third operation. suppose that job-lot j is split into js sublots, then our goal is to determine the sublot sizes for each job-lot and the schedule of all sublots and job lots to minimize the makespan. figure 5. optimal schedules with variable sublots for the single-job problem in example 3: (a) three-machine flow shop; (b) two-machine re-entrant flow shop. for the multi-job problem, we consider all assumptions made for the single-job problem. furthermore, we do not allow the intermingling of different job lots. that is, once a sublot of a job-lot is started on a machine, all other job lots should wait until all of the remaining sublots of that job-lot are completed on the same machine. note that intermingling the sublots belonging to different job lots may further reduce the makespan, but we focus on the no-intermingling case in our study. intermingling can be considered in a future study as future research, as we point out in section 5. as in the case of the single-job problem, we investigate two cases associated with the primary machine. 4.1. machine 2 is the primary machine the following lemma gives the basic structure of the job-sequence for the multijob problem where 2m is the primary machine. 25 (a) (b) 35 5 25 40 15 5 35 25 2m 1m 1 2 1 2 1 2 1 2 35 5 25 40 15 5 35 2m 1m 1 2 1 2 1 2 1 2 scheduling with lot streaming in a two-machine re-entrant flow shop 155 lemma 3. for an optimal solution of the multi-job problem where 2m is the primary machine, it is sufficient to consider the job-sequence in which the last two operations of each sublot belonging to a job-lot are processed successively on 2m . proof. omitted since it is similar to the proof of lemma 1. ■ the multi-job problem where 2m is the primary machine can be decomposed into two sub-problems: (a) the job-sequencing and (b) the sublot-sizing. 4.1.1. job-sequencing sub-problem the multi-job problem reduces to the determination of the optimal sequence of job lots when the sublot-sizing sub-problem for each job-lot has already been solved. that is, the job-sequencing sub-problem needs to be solved. suppose that each joblot j is independently split into sublots by corollary 2 or corollary 3. let jri = time lag between the start of the first operation on 1m and the latest start time of the second operation on 2m for job-lot j . i.e., the latest delay time, simply called run-in-delay for job-lot j on 2m without affecting the completion time of job-lot j (called as run-in delay for operation 2). jro = time lag between the completion times of the first and the second operations for job-lot j (called as run-out delay for operation 2). jir  = time lag between the latest start of the second operation on 2m and the latest start time of the third operation on 1m for job-lot j . i.e., the latest delay time, simply called run-in-delay for job-lot j on 1m without affecting the completion time of job-lot j (called as run-in delay for operation 3). jor  = time lag between the completion times of the second and the third operations for job-lot j (called as run-out delay for operation 3). the following theorem provides the optimal solution to the job-sequencing subproblem. theorem 3. given the solution of the sublot-sizing sub-problem, job-lot v precedes job-lot z in an optimal job-sequence if    vzzv rorirori ,min,min  , where jri =   1 1 ,1 , ,2 ,3 ,1 1 min ( ) j i i i s j j r j j j rr r p x p p x −   = = − +  , and ,2 ,3 ,1( )j j j j j jro ri p p p u= + + − for any job-lot j . proof. see the appendix b. ■ 4.1.2. sublot-sizing sub-problem the sublot-sizing sub-problem needs to be solved for each job-lot when the jobsequencing sub-problem has already been solved. the following theorem provides the optimal solution to the sublot-sizing sub-problem. çetinkaya & duman /oper. res. eng. sci. theor. appl. 4 (3) (2021) 142-175 156 theorem 4. given the solution of the job-sequencing sub-problem, the optimal sublot sizes in a job-lot processed in position  j of the job-sequence are     2 ,1 /(1  = + + j j x u   1 ... ) − + + s j ,    1, 1 , j i ij xx − = for  jsi ,...,2= where      1,3,2, /)( jjj ppp += . proof. see the appendix c. ■ from theorems 3 and 4, we have the following result. corollary 4. solving the sublot-sizing sub-problem using theorem 4 and then solving the job-sequencing sub-problem using theorem 3 provides the optimal solution to the multi-job problem where 2m is the primary machine. based on corollary 4, we propose the following exact-solution algorithm with a computational complexity of )log( nno to solve the multi-job problem where 2m is the primary machine and n is the total number of job lots. algorithm 1. step 1: [sublot-sizing] calculate the size for each sublot of the job-lot in the set  1, 2,...,j j j n= = as 12 ,1 / (1 ... ) j s j jx u    − = + + + + and 1, ,1 i j i jx x − = for 2,..., ji s= where ,2 ,3 ,1( ) /j j jp p p = + . step 2: [job-sequencing] (a) set 12 ,1 /(1 ... ) j s j j jri p u    − = + + + + and ,2 ,3(j j j jro ri p p= + + − ,1)j jp u . (b) to obtain the job-sequence    1, 2,..., = =j j n , consider all jobs in the job-lot set j and apply johnson’s algorithm with processing times on 1m and 2m replaced by jri and jro , respectively. (ii) calculate the associated makespan as    ( )       1 max 1 ,2 ,31 1 1 max ( ) w w n w n j j j j jj j j c ri ro p p u      −   = = = = − + +   4.2. machine 1 is the primary machine this section considers the multi-job problem where 1m is the primary machine. unfortunately, this problem is more complicated than the multi-job problem where 2m is the primary machine discussed in section 4.1. theorem 5. the multi-job problem where 1m is the primary machine is np-hard in the strong sense. proof. suppose that each job-lot has one sublot only. this special case of our multijob problem is equivalent to the multi-job problem without lot streaming in the basic two-machine re-entrant flow shop where 1m is the primary machine. it has been scheduling with lot streaming in a two-machine re-entrant flow shop 157 proven by wang et al. (1997) that this special case is np-hard in the strong sense. thus, our multi-job problem where 1m is the primary machine is also strongly nphard. ■ the following lemma restricts our search to the compact and permutation schedules of the job lots for the optimal schedule of the multi-job problem where 1m is the primary machine. lemma 4. for an optimal solution of the multi-job problem where 1m is the primary machine, it is sufficient to consider only compact and permutation schedules of the job lots. proof. omitted since it is similar to the proof of lemma 2. ■ 4.2.1. a polynomial-time solvable case since the multi-job problem where 1m is the primary machine has been shown to be np-hard in theorem 5, an optimal algorithm solving the problem in polynomialtime is impossible. therefore, we first examine a polynomial-time solvable case of the problem that corresponds to the case, in which the sublots of all job lots are independently determined by corollaries 2 or 3 and the idle time between the first and the third operations of all jobs on 1m is zero. let ji be the idle time on 1m between the first and the third operations of job-lot j when it is independently split into sublots by corollaries 2 or 3. the following theorem provides the optimal schedule for this special case. theorem 6. if 0=ji for every job-lot j , then arbitrarily sequencing all jobs as illustrated in figure 6 is an optimal schedule for the multi-job problem where 1m is the primary machine. proof. if 0=ji for every job-lot j , there will be no idle time between the first and the third operations of job-lot j on 1m when job lots are arbitrarily sequenced. then, the time to complete all operations of job-lot j becomes ,1 ,3 ( ) j j j j t p p u= + ,1 ,3 ( ) j j j j i p p u+ = + when it is independently split into sublots, and max 1 n jj c t = = = ,1 ,31 ( ) n j j jj p p u = + becomes the optimal makespan. figure 6. optimal schedule obtained by theorem 6 nt 2t 1t 1m 2m 1 1 2 2 n n 1 2 n   çetinkaya & duman /oper. res. eng. sci. theor. appl. 4 (3) (2021) 142-175 158 4.2.2. proposed heuristic algorithm for a given job-sequence  , we define the job-lot  d such that    ,11 ,2 ,21 − =   n j jd dj c p u c where   2,dc is the time to complete the second operation of job-lot  d , and        (2,2 ,21 11,..,( ) max    = + === − = −  n j d j d ij d ij n c c p u ri   )   ( ) 1 ,21 1   − = = +  j n ji ji j ro p u where )(2 c is the completion time of all job lots in sequence  on 2m , and        1 ,2 ,2 ,2d d d dc c p u   − = − . here job-lot  d that will be used to develop the proposed algorithm is called a partition job-lot and is the first job whose second operation finishes later than the completion of all first operations on 1m (see figure 7). from the definition of the job-lot  d , it is clear that no idle time exists between job lots following job-lot  d on 2m . thus, permutation sequence  is partitioned into three subsequences:   | 1,...,bj j j= = 1d − ,   djjjd == |  , and   ndjjja ,...,,1| +==  . we propose the following heuristic algorithm with a computational complexity of )log( nno to solve the multi-job problem where 1m is the primary machine. figure 7. partition job-lot in position d of the job-sequence  algorithm 2. step 1: for each job lot j , (a) if sublots are considered as consistent, then use the sublot sizes in corollary 2; otherwise (variable sublots), use the sublot sizes in corollary 3. (b) compute the makespan jt , and idle time on 1m as ,1(j j ji t p= − + ,3 ) j j p u . step 2: divide the job-lot set j into two sets:  0|1 == jijj and   2 | 0 j j j i=  . step 3: if = 2 j , then any arbitrary sequence of job lots is optimal, and the optimal makespan is ,)( 1 3,1, * max j n j jj uppc  = += stop; otherwise, go to step 4. )(max c )(2 c 1m 2m   2,dc   2,1−dc )(1 c bj dj aj bj dj aj bj aj dj scheduling with lot streaming in a two-machine re-entrant flow shop 159 step 4: compute the run-in delays ( jri and jir  ) and run-out delays ( jro and jor  ). schedule all job lots  njjj ,...,1| == by applying johnson’s algorithm with processing times on 1m and 2m replaced by jri and jro to obtain the job-sequence   njj ,...,1| ==  . step 5: in the job-sequence  , determine the partition job-lot  d such that    ,11 ,2 ,21  − =   n j jd dj c p u c where      ( ) 1 ,2 1 11,.., max    − = == = − +  j j d i ii ij n c ri ro   ( ),21 = d jjj p u , and        dddd upcc  2,2,2,1 −=− . step 6: compute the associated makespan )(max c as:           1 max ,1 ,31 1 11,.., ( ) max , max n d j j j j j ij j ij n c p u p u ri       − = = == = + −              1 1 1 ,21 1 ,.., max j d j j i j j i ii j i d i dj d n ro p u ri ro      − − − = = = ==   + + −          ,3 n j jj d p u  = + step 7: if j n j jj uppc )()( 1 3,1,max  = += , then the job-sequence  is optimal, stop; otherwise, go to step 8. step 8: consider the job lots in   ndjjjj ad ,...,| ==  , and apply johnson’s algorithm with processing times on 1m and 2m replaced by jir  and jor  to obtain the partial job-sequence   1,...,1| +−== dnjj . step 9: set the final sequence of job lots as   ,= where   1,...,1| −== djj followed by   1,...,1| +−== dnjj . the associated makespan is           1 1 max ,1 ,31 1 1 11,.., ( ) max , max n d j j j j j j ij j i ij n c p u p u ri       − − = = = == = + −               1 1 ,21 ,.., max d j j i j j i ij i d i dj d n ro p u ri ro      − − = = ==  + + − +      ,3 n j jj d p u  = 4.2.2. lower bounds on the makespan we now develop four lower bounds on the makespan, and then we take the maximum of these lower bounds as a global lower bound, which will be used to test algorithm 2. lower bound 1. this lower bound is obtained by assuming that there will be no idle time between the first and the third operations of each job lot on 1m . thus, the natural lower bound is çetinkaya & duman /oper. res. eng. sci. theor. appl. 4 (3) (2021) 142-175 160  = += n j jjj upplb 1 3,1,1 )( , (1) which is equivalent to the total processing time of all job lots on 1m . lower bound 2. we derive the second lower bound as ( ) ( )j nj j n j jjnj oruprilb ++= ===  ,..,11 2, ,..,1 2 minmin (2) by assuming that the job lot with the minimum run-in delay for operation 2 is processed as the first job-lot in the job-sequence, 2m operates continuously without any idle time between job lots, and the job lot with the minimum run-out delay for operation 3 is processed as the last job lot in the job-sequence. lower bound 3. to derive our third lower bound, we assume that all job lots do not wait for their operations to be performed on 2m . for a sequence  , we can establish the third lower bound as       ( ) ( )j nj n ji ii j i i j i inj oruprilb +     ++= == − ===  ,..,1 2, 1 1 2,1 1,..,1 3 min max  (3) where  i is the job-lot in position i of the job-sequence  , and   2,1 i  is the overlapping time for job lot  i when both 1m and 2m are busy (i.e., operating continuously without idle time between sublots), as illustrated in figure 8. figure 8. run-in and run-out delays we can rewrite (3) as                1 3 ,2 ,21 1 1,..,1,.., max ( ) min j j n ji i i i i ii i i j j nj n lb ri p u ro p u ro       − = = = == = + − + +                  1 1 ,2 ,21 1 1 1,..,1,.., max min j j j n ji i i i i ii i i i j j nj n ri p u ro p u ro       − − = = = = == = + − + +               1 ,21 1 1 1,..,1,.., max min j j n ji i i ii i j j nj n ri ro p u ro   − = = = == = − + +   (4) note that the last two terms in (4) are constant and independent from the sequence, and the first term,    == j i inj ri 1,..,1 max     − − = 1 1 j i i ro , gives the total idle time   3,2 i   )iro  ior    2,1 i   iri  iir  31 mm  1m 2m scheduling with lot streaming in a two-machine re-entrant flow shop 161 on 2m before completing the second operations of all job lots. the first term equals johnson’s expression in which the processing times on 1m and 2m are replaced by the run-in and run-out delays, respectively. thus, the job-sequence  is obtained by job-lot k preceding job-lot l if    min , min ,k l k lri ro ro ri . therefore, we obtain the third lower bound as ( )( )  j nj orrorijaclb += = ,..,1 * max3 min, (5) where ( )( )rorijac ,*max is the makespan obtained by johnson’s algorithm (ja) with processing times on 1m and 2m replaced by jri and jro , respectively. lower bound 4. for any job-sequence  , we can establish the fourth lower bound as            1 2,3 4 ,31 11,.., 1,.., min max j j n j i i iii i i jj n j n lb ri ri p u    − = = == = = + +  +   (6) where   3,2 i  is the overlapping time of the second and third operations for job lot )(i as shown in figure 8. equation (6) can be rewritten as                1 4 ,3 ,31 11,.., 1,.., min max ( ) j j n j i i i i i ii i i jj n j n lb ri ri p u ro p u       − = = == =  = + + − +              1 ,31 1 11,.., 1,.., min max j j n j i i i ii i ij n j n ri ri ro p u     − = = == =  = + − +   (7) note that the second term in (7),      1 1 11,.., max j j i ii ij n ri ro   − = ==  −  , is minimized by job-lot k preceding job lot l in the job-sequence if    min , min ,k l k lri ro ro ri    . therefore, we obtain the fourth lower bound as   ( )( )orirjacrilb j nj += = ,min * max ,..,1 4 (8) where ( )( )orirjac ,*max is the makespan obtained by johnson’s algorithm with processing times on 1m and 2m replaced by jir  and jor  , respectively. the global lower bound glb becomes the maximum of the lower bounds developed above. i.e.,  1,...,4maxi iglb lb== . example 4. as an illustration of the proposed algorithm and the global lower bound, we consider the five-job problem in table 1. çetinkaya & duman /oper. res. eng. sci. theor. appl. 4 (3) (2021) 142-175 162 table 1. processing times, number of sublots, and lot sizes j 1,j p 2,j p 3,j p j s j u 1 3 2 3 4 40 2 1 2 2 3 30 3 1 2 7 2 20 4 1 4 2 3 70 5 2 2 1 3 35 when all job lots are independently split into their number of consistent sublots, the sublot sizes and jt and ji values are obtained, as illustrated in table 2. table 2. sublot sizes with jt and ji values j 1,j x 2,j x 3,j x 4,j x j t j i 1 10 10 10 10 240 0 2 6 12 12 90 0 3 5 15 160 0 4 10 40 20 330 120 5 14 14 7 105 0 job-lot set j is decomposed into two job-lot sets,  5 ,3 ,2 ,11 =j and  42 =j . we continue with step 4 of algorithm 2 since the job-lot set 2 j is not empty. the run-in and run-out delays for each job lot are obtained as shown in table 3. table 3. run-in and run-out delays j j ri j ro j ir  j or  1 30 20 20 30 2 6 24 12 24 3 5 105 10 105 4 10 220 180 40 5 28 28 42 7 the application of johnson’s algorithm with processing times on 1m and 2m replaced by jri and jro ; respectively, gives the job-sequence  1 ,5 ,4 ,2 ,3= . the partition job-lot is job 2, and it is in the second position (i.e., 2=d ) of the sequence  . the associated makespan )(max c for the sequence  is computed as 805. the global lower bound becomes   805,,,max 4321 == lblblblbglb where 1 ,1 ,31 ( ) (3 3)(40) (1 7)(20) (1 2)(70) (2 1)(35) 805 n j j jj lb p p u = = + = + + + + + + + = , ( ) ( )  2 ,211,.., 1,..,min min min 30, 6, 5,10, 28 ((2)(40) (2)(30)== = = + + = + + n j j j jjj n j n lb ri p u ro  (4)(70) (2)(35) min 30, 24,105, 40, 7 542+ + + = , ( )( ) ( ) ( )  * *3 max max 1,.., , min 4 2 3 1 5 min 30, 24,105, 40, 7 = = + = − − − − + j j n lb c ja ri ro ro c scheduling with lot streaming in a two-machine re-entrant flow shop 163 535 7 542= + = ,   ( )( )   ( )* *4 max max 1,.., min , min 30, 6, 5,10, 28 3 1 4 2 5 =  = + = + − − − − j j n lb ri c ja ri ro c 5 560 565= + = . the job-sequence  1 ,5 ,4 ,2 ,3= is optimal since the associated makespan equals the natural lower bound 1lb . thus, we stop. 4.2.3. computational experiments and results the efficiency measure of algorithm 2 is the computational time required to solve the problem. however, its computational time is not measured provided since it is relatively very short, less than a few seconds. on the other hand, to test the effectiveness of algorithm 2, we generate the parameters for our problem instances as follows: n : number of job lots ,  5,10,15, 20, 25,50, 75,100n . ,j k p : k th operation’s processing time for job lot j is randomly generated form from a discrete uniform distribution over 1, 10, including the lower and upper limits. j s : number of sublots for any job lot j is randomly generated form from a discrete uniform distribution over 2, 10. j u : lot size for any job lot j is randomly generated form from a discrete uniform distribution over 2, 50. for each possible number of job lots from 5 to 100, we first generate 100 problem instances in which the. the processing times for all operations are randomly distributed without any dominance of a specific operation, and a total of 800 problem instances are tested. the following statistics are collected: z nt = number of times percent deviation is zero (i.e., the heuristic makespan equals the global lower bound). ]1,0(nt = number of times the percent deviation is greater than zero but less than or equal to 1 (i.e., glbc h 01.1max  ). ave = average percent deviation. max = maximum percent deviation. from the results of our experiments, we observed that algorithm 2 finds the optimum makespan (i.e., the heuristic makespan equals the global lower bound) for all 800 test problems when all processing times are randomly generated without any dominance of a specific operation. that is, 800 z nt = . however, to evaluate the effectiveness of algorithm 2 when the same operation for all job lots is dominant, we repeated our computational experiments with three data sets. the first data set, d1, assumes that the maximum processing time is on the first operation for all job lots, i.e.,  3,2,1, ,max jjj ppp  for j . similarly, the second çetinkaya & duman /oper. res. eng. sci. theor. appl. 4 (3) (2021) 142-175 164 and third data sets d2 and d3 correspond to the cases where  ,2 ,1 ,3max ,j j jp p p and  ,3 ,1 ,2max ,j j jp p p for j , respectively. in each of the data sets, we assume that the processing time of the dominant operation for each job-lot is randomly generated form from a discrete uniform distribution over 6, 10, and the processing times of the other operations are randomly generated form from a discrete uniform distribution over 1, 5. our experiments with data sets d2 and d3 show that the global lower bound equals the heuristic makespan in all 800 problem instances tested when either the first or third operation is dominant. this result means that the global lower bound is effective when the first or third operation is dominant. however, the same argument is not valid for the case, where the second operation is dominant, since the global lower bound equals the heuristic makespan in 336 problem instances out of 800, as illustrated in table 4. from table 4, it is clear that the heuristic makespan deviates 1 percent from the global lower bound in 790 problem instances out of 800 for the case where the second operation is dominant. in the remaining ten problem instances when 5n = , the average and maximum deviations from the global lower bound are 0.352 percent and 2.055 percent, respectively. it should also be noticed that the average and maximum deviations decrease as the number of jobs increases. table 4. performance of algorithm 2 when the second operation is dominant n npis znt ]1,0(nt ave max 5 100 45 45 0.352 2.055 10 100 30 70 0.136 0.656 15 100 40 60 0.076 0.569 20 100 37 63 0.050 0.231 25 100 36 64 0.036 0.116 50 100 37 63 0.014 0.044 75 100 58 42 0.006 0.026 100 100 53 47 0.005 0.021 given the results of our computational experiments, we conclude that algorithm 2 is quite effective in solving the multi-job problem where machine 1 is the primary machine. 5. conclusions and future research in this study, we considered a problem in a two-machine re-entrant flow shop in which lot streaming is used for scheduling the single-job and multi-job cases separately. when machine 1 or machine 2 is the primary machine on which the third operation is performed, we proved that the single-job problem is polynomial-time solvable. we have also proved that the multi-job problem can be solved optimally when the third operation is performed on machine 2. however, we have also proved that the multi-job problem is np-hard when machine 1 is the primary machine, machine so that we have developed a simple heuristic algorithm. to examine the effectiveness of our algorithm, we have developed a global lower bound on the scheduling with lot streaming in a two-machine re-entrant flow shop 165 makespan. the results of our computational experiments imply that our heuristic algorithm is quite effective in solving the multi-job problem optimally in reasonably short computational times. our study has some limiting assumptions for the problem under study. as in most studies in the lot streaming literature, we assume that the number of sublots of each job lot is known in advance. however, a more realistic case is when the problem’s solution has to give its value along with the sublot sizes. in our study, as in almost all of the previous studies in the literature, we assume that sublots in each job lot should be processed successively for each operation on each machine. i.e., we do not allow the intermingling of the job lots for the multi-job case. we may or may not obtain a better schedule by relaxing this assumption, but it is worth investigating. furthermore, in our study, sublot sizes may not be integral, so rounding them to the nearest integer numbers without violating the job-lot size may be needed. however, this approach may not provide the optimal makespan. thus, this issue is also worthy of investigating. through our study for two machine and re-entrant flowshops, we hope that researchers working on scheduling problems will be aware that there is no study other than ours for scheduling with lot streaming in re-entrant manufacturing systems. our study will open a new direction in the literature of scheduling with lot streaming since it is the only study that applies lot streaming for singleand multijob cases in the re-entrant flow shops. we hope that our work will form a basis for developing algorithms to solve the scheduling problems in more complex re-entrant manufacturing systems where lot streaming is allowed. there are several research extensions of this study that are open for future investigation: • the assumption of knowing the number of sublots in advance could be relaxed, and investigating the problem under consideration without this assumption could be a future study issue. • the sublot sizes obtained for the no-setup case studied in this paper may not be valid for the setup case the so that problem under consideration can be extended to a case where an issue with attached or detached setup is made before processing a job-lot. • our study assumes that sublots in each job-lot should be processed successively for each operation on each machine. i.e., we do not allow the intermingling of the job lots for the multi-job case. relaxing this the no-intermingling assumption could be another future research issue. • our study could also be extended to the flow shops with more than two stages, having one machine at each stage, and a job lot may visit some stages more than once. and hybrid flow shops, which are the flow shops in which at least one of the stages has more than one machine, could also be studied. • different measures of performance rather than makespan could also be considered. for instance, the total completion time of sublots and job lots in the çetinkaya & duman /oper. res. eng. sci. theor. appl. 4 (3) (2021) 142-175 166 singleand multi-job cases, respectively, could be a more relevant performance measure than makespan if the inventory holding costs are minimized. appendix a. proof of theorem 1. as illustrated in the network representation given in figure 1, a lower bound on the makespan max c , which is based on the first sublot, is given as the first sublot’s processing time on 1m plus the total processing time of all sublots on 2m , i.e., max 1 1 1 2 3 1 2( )( ... )sc lb p x p p x x x = + + + + + . similarly, the total processing time of sublots 1 and 2 plus the total processing time of sublots 2 through s gives another lower bound, i.e., max 2 1 1 2 2 3 2 3 ( ) ( )( ... ) s c lb p x x p p x x x = + + + + + + . similarly, we can write max 1 2 31 ( ) i s i k kk k i c lb p x p p x = =  = + +  for each sublot si ,...,2= . it follows that  max 1 2 311 1 max max ( ) i s i k kk k ii s i s c lb p x p p x = =     = + +  . thus, the linear programming model below can formulate the single-job problem where 2m is the primary machine. ( p ) minimize maxc (a.1) subject to max 1 2 31 ( ) i s k kk k i c p x p p x = =  + +  for si ,...,2= (a.2) 1 s ii x u = = (a.3) max 0c  (a.4) 0ix  for si ,...,2= (a.5) assuming that each of the inequalities in (a.2) is satisfied as equality, i.e., all sublots are critical to determining the makespan maxc ; we can obtain a feasible solution to problem p . in such a case, both 1m and 2m operate without idle time from one sublot to another, and the adjacent pair of sublots must satisfy the following relationship: 1 1 2 3 1 2 31 1 1 ( ) ( ) i s i s k k k kk k i k k i p x p p x p x p p x − = = = = − + + = + +    for si ,...,2= (a.6) or equivalently, ( )1 2 3 1/i ix x p p p−= + for si ,...,2= (a.7) the idle time on 2m is only before the first sublot, and it equals 11xp . then solving the set of simultaneous equations (a.3) and (a.7) yields )...1/( 12 1 − ++++= s ux  , (a.8) 1 1 xx i i − = for si ,...,2= (a.9) where ( ) 132 / ppp += . scheduling with lot streaming in a two-machine re-entrant flow shop 167 using (a.2), (a.3), (a.8) and (a.9), the makespan is obtained as 2 1 max 1 1 2 3 1 2 31 ( ) ( / (1 ... ) ( )) s s ii c p x p p x p p p u   − = = + + = + ++ + + + + . (a.10) we have shown that the solution given by the theorem is feasible. note that this solution is the solution for the single-job lot streaming problem in the two-machine flow shop with processing times 1 p and 2 3 p p+ on 1m and 2m , respectively. now, to prove the optimality of this feasible solution, the problem p may be rewritten as ( p ) maximize maxc− (a.11) subject to max 1 2 31 ( ) 0 i s k kk k i c p x p p x = = − + + +   for si ,...,2= (a.12) 1 s ii x u = = (a.4) max 0c  , 0ix  for si ,...,2= (a.5) the dual of ( p ) is constructed as ( d ) minimize 0 u y (a.13) subject to 1 2 3 01 1 ( ) 0 s i k kk k p y p p y y = = + + −   for si ,...,2= (a.14) 1 1 s ii y = −  − (a.15) 0 i y  for si ,...,2= (a.16) 0 y unrestricted in sign (a.17) we can find a feasible solution to problem d by assuming that all constraints defined in the dual problem d are satisfied as equalities. it follows that a feasible solution to problem d is achieved when 1 1 2 3 1 2 31 1 1 1 ( ) ( ) s i s i k k k kk k k i k p y p p y p y p p y − = = = − = + + = + +    for 2,...,i s= (a.18) or equivalently, 1 1 2 3 / ( ) i i y y p p p − = + for 2,...,i s= . (a.19) solving the set of equations in (a.18) and 1 1 ii s y   = simultaneously yields 1 2 1 1 (1 / (1 ... )) s s y     − − = + ++ + + , (a.20) 1 1 i i y y − = for 2,...,i s= , (a.21) 2 1 0 1 2 3 / (1 ... ) ( ) s y p p p   − = + + + + + + + (a.22) where ( ) 132 / ppp += . çetinkaya & duman /oper. res. eng. sci. theor. appl. 4 (3) (2021) 142-175 168 the objective function of the dual problem 1d  is obtained as 2 1 0 1 2 3 ( /(1 ... ) ( )) s u y p p p u   − = + + + + + + . (a.23) from equations (a.10) and (a.23), it is clear that the problem p and its dual d have the same objective function values. thus, from the duality theory, it follows that equations (a.8)-(a.10) and (a.20)-(a.22) are the optimal solutions to the primal and dual problems, respectively. therefore, we can conclude that the sublot sizes given in the theorem statement are optimal for the single-job problem where 2m is the primary machine on which the third operation is performed. ■ appendix b. proof of theorem 3. for a job sequence  , let [j] = job lot sequenced in the j th position of the sequence  ,  ju = lot size of job lot [j],  j s = number of sublots of job lot [j], i = index for sublots (  1,..., ji s= ),  ,j ix = size of the i th sublot in job lot [j], k = index for machines ( 1, 2, 3k = ),  ,j kp = item (unit) processing time for the k th operation of job lot [j],  , ,j i kc = completion time of the k th operation for the i th sublot of job lot [j],  jri = time lag between the start of the first operation on 1m and the latest start time of the second operation on 2m for job lot [j],  jro = time lag between the completion times of the first and the third operations for job lot [j]. the completion time of the first operation for the i th sublot of job lot [j] is given by          1, ,1 , ,1 ,1 ,1j i j i j s j j rr c c p x − = = + for  1, 2,..., ji s= (b.1) where    00 , ,1 0 s c = . from equation (b.1), the completion time for the first operation of job lot [j], which is the completion time of the last sublot in this job on 1m , is obtained as                      1 1, ,1 1 ), ,1 ,1 , 1 , ,1 ,11 j j j j s j s j s j j i j s j ji c c p x c p u − − − −= = + = + . (b.2) the completion time of the third operation for the first sublot of job lot [j] on 2m is expressed as                 1,1,3 ,1,1 1 , ,3 ,2 ,1 ,3 ,1max , jj j j s j j j jc c c p x p x−−= + + scheduling with lot streaming in a two-machine re-entrant flow shop 169             1,1,1 1 , ,3 ,2 ,3 ,1max , ( )jj j s j j jc c p p x−−= + + . (b.3) substituting  ,1,1jc value from (b.2) into (b.3) yields                     1 1,1,3 1 , ,1 ,1 ,1 1 , ,3 ,2 ,3 ,1max , ( )j jj j s j j j s j j jc c p x c p p x− −− −= + + + . (b.4) similarly, we may obtain the completion time of the third operation for the second sublot of job lot [j] on 2m as                      1 1 1 ,2,3 1 , ,1 ,1 , ,2 ,3 , 1 , ,31 11 2 max max ( ) , j j i i j j s j j r j j j r j sr ri c c p x p p x c − − − − −= =  = + − +        2 ,2 ,3 ,1 ( ) j j j ii p p x = + + (b.5) repeating the process yields the completion time for the last operation of job lot [j], which is the completion time of the last sublot of this job lot on 2m ,                     1 1 , ,3 1 , ,1 ,1 , ,2 ,3 ,1 11 max max ( ) , j j j i i j s j s j j r j j j rr ri s c c p x p p x − − − = =   = + − +                 1 1 , ,3 ,2 ,3 ,1 ( )j j s j s j j j ii c p p x − − = + +                 1 1 1 , ,1 ,1 , ,2 ,3 ,1 11 max max ( ) , j j i i j s j j r j j j rr ri s c p x p p x − − − = =   = + − +              11 , ,3 ,2 ,3( )jj s j j jc p p u−− + + (b.6) by successive application of (b.6) using (b.2), the time to complete the last job lot processed on 2m ,    , ,3nn s c , is obtained as follows:                1 max, ,3 ,2 ,31 1 11 max ( ) n w w n n s j j j j jj j jw n c c ri ro p p u − = = =  = = − + +   (b.7) where                1 ,1 , ,2 ,3 ,1 11 max ( ) j i i j j j r j j j rr ri s ri p x p p x − = =  = − +  , (b.8)                          1 ,1 , ,2 ,3 , ,2 ,3 ,11 11 max ( ) ( ) j i i j j j r j j j r j j j j jr ri s ro p x p p x p p u p u − = =  = − + + + −           ,2 ,3( )j j j j jri p p p u= + + − (b.9) note that the second part,      ,2 ,31 ( ) n j j jj p p u = + , in (b.7) giving the makespan value is a constant so that it is enough to minimize the first part,      1 1 11 max w w j jj jw n ri ro − = =  −  , which is equivalent to the total idle time on 2m . note that the first part is similar to johnson’s expression, where the processing times on 1m and 2m are replaced by the run-in and run-out delays, respectively. therefore, çetinkaya & duman /oper. res. eng. sci. theor. appl. 4 (3) (2021) 142-175 170 job v precedes job z in an optimal schedule of job lots when  min , minv zri ro   ,z vri ro . ■ appendix c. proof of theorem 4. it is clear that the minimizing the first term in (b.7),              1 ,1 , ,2 ,3 ,1 11 max ( ) j i i j j r j j j rr ri s p x p p x − = =  − +  , minimizes the makespan for a given sequence of job lots. in other words, sublot sizes minimizing the makespan for any arbitrary sequence (hence the optimal sequence) are identical to those sublot sizes which are determined by solving the sublot-sizing problem for each job lot separately. therefore, the following linear programming model should be solved for every job lot in position [j]: minimize  jz (c.1) subject to             1 ,1 , ,2 ,3 ,1 1 ( ) i i j j j r j j j rr r z p x p p x − = =  − +  for  1, 2,..., ji s= (c.2)       ,1 j s j i ji x u = = (c.3)  , 0j ix  for  1, 2,..., ji s= . (c.4) the optimal solution to this model is trivial due to its special structure. the minimum value of the objective function  jz is achieved when      ,1 ,1j j jz p x= and the constraints in (c.2) are satisfied as equalities. thus, the sublot sizes must be                   1 , , 1 ,2 ,3 ,1 ,1 ,2 ,3 ,1 ( ) / (( ) / ) i j i j i j j j j j j j x x p p p x p p p − − = + = + for  2,..., ji s= . (c.5) substituting (c.5) into (c.3) yields       12 ,1 / (1 ... ) j s j j x u    − = + + + + , (c.6)     1 , ,1 i j i j x x − = for  2,..., ji s= (c.7) where      ,2 ,3 ,1( ) /j j jp p p = + . note that (c.6) and (c.7) are the same expressions as given in section 3 for the single-job problem, and substituting (c.6) and (c.7) into (b.8) and (b.9) yields                    1 ,1 , ,2 ,3 , ,1 ,11 11 max ( ) j i i j j j r j j j r j jr ri s ri p x p p x p x − = =  = − + =        12 ,1 / (1 ... ) j s j j p u    − = + + + + , (c.8)            ,2 ,3( )j j j j j jro ri p p p u= + + − . (c.9) scheduling with lot streaming in a two-machine re-entrant flow shop 171 acknowledgements: we would like to thank the editor and anonymous referees for their valuable comments and suggestions that helped us to improve the quality and presentation of this paper. references alfieri, a., glass, c. a., & van de velde, s. l. 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(2005). multi-job lot streaming to minimize the mean completion time in m–1 hybrid flowhops. international journal of production economics, 96(2), 189–200. https://doi.org/10.1016/j.ijpe.2004.04.005 © 2021 by the authors. submitted for possible open access publication under the terms and conditions of the creative commons attribution (cc by) license (http://creativecommons.org/licenses/by/4.0/). plane thermoelastic waves in infinite half-space caused operational research in engineering sciences: theory and applications vol. 2, issue 3, 2019, pp. 26-39 issn: 2620-1607 eissn: 2620-1747 doi: https://doi.org/10.31181/oresta19030026l * corresponding author. lukovacvesko@yahoo.com (v. lukovac), tomiclazar17@gmail.com (l. tomić), pavlegladovic@uns.ac.rs (p. gladović) using the process function method to assess the organizational level in dangerous goods transportation1 vesko lukovac a*, lazar tomić b, pavle gladović c a university of defense in belgrade, military academy, belgrade, serbia b serbian armed forces, serbia c university of novi sad, faculty of technical sciences, republic of serbia received: 18 october 2019 accepted: 27 november 2019 first online: 02 december 2019 original scientific paper abstract. as one of the most well-known methods for assessing the organizational level, the process function method represents a very effective tool for diagnosing the existing conditions and identifying what needs to be improved. the process function method can be used to evaluate the organization of business functions, organizational units, work areas work, business elements, workplaces, etc. in this paper, the process function method is applied in order to evaluate the organizational level in the dangerous goods transportation process in one of the units of the serbian armed forces. following the implementation of the methodology, the elements which should be improved to increase the existing level of the organization of dangerous goods transportation in the unit that was the subject matter of analysis were identified. key words: process function; estimation, organization; dangerous goods transportation. 1. introduction transportation is the most dynamic process nowadays, without which the life and survival of people would be unthinkable. in the world today, it cannot be imagined – not for a moment – that no transportation of goods or passengers takes 1 this paper is an extended and amended version of the paper entitled “application of process function method for estimating the level of organization in transporting dangerous goods”, which was published at the conference entitled: “security and crisis management – theory and practice, 2019”. mailto:lukovacvesko@yahoo.com using the process function method to assess the organizational level in dangerous goods transportation 27 place. in addition to everything positive in terms of the development of society, the development of technologies, the urbanization of cities and towns, the development of the infrastructure and industry as a whole, pose a greater danger to the safety and health of both people and the environment. in traffic, the increasing presence of goods containing dangerous substances causes a greater use of vehicles for transporting them. in order to protect ourselves against the effects of the harmful effects of hazardous substances, we are compelled to study them, analyze their impact and determine the extent of such protection. dangerous goods transportation is particularly pronounced in the army, because handling this type of goods on a daily basis is a normal thing in that type of the environment. this fact requires that, in addition to the development of the economy, the infrastructure, the introduction of various technologies and systems, the construction of facilities in which a large number of people live or work, appropriate measures should be taken so as to protect against accidents caused by transporting dangerous goods. the rulebook on dangerous goods transportation at the ministry of defense and in the serbian armed forces (“official military gazette”, no. 8/2018) regulates dangerous goods transportation, organized by the ministry of defense and the military, as well as the military forces of the other states and organizations that use the traffic infrastructure of the republic of serbia under a special agreement. this rulebook is harmonized with the national law on dangerous goods transportation (“official gazette of the republic of serbia”, 95/2018) and the european agreement concerning the international carriage of dangerous goods by road (adr, 2017), the regulations concerning the international carriage of dangerous goods by rail (rid, 2017) and the european agreement concerning the international carriage of dangerous goods by inland waterways (adn, 2017). this paper is aimed at assessing the level of the organization of the work done by the person in charge of organizing the dangerous goods transportation process in one of the units of the serbian armed forces. the process of solving the considered problem was carried outby the application of the process function method. apart from the introduction and the conclusion sections, this paper also consists of the following sections: in section 2 of the project entitled “dangerous goods in transport”, the notion of dangerous goods, the proportion of accidents in the case of the improper handling of dangerous goods, as well as the international agreements governing dangerous goods transportation by certain transportation modes, are emphasized. rating the organizational process of dangerous goods transportation by means of the process function method is the title of section 3, in which the process function method is described and accordingly applied to the considered problem. in the conclusion, i.e. in section 4, the results are discussed and suggestions for the improvement of the current situation are given. 2. dangerous goods transportation in order to more accurately understand potential hazards associated with working with a substance, it is necessary to know and analyze a large number of the physical and chemical properties of a substance, e.g. (vidović et al., 2019): • the type of a danger, lukovac et al./oper. res. eng. sci. theor. appl. 2 (3) (2019) 26-39 28 • the physical state, • viscosity, • the boiling point, • melting temperatures, • density, • the voltage of the steam, • flammability temperature, • auto-ignition temperature, • the limits of explosive mixtures, • reactivity with respect to other substances, and so on. the term “dangerous substance” refers to the factory declared physical-chemical characteristics of a substance determined based on the recognized and corresponding criteria. from the chemistry standpoint, the above-mentioned term “dangerous substance” is not adequate in order to define such a substance; the term “hazardous substance”, however, should rather be used (jovanović et al., 2010). using a wrong term may erroneously direct the determination of the status of dangerous substances during the transportation process, which directly affects both the application of an appropriate recovery procedure in the case of accidents, and finally the application of the methods that are contrary to the international rules and obligations. the term “dangerous goods” refers to a situation when a hazardous matter/substance is contained in an appropriate packaging/container or vehicle during the transportation process. , criteria for the potential risks of hazardous substances are specifically determined for the transportation conditions (jovanović et al., 2010). according to the rulebook on dangerous goods transportation at the ministry of defense and in the serbian armed forces (“official military gazette” no. 8/2018) and the law on dangerous goods transportation (“official gazette of the republic of serbia”, no. 95/2018), dangerous goods are substances and articles forbidden from transport, i.e. those that are allowed if such transport takes place under international agreements on and regulations for dangerous goods transportation by the type of traffic (adr, rid, adn). there are numerous examples of an unprofessional and negligent treatment while handling (manipulating) dangerous goods transportation, having resulted in the suffering of people and the degradation of property and the environment. the consequences of road traffic accidents with vehicles transporting dangerous goods may also be such as to amount to a catastrophe. for example: − in halifax (nova scotia) on 6th december 1917 (figure 1), there was a collision caused by the accident of a french ship, “mont blanc”, and a norwegian ship, “ss imo”, in the halifax access port and channel, which had been moving at a low speed of about 2.5 km/h. the mont blanc was carrying about 3.2 million pounds of picric acid and tnt for the needs of the french army in world war ii. the effect of the explosion reflected in the fragments of the ship, a shock wave and a tsunami of 18 meters in height created by the explosion. the estimated temperature of the explosion was about 5000°c. a pyro-trophic cloud rose to an altitude of about 3600m. the number of the victims has never been precisely determined. it is believed that about 1600 people were killed immediately and about 400 succumbed to injuries, 9000 were injured, 1600 homes were destroyed in a series of fires and 12000 homes were damaged. the industrial using the process function method to assess the organizational level in dangerous goods transportation 29 sector of the city was completely destroyed. the halifax disaster was the unofficial start of a systematic consideration of hazardous substances (janković, 2016). figure 1. the halifax disaster in 1917; the explosion of the ship and the consequences (janković, 2016); − in los alfaques (spain) in 1978, a fuel tank was overloaded. due to high heat and pressure, the tank exploded and the fuel caught fire, killing 216 people (figure 2). figure 2. the consequences of the tank accident on the way to los alfaques in 1978. − in okobie (a nigerian town) on 12th july 2012, there was an explosion of road tanker gas transportation vehicles (figure 3). a total of 121 people were killed in the accident and 75 were injured. lukovac et al./oper. res. eng. sci. theor. appl. 2 (3) (2019) 26-39 30 figure 3. the consequences of the accident in okobie (nigeria) on 12th july 2012 (janković, 2016); − in šabac in 1986, a railroad tank carrying ammonia (nh3) was hanging off the overpass due to the consequences of the accident. the valves were loose and the gas began to release. a favorable wind and the timely intervention of specially trained workers prevented a greater catastrophe from happening. in order to avoid suchlike and similar situations and reduce risks to a minimum, it is necessary that all persons coming into contact with dangerous goods, or those such dangerous goods may have an impact on, should comply with the regulations and guidelines defining the manner in which dangerous goods should be handled and also the way in which they should properly trained and prepared for their work. based on these problems, the experts of the united nations considered giving the basic recommendations and guidelines for the international agreements on the convention-related procedure for dangerous goods in certain transportation modes (vidović et al., 2019; jovanović et al., 2010; janković, 2016; jovanović, 2004; petrović, 2004), as in figure 4: − adr – european agreement concerning the international carriage of dangerous goods by road; − rid – regulations concerning the international carriage of dangerous goods by rail; − icao–ti – international civil aviation organization – technical instructions for the safe transport of dangerous goods by air; − imdg–code – international maritime dangerous goods–code; − adn – european agreement concerning the international carriage of dangerous goods by inland waterways. using the process function method to assess the organizational level in dangerous goods transportation 31 figure 4. international agreements on dangerous goods transportation 3. rating the organizational process of dangerous goods transportation by means of the process function method the process function method can be used to evaluate the organizational level of an entire organization or only certain organizational units, functions, and so forth. according to (erić, d., 2000), the term ‘process functions’ implies the activities necessary for the successful completion of the entire task at all workplace levels in an organization. there are 10 basic phases of the process functions (pamučar, 2013; lukovac et al., 2018; lukovac et al., 2015; savić et al., 2017; tomić, 2019) that appear in the work process, as in table 1. table 1. an overview of the process functions with tags and the meaning name of the function index meaning recording rec covering all business developments in the organization informing inf delivering data and information to all workplaces in the organization controlling con comparison of the activities performed with pre-set benchmarks, standards and guidelines analysis an disassembling, comparing and concluding on the causes of deviations deciding de re-intervening on developments in the existing processes and shaping future processes lukovac et al./oper. res. eng. sci. theor. appl. 2 (3) (2019) 26-39 32 planning pl providing the necessary elements to execute decisions synchronization sy combining and directing individual efforts into a total effort organizing org finding and designing appropriate organizational procedures and performing work tasks performance per concrete execution of tasks in all workplaces in the organization command co assigning tasks to subordinate units and authorities. in this paper, the activities performed by the person in charge of organizing the dangerous goods transportation process in one of the units of the serbian armed forces are analyzed, as in table 2. table 2. the jobs analyzed index jobs 01 determining the availability of the drivers capable of transporting dangerous goods 02 determining the availability of the vehicles intended for dangerous goods transportation 03 consulting with the safety advisor on dangerous goods transportation 04 developing an engagement plan 05 preparing the driver to complete the task 06 controlling the equipment that a dangerous goods transportation vehicle must have 07 controlling the driver and the vehicle documentation 08 checking the knowledge of the procedure in the event of a failure or a traffic accident 09 communicating occupational safety and health, environmental and fire safety measures when performing the task 10 tracking the completion of the task 11 submission of reports within prescribed deadlines the listed tasks are performed within the individual work areas by the process functions. given the fact that not every job has to contain all the process functions, it is necessary to determine their connection with the process function, which is determined by entering a “+” sign into the “the connection between the jobs and the process functions” table where the sum of such “+” signs represents the sum of the frequencies (f) (table 3) for the job containing one of the process functions. if a job contains no process functions, a “-” sign is entered into the table. using the process function method to assess the organizational level in dangerous goods transportation 33 table 3. the connection between the jobs and the process functions jobs process function f rec inf con an de pl sy org per co 01 + + + + + + + + + + 10 02 + + + + + + + + + + 10 03 + + + + + + + + + + 10 04 + + + + + + + + + + 10 05 + + + + + + + + + + 10 06 + + + + + + + + + + 10 07 + + + + + + + + + + 10 08 + + + + + + + + + + 10 09 + + + + + + + + + + 10 10 + + + + + + + + + + 10 11 + + + + + + + + + + 10 not all jobs have the same importance. some are more significant, whereas others are less significant; it is necessary to perform their weighting. the weighting is performed by selecting one of the weights on a scale from 0 to 5, according to the criteria accounted for in table 4. table 4. the weighting criteria weight criterion 5 the execution of the jobs is necessary, without which no business would be possible 4 the execution of the jobs has a big impact on the overall business 3 the execution of the jobs affects the economy of the business 2 a failure to do the job causes a deficiency in business, but business is nonetheless possible 1 the execution of the jobs affects the integrity of business 0 the execution of the jobs is unnecessary the process functions are weighted according to the same criteria, because not all of them have the same importance for the job. the selected job weights, as well as the process function weights, are a result of a survey conducted with the person performing these tasks in the serbian military unit that was the subject matter of this analysis. the weighting of the jobs and the process functions was performed by multiplying the selected job weights by the selected process function weights, and the resulting products are the theoretical weights for the jobs by process function, or for the process functions by job, as given in table 5. lukovac et al./oper. res. eng. sci. theor. appl. 2 (3) (2019) 26-39 34 table 5. the theoretical weighting of the jobs by process function jobs process function ∑ re c inf co n an de pl sy or g pe r co weight index weight 3 3 5 5 5 5 4 5 5 5 01 5 15 15 25 25 25 25 20 25 25 25 225 02 5 15 15 25 25 25 25 20 25 25 25 225 03 5 15 15 25 25 25 25 20 25 25 25 225 04 5 15 15 25 25 25 25 20 25 25 25 225 05 4 12 12 20 20 20 20 16 20 20 20 180 06 4 12 12 20 20 20 20 16 20 20 20 180 07 5 15 15 25 25 25 25 20 25 25 25 225 08 4 12 12 20 20 20 20 16 20 20 20 180 09 5 15 15 25 25 25 25 20 25 25 25 225 10 5 15 15 25 25 25 25 20 25 25 25 225 11 4 12 12 20 20 20 20 16 20 20 20 180 ∑ 15 3 15 3 25 5 25 5 25 5 25 5 20 4 25 5 25 5 25 5 2295 the next step implies the evaluation of the jobs by process functions, with the rating from 1 to 5, according to the criteria for determining the ratings based on the observed organizational attitude in the observed workplace, as shown in table 6. table 6. the job evaluation criteria rating criterion 1 the jobs are not done 2 the jobs are done occasionally 3 the jobs are not done on employees’ own initiative, but upon order 4 the jobs are done according to the instructions received from the superiors 5 the jobs are done according to the organizational regulations the job ratings by process function are shown in table 7 and they are also a result of the survey conducted with the person performing the tasks that were the subject matter of this analysis. using the process function method to assess the organizational level in dangerous goods transportation 35 table 7. the job ratings jobs process function rec inf con an de pl sy org per co 01 3 3 3 3 5 5 4 5 5 5 02 3 3 3 3 5 5 4 5 5 5 03 4 3 4 4 5 5 4 5 5 5 04 5 5 4 3 5 4 4 5 5 5 05 5 5 4 4 5 5 4 5 5 5 06 3 3 3 4 5 5 4 5 5 5 07 5 3 5 3 5 5 4 5 5 5 08 3 3 5 3 5 5 4 5 5 5 09 5 5 5 5 5 5 5 5 5 5 10 5 3 5 5 5 5 5 5 5 5 11 3 5 5 4 5 5 5 5 5 5 after the job evaluation by process functions, the calculation of the actual job weights ( s p ) is performed by using equation 1: = p s o p ×o p s (1) where − p p – the required (theoretical) weighting of the job, − o – the job evaluation by process functions, − o s – the rating scale (5). the actual job weights are shown in table 8. table 8. the actual jobs weights jobs process function ∑ rec inf con an de pl sy org per co 01 9 9 15 15 25 25 16 25 25 25 189 02 9 9 15 15 25 25 16 25 25 25 189 03 12 9 20 20 25 25 16 25 25 25 202 04 15 15 20 15 25 20 16 25 25 25 201 05 12 12 16 16 20 20 12.8 20 20 20 168.8 06 7.2 7.2 12 16 20 20 12.8 20 20 20 155.2 07 15 9 25 15 25 25 16 25 25 25 205 08 7.2 7.2 20 12 20 20 12.8 20 20 20 159.2 09 15 15 25 25 25 25 20 25 25 25 225 10 15 9 25 25 25 25 20 25 25 25 219 11 7.2 12 20 16 20 20 16 20 20 20 171.2 ∑ 123. 6 113. 4 213 190 255 250 174. 4 255 255 255 2084. 4 lukovac et al./oper. res. eng. sci. theor. appl. 2 (3) (2019) 26-39 36 the next step in applying this method implies the calculation of the average job ratings (o ) by using equation 2:   s o p p o= ×s p (2) the average job ratings are shown in table 9. table 9. the average job ratings jobs  sp  pp o 01 189 225 4.20 02 189 225 4.20 03 202 225 4.49 04 201 225 4.47 05 168.8 180 4.69 06 155.2 180 4.31 07 205 225 4.56 08 159.2 180 4.42 09 225 225 5.00 10 219 225 4.87 11 171.2 180 4.76 total 2084.4 2295 4.54 analogously to equation 2, the average ratings of the process functions ( pf o ), which are shown in table 10, are calculated by using the weights given in tables 5 and 8. table 10. the average ratings of the process functions process function  sp  pp pfo recording 123.6 153 4.04 informing 113.4 153 3.71 controlling 213 255 4.18 analysis 190 255 3.73 deciding 255 255 5.00 planning 250 255 4.90 synchronization 174.4 204 4.27 organizing 255 255 5.00 performance 255 255 5.00 command 255 255 5.00 total 2084.4 2295 4.54 based on the average job and process function ratings, the jobs (table 11) and the process functions are ranked, as in table 12. using the process function method to assess the organizational level in dangerous goods transportation 37 table 11. the job ranks rank job index weights o 1. 09 5 5.00 2. 10 5 4.87 3. 11 4 4.76 4. 05 4 4.69 5. 07 5 4.56 6. 03 5 4.49 7. 04 5 4.47 8. 08 4 4.42 9. 06 4 4.31 10. 01 5 4.20 10. 02 5 4.20 table 12. the process function ranks rank process function weights pfo 1. deciding 5 5.00 1. organizing 5 5.00 1. performance 5 5.00 1. command 5 5.00 2. planning 5 4.90 3. synchronization 4 4.27 4. controlling 5 4.18 5. recording 3 4.04 6. analysis 5 3.73 7. informing 3 3.71 4. conclusions average job evaluation is an assessment of the organizational level in a particular workplace. accordingly, based on the value of the average job rating (4.54) obtained in this research study, it can be concluded that it is characteristic of the organizational level that the execution of jobs does not entirely base on organizational regulations, but also on the instructions received from superiors. this especially applies to the jobs rated lower than the average job rating; in this case, these are the following jobs: − 01 – determining the availability of the drivers capable of transporting dangerous goods, − 02 – determining the availability of the vehicles intended for dangerous goods transportation, − 06 – controlling the equipment that a dangerous goods transportation vehicle must have, − 08 – checking the knowledge of the procedure in the event of a failure or a traffic accident, − 04 – developing an engagement plan, and lukovac et al./oper. res. eng. sci. theor. appl. 2 (3) (2019) 26-39 38 − 03 – consulting with the safety advisor on dangerous goods transportation. based on the average process function rating, we came to know the process functions that need to be upgraded. this primarily applies to those process functions that are rated lower than the average (4.54); so, in this specific case of ours, the improvement measures should focus on the process functions of: − synchronization, − controlling, − recording, − analysis, and − informing. the good and the bad sides of the organizational level can also be seen from the analysis of the relationship between the assigned weights and the calculated ratings. according to the analysis carried out, it is also possible to see which process functions and jobs need to be paid greater attention to, which primarily applies to those process functions and jobs that are assigned high weights and have low average ratings. from this point of view, the jobs marked “01”, “02”, “03” and “04” are interesting, as well as the “controlling” and “analysis” process functions. given the fact that the jobs marked “01”, “02”, “03” and “04”, as well as the “controlling” and “analysis” process functions, were identified as the weaknesses in both cases, the measures for the improvement of the existing situation should first focus on improving these jobs and process functions. however, it is necessary to emphasize that the results of this analysis should be critically viewed in order for a more appropriate analysis of the observed problem to be performed and that the opinions of a larger number of persons (or groups of experts) involved in the subject-matter problem should be considered. references erić, d. (2000). uvod u menadžment, čigoja štampa, beograd. european agreement concerning the international carriage of dangerous goods by road (2017). european agreement concerning the international carriage of dangerous goods by inland waterways (2017). janković, z. (2016). razvoj modela za proračun rizika u logističkim sistemima opasnih materija, doktorska disertacija, fakultet tehničkih nauka univerziteta u novom sadu, novi sad. jovanović, v. (2004). transport opasnih materija, saobraćajni fakultet univerziteta u beogradu, beograd. jovanović, v., milovanović, b. & mladenović, d. (2010). transport opasne robe u drumskom saobraćaju, saobraćajni fakultet univerziteta u beogradu, beograd. law of the transport of dangerous goods (official gazette of the republic of serbia, 95/2018) lukovac, v., pamučar, d. & miletić, a. (2015). primena metode procesnih funkcija za procenu nivoa organizovanosti zaštite od požara i eksplozija, rizik i bezbednosni inženjering, kopaonik. using the process function method to assess the organizational level in dangerous goods transportation 39 lukovac, v., savić, d. & jovanović, v. (2018). fuzzy process approach to level assessment of environmental protection organization, the 2nd international conference on management, engineering and environment icmnee 2018, beograd. pamučar, d. (2013). dizajniranje organizacione strukture upravnih organa logistike korišćenjem fuzzy pristupa, doktorska disertacija, vojna akademija, beograd. petrović, lj. (2004). transport opasne robe u drumskom saobraćaju – upoznavanje restrukturiranog adr-a, trigon inženjering, beograd. regulations concerning the international carriage of dangerous goods by rail (2017). rulebook of the transport of dangerous goods in the ministry of defense and the serbian armed forces (official military paper number 8, 2018.) savić, d., lukovac, v. & urošević, l. (2017). application method of process function for evaluation of the of organisational level of workplace, icdqm 2017, prijevor. tomić, l. (2019). analiza transporta opasne robe u ministarstvu odbrane i vojsci srbije u periodu 2016. – 2018. godine, završni rad, vojna akademija, beograd. vidović, m., radivojević, g. & ratković, b. (2019). roba u logističkim procesima, saobraćajni fakultet univerziteta u beogradu, beograd. © 2019 by the authors. submitted for possible open access publication under the terms and conditions of the creative commons attribution (cc by) license (http://creativecommons.org/licenses/by/4.0/). plane thermoelastic waves in infinite half-space caused operational research in engineering sciences: theory and applications vol. 5, issue 2, 2022, pp. 117-151 issn: 2620-1607 eissn: 2620-1747 doi: https://doi.org/10.31181/oresta060722090g * corresponding author. hakangokhangundogdu@anadolu.edu.tr (h. g. gündoğdu), ahmetaytekin@artvin.edu.tr (a. aytekin) effects of sustainable governance to sustainable development hakan gökhan gündoğdu 1, ahmet aytekin 2* 1 department of political science and public administration, faculty of economics, anadolu university, turkey 2 department of business administration, faculty of hopa economics and administrative sciences, artvin çoruh university, turkey received: 06 april 2022 accepted: 20 june 2022 first online: 06 july 2022 research paper abstract: sustainable development advocates effective and efficient planning of both present and future use of resources. governance, on the other hand, is based on the joint and coordinated management of multidimensional variables, which is the basis of the sustainability approach. this study aims to determine how much sustainable governance influences the fulfillment of multidimensional sustainable development. multiple regression analysis was used to determine the variables that reveal the impact of governance on development in terms of sustainability while the gray relational analysis method was used to rank the countries. the results reveal that increases in the number of people using the internet in society, as well as in the levels of developments in e-government and human development, environmental performance, and political reform, all assist countries achieve their sdgs. furthermore, it was found that governance has a positive and significant impact on sdgs. in addition, an mcdm model consisting of bwm and gray relational analysis was used to evaluate countries based on their performance in sustainable development, the economic, governance and environment. the gray relational analysis results, on the other hand, revealed that developed and wealthy countries ranked first, while underdeveloped countries experiencing instability, such as war and conflict, ranked last. the nordic countries outperform other countries in terms of governance and sustainability, depending on the strength of their democracy and executive capacity. key words: sustainable development, sustainable governance, best worst method, gray relational analysis. 1. introduction production and consumption needs have become more prominent as development resources because of the rise of industrialization, excessive resource gündoğdu & aytekin/oper. res. eng. sci. theor. appl. 5(2) 2022 117-151 118 use, and environmental degradation have been criticized as the main culprits (caradonna, 2014). the considerable rate of economic expansion experienced during the "golden age of capitalism" (marglin & schor, 1991; middleton, 2000; skidelsky, 2009), particularly following the second world war, underscored the necessity to strike a balance between development and the environment (caradonna, 2014). the development of sustainability and governance initiatives has been accelerated by factors such as increased competitiveness and development on a global, regional, and local scale, diversification of commercial and public sector service provision, and the avoidance of climate change and pollution. sustainable development has become a key idea while addressing issues in different fields, and governance indicators have been used as solution tools (meadowcroft, 2007). the global ecosystem, on the other hand, is negatively impacted by global population growth and the resulting increase in production and consumption requirements. for example, the world population, which was around four billion in 1975, has almost doubled to 8 billion by 2021 (worldometer, 2021). this massive increase has several negative consequences for the environment, including global warming and climate change. therefore, the importance of future population, production, and consumption control and transformation into planned sustainable development has resurfaced. there are also global obstacles such as education and health issues, poverty, inequality, and the recent covid-19 pandemic, all of which have a negative impact on the development of all countries. to achieve the sustainable development goals (sdgs), it is essential to solve these problems and use resources wisely. moreover, it has once again become apparent that countries must collaborate and coordinate their efforts to attain these goals (barbier & burgess, 2020). the study focuses on the impact of governance on the sustainability of development, which is linked to systematic and planned development (sustainable development). furthermore, the variables presented in this study are used to assess the relationship and change of sustainable governance to sustainable development. as a result, the purpose of this study is to examine how the independent variables connected to sustainable governance affect the variable of sustainable development. in this study, regression analysis will be used to determine the ones that are effective on sustainable development among sustainable governance indicators. regression models, on the other hand, reflect the existence and degree of relationships between variables, but they cannot reveal the superiority of the countries, which are the study's units, over one another. a multi-criteria decision model will be used to assess countries' performance in terms of both sustainable governance and sustainable development in this context. it will be possible to provide policy suggestions as a result of the multi-criteria decision analysis by determining the positive features of the prominent countries and the negative features of the remaining countries. as a result of the application of the regression model and the multi-criteria decision model, a holistic evaluation will be provided. to determine the causality and effect levels between the variables, multiple regression analysis (mra) will be used. gray relational analysis (gra) will be used to rank countries' performance in terms of sustainable development and governance. gra was selected for the study because it provides a comparable solution to the references to be determined in the criteria. in addition, the best-worst method (bwm) was chosen to determine the weight values of the criteria because it provides consistency with fewer pairwise comparisons than other methods in the literature. effects of sustainable governance to sustainable development 119 there is a positive and statistically significant association between sustainable governance and sustainable development, according to the literature. to put it another way, as countries' levels of sustainable governance increase, so do their degree of sustainable development. it is critical for countries to concentrate on sustainable governance policies to achieve long-term sustainable development. studies on sustainable development, which fall under the category of quantitative analysis, have mostly been the focus of investigations1 in domains such as economics, business, the environment, and energy. however, no research has been found that analyzes the link between sustainable governance and sustainable development. some studies have specifically explored the relationship between governance and sustainable development (meadowcroft, 2007; kardos, 2012; stojanović et al., 2016; davis, 2017; güney, 2017; omri & ben mabrouk, 2020). others have investigated the link between one facet of sustainable development and the quality of governance (rajkumar & swaroop, 2008; farag et al., 2013; jindra & vaz, 2019). none of these studies focused on the role of sustainable governance in achieving sustainable development and evaluated them from the perspective of public administration. accordingly, this study offers significant contributions to the empirical literature on the interaction between environmental, economic, social, political, and technological variables, which are the components of sustainable governance, and sustainable development. the study seeks to explore the existence of a connection between economic, technological, human, and legal development in sustainable governance and sustainable development. we also look at the variables which may be considered to have a substantial effect among the variables often considered in this area. do the rankings determined using gra differ between developed, emerging, and underdeveloped (high, medium, and low level) countries? this study is primarily based on the responses to these two questions, as well as the related evaluations. in addition, the study incorporated data from 149 high, middle, and low-income nations from a variety of international agencies. the data for the study's independent variables were compiled by merging current data from international institutions. in this regard, the study stands out for its inclusiveness and for contributing to the field in a current manner. according to the results of the research, individuals using the internet in society and in e-government development contribute to sdgs. similarly, human development, environmental performance, and political transformation have all had a favorable impact on the sdgs. governance, in addition to all these variables, has been shown to have a substantial impact on sdgs. first, the background of sustainable development will be examined in the chapters of this study and a theoretical framework will be developed for the link between sustainable governance and sustainable development. second, information on the dimensions affecting sustainable development and sustainable governance will be provided. then, the research method, research findings, and their interpretation are included. finally, the research findings are evaluated. 1 for these studies, see: (stojanović et al., 2016; davis, 2017; güney, 2017; glass & newig, 2019; jindra & vaz 2019; omri & ben mabrouk, 2020). gündoğdu & aytekin/oper. res. eng. sci. theor. appl. 5(2) 2022 117-151 120 2. literature following the 1970s, the topic of sustainability has been a major topic in a variety of sectors, particularly in the environment and economy. meeting the requirements emerging from rapid population expansion, utilizing resources evenly, and safeguarding the natural environment have all been recognized as issues of research in the context of sustainable development (harborth, 1991). the substantial increase in consumption, rapid population expansion, and economic growth in this period had severe consequences on the natural environment, causing environmental problems to reach a worldwide scale (meadows et al., 1972; turner, 2008). as a consequence, the necessity for a balanced interaction between development and the natural environment has emerged, prompting solution proposals for "sustainable future planning." sustainable development has been frequently used as a solution tool in this context since the 1980s. this notion has been evaluated in particular by associating it with economic progress in the face of global difficulties, efficient use of natural resources, and resolving social and environmental challenges. in this context, the literature will be discussed in the study in several subsections. 2.1. the evolution of the sustainable development concept in the literature, there is no one, agreed-upon definition for the terms sustainability and sustainable development. the way researchers approach the subject may differ in both concepts. however, sustainability can be defined as the continuing of something that already exists (meadowcroft, 1997). sustainability is conceptually linked to a wide range of themes in the literature. in this context, studies for the welfare of future generations, equality policies for the fair distribution of incomes across generations, studies for global environmentalism, and biodiversity policies for maintaining the ecological balance are some of these issues (basiago, 1999). sustainability research has been performed in a wide variety of fields, including economic (jackson, 2009), financial (quayes, 2012), environmental (goodland, 1995; morelli, 2011), social (torjman, 2000), political (patashnik, 2003), socio-cultural (chiu, 2004), corporate (bansal, 2005), digital (funk, 2015; gouvea et al., 2018) and urban (alberti, 1996). moreover, the studies on the relationship between digitalization, or technological transformation, and sustainability (funk, 2015; gouvea et al., 2018; kostoska & kocarev, 2019; del río castro et al., 2020) have exploded in popularity in recent years. in this context, a group of academics has drawn attention to the link between digital transformation, big data, and sustainable society, and have proposed the "digital transformation and sustainability" model for achieving sustainable development (pappas et al., 2018). furthermore, while some researchers proposed models for studies in various fields related to sustainability (boulanger & bréchet, 2005; bebbington et al., 2007), others drew attention to criticisms on various issues related to sustainable development (de graaf et al., 1996; marcuse, 1998; robinson, 2004). sustainable development has been characterized in the literature as a crucial concept that "solves all problems" (fischer-kowalski & haberl, 1998), and various scientific studies have been conducted on this subject (barbier, 1987; harborth, 1991; harris, 2000; ciegis et al., 2009). economic, social, and environmental/ecological policies are all evaluated equally and simultaneously at all effects of sustainable governance to sustainable development 121 stages of sustainable development in this framework (basiago, 1999; harris, 2000; bell & morse, 2003; ciegis et al., 2009). to put it another way, research on sustainable development often emphasizes that it is not possible to achieve sustainable development solely through economic efficiency (garrod & fyall, 1998; harris, 2000; ciegis et al., 2009; morelli, 2011). in this context, sustainable development attempts to construct a multidimensional and socioeconomic system that considers factors like income, education, living standards, and health (ciegis et al., 2009). on the other hand, there is a discussion of strong and weak sustainability in terms of the fact that resources can be substituted or not substituted according to their original forms in appropriate situations. the key topic of discussion in this context is the contrasts in sustainability between the environment and the economy (ayres et al., 2001). as a result, the concept of sustainable development is a fundamental concept that may be applied to a wide range of fields and different perspectives. the notion of sustainable development was used particularly in terms of industrialized countries' ability to achieve balanced growth and effective resource management in all sectors, including the environment, the economy, and security (mckenzie, 2004). the un world commission on environment and development's report "our common future2" in 1987 provided the most comprehensive and widely acknowledged explanation of the idea of sustainable development (basiago, 1999). the notion of sustainable development is defined in the report as "development that seeks to meet the needs of the present without compromising the ability of future generations to meet their own needs" (wced, 1987). besides, after the publication of this report, the idea of "sustainable development" has become a contentious and vital topic in the public debate (mitcham, 1995). another key feature of the aforementioned report is that it emphasizes the significance of establishing justice (equality between generations) between present and future generations, not merely on the basis of economic efficiency in-country growth or development (garrod & fyall, 1998). as a result, rather than focusing on a one-dimensional and limited view of growth, a multidimensional and inclusive development model was highlighted. on the issues of environment and development, the "un conference on environment and development," also known as the "rio conference," was held in 1992. in 1993, the united nations commission on sustainable development was founded. various conferences, summits, and forums were organized in the following years to discuss decisions on sustainable development and environmental protection. the "millennium development goals" (mdgs), which support country development and were implemented between 2000 and 2015, were one of the most important moves done in recent years in terms of sustainable development. in the period 2001-2015, the mdgs made some progress in developing countries. developed and underdeveloped countries, on the other hand, painted a picture of development that fell far short of expectations throughout the same time period (sachs, 2012). sdgs that broaden the scope and limitations of the mdgs has come to the fore in the un as of the end of this period (biermann et al., 2017). in contrast to 2 the report, commonly known as the brundtland report, addresses worldwide problems and solutions for the common future. gündoğdu & aytekin/oper. res. eng. sci. theor. appl. 5(2) 2022 117-151 122 previous development goals, sdgs include more comprehensive and holistic aims as well as a vision of progress (le blanc, 2015; fukuda-parr, 2016). in 2015, the "un sustainable development summit3" on sustainable development took hold in addition to all of these events. at this summit, 17 sdgs were adopted, with all member states committing to achieving them between 2015 and 2030. these goals are made up of 17 major goals and 169 sub-goals that have been endorsed as an urgent call to action by all un member states. in this framework, it aims to overcome global challenges on important issues such as education, poverty, inequality, climate change, global warming, environmental degradation, economic growth and innovation, peace, and justice, which are relevant to all countries and should be implemented4 (un general assembly, 2015). in addition to these issues, the covid 19 outbreak is still affecting humans worldwide as of 2020. during the pandemic process, all countries' ability to reach their 2030 goals, especially economic growth, has been interrupted. 2.2. the sustainable governance and sustainable development: what's the connection? the term "governance" refers to multidimensional management involving formal and informal actors (huther & shah, 1998; hyden et al., 2004; gündoğdu, 2020). the concept was officially used for the first time in the world bank's 1989 report on africa's development. this report emphasized the importance of under-developed and developing countries having proper governance processes or mechanisms to develop by creating a link between development and governance (world bank, 1989). moreover, the notion of governance was used to relate to the concepts of accountability, openness, and transparency in a 1992 report from the same agency (world bank, 1992). several international agencies, including the un, the oecd, and the imf, have used the concept of governance in the years afterward. the un's "mdgs" and research on the issue underline the relevance of the idea of "governance" (un, 2007). some researchers have attempted to explain the definition of governance in the literature (e.g., huther & shah, 1998; pierre, 2000; hyden et al., 2004; benz, 2007; treib, bähr & falkner, 2007; bevir, 2009; osborne, 2010). treib, bähr, and falkner (2007) define governance as a multidimensional notion that incorporates various actors, processes, structures, and agencies engaged in political decision-making and execution. to put it another way, in order to comprehend governance, the government must be viewed as a "cooperative state," and decision-making procedures must be developed in collaboration with the public, private sector (market), non-governmental organizations, and citizens (benz, 2007; osborne, 2010). in this regard, governance emphasizes the coordination, cooperation, and harmony of actors at all levels (pierre, 2000). besides, gündoğdu (2019) stresses that multi-level governance and participatory democracy will evolve as a collaborative strategy involving numerous actors. 3 every year, the un general secretariat also publishes a "report" on the sdgs, which covers current progress. 4 in addition, there is a sustainable development index/indicator that ranks and evaluates countries based on the sdgs (kroll, 2015). effects of sustainable governance to sustainable development 123 the concept of sustainable governance is defined as “socio-political governance processes that contribute to the realization of sustainable development” (meadowcroft, 2007). as a result, sustainable governance plays a significant role in the sustainable management of various actors (awuzie & monyane, 2020) as well as the achievement of countries' long-term goals (aytekin & gündodu, 2021). governance, in particular, is critical to achieving the sdgs and overcoming global issues (un, 2012). the "sustainable governance index" is a crucial tool for measuring a country's level of sustainable governance. the sustainable governance index and the sdgs are complementary in this context. for example, in order to achieve strong and sustainable governance, countries have to overcome issues such as economic globalization, social inequality, climate change, resource scarcity, and demographic transition (brusis & siegmund, 2011). for the sdgs, a similar explanation applies. in this context, an answer is sought to the extent to which countries are successful in economic, social, and environmental policies, both in the sustainable governance indicators and in the sdgs. there have been studies that show that there is a theoretical link between sustainable development and governance (kemp, parto & gibson, 2005; sachs, 2012). several studies have concluded that using a sustainable governance approach to natural catastrophes and crisis management is critical in this context (ahrens & rudolph, 2006; ansell et al., 2010; tierney, 2012). some studies, according to rothstein and teorell (2008), underline that there is a significant relationship between economic growth and governance, which they regard as a critical component of development. similarly, in previous research on the ties between sustainable development and sustainable governance, economic, social, and ecological factors, as well as relationships between official and non-official agencies, have been mentioned (spangenberg, 2002; meadowcroft et al., 2005). various studies have been conducted examining the impact of governance on development outcomes. in this context, it has been discovered that in countries with a high level of governance, it has a regulatory and considerable effect on public health and primary education expenditures (rajkumar & swaroop, 2008; farag et al., 2013). according to certain studies, there is a strong link between a country's per capita income and its degree of governance quality (campos & nugent, 1999, kaufmann et al., 1999; kaufmann et al., 2010; fayissa & nsiah, 2013). as a result, it has been stressed that governance is critical to a country's development and attainment of higher wealth levels (oster, 2009). another study concluded that, in the next years, sustainability will make more positive development if governance worldwide improves (joshi et al., 2015). in other studies, the relationship between corruption prevention, which is a component of governance, and sustainable development has been investigated, and it has been discovered that there is a negative relationship between increased corruption and sustainable development (aidt, 2009; bentzen, 2012). additionally, lennan and ngoma (2004) stressed the significance of institutional capacity building to support good governance and sustainable development. the literature-based on quantitative analysis (rajkumar & swaroop, 2008; stojanović et al., 2016; davis 2017; güney, 2017; glass & newig, 2019; omri & ben mabrouk, 2020) emphasizes that there is a multidimensional relationship between gündoğdu & aytekin/oper. res. eng. sci. theor. appl. 5(2) 2022 117-151 124 sustainable development and governance. in this context, stojanović et al. (2016) used the world bank governance indicator data set to establish the relationship between sustainable development and governance. davis (2017) has examined the associations between good governance and human development indicators in subsaharan africa. güney (2017), on the other side, used the adjusted net saving indicator to examine the relationship between sustainable development and governance in 121 countries using data spanning the years 1996 to 2012. moreover, jindra and vaz (2019) discussed the relationship between multidimensional poverty prevention, which is a component of sustainable development, and governance quality. glass and newig (2019) used multiple governance indicators (participation, policy coherence, reflexivity, adaptation, and democratic institutions) to examine sdg achievement in 41 high and upper-middle-income countries. finally, omri and ben mabrouk (2020) analyzed data on governance and sustainable development from 1996 to 2014 to study countries in 20 mena (middle east and north africa-) areas. as can be seen from all these studies, it is desirable to analyze and quantify the institutional development and governance quality of countries based on certain variables in studies where sustainable development and governance indicators are accepted as data. ultimately, it has been underlined that the relationship between sustainable development and governance is multidimensional and interdependent. 3. methodology the study's aim is to obtain a comprehensive evaluation based on the results of two different models. the mra will be used to investigate the relationship between sustainable development and sustainable governance in this context. countries are the units considered in the mra. the bwm-gra multi-criteria decision model will be used to assess the countries' sustainable development and governance performance. figure 1 depicts the methodology used in the study. figure 1. the scheme of methodology effects of sustainable governance to sustainable development 125 different variables or indicators are used to measure sustainability goals and the dimensions associated with these goals, as shown by the literature (munda and nardo, 2005; gasparatos et al., 2008; wu and wu, 2012; diaz-balteiro et al., 2017; croissant and pelke, 2022). however, the relative superiority, validity, and reliability of these various indicators and data are debatable. because of this problem, researchers have looked for a single variable/criterion from sources that measure the same variable/criterion with different units. for this reason, data collected from various sources with the aim of measuring the same variable were standardized and integrated. as a result, data that was comparable and clear of measurement differences were created. the study was done using data collected from a variety of sources (bti, 2021; data world bank, 2021; freedom house, 2021; human development reports, 2021; sdgs database, 2021; sgi, 2021; the economist intelligence unit, 2021; worldometer, 2021; wvs, 2021; wjp, 2021). in this context, political transformation, political participation, rule of law, quality of democracy, political integration, economic transformation, and governance variables were created using various indicators, and data sources. the normalization process was used to eliminate data measurement differences and create a one-dimensional data frame that was comparable. eq. (1) has been applied in this context. * ij j ij j j x x z x x − − − = − (1) in eq. (1), the best value in the related indicator is * j x , while the worst value is j x − . because of the normalization process, the best value is 1 and the worst value is 0 in the indicators. in the variables formed by integrating more than one indicator, the arithmetic average of the normalized values of the relevant indicators was used. table 1 shows the indicators that were used to form the variables. table 1. indicators and variables notation variables/criteria indicators c1 sdg sdg index c2 political transformation bti-stateness, sgi-executive capacity, wgipolitical stability and absence of violence/terrorism, wgi-government effectiveness, wgi-regulatory quality c3 political participation freedom house-freedom index, bti-political participation, sgicitizens' participatory competence c4 rule of law wgi-rule of law, wjprule of law index, bti rule of law, sgi-rule of law c5 quality of democracy btistability of democratic institutions, sgi quality of democracy c6 political integration bti-political and social integration, sgisocial policies c7 economic transformation btieconomic performance, sgi-economic policies c8 governance bti-governance index, sgi-governance gündoğdu & aytekin/oper. res. eng. sci. theor. appl. 5(2) 2022 117-151 126 c9 hdi hdi c10 democracy index democracy index c11 cpi cpi score c12 e-government e-government index c13 epi epi c14 co2 emissions co2 emissions (metric tons per capita) c15 gdp growth gdp growth (annual %) the effects of governance variables on the sdg will be investigated using regression analysis in this study. the variables c1-c8 in table 1 will be used in the regression analysis in this context. also, countries will be ranked according to their levels of sustainable development and sustainable governance using gray relational analysis, one of the multi-criteria decision-making methods. c1-c15 criteria will be considered in gra evaluations. as a result, it aims to provide a more comprehensive assessment. in the following part, it will be given some explanatory information about mra, and gra used in this study. 3.1. multiple regression analysis the regression analysis is a collection of procedures that uses one or more independent variables to explain changes in a dependent variable. at the end of this process, the model specified in eq. (2) is obtained where dependent variable is y, independent variables are i x , constant term is 0  , regression coefficient of p variables are p  , error term is  , and p=1,…,k (tabachnick & fidell, 2013; kalaycı, 2014; i̇slamoğlu & alnıaçık, 2014). 0 p p y x  = + + (2) in eq. (2),  denotes the error caused by variables that were not included in the analysis for various reasons, whereas 0  represents the value of the dependent variable when all the independent variables regression coefficient values in the model are zero. the null hypothesis that all regression coefficients for the p independent variable are equal to zero and the alternative hypothesis that at least one regression coefficient is different from zero are both tested in multiple linear regression analysis. the t-test is used to determine the singular significance of the specified parameters, while the f-test is used to determine the model's overall significance. the assumptions of normal distribution, linearity, zero mean of error terms, constant variance, no autocorrelation, and no multiple correlations must all be met in multiple linear regression analysis. additionally, the level of explanation of the change in the dependent variable of the independent variables included in the model can be calculated as a percentage using the coefficient of determination, 2 r . if the model contains many independent variables, the adjusted coefficient of determination, 2 r , is used instead of 2 r (tabachnick & fidell, 2013; kalaycı, 2014; i̇slamoğlu & alnıaçık, 2014). among the recent studies in which the mra has been used, we can indicate financial risk measurement and prediction (valaskova et al., 2018), evaluating the impact of corporate social sustainability culture on financial success (schönborn et al., 2019), the influence of different aspects of governance, namely participation, policy coherence, reflexivity, adaptation and democratic institutions on sdg effects of sustainable governance to sustainable development 127 achievement (glass & newig, 2019), determining the factors influencing the integration of sustainability indicators into a company’s performance management system (zharfpeykan & akroyd, 2022), and investigating the factors attracting the population (kokubun, 2022). 3.2. best-worst method weighting processes are used to determine the importance levels of the criteria on the solution of multi-criteria decision problems. there are numerous methods for determining criteria weighting based on the data structure of a decision matrix or subjective evaluations of experts/decision-makers. subjective weighting techniques based on pairwise comparisons are frequently used in this context. bwm, one of the pairwise comparison methods, will be used in this study. in general, for n criteria, n(n-1)/2 comparisons are usually required in the pairwise comparison-based techniques. the large number of pairwise comparisons appears to be a significant impediment to effective weighting, especially in problems with a large number of criteria. when compared to the commonly used ahp (analytic hierarchy process), which provides weighting with pairwise comparisons, bwm allows the weighting process to be completed with fewer pairwise comparisons. fucom (full consistency method), which has a similar structure to bwm, prevents inconsistency in expert evaluation and ensures complete consistency. however, bwm allows for pairwise criteria comparisons in the context of the most and least important criteria. as a result, bwm was preferred because it allows comparison with both the least important and most important criteria, making the expert feel at ease with the evaluations. furthermore, bwm, like fucom, allows for the measurement of consistency analysis using a mathematical programming model and reduces pairwise comparison inconsistency (rezai, 2015; 2016; aytekin, 2020). on the other hand, bwm provides weighting based on the subjective assessments of experts or decision makers. as a result, it is lacking in objectivity. bwm also employs saaty's 1-9 fundamental scale. criticisms of the saaty fundamental scale are valid for bwm. in the study, bwm will be used to obtain criteria weight values based on expert judgments in a way that minimizes inconsistency. bwm has recently been used to solve decision problems such as wagons for the internal transport (stević et al., 2017), evaluating financial performance of companies (aytekin, 2020), off-road vehicle selection (pamučar & savin, 2020), supplier selection for biofuel companies (kazemitash et al., 2021), analyzing barriers to industrial sharing economy (govindan et al., 2020). implementation steps of bwm are outlined below (rezai, 2015; rezai, 2016; aytekin, 2020). step 1: determine the criteria to be used: the criteria that will be used to solve multi-criteria decision-making problems are identified. step 2: determine the most important and the least important criteria: among the criteria, the most important (the best) and least important (the worst) criteria are determined. b denotes the most important criterion, while k denotes the least important criterion. step 3: make pairwise comparisons of criteria based on the most important one: the saaty 1-9 fundamental scale is used to determine the importance level of the most important criterion in relation to other criteria, and the vector in eq. (3) is created. gündoğdu & aytekin/oper. res. eng. sci. theor. appl. 5(2) 2022 117-151 128 ( )1 2, , ,b b b bna a a a= k (3) when using saaty's 1-9 fundamental scale to determine the importance level of b according to the j criterion, a value of 1 indicates equal importance, a value of 2 indicates very little importance, and a value of 3 indicates a little more importance. similarly, a value of 4 denotes more than a little importance, a value of 5 denotes strong importance, a value of 6 denotes slightly more than strong importance, a value of 7 denotes very strong importance, a value of 8 denotes more than very strong importance, and a value of 9 denotes absolute importance (saaty, 1977; aytekin & durucasu, 2020). step 4: make pairwise comparisons based on the least important criteria: the saaty 1-9 fundamental scale is used to determine the importance levels of the criteria other than the least important criteria in relation to the least important criteria, and the vector in eq. (4) is created. ( )1 2, , , t k k k nk a a a a= k (4) step 5: calculate the optimal criteria weight values: the weight values of the criteria are determined using the linear programming model in eq. (4). the aim of this process is to make the largest of the b bj j w a w − and the smallest of j jk k w a w − differences for each j criterion. the purpose of equation (5) is to find criterion weights that minimize the value of ξ. 1 to , , 1 0, b bj j j jk k n j j j min subject w a j w w a j w w w j    = −   −   =    (5) step 6: check consistency: in this step, the consistency of pairwise comparisons of criteria is determined. ξ shows the model's inconsistency in eq. (5). as a result, it is tried to achieve high consistency criterion weight values. rezai (2016) proposed the consistency index (ci) in table 2 for the control of consistency in the context of the importance level of the most important criterion relative to the least important criterion (abk). table 2. consistency index abk 1 2 3 4 5 6 7 8 9 ci (enb ξ) 0,00 0,44 1,00 1,63 2,30 3,00 3,73 4,47 5,23 effects of sustainable governance to sustainable development 129 table 2 shows the maximum acceptable ξ values based on the number of criteria. the fact that the objective function ξ value obtained from solving the model in equation (4) is less than the value in table 1 indicates that the comparisons are consistent. also, the consistency ratio (cr, or ξ*) given in eq. (6) can also be used for consistency analysis. cr ci  = (6) while the cr value is between 0 and 1, it is important to note that consistency increases as it approaches 0, and inconsistency increases as it approaches 1. bwm is said to produce more consistent and reliable results than other weighting techniques (rezai, 2015; rezai, 2016). 3.3. grey relational analysis julong (1989) proposed gray system theory to solve problems with insufficient or uncertain information. gray system theory is based on the idea that understanding a system is insufficient to construct a relational analysis or a model to characterize it. gray is employed to express uncertain or incomplete information in this theory. white denotes the possession of certain/complete information, while black denotes the absence of such information. systems analysis, data processing, modeling, forecasting, decision making, and control are all fields where gray theory is applied. gray relational analysis (gra) is a form of quantitative analysis that involves the evaluation of alternatives and is used in the field of decision making. at this point, gray theory, like fuzzy set theory, has a mathematical structure that can process weak information (julong, 1989; wu, 2002; lin & liu, 2004; sallehuddin et al., 2008; tzeng & huang, 2011). as previously stated, the data used in the evaluation of countries was compiled from various sources and normalized. the values of the indicators in such data are difficult to interpret. in other words, as the values of an indicator rise, the level of sustainability rises or falls, but there is no direct equivalent of this value. as a result, the gray relational analysis method, which allows for the creation of a comparability series known as a reference series, was chosen for the study by taking into account the performances of the alternatives with incomplete information. the reference series is used to calculate the gray relational coefficient values for the alternatives. finally, the gray relationship degrees are calculated using these values. if an alternative has the highest gray relational degree with the reference series, it means that the corresponding alternative is the most similar to the reference series and will be the best choice (liu et al., 2013; biswas et al., 2014). however, problems can arise when using the normalization operation, which is commonly used in gra, in decision matrices containing some data structures, such as the reference series value being 0 or greater than the values in the decision matrix (aytekin, 2021a). different normalization techniques can be used in this case to generate a comparable decision matrix. gra, which is widely used in the field of multi-criteria decision making, provides a solution by defining the ideal values (points) for each criterion in the decision matrix and using this reference series to measure the relational degree of the alternatives. as a result, the alternative with the highest degree of relation is chosen gündoğdu & aytekin/oper. res. eng. sci. theor. appl. 5(2) 2022 117-151 130 as the solution. gra might be called a reference-based method because of this basic feature. furthermore, many integrated decision models and fuzzy derivatives where gra is used in combination with other multi-criteria decision-making methods can be found in the literature. supplier selection (yang & chen, 2006), determination of the most appropriate parameters in the drilling process (tosun, 2006), wastewater treatment method selection (zeng et al., 2007), facility layout (kuo et al., 2008), sustainable electricity generation planning (malekpoor et al., 2018), identification of factors affecting taiwan's economic growth (huang et al., 2020), and evaluation of countries' climates are examples of decision problems to which gra is applied (niazi et al., 2021). among the recent studies in which gra has been used, we can indicate evaluation of healthcare service quality factor (aydemir & şahin, 2019), measurement of city sustainability (yi et al., 2021), investigation of life cycle assessment barriers for sustainable development (kaswan & rathi, 2021), evaluation of water quality (tao et al., 2022), and sustainable industrialization performance evaluation of european union countries (candan & cengiz toklu, 2022). the gra process steps can be summarized as follows (wu, 2002; tzeng & huang, 2011): step 1. construct the decision matrix: the decision matrix x indicated in eq. (7) is constructed where i=1,…,m alternatives and j=1,…,n criteria. 11 1 1 n m mn x x x x x     =       k m o m l (7) step 2. create the reference series: the ideal values for each criterion are determined to generate a reference series ( 0 j x ). the reference series can be assigned independently of the decision matrix by the decision maker. the values in the decision matrix, on the other hand, are primarily considered in the gra implementation, and the best ones are determined as a reference. the reference series is obtained with eq. (8) if the best values in the decision matrix are used as a reference. ( ) ( ) 0 max , minj ij ij ii x x j j x j j + − =   (8) j + denotes for benefit-oriented criterion, while j − shows for cost-oriented criteria in eq. (8). step 3. construct the normalized decision matrix: the normalized matrix is constructed using eq.s (4-5), depending on how the ideal values are derived. when a reference is decided in the context of the decision matrix's values, eq. (9) is used, and when a reference is determined independently of the decision matrix, eq. (10) is used. * max max min , max , max min ij ij j ij ij jj ij ij ij j ij ij jj x x x x j j x x x j j x x + + −  −  =  −   − (9) effects of sustainable governance to sustainable development 131 0* 0 max ij j ij ij j j x x x x x − = − (10) other reference-based normalization techniques can be used if the operation specified in eq. (10) does not provide effective normalization under certain decision matrices (aytekin, 2021a). step 4. calculate the distances between the alternatives from the references: eq. (11) is used to compute the distances of the alternatives from the reference series using the normalized values, where * 0 j x is the normalized reference value for the criterion j. * * 0ij j ij x x = − (11) ij  represents the distance between the alternative i and the reference series in criterion j in eq. (11). as a result, the distance matrix δ will be constructed according to eq. (12). 11 1 1 n m mn       =       k m o m l (12) step 5. calculate gray relational coefficients: to calculate gray relational coefficients, first determine the largest and smallest values in the δ matrix, as well as the discriminant coefficient (ζ). the largest and smallest values in the δ matrix are determined using eq.s (13-14). max max max ij i j  =  (13) min min min ij i j  =  (14) the ζ coefficient regulates the relationship between min  and max  values by taking a value in the range [0,1]. to put it another way, the range of the ζ coefficient and gray relationship coefficient can be increased or compressed. the ζ coefficient is generally defines as 0.5 for averaging. after determining the ζ, min  and max  values, eq. (15) is used to derive the gray relational coefficients ( ij  ). min max max ij ij     +  =  +  (15) step 6. calculate the gray relational degrees: eq. (16) is used to determine the gray relational degree (γi), which is a measure of how similar the alternatives are to the reference series. it takes into consideration weighting of criteria. 1 1 1 , the criteria are not weighted , the criteria are weighted n ij j i n ij j j n w   = =     =       (16) gündoğdu & aytekin/oper. res. eng. sci. theor. appl. 5(2) 2022 117-151 132 alternative’s closeness to the reference series representing ideal solutions is measured by the γi value. as a result, the problem's solution is finished by ordering the alternatives from largest to smallest based on the γi values. 4. results mra is used to examine causality relationships in this study, which is discussed in the context of sustainable governance and development. the countries were then evaluated using the gra in terms of sustainable development and governance. four different models were used in the mra analyses, which took into consideration the relationships between independent variables. these models have been used to examine the relationships between various dimensions of sustainable governance and development. table 3 summarizes the models and analysis findings. table 3. results of mra dependent variable sdg sdg sdg sdg technology, economy, environment, social political, economy, environment, social rule of law, economy, environment, social governance, economy, environment, social independent variables model 1 model 2 model 3 model 4 constant 43.487*** 23.732*** 48.112*** 48.835*** individuals using the internet (% of population) .116*** population growth (annual %) -.746* -2.399*** -3.031* gdp per capita (current us$) 2.893e-5 -1,011e-5 -5.784e-5 gdp growth (annual %) .439*** co2 emissions (metric tons per capita) -.455*** -.373*** human development index (hdi) 64.527*** political transformation 20.419*** political participation -3.183 political integration -1.291 2.943 e-government index 31.406*** governance 6.312* quality of democracy -3.884 economist democracy index -.018 environmental performance index .303*** .381*** ∆r2 0.827 0.863 0.765 0.74 f 142.460*** 156.569*** 81.178*** 106.088*** note: *, **, and *** indicate the significance at 10%, 5%, and 1% levels, respectively. it is obvious that the relationship between sustainable governance and sustainable development. by focusing on management and governance, the scope of this research has been narrowed. the effects of the economy, environment, and social policies, which are the foundations of sustainable development, are included as dependent variables in all four models in this context. in addition, the independent effects of sustainable governance to sustainable development 133 variables were analyzed for the meaning of technology influence in model 1, political influence in model 2, rule of law and democracy effect in model 3, and governance effect covering all of these in model 4. the increase in the number of people utilizing the internet in the country, as well as the value of the e-government index, had a positive impact on the sdg in model 1. countries that have advanced in icts (for example, the increase in internet usage rates of countries and the spread of eparticipation policies) have also achieved a certain level in terms of sustainable development. individuals' increased internet access, in particular, has an impact on their policymaker's ability to be more transparent, democratic, and accountable in front of the public. as a result, citizens' demands for information, consultation, and active participation in the delivery of public services are on the rise. some of these expectations are being met by the public agencies, particularly through their websites (gündoğdu, 2021). indeed, people's expectations for the development of egovernment and e-participation opportunities have risen as they increasingly use the internet, smartphones, and social media (itu-international telecommunication union, 2020). as a result, the global expansion of icts has had an impact on egovernment and digitalization in public administration (sandoval-almazan & gilgarcia, 2012). in this regard, the findings of the research are consistent with those of other studies that have concluded that digitization has a favorable impact on sustainability (funk, 2015; gouvea et al., 2018; pappas et al., 2018; del río castro et al., 2020). another finding made possible by this model is that increased carbon emissions have a negative effect on the sdgs. to put it another way, countries' sustainable development and technological progress are effective in lowering carbon emissions. in this aspect, the research findings gained are similar to funk's (2015) and omri and ben mabrouk's research findings (2020). the increase in the human development index (hdi) as an independent variable and the increase in sdgs are exactly related in model 2, which we derived by adding the political element influence on the primary components of sustainable development. the results are consistent with previous research (garrod & fyall, 1998; harris, 2000; ciegis et al., 2009; morelli, 2011) that emphasizes that evaluating development solely by economic growth is insufficient. the hdi, in particular, is based on three fundamental components: health, knowledge, and income level. these elements emphasize the importance of fulfilling social, economic, and political goals in human development. as a result, sustainable development helps to create a diverse socio-economic system that includes income, education, living standards, and health (ciegis et al., 2009). the findings support the link between political (political participation + political transformation + political integration) and social factors (hdi). in addition, this finding indicates that studies dealing with the subject of sustainability in political (patashnik, 2003) and social (torjman, 2000; mckenzie, 2004) dimensions may be related to each other. another result of this model is the prediction that as the population grows, sustainable development would decline. the major goal of the sustainable development issue is to come up with answers to the problems that will arise as the world's population grows. as a result, population increase has an impact on many aspects of a country, including production, consumption, social, and environmental variables. there is a direct link between a country's sustainable development and population planning in this context. the relationship between the rule of law and the sdgs, as well as independent variables, was investigated in model 3 developed as part of the research. in this gündoğdu & aytekin/oper. res. eng. sci. theor. appl. 5(2) 2022 117-151 134 context, it has been determined that countries with democratic, free, and independent judicial systems have greatly improved environmental and, in particular, political performance. it has been discovered that there is a positive and significant relationship between political transformation (stateness, political participation, rule of law, democratic institutions, political and social integration) and sustainable development, particularly in these countries. other research analyzing the relationship between judicial independence and democracy and sustainable development (stojanović et al., 2016; güney, 2017; glass & newig, 2019; omri & ben mabrouk, 2020) used the rule of law, sdgs, and governance variables. as a result, countries with legitimacy and democratic governance are more likely to achieve the sdgs. finally, in model 4, it was discovered that governance indicators and sdgs had a directly proportional relationship. while achieving the sdgs, it is critical for governments to develop solution policies that analyze the interactions between goals with a broad and holistic governance perspective. policymakers can solve development problems by implementing a multi-level governance process that includes all relevant stakeholders and follows a transparent, responsible, and effective governance strategy. as a result, governments are advised to develop integrated and coordinated sustainable policies. in this regard, the study, like others (stojanović et al., 2016; davis, 2017; güney, 2017; jindra & vaz, 2019; omri & ben mabrouk, 2020), has confirmed that governance has a favorable impact on sustainable development through quantitative analysis. in reality, like güney's research (2017), the findings of this study demonstrated that as the quality of governance rises, so does the level of sustainable development in both developed and developing countries. the research's original finding is that it indicates a link between several variable groups and sustainable development and governance. the level of governance, on the other hand, should be questioned considering each country's particular characteristics. a multi-criteria decision-making model was used to evaluate countries in terms of sustainable development and governance. bwm was used to weight criteria in this model. the criteria weights obtained by the bwm method are shown in table 4. table 4. results of bwm criteria c1 c2 c3 c4 c5 c6 c7 c8 weights 0.1307 0.0637 0.0637 0.0637 0.0637 0.0318 0.0955 0.0955 importance rankings 1 9 5 5 5 14 2 2 criteria c9 c10 c11 c12 c13 c14 c15 weights 0.0477 0.0637 0.0477 0.0101 0.0955 0.0637 0.0637 importance rankings 12 5 13 15 4 10 10 according to the bwm weighting results in table 3, the most important criterion was sdg, while e-government was the least important criterion. also, the cr value specified in eq. (6) is very close to zero for these comparisons (cr=0.06). thus, it can be said that a high level of consistency is achieved. economic, social, and environmental dimensions are the basis of sustainable development (basiago, 1999; mitcham, 1995). there are economic, social, and environmental components to the relationship between sustainable development and sustainable governance, as well effects of sustainable governance to sustainable development 135 as certain related institutional dimensions (spangenberg, 2002; bansal, 2005; meadowcroft et al., 2005). therefore, sustainable development was used as the best criterion in bwm, and the economic, social, and environmental criteria (economic transformation, governance, and epi) that directly affect the sdg were weighted as criteria near to the best. other criteria used within the scope of the study were correlated according to their importance. gra was used to evaluate countries in terms of sustainable development and governance, and to identify leading and behind countries and make comparisons. the analysis included 149 countries with no missing data in the criteria used in the study. the weight values of the criteria obtained using bwm are included in the gra processes. table 5 shows the ranking results obtained by gra. table 5. results of gra rank country rank country rank country rank country 1 sweden 41 ghana 81 nepal 121 saudi arabia 2 denmark 42 greece 82 gambia 122 mauritania 3 norway 43 jamaica 83 côte d'ivoire 123 laos 4 finland 44 hungary 84 kuwait 124 oman 5 switzerland 45 romania 85 bosnia and her. 125 myanmar 6 new zealand 46 bulgaria 86 morocco 126 iraq 7 germany 47 india 87 thailand 127 nigeria 8 estonia 48 peru 88 belarus 128 nicaragua 9 uruguay 49 argentina 89 rwanda 129 cameroon 10 united kingdom 50 malaysia 90 burkina faso 130 mozambique 11 ireland 51 montenegro 91 kenya 131 pakistan 12 netherlands 52 colombia 92 jordan 132 angola 13 austria 53 georgia 93 malawi 133 afghanistan 14 canada 54 armenia 94 tanzania 134 eswatini 15 iceland 55 brazil 95 p.n. guinea 135 congo, dem. rep. 16 czechia 56 north macedonia 96 cambodia 136 iran 17 australia 57 albania 97 sierra leone 137 zimbabwe 18 france 58 serbia 98 guinea 138 congo, rep. 19 slovenia 59 dominican rep. 99 turkey 139 eritrea 20 lithuania 60 uae 100 uganda 140 haiti 21 costa rica 61 ukraine 101 algeria 141 cent. afr. rep. 22 belgium 62 el salvador 102 niger 142 burundi 23 latvia 63 paraguay 103 kazakhstan 143 chad 24 korea, rep. 64 indonesia 104 guinea-bissau 144 venezuela 25 mauritius 65 vietnam 105 honduras 145 syrian ar. rep. 26 japan 66 philippines 106 azerbaijan 146 libya 27 spain 67 sri lanka 107 uzbekistan 147 yemen 28 chile 68 ecuador 108 egypt 148 sudan 29 malta 69 tunisia 109 ethiopia 149 south sudan 30 portugal 70 senegal 110 russian fed. 31 slovak rep. 71 benin 111 madagascar 32 israel 72 mongolia 112 djibouti 33 united states 73 china 113 guatemala 34 botswana 74 south africa 114 gabon 35 poland 75 moldova 115 mali 36 panama 76 bolivia 116 zambia 37 italy 77 namibia 117 togo 38 croatia 78 mexico 118 tajikistan 39 bhutan 79 bangladesh 119 liberia 40 cyprus 80 kyrgyzstan 120 lebanon when looked at the findings in table 5, it's clear that sweden is in top place and south sudan is in worst place. denmark, norway, finland, switzerland, new zealand, gündoğdu & aytekin/oper. res. eng. sci. theor. appl. 5(2) 2022 117-151 136 germany, estonia, uruguay, and the united kingdom also include the top ten countries. zambia, togo, tajikistan, liberia, lebanon, syrian arab republic, libya, yemen, sudan and south sudan include the bottom ten. sweden's focus on environmental integration and welfare policies in social and political terms might be seen as the cause for its ranking in first place in terms of sustainable development and governance. this country also has adaptable and effective action plans that are economically, environmentally, and socially viable (government offices of sweden, 2021). according to table 5, several leading european countries (denmark, norway, finland, switzerland, germany, and england) have enacted sustainability policies that are similar to sweden's. the gra results showed that developed and wealthy countries were first, while underdeveloped countries experiencing instability, such as war and conflict, were last. also, the countries in the first place are those that are at the top of several international institutions and organizations' indices of economic and democratic development levels. northern european and scandinavian countries do better in terms of governance and sustainability than other countries, depending on the strength of their democracy and executive capacity. it should also be stated unequivocally that the economic and social problems caused by the covid-19 pandemic have severely harmed several countries' political, administrative, and reform capacities. 4.1. validation of results and sensitivity analysis sensitivity analysis is commonly used to evaluate the effects of parameter changes, the reliability, and the validity of multi-criteria decision analysis solutions. sensitivity analysis can be performed using various approaches, such as changing the weighting coefficients of the criteria, changing the units of measurement in which the values of the alternatives are expressed, changing the scales presenting the linguistic criteria, changing the type of criteria (cost/benefit), and comparing the results obtained by various methods. most studies, however, conduct a sensitivity analysis based on changes in the weighting coefficients of the criteria and compares similar mcda methods’ results (biswas, 2020; durmić et al., 2020; božanić et al., 2021; puška et al., 2021; biswas et al., 2021a; biswas et al., 2021b; aytekin, 2022). for this reason, changing criteria weight coefficients and comparing similar mcda methods’ results are used to make sensitivity analysis for the validation of results. the sensitivity analysis on the criterion weight values is used to assess the impact of the most influential criterion on the ranking performance of the proposed model. in this context, to investigate changes in criterion weighting coefficients, fourteen different sets were created. the weight values of the other criteria were changed only once for each criterion to create these sets (aytekin, 2022). these sets, which include new criterion weight coefficients, are shown in table 6. effects of sustainable governance to sustainable development 137 table 6. the sets for changing criteria weight coefficients c1 c2 c3 c4 c5 c6 c7 c8 c9 c10 c11 c12 c13 c14 c15 set 0 0.1307 0.0637 0.0637 0.0637 0.0637 0.0318 0.0955 0.0955 0.0477 0.0637 0.0477 0.0101 0.0955 0.0637 0.0637 set 1 0.0637 0.0637 0.0637 0.0637 0.0318 0.0955 0.0955 0.0477 0.0637 0.0477 0.0101 0.0955 0.0637 0.0637 0.1307 set 2 0.0637 0.0637 0.0637 0.0318 0.0955 0.0955 0.0477 0.0637 0.0477 0.0101 0.0955 0.0637 0.0637 0.1307 0.0637 set 3 0.0637 0.0637 0.0318 0.0955 0.0955 0.0477 0.0637 0.0477 0.0101 0.0955 0.0637 0.0637 0.1307 0.0637 0.0637 set 4 0.0637 0.0318 0.0955 0.0955 0.0477 0.0637 0.0477 0.0101 0.0955 0.0637 0.0637 0.1307 0.0637 0.0637 0.0637 set 5 0.0318 0.0955 0.0955 0.0477 0.0637 0.0477 0.0101 0.0955 0.0637 0.0637 0.1307 0.0637 0.0637 0.0637 0.0637 set 6 0.0955 0.0955 0.0477 0.0637 0.0477 0.0101 0.0955 0.0637 0.0637 0.1307 0.0637 0.0637 0.0637 0.0637 0.0318 set 7 0.0955 0.0477 0.0637 0.0477 0.0101 0.0955 0.0637 0.0637 0.1307 0.0637 0.0637 0.0637 0.0637 0.0318 0.0955 set 8 0.0477 0.0637 0.0477 0.0101 0.0955 0.0637 0.0637 0.1307 0.0637 0.0637 0.0637 0.0637 0.0318 0.0955 0.0955 set 9 0.0637 0.0477 0.0101 0.0955 0.0637 0.0637 0.1307 0.0637 0.0637 0.0637 0.0637 0.0318 0.0955 0.0955 0.0477 set 10 0.0477 0.0101 0.0955 0.0637 0.0637 0.1307 0.0637 0.0637 0.0637 0.0637 0.0318 0.0955 0.0955 0.0477 0.0637 set 11 0.0101 0.0955 0.0637 0.0637 0.1307 0.0637 0.0637 0.0637 0.0637 0.0318 0.0955 0.0955 0.0477 0.0637 0.0477 set 12 0.0955 0.0637 0.0637 0.1307 0.0637 0.0637 0.0637 0.0637 0.0318 0.0955 0.0955 0.0477 0.0637 0.0477 0.0101 set 13 0.0637 0.0637 0.1307 0.0637 0.0637 0.0637 0.0637 0.0318 0.0955 0.0955 0.0477 0.0637 0.0477 0.0101 0.0955 set 14 0.0637 0.1307 0.0637 0.0637 0.0637 0.0637 0.0318 0.0955 0.0955 0.0477 0.0637 0.0477 0.0101 0.0955 0.0637 set 0 in table 6 represents the original weight values obtained using bwm in this study. table 7 shows the spearman rank correlation (r s) results of the ranking results obtained with the sets created with the criterion weight values in table 6. gündoğdu & aytekin/oper. res. eng. sci. theor. appl. 5(2) 2022 117-151 138 table 7. the values of the spearman’s rank coefficient set 0 set 1 set 2 set 3 set 4 set 5 set 6 set 7 set 8 set 9 set 10 set 11 set 12 set 13 set 14 set 0 1 0.994 0.982 0.997 0.990 0.988 0.994 0.987 0.986 0.996 0.992 0.991 0.992 0.992 0.993 set 1 0.994 1 0.976 0.991 0.986 0.979 0.988 0.987 0.983 0.994 0.987 0.986 0.983 0.989 0.987 set 2 0.982 0.976 1 0.987 0.965 0.985 0.963 0.951 0.996 0.980 0.983 0.985 0.975 0.971 0.992 set 3 0.997 0.991 0.987 1 0.990 0.993 0.991 0.982 0.989 0.993 0.995 0.995 0.994 0.993 0.996 set 4 0.990 0.986 0.965 0.990 1 0.987 0.995 0.995 0.968 0.981 0.990 0.987 0.994 0.996 0.986 set 5 0.988 0.979 0.985 0.993 0.987 1 0.983 0.975 0.985 0.979 0.991 0.995 0.993 0.990 0.996 set 6 0.994 0.988 0.963 0.991 0.995 0.983 1 0.994 0.970 0.989 0.986 0.986 0.993 0.994 0.985 set 7 0.987 0.987 0.951 0.982 0.995 0.975 0.994 1 0.958 0.979 0.981 0.977 0.985 0.992 0.976 set 8 0.986 0.983 0.996 0.989 0.968 0.985 0.970 0.958 1 0.986 0.984 0.989 0.977 0.977 0.993 set 9 0.996 0.994 0.980 0.993 0.981 0.979 0.989 0.979 0.986 1 0.985 0.987 0.986 0.984 0.988 set 10 0.992 0.987 0.983 0.995 0.990 0.991 0.986 0.981 0.984 0.985 1 0.992 0.993 0.994 0.992 set 11 0.991 0.986 0.985 0.995 0.987 0.995 0.986 0.977 0.989 0.987 0.992 1 0.994 0.992 0.995 set 12 0.992 0.983 0.975 0.994 0.994 0.993 0.993 0.985 0.977 0.986 0.993 0.994 1 0.995 0.992 set 13 0.992 0.989 0.971 0.993 0.996 0.990 0.994 0.992 0.977 0.984 0.994 0.992 0.995 1 0.989 set 14 0.993 0.987 0.992 0.996 0.986 0.996 0.985 0.976 0.993 0.988 0.992 0.995 0.992 0.989 1 table 7 shows that the spearman's rank correlation coefficients of the sets have a very high correlation degree (r s ≥ 0.95). these results show that changes in the criterion weighting coefficients have no significant effect on the model. on the other hand, a comparative analysis of the stability of the obtained results using gra was executed throughout the application of other methods. the proposed model was compared to recent techniques such as cradis (compromise ranking of alternatives from distance to ideal solution) (puška et al., 2021), mairca (multi-attributive ideal-real comparative analysis) (pamučar et al., 2014; 2017). ref-i (nearest solution to references-i) (aytekin and durucasu, 2021), ref-ii (aytekin, 2021b), waspas (weighted aggregated sum product assessment) (zavadskas et al., 2012), psi (preference selection index) (maniya and bhatt, 2010), mabac (multi-attributive border approximation area comparison) (pamučar and ćirović, 2015). the t-score conversion (aytekin, 2022) was determined for those affected by negative values, λ=0.5 in waspas, and reference values in ref-i and ref-ii were determined depending on the optimization aspect of the criteria in the applications performed with these methods. figure 2 depicts the obtained results in the form of a ray graph. effects of sustainable governance to sustainable development 139 figure 2 comparative analysis of ranking results using different methods and gra figure 2 shows the reliability of the gra rankings. as shown in figure 2, all methods produced remarkably similar results. the rank correlation coefficients of the methods also shed light on the ranking's similarity and validity. as a result, the gra method produces strong rank coefficients when compared to the ranking results of cradis (rs=0.996), mairca (rs=0.993), ref-i (rs=0.988), ref-ii (rs=0.986), waspas (rs =0.981), and mabac (rs =0.993). gra ranking results are valid and reliable for the nature of the problem determined. 5. conclusions the subject of sustainable development and sustainable governance has universal characteristics in that it contains sdgs and sustainable governance indexes that apply to a wide range of disciplines. this study, which considers variables connected to governance, has investigated the effect of sustainable governance on sustainable development. the link between sustainable governance and sustainable development in a sample of 149 countries was discovered. in this context, we have determined that, despite some variances, sustainable governance has an impact on sustainable development. the study's most notable feature is that it uses multiple gündoğdu & aytekin/oper. res. eng. sci. theor. appl. 5(2) 2022 117-151 140 regression analysis to find the sustainable governance variables that influence sustainable development. in addition, the bwm-gra multi-criteria decision model is used to classify and evaluate the countries included in the study based on their performance. as a result, by combining two quantitative analytic methods, this study is able to draw a thorough conclusion regarding the research topic. also, it was limited by considering the criteria/variables, datasets, and countries, and studies relating to this issue were used to determine the variables. in addition, the data diversity has been extended by incorporating data sets from a variety of international agencies and organizations concerned with sustainable governance. multiple regression analysis was utilized in this study to investigate the change and relationship between sustainable governance and sustainable development, and four models were estimated. significant findings were obtained as a result of the established models. it has been established that there is a link between several variable groups and sustainable development and governance. according to the results obtained in the study, variables like the number of people utilizing the internet in a country, the e-government index, hdi, the population growth, the rule of law with political transformations, and governance influence sustainable development. the findings are consistent with previous research (stojanović et al., 2016; davis, 2017; güney, 2017; omri & ben mabrouk, 2020). in addition, we also observed that the population growth rate is the strong control variable in analyzing the relationship between sustainable governance and sustainable development indicators. in conclusion, there is an inverse relationship between population increase and sustainable development. this outcome is consistent with the characteristics of the sustainable development paradigm. on the one hand, components of good governance such as democracy, rule of law, and accountability have a favorable impact on the implementation of sustainability policies. political polarization and unilateral policies that are not inclusive, on the other hand, have a detrimental impact on sustainability. there is a similarity between the development level indicators of many international agencies and organizations and the gra results acquired in the study in terms of sustainable development and governance. according to the mcdm findings, countries at the forefront, such as sweden, denmark, norway, and finland, are also ahead in terms of sustainable development and governance policies. the gra results obtained for the countries in the study also confirm the literature in this regard. sustainable development is also on the rise in some developed and developing countries with average or above-average sustainable governance. the situation in low-income or undeveloped countries where governance quality is below average has a detrimental impact on development sustainability. we confirm that governance has a good and significant impact on sdgs, indicating that this idea will continue to play a unifying and auxiliary role today and in the future. as a matter of fact, reports from international institutions and extraordinary events like the present covid-19 epidemic demonstrate that systems based on governance, coordination, and cooperation among stakeholders have regained prominence. by properly implementing the rule of law, an independent judiciary, democracy, and related governance features, rules, and regulations, countries can help ensure that present resource use is at a level that is least damaging to future resource use. additionally, the impact of ict-related advancements such as the internet continues to have an impact on governance and development sustainability. therefore, we suggest that effects of sustainable governance to sustainable development 141 when developing methods to address global concerns, the above-mentioned variables be considered. we believe that it is important to explore the sustainability relationship between governance and 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(2022). factors influencing the integration of sustainability indicators into a company's performance management system. journal of cleaner production, 331, 129988. https://doi.org/10.1016/j.jclepro.2021.129988 © 2022 by the authors. submitted for possible open access publication under the terms and conditions of the creative commons attribution (cc by) license (http://creativecommons.org/licenses/by/4.0/). plane thermoelastic waves in infinite half-space caused operational research in engineering sciences: theory and applications vol. 2, issue 3, 2019, pp. 55-64 issn: 2620-1607 eissn: 2620-1747 doi: https://doi.org/10.31181/oresta1903055k * corresponding author. inz.84kula@gmail.com (n. kovačević), aleksandra.stoiljkovic@yahoo.com (a. stoiljkovic), mitar.kovac21@gmail.com (m. kovač) application of the matrix approach in risk assessment1 nenad kovačevića*, aleksandra stojiljkovićb, mitar kovačc a university of defence, military academy, belgrade, serbia b university of novi sad, faculty of economics, subotica, serbia c “educons” university, faculty for project and innovation management, belgrade, serbia received: 16 october 2019 accepted: 24 november 2019 first online: 11 december 2019 professional paper abstract. the risk assessment process is based on risk management. risk assessment is, in principle, an entirely empirical decision-making process, based on risk assessors’ knowledge and experience, necessary to identify (a) hazard(s) as the cause for risk by using specific and well-known and recognized methods so far. currently, there are a large number of methods recognized for risk assessment, which are mostly formed by various organizations and associations of engineers, usually in insurance companies. the paper presents the most pragmatic matrix (qualitative) risk assessment methods, such as: a 3x3 matrix (ohsas), a 4x4 matrix (as/nzs 4360) and a 5x5 matrix (mil-std-882b). the paper is significant in that the matrix approach in risk assessment is the basis for the development of risk assessment methods, regardless of the method of the group which they belong to. key words: decision-making, risk assessment, matrix approach 1. introduction one of the main characteristics of the modern era is the permanence of change in all spheres of life and work. a science ratio and the frequency of change are in a causal relationship, given the fact that science (especially the field of technicaltechnological sciences) is usually the cause of changes, as well as the sphere of the 1 this paper is an extended and amended version of the paper entitled “risk assessment in engineering protection-matrix approach”, published at the conference entitled “security and crisis management –theory and practice, 2019”. kovačević et al./oper. res. eng. sci. theor. appl. 2 (3) (2019) 55-64 56 human action, which is permeated by the repercussions reflections of the same. however, as part of planning (the initial process functions of management), decision-making is also present in the other functions (organization, coordination and control). risk management and decision-making are inextricably linked to each other, because there is no decision without a certain level of risk. consequently, risk management is the state of the process or a set of environmental conditions which can be treated adequately and comprehensively in order to make timely, accurate and correct decisions. risk assessment is the basis of risk management. it is, however, important to point out the fact that, although purely empirical, risk assessment is simultaneously also a subjective process (which depends on the knowledge of the stages of the work process by the risk assessor); if, however, certain algorithms, tools and principles are followed and applied, that subjectivity may yet be reduced to the lowest possible level. in this paper, a group of risk assessment methods (one approach), namely the matrix risk ones, are presented. the characteristic features of this group of risk assessment matrix method in general are that they (a) are developed the first, (b) are the starting point for the other groups of methods, and (c) in practice, have proven to be most susceptible to all participants of the risk assessment process. 2. decision-making in terms of risk the very issue of decision-making as a process of coming to a decision is highly interdisciplinary and can be studied from different aspects. business environments and organizations constantly change, so the future consequences of decisions are impossible to fully predict. in a turbulent, dynamic, uncertain and changing environment, the decision-making process becomes increasingly complex and demanding, and to make informed decisions requires a certain extensive preparation. in this regard, in an effort to comprehensively examine this problem, scientists are faced with the fact that there is poor knowledge of classical economic/financial theory included in a number of other scientific disciplines (kolev et al. 2015). decision-making theory is a result of the joint efforts of experts in the fields of economics, psychology, philosophy, mathematics and statistics (damjanovic & jankovic, 2014). the theory of creating a set of knowledges and appropriate analytical techniques with different degrees of formality is designed to help the decision-maker to choose alternatives based on implications (miskovic, 2016). it is necessary to make a distinction between the normative and descriptive (behavioral) decision theory. normative decision theory deals with the way in which decisions need to be made. the best decision is always sought, it being implied that the ideal decisionmaker (dm) is fully informed and rational (miskovic, 2016). normative theory deals with the concept of the rationality and logic of decision-making as they should actually be (milicevic et al. 2007). in the normative approach, the decision-making problem is well defined – -the principles of normative theory showing how a perfectly rational individual should make decisions. this approach assumes certain rules that people, if abiding by them, may rely on in a situation when they have to make the best decision (damjanovic & jankovic, 2014). application of the matrix approach in risk assessment 57 descriptive theory describes how decisions are actually made and discusses the practical application of normative theory. the primary objective of descriptive theory is to help understand and explain how individuals consider available information and, based on such information, come to a certain decision or make a certain choice. descriptive decision-making theory is concerned with what is singled out in normative theory as a deviation from criteria for rational behavior. the focus of interest consists of both the characteristics and the limitations of the dm’s cognitive system, on the one hand, and other psychological causes for the mistakes that he makes when making a decision. descriptive theories are focused on finding tools, methods and software to help make better decisions (miskovic, 2016). in theory and practice, one can find different approaches to decision-making. the access to decision-making that is increasingly gaining in importance is decisionmaking based on risk assessment. the term ‘risks’ can be associated with the uncertainty of those future events that may affect the outcome of the reporting process (crnjac & masle, 2013). in general, there are three different conditions in which decisions are made, and which are based on the degree of the predictability of the outcome of a future decision. in terms of security, decision-making implies that the choice of one among the alternatives based on the outcome of having chosen the alternative the most appropriate for the organization should also depend on the known outcome (result) of each alternative. however, there are situations when it is impossible for the dm to know with certainty what will happen in the future; on their own part, alternative outcomes depend on the circumstances often unknown to us. in such cases, we speak about decision-making under uncertainty and risk conditions (detectable uncertainty). in conditions of uncertainty, it is possible to determine future events, i.e. different outcomes of each alternative are possible to predict, but probability distributions are unknown, whereas in conditions of risk, each alternative has one of several possible consequences, and the likelihood of the occurrence of each such consequence is known (damjanovic & jankovic, 2014). given the variability of both organizations, as well as the environment in which they exist, future implications of decisions cannot be fully predicted. most decisions made in organizations contain a certain amount of risk. the condition of risk(s) is actually a wide range and, inside it, the degrees of risk may be associated with decisions, in the sense that the lower the quality of information on the outcome of the alternative, the closer the situation is to complete uncertainty, for which reason the risk of selecting that particular alternative is higher (certo & certo, 2008). management seeks to know the size and nature of the risks associated with the adoption of economic decisions in a particular situation. in most cases, risk analysis is based on economic analysis and estimates of probability (kolev et al. 2015). 3. risk assessment procedure in order to understand risk assessment and its applicability, it is necessary to make a clear distinction between the concepts of governance and risk assessment. the importance of the above-mentioned is also reflected in the fact that this issue is regulated by a set of internationally recognized documents, such as the iso 31000:2015 (risk management) standard. as a potential, principled, yet nonbinding framework for risk management, the mentioned standard uses the pdca kovačević et al./oper. res. eng. sci. theor. appl. 2 (3) (2019) 55-64 58 (the acronym for: plan, do, check, act) cycle, the elements of which are shown in table 1; it is possible to notice that the first step, as well as the basis for risk management, is the identification and valorization of risks. according to iso 31000:2015, risk management is a more general concept in relation to estimation (assessment) i.e. risk management is based on estimation, also including the following: (1) the context establishment and (2) risk actions, i.e. risk treatment. risk assessment itself (evaluation)consists of: ✓ risk identification, ✓ risk analysis, and ✓ risk evaluation. table 1. the pdca cycle according to iso 31000:2015 pdca cycle framework elements plan context determination risk assessment risk treatment plan residual risk acceptance do plan implementation check continuous monitoring and inspection (surveillance) act risk management maintenance and improvement source: www.risk assessment matrix.com risk identification is carried out in order to form: (1) a list of risk sources, (2) a list of risk causes, (3) a list of the events that may affect the achievement of the objectives defined in the context of risk management, and (4) the development of a scenario of the events. accordingly, the standard srps a.l2.003 – risk assessment to protect persons, property and operations provides for the following types of risk: (a) risks within general business; (b) risks to occupational safety and health and safety and health in the work environment; (c) the risk of natural disasters or other disasters; (d) legal risks; (e) risks from the illegal operation of risks; (f) the risk of fire, and (g) risks of non-compliance with standards. through risk identification, the following techniques are commonly used: (1) survey, (2) interviewing, (3) the control list (checklist), (4) the trackingand experience-based judgments (5) scenario analysis and (6) the analysis of engineering system techniques. risk analysis is an input element to: (a) risk evaluation and (b) a decision on whether it should be treated with risks. the risk analysis procedure includes the following activities: (1) a description of the identified risks; (2) grouping related risk sources and risks; (3) the analysis of the influence of individual causes of risk; (4) the evaluation of the likelihood and the result of implementation risk; (5) the evaluation and quantification of risk valorization; (6) the identification of the factors that influence the effects and the likelihood; (7) a list of priority risks; (8) proposing a method/option for risk treatment and (9) defining measures for risk monitoring. accordingly, risk assessment is the most important part of risk evaluation (estimation being additional) because a valued risk is the product of risk analysis; application of the matrix approach in risk assessment 59 consequently, all methods are based on the risk analysis developed for the purpose of valorizing risk. the methods used in risk assessment can be divided into three major groups: (1) qualitative, (2) semi-quantitative (or a combination of the qualitative and quantitative) and (3) quantitative. qualitative and semi-quantitative risk analysis techniques and methods include: (a) polling; (b) the swot analysis; (v) causal diagrams; (c) the methods of expert marks; (d) the delphi method; (e) a preliminary analysis of a danger; (f) the fault tree/fault/failure method, (g) the event tree method and (h) the result of the probability matrix. the quantitative risk analysis techniques and methods are as follows: (a) probability theory; (b) mathematical statistics; (c) operational research; (d) sensitivity analysis; (e) scenario methods; (f) the error log method; (g) the event tree method; (h) the monte carlo method, and (i) the modeling and simulation method. in this paper, considers the probability and consequence matrix or the matrix methods for risk ranking/assessment are considered as actually the basis for all the aforementioned qualitative risk assessment methods (kovacevic et al. 2019). risk evaluation involves a comparison of the level of the risk detected in the risk analysis process, the risk criteria defined in the risk management context determination process, the determination of risk significance and dealing with risk. if the estimated risk meets the established criteria, that is considered as acceptable and does not require additional any control options. otherwise, it is necessary to establish a list of priority risks and the ways to deal with these risks. value at risk is regulated by specific standards and iso-iec 31010, which provides specific instructions on risk assessment techniques. in order to answer the question how risk assessment should be performed and what the steps or procedures for risk assessment performance are, the following must first be defined: ✓ the risk assessment performance methodology, and ✓ the risk assessment performance procedure. the risk assessment performance methodology defines the algorithm of and the tools for the implementation of and a concrete way to implement the risk assessment process, whereas the risk assessment process implementation procedure defines standardized series of steps necessary in order to ensure the process implementation in accordance with the recommendations of the relevant laws, regulations and best practice (nikolic & gavanski, 2010). figure 1. the steps of the risk assessment methodology kovačević et al./oper. res. eng. sci. theor. appl. 2 (3) (2019) 55-64 60 in the modern literature, the method published in risk assessment guidelines and manuals by the european agency for safety and health at work is usually used as the baseline risk assessment methodology. based on the experience of the author of the risk assessment paper, figure 1 is a schematic presentation of the steps of the risk assessment methodology. 4. risk assessment qualitative methods risk assessment qualitative methods are primarily based on the risk assessment team participants’ (risk assessors’) personal experiences and judgments and/or the use of available qualitative data. this approach does not require information about prior threats, hazards, causes and effects, but it does cause the end result of the risk assessment to be a descriptive statement of the qualitative risk size (e.g. high risk, moderate risk, etc.). qualitative criteria use the words such as: “rarely”, “amazing”, “possible”, “probable” or “almost certain” in order to describe the probability of unwanted events, as well as the words like “fatal”, “serious”, “small”, or “negligible” in order to describe the size of a damage-consequence. risk assessment qualitative methods most commonly use the subjective criteria that are measured by qualitative scales. consequently, risk assessment is subjective in nature, and therefore is subject to an error. in practice, qualitative scales with three to seven qualitative descriptions are optimally used, which requires a pronounced professional approach to potential threats and/or hazards analysis. the methods with fewer than three qualitative descriptions of risk factors are very simple, whereas if methods have more than seven such descriptions, that may lead to significant difficulties which are subjective in character associated with the inability of the risk assessment team participants to relatively precisely identify the qualitative description of risk factors/ constituents. the best-known representatives of this group of risk assessment methods are the matrix risk or the matrix risk rating. these methods are actually the essential methods also belonging in the group of both semi-quantitative and quantitative methods. risk assessors are often used in a risk matrix operation for the purpose of establishing a logical connection between the result and the probability of the risk assessment of identified hazards/harmfulness. also, they are used as defined by the uniform method for the determination of the degree or level of individual estimated risks. a risk matrix is formed through the following three steps: ranks of ordinates are applied to the probability (step 1), and abscissas are applied to the result of the ranks/severity (step 2). a combination of the above ranking levels results in the ranking of risks (step 3), as is shown in figure 2. in order to reach these data (probability and consequences), it is necessary to collect information, which is the first step in all risk assessment methods. practical experience has shown that “checklists” are an ideal tool for collecting information useful for the identification of dangers/hazards in the workplace and the working environment. to obtain a comprehensive picture of all potential risks and hazards, and consequently a better risk assessment, it is necessary to examine all the participants (administrative and executive bodies and end-users/workers) in the work process. application of the matrix approach in risk assessment 61 figure 2. forming a risk matrix (www.risk assessment matrix.com) n practice, the following three types of the matrix risk rating are used most frequently: (1) a 3x3 risk matrix (ohsas), (2) a 5x5 risk matrix (mil-std-882b), and (3) a 4x4 risk matrix (as/nzs 4360 2004). in its guidance on risk assessment, the european agency for safety and health at work recommends a 3x3 matrix, which was first defined in the standard ohsas 18001 and which is shown in figure 3. the matrix has three levels for the qualitative description of probability (bit-amazing, mediumprobably; high-very likely), as well as consequences (minor, major and serious). risk is also ascribed three levels, marked as a qualitative description of: low, moderate, and high. in the contemporary literature, this method is often called the “singaporean method/model”, which is but a variation of the above-mentioned methods (kovacevic et al. 2017). result of a dangerous event minor (1) moderate (2) serious (3) probability of a dangerous event rare (1) low risk (1) low risk (2) moderate risk (4) possible (2) low risk (2) moderate risk (4) high risk (6) almost certain (3) moderate risk (3) high risk (6) high risk (9) figure 3. risk matrix 3x3 the 4x4 risk matrix (as/nzs 4360) was formed according to the standards of australia and new zealand and belongs to the standard iso 31000, which relates to the risk management field. first, it appeared in 1995, and the last variation of this type of the risk ranking matrix appeared in 2009. the matrix is shown in figure 4. the categorization of the probability of the 4x4 risk matrix according to the recommendations of the standard a/nzs 4360 is as follows: (1) highly unlikely (-) may occur, but it will probably never be the case; (2) unlikely (-) may occur very rarely, and (3) is likely to (+) may occur at times; (4) very likely (++) may occur at any moment, i.e. its occurrence is almost certain. the categorization of the results of a dangerous event for the 4x4 risk matrix according to the recommendations of the kovačević et al./oper. res. eng. sci. theor. appl. 2 (3) (2019) 55-64 62 standard as /nzs 4360 is as follows: (1) small, (i) only the most basic first-aid measures; (2) moderate, (ii) a medical treatment is needed; a few days of a sickleave; (3) serious, (iii) a serious injury, or a long-term disease; (4) disastrous, (iv) death and permanent damage and a permanent disability to work. risk is categorized into six levels, the “s” level being a top priority, and an unacceptably high-risk category according to the priorities of “p1” to “p5”. the priorities define the order and importance of the action to be undertaken in order to reduce risk. the result of a dangerous event small (i) moderate (ii) serious (iii) disastrous (iv) t h e p r o b a b il it y o f a d a n g e r o u s e v e n t very likely (+ +) p2 p1 s s likely (+) p3 p2 p1 s unlikely (–) p4 p3 p2 p1 highly unlikely (– –) p5 p4 p3 p2 figure 4. the 4x4 risk matrix (www.risk assessment matrix.com) the 5x5 risk matrix (mil-std-882b) was formed by estimating risk in the armed forces of the united states, and the mentioned matrix is implemented in the american military standard (american military standard or the abbreviation milstd), which recommends three types of the risk assessment matrix of this type, namely: (1) 4x6 (mil-std-882c), (2) 5x5 (mil-std-882b) and (3) 4x5 (mil-std882d). the 5x5 risk matrix (mil-std-882c) comprises five levels (1 – negligible, 2 – minor, 3 – moderate, 4 – significant and 5 – severe), or a qualitative description of the effects of the event/impact which relates to professional illnesses, injuries, a loss of equipment and the hours of operation and the environmental impact. the interpretation of the 5x5 risk matrix for the purpose of assessing the risk of milstd-882b is shown in figure 5. figure 5. the 5x5 risk matrix (www.risk assessment matrix.com) application of the matrix approach in risk assessment 63 the quantity of the description and definition of the probability/likelihood of an adverse event is represented by the five levels (1 – very unlikely, 2 – unlikely, 3 – possible, 4 – likely and 5 – very likely). when using this risk matrix, five quantitative descriptions of the risk level are identified (low, low medium, medium, medium high and high). risk is considered to be unacceptable, if it is estimated to be very high and high, and acceptable, if it belongs to the field of secondary (medium, low medium) or low risk. 5. conclusion decision-making is a process very similar to the problem-solving process in that decision-making also actually determines what needs to be done, ultimately aimed at taking an action. accordingly, a decision is a specific commitment to an action, but does not end with a choice of some action, because the selection of an action is based on the consequences the dm expects from the action. here, it is possible to notice the two risk constituents: a likelihood and a consequence. in order to make good decisions, it is necessary to go through the risk management and risk assessment processes appearing in the decision-making process. in the modern literature, there are a multitude of risk assessment methods; therefore, the problem of the selection of an adequate method against the process for which risk is assessed, or valorized, appears. in this paper, a group of the methods considered to be basic for other methods, and simultaneously the simplest for understanding the significance and essence of risk assessment in one of decisionmaking segments, are presented. based on the foregoing, it is possible to conclude that the preference favoring the use of the risk matrix in the risk assessment process reflects in the fact that there is no possibility of accepting risks present in the unsafe work domain; consequently, it produces a possibility of making a large number of administrative and engineering decisions intended to reducing risk to an acceptable level. however, practical experience has shown that, when using the risk matrix, risk assessors are faced with a certain kind of limitations, including: a possibility of only applying the risk matrix to an identified threat or harm, or of the risk matrix not being the tool for hazard identification or identification, a high degree of subjectivity in risk assessment, and a possibility of only a comparative analysis of the risk level (kovacevic & stoiljkovic, 2019). references certo, s. c. & certo, s. t. (2008). moderni menadžment. zagrebačka škola ekonomije i menadžmenta, zagreb crnjac, d. & masle, d. (2013). the possibility of using monte carlo method in the case of decision-making under conditions of risk concerning an agricultural economics issue. ekonomski vjesnik, 26/1, 309-313. damnjanović, k. & janković, i. (2014). normativna i deskriptivna teorija donošenja odluka u uslovima rizika. theoria, pp. 25-50. kovačević et al./oper. res. eng. sci. theor. appl. 2 (3) (2019) 55-64 64 kolev, d., njegovanović, a. & ćosić, p. k. (2015). neuro-ekonomija kao savremena metoda istraživanja donošenja ekonomskih odluka. časopis za ekonomiju i tržišne komunikacije, 10/2, 278-296. kovačević, n., babić, b. & dimitrijević n. (2017). jedan pristup proceni rizika pri održavanju motornih vozila u vojsci srbije. rizik i bezbednosni inženjering, savić, b. (ed.), pp. 30-39., kopaonik, januar 2017, vtšss, novi sad kovačević, n., đorđević, n. & kovač, m. (2019). primena menadžmenta rizikom u realizaciji nastavno-obrazovnog procesa u vojnoj akademiji. vojno delo, 71/6, 166199. kovačević, n. & stoiljković, a. (2019). risk assessment in engineering protectionmatrix approach. security and crisis management-theory and practice, komazec, n. (ed.), pp. 41-49., october 2019, rabek, belgrade milićević, a., pavličić, d. & kostić, a. (2007). odlučivanje u uslovima rizika i teorija izgleda. psihologija, 40/1, 147-164 mišković, v. (2016). sistemi za podršku odlučivanju. univerzitet singidunum, beograd nikolić, b. & gavanski, d. (2010). mašine, oruđa za rad, uređaji radno mesto i okolina. vtšss, novi sad http://www.risk assessment matrix.com accessed 18 june 2019. © 2019 by the authors. submitted for possible open access publication under the terms and conditions of the creative commons attribution (cc by) license (http://creativecommons.org/licenses/by/4.0/). plane thermoelastic waves in infinite half-space caused operational research in engineering sciences: theory and applications vol. 3, issue 1, 2020, pp. 16-27 issn: 2620-1607 eissn: 2620-1747 doi: https://doi: 10.31181/oresta200113b * corresponding author. tapasbiswasmckv@gmail.com (t. biswas), prasenjit2007@gmail.com (p. chatterjee), choudhurib@gmail.com (b. choudhuri) selection of commercially available alternative passenger vehicle in automotive environment tapas biswas 1, prasenjit chatterjee 2*, bikash choudhuri 3 1 department of automobile engineering, mckv institute of engineering, howrah-711204, india 2 department of mechanical engineering, mckv institute of engineering, howrah-711204, india 3 department of mechanical engineering, dr. sudhir chandra sur degree engineering college, kolkata700074, india received: 25 october 2019 accepted: 27 december 2019 first online: 09 february 2020 research paper abstract. there has been a paradigm shift in the automobile industry due to e-mobility which reduces green-house gas emission and air pollution. in this context, selection of the most feasible automotive passenger vehicle is a complex decision-making problem due to the use of different power source, technology, specification and price. in this paper, five alternative vehicles based on fuel cell, hybrid electric, battery electric, plug in hybrid electric and compressed natural gas bi-fuel are evaluated using an integrated criteria importance through inter-criteria correlation (critic) combined compromise solution (cocoso) method. critic method is used to obtain the weights of the vehicle selection criteria, whereas, cocoso method is employed to rank the vehicles considering different technical and operational criteria such as greenhouse gas emission, fuel economy, vehicle range, accelerating time, annual fuel cost and vehicle base model cost. it is found that battery electric vehicle out performs all other considered alternatives. the validity of the results is verified by comparing with other well popular mcdm methods. further, a sensitivity analysis is conducted by changing the criteria weights to establish the stability of the model. key words: alternate passenger vehicle selection, cocoso, critic, sensitivity analysis 1. introduction alternate fuel vehicles are those which can be fueled in part or full by electricity, hydrogen, biodiesel, compressed natural gas (cng), liquefied petroleum gas (lpg) selection of commercially available alternative passenger vehicle in automotive environment 17 and ethanol as compared to the conventional petrol and diesel-based vehicles. the most commonly used alternate vehicles are battery-electric, hybrids, plug-in hybrids and fuel cell vehicles in addition to vehicles based on ethanol, biodiesel, biogas and hydrogen. the total environmental impact of the vehicle fleet is likely to decrease if conventional vehicles are replaced by alternate fuel vehicles. the alternate electric vehicle (ev) technology reduces emission, increases energy efficiency, does not have any energy consumption at static condition and also boosts with low ambient noise. fuel cells, similar to evs, also have no tailpipe emission, no corrosion to the engine and it is also quiet in operation. hybrid evs (hevs) and plug-in hevs (phevs) use a combination of internal combustion engines (ice) along with an electric motor and reduce fuel consumption and green-house gases (ghgs). bi-fuel vehicle is another type of alternate vehicle which recues the tailpipe emission than petrol and diesel engines. according to a report (iea 2019) that in 2018, more than 5.1 million the electric car was sold globally, out of these more than 66% of electric cars were battery evs (bevs). market share of electric car has been steadily increasing from 50% (2012) to 68% (2018). china, europe and united states are the world’s largest electric car market. the report also indicated that by the end of 2018, global stock of electric busses was 4,60,000 while the same for two wheelers was 260 million. in 2018, sales of light-commercial vehicles were around 2,50,000 units and medium electric truck reached in the range of 1000-2000 units. in the same year, global ev stock aided publicly accessible 5.2 million light-duty vehicle chargers and 1,57,000 fast chargers for buses. it is also observed that, in 2018, evs used about 58 terawatt-hours of electricity and produced 41 million tonnes of carbon-dioxide equivalent (co2e) on the road, that mean evs saved 36 million tonnes of co2e as compared to an equivalent internal combustion engine vehicle. in ev 2030 scenario, global ev sales are expected to be around 23 million (excluding two/three-wheelers) and would cut demand for fuel-based vehicles. bevs and phevs are presently using electricity for battery charging. the current global average carbon intensity of electricity generation (518 gms of co2e /kwh) emits huge amount of ghg if the power generation mix is controlled by a high carbon source. co2 emissions at evs are significantly reduced as the power generation is controlled by a low carbon power source. but in some countries, like india where the electric power is mainly produced by coal, therefore, hybrid vehicles emit lower ghg than the evs. further, the emission reduction potential of evs over their entire life cycle can further be raised if electricity generation can be made decarbonized. future concept in automobile sector now has been drastically changed. therefore, the future demand for automobile sectors are renewable or alternate energy-based vehicles which can reduce emission from tailpipe and equivalent co2 emission from different sources. therefore, appropriate selection of the alternate fuel car is now one of the most challenging areas and considered as a multi-attribute decision-making (madm) process for stake holders like customers and governmental agencies due to the presence of several mutually conflicting attributes/criteria. it has been observed that very less research works have yet been carried out in madm domain focusing on the selection of the most feasible alternate fuel cars. biswas & das (2018a) applied entropy and multi-attributive border approximation area comparison (mabac) methods for hybrid vehicle selection problems. car model biswas et al./oper. res. eng. sci. theor. appl. 3 (1) (2020) 16-27 18 cost, fuel economy, tank size, tail pipe emission and passenger volume were considered as the predominant selection criteria. further, biswas & das (2018b) adopted fuzzy-analytic hierarchy process (ahp) and mabac method for commercially available electric vehicle selection for a case study of united states. various technical and operational attributes like fuel economy, base model pricing, quick accelerating time, battery range and top speed were considered. biswas & saha (2019) proposed a novel madm approach for evaluating commercially available scooters and considered kerb weight, mileage, top speed, fuel tank capacity and price as the influential criteria. in this paper, an endeavor is attempted to integrate two vastly used madm methods, namely criteria importance through inter-criteria correlation (critic) and combined compromise solution (cocoso) for the evaluation and ranking of five alternative environment friendly vehicles. the critic method is used to determine the weight coefficients associated with each vehicle selection criterion. ranking of the vehicles is achieved using the cocoso method. five different types of passenger vehicles such as toyota mirai (fuel cell vehicle), tesla model 3 (bev), toyota prius eco (hev), honda clarity plug in (phev) and chevrolet impala bi-fuel (cng vehicle) are considered as the alternatives. fuel economy, range in mile, annual fuel cost (in $), accelerating time from 0 to 60 mile per hour, vehicle cost (in $) and tail pipe emission in gram/mile are considered as the attributes based on the data available in manufacturers’ websites and catalogues. finally, a sensitivity analysis is also performed to check the effect of changing criteria weights on the ranking performance of the integrated model. the paper is organized as follows: after the introduction and literature review, section 2 presents the mathematical formulation of critic and cocoso methods. section 3 presents an application of the hybrid method for ranking of cars. a sensitivity analysis for the novel method is presented in section 4. section 5 presents the discussion and concluding remarks and directions for future research is presented in section 6. 2. methodology this section presents the mathematical formulations of critic and cocoso methods which are subsequently applied for the evaluation of the alternate passenger cars. 2.1. critic method critic method was originally developed by diakoulaki et al. (1995) for estimating criteria weights in madm environment. here correlation analysis is used to distinguish between different criteria (yılmaz & harmancıoglu, 2010). this method is basically based on analytical testing of the decision matrix in order to determine the information contained by the criteria. there are many successful applications of critic method for a wider range of applications such as pharmaceutical industries (diakoulaki et al., 1995), water resource management model (yılmaz & harmancıoglu, 2010), index system of city’s soft power (guo et al., 2013), financial statement of stock exchange (kazan & ozdemir, 2014) and non-traditional machining process (madic & radovanovic, 2015). critic method has the following simple steps, as detailed below: selection of commercially available alternative passenger vehicle in automotive environment 19 step-1. formation of the decision matrix: ....,,2,1;...,,2,1; ... ............ ... ... 21 22221 11211 njmi xxx xxx xxx x m nmm n n ij ==             = (1) step-2. normalization of the decision matrix using the following equations: ; minmax max ijij ijij ij xx xx r − − = for benefit criteria (2) ; minmax max ijij ijij ij xx xx r − − = for cost criteria (3) step3: calculation of symmetric linear correlation matrix (mij): a linear correlation coefficient between the each pair of criteria is estimated using the following equation to quantify the conflict resulted among different criteria. it can be seen that the more discordant the scores of the alternatives in two criteria i and j, the lower the value mij. 2 1 2 1 ) 1 )()( ))(( k m i ikj m i ij kikj m i ij ij rrrr rrrr m −− −− =   == = (4) step4: determination of the objective weight of a criterion also requires the estimation of both standard deviation of the criterion and its correlation with other criteria. in this regard, the weight of the jth criterion (wj) is obtained using the following expression.  = = n j j j j c c w 1 5) where, cj is the amount of information contained in the criterion j and is determined as follows:  −= = n j ijj mc 1 1 (6) where σ is the standard deviation of jth criterion and is the correlation coefficient between the two criteria. a higher value of cj signifies greater amount of information contained in a particular criterion, hence it is provided with higher weight value. 2.2. combined compromise solution (cocoso) method yazdani, zarate, zavadskas, & turskis, (2018) established the cocoso method. it is based on the integration of two most popular mcdm methods namely simple biswas et al./oper. res. eng. sci. theor. appl. 3 (1) (2020) 16-27 20 additive weighting (saw) and exponentially weighted product (mep). previous researchers applied cocoso methods in different area such as evaluation of electric vehicles under sustainable automotive environment (biswas et al. 2019), manufacturing process (acharya & murmu, 2019), sustainable supplier selection (zolfani et al. 2019). cocoso method consists of the following easy steps: step1. formation of the original decision matrix x=[xij]mxn.. step2. then normalize the decision matrix as n=[nij]mxn using eqs (2) and (3). step3. estimation of sum of weighted comparability (si) sequence and power weighted comparability sequences (pi) for each alternative respectively. (7) jw n j ij rpi )( 1  = = (8) step 4. computation of relative weights of the alternatives: in this step, three aggregated appraisal scores are used to generate relative performance scores of the alternatives, using the following equations:  = + + = m ni ii ii ia sp sp k )( (9) i i i i ib p p s s k minmin += (10) )max)1(max( ))(1()( ii ii ic ps ps k   −+ −+ = (11) step 5: the final ranking of the alternatives is determined based on ki, values: higher ki values indicate better position of the alternatives in the ranking pre-order. ki=(kia kib kic)1/3+1/3(kia+kib+kic) (12) 3. case study now to explore the application potentiality of the integrated critic-cocoso model, a case study comprising five alternative vehicles is now considered under passenger car category with six criteria. the details are given in table 1. the data set is retrieved from different manufacturers’ websites and catalogue. description of the considered evaluation criteria is provided in table 2. out of the six criteria, fuel economy (c1) and range (c2) are considered as beneficiary criterion or higher the better and rest four criteria are considered as non-beneficiary criterion or lower the better. fuel cell evs (fcevs) are fueled with pure hydrogen gas and this is converted to electricity by the fuel cell. it is produce no harmful tailpipe emissions. fcevs are attached with other advanced technologies like regenerative braking systems, which capture the energy lost during braking and store it in a battery. driving range of this )( 1  = = n j ijj rwsi selection of commercially available alternative passenger vehicle in automotive environment 21 vehicle is very high. fcevs are beginning to enter the consumer market in around the world. toyota mirai is the popular car under category of fcev. all bevs get electricity from rechargeable battery packs. benefits of the s as compare to conventional fuel are energy efficiency (ev convert above 60% of the electrical energy to power at the wheels), environmental friendliness, reduced energy dependency, smooth operation, less noise and less maintenance. only the drawbacks are shorter driving range and high recharging time. an example of bev is tesla model 3. hevs run by an ice in combination with electric motors. in case of full hybrid vehicles, battery charging is done through a regenerative braking mechanism and ice. this type of vehicle does not require plug in to charge. the benefits of hevs are high fuel economy and low tailpipe emissions over ice-based vehicles. example of hev is toyota prius eco. phevs have an ice and an electric motor where batteries provide the power to the motor and liquid fuel (mainly petrol or diesel) is used for the ice. this type of vehicle has lower operating costs and low amount of fuel consumption in comparison to the conventional vehicles. phevs produce lower levels of ghgs, depending on the electricity source. the example of phev is honda clarity. in ice vehicles, cng is stored in a tank as compressed gaseous state. this fuel is used in light, medium, and heavy duty applications. driving range is generally less in these vehicles than that of a diesel or petrol powered vehicle due to the the lower energy density. the advantages of cng are high mileage and reduced ghg emissions over conventional petrol and diesel fuels. light commercial vehicles are typically equipped with dedicated or bi-fuel systems. chevrolet impala bi-fuel car is a popular example of cng vehicle. table 1. decision matrix for selection of alternate car alternate fuel car fuel economy (mi/ galon) (c1) range (miles) (c2) annual fuel cost($) (c3) acceleration (0-60mph) (c4) cost ($) (c5) tail pipe emission (gms/mile) (c6) toyota mirai (a1) 67 312 1250 9.4 58365 0 tesla model 3 (a2) 133 240 500 3.7 39500 0 toyota prius eco (a3) 56 633 700 10.2 28000 158 honda-cla rity plug in (a4) 110 340 700 9.5 34320 57 chevrolet impala bi-fuel (cng) (a5) 20 360 1850 7.9 37,570 405 sources: manufacturing website and www.fueleconomy.gov https://afdc.energy.gov/vehicles/electric_emissions.html biswas et al./oper. res. eng. sci. theor. appl. 3 (1) (2020) 16-27 22 table 2. descriptions of different criteria for selecting best alternate car criteria description c1 it indicates that how much mile the vehicle can go by using a quantity of fuel. it is expressed in mile per gallon. improve fuel economy saves money, reduces climate change, and reduces oil dependence cost. c2 range means that the maximum distance the car can travel between two subsequent charging for electric vehicle but in case of petroleum fuel it indicates that how much distance covered a car by from full tank to empty tank. its unit is mile. range on a tank assumes 100% of fuel in tank will be used before refueling. c3 its calculates, based on 45% highway, 55% city driving, 15,000 annual miles and current fuel prices. (diesel per gallon price $2.97, petrol regular fuel price $2.55 and electricity $0.13/kwh) c4 it signifies that how much time is required to accelerate the car from 0 to 60 mile per hour. it is identifies by time(in seconds) c5 it is the selling price of vehicle in dollar. c6 tail pipe emission is the exhaust gas of the vehicle which produced after the combustion of fossil fuels. it is expressed as gram per mile. these are the responsible for greenhouse effect, causing climate change, photochemical smog, acid rain, reducing visibility, aggravating heart and lung diseases. at first, the criteria weights for the alternate fuel car selection case study are computed using critic method. as the initial step, the decision matrix of table 1 is first normalized using eqs. (2) and (3) respectively for beneficial and cost criteria, as shown in table 3. this table also presents the σ values. subsequently, inter criteria correlation values are presented in table 4. finally, the criteria weights are estimated using eqn. (5), as shown in table 5. according to the weight values of table 5, c2 is the most important criterion, whereas c3 is the least important criterion. table 3. normalized decision matrix alternate fuel car c1 c2 c3 c4 c5 c6 a1 0.42 0.18 0.44 0.12 0.00 1.00 a2 1.00 0.00 1.00 1.00 0.62 1.00 a3 0.32 1.00 0.85 0.00 1.00 0.61 a4 0.80 0.25 0.85 0.11 0.79 0.86 a5 0.00 0.31 0.00 0.35 0.68 0.00 standard deviation (σ) 0.396 0.382 0.408 0.403 0.375 0.419 selection of commercially available alternative passenger vehicle in automotive environment 23 table 4. correlation coefficient values of paired criteria criteria c1 c2 c3 c4 c5 c6 c1 1 -0.4753 0.8368 0.5254 0.0038 0.8128 c2 -0.4753 1 0.0784 -0.636 0.5809 -0.3156 c3 0.8368 0.0784 1 0.2341 0.3286 0.7452 c4 0.5254 -0.636 0.2341 1 -0.0522 0.1747 c5 0.0038 0.5809 0.3286 -0.0522 1 -0.3741 c6 0.8128 -0.3156 0.7452 0.1747 -0.3741 1 table 5. weights of the bev selection criteria criteria c1 c2 c3 c4 c5 c6 cj 1.306 2.204 1.134 1.916 1.692 1.659 wj 0.132 0.222 0.114 0.193 0.171 0.167 after finding out of criteria weights using the critic method, the considered alternate fuel car selection problem is now solved by cocoso method. after the formation of the decision matrix of table 1, normalized decision matrix, sum of weighted comparability sequence, power weight of comparability sequences and the overall score of the alternatives are determined using the respective equations provided in section 2. the final ranking of the considered vehicle alternatives is obtained according to the descending order of the k values (table 6). this table indicates that tesla model 3 (a1) is the most favorite vehicle while chevrolet impala bi-fuel (a5) emerges out as the least preferred alternative. in table 6, ranking of the alternative cars is also verified by comparing the performance of the integrated critic-cocoso method with some of the well popular madm methods like technique for order preference by similarity to an ideal solution (topsis) (chiang & cheng , 2009) and mabac (pamucar & cirovic, 2015) methods. as can be seen from table 6 that a2 (tesla model 3) remains the best alternative for all the considered madm methods. table 6. calculated score values in cocoso method and rank comparison alternate fuel car si pi kia kib kic ki cocoso mabac topsis a1 0.34 4.15 0.19 2.98 0.75 2.05 4 4 4 a2 0.71 4.92 0.23 4.77 0.94 3.00 1 1 1 a3 0.63 4.76 0.22 4.39 0.90 2.80 3 2 3 a4 0.56 5.28 0.24 4.30 0.97 2.84 2 3 2 a5 0.25 2.52 0.12 2.00 0.46 1.33 5 5 5 biswas et al./oper. res. eng. sci. theor. appl. 3 (1) (2020) 16-27 24 4. sensitivity analysis the aim of the sensitivity analysis (sa) is to assess the impact of different parameters on the ranking performance of the integrated model. 4.1 influence of criteria weights results of any madm method depend on criteria weights to a great extent. sometimes, the final selection may change when there is a change in the weight coefficients of the criteria. in this section, a sensitivity analysis is performed to assess how changes in the criteria weights affect the ranking of the alternative fuel cars by interchanging the criteria weight values in order of 6c2 i.e. for the six considered criteria (c1–c6), the total number of possible interchanges becomes fifteen (6c2). here, 6 represents the number of criteria and 2 represents the number of criteria chosen at a time. thus, in the sensitivity plot (fig. 1), all sets of priority rankings of alternate fuel vehicle are presented. it may be observed from the sensitivity plot that the rank of the alternatives have no changes with the interchanging of criteria weights. from fig. 1, it is clear that tesla model 3 remains the best alternative and chevrolet impala bi-fuel (cng) remains the least preferred choice for the considered case study. figure 1. sensitivity analysis by varying criteria weights 4.2 influence of λ value in cocoso ranking while applying the cocoso method, the associated λ value is generally assumed to be 0.5. however, in actual practice, it ranges from 0 to 1. fig. 2 shows the effects of varying λ values in the range of 0 to 1. it is observed that there is no change in the ranking orders of the considered alternatives, thus establishing the stability of the ranking order, given by the integrated model. selection of commercially available alternative passenger vehicle in automotive environment 25 figure 2. sensitivity analysis for alternate fuel car by changing the λ value 5. results and discussion in the context of global sustainability scenario, alternate fuel cars with higher mileage, longer range, lower annual fuel cost, quick acceleration, low price possible vehicle and reduced tail pipe emission can further reduced the tendency of global warming. in this paper, six important vehicle selection criteria has been considered and explained. the first two criteria (c1 and c2) are considered as beneficiary criterion (higher the better) and rest four criteria are considered as non-beneficiary criterion (lower the better). in order to avoid subjective judgments, critic method is used for computing the criteria weights. finally, a sensitivity analysis is shown to confirm the robustness of the ranking and further support the decision when selecting the final result. tesla model 3 emerges out as the best alternative, which has been supported by other madm methods like mabac and moora that has been shown in fig. 1. it is well understood from fig. 2 that there are no changes of ranking of the alternative even their change in criteria weights. fig. 3 establishes the robustness of the method as altering the values of λ in the range of 0.1 to 1, could not affect the ranking order at all. it is also observed that in comparison to other madm methods in the literature, the adopted integrated model is very simple to understand and easy to execute and involves very less amount of mathematical calculations. 6. conclusions the proposed critic-cocoso model is proven to be an effective decision-making 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(2019). a structured framework for sustainable supplier selection using a combined bwm-cocoso model. procs. of international scientific conference: contemporary issues in business, management and economics engineering, 9th 10th may, vilnius, lithuania. https://doi.org/10.3846/cibmee.2019.081. © 2020 by the authors. submitted for possible open access publication under the terms and conditions of the creative commons attribution (cc by) license (http://creativecommons.org/licenses/by/4.0/). operational research in engineering sciences: theory and applications vol. 5, issue 3, 2022, pp. 92-107 issn: 2620-1607 eissn: 2620-1747 doi: https://doi.org/10.31181/oresta031022046o * corresponding author nasihao@yahoo.com (n. osmanovic), shaista.h@hotmail.com (s. alvi) determinants of fdi in the economy of gcc countries: a pmg ardl approach nasiha osmanovic 1*, shaista alvi 2 1 herriot watt university, dubai-uae 2 amity university, dubai-uae received: 17 july 2022 accepted: 27 august 2022 first online: 03 october 2022 research paper abstract: the main determinant of the growth of gulf cooperation council (gcc) countries is inward foreign direct investment stock (fdi). the paper shows the effects of economic growth, cost of living, economic freedom indices, global oil price, and construction value-added on the inward foreign direct investment stock in gcc in the long term and short term for an unbalanced data period of study from 1996 to 2020(bahrain, kuwait, oman, saudi arabia, and the united arab emirates) and qatar from 1999 to 2020. we use the pmg ardl model to have a long-run and short-run estimate between these variables in the gulf council region. empirical results evidence positive correlation that economic growth and construction industry volumes and cost of living and economic freedom indices have an inverse relationship in long term on regional fdi stock. at the same time, results confirm that there is cross-sectional dependence among these countries of gcc. keywords: foreign direct investment stock, gcc, pmg/ardl model, gdp, economic freedom. 1. introduction foreign direct investment stock is a form of international capital movement that contributes to more efficient business operations, growth of the international market, and raising the standard of living in society. it contributes to augmenting the knowledge stock through labor training and new technology (de mello, 1999). in this context, evaluation efficiency of investments plays the main role in making investment decisions, from one to another country, inside and outside of gcc, to improve business operations. foreign investments and trade represent an important development factor in the economy today. fdi is a very important means of business operations, organization of production, and supply of goods and services. it reduces the gap between investment and savings (sabir and khan 2018). through foreign determinants of fdi in the economy of gcc countries: a pmg ardl approach 93 investments, firms organize production, provide a supply of raw materials and labor input, and then place the products and services as an output in the different markets, in the most efficient way. based on such business, companies can optimally take advantage of their technology, knowledge, and economies of scale advantages. foreign direct investment is not just about the transfer of capital from one place to another, but about an investment package that contains new technologies, managerial skills, profitable leadership, and the market. fdi and its relationship with economic growth are well-known phenomena in the research literature, with enough empirical and theoretical evidence. although a lot of research is done on this topic, there are different opinions and results on how fdi affects growth and vice versa. there is also enough evidence of fdi determinants, consumer price index (cpi), construction value-added, economic freedom indices (efi), and oil prices in gcc countries. the paper does not test how each determinant affects the other, but we are going to show how the growth of gcc economies affects fdi. it can decrease unemployment and increase the productivity level of the country (lipsey 2001). the study aimed to identify the measures at regional and independent country levels which would have magnetic powers for foreign direct investment stock. the study takes into account capital formation from the construction industry as a consideration influencing factor as is it the leading economic activity of the region. the other indicator is gross domestic product (gdp) per capita at the current price indicates economic growth. consumer prices indices represent the prices of a basket of goods, hence a representation of the cost of living. the economies run on business and providing business conducive environment helps the country to foster new and existing business, economic freedom indices are a measure of ranking and scoring various nations based 4 main parameters for a degree of freedom to residents indicating a business-friendly environment. due to the fact these countries are hydrocarbon export countries oil prices were taken as another factor. hence, for this study, all the above factors were identified to measure the influence on the foreign investor's decisions for fdi stock in the gulf cooperation council and its member states. considering the absence of such research, it warranted research to understand the causal relationship between fdi stock and other factors gdp per capita at current prices representing the economic growth of the country, gross value added by construction at current prices us dollars represent the capital formation due to construction, cpi is the consumer price index representing cost of living in host countries, efi is the economic freedom indices representing the openness and business-friendly of a country, oil is cushing, ok wti spot price fob (dollars per barrel).to determine the causal effect econometric model of pooled mean group (pmg )/ autoregressive distributed-lagged (ardl) methodology is adopted. the uniqueness of this paper is our effort to examine the interdependence of gcc countries in responsive parameters understudy to attract foreign direct investment. fdi is a visible driver of the interdependence of these countries. the structure of the paper is divided into the following sections: section 1 explains the various factors which are important for foreign direct investment. section 2 the related existing literature reviews, and section 3 describes the research methodology including data collection. section 4 interprets the result of the empirical study and section 5 concludes with future research needs and policy suggestions. osmanovic and alvi/oper. res. eng. sci. theor. appl. first online 5(3)2022 92-107 94 2. literature review foreign direct investment and economic growth or gdp could be studied from two perspectives. one dimension is that fdi affects economic growth and economic growth also affects fdi. some of the authors agree that foreign direct investment impacts economic growth positively and vice versa, while some authors are of the view that fdi inflows have no positive impact on economic growth and vice versa. the main driver of this positive impact is the technology that is adopted by foreign direct investors. in their research de mello (1999), johnson (2006) barro (1991), barro and sala-imartin (1995), kumari & sharma (2017), adnan, chowdhury, and mallik (2019), and shah (2018), have been studied foreign direct investment and economic growth and concluded that there is a positive relationship between these two variables, and fdi has a positive impact on economic growth. if there is an increase in fdi, it will automatically increase demand for the currency of that country and increase the exchange rate. on the other hand, carkovic and levine (2002), sadik and bolbol (2001), akinlo (2004), el heddad (2016), and alfaro (2003), concluded in their study that fdi has no positive impact on economic growth. they show that there is an opposite direction between economic growth and fdi in which fdi inflow impact negatively economic growth of the country. other studies that tested the effect of growth on fdi have also two dimensions. mencinger (2003,) chowdhury and mavrotas (2006), saha (2005), and choe (2003) concluded that higher growth of the country will attract more fdi. more foreign investment would come to the fast-growing economy. considering economic freedom hamdi & hakimi (2021) in their research examined twenty-two developed and sixty developing countries. they concluded that openness in the trade may significantly affect the growth of the countries. bengoa and sanchez-robles (2003) perform panel data analysis in latin american countries from the period 1970-1999 to see the relationship between economic freedom and fdi. their results show that economic freedom has a positive and significant effect on fdi in all 18 latin american countries. (pearson et al., 2012) have done their research on the impact of economic freedom on fdi in the united states. by using a panel data analysis in the period 1984-2007 they concluded that economic freedom and growth have a significant effect on the fdi. their results also show that the per capita income of states and the unemployment rate hurt fdi. states whose per capita income is higher prevent fdi inflows because higher income impact higher wages while high unemployment leads to the crime ratio which automatically discourages investors to invest. dondashe and phiri (2018) examined the correlation between fdi and trade in south african countries and concluded that there is a significant correlation between fdi and trade. abdelaziz and algammal (2019) studied the determinants of foreign direct investment (fdi) in oil-dependent economies. they use panel data for 6 gcc countries in the period from 1990 to 2015. their results show that there is a positive relationship between oil price, growth, trade openness, and fdi. he concluded that oil reserves hurt fdi. the reason could be according to him that gcc countries have enough financial resources to manage their economic development. in that case, according to this governments put restrictions to protect their resources, reducing the amount of resource-seeking fdi. asiedu (2011) concluded in his research that https://journals.sagepub.com/doi/full/10.1177/0972652719880153 determinants of fdi in the economy of gcc countries: a pmg ardl approach 95 due to oil production and exploration, there is an increase in fdi in extractive industries. he concluded that oil-reliant countries, like the gcc, have a bright future to attract fdi. according to his research, gcc countries should follow less restrictive government policies and reduce barriers to fdi to attract foreign investors. (corden & neary, 1982) shows that an increase in the oil price and gas sector hurts the manufacturing sector. an increase in the revenue from oil impacts the real exchange rate by pushing it up, influencing the domestic manufacturing sector less competitive which makes fdi expensive for foreign investors. research that has been done by jadhav (2012) shows the factors affecting fdi attraction in brazil, russia, india, china, and southern africa in the period 2000-2009. his results show that cpi has a positive impact on the attraction of fdi. hunady and orviska (2014) researched 27 countries in europe during the period 2004-2011. their results show that cpi has no impact on fdi. similar research has been conducted by ali lamah et al., (2021) on the indonesian economy. he examines the impact of cpi and fdi on the growth of the indonesian economy. he used the data from 2005 to 2019 and concluded that cpi has no positive impact on the gdp of the economy in a short term and long term, while fdi has a positive impact on gdp in the short and long term. wigren and wilhelmsson (2007) studied the relationship between gdp, different groups of construction, and the importance of crowding-out in the construction industry in europe. the results show there is no crowding-out effect inside the construction industry. investments in infrastructure have a filling-in effect by growth in residential and other buildings. giang and pheng (2011) study the importance of the construction industry in economic development. the results of his research show a significant relationship between the construction industry and economic growth in developing countries. ozkan et al., (2012) examined the relationship between economic growth and the construction sector in turkey. his results show that the construction sector acts as a significant argument catalyzing an economic policy of the country. if there would be a shortage of demand in the economy, in that case, governments would yield gdp by increasing investments of construction investments and stimulating the growth of the sector. 3. research methodology the paper shows the effects of efi, gdp, cpi, construction value-added, and global oil prices on the inward foreign direct investment stock in gcc (namely bahrain, qatar. kuwait oman saudi arabia, and the united arab emirates) in the long term and short term. furthermore, an investigation into the individual nation's effect on the various variables with the annual data is collected for all countries in gcc in the interval period of 1996 to 2020 except qatar which is from 1999 to 2020. to examine the relationship between the dependent variable inward foreign direct investment held in the receiving country in the forms of equity or loans to domiciled companies in the host countries, and domestic factors i.e. economic growth, the capital formation due to construction economic activities, cost of living, a conducive climate for a business and the global oil prices, we apply pmg ardl for the short and long term: https://journals.sagepub.com/doi/full/10.1177/0972652719880153 https://journals.sagepub.com/doi/full/10.1177/0972652719880153 osmanovic and alvi/oper. res. eng. sci. theor. appl. first online 5(3)2022 92-107 96 (1) where, = regressand = the vector of explanatory variables (regressors) for the group, µi =represent the fixed effects, the coefficient on the lagged dependent variable = scalar coefficients on lagged first-differences of dependent variables = kx1 coefficient vectors to estimate the relationship among the above-mentioned variables we use the following ardl model in the following equation: (2) where, α =the intercept term λ, δ =subsequent long-term and short-term coefficient ε= being the error term, = group effect, ln fdi represents the foreign direct investment held in the country in form of equity or loans to domiciled companies in the host countries, ln gdp is the log-transformed gdp per capita at current prices representing the economic growth of the country, ln const is the log-transformed gross value added by construction at current prices us dollars represent the capital formation due to construction, cpi is the consumer price index representing cost of living in host countries, efi is the economic freedom indices representing the openness and business-friendly of a country, oil is cushing, ok wti spot price fob (dollars per barrel) to achieve the research objective with the unbalance data we employ the pooled mean group (pmg)/auto regressive distributed lag ardl models (pesaran 1997), pesaran and shin (1998), (pesaran et al., 1999) and pesaran, shin and smith (2001) with the variable presented in table 1. determinants of fdi in the economy of gcc countries: a pmg ardl approach 97 table 1. research variables variables measures source fdi fdi in stock unctad, fdi/mne database gdp per capita gdp at current prices us dollars united nations statistics division const gross value added by construction activity at current prices us dollars united nations statistics division cpi annual-consumer price indices (cpi) with the base year 2010 unctad efi economic freedom indices the wall street journal and the heritage foundation oil cushing, ok wti spot price fob (dollars per barrel) eia-refinitiv, an lseg business source: developed by authors 4. research results the descriptive statistics on the panel data have been presented in table 2 composed of six countries with a total observation of 147. it is preferred to use the natural logarithm (ln) of variables of fdi stock and gdp per capita and gross value added by construction activity. the statistics results state that ln fdi stock has a mean 0f 9.53 and maximum of 12.39 and a minimum of 5.95 with a standard deviation of 1.6. the ln gdp per capita indicates a mean of 10.08 and maximum of 11.35 and a minimum of 8.73. the ln gross value added by construction means is 22.23 and maximum of 24.53 and a minimum of 19.39. the consumer price index calculated annually at the base year of 2010 shows that the mean is 93 .34 and maximum of 129, 68, and a minimum of 54.12. the countries are ranked based on economic freedom indices which are formed to include indices of four broad categories namely government size, legal environment, regulatory environment, and the market environment we have included indices of six countries for which the mean is 67.65 with the minimum and maximum at 59.6 and 77.7 respectively. the annual oil prices are wti spot prices with a mean of 54.79 and maximum of 99.67 and a minimum of 14.42. table 2. descriptive statistics parameters lnfdi lngdp lnconst cpi efi oil mean 9.53925 10.07846 22.23575 93.34094 67.65986 54.79327 median 9.74800 10.05780 22.09317 95.69701 66.70000 50.80000 maximum 12.39576 11.35130 24.52993 129.6481 77.70000 99.67000 minimum 5.95007 8.734834 19.39695 54.12815 59.60000 14.42000 std. dev. 1.60823 0.617912 1.433903 18.97235 4.848297 26.89772 skewness -0.32053 -0.052741 -0.088588 -0.179757 0.409431 0.277139 kurtosis 2.65042 2.422908 1.933116 1.912899 2.039754 1.832379 jarque bera 3.26565 2.107989 7.163994 8.030106 9.754715 10.23221 probability 0.19538 0.348543 0.027820 0.018042 0.007617 0.005999 sum 1402.26900 1481.533 3268.655 13721.12 9946.000 8054.610 sum sq. dev. 377.61660 55.74498 300.1874 52552.72 3431.873 105629.2 observations 147 147 147 147 147 147 osmanovic and alvi/oper. res. eng. sci. theor. appl. first online 5(3)2022 92-107 98 source: developed by the authors the correlation between the variables under study is exhibited in table 3. it is evident from the analysis of the matrices that none of the dependent variables has more than a 0.7 value which indicates the model does not have multi-collinearity amongst the dependent variables. furthermore, there seems to be a negative correlation between fdi and efi. table 3. correlation matrix correlations lnfdi lngdp lnconst cpi efi oil lnfdi 1.000000 lngdp 0.247136 1.000000 lnconst 0.767106 0.4048 1.000000 cpi 0.722729 0.318584 0.431421 1.000000 efi -0.062553 0.100493 -0.133339 0.029813 1.00000 oil 0.528009 0.528087 0.36795 0.533709 -0.075806 1.000000 source: developed by the authors to depict the stationarity in time series the unit root test was performed using levin, lin, and chu (2002) augmented dickey-fuller (1979), and phillips-perron (1988) fisher chi-square tests which state that null hypothesis = unit root at conventional significance levels. hence at a p-value <0.05% significance, the null hypothesis is accepted. all the variables at level (i(0)) are non – stationary hence, reiteration was performed and it was found that all variables are stationary at 1st difference(i(1)) with exogenous repressor at constant. thus concluding that all variables are station at i (1) for which the statistics and relative probability are stated in table 4. table 4. first-generation panel unit root tests variables names levin, lin & chu t* levin, lin & chu t* adf fisher chisquare adf fisher chisquare pp fisher chisquare pp fisher chisquare order of integration statistic prob. statistic prob. statistic prob. lnfdi -3.61723 0.0001* 29.5878 0.0032* 51.0394 0.0000* i(1) lngdp -7.49988 0.0000* 67.6661 0.0000* 94.1081 0.0000* i(1) lnconst -3.85801 0.0001* 28.2324 0.0051* 43.3131 0.0000* i(1) cpi 2.753348 0.0029* 22.5619 0.0317* 32.0915 0.0013* i(1) efi -7.79051 0.0000* 80.6264 0.0000* 124.943 0.0000* i(1) oil -8.85849 0.0000* 83.1284 0.0000* 122.496 0.0000* i(1) note: * is p-value <0.05% source: developed by authors second-generation panel unit root tests are required to be undertaken to seek asymptotic results for cross-sectional dependence, we conduct the breusch‐pagan lagrange multiplier (lm), the pesaran scaled lagrange multiplier (lm), and the pesaran cross-sectional dependence (cd). the null hypothesis of no cross‐sectional dependence, i.e., there is cross‐section dependence among the repressors at the significance level. evidence from table 5 the null hypothesis is rejected at a 1% level of significance indicating there is cross dependence and which also confirms confirming the appropriateness of the first‐generation panel unit root tests for this study. determinants of fdi in the economy of gcc countries: a pmg ardl approach 99 table 5. cross-sectional dependents test variables names breusch-pagan lm pesaran scaled lm bias-corrected scaled lm pesaran cd statistic prob. statistic prob. statistic prob. statistic prob. lnfdi 327.5432 0.0000* 57.06233 0.0000* 56.93733 0.0000* 18.08203 0.0000* lngdp 296.7872 0.0000* 51.44708 0.0000* 51.32208 0.0000* 17.19477 0.0000* lnconst 331.9510 0.0000* 57.86707 0.0000* 57.74207 0.0000* 18.21267 0.0000* cpi 334.9549 0.0000* 58.41550 0.0000* 58.29050 0.0000* 18.28290 0.0000* efi 61.86011 0.0000* 8.555447 0.0000* 8.430447 0.0000* 0.034348 0.9726 oil 360.0000 0.0000* 62.98809 0.0000* 62.86309 0.0000* 18.96525 0.0000* note: * is p-value <0.05% source: developed by the authors (pedroni 1999, 2004), and (kao 1999) tests are conducted to establish a longterm co-integration relationship between panel variables. the null hypothesis for the pedroni residual co integration test is no integration. the test was performed under the three deterministic trends: no intercept or trend, individual, intercept and individual intercept and individual trend. the results in table 6 indicate that out of 11 tests of which four tests for within-dimension and three tests for betweendimension, the majority of the test have a p-value above 5% of significance which explains that there is strong co-integration between the series. the second cointegration test i.e. kao residual co-integration test administered in individual intercept with the null hypothesis of no integration. the results with a p-value below 5% significance reaffirm the result received under the pedroni test set forth a stronger proof of co-integration amongst the analyzed variables. we can, therefore, conclude that the variables being analyzed possess a long-term relationship. table 6. co-integration test pedroni residual cointegration test deterministic trend no intercept or trend individual intercept individual intercept and individual trend parameters statistic prob. statistic prob. statistic prob. panel v-statistic withindimension 0.411668 0.3403 0.130931 0.4479 0.048561 0.5194 panel rho-statistic 1.302734 0.9037 1.72753 0.9580 2.516635 0.9941 panel pp-statistic 0.2658 0.5106 0.805513 0.7897 0.297044 0.6168 panel adf-statistic -1.331953 0.0914 0.235488 0.4069 3.090974 0.001* panel v-statistic weighted statistics 0.422901 0.3362 0.479216 0.3159 0.227002 0.4102 panel rho-statistic weighted statistics 1.121314 0.8689 1.350284 0.9115 2.261329 0.9881 panel pp-statistic weighted statistics -0.330299 0.3706 0.272074 0.6072 0.011147 0.5044 panel adf-statistic weighted statistics -1.77194 0.0382* 0.292091 0.3851 2.371839 0.0088* group rho-statistic for betweendimension 2.01969 0.9783 2.31277 0.9896 3.000602 0.9987 group pp-statistic 0.094858 0.5378 0.985689 0.8379 0.371814 0.355 group adfstatistic -3.197363 0.0007* 1.574682 0.0577 2.835366 0.0023* kao residual cointegration test (individual intercept) tstatistic prob. adf -3.539922 0.0002* note: * is p-value <0.05%source: developed by the authors osmanovic and alvi/oper. res. eng. sci. theor. appl. first online 5(3)2022 92-107 100 considering that the pmg/ardl model is reactive to lag length; therefore, to determine the optimal lag structure. as per table 7, we have based our decision on sc: schwarz information criterion hq: hannan-quinn information criterion for which results exhibited that ardl (1, 1, 1, 1) was optimal. table 7. lag structure lag lolo lr fpe aic sc hq 0 -1418.963 na 128011.2 28.78713 28.94441 28.85077 1 -601.1990 1519.885 0.017740 12.99392 14.09488* 13.43937* 2 -552.8511 83.99837 0.013931 12.74447 14.78911 13.57173 3 -526.6349 42.36950 0.017314 12.94212 15.93044 14.15120 4 -474.8814 77.36888 0.013084 12.62387 16.55587 14.21476 5 -438.5711 49.88083 0.013855 12.61760 17.49328 14.59031 6 -400.3779 47.83802 0.014615 12.57329 18.39265 14.92781 7 -356.6110 49.51403 0.014405 12.41638 19.17942 15.15272 8 -295.1570 62.07479* 0.010532* 11.90216* 19.60888 15.02031 note -* indicates lag order selected by the criterion.lr: sequentially modified lr test statistic (each test at 5% level) fpe: final prediction error aic: akaike information criterion sc: schwarz information criterion hq: hannan-quinn information criterion source: developed by the authors to determine the determinants for bivouac of inward foreign direct investment stock in the region and country-specific in hydrocarbon-based economies. the pooled mena group autoregressive distributed lag model (pmg ardl) method was adopted as autoregressive distributed lag model (ardl)s are standard least squares regressions with lags of the dependent variable and explanatory variables as repressors (greene, 2008). the model permits intercept and slopes to vary between the cross-section of countries along with differentiating between the short-run and the long-run estimation. the advantage of using pmg /ardl is that it provides a solution to the situation in which there is short-run heterogeneity and long-run homogeneity of the estimated coefficients in a panel framework (pesaran, shin, & smith, 1999) based on lag structure criteria we have run the model at lag 1 for independent variable ln fdi and ln gdp, ln cont, cpi, oil efi as the repressors. as per the test results depicted in table 8 during the period of study the coefficients for the log of gross domestic product per capita, and log of construction value-added are statistically significant. they have a positive impact on the dependent variable while oil prices are statistically insignificant to the dependent variable log of foreign direct investment in the long run equation. the consumer price index and economic freedom indices have an inverse relationship with inward foreign direct investment stock. from table 9, the findings state that in long term a percentage increase in ln gdp and ln const elevates the ln fdi by 1.5% and 2. 56%. a unit increase of cpi and efi decreases the ln fdi by 0.109% and 0.17% respectively. this indicates that construction value-added capital formation and economic growth are the main drivers for foreign investors to invest and hold investments in the region. oil prices have no impact on foreign investment in the host region. results show that cost of living indicators cpi and economic freedom indices do not drive the inward foreign direct investment in the region. on the contrary, in the short run, during the period of research, none of the variables are statistically significant which indicates that collectively they may not determinants of fdi in the economy of gcc countries: a pmg ardl approach 101 have an impact on fdi. however, in that way, we would have to investigate the shortterm effect on individual countries. the rate of adjustment toward long-run equilibrium was -0.1018, which indicates that inclusive growth's deviation from the previous was reduced by 10.18% in the following year. therefore, a lengthy period would be necessary to reach a long-term balance or equilibrium (roughly 10 years). table 8. pmg panel autoregressive distributed lagged (ardl (1, 1, 1, 1, 1, 1)) dependent variable: ln fdi regresso rs coefficient std. error t-statistic prob. long run equation lngdp 1.506180 0.843550 1.785527 0.0772*** lnconst 2.568995 1.069795 2.401389 0.0182** cpi -0.109096 0.056795 -1.920888 0.0576*** efi -0.178904 0.079411 -2.252894 0.0265** oil 0.012641 0.012518 1.009787 0.3150 short run equation cointeq01 -0.101824 0.038252 -2.661931 0.0091* d(lngdp) 0.012097 0.250175 0.048355 0.9615 d(lnconst) 0.070813 0.522488 0.135531 0.8925 d(cpi) 0.013691 0.028326 0.483326 0.6299 d(efi) 0.006296 0.013888 0.453360 0.6513 d(oil) 0.002396 0.003200 0.748589 0.4559 c -4.171515 1.658240 -2.515629 0.0135** note: * ,**,*** is p-value <0.01% ,0.05%.0.10% source: developed by the author analyzing the individual cross-sectional short-run coefficient annexure -1 during the period of the investigation indicates that there is a mixed range of rates of adjustment toward long-term equilibrium in individual countries. even though uae has a non-negative coefficient it means that there is no convergence to long-run equilibrium. bahrain, oman, kuwait, qatar, and saudi arabia indicate varied tenor that is required to reach a long-term balance. bahrain takes the longest period at approx. 37 years. the shortest period shows qatar with approx. 4 years duration. the difference may be attributed to different economic and social structures. it is witnessed that economic freedom indices is the driver for each nation on inward foreign direct investment except uae. thus, in long run, gcc collectively draws policy that increases the economic health of the gcc region as reflected by improved gdp per capita and the capital formation from construction activity. these variables affect positively the total equity share and net loans provided by foreign investors to local enterprises in the region. however, results show that in the short run, country-specific policies towards improving the composite factors included in economic freedom indices may improve the inward foreign direct investments held in recipient nations. 5. conclusion we examine the determinants of inward foreign direct investment stock in the gulf cooperation council countries. the panel data of the countries bahrain, oman, kuwait, saudi arabia, and uae were from 1996 to 2019 and for qatar from 1999 to osmanovic and alvi/oper. res. eng. sci. theor. appl. first online 5(3)2022 92-107 102 2020. in this paper, we study the gulf council nation's economic growth, capital formation by construction activity, cost of living, economic freedom, and global oil prices as determinants for foreign investors to invest in domestic enterprises in the host region of gcc. the research employs pooled mean group ardl as the method that enables finding the long-term and short-term effects collectively and independently. as discussed, various research has been conducted to determine the factors which attract inward fdi such as economic growth, trade openness inflation, etc. however, this research provides novel parameters which impact the foreign investor's decision to invest in domestic enterprises of hydrocarbon-based economies. as a result, by offering quantitative metrics that independent nations and regions can use as a whole, this research fills a research need. both short-term and long-term impacts are supported by empirical findings. the study demonstrates that the nations in the gulf economic integration have a significant economic crosssectional dependency for encouraging foreign direct investment. it is well established that the gcc's member nations are highly interdependent economically. the empirical results suggest that in the regional integration among the variables with economic growth, capital formation due to construction activities demonstrate a beneficial impact on foreign direct investment stock in the long run. however, the cost of living and economic freedom index have long-term detrimental effects and global oil prices are statistically insignificant to influence the foreign investors for fdi stock in the gcc. in the short run, the block remains statistically insignificant and the speed of adjustment toward long-run equilibrium appears medium-term at about 10 years for the chosen nation. further analysis of the cross-section short-run coefficients indicates that singularly all countries in short term have the fdi stock positive, affected by economic freedom except the uae who has a negative effect. however economic growth remains statistically insignificant for all countries except for bahrain which has a positive influence on other predicted variables. in general, each country shows a diverse impact on fdi stock in its economies. global oil prices remain insignificant to the region as these are hydrocarbon exporting countries. further research is suggested to be conducted in a large number of countries that are non-hydrocarbon-based economies for more robustness of the result. our research results suggest bringing regional common policies for long-term economic development and capital formation in terms of construction activities. references abdelaziz e. and, algammal, m. 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(n.d.-b). https://www.eia.gov/dnav/pet/hist/leafhandler.ashx?n=pet&s=rwtc&f=a. © 2022 by the authors. submitted for possible open access publication under the terms and conditions of the creative commons attribution (cc by) license (http://creativecommons.org/licenses/by/4.0/). https://www.eia.gov/dnav/pet/hist/leafhandler.ashx?n=pet&s=rwtc&f=a determinants of fdi in the economy of gcc countries: a pmg ardl approach 107 appendix1 country variable coefficient std. error t-statistic prob. are cointeq01 0.003711 0.000684 5.426477 0.0123 d(lngdp) -0.632869 1.008287 -0.627668 0.5747 d(lnconst) 2.580843 1.903508 1.355835 0.2682 d(cpi) -0.056767 0.001487 -38.17406 0.0000 d(efi) -0.061508 0.000865 -71.08551 0.0000 d(oil) 0.001819 4.62e-05 39.38285 0.0000 c 0.344533 1.382210 0.249262 0.8192 bhr cointeq01 -0.027067 0.000233 -116.0857 0.0000 d(lngdp) 0.932739 0.183684 5.077944 0.0148 d(lnconst) -0.224895 0.019905 -11.29840 0.0015 d(cpi) -0.020303 9.90e-05 -204.9827 0.0000 d(efi) 0.011475 7.45e-05 153.9941 0.0000 d(oil) -0.000419 3.30e-06 -127.0852 0.0000 c -0.856516 0.189720 -4.514628 0.0203 kwt cointeq01 -0.084455 0.001783 -47.36281 0.0000 d(lngdp) -0.714882 0.701329 -1.019324 0.3831 d(lnconst) -0.650841 0.316139 -2.058722 0.1317 d(cpi) 0.143868 0.001743 82.52715 0.0000 d(efi) 0.018903 0.001211 15.61126 0.0006 d(oil) 0.017609 8.23e-05 213.9144 0.0000 c -3.665131 2.325043 -1.576371 0.2130 omn cointeq01 -0.114123 0.002855 -39.97638 0.0000 d(lngdp) 0.063731 0.103172 0.617717 0.5805 d(lnconst) -0.044272 0.012663 -3.496300 0.0396 d(cpi) -0.012768 0.000127 -100.3169 0.0000 d(efi) 0.012848 9.36e-05 137.2482 0.0000 d(oil) 0.001739 6.69e-06 259.8612 0.0000 c -4.337183 1.982610 -2.187612 0.1165 qat cointeq01 -0.263561 0.010080 -26.14573 0.0001 d(lngdp) 0.173028 0.169404 1.021394 0.3823 d(lnconst) -0.218466 0.054310 -4.022561 0.0276 d(cpi) 0.001731 0.000111 15.59489 0.0006 d(efi) 0.030797 0.000108 284.1740 0.0000 d(oil) -0.004731 1.15e-05 -409.6437 0.0000 c -11.21003 6.472918 -1.731836 0.1817 sau cointeq01 -0.125448 0.002520 -49.78620 0.0000 d(lngdp) 0.250835 0.120687 2.078397 0.1292 d(lnconst) -1.017489 0.147379 -6.903903 0.0062 d(cpi) 0.026382 8.02e-05 328.9397 0.0000 d(efi) 0.025261 4.79e-05 527.0555 0.0000 d(oil) -0.001643 6.02e-06 -273.1864 0.0000 c -5.304761 1.476998 -3.591583 0.0370 determinants of fdi in the economy of gcc countries: a pmg ardl approach nasiha osmanovic 1*, shaista alvi 2 1. introduction 2. literature review 3. research methodology 4. research results 5. conclusion references operational research in engineering sciences: theory and applications vol. 5, issue 3, 2022, pp. 210-229 issn: 2620-1607 eissn: 2620-1747 doi: https://doi.org/10.31181/oresta241122181y * corresponding author. morteza.yazdani@uam.es (m. yazdani), dr.prasenjitchatterjee6@gmail.com (p. chatterjee), zeljkostevic88@yahoo.com (ž. stević) a two-stage integrated model for supplier selection and order allocation: an application in dairy industry morteza yazdani 1, prasenjit chatterjee 2*, željko stević 3 1 universidad internacional de valencia, spain 2 department of mechanical engineering, mckv institute of engineering, howrah, india 3 university of east sarajevo, faculty of transport and traffic engineering, doboj, bosnia and herzegovina received: 06 july 2022 accepted: 16 november 2022 first online: 24 november 2022 research paper abstract: selecting the best supplier is a recurrent organizational challenge that occurs in a supply chain (sc) as a result of the presence of complex variables, restrictive criteria, and conflicting priorities. since an sc network is often developed with ambiguous conditions and information due to the industrialization of society and the intricacy of market competitiveness, fuzzy decision-making models are more effective. this paper proposes a two-stage decision-making model to select suppliers and to estimate cost-effective order numbers per supplier. the initial stage of the proposed model involves identifying fuzzy linguistic variables, interpreting appropriate decision criteria for evaluating suppliers, and modelling fuzzy technique for order preference and similarity to ideal solution (topsis) method. the goal of fuzzy topsis method is to attenuate the ambiguous expert inputs. in the second stage, economic order quantity is determined and assigned to each supplier using topsis scores as inputs for a linear programming (lp) model. different constraints, including demand, density qualification, acidity qualification, price, and capacity are formulated using the lp model. the mathematical model seeks to optimize total value of purchasing. the model is implemented in a dairy company to show its applicability and effectiveness. it has been found that supplier a1 and supplier a4 need to deliver 8000 kg of dry milk to the company, while supplier a5 needs to supply only 3500 kg. it is expected that the obtained results will assist organizations in developing a methodical strategy for addressing order allocation and supplier selection problems in more a realistic context. key words: supplier selection, order allocation, integrated model, fuzzy topsis, linear programming mailto:dr.prasenjitchatterjee6@gmail.com a two-stage integrated model for supplier selection and order allocation: an application in dairy industry 211 1. introduction business organizations are increasingly required to use knowledge-based operations due to the very dynamic nature of corporate affairs. their entire strategy would be geared around improving their competitive position. supplier selection, one of the key supply chain management (scm) activities, has contributed to a wide range of researches. this has encouraged businesses to pursue more reliable and competitive goals (udenio et al. 2015). two of the most crucial tasks for purchasing decision-makers (dms) to complete are selecting the best supplier and allocating order quantities because they have an impact on the company's long-term profitability. the key objective is to get the right product in the right quantity from the right supplier at the right time and at a fair price. purchasing is a strategic action in addition since it lowers costs and raises profits. decisions about order allocation in supplier selection are crucial in establishing the cost-effectiveness of the business. because an organization's needs could exceed the capability of a single supplier, this process entails determining various quantities of goods that are purchased from several suppliers. supplier selection is one of the most prevalent multi-criteria decision-making (mcdm) problems since it is driven by competing considerations like performance, cost, and timely delivery (wu et al. 2016; rao et al. 2017). in the sc network, knowledge-based decision models are receiving a lot of attention. making effective decision support systems to aid managerial decisions has been the subject of a significant amount of original research work. computerized information systems that support management decision-making processes are referred to as decision support systems. early in the 1970s, scott morton's research gave rise to the idea of decision support systems. in an intricate and poorly organized situation, the approach seeks to examine strategic decisions in order to provide decision makers (dms) with support. an integrated decision support model offers various benefits in the decisionmaking process by assisting policymakers with their responsibilities and improving quality of the planning phase (zarate, 2012). a decision support system is a concept that combines computer information processing with human judgement. the development of new theories and methods for scm may lead to more sophisticated and intelligent systems. sc experts may make highly skilled decisions, information exchange, and internal coordination simpler by utilizing these kinds of solutions, which will raise the value of products and services (chandra and kumar, 2000). scm has teamed up with the application of information and decision-making technology to develop competitive advantages with customers and stakeholders by improving coordination and communication across suppliers and partners for organizations (negi and anand, 2014). the market has a significant impact on the suppliers chosen in a logistics network. one of the fastest-growing industries with a significant impact on a nation's economic performance is the sc and logistics sector, which aid in activities relating to the flow of goods efficiently (mešic et al. 2022; puška et al. 2022). over the past few decades, the development of decision support systems has undergone a fundamental change. by keeping track of the materials cost, a decision support model has helped dms select practical strategies for reducing overall manufacturing costs (wong et al. 2009). a few review studies on intelligent models, decision support systems, and systems have been done in the area of scm (seuring, 2013; taticchi et al. 2013). according to seuring (2013), a strategic decision-making support model must be used to conduct practical research on the performance of yazdani et al./oper. res. eng. sci. theor. appl. 5(3)2022 210-229 212 sustainability and scm. liu et al. (2012) developed a sustainability evaluation method that combined life cycle assessment with an mcdm framework to aid the ecological, sociological, and financial implications of scm. using a fuzzy analytical network process (anp), bhattacharya et al. (2014) sought to build a collaborative decisionmaking model while demonstrating a sc performance measurement perspective. over time, a number of decision-making strategies have been developed to provide more useful supplier selection possibilities. numerous methods have been used extensively in the literature, including linear programming (lp), data envelopment analysis (dea), neural networks, fuzzy approaches, and technique for order preference by similarity to ideal solution (topsis). chen et al. (2006) used a fuzzy systematic approach to enhance topsis and handle the elements of supplier revenue, interpersonal intimacy, technical proficiency, adherence to quality, and conflict resolution in their solution to the supplier selection problem. in order to choose the best supplier in a situation involving group decision-making, cao et al. (2015) developed the topsis method in conjunction with intuitionistic fuzzy sets. overall, integrated models aid researchers in developing their concepts. uncertainty and fuzziness will surely be prevalent for experts, dms, and managers. fuzzy theory was utilized by combining quality function deployment (qfd) and lp, respectively, in bevilacqua et al. (2006) and guneri et al. (2009). however, one of the main issues with utilizing such approaches is that they overlook the probable, potential, unpredictable, and unknown elements that might change the features of the problem, such as cost, quality, production volume, etc., which can have a big impact on the result. thus, it is essential to take into account and incorporate uncertainties that may have an impact on the final decision in order to develop realistic decision-making models to deal with problems of order allocation and supplier evaluation. fuzzy logic is one of the methods that has a lot of potential for accounting for uncertainty during the decision-making process. by applying fuzzy logic, decision-makers in real-world industries can share their own viewpoints and offer more dependable and accurate choice solutions (torkayesh et al. 2020; yazdani et al. 2020a; yazdani et al. 2020b). fuzzy logic is being implemented into decisionmaking procedures to enable appropriate assessment of relative importance of decision criteria for evaluating suppliers. this will result in more accurate decisions for supplier selection that further the sustainability goals. to overcome these challenges, a two-stage integrated decision making model using fuzzy topsis and lp has been put out in this study. the goal of this study is to develop a mathematical model that can be applied to address the problem of combining supplier choice and order allocation. a case study for the diary sector in real life is taken into consideration to demonstrate the importance and applicability of the model. trapezoidal fuzzy logic is used in the proposed decision-making model to reduce the adverse effects of the decision-making outputs and hence, weights of the supplier selection criteria are calculated and the suppliers are ranked. adoption of a single mcdm method or mathematical model to address the supplier selection and order allocation problems is one of the major problems noted in the literature. in this study, two methods are combined to produce a more trustworthy model that can be used to rank suppliers and determine how much of an order should be distributed among them. in order to evaluate suppliers in a fuzzy environment and establish the appropriate order size, this study employs an lp method. the paper is broken down into four sections: an introduction, a literature review, a discussion of fuzzy logic, fuzzy numbers, and the fuzzy topsis method in section 3, a case study of a dairy company to find the best supplier of dry milk (milk powder) and the best quantity order in a two-stage integrated model for supplier selection and order allocation: an application in dairy industry 213 section 4, and finally, a possible framework for further research along with conclusions are presented in section 5. 2. literature review this section presents a thorough assessment of the literature as well as significant case studies and decision-making methods. the goal of this section is to give a thorough background on the subject and information on the benefits of decisionmaking models and strategies for coping with uncertainty in real-world circumstances. to do this, studies based on the integration of mcdm and optimization models are explored after studies that have just used only mcdm models to address the supplier selection problems. mcdm methods (badi et al. 2022) are one of the widely used decision-making strategies that allow decisionand policy-makers to compare a number of options based on a number of criteria and then choose the one that will best serve their needs. one of the issues in which mcdm methods have frequently been developed is the challenge of supplier selection and order allocation. due to the significance of suppliers and their features, industries would suffer irreparable consequences from a poor supplier selection. in this regard, mcdm methods are crucial in assisting industries in making the best choice in order to maximise their earnings and lower the chance of unfavourable outcomes from choosing the incorrect suppliers. for supplier selection problems in electronics industry while taking into account green criteria, kuo et al. (2015) developed an integrated decision making model employing anp and vlsekriterijuska optimizacija i komoromisno resenje (vikor) methods based on dnumbers. parkash and barua (2016) employed ahp and vikor methods for thirdparty logistics selection under fuzzy numbers using a similar methodology. in order to choose the best supplier in the manufacturing of pipes and fittings, rezaeisaray et al. (2016) proposed an integrated decision making framework using the decision making trial and evaluation laboratory (dematel), analytic network process), and the data envelopment analysis (dea) model. for supplier selection problem in the catering industry, fu et al. (2019) used a multi-choice goal programming model with ahp and additive ratio assessment (aras) methods. to address the supplier selection issue in a trapezoidal fuzzy environment, ghorabaee et al. (2016) introduced an extended form of assessment based on distance from average solution (edas) method. the proposed decision-making method was used to evaluate suppliers of a detergent manufacturer. in order to take into account the uncertainties in evaluating suppliers, wan et al. (2017) developed a novel integrated mcdm model employing anp and elimination and choice translating reality (electre ii) in an interval 2-tuple linguistic environment. in order to handle the supplier selection issue under green factors, yazdani et al. (2017) developed a novel decision-making model by fusing the dematel approach with the quality function deployment (qfd) and complex proportional assessment (copras) methods. ahp and topsis methods were utilised by jain et al. (2020) to assess suppliers in the steel industry while taking sustainability concerns into consideration. the weights of the sustainable supplier selection criteria were calculated using the fuzzy ahp, and suppliers were assessed using the fuzzy topsis method. for a problem involving the selection of green suppliers, đalić et al. (2020) suggested a unique integrated fuzzy-rough mcdm model incorporating the yazdani et al./oper. res. eng. sci. theor. appl. 5(3)2022 210-229 214 fuzzy pivot pairwise relative criteria importance assessment (piprecia) and interval rough saw methods. in order to address the supplier selection issue in the healthcare industry, stevic et al. (2020) suggested a new mcdm model called measurement of alternatives and ranking according to compromise solution (marcos method). a novel integrated mcdm model was developed by yazdani et al. (2020) using a weighting system and edas method that were coupled. they devised a combined weighting system based on the best worst method (bwm) and dematel approaches in order to compute the ideal weights of decision criteria because weight determination is the most important phase in addressing mcdm problems. they applied the proposed method to a real-world case study in the spanish healthcare sector to demonstrate its applicability. yazdani et al. (2020) introduced a qfd-based ahp-vikor decision making tool that deals with choosing the appropriate supplier because of the importance of the dairy business. they employed the ahp and qfd methods to calculate the weights of the choice criteria before using the vikor method to evaluate the suppliers. to select the best sustainable supplier, ecer and pamucar (2020) used the fuzzy bwm and bonferroni mean functions-based combined compromise solution (cocoso) method. durmić et al. (2021) investigated a combined application of the full consistency approach (fucom) and rough simple additive weighting (saw) method in order to eliminate uncertainty and imprecision in the supplier evaluation process for a lime production industry. puška et al. (2021) applied fuzzy marcos method to deal with sustainable supplier selection problem in a food industry. ulutaş et al. (2021) proposed multimoosral, a novel mcdm approach for a textile supplier selection problem. three widely used techniques, multi-objective optimization on the basis of simple ratio analysis (moosra), multi-objective optimization on the basis of ratio analysis (moora), and the complete multiplicative form of moora (multimoora), were combined to develop this method. hoseini et al. (2022) created a combined model for resilient supplier selection in the construction industries using interval type-2 fuzzy (it2f) topsis and it2f bwm. in order to address supplier selection issues, zakeri et al. (2022) introduced a unique mcdm technique called the alternative ranking process by alternatives' stability scores (arpass). the new method computes the stabilities of the options using standard deviations and shannon's entropy. nguyen et al. (2022) proposed a combination model employing dea, the spherical fuzzy ahp (sf-ahp), and the spherical fuzzy weighted aggregated sum product assessment (sf-waspas) to find the sustainable supplier for a steel manufacturing industry. ecer (2022) used an extended ahp in an interval type-2 fuzzy environment to solve a supplier selection problem while taking into account green notions. afrasiabi et al. (2022) proposed a hybrid fuzzy mcdm method to solve issues with sustainable-resilient supplier selection in manufacturing scenarios. initial calculations for the weights of the selection criteria were made using fuzzy bwm. next, a combined grey relational analysis (gra) and topsis method was used to evaluate the suppliers in a fuzzy environment. using the fucom method and an unique extension of mixed aggregation by comprehensive normalizing technique under fuzzy environment, ecer and torkayesh (2022) suggested a stratified fuzzy decision-making approach for sustainable circular supplier selection in the textile industry. although mcdm methods can be used as a trustworthy decision-making approach to address the supplier selection problem, real-world situations necessitate decisionmaking approaches that simultaneously evaluate suppliers and then allocate the best number of orders to maximise economic, environmental, and social goals. a hybrid a two-stage integrated model for supplier selection and order allocation: an application in dairy industry 215 mcdm and multi-objective programming approach for the supplier selection and order allocation problem that takes into account green criteria was given by kannan et al. (2013). in the first step, the ahp and topsis methodologies were employed to determine the relative ranking orders of suppliers. then, an optimization model was applied to determine order allocation with respect to order constraints and quality constraints. for the supplier selection and order allocation problem, hamdan and cheaitou (2017) suggested an mcdm and multi-objective programming model that takes into account environmental aspects. they first evaluated the providers using fuzzy ahp and topsis before allocating orders using an optimization model. in order to maximise the clean environmental goals, babbar and amin (2018) proposed a fuzzy qfd-based multi-objective programming model for the supplier selection and order allocation problem in the beverage industry. with regard to sc disruption issues, cheraghalipour and farsad (2018) suggested a new decision-making model for the supplier selection and order allocation problem utilising mcdm models and mixedinteger lp. to address the problems of supplier selection and order allocation, mohammad et al. (2019) employed a hybrid model that combined fuzzy ahp and topsis methods with fuzzy multi-objective programming. to address it, they turned the multi-objective model into a single-level model using the e-constraint technique. the ultimate pareto solution was then chosen using the topsis method. rezaei et al. (2020) devised an integrated decision-making model for the supplier selection and order allocation problems in lean manufacturing combining fuzzy ahp and multiobjective optimization models. khalili nasr et al. (2021) introduced a novel two-stage fuzzy supplier selection and order allocation model for a case study in the clothing sector. this model worked in a closed-loop sc. fuzzy bwm was used in stage 1 to select the best suppliers based on economic, environmental, social, and circular factors, and a multi-objective mixed-integer lp model was employed in stage 2 to distribute orders. li et al. (2021) presented a two stage mathematical model for selecting a group of suppliers and assigning an order quantity to each source. the risk value, which was determined using qualitative and quantitative approaches based on bwm, was used as the basis for the initial selection of alternative suppliers. for the second step, which deals with dynamic supplier selection and order allocation, a multiobjective mathematical model was constructed. zhao et al. (2021) developed a new integration strategy based on decision-theoretic rough set and the extended vikor methods to address the resilient-sustainable supplier selection and order allocation problem. aouadni and euchi (2022) developed a hybrid model based on bwm, meaningful mixed data (mmd)-topsis, and lp model to address both the supplier selection and fair order allocation concerns. bwm was considered for determining the criteria's weights. utilizing the mmd-topsis technique, suppliers were ranked. in a manufacturing setting, a bi-objective lp was used to fairly distribute the order quantity among the providers by accounting for each supplier's meaningful suitability index (msi). goodarzi et al. (2022) suggested an integrated fuzzy-delphi, gray correlation-based topsis (gc-topsis), and an integer mixed bi-objective nonlinear planning model to pick the best supplier and determine the optimal values of the order from each selected supplier. despite extensive study on the application of supplier selection and order allotment models, as presented in the literature review, it is observed that there is a relatively little research on the dairy supplier selection and order allocation issue simultaneously and additional knowledge is still required regarding model application yazdani et al./oper. res. eng. sci. theor. appl. 5(3)2022 210-229 216 at the managerial level. food items, especially dairy products, are greatly impacted by perishability, which causes food quality to degrade over time. an efficient scm has to deal with infrastructure problems, which increase chain dynamics risks and reduce chain operations dependability. since scm activities are closely related to the issue of food safety and security, it is important to give them top priority (sharma et al. 2021). it is well known that inherent uncertainties like incomplete information, supply capacity restrictions, supply quality, delivery issues, item availability, logistics and transportation bottlenecks, demand unpredictability, and information misinterpretation have a significant impact on the selection process for dairy suppliers and order allocation. data inaccuracies have a direct impact on system results and can lead dms to make poor strategic choices when choosing suppliers and allocating orders. therefore, one of the key goals and incentives for sc practitioners and academics is the development of such models that can assist dms while confronting ambiguous circumstances to overcome uncertainty. utilizing the fuzzy set is the underlying idea behind overcoming ambiguities in decision-making processes. using the aforementioned ideas as a foundation, this research suggests a two-stage integrated model for supplier selection and order allocation problems in dairy industry to maximise the overall value of the purchase. the developed model is built on the use of fuzzy topsis to reduce ambiguous expert inputs in the first stage, while in the second stage, fuzzy topsis scores are used as inputs for an lp model to predict economic order quantity to be assigned to each supplier. several constraints including demand, density qualification, acidity qualification, price, and capacity are considered to present a realistic model. 3. fuzzy topsis method given the few experts involved and the need for quick and precise information processing, the topsis method was chosen for this endeavor because of its simplicity and flexibility. a further benefit is that it distinguishes between the cost (the lower the better) and benefit (the higher the better) criteria and chooses the solutions that are both closest to and farthest from the positive and negative ideal solutions. the conventional topsis, despite being commonly used, has certain drawbacks. the primary one has to do with the use of sharp numbers, which are typically ineffective at capturing the subjective character of human thought and may, in actual circumstances, result in the approach failing to effectively reflect dms' preferences. since expert evaluations contain unclear or confusing information, standard topsis cannot address it. this work uses the topsis method and fuzzy logic to address this shortcoming. fuzzy topsis method has been developed and conducted in many applications like renewable energy and landfill site selection (sengul et al. 2015; beskese et al. 2015), reliability and risk evaluation in process industry (gopal and panchal, 2021), modeling performance assessment for managing transportation businesses (dimitriou and sartzetaki, 2022), optimizing investment decision making (cao and xu, 2022) to name a few. in this paper, the rating of criteria and corresponding weights are considered as linguistic variables, as shown in figures 1 and 2 respectively. a two-stage integrated model for supplier selection and order allocation: an application in dairy industry 217 suppose that k dms have presented trapezoidal fuzzy numbers both for rating and importance weights of criteria. and k = 1, 2…, k. then the aggregated fuzzy rating can be considered as; 𝑅 = (𝑎, 𝑏, 𝑐, 𝑑), k = 1, 2…, k (1) where k k aa }min{ , 𝑏 = 1 𝑘 ∑ 𝑏𝑘 𝑘 𝑘=1 , 𝑐 = 1 𝑘 ∑ 𝑐𝑘 𝑘 𝑘=1 , k k dd }max{ by applying eq. (3) the aggregated fuzzy weights (wj) for each criterion, c = {c1, c2…cn}, and also the aggregated fuzzy rating (xij) of suppliers, a = {a1, a2…am}, regarding each criterion can be computed. as presented a supplier selection problem is formed by arranging columns of alternatives with rows of criteria as shown below: 𝐷 = [ 𝑥11 𝑥12 . . . . . 𝑥1𝑛 𝑥21 𝑥22 . . . . . 𝑥2𝑛 . . . . . . . . . . . . . . . . 𝑥𝑚1 𝑥𝑚2 . . . . . 𝑥𝑚𝑛] (2) from the eq. (4) the normalized fuzzy decision matrix can be calculated as;   nmij rr   , (3) in this matrix, transformation formulae for benefit criteria and cost criteria are the following, respectively. b and c are the sets of benefit and cost criteria. 𝑟𝑖𝑗 = ( 𝑎𝑖𝑗 𝑑𝑗 ∗ , 𝑏𝑖𝑗 𝑑𝑗 ∗ , 𝑐𝑖𝑗 𝑑𝑗 ∗ , 𝑑𝑖𝑗 𝑑𝑗 ∗ ) , 𝑗 ∈ 𝐵, (4a) 𝑟𝑖𝑗 = ( 𝑎𝑗 − 𝑑𝑖𝑗 , 𝑎𝑗 − 𝑐𝑖𝑗 , 𝑎𝑗 − 𝑏𝑖𝑗 , 𝑎𝑗 − 𝑎𝑖𝑗 ) , 𝑗 ∈ 𝐶, (4b) where bjdd i ijj  ,max * cjaa i ijj   ,max now based on normalized fuzzy matrix the weighted normalized fuzzy decision matrix can be calculated as; 𝑉 = [𝑣𝑖𝑗]𝑚×𝑛 ,,...,2,1 mi  ,,...,2,1 nj  (5) where 𝑣𝑖𝑗 = 𝑟𝑖𝑗(. )𝑤𝑗. fuzzy positive and negative ideal solutions can be constructed as; 𝐴∗ = {(𝑚𝑎𝑥 𝑗 𝑣𝑖𝑗|𝑖 ∈ 𝐵), (𝑚𝑖𝑛 𝑗 𝑣𝑖𝑗|𝑖 ∈ 𝐶)|𝑖 = 1,2, . . . . , 𝑛} (6) 𝐴− = {(𝑚𝑖𝑛 𝑗 𝑣𝑖𝑗|𝑖 ∈ 𝐵), (𝑚𝑎𝑥 𝑗 𝑣𝑖𝑗|𝑖 ∈ 𝐶)|𝑖 = 1,2, . . . . , 𝑚} (7) yazdani et al./oper. res. eng. sci. theor. appl. 5(3)2022 210-229 218 the closeness coefficient of all suppliers to positive and negative ideal solution can be described as; 𝐶𝐶𝑖 = 𝑑𝑖 − 𝑑𝑖 ∗+𝑑𝑖 −, ,,...,2,1 mi  (8) where the 𝑑𝑖 − is the distance between each alternative and fuzzy negative ideal solution and 𝑑𝑖 ∗ is distance between alternative and fuzzy positive ideal solution. 4. case study, model description and results the problem of supplier selection in many industries leads to a global decisionmaking challenge that require considerable attention and control. in this article we proposed to evaluate and optimize the suppliers in a dairy company in iran. the study is presented in a two-stage evaluation model that evaluates suppliers and provides the best quantity that should be ordered to the suppliers. in the first stage, suppliers are evaluated based on five criteria and then based on topsis scores (which are the inputs to the 2nd stage). suppliers were reconsidered in the lp model based on different constraints including demand, density qualification, acidity qualification, price, and capacity. the criteria are identified from the literature review as presented earlier. in addition, to purchase the optimized quantity of dry milk as a main material for dairy products, an lp has been developed model to determine the solution. in order to choose the best supplier from the five prospective alternative suppliers, a selection committee made up of three dms has been constituted. dm1 (d1) is a 10-year experienced production manager and worked in dairy and food sectors. d2 is quality manager and technician in milk quality control department. finally, d3 is director of logistic and purchase department and has more than 20 years of experience in food logistics. five criteria are considered as: quality (c1), price (c2), performance history (c3), management & organizations (c4) and production capacity & facilities (c5). the decision-making problem has a hierarchical structure, as shown in figure 3, which can be described in more detail using the following stages and steps: stage a: step 1: three dms used the linguistic elements of table 1 to express their opinions. table 2 presents the opinions for assessing the weights of the criteria. table 1. the linguistic variables used for criteria weights with the associated fuzzy numbers linguistic variable fuzzy number very low (vl) (0, 0, 0.1, 0.2) low (l) (0.1, 0.2, 0.3, 0.4) moderately low (ml) (0.3, 0.4, 0.4, 0.5) moderate (m) (0.4, 0.5, 0.6, 0.7) moderately high (mh) (0.6, 0.7, 0.7, 0.8) high (h) (0.7, 0.8, 0.8, 0.9) very high (vh) (0.8, 0.9, 1, 1) a two-stage integrated model for supplier selection and order allocation: an application in dairy industry 219 vp p mp f g vgmg 1 0 1 2 3 4 5 6 7 8 9 10 figure 1. linguistic variables for rating vl l ml m h vhmh 1 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 figure 2. linguistic variables for weights table 2. criteria weights given by the dms d1 d2 d3 c1 vh h vh c2 h h vh c3 h h h c4 mh mh h c5 h vh h step 2: as illustrated in table 4, the three dms also expressed their opinions regarding the suppliers using linguistic variables. based on table 3, trapezoidal linguistic variables are converted to associated fuzzy numbers to evaluate the rating of alternative suppliers regarding the considered criteria, as also shown in table 5. this table also shows the converted fuzzy numbers (as determined using table 1) for estimating criteria weights. yazdani et al./oper. res. eng. sci. theor. appl. 5(3)2022 210-229 220 figure 3. hierarchical structure of the decision problem table 3. linguistic variables for the performance scores and associated fuzzy numbers linguistic variable fuzzy number very poor (vp) (0, 0, 1, 2) poor (p) (1, 2, 3, 4) moderately poor (mp) (3, 4, 4, 5) fair (f) (4, 5, 6, 7) moderately good (mg) (6, 7, 7, 8) good (g) (7, 8, 8, 9) very good (vg) (8, 9, 10, 10) table 4. rating of five alternative suppliers with respect to five criteria criteria supplier dms d1 d2 d3 c1 a1 vg g vg a2 g g g a3 g mg g a4 mg g g a5 vg vg vg c2 a1 mg mg g a2 g mg mg a3 g g g a4 vg g vg a5 g vg g c3 a1 mg mg g a2 mg g mg a3 g g g a4 vg vg g a5 g vg g c4 a1 mg mg mg a2 g g g a3 g g vg a two-stage integrated model for supplier selection and order allocation: an application in dairy industry 221 a4 vg vg g a5 vg g g c5 a1 mg mg vg a2 mg mg g a3 g g mg a4 vg g g a5 g vg mg step 3: normalized fuzzy decision matrix, as shown in table 6, is formed using the values of fuzzy decision matrix of table 5. the weighted normalized fuzzy decision matrix is also calculated, as presented in table 7. step 4: fnis and fpis are determined as: a* = [(1,1,1,1),(1,1,1,1),(0.9,0.9,0.9,0.9),(0.9,0.9,0.9,0.9),(1,1,1,1)] a-=[(0.42,0.42,0.42,0.42),(0.42,0.42,0.42,0.42),(0.42,0.42,0.42,0.42), (0.36,0.36,0.36,0.36),(0.42,0.42,0.42,0.42)] table 5. fuzzy decision matrix and fuzzy weights c1 c2 c3 c4 c5 a1 (6,8,8.3,9) (6,7.3,7.3,9) (6,7.3,7.3,9) (6,7,7,8) (6,7.7,8,10) a2 (7,8,8,9) (6,7.3,7.3,9) (6,7.3,7.3,9) (7,8,8,9) (6,7.3,7.3,9) a3 (6,7.7,7.7,9) (7,8,8,9) (7,8,8,9) (7,8.3,8.7,10) (6,7.7,7.7,9) a4 (6,7.7,7.7,9) (6,8,8.3,9) (6,8,8.3,9) (6,8,8.3,9) (7,8.3,8.7,10) a5 (8,9,10,10) (7,8.3,8.7,10) (7,8.3,8.7,10) (7,8.3,8.7,10) (6,8,8.3,10) weight (0.7,0.6,0.93,1) (0.7,0.83,0.87,1) (0.7,0.8,0.8,0.9) (0.6,0.73,0.73,0.9) (0.7,0.83,0.87,1) table 6. normalized fuzzy decision matrix c1 c2 c3 c4 c5 a1 (0.6,0.8,0.83,0.9) (0.6,0.73,0.73,0.9) (0.6,0.73,0.73,0.9) (0.6,0.7,0.7,0.8) (0.6,0.77,0.8,1) a2 (0.7,0.8,0.8,0.9) (0.6,0.73,0.73,0.9) (0.6,0.73,0.73,0.9) (0.7,0.8,0.8,0.9) (0.6,0.73,0.73,0.9) a3 (0.6,0.77,0.77,0.9) (0.7,0.8,0.8,0.9) (0.7,0.8,0.8,0.9) (0.7,0.83,0.87,1) (0.6,0.77,0.77,0.9) a4 (0.6,0.77,0.77,0.9) (0.6,0.8,0.83,0.9) (0.6,0.8,0.83,0.9) (0.6,0.8,0.83,0.9) (0.7,0.83,0.87,1) a5 (0.8,0.9,1,1) (0.7,0.83,0.87,1) (0.7,0.83,0.87,1) (0.7,0.83,0.87,1) (0.6,0.8,0.83,1) table 7. weighted normalized fuzzy decision matrix c1 c2 c3 c4 c5 a1 (0.42,0.48,0.77,0.9) (0.42,0.6,0.63,0.9) (0.42,0.58,0.58,0.81) (0.36,0.51,0.51,0.72) (0.42,0.64,0.7,1) a2 (0.49,0.48,0.74,0.9) (0.42,0.6,0.63,0.9) (0.42,0.58,0.58,0.81) (0.42,0.58,0.58,0.81) (0.42,0.6,0.63,0.9) a3 (0.42,0.46,0.72,0.9) (0.49,0.66,0.7,0.9) (0.49,0.64,0.64,0.81) (0.42,0.6,0.63,0.9) (0.42,0.64,0.67,0.9) a4 (0.42,0.46,0.72,0.9) (0.42,0.66,0.72,0.9) (0.42,0.64,0.66,0.81) (0.36,0.58,0.6,0.81) (0.49,0.69,0.76,1) a5 (0.56,0.54,0.93,1) (0.49,0.69,0.76,1) (0.49,0.66,0.7,0.9) (0.42,0.6,0.63,0.9) (0.42,0.66,0.72,1) step 5: vertex method is used to calculate the distance of suppliers from fpis and fnis. tables 8 and 9 are the results of vertex method calculations. step 6: the closeness coefficient of suppliers is computed in table 10. these scores are used as coefficients for objective function of the mathematical problem: cc1 = 0.414, cc2 = 0.42, cc3 = 0.456, cc4 = 0.457, cc5 = 0.521 yazdani et al./oper. res. eng. sci. theor. appl. 5(3)2022 210-229 222 table 8. distance between fpis and supplier rating c1 c2 c3 c4 c5 d(a1,a*) 0.408 0.401 0.333 0.396 0.373 d(a2,a*) 0.39 0.401 0.333 0.333 0.401 d(a3,a*) 0.423 0.345 0.279 0.314 0.382 d(a4,a*) 0.423 0.368 0.302 0.351 0.322 d(a5,a*) 0.32 0.322 0.281 0.314 0.364 table 9. distance between fnis and supplier rating c1 c2 c3 c4 c5 d(a1,a-) 0.299 0.277 0.225 0.209 0.34 d(a2,a-) 0.292 0.277 0.225 0.275 0.277 d(a3,a-) 0.284 0.305 0.252 0.326 0.292 d(a4,a-) 0.284 0.307 0.254 0.278 0.364 d(a5,a-) 0.397 0.364 0.305 0.326 0.348 table 10. computation of di*, diand cci dd* d+ d* cci a1 1.35 1.911 3.261 0.414 a2 1.346 1.858 3.204 0.420 a3 1.459 1.743 3.202 0.456 a4 1.487 1.766 3.253 0.457 a5 1.74 1.601 3.341 0.521 table 11. the model parameters xi order quantity of dry milk for ith supplier pi unit price of ith supplier d demand (30000 kg in model) p determined unit price respect to budget (7.5 thousand in model) cci topsis score of ith suppliers ci capacity of delivery of ith supplier di density of dry milk for ith supplier ai acidity percentile in dry milk of ith supplier a company acceptance limit for acidity of dry milk (15 in model) b company acceptance limit for density of dry milk (38 in model) stage b: after having the closeness coefficients of table 10 and according to the model parameters as shown in table 11, the best order quantity is attained in stage b by maximizing the total value of purchasing (z). an integrated lp model is formed as follows: objective function: a two-stage integrated model for supplier selection and order allocation: an application in dairy industry 223 𝑀𝑎𝑥(𝑍) = ∑ 𝐶𝐶𝑖𝑋𝑖 𝑛 𝑖=1 subject to: ∑ 𝑋𝑖 𝑛 𝑖=1 = 𝐷 (demand constraint) ∑ 𝑋𝑖 𝑛 𝑖=1 𝑑𝑖 ≤ 𝐵𝐷 (density qualification constraint) ∑ 𝑋𝑖 𝑛 𝑖=1 𝑎𝑖 ≤ 𝐴𝐷 (acidity qualification constraint) ∑ 𝑋𝑖 𝑛 𝑖=1 𝑝𝑖 ≤ 𝑃𝐷 (price constraint) 𝑋𝑖 ≤ 𝐶𝑖 (capacity of suppliers’ constraint) 𝑋𝑖 ≥ 0, 𝑖 = 1,2, . . . , 𝑛 (non-negativity of variables) 𝑀𝑎𝑥(𝑍) = 0.414𝑋1 + 0.42𝑋2 + 0.456𝑋3 + 0.457𝑋4 + 0.521𝑋5 subject to: 𝑋1 + 𝑋2 + 𝑋3 + 𝑋4 + 𝑋5 = 30000 36𝑋1 + 38𝑋2 + 37.5𝑋3 + 39𝑋4 + 41𝑋5 = 1140000 13.1𝑋1 + 14.4𝑋2 + 12.5𝑋3 + 16𝑋4 + 12.8𝑋5 = 450000 6.9𝑋1 + 7.2𝑋2 + 7𝑋3 + 7.8𝑋4 + 8𝑋5 = 225000 𝑋1 ≤ 8000 𝑋2 ≤ 9000 𝑋3 ≤ 5000 𝑋4 ≤ 8000 𝑋5 ≤ 12000 𝑋𝑖 ≥ 0, 𝑖 = 1,2,3,4,5 the model is solved by win qsb software for more accurate and precise results, as shown in fig 4. the optimized amount of order from each supplier are as follows: 𝑋1 = 8000, 55002 x , 50003 x , 80004 x , 35005 x , 𝑍 = 13381.50 in the similar manner, supplier a1 and supplier a4 needs to deliver to the company the 8000 kg of dry milk, while supplier a5 just provides 3500 kg. the total cost for each period of order will be almost 13381.50 thousand. it is seen a supplier selection problem has been formulated and then the optimal quantity of order divided by each supplier has been assigned to them. the planning department presents this plan to the financial department and one copy to each supplier for further operations. yazdani et al./oper. res. eng. sci. theor. appl. 5(3)2022 210-229 224 figure 4. model solution in win qsb 5. managerial implications: results of this research work has been communicated to the sc manager of the company to put them into practice for further validation. the manager demonstrated keen interest in the outcomes and stated that once the top management decided to apply the outcomes, the efficacy of the suggested framework could be further investigated. the following suggestions were also made to the scm department: to analyze the system dynamics of the entire scm after implementing the results. to take into account the ambiguities and fuzziness related to raw data by utilizing a fuzzy-based models as adopted in this work. 6. conclusions supplier selection problem is a strategic operation in production sector, especially when the products are connected with food, dairy and mineral water areas. this study investigates the problem of supplier evaluation in a dairy production factory and utilizes a two-stage model. in order to deal with uncertainty, fuzzy method helps organizations to tackle complicated decision problems even when they lack information and decision structure is not well defined. a problem of supplier selection in a dairy company was defined and a fuzzy topsis model identified the most important suppliers with the relevant performance score. then a linear programming model has been designed to obtain efficient order quantity for each supplier. the model solved the model with software and reported to the manager of purchasing a two-stage integrated model for supplier selection and order allocation: an application in dairy industry 225 department. it has been realized that fuzzy decision-making techniques are effectively implemented in such kind of problems to help operation and purchasing managers in practice. during the data elaboration, participants and managers with various expertise participated and helped us to have better understanding of supplier performance. the idea this study is to deliver potential supplier and inform managers to construct a visionary scale toward supplier problem and improve sc efficiency. the single objective nature of the proposed model is one of its drawbacks; 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(2021). an integrated approach based on the decision-theoretic rough set for resilient-sustainable supplier selection and order allocation. kybernetes. https://doi.org/10.1108/k-11-2020-0821. © 2022 by the authors. submitted for possible open access publication under the terms and conditions of the creative commons attribution (cc by) license (http://creativecommons.org/licenses/by/4.0/). a two-stage integrated model for supplier selection and order allocation: an application in dairy industry morteza yazdani 1, prasenjit chatterjee 2*, željko stević 3 1. introduction 2. literature review 3. fuzzy topsis method 4. case study, model description and results 5. managerial implications: 6. conclusions references plane thermoelastic waves in infinite half-space caused operational research in engineering sciences: theory and applications operational research in engineering sciences: theory and applications vol. 2, issue 3, 2019, pp. 1-25 issn: 2620-1607 eissn: 2620-1747 doi: https://doi.org/10.31181/oresta1903001h * corresponding author. malek.hassanpour@yahoo.com (m. hassanpour). dpamucar@gmail.com (d. pamucar) evaluation of iranian household appliance industries using mcdm models malek hassanpour *1, dragan pamučar 2 1 department of environmental science, ucs, osmania university, telangana state, india 2 department of logistics, military academy, university of defence in belgrade, serbia received: 25 july 2019 accepted: 09 october 2019 first online: 12 november 2019 original scientific paper abstract. technology development and maturation in the field of household appliance industries, approach to the initial media and aims of industry 4.0 are promising scenarios for the future. however, the present cluster study of iranian household appliance industries (ihai) empirically seeks the full details of ihai based on the preliminary studies of both iranian industries organization and iranian environment protection agency once in the industry confirmation step and issue the authorities and licenses to stakeholders. simple additive weighing (saw), additive ratio assessment (aras) and combinative distance-based assessment (codas) method and data envelopment analysis (dea) were employed to classify ihai based on the main criteria via spss and excel 2013 soft-wares. by the way, the friedman test and entropy shannon weighing systems were also applied to distinguish the values of weights. the findings were revealed three prominent steps to achieve sustainable development purposes, economic estimation and efficiency appraise of industries in the easiest possible situation. also, by current study ihai were classified by a ranking system of dea, in terms of efficiency score. key words: evaluation, household appliance industries, aras, codas, dea models. 1. introduction population growth and community development have increased the use of home appliances. the first home appliance industry commenced in 1316 in iran. according to the home appliance industry, the statistics office of iran, which has been published for six months until this date, shows that the economic growth of the first six months of the present year is 0.4%. the supply chain in the home appliance industry besets the upstream industries such as steel, copper, aluminum, petrochemicals, etc. are directly linked to this collection, so the industry is considered to be the accelerator of hassanpour & pamučar /oper. res. eng. sci. theor. appl. 2 (3) (2019) 1-25 2 economic development all over the world. ihai are in a complicated phase due to changes in the conditions and factors that are accelerating day by day. globalization and presence in international markets require the production of high-quality, affordable, world-class appliances and increased production beyond the minimum requirements for consumption. exploiting opportunities and reaching new markets and meeting the demands and expectations of customers and society require the principled government support and the transformation to reduce the cost of products. however, the most important obstacles to the presence of home appliances products in the world market can be the montage of the home appliance equipment and the joint production of some products with the lowest internal depth, the lack of intelligence and the use of electronic infrastructure in the export products. other major reasons are the burnout of machinery and equipment, the trafficking of home appliances to the country, and the reduction of the power and ability to produce and sell domestic companies, and consequently the loss of power in exports. on the other hand, the lack of allocation of foreign currency to machinery of the production line and intermediary goods, the lack of identification and absence of the program for joining the global value chain and the poor attendance at credible international exhibitions and the absence of a permanent exhibition or sales center in the target countries of export; also other factors of frustration considering the above mentioned cases, proper planning should be done to remove the weaknesses from the country's capacity so that the domestic appliance industry can play an effective role in the country's economic development with the presence of high-power target markets (jandaghi et al, 2011). therefore, according to human demands, the nations follow the rules in the implementation of ihai projects. in the beginning, industrial projects come through of project identification steps, screening of project and further studies associated with decision making processes to final steps of approving the projects. the present study passed the initial checking and public involvement of projects in raw data and reached to come through of decision-making models (munn, 1979). lots of multi-criteria decision makings techniques introduced by scientists over the world. the present study examined four decision-making systems such as saw, codas, aras, and dea. codas is one of the multi-attribute decision-making methods. the codas model is based on an evaluation combined distance. this technique was first introduced in 2016. this technique, like other techniques of the same family, aims to rank research alternatives based on the number of criteria. the decision matrix of this technique is an optional criterion matrix. aras technique was posed in 2010. the word aras means a collective ratio evaluation. this method is also employed for ranking options of research. the decision matrix of this method is also an optional matrix, the matrix in which its columns are criteria and its rows are research choices. in general, the aras technique, like many multivariate decisionmaking techniques, is seeking a solution to choose the best option. this technique is comparable in terms of purpose with family decision matrix techniques such as promethee, sir, oreste, and electere, but is comparable with topsis, vikor and saw in terms of simplicity. the ranking results of the aras model provide the same results with the saw model. dea is a non-statistical practice that is applied to judge the performance in a relative manner depend on output and input ratios or divisions in industry availability. the higher the number of input and output units with extensive duration, the better the comparison and the more realistic results will appear (rezaee and ghanbarpour 2016; tupenaite et al. 2010; badi et al 2018). evaluation of iranian household appliance industries using mcdm models 3 the weighing systems of the friedman test and entropy shannon were employed to estimate the values of weights for the criteria. the friedman test is a nonparametric test used to compare three or more dependent groups that are measured at least at the rank level. this test can also be applied to continuous data, but its ranking is also taken into account when calculating this data. the friedman test is the nonparametric f-dependent test for analysis of variance of repeated measures. in this case, there is no need for assumptions such as normality of distribution, equality of variances, and consistency of the scale to perform variance analysis of the repeated data. therefore, the friedman test is used to analyze the variance of repeated measures if one or all of the above hypotheses are rejected. the null hypothesis in this test states that the distributions of observations are the same in repeated measurements. in other words, there is no difference between the distributions created by repeated measurements on one group or between groups on the dependent variable. entropy in information theory is a numerical criterion of the amount of information or the degree of randomness of a random variable. more precisely, the entropy of a random variable is the average value (mathematical expectation) of the amount of information it observes. in other words, the simpler the entropy of a random variable, the greater our uncertainty about that random variable, so by observing the definitive result of that random variable is more information, so the more entropy a random variable is, the more likely it is that the data will come from a definite observation. information from observing an event is defined as a negative logarithm of the probability of it occurring; there is naturally every appropriate function to measure the amount of information an expecting observation contains, including information from an observation that is negligible. the data obtained from observing a definite event (ie, with probability one) is zero, and most importantly the data obtained from two independent observations is equal to the sum of the data obtained from observing each one. it can be shown that the only function satisfying the above three properties is the negative function of the logarithm of probability. the amount of information with different logarithmic bases is only one constant coefficient. the most common base of the logarithm calculates the information in shannon units (eisinga et al., 2017; hassanpour 2018, 2019). by the present study as evaluation of ihai our efforts spent on below objectives; • to identify the input and output materials introduced into industries. • to investigate the energy consumed (power, fuel, and water) in industries. • to examine the weighted average of factors among whole industries. • to develop a new type of classification (ranking) for industries. • to study and depict the flow-diagram of industries. • to find the significant differences and correlations among 5 main criteria of industries. it needs to explain that current research is the first study comprising all details of ihai in the project identification assessment of the iranian evaluator team. therefore, the validity of data is very obvious to depend on its initial source. also, there is no similar research that managed to execute the materials and energy demand of ihai. hassanpour & pamučar /oper. res. eng. sci. theor. appl. 2 (3) (2019) 1-25 4 2. literature review to prioritize the criteria and factors (indoor air circulation, air humidity, air temperature, illumination intensity, airflow rate, and dew point) of microclimate in office rooms have been used aras method by zavadskas and turkis (2010). the study targeted the convenience of staff in their working ambient in vilnius. a classification of alternatives has done by the study. turskis et al (2012) utilized the aras model to select the right place among 7 selected locations to remove the nonhazardous waste combustion plant in lithuania. tupenaite et al (2010) applied the aras model to prioritize lots of criteria and alternatives of the built and human ambient renovation in bulgarian cultural heritage projects. a study appraised and ranked 4 companies possessing 32 criteria based on the aras model. it was sorted out the companies according to their indicators in the best possible position. kersuliene and turskis (2011) found and distinguished many styles in the architect selection via the aras model. by the research apprised n2o, ch4, and co2 dissipation from grasslands exposed to various mineral fertilizers in a period of vegetation with regard to physical and chemical properties of soil, etc. via the aras model. the ranking system classified 6 alternatives and 11 criteria as a result (balezentiene and kusta 2012). the faculty web site appraisal has been done via the aras model considering accuracy, authority, objectivity, currency, coverage of the website with three alternatives. so, the ranking system prioritized the items based on the prominent factor to unessential one (stanujkic and jovanovic 2012). two studies classified iranian leather and textile industries and iranian food industries in lists of about 38 and 57 classes regarding the main 5 criteria such as the number of staff, the land occupied by industry, water, fuel, and power consumed in the industries via saw model. the friedman test used as a weighting system in the studies (hassanpour 2018, 2019a). also saw method employed in lots of recent studies because of simplicity in understanding and managing the values. dea model applied to determine efficiency estimation for a set of portuguese water and sewerage services in the economic and privatization aims via 6 input criteria (total cost, the opex, the capex, the mains length, the number of staffs and the others opex (opex minus labour outlay oopex)) and 3 outputs criteria (water volume, costumers, length factors) (emrouznejad and podinovski 2004). rezaee and ghanbarpour (2016) complemented two studies via the dea method for assessing 59 iranian manufacturing units under 23 classes to distinguish the energy resources such as the amount of fossil fuel, water, electricity consumption, and employee numbers. rahimi et al (2017) used a dea model for determining the performance of the industry in iran. dea model assigned to estimate the efficiency level of 15 insurance companies from 2005 to 2012 by sinha (2015). saranga and nagpal (2016), bulak and turkyilmaz (2014), amini and alinezhad (2016), lu et al., [19], xavier et al., (2014), keramidou et al., (2011) and ahmadi and ahmadi (2012) used a model of dea to find the efficiency of airline companies, the performance of 744 small and medium enterprises in turkey, for ranking 15 iranian industries, the efficiency of chinese life insurance companies from 2006 to 2010, the performance analysis of around 40 retail workshops in the portuguese during 2010 to 2013, for estimating the industrial productivity, the efficiency of the greek meat products industry during 1994 to 2007 and efficiency estimation among 23 main iranian industries during 2005 to 2007 respectively. krmac and djordjevic (2019) used non‐radial dea model to select and assess the environmental performance of suppliers with regard to evaluation of iranian household appliance industries using mcdm models 5 undesirable inputs and outputs such as number of employees, energy consumption (kwh/year), sales (1000 korean won), return on assets, environmental & investment (100,000 korean won), co2 (kg). the applied model classified the suppliers in the range of 0 to ≥ 1. a codas model used to prioritize the difficulties discovered in a company in libya. codas model possesses both euclidian and taxicab distances calculations for distinguishing the desirability of an option. findings showed that the codas model was reliably and efficiently able to cope with the supplier selection difficulties (badi et al 2018). ghorabaee et al (2016) tried to explain the applications of the codas model via some numerical examples associated to choose the most relevant industrial robot considering some criteria such as load capacity, maximum tip speed, repeatability, memory capacity, and manipulator reach. the findings classified alternatives based on weighing and ranking styles. a study tried to explain the codas model applications in the material handling facilities alternatives including 4 alternatives with 6 criteria such as fixed cost, the variable cost, and speed of conveyor, item width, item weight, and flexibility. finally, the ranking system appeared as a classification of alternatives (mathew and sahu 2018). badi et al (2016) utilized the codas model to find the best location of desalination plant assuming criteria of proximity, quality, network, vicinity and cost with 5 selected locations in libya. roy et al (2019) used the codas model to choose sustainable materials in construction projects containing lots of criteria and options to rank and weight. a new fuzzy codas model offered for removing decision difficulties in a technique of an ammonia synthesis unit of a urea fertilizer industry located in north india. the weights for criteria and factors have been calculated based on geometric mean procedures (panchal et al 2017). pumcar et al (2018) employed the pairwisecodas model supported by the linguistic neutrosophic numbers weighing system in the selection of optimal power-generation technology in libya. to assess the enterprise systems at a satisfaction level of promotion in parallel with business intelligence and excellence, the collected data containing 5 enterprises and 34 criteria came through of the codas model (dahooei et al 2018). roy et al (2018) attempted to sort out the difficulties emerged in aerospace framework alleys selection. so, results managed to present in the reasonable media to be applicable in real utilization. mukhametzyanov and pamucar (2018) utilized various methods of multicriteria decision-making systems (such as saw, topsis, aras, codas, etc.) for analyzing the sensitivity. so a statistical output declared the objectives of research and ranking systems applied to prioritize the factors and alternatives. the normal distribution, sensitivity concepts, weighing and ranking items followed by dynamic simulations. 3. methodology with regard to this fact that the final purpose of evaluation studies is, survey the implementation pattern of sustainable development based on economic outcomes. but it needs a full inventory of availability in ihai. a lack of valuable database and information about the preliminary screening of iranian industries prior to constructing them that has been experienced in recent researches in iran. the below flow-chart describes the mentioned steps and discussed methods in this paper. hassanpour & pamučar /oper. res. eng. sci. theor. appl. 2 (3) (2019) 1-25 6 figure 1 represents the flow-diagram of followed work and initial screening of ihai by the iranian evaluator team. figure 1. flow-diagram of followed work along with the eia program in iran 3.1. the weighing system based on the friedman test the method to carry out the step of the friedman test is accomplished by equations of 1-5 using spss software. in the designed matrix rij is the initial values (hassanpour, 2019). (1) (2) evaluation of iranian household appliance industries using mcdm models 7 (3) (4) (5) 3.2. the weighing system based on entropy shannon an entropy shannon method is a multi-criteria decision-making method for calculating the weights of criteria. this method requires matrix-option. this method was presented in 1974. entropy expresses the amount of uncertainty in a continuous probability distribution. the main idea of this method is that the more dispersion in the values of one indicator, the more important it will appear. the steps in this method are as below. we first make the decision matrix. to form this matrix, it is sufficient if the criteria are qualitative to obtain the verbal expressions of each option in relation to each criterion, and if the criteria are small, we will put the actual number of that assessment. in below, the matrix chooses the columns for the criteria and the rows are the options (according to table 1). in the second step, we normalize the matrix and call each normalized value as pij. the normalization is such that we divide the column of each column into the total sum of the column. the third step is to calculate the entropy of each ej index, and k holds the value of ej between 0 and 1 as the fixed value. the fourth step is to calculate the value of dj (degree of deviation), which states that the relevant index (dj) is the amount of useful information for decision making. whichever measured value is the indicator, the donor is that rival options do not differ much from one indicator to the other. the fifth step is to calculate the weights (wj) (hassanpour 2019b). (6) (7) (8) (9) (10) 3.3. the ranking system of aras and saw aras method like all other methods requires to set up a general decision matrix. in this matrix, m is the number of options (number of industries), n the number of criteria, and xij represents the performance of option i on the basis of j and xjo, the optimal value of the j criterion. if the optimal value of j is uncertain, the equations are as follows. the normalization of the initial values of the decision matrix was made from the following equation numbered by 13. equation 14 was used to form the normalized and weighted matrix. in this formula, wj represents the weight of the criterion. the following equation (15) was used to determine the value of the hassanpour & pamučar /oper. res. eng. sci. theor. appl. 2 (3) (2019) 1-25 8 optimality function and the degree of utility of each option. the option with a larger si has a higher priority. the degree of utility of each option was evaluated as equation 16. it needs to explain that equations 13 and 13-1 were used for normalization and ranking the data in the procedure of the saw model. it needs to declare that equation 13-1 has not belonged to the steps of the aras model. (11) (12) (13) (13.1) (14) (15) (16) 3.4. dea dea implication relies on distinguishing efficient and inefficient industries, companies and etc. in the following, it was sorted the input and output criteria and then the weighing system of friedman test was assigned to calculate the values of weights for criteria. the efficiency score of the industries was obtained via uniting aras and dea models according to equations 11, 12, 13, 14 and 15 of the aras model in the mix with equations 17 to 21 of the dea model. after the normalization process (using equation 13) the dea rank score was devoted to industries via division of weighted average of outputs to the weighted average of inputs (via equation 14 and 15) (xavier et al 2015). the division of the weighted average of outputs to the weighted average of inputs complies from equation 17 to 21 of the dea model. (17) (18) (19) (20) (21) evaluation of iranian household appliance industries using mcdm models 9 3.5. codas model to estimate normalized values in the decision matrix, linear normalization was used according to equations 22 and 23 for the weighted normalized decision matrix. the euclidian and taxicab distances were determined using equations 25 to 28. equations 27 and 28 were employed to construct the relative assessment matrix where k belongs as (1, 2… n) and ψ presents a threshold function to recognize the equality of the euclidean containing . by the equation 29, the option holding the highest h is the best choice among the alternatives (ghorabaee et al. 2016). (22) (23) (24) (25) (26) (27) (28) (29) 4. results and discussion 4.1. ihai technologies technology development and maturation in the field of the ihai approach to the initial media and aims of industry 4.0 are promising scenarios for the future. according to figure 2, the flow-diagram of ihai depicted as below for industries individually. hassanpour & pamučar /oper. res. eng. sci. theor. appl. 2 (3) (2019) 1-25 10 (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) evaluation of iranian household appliance industries using mcdm models 11 (14) (15) (16) (17) (18) (19) (20) (21) (22) (23) (24) (25) figure 2 ihai, and their generation processes earphone (1), hairdryer handheld (2), household ventilator (3), household crystal containers (4), pyrex glass containers (5), semiautomatic washing machine (6), tea flask (7), teflon containers (8), water cooler (9), gas oven (10), steam iron (11), juicer (12), hassanpour & pamučar /oper. res. eng. sci. theor. appl. 2 (3) (2019) 1-25 12 electrical miller and mixer (13), steam cooked double glazed steel (14), electrical stove (15), gas stove (16), semi-automatic electric cooker (17), ceiling fan (assembly) (18), desktop fan (19), household vacuum cleaner (assembly) (20), meat grinders (assembled) (21), chinese dishes (22), chinese decorative dishes (23), samovar (electric and oil) (24), household refrigerator (25). table 1 shows valuable information about 5 main criteria of ihai as an initial assessment of above-named organizations. the initial feed is the existing data of the input materials stream. with regard to a rise in the nominal capacity of industries, a rise will appear in the existing data in table 1. but it is the same for the industries with the same nominal capacity. table 1 ihai, input materials, number of staff, energy consumptions based on nominal capacity )2land (m fuel (gj/d) water )/d3(m power (kw/d) employee/d* initial feed (annually) nominal capacity industry 1300 2 5 60 6 43.231t+410450 no 20000 no (1) 2100 4 5 24 24 2054000 no+286 m2+0.054t 100000 no (2) 3300 5 7 201 31 60.5t+1151000 no 100000 no (3) 3300 5 6 100 29 649.1t+70000 no 500t (4) 15000 116 41 1026 83 3597.5t+1950.8 no 100000 no (5) 2300 3 2 21 12 909400 no+21500 m 10000 no (6) 2600 4 7 46 31 23.665t+952400 no 100000 no (7) 6000 9 10 238 39 238.65t+1678500 no 211t (8) 8300 16 11 375 37 1689t+898000 no 20000 no (9) 5800 13 10 207 45 117.9 t+3300 m2, 120240 no 12000 no (10) 2600 4 6 91 26 6.035t+480000 20000 no (11) 2200 3 4 20 17 774300 48000 no (12) 1700 3 4 20 18 389100 n0+2472 m 20000 no (13) 4900 3 4 49 17 151.75t+650250 no 50000 no (14) 2400 10 7 126 35 2857.2t+28000 m+2611400 no 30000 no (15) 4900 15 5 244 15 703.55t+60900 no 20000 no (16) evaluation of iranian household appliance industries using mcdm models 13 4500 7 19 435 37 142.85t+209000 n0 20000 no (17) 2500 4 6 33 29 23.795t+947467 no 50000 no (18) 7300 7 22 330 88 266.17t+800000 no 100000 no (19) 3900 4 5 33 23 769050 no 30000 no (20) 2900 4 5 35 19 623244 no 40000 no (21) 17100 179 33 519 113 1119t 800t (22) 11600 168 24 260 115 2083.7t 500t (23) 4500 5 38 316 36 428.5t+3483500 no 82500 no (24) 8400 8 14 313 63 154449 no+611.2t 15000 no (25) *d=day according to the null hypothesis, the categories of employee, water, and fuel have occurred with equal probabilities based on the onesample chi-square test. therefore, the null hypothesis was retained. the distribution of power and land was obtained normally based on a one-sample kolmogorov smirnov test. therefore, the null hypothesis was retained. the test statistic based on chi-squared was revealed the values about 2.720, 1.68, 11.400, 17.00, and 2.720 for the employee, power, water, fuel, and land respectively. the one-sample kolmogorovsmirnov z test has presented the values around 1.335, 1.032, 1.365, 2.218 and 1.073 for the employee, power, water, fuel, and land respectively. the friedman test analysis had represented the ranks about 2.84, 3.98, 1.72, 1.46, and 5 for employee, power, water, fuel, and land respectively. in the following, the test statistic (n=25) resulted in chi-square around 90.321 supported by the friedman test. the correlation analysis had shown the highest value of around 0.879 between the data of land area used and employee. the one-sample t-test had shown a significant difference (p-value ≤ 0.025) for the variable of fuel among 5 main criteria in table 1. 4.2. findings based on friedman test, saw and aras model the friedman test analysis had represented the ranks about 2.84, 3.98, 1.72, 1.46 and 5 for employee, power, water, fuel, and land respectively. in the following steps the normalized, weighted and ranked matrix was composed using equations 11 to 16 according to table 2. the ranking systems have appeared as the last columns of table 2 with the same results in both models of saw and aras with the weighing system of the friedman test. there is no significant difference between weights in table 2 (ki values and weights of saw model) using both ttest and pair test outputs. hassanpour & pamučar /oper. res. eng. sci. theor. appl. 2 (3) (2019) 1-25 14 table 2 normalized, weighted and ranked matrix saw (rank) weights aras (rank) ki si land fuel water power employees industry 25 0.1468 25 0.0691 0.1468 0.0098 0.0033 0.0166 0.0117 0.0060 1 21 0.2059 21 0.0969 0.2059 0.0159 0.0066 0.0166 0.0046 0.0242 2 12 0.4231 12 0.1992 0.4231 0.0251 0.0083 0.0233 0.0392 0.0313 3 14 0.3331 14 0.1569 0.3331 0.0251 0.0083 0.02 0.0195 0.0293 4 1 2.1234 1 1 2.1234 0.1141 0.1930 0.1366 0.2003 0.0840 5 24 0.1570 24 0.0739 0.1570 0.0175 0.0049 0.0066 0.0040 0.0121 6 18 0.2736 18 0.1288 0.2736 0.0197 0.0066 0.0233 0.0089 0.0313 7 9 0.6045 9 0.2846 0.6045 0.0456 0.0149 0.0333 0.0464 0.0394 8 6 0.8155 6 0.3840 0.8155 0.0631 0.0266 0.0366 0.0732 0.0374 9 10 0.5998 10 0.2824 0.5998 0.0441 0.0216 0.0333 0.0404 0.0455 10 16 0.2884 16 0.1358 0.2884 0.0197 0.0066 0.02 0.0177 0.0263 11 22 0.1783 22 0.0839 0.1783 0.0167 0.0049 0.0133 0.0039 0.0172 12 23 0.1621 23 0.0763 0.1621 0.0129 0.0049 0.0133 0.0039 0.0182 13 15 0.3036 15 0.1429 0.3036 0.0372 0.0049 0.0133 0.0095 0.0172 14 13 0.3542 13 0.1668 0.3542 0.0182 0.0166 0.0233 0.0245 0.0354 15 11 0.4842 11 0.2280 0.4842 0.0372 0.0249 0.0166 0.0476 0.0151 16 8 0.7415 8 0.3492 0.7415 0.0342 0.0116 0.0633 0.0849 0.0374 17 19 0.2482 19 0.1169 0.2482 0.0190 0.0066 0.02 0.0064 0.0293 18 4 0.9302 4 0.4381 0.9302 0.0555 0.0116 0.0733 0.0644 0.0890 19 17 0.2785 17 0.1311 0.2785 0.0296 0.0066 0.0166 0.0064 0.0232 20 20 0.2305 20 0.1085 0.2305 0.0220 0.0066 0.0166 0.0068 0.0192 21 2 2.0028 2 0.9431 2.0028 0.1301 0.2978 0.11 0.1013 0.1143 22 3 1.5197 3 0.7156 1.5197 0.0882 0.2795 0.08 0.0507 0.1163 23 7 0.7502 7 0.3533 0.7502 0.0342 0.0083 0.1266 0.0616 0.0364 24 5 0.8436 5 0.3972 0.8436 0.0639 0.0133 0.0466 0.0611 0.0637 25 evaluation of iranian household appliance industries using mcdm models 15 4.3. findings based on entropy shannon weighing system and aras model it was used the equations 6-10 for calculating the values of weights by the entropy shannon method according to table 3. the same procedure was done to obtain the normalized, weighted and ranked matrix in table 4. a ranking system appeared as the last column of table 4. table 3. weighted values based on entropy shannon procedure employee power water fuel land e 0.927491457 0.850741096 0.89502861 0.634662697 0.925152169 dj=1-ej 0.072508543 0.149258904 0.10497139 0.365337303 0.074847831 wj 0.09454463 0.19462021 0.136873268 0.476367041 0.097594852 0.766923971 k 0.310667467 hassanpour & pamučar /oper. res. eng. sci. theor. appl. 2 (3) (2019) 1-25 16 table 4 normalized, weighted and ranked matrix saw (rank) weights aras (rank) ki si land fuel water power employees industry 24 0.0076 24 0.0383 0.0076 0.0098 0.0033 0.0166 0.0117 0.0060 1 21 0.0102 21 0.0510 0.0102 0.0159 0.0066 0.0166 0.0046 0.0242 2 13 0.0202 13 0.1009 0.0202 0.0251 0.0083 0.0233 0.0392 0.0313 3 14 0.0157 14 0.0785 0.0157 0.0251 0.0083 0.02 0.0195 0.0293 4 3 0.1687 3 0.8428 0.1687 0.1141 0.1930 0.1366 0.2003 0.0840 5 25 0.0069 25 0.0346 0.0069 0.0175 0.0049 0.0066 0.0040 0.0121 6 16 0.0130 16 0.064 0.0130 0.0197 0.0066 0.0233 0.0089 0.0313 7 10 0.0289 10 0.1445 0.0289 0.0456 0.0149 0.0333 0.0464 0.0394 8 5 0.0416 5 0.2080 0.0416 0.0631 0.0266 0.0366 0.0732 0.0374 9 9 0.0313 9 0.1565 0.0313 0.0441 0.0216 0.0333 0.0404 0.0455 10 15 0.0137 15 0.0688 0.0137 0.0197 0.0066 0.02 0.0177 0.0263 11 22 0.0082 22 0.0410 0.0082 0.0167 0.0049 0.0133 0.0039 0.0172 12 23 0.0079 23 0.0397 0.0079 0.0129 0.0049 0.0133 0.0039 0.0182 13 19 0.0113 19 0.0566 0.0113 0.0372 0.0049 0.0133 0.0095 0.0172 14 12 0.0210 12 0.1051 0.0210 0.0182 0.0166 0.0233 0.0245 0.0354 15 11 0.0285 11 0.1424 0.0285 0.0372 0.0249 0.0166 0.0476 0.0151 16 7 0.0376 7 0.1879 0.0376 0.0342 0.0116 0.0633 0.0849 0.0374 17 18 0.0117 18 0.0589 0.0117 0.0190 0.0066 0.02 0.0064 0.0293 18 4 0.0419 4 0.2096 0.0419 0.0555 0.0116 0.0733 0.0644 0.0890 19 17 0.0118 17 0.0589 0.0118 0.0296 0.0066 0.0166 0.0064 0.0232 20 20 0.0107 20 0.0537 0.0107 0.0220 0.0066 0.0166 0.0068 0.0192 21 1 0.2001 1 1 0.2001 0.1301 0.2978 0.11 0.1013 0.1143 22 2 0.1736 2 0.8673 0.1736 0.0882 0.2795 0.08 0.0507 0.1163 23 6 0.0400 6 0.2003 0.0400 0.0342 0.0083 0.1266 0.0616 0.0364 24 8 0.0368 8 0.1842 0.0368 0.0639 0.0133 0.0466 0.0611 0.0637 25 evaluation of iranian household appliance industries using mcdm models 17 the ranking systems have appeared with the same results in both models of saw and aras with the weighing system of the entropy shannon. it was found a significant difference (p-value between weights in table 2 (ki values and weights of saw model) using both t-test and pair test outputs. the ranking system offered different results in both the weighing systems of the friedman test and entropy shannon using aras and saw models. 4.4. dea dea employed empirically to realize the relative efficiency of any company and industry etc. the procedure is run by exploiting inputs for releasing outputs. dea implication encompassed some steps to definition (1) the charnes-cooper-rhodes (ccr) ratio model: (a) determination of net technical efficiency by a distinguished measure of operations, (b) demystifying rising, falling, or fixed return on the scale. (2) coefficient models (3) additive model and additive developed model. dea model is assigned to compute the efficiency (around 1), inefficiency (below 1) and super efficiency (upper than 1) with regard to optimal weights associated with the input and output criteria. the most difficulties discovered in the dea procedure need to pay attention to a scarcity of data including a time interval in this regard as well as existing various dimensions for the criteria (rezaee and ghanbarpour 2016). as mentioned above, our data collected from the iranian evaluation team of both iranian industries organization and iranian environment protection agency assessments once in the preliminary studies of industrial projects. so, the mentioned data were tabulated in table 5 annually. then, criteria were classified into two groups such as outputs and inputs. the nominal capacity of industries comprised the outputs criteria and the remaining criteria belong to inputs. due to the existing variety of criteria containing different scales and dimensions, the aras model integrated with the dea model according to equations 11, 12, 13, 14, 15 and 17 to 21. the values of weights were obtained around 8.24, 2.4, 10, 3.9, 2.82, 8.12, 9.7, 6.04, 5.82, 6.72 and 2.24 for the criteria of nominal capacity (no), nominal capacity (t), initial feed (no), initial feed (t), initial feed (m2), employees, power, water, fuel, land and initial feed (m) in table 5 respectively. finally, the tabulated criteria were passed through the efficiency assessment and were emerged the efficiency score for ihai after introducing the vector of weights. table 5 displays the annual requirements of ihai. table 5. annual requirements of ihai initial feed (m2) initial feed (t) initial feed (no) nominal capacity (t) nominal capacity (no) industry 0.00 43.231 410450 0.00 20000 (1) 286 0.054 2054000 0.00 100000 (2) 0.00 60.5 1151000 0.00 100000 (3) 0.00 649.1 70000 500 0.00 (4) 0.00 3597.5 1950.8 0.00 100000 (5) 0.00 0.00 909400 0.00 10000 (6) 0.00 23.665 952400 0.00 100000 (7) 0.00 238.65 1678500 211 0.00 (8) 0.00 1689 898000 0.00 20000 (9) 3300 117.9 120240 0.00 12000 (10) 0.00 6.035 480000 0.00 20000 (11) 0.00 0.00 774300 0.00 48000 (12) 0.00 0.00 389100 0.00 20000 (13) hassanpour & pamučar /oper. res. eng. sci. theor. appl. 2 (3) (2019) 1-25 18 0.00 151.75 650250 0.00 50000 (14) 0.00 2857.2 2611400 0.00 30000 (15) 0.00 703.55 60900 0.00 20000 (16) 0.00 142.85 209000 0.00 20000 (17) 0.00 23.795 947467 0.00 50000 (18) 0.00 266.17 800000 0.00 100000 (19) 0.00 0.00 769050 0.00 30000 (20) 0.00 0.00 623244 0.00 40000 (21) 0.00 1119 0.00 800 0.00 (22) 0.00 2083.7 0.00 500 0.00 (23) 0.00 428.5 3483500 0.00 82500 (24) 0.00 611.2 154449 0.00 15000 (25) initial feed (m) land (m2) fuel (gj) water (m3) power (kw) employee 0.00 1300 720 1800 21600 2160 0.00 2100 1440 1800 8640 8640 0.00 3300 1800 2520 72360 11160 0.00 3300 1800 2160 36000 10440 0.00 15000 41760 14760 369360 29880 21500 2300 1080 720 7560 4320 0.00 2600 1440 2520 16560 11160 0.00 6000 3240 3600 85680 14040 0.00 8300 5760 3960 135000 13320 0.00 5800 4680 3600 74520 16200 0.00 2600 1440 2160 32760 9360 0.00 2200 1080 1440 7200 6120 2472 1700 1080 1440 7200 6480 0.00 4900 1080 1440 17640 6120 28000 2400 3600 2520 45360 12600 0.00 4900 5400 1800 87840 5400 0.00 4500 2520 6840 156600 13320 0.00 2500 1440 2160 11880 10440 0.00 7300 2520 7920 118800 31680 0.00 3900 1440 1800 11880 8280 0.00 2900 1440 1800 12600 6840 0.00 17100 64440 11880 186840 40680 0.00 11600 60480 8640 93600 41400 0.00 4500 1800 13680 113760 12960 0.00 8400 2880 5040 112680 22680 one sample t-test analysis proved significant differences around 0.063, 0.005 and 0.025 among the criteria such as nominal capacity (no), nominal capacity (t), initial feed (t), initial feed (m2), initial feed (m), employee, power, water, fuel, and land. the values of weights were obtained around 8.24, 2.4, 10, 3.9, 2.24, 2.82, 8.12, 9.7, 6.04, 5.82 and 6.72 for nominal capacity (no), nominal capacity (t), initial feed (no), initial feed (t), initial feed (m2), initial feed (m), employee, power, water, fuel and land respectively. in the next step of the dea model table 6 included a normalized matrix based on the united dea and aras models and efficiency score for ihai. hereby, in the last column of table 6, the dea score classified ihai. evaluation of iranian household appliance industries using mcdm models 19 table 6. normalized matrix based on aras model and dea score for ihai initial feed initial feed initial feed si (for outputs) nominal capacity nominal capacity industry 0 0.0029 0.0203 0.1668 0 0.0202 1 0.0797 3.64e-06 0.1016 0.8344 0 0.1012 2 0 0.0040 0.0569 0.8344 0 0.1012 3 0 0.0438 0.0034 0.5967 0.2486 0 4 0 0.2428 9.658e-05 0.8344 0 0.1012 5 0 0 0.0450 0.0834 0 0.0101 6 0 0.0015 0.0471 0.8344 0 0.1012 7 0 0.0161 0.0830 0.2518 0.1049 0 8 0 0.1140 0.0444 0.1668 0 0.0202 9 0.9202 0.0079 0.0059 0.1001 0 0.0121 10 0 0.0004 0.0237 0.1668 0 0.0202 11 0 0 0.0383 0.4005 0 0.0486 12 0 0 0.0192 0.1668 0 0.0202 13 0 0.0102 0.0321 0.4172 0 0.0506 14 0 0.1928 0.1292 0.2503 0 0.0303 15 0 0.0474 0.0030 0.1668 0 0.0202 16 0 0.0096 0.0103 0.1668 0 0.0202 17 0 0.0016 0.0469 0.4172 0 0.0506 18 0 0.0179 0.0396 0.8344 0 0.1012 19 0 0 0.0380 0.2503 0 0.0303 20 0 0 0.0308 0.3337 0 0.0405 21 0 0.0755 0 0.9547 0.3978 0 22 0 0.1406 0 0.5967 0.2486 0 23 0 0.0289 0.1724 0.6884 0 0.0835 24 0 0.0412 0.0076 0.1251 0 0.0151 25 hassanpour & pamučar /oper. res. eng. sci. theor. appl. 2 (3) (2019) 1-25 20 rest of table 6 dea score dea (outputs/inputs) si (for inputs) initial feed land fuel water power employee industry 10 0.2958 0.5640 0 0.0098 0.0033 0.0166 0.0117 0.0060 1 5 0.4819 1.7313 0 0.0159 0.0066 0.0166 0.0046 0.0242 2 3 0.5283 1.5793 0 0.0251 0.0083 0.0233 0.0392 0.0313 3 2 0.6143 0.9712 0 0.0251 0.0083 0.02 0.0195 0.0293 4 16 0.1326 6.2891 0 0.1141 0.1930 0.1366 0.2003 0.0840 5 24 0.0490 1.7022 0.4136 0.0175 0.0049 0.0066 0.0040 0.0121 6 1 0.7369 1.1322 0 0.0197 0.0066 0.0233 0.0089 0.0313 7 19 0.1114 2.2604 0 0.0456 0.0149 0.0333 0.0464 0.0394 8 21 0.0617 2.7044 0 0.0631 0.0266 0.0366 0.0732 0.0374 9 25 0.0245 4.0713 0 0.0441 0.0216 0.0333 0.0404 0.0455 10 14 0.1818 0.9177 0 0.0197 0.0066 0.02 0.0177 0.0263 11 4 0.5115 0.7830 0 0.0167 0.0049 0.0133 0.0039 0.0172 12 12 0.2448 0.6815 0.0475 0.0129 0.0049 0.0133 0.0039 0.0182 13 6 0.4370 0.9545 0 0.0372 0.0049 0.0133 0.0095 0.0172 14 22 0.0604 4.1386 0.5387 0.0182 0.0166 0.0233 0.0245 0.0354 15 17 0.1286 1.2972 0 0.0372 0.0249 0.0166 0.0476 0.0151 16 20 0.0856 1.9494 0 0.0342 0.0116 0.0633 0.0849 0.0374 17 8 0.3922 1.0635 0 0.0190 0.0066 0.02 0.0064 0.0293 18 9 0.3092 2.6983 0 0.0555 0.0116 0.0733 0.0644 0.0890 19 11 0.2577 0.9711 0 0.0296 0.0066 0.0166 0.0064 0.0232 20 7 0.4076 0.8187 0 0.0220 0.0066 0.0166 0.0068 0.0192 21 15 0.1742 5.4785 0 0.1301 0.2978 0.11 0.1013 0.1143 22 18 0.1272 4.6894 0 0.0882 0.2795 0.08 0.0507 0.1163 23 13 0.1823 3.7753 0 0.0342 0.0083 0.1266 0.0616 0.0364 24 23 0.0585 2.1368 0 0.0639 0.0133 0.0466 0.0611 0.0637 25 evaluation of iranian household appliance industries using mcdm models 21 the ranking system offered different results in both the weighing systems of the friedman test and entropy shannon using codas models. 4.6. ranking values in various models for ihai table 9 shows the ranking values for the data of ihai in aras, saw, dea and codas models. the reason to use the entropy shannon weighing system for the ihai gets back to this fact that for future development and expansion withholding negative and positive criteria we need this system. therefore, any expansion in industries demands the extension in the land area used and the number of staff as negative points that influence the outlays in industries. therefore, both weighing systems were chosen to conduct this research. table 9. ranking values in various models dea 6codas 5saw aras4 3codas 2saw aras1 industry 10 22 24 24 25 25 25 1 5 21 21 21 21 21 21 2 3 13 13 13 12 12 12 3 2 14 14 14 15 14 14 4 16 3 3 3 1 1 1 5 24 25 25 25 22 24 24 6 1 16 16 16 18 18 18 7 19 11 10 10 9 9 9 8 21 5 5 5 5 6 6 9 25 10 9 9 10 10 10 10 14 15 15 15 17 16 16 11 4 23 22 22 23 22 22 12 12 24 23 23 24 23 23 13 6 19 19 19 13 15 15 14 22 12 12 12 14 13 13 15 17 9 11 11 11 11 11 16 20 6 7 7 7 8 8 17 8 17 18 18 19 19 19 18 9 7 4 4 4 4 4 19 11 18 17 17 16 17 17 20 7 20 20 20 20 20 20 21 15 1 1 1 2 2 2 22 18 2 2 2 3 3 3 23 13 4 6 6 8 7 7 24 23 8 8 8 6 5 5 25 1, 2 and 3 based on the weighing system of friedman test 4, 5 and 6 based on the weighing system of entropy shannon 4.7. importance of data in economic estimations the collected data of initial screening of ihai projects were used to underpin data of the dea method and further studies in the economic estimation (according to equations 30 to 39 (hassanpour 2019b)). however, we know an inventory of input and outputs materials stream and available facilities seek the best channels of hassanpour & pamučar /oper. res. eng. sci. theor. appl. 2 (3) (2019) 1-25 22 management strategies in the industries and look for the best procedures to produce and replace green materials as well as the approach to industry 4.0 aims. aew = )(75.0 w (electrical energy demand), e (total electrical energy employed in lines), a (area, m2) (30) pc = 005.0 c (selling outlays), p (selling rate) (31) ))(( cffaepv +++−= v(value-added), aʹ(initial materials applied), f(maintenance), cf (unforeseen outlays) (32) pvv /100% = (33) ))(( sdlivqp +++−= qp (revenue), i (insurance), l (expenditures of interest and fees), d (depreciation), s (salary) (34) cpcvdcv /= cv (variable outlays of commodity unit), cvd (variable project outlays), cp (production capacity) (35) cscvtfph −= / ph (the breakeven point), tf (fixed manufacturing outlays), cs (total fixed outlays) (36) cfpcvpcpi += cpi (selling outlay of commodity unit), cvp (manufacturing outlays), cfp (variable manufacturing outlays) (37) cpitsai −= ai (annual revenue), ts (total selling expenses) (38) aiifvt /= vt (time of return on investment) and if (fixed capital) (39) 5. conclusion by the present study, we achieved to seek the sustainability of ihai by considering the whole availability of industries. ihai were classified based on the main criteria using weighing and ranking systems. dea procedure was used to figure out the efficiency score of ihai according to the normalization process and division of output to inputs values. totally the main achievement of the present study was about offering a coherent channel to appraise the sustainable development process including the easiest way to the economic and financial estimation of industries, figuring out the efficiency of industries and classification of them by an inventory of input and output materials streams. the economic estimation, efficiency evaluation and sustainable development trend of industries were paved to mature by present research. 6. acknowledgment this research was conducted as part of the corresponding 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(2010). a new additive ratio assessment (aras) method in multi-criteria decision-making technological and economic development of economy, 16(2): 159–172. © 2019 by the authors. submitted for possible open access publication under the terms and conditions of the creative commons attribution (cc by) license (http://creativecommons.org/licenses/by/4.0/). plane thermoelastic waves in infinite half-space caused operational research in engineering sciences: theory and applications vol. 2, issue 3, 2019, pp. 40-54 issn: 2620-1607 eissn: 2620-1747 doi: https://doi.org/10.31181/oresta1903040d * corresponding author. an.dobrosaljevic@gmail.com (a. dobrosavljević), surosevic@tfbor.bg.ac.rs (s. urošević) analysis of business process management defining and structuing activities in micro, small and medium-sized enterprises andrea dobrosavljević, snežana urošević* technical faculty in bor, university in belgrade, vojske jugoslavije 12, 19210 bor, serbia received: 14 october 2019 accepted: 29 november 2019 first online: 03 december 2019 research paper abstract. business process defining and structuring influences the evolution of organizations’ business activities. it represents the starting point on the path to establishing of an process mature organization. a number of elements is needed to be met to get the organization out of a state of complete unstructuredness. micro, small and medium enterprises are interesting for considering the adoption of the concept of business process management (bpm), not only because of their size but also because of managerial role of the owner, the way of managing and decision making, as well as assigning multiple roles and responsibilities to one employee. this paper analyzes the defining and structuring of bpm within groups of micro, small and medium sized enterprise. the topsis method was applied for the purpose of ranking enterprise groups in accordance with the establishment of defining and structuring elements. key words: business processes, defining, structuring, business process management (bpm), micro, small and medium enterprises, topsis 1. introduction business processes can be viewed as a chain of events, activities and decisions (dumas et al., 2013). it can be stated that business processes pass the boundaries of organization units within an organization, but also the boundaries of multiple organizations, if we take into consideration inter-organization processes in which core lies cooperation (smirnov et al., 2012; knuplesch et al., 2012). the process gets to be established by structuring the activities of all process participants, as well as forming necessary communication connections between them (fleishmann et al., 2012). well-structured business processes influence the evolution of business activities (böhringer, 2010). organization needs to establish the system of execution of analysis of business process management defining and structuring activities in micro, small and medium – sized enterprises 41 business processes in wright manner, but also to ensure that the right business processes that contribute to the business are executed (schmiedel et al., 2015). whereby it should be borne in mind that the transformation from the current state to the more mature and more structured state is not linear (fisher, 2004). research of bpm systems implementation are mostly conducted taking into consideration the business of large organizations (pejić bach, et al., 2019). smes are very important for successful market development of countries in transition (urošević, 2011). they differ from large companies not only by the number of employees and capital. the main differences are in management, decision-making processes and organizational structure (ghahramany dehbokry & chew, 2014). in many smes, especially micro enterprises, the owner takes the role of manager, so the decisions and business moves are under the influence of its own subjectivity (johnson, 2002; delavande et al., 2011). standardization and formalization of core processes is necessary in order to adopt and apply certain business practices within micro, small and medium-sized enterprises (handayani et al., 2013). it is being approached to the research in this paper with the assumption that the pace of formulating and adopting the basic elements of business process management practice is of great importance for the functioning of this practice within the enterprise, and that it depends on the size of the organization, bearing in mind the mentioned differences. therefore, by considering the defining and structuring elements of business process management, this paper seeks to understand the level of readiness of micro, small and medium-sized organizations to establish the basic elements of process orientation and to build process mature organization on a solid base. the following section covers the literature overview of bpm defining and structuring elements. conducted analysis is based on expert assessment of extracted elements and assigning weights to each of them, and ranking micro, small and medium-sized enterprise groups based on the mean of each group's response to the elements of defining and structuring by the topsis method. 2. literature overview of defining and structuring elements defining and structuring elements are present through all levels of process maturity. patig et al. (2010) present the description of four levels of process maturity of organizations. undefined processes and existence of functional structure characterize first level, according to these authors. within second level, core and most used processes, are being defined. at third level of process maturity all processes are defined, bpm is applied with strategic intension and process roles and responsibilities are being deployed. establishment of company relations with external environment, first and second order suppliers and first and second order buyers describes fourth level. within this level, the functional organizational structure becomes subordinate to the process organizational structure. dobrosavljević and urošević/oper. res. eng. sci. theor. appl. 2 (3) (2019) 40-54 42 core processes, or organizations identity processes, represent the primary resources of value creation. dimitrijević et al. (2019) state that the basic processes are management, planning, technology and product development, procurement and supply, production management, equipment maintenance, sales and monitoring and management of economic and financial flows. interactions with customers and suppliers are the driver of core processes, and their outcome is directed at customers. support processes are internal processes, which enable functioning of core processes (zur muehlen & ho, 2005). harmon (2010) emphasizes the division of basic operating processes and support processes based on porter's value chain, which is used as an organizational principle for defining and editing the processes themselves, and process structure within different organization, as he states, more than two decades. many bpm teams try to understand which business processes are priority for business and which problems should be solved for each of the given processes (dumitraşcu i seremeta, 2011). core processes consist of functions intended for development, production, providing specific products to specific customer groups (laguna i marklund, 2013). isoherranen et al. (2016) state that within smes sales, production and supply processes take the form of core processes. business processes can be defined as set of activities that transform inputs into outputs (lindsay et al., 2003). for the process to function, that is, the activities to be adequately implemented within process, it is necessary to define inputs, but also to describe the expected output of certain business process activities (kueng i kawalek, 1997). outputs generated within one process may represent the input for next business process (scheer et al., 2005). standardized processes allow execution of standardized tasks, given that they are performed in a consistent manner while respecting the rules and specifications. however, rigid rules are a barrier to innovation, so companies should take into account the nature of the process (trkman, 2010). this applies to creative processes within the creative industries such as clothing and fashion of micro, small and medium-sized enterprises as well as the large ones (mete, 2006; jelić-aksentijević, 2009). standardized processes are a success factor, so organizations can perform in a broader environment by performing standardized and streamlined processes (bask et al., 2010; milošević & patanakul, 2005). the adoption of a process approach entails the need to create new patterns of responsibility and thus new roles. process owners, process managers, and chief process officers (cpos) are some of the roles that a successful implementation of the bpm concept requires (becker et al., 2013). introducing formal roles and responsibilities of human resources into bpm practices ensures the presence of horizontal discipline and rebalancing the organization for the purpose of horizontal job integration and customer focus (vom brocke et al., 2014). in this regard, it is necessary to redefine roles and responsibilities for managers to monitor processes instead of activities and to work on the development of people within the organization (hammer, 2007). the literature most commonly describes the role of the process owner, that is, the person in charge of the process functioning, but also includes roles such as process manager, process supervisor, and process director (becker et al., 2000; burlton, 2015). in large organizations, these roles can be assigned to different people. in small and medium-sized enterprises, especially micro-organizations, one person may be in charge of multiple roles (burlton, 2015). analysis of business process management defining and structuring activities in micro, small and medium – sized enterprises 43 many smes do not provide sufficient human resources or assign roles in managing business processes (pejić bach, 2019). process businesses are characterized by multidimensionality with demands for constant learning and problem solving (tang et al., 2013). as they are not just ordinary tasks, employees need adequate training in order to acquire new skills and knowledge to manage them (vukšić & štemberger, 2010). the description of all jobs by business processes should be defined (mičić, et al., 2019). the goal of a process-oriented organization in terms of organizational structure is reflected in the achievement of profitability and practicality of the organization. which is true for any type of organizational structure (becker et al., 2013). a more significant difference between traditional and process structures is the existence of process teams. these teams replace the structure in which the division is made into sectors. process teams include line-independent individuals who work together to complete a range of activities to complete the process. the responsibility for carrying out the whole process is equally shared among the members of the process team (bojanić et al., 2013; hernaus, 2016). the ownership of the process must be permanent. in line with business changes, there are changes in the design of the process and the process owner is the one in charge of implementing the changes. absence of a strong process owner can lead to a return to traditional functioning patterns and abandonment of process orientation (hammer & stanton, 1999). research methodology separating the dimensions of process orientation adoption and separately considering their presence in micro and smes can contribute to a better understanding of how these businesses adopt business practices and how they adapt to change. in this case, considering the defining and structuring of bpm, the establishment of the basic elements of process orientation and the willingness of micro, small and medium-sized organizations to build the organizational process maturity is covered by the research, as already pointed out earlier. input data from the analysis were collected between january and june 2019. two instruments were involved in the data collection, one intended for gathering the answers of experts who are involved in bpm activities in practice or at a scientific research level familiar with the concept, the other intended for collecting the responses of executives in micro, small and medium-sized enterprises in serbia. on this occasion, a sample of 8 expert responses and 238 responses from the executives of micro, small and medium-sized enterprises was collected. the definition and structure of business processes can be assessed on the basis of the criteria presented in table 1. these criteria are extracted from previous research (mccormack, 2001; škrinjar & trkman, 2013). each of the criteria in the list and its importance for the definition or structuring of business processes is explained in the section on the literature review of the elements of defining and structuring. dobrosavljević and urošević/oper. res. eng. sci. theor. appl. 2 (3) (2019) 40-54 44 table 1. criteria for defining and structuring business processes code criteria c1 defining of core and support business processes c2 defining of business process inputs and outputs c3 standardized methodology usage for business process description c4 process roles and responsibilities defining c5 multidimensionality of process jobs c6 coherence of organizational structure with process approach c7 functioning of teams of employees from different organizational units c8 defining of process ownership the analysis covers two parts. the results of the first part are actually inputs of the second part. an illustration of the research structure is shown in figure 1. defining criteria of business process definition and structuring collecting data analysis of deffining and structuring criteria phase 1 phase 2 phase 3 experts assesments micro, small and mediumsized enterprise exeutives rating comparison matrix criteria weight coefficients topsis defining and structuring criteria ranking saw r e s u lt c o m p a r is o n figure 1. illustration of research structure first phase of the research begins with construction of a list of business process definition and structuring criteria. the second phase includes the data collection according to expert and micro, small and medium-sized enterprise executives evaluations. third phase involves the use of a comparison matrix to generate weighting coefficients of each of the criteria, which are of importance in the further analysis of the bpm defining and structuring. after the calculation of the weight coefficients, a consistency test of expert ratings is conducted. the second section of third phase focuses on the implementation of the multi-criteria decision-making methods called saw (simple additive weighting) and topsis (technique for order preference by similarity to an ideal solution), which in this case applies to the ranking of micro, small and medium-sized enterprise groups based on the responses of 238 executives. in order to provide a more clear solution, the comparison of saw and topsis solution is provided. calculations by comparison matrix represent an integral part of the implementation of the saw method, therefore the ranking of alternatives is done using two methods, saw and topsis, in order to compare solutions. saw represents the simple method for alternative ranking while topsis has a characteristic of providing a solution not only closest to the hypothetically best, analysis of business process management defining and structuring activities in micro, small and medium – sized enterprises 45 but also farthest from the hypothetically worst (gadakh, 2012). this method differ in the way of conducting, but the weight criteria, obtained by comparison matrix, are included in both methods in addition to the mean scores of the respondents based on the extracted criteria obtained using descriptive statistics in the spss v20 software package. 3.1. description of the comparison matrix the interval comparison matrix should provide the result in the form of estimated interval weights (wang & elgah, 2007). there are different approaches to determining weights, among them a comparison matrix that describes the relationship of the scale between goals and alternatives (jones & mardle, 2004). examples of applying a comparison matrix for the calculation of weight criteria can most often be found within methods such as ahp (analytical hierarchy process) and saw (simple additive weighting), (zolfani et al., 2012; jain & raj, 2013). a comparison matrix (n x n) is constructed to compare pairs of criteria of relevance to the research. comparisons are made on the basis of expert evaluations obtained using the appropriate scale. the following steps provide a description of how to calculate weighting criteria based on a comparison matrix: (a) construction of matrix (n x n) input of expert ratings based on scale fror pairwise comparison. (b) calculate the sum of the columns and priority vectors according to the row averages. (c) the weighted sum matrix is then calculated by multiplying the comparison matrix and the priority vector. (d) divide all elements of the weighted sum matrix by their corresponding vector priority element. (e) calculate the mean of the previously obtained value to calculate the value of max. (f) calculate the value of the consistency index, ci, using the following formula: 1 max − − = n n ci  , (1) where n denotes the number of criteria in the matrix. (g) calculate the consistency ratio, cr, using the following formula: ri ci cr = (2) the consistency estimation takes into account the previously obtained value of the consistency index and the average random consistency (ri) value, which can be read from table 2. consistency in expert responses is acceptable if the calculated value does not exceed 0.10. in order to obtain more consistent responses the experts' dobrosavljević and urošević/oper. res. eng. sci. theor. appl. 2 (3) (2019) 40-54 46 assessments should be revised and improved by the implementation of the second round (afshari et al., 2010). table 2. average random consistency, ri (son, 2013) n 1 2 3 4 5 6 7 8 9 10 ri 0 0 0,58 0,9 1,12 1,24 1,32 1,41 1,45 1,49 3.2. description of saw method saw (simple additive weighting) method is simple method known also as ws (weighted sum), and it is implementable in many different problem solution cases (urošević et al., 2018). after calculating the weight criteria using a comparison matrix, as already explained, proceeds with the saw calculation by following the next steps (venkateswarlu & sarma, 2016; afshari et al., 2010): (a) constructing an (m x n) decision matrix which includes collected data. (b) calculating normalized decision matrix for positive criteria using: ; i=1,2,3,…,m,; j=1,2,3,…,n. (3) in addition, for negative criteria: i=1,2,3,…,m, j=1,2,3,…,n. (4) (c) evaluation of each alternative, ai is then calculated by following formula: ,; i=1,2,3,…,m,; j=1,2,3,…,n, (5) where xij is the score of the ith alternative with respect to the jth criteria , and where wj is the weight coefficient. 3.3. description of topsis method hwang & yoon develop topsis (technique for order preference by si-milarity to an ideal solution) method in 1981. (lotfi et al., 2011; kahraman et al., 2007). the basic principle of the topsis method is choosing alternatives with the shortest distance to the ideal solution and the longest distance from the negative extreme of the ideal solution (opricović & tzeng, 2004). the topsis method is applicable in many decision-making fields. it is common to use this method using fuzzy numbers (chatterjee & stević, 2019). krmac and đorđević (2019) apply the topsis method to evaluate the capacity of the application of the train control information system in the case of the railways of serbia and austria. olson (2004) performs weight comparison using the topsis method. ahmadi et al. (2013) rank critical factors for the adoption of electronic medical records at the micro level using the topsis method. urošević et al. (2018) lists the steps to follow when applying the topsis method: analysis of business process management defining and structuring activities in micro, small and medium – sized enterprises 47 (a) formation of a normalized decision matrix r=[rij]mxn. the vector normalization procedure normalizes the values of the elements of the decision matrix. the value rij can be calculated by following formula: 2 1 ij m i ij ij x x r =  = (6) (b) calculation of the weighted normalized decision matrix v=[vij]mxn. the values of the weighted normalized matrix elements vij can be calculated using formula: ijjij rwv += (7) (c) the calculation of the ideal solution a+ and negative ideal solution afollows: = + a { +++ n vvv ,...,, 21 }={ )min(),max( minmax  ivjv ij i ij j }, i (8) = − a { −−− n vvv ,...,, 21 }={ )max(),min( minmax  jvjv ij i ij i , (9) whereby ωmax indicates a set of incoming and ωmin a set of expenditure criteria. (d) determining the distance of alternatives from the ideal and the negatively ideal solution by applying the n-dimensional euclidean distance. ,)( 1 2  = ++ −= n j jiji vvd (10)  = −− −= n j jiji vvd 1 2 )( . (11) (e) calculation of the coefficient of relative closeness to the ideal solution ci is done by applying the following formula: −+ − + = ii i i dd d c . (12) for 0 − i d i 0 + i d  1,0ic . (f) ranking alternatives in ascending order based on the value of ci, based on the following formula:   i i i caa max **  . (13) dobrosavljević and urošević/oper. res. eng. sci. theor. appl. 2 (3) (2019) 40-54 48 5. results of the methodology application the calculation of criteria weighting coefficients for the bpm defining and structuring is done by using the comparison matrix. table 3. provides an overview of the expert pairwise comparison values and the values of the weight coefficients of each criteria. table 3. calculation of weight coefficients using comparison matrix criteria c1 c2 c3 c4 c5 c6 c7 c8 weights c1 1 0.5 3 0.5 5 3 2 0.5 0.132 c2 2 1 4 1 5 3 4 0.33 0.181 c3 0.33 0.25 1 0.25 3 0.33 0.5 0.2 0.047 c4 2 1 4 1 5 3 4 0.5 0.187 c5 0.2 0.2 0.33 0.2 1 0.25 0.33 0.16 0.028 c6 0.33 0.33 3 0.33 4 1 2 0.33 0.087 c7 0.5 0.25 2 0.25 3 0.5 1 0.25 0.062 c8 2 3 5 2 6 3 4 1 0.277 total 8.36 6.53 22.33 5.53 32 14.08 17.83 3.27 1 the degree of consistency of the experts' answers was obtained by applying the formula (2). for calculating using this formula, the ri value must be read from table 2. in this particular case, the number of criteria considered is 8, so the consistency index is divided by an ri of 1.41. the obtained value of 0.039, which is less than the value of 0.10, indicates that the experts' answers are sufficiently consistent. when weight coefficients have been obtained based on expert evaluations of the selected criteria for defining and structuring business processes, and consistency test has been carried out, the analysis of the bpm defining and structuring in micro and medium organizations continues. the survey included 167 (70.2%) micro, 44 (18.5%) small and 27 (11.3%) medium enterprises out of 238 enterprises. these groups of companies evaluated the applicability of the criteria for the definition and structure of bpm in their operations. descriptive statistics within the spss software package calculate the mean of the response values of each of the groups of organizations participating in the survey. these values are presented in table 4. within which it is noticeable that the answers have approximate values although there are still differences between the groups. table 4. mean criteria scores obtained by executives of micro, small and medium-sized organizations assessments c1 c2 c3 c4 c5 c6 c7 c8 micro 3,9461 4,0240 4,0539 3,9521 4,0060 3,9042 3,8024 3,9222 small 4,1591 4,2045 4,1818 4,0000 3,7500 4,1136 3,6818 4,1591 medium 4,4074 4,2222 4,3704 4,2963 4,1852 4,1852 4,0741 4,4444 table 5. the normalized decision matrix within saw method c1 c2 c3 c4 c5 c6 c7 c8 micro 0,8953 0,9531 0,9276 0,9199 0,9572 0,9329 0,9333 0,8825 small 0,9437 0,9958 0,9568 0,9310 0,8960 0,9829 0,9037 0,9358 medium 1,0000 1,0000 1,0000 1,0000 1,0000 1,0000 1,0000 1,0000 analysis of business process management defining and structuring activities in micro, small and medium – sized enterprises 49 based on the collected data and calculated weight coefficients forming of normalized decision matrix according to steps of saw method is enabled. the normalized decision matrix according to saw method is presented within table 5. table 6. provides a result of alternatives evaluation calculated by the formula (5). values of alternative evaluations make it possible to rank listed alternatives. table 6. ranking of alternatives using the saw method alternatives altrernatives evaluations rank micro 0,92 3 small 0,95 2 medium 1,00 1 evaluation values presented in the table 6. show slight difference between evaluated alternative. the medium-sized enterprises are the ones best ranked according to saw method. the calculation of the topsis method was performed based on the application of the presented input data and the calculated weight criteria, as well, followed by the steps of applying the method. the final performance of micro, small and medium-sized enterprise groups in terms of the bpm defining and structuring is ranked in table 7. table 7. performance and ranking of alternatives using the topsis method alternatives d+ dci rank micro 0.03 0.00 0.05 3 small 0.02 0.01 0.37 2 medium 0.00 0.03 1.00 1 based on the results presented in table 7, it can be concluded that among the three ranked alternatives, or three groups of organizations grouped by size, the group of medium-sized organizations is the one that defined and structured bpm at the higher level compared to the other groups considered. the assigned rank actually tracks the size of the organizations. therefore, it can be found that medium-sized enterprises are most prepared to move to higher stages and upgrade their process maturity. figure 2. comparison between results from saw and topsis method dobrosavljević and urošević/oper. res. eng. sci. theor. appl. 2 (3) (2019) 40-54 50 radar diagram is here useful, and it shows the variations in values calculated by two different mcdm methods, saw and topsis. in addition, it clearly shows the separation of medium-sized enterprises from micro and small enterprises in the case of topsis method. alternatives have the same ranking order according to each used method. 6. conclusion the conducted analysis of bpm defining and structuring by applying saw and topsis methods allowed the assessment of differences between micro, small and medium-sized enterprises regarding the establishment of the basic elements of process orientation. in this way, differences in the achieved willingness and ability of organizations to continue to work on the process maturity development were noted, with medium-sized companies standing out as the best-ranked ones, by both used methods. from the results of this analysis can be concluded that the pace of the individual bpm practice elements adoption and building a process mature organization can vary according to the size of the organization. organization size is just one of the factors, which entails a number of influential sub-factors that will largely determine this pace. thereby we can talk about the managerial role of the owner in many small, especially micro-enterprises, then the responsibility of one worker for a large number of jobs, which are multidimensional in their nature. only a few sub-factors are listed, but it can be seen that most of the impact is directed on human resources. implementation of bpm practices requires, primarily, adequate top management awareness and then adequate employee education and training. all efforts to define and structure the management of business processes are pointless if they remain only a dead letter on paper. top management is in charge of the process, but employees are assigned to work within the process. the results of this research provide insights to micro, small and medium-sized organizations on the pace of adopting the elements of defining and structuring as part of business process management and their mutual positioning at the considered pace. based on these results, companies can take adequate measures concerning the adoption of the considered elements and improvement of the development of mature and stable 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(2005). risk management in the bpm lifecycle. in proceedings of international conference on business process management, september 2005., springer, berlin, heidelberg, 454-466, doi:10.1007/11678564_42. © 2019 by the authors. submitted for possible open access publication under the terms and conditions of the creative commons attribution (cc by) license (http://creativecommons.org/licenses/by/4.0/). https://doi.org/10.1016/j.im.2013.07.002 https://doi.org/10.1108/bpmj-06-2013-0074 https://doi.org/10.1016/j.ejor.2005.10.066 https://doi.org/10.1007/11678564_42 operational research in engineering sciences: theory and applications first online issn: 2620-1607 eissn: 2620-1747 doi: https://doi.org/10.31181/oresta101122091d * corresponding author. doductrung@haui.edu.vn (d.t.do), duatv@haui.edu.vn (v.d. tran), duongvanduc@haui.edu.vn (v.d. duong), tungnn@haui.edu.vn (nhu-tung. nguyen) investigation of the appropriate data normalization method for combination with preference selection index method in mcdm duc trung do 1, van dua tran 1, van duc duong 1, nhu-tung nguyen 2* 1 faculty of mechanical engineering, hanoi university of industry, vietnam 2 haui institute of technology, hanoi university of industry, vietnam received: 11 august 2022 accepted: 06 october 2022 first online: 11 october 2022 research paper abstract: preference selection index (psi) that is a multi-criteria decision making method (mcdm) does not need to determine the weights for criteria and it has been applied in many different fields. however, using only the data normalization method (dnm) proposed by the inventor of the psi method may narrow the application scope of this method. this study aims to expand the application range of the psi method by identifying the appropriate dnms in combination with the psi method. twelve different dnms were used in combination with the psi method. these twelve combinations were used in turn to solve several problems in different fields. the ranked results of solutions by these combinations were all compared with the results in the published studies. the sensitivity analysis of the ranked results of the solutions in each case also was performed. in this study, four out of twelve dnms were found to be appropriate in combination with the psi method. this discovery has extended the application scope of the psi method that the previous methods have not met. keywords: mcdm, psi, dnm 1. introduction most mcdm methods perform the steps of determining the weights and normalizing the data. therefore, the ranked results of the solutions depend significantly on the selection of the weighting method and the data normalization method. the research direction to rank solutions using the mcdm method without using the weighting method or without using the data normalization method is being studied by scientists to improve the stability of mcdm. psi that is a mcdm method does not need to determine the weights for the criteria. the detailed steps to ranking the solutions according to this method will be presented duc trung do et al./oper. res. eng. sci. theor. appl. first online in section three of this paper. the application of this method is also considered to be very simple with a small number of calculations (yadav et al., 2019). this method has been applied to multi-criteria decision making in many cases, in many different fields: to evaluate the performance of machines (sari, 2019), to propose a method for waste recovery from electrical/electronic products (sari, 2020), to choose an automated system development method in selecting the students with enough conditions to receive the scholarship (arifin and saputro, 2022), for decision-making in the selection of materials for tooth restoration/beautification (yadav, 2022), to choose the life cycle design solutions of the product system (attri and grover, 2015), to select the technological parameters for turning (prasad et al., 2018), to select the parameters of electrical discharge machining (phan et al., 2022), to select the technological parameters for the grinding process (tien et al., 2021), to rank the efficiency of production lines (akyuz and aka, 2015), to rank the types of materials for engineering (maniya and bhatt, 2010), to rank the individuals with enough conditions for credit loans in indonesia (sianturi et al., 2020), to choose where to sell used computers (sahir et al., 2018) , to compare the tourism potential of some countries (stanujkic et al., 2020), to select the machines in the manufacturing companies (jian et al., 2015), and so on. thus, it is seen that the psi method has been successfully applied for mcdm in many different fields. however, the authors of this study can confirm that all applied psi studies used linear normalization to normalize the data. linear normalization is also the method used by the scientists who proposed the psi method. the formulas for normalizing data in this way as well as many other ways of data normalization will be presented in the second section of this study. however, linear normalization cannot be used if some criterion is equal to zero in some solutions. in these cases, if cannot find other dnms in combination with the psi method, the application of the psi method will not be possible. from this point of view, this study will combine all twelve above-mentioned dnms with psi method to identify the appropriate dnms in combining with psi method. this is the first study using all twelve dnms in combination with one mcdm method. those twelve combinations were used to rank the solutions from different fields. in addition to the linear normalization method, this study identified three other dnms that were determined to be suitable for combining with the psi one. this obtained result contributes to extend the application scope of the psi method. the structure of the next sections of this study is presented as follows: (1) the literature review presented the importance of determining an appropriate dnm to combine with one of the mcdm methods. this section also presented the formulas for normalizing data by twelve different methods. the suitability of combining some dnms with some mcdm methods was also confirmed in published studies as the third content in this section; (2) summary the performed steps according to the psi method; (3) perform the calculations in different cases to rank the solutions in different fields using the psi method; (4) identify the dnms (when combined with psi method) that show the same best solution as in the published studies; (5) analyze the sensitivity of the ranking results in each case by creating different scenarios to confirm the appropriate dnms when combined with the psi method; (6) discuss the obtained results and draw the conclusions from this study as well as propose the research directions in the future. investigation of the appropriate data normalization method for combination with preference selection index method in mcdm 2. literature review except for some methods such as collaborative unbiased rank list integration (curli) and ranking of the attributes and alternatives (r), for most of the remaining mcdm methods, data normalization is the work that needs to be conducted when apply them (trung, 2022a). each mcdm method that was proposed often contains at least one dnm. however, because the implementation method in mcdm methods as well as in dnms is not the same, the ranked results of the solutions when using mcdm methods are also not the same (zopounidis and doumpos, 2017). selection of the dnm has a great influence on the ranking results of the solutions (budiman et al., 2021; souissi and hafdhi, 2021; aytekin, 2021). when comparing the two methods vlsekriterijumska optimizacijai kompromisno resenje (vikor) and technique for order preference by similarity to ideal solution (topsis), the authors have concluded that the ranked results of the solutions are different when using these two methods. the reason is that these two methods used different dnms (opricovic and tzeng, 2004). mhlanga and lall (2022) used the vikor method to rank ten websites in combination with five different dnms. this study has shown very different results in those combinations. a solution may rank number one when using one dnm but rank number ten (last rank) when using another dnm. yazdani et al. (2017) used the complex proportional assessment of alternatives with grey relations (copras-g) method to rank the material types. the authors concluded that the suitability of a dnm when combined with an mcdm method depends on the number of solutions as well as the number of criteria. sarraf and mcguire (2021) also concluded that with the same dnm but when combined with different mcdm methods, the ranking results can also be different. the above analysis shows that the determination of the suitable dnm for each mcdm method has a decisive influence on the ranking results of the solutions. it is a very important work to ensure the accuracy of the ranking results of the solutions. twelve dnms that listed below are the combined results from two studies of (aytekin, 2021; ersoy, 2021a). linear normalization (n1) 𝑁𝑖𝑗 = 𝑦𝑖𝑗 𝑚𝑎𝑥 𝑦𝑖𝑗 , if j  b (1) 𝑁𝑖𝑗 = 𝑚𝑖𝑛 𝑦𝑖𝑗 𝑦𝑖𝑗 , if j  c (2) weitendorf normalization (n2) 𝑁𝑖𝑗 = 𝑦𝑖𝑗−𝑚𝑖𝑛 𝑦𝑖𝑗 𝑚𝑎𝑥 𝑦𝑖𝑗−𝑚𝑖𝑛 𝑦𝑖𝑗 , if j  b (3) 𝑁𝑖𝑗 = 𝑚𝑎𝑥 𝑦𝑖𝑗−𝑦𝑖𝑗 𝑚𝑎𝑥 𝑦𝑖𝑗−𝑚𝑖𝑛 𝑦𝑖𝑗 , if j  c (4) sum linear normalization (n3) duc trung do et al./oper. res. eng. sci. theor. appl. first online 𝑁𝑖𝑗 = 𝑦𝑖𝑗 ∑ 𝑦𝑖𝑗 𝑚 𝑖=1 , if j  b (5) 𝑁𝑖𝑗 = 1 𝑦𝑖𝑗⁄ ∑ 1 𝑦𝑖𝑗⁄ 𝑚 𝑖=1 , if j  c (6) vector normalization (n4) 𝑁𝑖𝑗 = 𝑦𝑖𝑗 √∑ (𝑦𝑖𝑗) 2𝑚 𝑖=1 , if j  b (7) 𝑁𝑖𝑗 = 1 − 𝑦𝑖𝑗 √∑ (𝑦𝑖𝑗) 2𝑚 𝑖=1 , if j  c (8) logarithmic normalization (n5) 𝑁𝑖𝑗 = 𝑙𝑛𝑦𝑖𝑗 𝑙𝑛(∏ 𝑦𝑖𝑗 𝑚 𝑖=1 ) , if j  b (9) 𝑁𝑖𝑗 = 1 − 𝑙𝑛𝑦𝑖𝑗 𝑙𝑛(∏ 𝑦𝑖𝑗 𝑚 𝑖=1 ) , if j  c (10) max linear normalization (n6) 𝑁𝑖𝑗 = 𝑦𝑖𝑗 𝑚𝑎𝑥 𝑦𝑖𝑗 , if j  b (11) 𝑁𝑖𝑗 = 1 − 𝑦𝑖𝑗 𝑚𝑎𝑥 𝑦𝑖𝑗 , if j  c (12) min linear normalization (n7) 𝑁𝑖𝑗 = 1 − 𝑚𝑖𝑛 𝑦𝑖𝑗 𝑦𝑖𝑗 , if j  b (13) 𝑁𝑖𝑗 = 𝑚𝑖𝑛 𝑦𝑖𝑗 𝑦𝑖𝑗 , if j  c (14) jüttler-körth normalization (n8) 𝑁𝑖𝑗 = 1 − | 𝑚𝑎𝑥 𝑦𝑖𝑗−𝑦𝑖𝑗 𝑚𝑎𝑥 𝑦𝑖𝑗 |, if j  b (15) 𝑁𝑖𝑗 = 1 − | 𝑚𝑖𝑛 𝑦𝑖𝑗−𝑦𝑖𝑗 𝑚𝑎𝑥 𝑦𝑖𝑗 |, if j  c (16) peldschus normalization (n9) 𝑁𝑖𝑗 = ( 𝑦𝑖𝑗 𝑚𝑎𝑥 𝑦𝑖𝑗 ) 2 , if j  b (17) investigation of the appropriate data normalization method for combination with preference selection index method in mcdm 𝑁𝑖𝑗 = ( 𝑦𝑖𝑗 𝑚𝑎𝑥 𝑦𝑖𝑗 ) 3 , if j  c (18) stop normalization (n10) 𝑁𝑖𝑗 = 100𝑦𝑖𝑗 𝑚𝑎𝑥 𝑦𝑖𝑗 , if j  b (19) 𝑁𝑖𝑗 = 100𝑚𝑖𝑛 𝑦𝑖𝑗 𝑦𝑖𝑗 , if j  c (20) z-score normalization (n11) 𝑁𝑖𝑗 = 𝑦𝑖𝑗− ∑ 𝑦𝑖𝑗 𝑚 𝑖=1 𝑚 √∑ (𝑦𝑖𝑗−𝜇𝑗) 2 𝑚 𝑖=1 𝑚 , if j  b (21) 𝑁𝑖𝑗 = − 𝑦𝑖𝑗− ∑ 𝑦𝑖𝑗 𝑚 𝑖=1 𝑚 √∑ (𝑦𝑖𝑗−𝜇𝑗) 2 𝑚 𝑖=1 𝑚 , if j  c (22) enhanced accuracy normalization (n12) 𝑁𝑖𝑗 = 1 − 𝑚𝑎𝑥 𝑦𝑖𝑗−𝑦𝑖𝑗 ∑ (𝑚𝑎𝑥𝑦𝑖𝑗−𝑦𝑖𝑗) 𝑚 𝑖=1 , if j  b (23) 𝑁𝑖𝑗 = 1 − 𝑦𝑖𝑗−𝑚𝑖𝑛𝑦𝑖𝑗 ∑ (𝑦𝑖𝑗−𝑚𝑖𝑛𝑦𝑖𝑗) 𝑚 𝑖=1 , if j  c (24) in the equations from eq. (1) to eq. (24), yij is the value of criterion j at the solution i; nij is the normalized value of criterion j in solution i; b describes the larger the better criterion; c describes the smaller the better criterion; m is the number of solutions; j is the mean value of the solutions of the criterion j. in addition to have to determine the appropriate dnm in combining with each mcdm method as mentioned above, even if a suitable dnm has been identified, but if only one dnm in combining with a mcdm method may narrow the application scope of that mcdm method. the analysis results from mentioned above about twelve dnms show that, if there exists a certain criterion whose maximum value is zero, then the methods n1, n3, n5, n6, n7, n8, n9, and n10 will not be available. or when there exists at least one value of a certain criterion is negative, the n5 method cannot be used. at that time, if an alternative dnm cannot be identified, the decision-making will be difficult, even impossible. however, even if a different dnm is chosen to instead, will the ranked results of the solutions be accurate? because the ranked results of the solutions are heavily influenced by the used dnms (trung, 2022b; aytekin, 2021; kaplinski and tamosaitiene, 2015; dragisa et al., 2013). from this aspect, many studies that have been performed to combine each mcdm method with several different dnms. the aim of these studies is determination of the duc trung do et al./oper. res. eng. sci. theor. appl. first online suitable dnms when combining with each mcdm method. sanjib and dragan (2021) simultaneously used two methods n1 and n5 to combine with combinative distancebased assessment (codas) method when ranking the smartphones. they found that in determining the best solution, n1 was equivalent to n5, but in terms of rank inversion, n5 was better than n1. trung (2022b) combined the codas method with six methods including n1, n2, n3, n4, n5, and n6 to make a decision in choosing a robot, assessing the air quality in the working room, and evaluating the machining in lathe machine. the author showed that if only in terms of finding the best solution, the five methods including n1, n2, n3, n4, and n5 are all suitable to combine with codas method except for n6 method. vafaei et al. (2022) combined the simple additive weighting (saw) method with four methods including n2, n3, n4, and n6 to make decisions in the evaluation of the phd candidates. they showed that only n2 is suitable for combination with the saw method. ersoy (2021a) combined the proximity indexed value (piv) method with n2, n11, and n12 to rank the financial position of forty-five companies. he showed that only n2 is suitable to combine with the piv method. ersoy (2021b) combined the range of value (rov) method with eight methods including n1, n2, n3, n4, n6, n7, n9, and n12 to rank the financial performance of ten companies. he concluded that only n9 was suitable for combining with the rov method. vafaei et al. (2016) combined the analytic hierarchy process (ahp) method with 5 methods including n2, n3, n4, n5, and n6 to rank smart parking locations. they concluded that n6 was the most suitable method to combine with ahp, whereas the combination of ahp and n3 was the worst method. martin (2021) combined two methods weighted aggregates sum product assessment (waspas) and topsis with four dnms including n1, n2, n3, and n4 to select the food processing methods. this research showed an amazing result that all those combinations determine the best solution. mic & antmen (2021) used simultaneously three methods including the waspas, topsis, and multiobjective optimization on the basis of ratio analysis (moora) to select the location of universities in turkey. although the dnms that were used in combination with the mcdm methods were different, all three cases gave a similar ranked result in all solutions. zavadskas et al. (2022) combined the simple weighted sum product (wisp-s) method with three methods including n1, n3, and n4 to rank the solutions for a set of random numbers. the authors have confirmed that the wisp-s method is really powerful when combined with all three dnms. all these combinations gave the same ranking results. vafaei et al. (2018) combined the topsis method with six methods including n1, n2, n3, n4, n5, and membership function to rank the drone landing solutions. they confirmed that only n3 is suitable for combination with the topsis method. in another study, vafaei et al. (2021) also combines the topsis method with six methods including n1, n2, n3, n4, n5, and membership function to select the cars. in this case, the authors point out that the membership function is the best method when combined with the topsis method. baghla and bansal (2014) combined the vikor method with three methods including n1, n2, and n4 to rank the wireless internet systems. they showed that combining n2 with the vikor method gives the best results. alrababah and atyeh (2019) combined the vikor method with four methods including n1, n2, n3, and n4 to rank the products through the customer feedback. they showed that the combination of vikor and n4 gives the best results. mathew et al. (2017) combined the waspas method with six methods including n2, n3, n4, n5, n6, and n12 to rank the robots. the authors found that the combination of waspas with n2 gave the best results. even, in several studies, when applying a certain mcdm method, people did not even use the dnms investigation of the appropriate data normalization method for combination with preference selection index method in mcdm available by itself but use other dnms. zolfani et al. (2020) combined simultaneously n5 with topsis and vikor methods to rank the solutions in two cases, case one is the ranking of the apartments in madrid (spain) and the other is the ranking of the solutions with a set of random data. it should be noted that n5 is not the dnm proposed by the authors of both topsis and vikor methods. however, an unexpected result occurred, the ranked results when combining topsis with n5 completely coincided with the case when combining vikor with n5. thus, it is seen that finding the appropriate dnms for each mcdm method has been carried out by many scientists and has also been applied in many different fields. in addition, any study that has done in this direction has attracted a lot of interest. based on the characteristics of the psi method as discussed in the introduction, this study was selected the psi method to perform the research mission follow the proposed research direction. 3. psi method the order of the performing the ranking of solutions according to the psi method is presented as follows (maniya and bhatt, 2010). build a decision matrix including the solutions and the criteria. standardized the data. + for the larger the better criterion. 𝑁𝑖𝑗 = 𝑦𝑖𝑗 𝑚𝑎𝑥𝑦𝑖𝑗 (25) + for the smaller the better criterion. 𝑁𝑖𝑗 = 𝑚𝑖𝑛𝑦𝑖𝑗 𝑦𝑖𝑗 (26) eq. (25) and (26) that are data normalization formulas used by the proponent of the psi method (method n1). the application cases in the next sections of this paper will fully apply all twelve dnms as presented in section 2. calculate the mean values of the standardized data (n). 𝑁 = 1 𝑛 ∑ 𝑁𝑖𝑗 𝑛 𝑖=1 (27) determine the preference values from the mean values (j). 𝜑𝑗 = ∑ [𝑁𝑖𝑗 − 𝑁] 2𝑛 𝑖=1 (28) determine the deviation in the preference values (j). 𝜃𝑗 = [1 − 𝜑𝑗 ] (29) determine the overall preference value (j) for the criteria. duc trung do et al./oper. res. eng. sci. theor. appl. first online  𝒋 = 𝜃𝒋 ∑ 𝜃𝒋 𝒎 𝒋=𝟏 (30) calculate the psij of each solution, with i = 1÷m. 𝑃𝑆𝐼𝑗 = ∑ 𝑁𝑖𝑗 . 𝑗 𝑚 𝑗=1 (31) where n is the number of criteria. rank the solutions according to the principle that the solution with the largest psij is the best one. to identify the appropriate dnms when combined with the psi method, this study performed ranking in several cases from the different fields. in each case, the number of criteria and the number of solutions is also different. selecting the cases from different fields will lead to draw the most general conclusions. the selected cases were all referenced from published studies. the reason for this is: in those studies, the solutions were also ranked either by psi method combined with n1 or by another mcdm method. the ranking results of the solutions in the published studies will be used to compare with the obtained ranking results in this study. specific contents when ranking the solutions in each case are presented in the section 4 of this paper. 4. results and discussion 4.1. application cases in this section, a combination of the psi method and the twelve data normalization methods as described above will be used to rank the solutions in four different cases. the data of all four cases were referenced from published studies. in those studies, the ranking of the solutions was also performed by different mcdm methods. the ranked results of the solutions when using different mcdm methods will be used to compare with those ones when using psi method. case 1 the data on the personnel selection solutions for a textile company in denizli (turkey) were used in this example (tus and adalı, 2018). selection of a marketing assistant from seven candidates was performed. table 1. the data of case 1 (tus and adalı, 2018) no. c1 c2 c3 c4 c5 a1 2 110 3 2 3 a2 5 100 5 3 3 a3 3 90 4 5 2 a4 10 80 3 4 4 a5 4 85 2 4 5 a6 8 80 3 4 4 a7 5 95 2 4 3 investigation of the appropriate data normalization method for combination with preference selection index method in mcdm five criteria to evaluate the candidates include work experience (c1), foreign language ability (c2), problem-solving ability (c3), communication ability (c4), and group management ability (c5). the scores for each criterion for each candidate are presented in table 1. in which, all five criteria are in the form of the larger the better criteria. in this study, the ranking of solutions was conducted by two methods: one is the psi method combined with n1 and the other one is the codas method. the ranked results from two above methods will be used for comparison with the ranked results from this study. and next, the ranking of solutions according to the psi method combined with different dnms will be performed. first of all, the data normalization by the n2 method will be applied. eq. (3) and eq. (4) were used to normalize the data according to the n2 method, the normalized data are presented in table 2. table 2. the data normalization values in case 1 according to the n2 method no. c1 c2 c3 c4 c5 a1 0.0000 1.0000 0.3333 0.0000 0.3333 a2 0.3750 0.6667 1.0000 0.3333 0.3333 a3 0.1250 0.3333 0.6667 1.0000 0.0000 a4 1.0000 0.0000 0.3333 0.6667 0.6667 a5 0.2500 0.1667 0.0000 0.6667 1.0000 a6 0.7500 0.0000 0.3333 0.6667 0.6667 a7 0.3750 0.5000 0.0000 0.6667 0.3333 eq. (27) and eq. (28) were used to determine the preference values from the mean (j). the calculated results are presented in table 3. table 3. values of j in case 1 when data normalization according to the n2 method c1 c2 c3 c4 c5 j 0.7411 0.8175 0.7619 0.6032 0.6349 the deviation in the preference value (βj) is calculated by eq. (29), the overall preference value (j) is determined by eq. (30), and the calculated results are presented in table 4. table 4. values of βj and j in case 1 when data normalization according to n2 method c1 c2 c3 c4 c5 βj 0.2589 0.1825 0.2381 0.3968 0.3651 j 0.1796 0.1266 0.1652 0.2753 0.2533 the psii is calculated according to eq. (31), the calculated results are presented in table 5. the ranked results of the solutions according to the values of the psi were also stored in this table. duc trung do et al./oper. res. eng. sci. theor. appl. first online table 5. psii values in case 1 when data normalization according to the n2 method and ranked results of the solutions no. psii rank a1 0.2661 7 a2 0.4931 4 a3 0.4501 5 a4 0.5871 1 a5 0.5028 3 a6 0.5422 2 a7 0.3986 6 thus, the ranking of the solutions for case 1 when normalizing data by the n2 method was completed. the ranking of solutions using other dnms (from n3 to n12) was also performed. table 6 presents the ranking results of the solutions when using all dnms. the ranked results of the solutions according to the codas method and psi method combined with n1 by tus and adalı (2018) were also included in this table. table 6. the ranked results of solutions in case 1 no. codas n1 n2 n3 n4 n5 n6 n7 n8 n9 n10 n11 n12 a1 7 7 7 7 1 7 7 7 7 7 7 7 7 a2 3 3 4 3 2 1 3 1 3 1 3 2 2 a3 5 5 5 5 4 4 5 6 5 3 5 5 5 a4 1 1 1 1 7 2 1 2 1 2 1 1 1 a5 4 4 3 4 5 5 4 4 4 4 4 4 4 a6 2 2 2 2 6 3 2 3 2 5 2 3 3 a7 6 6 6 6 3 6 6 5 6 6 6 6 6 from the results in table 6. when using eleven dnms to combine with the psi method, all confirmed a1 as the worst solution (except for n4). solution a1 was also confirmed to be the worst one when using the codas method (tus and adalı, 2018). from these results, a solid conclusion can be drawn that a1 is the worst solution. solution a4 was determined to be the best solution when using codas method (tus and adalı, 2018). when using the psi method in combination with eight dnms including n1, n2, n3, n6, n8, n10, n11, and n12, a4 was also determined to be the best solution. however, it would be a subjective statement if only considering the results in case 1 to conclude that all eight methods including n1, n2, n3, n6, n8, n10, n11, and n12 are all suitable to be combined with the psi method. to draw the generalized conclusions, it is necessary to perform more applications with many cases in many different fields. furthermore, sensitivity analysis in different situations is also required to ensure the accuracy of the conclusions. case 2 the investigated data on robots were used in this case (keshavarz-ghorabaee et al., 2016; trung, 2022b). seven types of robots were given for the ranking process. five criteria were selected to evaluate the robots including load capacity (c1), maximum tip speed (c2), memory capacity (c3), manipulator reach (c4), and repeatability (c5). in which c1, c2, c3, and c4 are the larger the better criteria, investigation of the appropriate data normalization method for combination with preference selection index method in mcdm whereas c5 is the smaller the better criterion. the investigated data is presented in table 7. similar to case 1, for this case, the ranking results of the solution when applying the psi method with twelve different dnms (n1 to n12) are presented in table 8. the ranking results of the solutions using the codas method (keshavarz-ghorabaee et al., 2016) and the two methods r and curli (trung, 2022a) are also presented in this table. table 7. the data of case 2 (keshavarz-ghorabaee et al., 2016; trung, 2022b) no. c1 c2 c3 c4 c5 a1 60 0.4 500 990 2540 a2 6.35 0.15 3000 1041 1016 a3 6.8 0.1 1500 1676 1727.2 a4 10 0.2 2000 965 1000 a5 2.5 0.1 500 915 560 a6 4.5 0.08 350 508 1016 a7 3 0.1 1000 920 1778 the obtained results in table 8 show that a2 is the best solution when ranking by the codas method (keshavarz-ghorabaee et al., 2016) and when ranking by two methods r and curli (trung, 2022a). a2 was also identified as the best solution when combining the psi method with six dnms including n1, n4, n5, n6, n8, and n11. table 8. the ranked results of solutions in case 2 no. codas r curli n1 n2 n3 n4 n5 n6 n7 n8 n9 n10 n11 n12 a1 3 2 2 2 3 1 3 1 3 3 3 1 1 2 3 a2 1 1 1` 1 2 2 1 5 1 2 1 3 2 1 2 a3 2 4 4 4 1 4 4 2 4 4 4 2 4 4 7 a4 5 3 3 3 4 3 2 3 2 1 2 4 3 3 1 a5 7 5 5 5 5 5 5 7 5 5 5 6 5 5 4 a6 6 7 7 7 7 7 7 4 7 7 7 7 7 7 6 a7 4 6 6 6 6 6 6 6 6 6 6 5 6 6 5 thus, if we only consider the results in this case, it is seen that five methods n1, n4, n6, n8, and n11 are suitable methods to combine with the psi method. however, to draw general conclusions, further applications of the ranking of these processes in other fields are still needed to perform. case 3 the experimental data about the turning processes were used in this case (prasad et al., 2018). in this study, nine different solutions to a turning process were implemented. each solution is evaluated through three criteria including arithmetic average roughness height (c1), ten-point mean roughness (c2), and material removal rate (c3). in which, c1 and c2 are the smaller the better criteria, whereas c3 is the larger the better criterion. the calculated results are presented in table 9. duc trung do et al./oper. res. eng. sci. theor. appl. first online table 9. the data of case 3 (prasad et al., 2018) no. c1 c2 c3 a1 2.11 9.04 9.21 a2 5.023 22.68 24.85 a3 9.17 36.103 32.57 a4 2.036 8.546 20.57 a5 7.16 26.94 39 a6 11.59 43.963 24.85 a7 3.35 13.263 41.14 a8 7.25 26.086 27 a9 11.75 45.376 39.85 the ranking of solutions according to the psi method when combined with eleven different dnms (n2 to n11) was performed similarly to case 1. the calculation results are presented in table 10. the ranking results of the solutions when using the psi method in combination with n1 (prasad et al., 2018) were also summarized in this table. table 10. the ranked results of solutions in case 3 no. n1 n2 n3 n4 n5 n6 n7 n8 n9 n10 n11 n12 a1 6 1 2 3 2 8 9 8 7 1 4 9 a2 7 4 5 5 4 4 5 4 6 8 5 7 a3 5 7 8 7 7 6 6 6 3 5 7 3 a4 2 2 1 2 1 3 1 3 8 9 2 8 a5 3 6 4 4 5 2 3 2 5 4 3 4 a6 9 8 9 9 8 9 8 9 1 7 9 2 a7 1 3 3 1 3 1 2 1 9 3 1 6 a8 8 5 6 6 6 5 7 5 4 6 6 5 a9 4 9 7 8 9 7 4 7 2 2 8 1 the obtained results in table 10 show that a7 is determined to be the best solution when using the psi method in combination with n1 (prasad et al., 2018). when four methods n4, n6, n8, and n11 were used in combination with the psi method, it was also determined that a7 was the best solution. in this case, it can be concluded that the five methods n1, n4, n6, n8, and n11 are suitable methods to combine with the psi method. case 4 the investigated data on air condition in offices was used in this case (keshavarzghorabaee et al., 2016). six criteria were used to evaluate the air condition in the office including the amount of air per head (c1), relative air humidity (c2), air temperature (c3), illumination during work hours (c4), rate of airflow (c5), and dew point (c6). in which, the criteria c1 to c4 are the large the better criteria, whereas c5 and c6 are the smaller the better criteria. the data about the solutions and the criteria in this case are presented in table 11. investigation of the appropriate data normalization method for combination with preference selection index method in mcdm table 11. the data of case 4 (keshavarz-ghorabaee et al., 2016) no. c1 c2 c3 c4 c5 c6 a1 7.6 46 18 390 0.1 11 a2 5.5 32 21 360 0.05 11 a3 5.3 32 21 290 0.05 11 a4 5.7 37 19 270 0.05 9 a5 4.2 31 19 240 0.1 8 a6 4.4 38 19 260 0.1 8 a7 3.9 42 16 270 0.1 5 a8 7.9 44 20 400 0.05 6 a9 8.1 44 20 380 0.05 6 a10 4.5 46 18 320 0.1 7 a11 5.7 48 20 320 0.05 11 a12 5.2 48 20 310 0.05 11 a13 7.1 49 19 280 0.1 12 a14 6.9 49 16 250 0.05 10 in this case, the ranking of the solutions according to the psi method in combining with twelve different dnms (n1 to n12) was performed similarly to case 1. the calculated results are presented in table 12. the ranking results of the solutions when using the codas method (keshavarz-ghorabaee, et al., 2016) were also summarized in this table. table 12. the ranked results of solutions in case 4 no. codas n1 n2 n3 n4 n5 n6 n7 n8 n9 n10 n11 n12 a1 3 3 9 7 7 3 3 3 3 1 9 5 6 a2 6 8 6 6 6 8 8 8 8 10 7 6 5 a3 9 12 8 9 9 9 11 11 11 12 8 9 9 a4 10 10 7 8 8 6 10 9 10 14 6 7 8 a5 14 14 14 14 14 13 14 14 14 5 14 14 14 a6 13 13 13 13 13 12 13 13 13 4 13 12 12 a7 12 11 12 10 12 14 12 12 12 6 10 13 13 a8 1 1 1 1 1 2 1 1 1 9 1 1 1 a9 2 2 2 2 2 1 2 2 2 11 2 2 2 a10 11 7 11 11 10 11 6 7 6 3 11 11 11 a11 4 4 3 3 3 7 4 4 4 7 4 3 3 a12 7 5 4 4 4 10 5 5 5 8 5 4 4 a13 8 6 10 12 11 4 7 6 7 2 12 10 10 a14 5 9 5 5 5 5 9 10 9 13 3 8 7 the calculated results in table 12 show that a8 is determined to be the best solution when using the codas method (keshavarz-ghorabaee, et al., 2016). a8 was also determined to be the best solution when using other methods n1, n2, n3, n4, n6, n8, n10, and n11 in combination with the psi method. from the analyzed results, it is shown that, in this case, eight methods that include n1, n2, n3, n4, n6, n8, n10, and n11 are suitable methods to combine with the psi method. 4.2. sensitivity analysis the combined results from the four above cases give an overview of the fit/nonconformity when combining the dnms with the psi method and as presented duc trung do et al./oper. res. eng. sci. theor. appl. first online in table 13. in which, the cells that were marked "✓" show the suitability of combining the dnm with the psi method. in contrast, the blank cells represent nonconformities when combining the dnm with the psi method. however, this suitability only considers the factors that the method of data normalization when combined with the psi method can determine the best solution in comparing to published studies. in order to confirm that a dnm is appropriate in combination with the psi method, it is necessary to analyze the sensitivity in ranking the solutions. of course, the sensitivity analysis only needs to be performed for the data normalized methods that was jointly identified the best solution. with above four cases, these methods were n1, n6, n8, and n11. table 13. suitable normalization methods for combining with the psi method examples normalization method n1 n2 n3 n4 n5 n6 n7 n8 n9 n10 n11 n12 example 1 ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ example 2 ✓ ✓ ✓ ✓ ✓ example 3 ✓ ✓ ✓ ✓ ✓ example 4 ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ the sensitivity analysis is the determination of the degree of variation in the ranking results of the solutions under the different scenarios. the scenarios that were commonly used for sensitivity analysis include changing the weight of the criteria, removing one/several solutions from the list of solutions, and changing the criterion type (bozanic et al., 2021; zopounidis and doumpos, 2017). in this case, the generation of different scenarios is done by eliminating a certain solution. in each case, the eliminated solution will also be selected differently. for case 1, solution a5 was removed from the list of solutions. according to the ranking results of the solutions in case 1 (section 4.1), a5 ranked 4, a1 ranked 7, and a4 ranked 1 (when using n1, n4, n8, and n11). therefore, if removing a5 from the list of solutions does not affect on the ranking of the solutions, then a4 is still the best solution and a1 is still the worst solution. after removing a5 from the list of solutions, the ranking results of solutions are shown in figure 1. figure 1. ranked results of the solutions without a5 solution in case 1 investigation of the appropriate data normalization method for combination with preference selection index method in mcdm it is seen that although the rank inversion occurred in some solutions, however, a4 is still the best solution, and a1 is still the worst solution for all four different dnms. it shows that the removal of a5 from the list of solutions does not change the best solution and the worst solution. in this case, it can be concluded that n1, n6, n8, and n11 methods are suitable methods to combine with the psi method. for case 2, solution a6 was removed from the list of solutions. according to the ranking of the solutions in case 2 (section 4.2), a6 is the worst solution and a2 is the best solution (when using n1, n4, n8, and n11). therefore, if removing a6 from the list of solutions does not influence on the ranking of solutions, then a2 is still the best solution. on the other hand, currently, a7 ranks 6, so if a6 is removed from the list of solutions, a7 will rank last. after removing a6 from the list of solutions, the ranking results of the solutions are shown in figure 2. figure 2. ranked results of the solutions without a6 solution in case 2 it is seen that although the rank inversion was occurred in some solutions, however, a2 is still the best solution, and a7 is still the worst solution when using four different dnms. that shows that the removal of a6 from the list of solutions was not changed the best and worst solution. in this case, it is again certainty established that methods n1, n6, n8, and n11 are suitable methods to combine with the psi method. for case 3, once again, the worst solution is removed from the list of solutions (solution a6). according to the ranking of solutions in case 3 (section 4.3), a7 is the best solution. if removing a6 from the list of solutions does not affect on the ranking of solutions, then a7 is still the best solution. after removing a6 from the list of solutions, the results of ranking solutions are shown in figure 3. it is seen that although the rank inversion also occurred in some solutions, however, a7 is still the best solution and ranks 2, 3, and 4 are the same those when using dnms. in this case, we can again confirm that n1, n6, n8, and n11 are suitable methods to combine with the psi method. duc trung do et al./oper. res. eng. sci. theor. appl. first online figure 3. ranked results of the solutions without a6 solution in case 3 for case 4, the best solution was removed from the list of solutions, (solution a8). according to the ranking results of the solutions in case 4 (item 3.4), a9 ranked 2 nd, and a5 ranked last. figure 4. ranked results of the solutions without a8 solution in case 4 therefore, if removing a8 from the list of solutions does not affect on the ranking of solutions, then a9 will rank 1, and a5 will still rank last. after removing a8 from the list of solutions, the ranking results of solutions are shown in figure 4. it is seen that rank inversion also occurred in some solutions. however, a9 is always the best solution, and a5 is always the worst solution. so, the removal of a8 from the list of solutions does not change the best solution and the worst solution. once again, we can confirm that methods n1, n6, n8, and n11 are suitable methods to combine with the psi method. 4.3. the appropriate dnm for combination with psi method from the above-performed analyzed results, it is seen that in the above-mentioned twelve dnms, there are only four dnms including n1, n6, n8, and n11 are suitable methods to combine with the psi method in all studied cases. these combinations not only consistently identified the same best solution, but also gave equivalent results in investigation of the appropriate data normalization method for combination with preference selection index method in mcdm comparing to other methods (codas, r, and curli) as analyzed in each case. the sensitivity analysis of the ranking results of the solutions was also performed with different scenarios. the results all confirmed that n1, n6, n8, and n11 are suitable methods to combine with the psi method. these obtained results could open a wide application range for the psi method. it can be said that because in the cases, there does not exist any value of yij equal to 0, all four methods of data normalization can be applied. however, when there exists a certain value yij = 0, then the method n1 cannot be applied, the remaining three methods (n6, n8, and n11) can still be applied. even when there exists a value max(yij) = 0, then all three methods n1, n6, and n8 cannot be applied, there is still an alternative method (n11). this can be considered a great discovery to be able to apply the psi method in all cases. the case that was applied immediately below will make this statement clearer. in this case, there are 3 different solutions a1, a2, and a3. each solution is evaluated through 5 criteria c1, c2, c3, c4, and c5. in which, c1, c2, and c3 are criteria as the larger the better, whereas c4 and c5 are criteria as the smaller the better. the values of the criteria at the solutions are selected at random, in which, there are both positive values, zero values, and negative values (table 14). it is clear that in this case, methods n1, n6, and n8 cannot be applied, but only method n11 can be applied to rank the solutions. using the psi method with the dnm (n11) to rank solutions, the ranking results were summarized in table 14. in addition, to verify the ranking results, r and curli methods were also applied with the ranked results as summarized in table 14. table 14. ranked results when using psi+n11, curli, and r methods no. criteria rank c1 c2 c3 c4 c5 psi + n11 curli r a1 5 -3 10 1 0 1 1 1 a2 6 -2 8 0 2 2 2 2 a3 3 0 6 3 1 3 3 3 the calculated results in table 14 show that when ranking the solutions by psi method in combining with n11, the ranking results are completely consistent with those ones when using curli and r methods. once again, we see that the n11 method is perfectly suited to combine with the psi method. this combination will create more effective when other dnms (n1, n6, and n8) cannot be applied. the identification of the appropriate dnms when combined with a specific mcdm method is a suitable research direction in studying on the mcdm. therefore, in this case, the first time the psi method was selected as the research object both showing the correctness of the approach as well as the novelty of this work. this study identified four dnms suitable to combine with the psi method. this discovery has expanded the psi method application scope that has not been considered in previous studies. 5. conclusion with the simplicity of application and no need to determine the weights for the criteria, the psi method has been widely applied for mcdm in many different fields. duc trung do et al./oper. res. eng. sci. theor. appl. first online however, the proponent of the psi method as well as all the studies that applied this method all normalized the data according to the n1 method. it is clear that in all mentioned cases, the author has not considered cases when a certain criterion has a value of 0 in a certain solution. in these cases, the n1 method cannot be applied, and then the psi method also cannot be applied. to overcome this limitation, this study investigated the suitability of combining twelve different dnms with the psi method. all those combinations were tested in four cases in four different fields. the number of solutions, the number of criteria, and the type of criteria (the larger the better, the smaller the better) are not the same in all cases. in this study, it was determined that in all four cases, four methods including n1, n6, n8, and n11 were identified as suitable methods to combine with the psi method. these results from this study open a wide application range for the psi method. specifically, when there exists yij = 0 and/or max(yij) = 0, then the n1, n6, and n8 methods cannot be applied, the n11 method can still be applied for multi-criteria decision making. however, all twelve dnms that were mentioned in this study cannot be applied if the criteria are in the qualitative form (color, preferences, etc.). in these cases, the assignment of these qualitative criteria to the numbers is necessary to be done before performing the data normalization. in these cases, the studies that apply the psi method for mcdm when having the qualitative criteria are the next research direction of this study. when the value of the criteria at each solution is a fuzzy set, the evaluation of the suitable degree when combining the dnms (n1, n6, n8, and n11) with the psi method, which is also a new research direction should be performed as soon as possible. all twelve used dnms in this study should 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(2017). multiple criteria decision making applications in management and engineering. springer. https://doi.org/10.1007/978-3-31939292-9 © 2022 by the authors. submitted for possible open access publication under the terms and conditions of the creative commons attribution (cc by) license (http://creativecommons.org/licenses/by/4.0/). https://doi.org/10.18485/aeletters.2022.7.2.2 http://dx.doi.org/10.17093/alphanumeric.432843 https://doi.org/10.1007/978-3-319-31165-4_26 https://doi.org/10.1504/ijids.2018.090667 https://doi.org/10.1007/978-3-030-78288-7_13 https://doi.org/10.1016/j.procs.2022.01.156 https://doi.org/10.1177/09673911211062755 https://doi.org/10.1007/s12046-018-1020-x https://econpapers.repec.org/repec:cys:ecocyb:v:50:y:2017:i:1:p:59-74 https://doi.org/10.48550/arxiv.2006.08150 https://doi.org/10.1007/978-3-319-39292-9 https://doi.org/10.1007/978-3-319-39292-9 investigation of the appropriate data normalization method for combination with preference selection index method in mcdm duc trung do 1, van dua tran 1, van duc duong 1, nhu-tung nguyen 2* 1. introduction 2. literature review 3. psi method 4. results and discussion 4.1. application cases case 1 case 2 case 3 case 4 4.2. sensitivity analysis 4.3. the appropriate dnm for combination with psi method 5. conclusion references operational research in engineering sciences: theory and applications vol. 2, issue 3, 2019, pp. 65-76 issn: 2620-1607 eissn: 2620-1747 doi: https://doi.org/10.31181/ 10.31181/oresta1903065b * corresponding author. tapasbiswasmckv@gmail.com (t. biswas), sudipto_chaki@yahoo.co.in (s. chaki), cd_manik@rediffmail.com (m. das) mcdm technique application to the selection of an indian institute of technology tapas kumar biswas*, sudipto chaki, manik chandra das department of automobile engineering, mckv institute of engineering, india received: 14 october 2019 accepted: 29 november 2019 first online: 16 december 2019 original scientific paper abstract. multi-criteria decision-making (mcdm) techniques are widely used in selecting the best alternative amongst a number of alternatives. in this paper, the quality of the operation of seven newly-established indian institutes of technology (iits) in india is analyzed by using the modified simple additive weighting (saw) method to subsequently rank them. the entropy method is used to determine the weights associated with the criteria under study. the criteria considered for the analysis are as follows: the percentage of vacant seats during student intake, the strength of the faculty, research publications, the sponsored research fund, the student success index, the number of the students who are employed through the placement cell, the number of the students who opted for higher studies and the number of phds awarded, respectively. the performance of this method is further compared with the moora, topsis and copras methods; the results obtained are found to corroborate well with those obtained by the modified approach. furthermore, a sensitivity analysis is conducted by changing the criteria weights so as to establish the stability of the ranking obtained. iit g is considered to have a better performance in all the methods than the other iits do. this research has shown that the modified saw is a useful and reliable tool for normal decision-making. key words: iit, entropy, mcdm, modified simple additive weighting (saw), sensitivity analysis 1. introduction: indian institutes of technology (iits), namely kharagpur iit, bombay iit, madras iit, kanpur iit, delhi iit, guwahati iit, roorkee iit, etc. are considered to be the most prestigious engineering and technology institutions in india. all the iits were established by a number of the scientists, technologists and engineers of the highest caliber who would engage themselves in research, design and development in order to help build the nation towards self-reliance in its technological needs. after that, nine biswas et al./oper. res. eng. sci. theor. appl. 2 (3) (2019) 65-76 66 more iits were established, namely bhubaneswar iit, gandhinagar iit, hyderabad iit, jodhpur iit, patna iit, ropar iit, indore iit, mandi iit and varanasi iit. there are also the seven most recently established iits, namely: palakkad iit, tirupati iit, dhanbad iit, bhilai iit, goa iit, jammu iit and dharwad iit. all the iits in india are also amongst the most heavily funded educational institutions in the country. as high-performing institutions, iits are included in several studies on the institutional ranking based on research performance. in those papers, however, iits were mostly used as the benchmark institute with several other governmental and privately-owned institutions. in the past, researchers tried to identify top indian engineering and technological institutions according to their research performance, including all the seven older iits in the list, based on which they found all the seven older iits to rank the highest on the list (prathap & gupta (2009), nishy et al. (2012), prathap (2013, 2014)]. for the ranking of the institutes, multi-criteria decisionmaking (mcdm) techniques were widely employed, because they involve multiple conflicting criteria in decisionmaking. tyagi et al., 2009, evaluated the performance efficiencies of the 19 academic departments of the roorkee indian institute of technology (iit) by applying the dea technique. das et al., 2010, used the fuzzy analytic hierarchy process (ahp) method for the purpose of evaluating the performance of six institutions. das et al., 2012, also carried out a comparative evaluation of seven indian institutes of technology (iits) by using the fuzzy ahp and copras methods. again, das et al., 2013, presented a combined sowia-moora approach so as to evaluate the performances of indian technical institutions. it was observed that the performance of two iits would need a considerable improvement. the research studies that have been conducted so far have included seven older iits only for the purpose of a comparative analysis according to different performance criteria. the performance analyses of newer iits have not been made a mention of in the literature. in the present study, a total of seven newly-established iits have been taken into consideration for analysis. in this work, eight criteria have been considered for the analysis, namely: vacant seats (in %) (vs), the strength of the faculty in respect of phds (fs), the number of the research papers (rp) published in a scopus-indexed journal in the last three years, the sponsored research fund (rf) (in lacs), the student success index (ss) or the pass percentage, the number of the students who are employed through the placement cell (e), the number of the students who opted for higher studies (hs) and the number of the phd awarded (pa). therefore, the present study contains a total of eight criteria and seven alternatives, as is presented in table 1. the dataset presented in table 1 was retrieved from the database of the national institutional ranking framework (nirf), an initiative by the ministry of human resource development, the government of india. it has been observed that, for different criteria, there are different alternatives that show the best performance. for example, the number of vacant seats is the highest in iit f and the lowest in iit g. in the present scenario, vacant seats in engineering education are the biggest threat in india. therefore, the smaller the number of vacant seats at a college, the more superior the college is. the strongest is the faculty in iit a. the number of the research papers published in a scopus-indexed journal during the last three years, however, is the biggest in iit g. iit c is also perceived to have the highest sponsored research fund compared to the other iits which are the subject matter of the research study. the student success index, i.e. the pass percentage, is the highest in iit d compared to the other newly-introduced iits. when students’ employment achievements made through the placement cell are concerned, however, it is iit c which shows the best mcdm technique application to the selection of an indian institute of technology 67 performance, being far ahead of iit d. it was observed that the number of the students who had opted for higher studies was maximum in iit f, whereas the phd awarded were at the maximum value in iit g. therefore, no selection of an iit demonstrating the best performance can be made intuitively; such a selection rather requires the involvement of the systematic decision-making process, such as the multi-criteria decision-making (mcdm) techniques generally used to rank or select one alternative or several alternatives from a set of the available options based on multiple and usually conflicting attributes. the prior findings show that the application of multiobjective optimization based on the ratio analysis (moora) (brauers & zavadskas 2006), the data envelopment analysis (dea) (charnes et al. 1978), sowia-moora (das et al. 2013), the complex proportional assessment (copras) (das et al. 2012), preference ranking organization method for enrichment of evaluations (promethee) (brans & vincke 1985) etc. algorithms are broadly used in the decision-making process. in this paper, the modified saw approach (biswas & saha 2019) is used for the ranking of the seven newly-established iits. the entropy method is used to determine the weight coefficients associated with each criterion. the ranking of the performance of the novel method is compared with moora and copras, and the technique for the order of preference by similarity to ideal solution (topsis) (wang & elhag 2006) method in order to judge its superiority. a sensitivity analysis of the ranking with changing criteria weights is also presented. the best ranking obtained is, again, compared with the nirf ranking, thus showing the efficacy of the methodology employed in this paper. the paper is organized into several sections, namely as follows: after the introduction and literature review sections, section 2 is a presentation of the entropy-based modified saw methodology with the mathematical formulation of the method. in section 3, the entropy-based modified saw method for the ranking of iits is applied. the sensitivity analysis for the novel method is presented in section 4. in section 5, the discussion is presented and the concluding remarks of the paper are given. section 6 is dedicated to the directions for future research. 2. methodology 2.1. weight assessment entropy method there are a number of weight assessment methods for decision-making processes, such as the eigenvector method, the weighted least square method, the entropy method, etc. however, the entropy method [safari et al. (2012)] is more suitable for use when the data of the decision matrix are known. the entropy method is especially valuable for the examination of disparities between sets of information. the formulation of the entropy method is given below: step 1: the formation of the initial decision matrix x=[xij]mxn step 2:  = −= n i ijij ppkej 1 ln j=1,2,3,……,j i=1,2,3,…….,n (1) biswas et al./oper. res. eng. sci. theor. appl. 2 (3) (2019) 65-76 68 where,  = = n i ij ij ij x x p 1 j=1,2,3,……,j i=1,2,3,…….,n (2) and n k ln 1 = (3) where pij is the discrete probability distribution of the ith alternative with respect to the jth attribute. the constant k used to ensure that 0 ≤ ej ≤ 1. the divergence degree dj can be calculated as follows: dj= 1-ej j=1,2,3,……,j (4) step 3: the final relative weights for the jth attribute can be obtained by means of a simple additive normalization:  = = j j j j j d d w 1 j=1,2,3,……,j (5) 2.2. modified saw method the general steps of the modified saw method are as follows: step 1: every decision matrix is formed and expressed in the following manner: nj ffff ....21                         m nm jmm inijii nj nj     ..... .. .. .. .. .. .. .. .. .. .. .. .. .. .. ............ ............ .... .... 21 21 222221 111211 (6) where ai represents the alternatives, i = 1,2, . . . ,m; fj represents the jth attribute or criterion, j = 1, 2,. . . , n, related to the ith alternative; and θij indicates the performance rating of each alternative ai with respect to each criterion fj. the procedures of the modified saw method are as follows: step 2. the formation of the initial decision matrix x=[xij]mxn. step 3. the normalization of the decision matrix as n=[rij]mxn. in this method, several criteria dimensions are first converted into nondimensional criteria. for the benefit type criteria, rij, mcdm technique application to the selection of an indian institute of technology 69 −+ − − − = ii iij ij xx xx r (7) (a) for the non-benefit type criteria, rij, +− + − − = ii iij ij xx xx r (8) here, xij, xi+ and xiare the elements from the initial decision matrix (x), where xi+=max(x1, x2, ....,xm) and xi=min(x1, x2, ... , xm). step 4. for the sets of the benefit and non-benefit type criteria, each normalized criterion rij is computed on a scale from 0 to 1, where 0 corresponds to the minimum and 1 to the maximum assigned value for the corresponding indicator. the amount of rij is now classified into five scale values, ranging from 1 to 5, where 5 refers to extreme importance, 4 refers to very strong importance, 3 refers to strong importance, 2 refers to moderate importance and 1 refers to equal importance. for example, when the normalization values of all these criteria are in the interval of (>0.80, 1.00), then the scale value (g)=5 is taken. if the normalized value of one of these criteria is in the interval of (>0.60, 0.80), then g=4; when the normalized value of all criteria is in the interval of (>0.40, 0.60), then g=3; when the normalized value is in the interval (>0.20, 0.40), then g=2, and when the normalized value is in the interval (>0.00, 0.20), finally g finally equals 1. this scaled normalized decision matrix is identified by (vij). step 5. the elements of the weighted scale value matrix (qij) are calculated by applying the following equation: ijiij vwq = (9) where wi is the criteria weight. step5. compute the overall score (si) of the alternatives by using the following equation:  = = n j iji qs 1 . (10) ultimately, rank the alternatives based on the descending value of si. 3. new iit performance comparison in this paper, the entropy-based modified saw method is used to rank the seven newly-developed iits, namely iit a, iit b, iit c, iit d, iit e, iit f and iit g, respectively. there are three parameters by which the qualities or status of an biswas et al./oper. res. eng. sci. theor. appl. 2 (3) (2019) 65-76 70 engineering college can generally be measured: first, student admission to the college; second, the qualification, the research activity and the number of the faculty members; and third, the number of students’ examinations and the students who have obtained a university degree. a total of eight criteria were judiciously chosen in the paper so as to address those parameters adequately. the eight criteria considered for the analysis of the performances of the iits include the following: vacant seats (in %) (vs), the strength of the faculty with phd (fs), the number of the research papers (rp) published in a scopus-indexed journal in the last three years, the sponsored research fund (rf) (in lacs), the student success index (ss) or the pass percentage, the number of the students who are employed through the placement cell (e), the number of the students who opted for higher studies (hs) and the number of the phd awarded (pa). the dataset was retrieved from the published datasheet of the national institutional ranking framework (nirf), 2018, and they are given in table 1. the meaning and importance of the eight different criteria are explained and presented in table 2, which shows us that only the percentage of vacant seats is considered as the non-benefit type criterion, or the lower, the better; the seven remaining criteria are considered as the benefit type criterion, or the higher, the better. after the formation of the decision matrix, as shown in table 1, the calculations are completed and a normalized decision matrix is found, as well as the weighted scale normalization decision matrix, and the overall score of the alternatives by the following modified saw algorithm as mentioned in eqs (7-10) is computed. the final rank according to the modified saw method is presented in table 7. in order to avoid subjective judgments, the entropy method is used to compute the criteria weights. finally, a sensitivity analysis has confirmed the robustness of the ranking results achieved through the analysis of the sensitivity of the model. according to the modified saw method, iit g is found to be in rank 1, which is supported by the ranking of the iits further obtained by using the same dataset (table 1) by applying other popular methods, such as the moora, topsis and copras methods, and the results obtained are found to corroborate well with those obtained by applying the modified saw method. iit g is found to be the first in the modified saw method and the moora, topsis and copras methods as well. table 1: the quantitative data for the problem of the selection of a newlyestablished iit alternatives criteria vs fs rp rf ss e hs pa iit a 7.98 129 540 2979.72 94.6 107 16 31 iit b 2.97 115 401 1683.62 92.3 80 5 53 iit c 6.38 110 589 3275.76 96.7 112 16 54 iit d 5.05 105 449 88.64 98.27 79 3 2 iit e 4.36 64 374 612.44 83.58 68 11 16 iit f 11.67 54 223 677.54 91.71 67 28 5 iit g 1.13 116 654 2113.4 95.83 57 20 70 source: the national institutional ranking framework (nirf) datasheet, 2018. mcdm technique application to the selection of an indian institute of technology 71 table 2: the descriptions of the different criteria for the selection of the best iit criteria description vs vs stands for the number of vacant seats. in india today, the number of vacant seats in engineering education is becoming one of the biggest threats. therefore, the minimum vacant seats indicate the superiority of one institution over another in terms of the faculty, the infrastructure, the curriculum, teaching-learning, research and placement in comparison with contemporary institutes, which helps attract students. it is a non-benefit type criterion. fs fs stands for the strength of the faculty with phds. being the country’s premier institutes, iits always recruit faculty members with an excellent academic background and an exceptional research quality in order to impart the high quality of education and research. it will result in students’ overall improvement and produce quality engineers to cater for the needs of the industry and society as a whole. in india, however, there is an acute shortage of well-qualified faculties required for engineering disciplines at institutes like the iits, resulting in a tendency to decrease the faculty/student ratio. therefore, the higher the strength of the faculty in an iit, the greater the faculty/student ratio, which is desirable in order to achieve continuous improvement in education and research. it is a benefit type criterion. rp rp stands for the number of the research papers published in scopusindexed journals during the last three years. citation-based measurements are considered to be the quantitative measures of the research quality and impact. the higher its value, the better the quality of the research performance in iits. it is a benefit type criterion. rf rf stands for the sponsored research fund (rs. in lac). it is important for the iits to be the source of new ideas and innovators in technology and science, with the general goal to create an ambience in which new ideas, research and scholarship flourish, and from which the leaders and innovators of tomorrow emerge. in meeting these points of importance, iits have taken the initiative to promote innovations and carry out funded research studies sponsored by different agencies of the government of india and the industry. it is a benefit type criterion. ss ss stands for the student success index, or the pass percentage. academic success is important because it directly decides upon students’ positive outcomes after graduation. it lays out a framework for building institutions so designed as to promote student success outcomes. students with academic success will have more opportunities to choose their future jobs than those less educated. it is a benefit type criterion. e e stands for the number of the students who are employed through the placement cell. it has been shown that students in iits with a higher cgpa have a smaller probability of remaining unplaced. a survey among the graduating batch who had sat for placements strongly hints towards cgpa as one of the most important placement factors. it is the dream of every engineering student to find their place in a top-rank organization biswas et al./oper. res. eng. sci. theor. appl. 2 (3) (2019) 65-76 72 which is visiting their campus for the recruitment purpose. employment competition increases every day, and placement has become a challenging task. training students and equipping them with life skills has become an important institutional responsibility. along with technical expertise, the development of a holistic personality is also necessary. it is a benefit type criterion in this study. hs hs stands for the number of the students who opted for higher studies. higher studies assure the significance of their knowledge, identify gaps in skills, educate special programmers and build the right skills that can help the country to improve, economically prosper and achieve social cohesion, adapt the development of the workforce to the economy and changing demand for new skills, develop higher standards of transparency, strengthen the higher education sector and professionalize the sector through stronger institutional responsibilities that would help reprioritize the efforts and work around the complexities. it is a benefit type criterion in this study. pa pa stands for the number of the phd awarded. a phd is the doctoral degree awarded to the students who defend an original thesis which makes a significant new contribution to knowledge in their respective fields of interest. phd qualifications are available in all scientific, engineering and management subjects and are normally the highest level of the academic degree a person can achieve. it is a benefit type criterion. 3.1 steps of the calculation of the modified saw method: (i) the decision matrix for all the iits is shown in table 1. only one iit (i.e. iit a) is taken into consideration for the calculation. then, the normalization of the different criteria of the alternative iit a is calculated using equations 7 and 8. (ii) finally, the normalization of the different criteria of iit a is given in table 3. now, all the normalized values are split into the five scale values, ranging from 1 to 5, as is shown in table 4, where 5 pertains to extreme importance and 1 pertains to equal importance. for example, in the case of iit a, the fs, rf and e criteria normalization values are 1, 0.907114 and 0.909091, respectively, which implies the scale value of 5 in this case, because all the normalization values of the given criteria are in-between (0.8-1). in a similar fashion, the other criteria of iit a, such as vs, rp, ss, hs and pa, have the scale values of 2, 4, 4, 3 and 3, respectively. (iii) now, the individual scaled value is multiplied by a particular criterion weight. in the case of iit a, the scale value of the vs criteria is 2, which is now multiplied by wi (0.156402) value, the obtained result being 0.312804. in a similar fashion, all the weighted scale values of iit a are found and presented in table 6. (iv) then, we add all the qij of iit a and the obtained si values of iit a as follows: =0.312804+0.18223+0.171696+1.321135+0.00448+0.12749+0.495192+0.92495 7= 3.539984 (v) correspondingly, (iit b-iit g) are calculated applying the same procedure and the final ranks are obtained. mcdm technique application to the selection of an indian institute of technology 73 table 3: the normalized decision matrix alternatives criteria vs fs rp rf ss e hs pa iit a 0.350 1 0.735 0.907 0.750 0.909 0.52 0.426 iit b 0.825 0.813 0.413 0.500 0.594 0.418 0.08 0.75 iit c 0.502 0.747 0.849 1 0.893 1 0.52 0.765 iit d 0.628 0.68 0.524 0 1 0.4 0 0 iit e 0.693 0.133 0.350 0.164 0 0.2 0.32 0.206 iit f 0 0 0 0.185 0.553 0.182 1 0.044 iit g 1 0.827 1 0.635 0.834 0 0.68 1 table 4: the scaled decision matrix (v) criteria alternatives vs fs rp rf ss e hs pa iit a 2 5 4 5 4 5 3 3 iit b 5 5 3 3 3 3 1 4 iit c 3 4 5 5 5 5 3 4 iit d 4 4 3 1 5 2 1 1 iit e 4 1 2 1 1 1 2 2 iit f 1 1 1 1 3 1 5 1 iit g 5 5 5 4 5 1 4 5 table 5: the weight of the criteria calculated by applying the entropy method vs fs rp rf ss e hs pa σwi wj 0.156 0.036 0.043 0.265 0.001 0.025 0.165 0.308 1 table 6: the weighted scaled decision matrix, q criteria alternatives vs fs rp rf ss e hs pa iit a 0.313 0.182 0.172 1.321 0.005 0.127 0.495 0.925 iit b 0.782 0.182 0.129 0.793 0.003 0.076 0.165 1.233 iit c 0.469 0.146 0.215 1.321 0.006 0.127 0.495 1.233 iit d 0.626 0.146 0.129 0.264 0.006 0.051 0.165 0.308 iit e 0.626 0.036 0.086 0.264 0.001 0.025 0.330 0.617 iit f 0.156 0.036 0.043 0.264 0.003 0.025 0.825 0.308 iit g 0.782 0.182 0.215 1.057 0.006 0.025 0.660 1.542 biswas et al./oper. res. eng. sci. theor. appl. 2 (3) (2019) 65-76 74 table 7: the assessment values for the problem of the selection of the newly-established iit by applying the proposed mcdm method and a comparison with the other mcdm methods alternatives performance score si rank by modified saw method rank by topsis rank by copras rank by moora iit a 3.539984 3 4 3 3 iit b 3.363887 4 3 4 4 iit c 4.012303 2 2 2 2 iit d 1.69437 6 7 7 7 iit e 1.985513 5 6 6 5 iit f 1.662496 7 5 5 6 iit g 4.468717 1 1 1 1 4. sensitivity analysis the results of the mcdm methods significantly depend on the assigned value of the relative importance of each criterion, known as weights. sensitivity analysis is a popular means to estimate the effect of a change in weights associated with each criterion on the final ranking of alternatives. if changing weights associated with certain criteria finally result in a different ranking, the model is considered to be sensitive to those weights. therefore, the stability of an mcdm model is established if the final ranking determined by the model remains more or less unaffected by the change in weights during the sensitivity analysis. in this section, a sensitivity analysis is performed in order to assess how changes in criteria weights affect the ranking of the different alternatives of iit by interchanging the criteria weight values in the order of 8c2 i.e. for the eight considered criteria (c1–c8), there are a total of 28 (8c2) possible interchanges. here, 8 is the number of the criteria and 2 is the number of the criteria chosen at a time. therefore, there are maximum 28 possible interchanges in the weights during the sensitivity analysis. figure 1 clearly shows that the interchanges in the criteria weights have a very small effect on the rank of the alternatives and the ranking of the iits remains almost unaltered. in almost all the cases, iit g outperforms the other iits, which indicates the robustness of the ranking of the iits obtained by applying the proposed model. the better performance of iit g may be due to a very small number of vacant seats in comparison with the other iits which are the subject matter of this research study, a much greater number of the published research papers and the maximum number of the students awarded a phd degree in comparison with the other iits. therefore, the conducted sensitivity analysis allows us to conclude that iit g is the best iit (in comparison with the other six) in india, which is only followed by iit c, iit a, iit b, iit e, and iit d, while iit f ranks the last. it has been observed during the analysis that the proposed modified saw method is simple and easy to understand, and, given its lesser mathematical complexity, convenient to handle. furthermore, the robustness of the method is clearly envisaged through the sensitivity analysis conducted in this study with the normalized values of the different alternatives. in the past, researchers developed different mcdm techniques so as to cater for decision-making in different complex real-life problems. those methods, however, are found to be complicated and mathematically complex, mcdm technique application to the selection of an indian institute of technology 75 and generally to take too much time to compute, even requiring a linear programming tool to solve such models from time to time. the model proposed in this paper has been compared with the well-established mcdm techniques, such as topsis, copras and moora, which is accounted for in table 7. a higher degree of the similarity of the ranks between the proposed method and the other mcdm techniques is indicative of the efficacy of the proposed method. therefore, given its high degree of accuracy in decision-making involving lesser mathematical complexity and little computational time, the proposed method will undoubtedly be a very useful tool for decision-makers. the entropy method is successfully employed in this paper for the computation of the weights. therefore, the hybrid model consisting of the entropy method and the proposed novel method used in this paper have proven to render effective decisionmaking for the purpose of evaluating real-life problems, such as the evaluation of the performance of the newly-established iits and so forth. the modified saw method, therefore, can be envisaged as a useful and reliable tool for sensible decision-making. figure 1. the sensitivity analysis based on changing criteria weights 5. conclusion the overall scores calculated by the application of the method serve to evaluate the rank of the alternatives and lead to the selection of a suitable alternative. the modified saw method is logical and provides a good elaboration of the ranking method. the suggested methodology can be used for any type of the selection problem with any number of attributes. the conducted comparative performance analysis enables us to understand that the proposed method outperforms in comparison with the other existing and popular mcdm methods. practitioners may find this research study useful in that the same may enable them to use this novel approach to the evaluation of performance and the ranking and selection of alternatives in a given set. the 0 1 2 3 4 5 6 7 8 1 3 5 7 9 11 13 15 17 19 21 23 25 27 r a n k sensitivity analysis iit a iit b iit c iit d iit e iit f iit g biswas et al./oper. res. eng. sci. theor. appl. 2 (3) (2019) 65-76 76 performance demonstrated by the other higher-education institutions, such as nits and indian universities, is also possible to evaluate by applying the adopted approach. due to the generic nature of the given method, the same can also be applied to solving the ranking and selection problem in any sector of society. references biswas, t & saha, p. 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(2013). on the performance of indian technical institutions: a combined sowia-moora approach. opsearch, 50(3), 319333. nishy, p., panwar, y., prasad, s., mandal, g. k. & prathap, g. (2012). an impact citations exergy (icx) trajectory analysis of leading research institutions in india.scientometrics, 91(1), 245–251. prathap, g., & gupta, b. m. (2009). ranking of indian engineering and technological institutes for their research performance during 1999–2008.curr. sci., 97(3), 304– 306. prathap, g. (2013). benchmarking research performance of the iits using wosandscopus bibliometric databases.curr. sci., 105 (8), 1134–1138. prathap, g. (2014). the performance of research-intensive higher educational institutions in india.curr. sci., 107(3), 389–396. safari, h., fagheyi, m.s., ahangari, s.s. &fathi, m.r. (2012). applying pomethee method based on entropy weight for supplier selection. business management and strategy, 3(1), issn 2157-6068. tyagi, p., yadav, s.p. & singh, s.p. (2009). relative performance of academic departments using dea with sensitivity analysis. evaluation and program planning, 32(2), 168-177. wang, y. m., & elhag, t. m. s. (2006). fuzzy topsis method based on alpha level sets with an application to bridge risk assessment. expert systems with applications. © 2019 by the authors. submitted for possible open access publication under the terms and conditions of the creative commons attribution (cc by) license (http://creativecommons.org/licenses/by/4.0/). plane thermoelastic waves in infinite half-space caused operational research in engineering sciences: theory and applications vol. 2, issue 3, 2019, pp. 92-106 issn: 2620-1607 eissn: 2620-1747 doi: https:// 10.31181/oresta1903092b * corresponding author. ibrahim.badi@hotmail.com (i. badi), ali.shetwan@eng.misuratau.edu.ly (a. shetwan), ali_hemeda@yahoo.com (a. hemeda) a grey-based assessment model to evaluate health-care waste treatment alternatives in libya ibrahim badia*, ali shetwana, ali hemedab a faculty of engineering, misurata university, libya b faculty of economics and political science, misurata university, libya received: 13 november 2019 accepted: 11 december 2019 first online: 16 december 2019 original scientific paper abstract. medical waste is a problem which haunts environmental officials, considering the many environmental and health risks it causes, as well economic losses. perhaps the single most important resolve that top management should consider as regards medical waste management is to select an appropriate technology to address it. such a decision is so complex because there are many criteria that decision-makers should take into consideration. the objective of this paper is to develop a grey based decision-making model for evaluating health-care waste treatment alternatives in libya. this was based on investigating the reality of medical waste management in libya by collecting data from the most important and largest public hospitals in the major libyan cities. these data were compiled through direct contact with these hospitals and from the libyan medical waste organization website. this paper makes trade-offs between four technologies used in waste treatment, according to five criteria. the results show that microwave is the best technology, followed by steam sterilization, while landfilling comes as the last option. key words: healthcare waste, environment, grey decision, management 1. introduction nowadays health-care waste (hcw) management has become a crucial public health and environmental issue particularly in developing countries. this is mainly due to direct result of industrial development and rapid population growth as well as the number and size of health care facilities (liu et al., 2015). hcw refers to a special category of waste generated by health care facilities and laboratory facilities operating in hospital settings (dursun et al., 2011a; liu et al., 2013). it typically includes infectious pathogens, toxic chemicals, heavy metals, etc., which is potentially hazardous to human health and the public environment (dursun et al., 2011a; who, 2004). according to the world health organization (who), wastes a grey-based assessment model to evaluate health-care waste treatment alternatives in libya 93 from health-care institutions can be classified into nine main categories as follows (prüss-üstün et al., 1999): − infectious waste: waste suspected to contain pathogens e.g. laboratory cultures, waste from isolation wards, tissues (swabs), materials, or equipment that have been in contact with infected patients, excreta; − pathological waste: recognizable body parts and contaminated animal carcasses; − sharps: sharp waste e.g. needles, infusion sets, scalpels, knives, blades, broken glass; − pharmaceutical waste: waste containing pharmaceuticals e.g. pharmaceuticals that are expired or no longer needed; items contaminated by or containing pharmaceuticals (bottles, boxes); − genotoxic waste: highly hazardous, mutagenic, teratogenic or carcinogenic, such as cytotoxic drugs used in cancer treatment and their metabolites; − chemical waste: waste containing chemical substances e.g. laboratory reagents, film developer, disinfectants that are expired or no longer needed, solvents; − wastes with high content of heavy metals: batteries, broken thermometers, blood-pressure gauges; − pressurized containers: gas cylinders, gas cartridges, aerosol cans; − radioactive waste: such as glassware contaminated with radioactive diagnostic material or radio therapeutic materials. who has advocated that hospital waste is considered as special waste and it is now acknowledged that certain categories of medical waste are among the most hazardous and potentially dangerous of all waste arising in communities (who, 2004). improper waste management can cause environmental pollution and numerous harmful diseases to the human being. therefore, how to select safe and effective treatments and disposal of hcw is significantly important for the public health and human well-being. in the literature, a number of studies have been conducted in various contexts to assess hcw management practices. these studies used a variety of methods and techniques to manage hcw. on one side, a number of studies have been developed based on adopting the prepared questionnaires, field research and personnel interviews (hangulu and akintola, 2017; patwary et al., 2011; manga et al., 2011). on the other side, the selection of the best treatment and disposal technology for hcw management can be considered as a complex multi-criteria decision making (mcdm) problem and requires an extensive evaluation process of the potential disposal practices. many potential evaluation criteria, such as economic, technical, environmental and social criteria and their related sub-criteria, must be considered in the selection procedure of a hcw treatment alternative (dursun et al., 2011a; dursun et al., 2011b; kazimieras zavadskas et al., 2016; iglesias et al., 2008). therefore, classical mcdm techniques, such as analytic hierarchy process (ahp), have been applied to many case studies for assessment of technologies used for hospital waste management (brent et al., 2007; karamouz et al., 2007; hsu et al., 2008; karagiannidis et al., 2010). some researches were conducted using grey theory (thakur and ramesh, 2015), or a hybrid grey-ahp approach to select the best hcw treatment method (thakur and ramesh, 2017). badi et al./oper. res. eng. sci. theor. appl. 2 (3) (2019) 92-106 94 due to the complicated relationships among the multiple and hierarchical evaluation criteria, efficient decision models are required to select the most appropriate hcw treatment technology. hence, many approaches were presented and incorporated to trade-off multiple conflicting criteria with the involvement of a group of decision makers, such as, the visekriterijumska optimizacija i kompromisno resenje (vikor), multi-objective optimization by ratio analysis plus full multiplicative form (multimoora), technique for order preference by similarity to an ideal solution (topsis) (liu et al., 2013; liu et al., 2014; lu et al., 2016). in real life, decision making problems are evaluated by the experts based on the ratings of alternatives and the relative weights of criteria by utilizing the linguistic terms rather than the numerical values. this is because the decision makers’ judgments are usually vague and the linguistic terms are more intuitive for them to express the preferences (liu et al., 2014; lu et al., 2016). furthermore, decision makers express their personal assessments based on using multigranularity linguistic term sets (liu et al., 2014; lu et al., 2016; morente-molinera et al., 2015). therefore the potential assessment of hcw disposal cannot be quantified precisely where they are qualitative in nature. in many developing countries, medical wastes are still handled and disposed of together with other domestic wastes, thus posing significant health risks to municipal workers, the general population and the environment (who, 2004; patwary et al., 2011). according to a survey of the who on hcw management in 22 developing countries, the proportion of health care institutions with inappropriate waste disposal methods was between 18% and 64% (who, 2004). a study conducted in sudan identified that the hcw management practices observed in khartoum state hospitals were not fully safe and have harmful environmental effects, which was characterized by absence of continuous segregation, collection, transportation and final disposal methods of pathological and other medical wastes (ahmed et al., 2014). in ethiopia, like other african countries health care wastes in different hospitals are managed improperly. a study conducted in debre birhan zonal hospital identified that healthcare wastes were stored, collected, transported and disposed in a manner that creates health problems to the health worker, waste handler and the community (esubalew, 2007). in ghana, a study analyzed the healthcare waste management practices in the greater accra region, ghana. it was concluded that healthcare centers in the greater accra region do not abide to the accepted healthcare waste management policy of ghana (asante et al., 2014). in nigeria, a study conducted to assess the hcw management practices by hospital staff. the study involved the survey of a cross section of four tertiary health institutions. the study showed that there is significant variation in healthcare waste management practices and the sustainability factors. it was found that that the health institutions adopts minimal activities of recycling, reduce and reuse, although not regularly (uwa, 2014). in libya, very few studies on hospital waste have been conducted (altabet, 2004; alhamroush and altabet, 2005; sawalem et al., 2009). these studies are concerned with the classification of waste and present practices such as available procedures, techniques, and methods of handling and disposing of hospital waste. as can be noted that none of the previous studies investigated the evaluation of hcw management methods. despite libya having issued a number of laws and rulings regarding environmental issues, but these do not include specific mandates concerning the management of hcw (sawalem et al., 2009). in fact, there are no clearly defined regulations about the proper management of hcw in libya. as a grey-based assessment model to evaluate health-care waste treatment alternatives in libya 95 mentioned earlier, medical wastes in libya are also treated and disposed together with other domestic wastes. therefore, an appraisal of the current situation regarding hospital waste management in libya is essential. the aim of this work is to use a grey based assessment approach to find a compromised priority ranking of treatment alternatives according to the established criteria for a disposal method selection problem in hcw management. the rest of this paper is organized as follows: the situation of medical waste management in libya is provided in section 2. in section 3, a grey system theory is introduced. the case study for evaluating hcw treatment alternatives for libya is addressed in section 4. in section 5, results are provided along with discussion focusing on comparative analysis. finally, conclusions and directions for future research are given in section 6. 2. medical waste management situation in libya there are several methods of healthcare waste treatment such as incineration, steam sterilization, microwaving, landfilling, mechanical/ chemical disinfection, and plasma pyrolysis. each of them has its own advantages and disadvantages. healthcare waste incineration has been the major technique used in many countries, for many years, to dispose of medical waste. it is characterized by its relatively low financial cost in comparison with some other known waste treatment techniques. also, it reduces the remaining waste volumes, which is very important for countries producing enormous amounts of waste and suffering from insufficient space and land for use in sanitary land filling (ghasemi and yusuff, 2016). another important advantage of incinerators is that there is no need for waste segregation that would entail additional costs, as incineration process can almost dispose of certain types of waste arising from hospitals. by contrast, there are several constraints on incinerating and landfilling healthcare wastes as such waste can be a major source of dioxin and furan pollution that may pose health problems (ghasemi and yusuff, 2016). some countries have begun to abandon the use of these technologies because of the health risks that it may cause to employees or to people living nearby, and also for its impact on the environment. in libya, in the late 1970s and early 1980s, the authorities emphasized the need for, at least, one incinerator as a condition for building new hospitals (mwo, 2019). in this study, to investigate current practices of medical waste management in some hospitals in libya, data was collected from 11 public hospitals of 8 cities in different regions of libya which shown in figure 1. the data was collected through direct contact with those hospitals and from libyan medical waste organization (mwo). it was found that all hospitals have installed incinerators for medical waste disposal, but are no longer used as a result of aging of incinerators, smoke emission and complaints from residents. currently, the common types of medical waste disposal methods used by hospitals is collecting medical waste from the hospital in the backyard and is then burnt in open air or disposed in municipal dumps. this study uses a grey-based approach to select the best techniques for treating health care waste. decision makers’ comparison judgments and extent analysis method is used to decide the final priority of different decision criteria. to the best badi et al./oper. res. eng. sci. theor. appl. 2 (3) (2019) 92-106 96 knowledge of the authors, there is no literature for medical waste treatment technique selection in libya. an attempt in this regard could enhance decision makers for selecting the best techniques for healthcare waste treatment. figure 1: distribution of hospitals for the case study in libya 3. grey systems theory the multi-criteria decision making (mcdm) problems have received considerable attention from various researchers recently (roy et al., 2018; đorđević et al., 2019; anthony et al., 2019). the grey systems theory, introduced by deng in the early 1980s (deng, 1982), is a methodology that used to solve problems involving incomplete information or small samples (eshtaiwi et al., 2017). the technique works on uncertain systems with partially known information by generating, mining, and extracting useful information from available data (badi et al., 2018). grey theory considers that although the objective system appears complex, with a small amount of data, it always has some internal laws governing the existence of the system and its operation (liu et al., 2010). it uses a black-grey-white colour to describe complex systems. a grey number is a kind of figure that we only know the range of values, and do not know an exact value (liu et al., 2012; abdulshahed et al., 2017). this number can be an interval or a general number set to represent the degree of uncertainty of information. grey systems theory in a decision-making process is very useful, and could be used to tackle the disadvantage of ahp. this section describes the basics about grey systems theory and grey numbers in order to understand the model. a grey-based assessment model to evaluate health-care waste treatment alternatives in libya 97 3.1 definition of grey number let x is the universal set. then a grey set g of x is defined by its two mappings and : : and : such that , since the lower limit and upper limit can possibly be estimated, g is defined as an interval grey number where . let t be the information, the upper, the lower limit then if then is a white number with a crisp value which shows the existence of full knowledge. on the contrary, a black number is a grey number one known nothing about it (liu et al., 2012). 3.2 basic operations on grey numbers the arithmetic of grey numbers is similar to interval value (liu et al., 2012; li et al., 2007) and the operation rules of general grey numbers can be defined as operation rules of real numbers (abdulshahed et al., 2017). addition: subtraction: multiplication: division: length of grey number: comparison of grey numbers: the possibility degree of two grey numbers is expressed as: where according to this comparison of two grey numbers, there may be four distinct outcomes: if then if then if then if then otherwise if then 3.3 the grey model step 1. determine the attribute weights: attribute weight can be calculated as follows (li et al., 2007): (1) (2) badi et al./oper. res. eng. sci. theor. appl. 2 (3) (2019) 92-106 98 step 2. alternatives evaluated by the decision makers: decision makers use linguistic or verbal variables when evaluating alternatives according to various attributes. is the attribute value given by the kth decision maker to any attribute value of the alternative. in grey system this value is shown as, and computed as: step 3. the construction of grey decision matrix: (3) step 4. the normalization of decision matrix: (4) for a benefit attribute is expressed as where and for a cost attribute is expressed as where . step 5. weighted normalized grey decision matrix normalized matrix is weighted by the process which establishes the weighted normalized grey decision matrix . (5) step 6: determine the ideal alternative from a set m alternatives, , the ideal alternative is determined by: step 7. calculate the grey possibility degree the grey possibility degree can be obtained by comparing ideal alternatives and possible alternatives . step 8. rank the order of alternatives a grey-based assessment model to evaluate health-care waste treatment alternatives in libya 99 rank order of the alternatives according to the grey possibility degree determined in the 7th step. the smaller the grey possibility degree the better is the rank order of si. otherwise, the rank order is worse. 4. case study the qualitative criteria used for the medical waste treatment technique selection in this research are: net cost per ton, waste residuals, release with health effects, treatment effectiveness, and public acceptance. table (1) shows the description of these criteria. table 1. criteria description criterion description waste residuals describes the material that remains after the process of waste treatment has taken place. release with health effects refers to health effects related to the exposure to the treatment technique. treatment effectiveness relates to how well a treatment works in practice or real life. net cost per ton defines the net cost per ton. public acceptance refers to the active or passive approval of a certain technology or policy. a questionnaire was prepared and distributed to four experts who work in different areas related to the medical waste. the first three criteria are cost criteria, while the last two are benefit. the experts have been invited to participate in the determination of the importance of each criterion. the linguistic variables can be expressed in grey numbers by a scale shown in table 2. the waste treatment techniques were rated for their performances of attributes on grey scales shown in table 3. table 2. the importance of grey number for the weights of the attribute. importance abbreviation scale of grey number very low vl [0.0, 0.1] low l [0.1, 0.3] medium low ml [0.3, 0.4] medium m [0.4, 0.5] medium high mh [0.5, 0.6] high h [0.6, 0.8] very high vh [0.8, 1.0] table 3. linguistic assessment and the associated grey values. badi et al./oper. res. eng. sci. theor. appl. 2 (3) (2019) 92-106 100 performance abbreviation scale of grey number very poor vp [0.0, 1.0] poor p [1.0, 3.0] medium poor mp [3.0, 4.0] fair f [4.0, 5.0] medium good mg [5.0, 6.0] good g [6.0, 8.0] very good vg [8.0, 10.] the evaluation of the criteria given by the experts by using linguistic variables was collected, as shown in table 4. next, the attributes can be weighted using equation (1). table 4. the linguistic assessment of the attributes by experts. ci expert #1 expert #2 expert #3 expert #4 whitening degree c1 h m mh mh 0.50 0.63 0.56 c2 vh mh h h 0.63 0.80 0.71 c3 vh vh vh h 0.75 0.95 0.85 c4 h h vh h 0.65 0.85 0.75 c5 m vh mh l 0.45 0.60 0.53 table 5 shows the linguistic assessment of the waste treatment techniques which have done by the experts. transform the linguistic variables into grey numbers according to scales of grey numbers, equation (3). by the assessment of the consequences, grey decision matrix d is calculated. the normalization of decision matrix “d” to make the grey elements lying between 0 and 1 as follows: table 5. experts views on waste treatment techniques selection criterion. cj technique expert #1 expert #2 expert #3 expert#4  gij c1 incineration g g f mg [5.25 6.75] steam sterilization p mp f mp [2.75 4.00] microwave p f p p [1.75 3.50] landfill vg mp vg mg [6.00 7.50] c2 incineration f vg mp vp [3.75 5.00] steam sterilization vg g g vp [5.00 6.75] microwave g g g p [4.75 6.75] landfill f p p g [3.00 4.75] c3 incineration p vp p vp [0.50 2.00] steam sterilization g vg g mg [6.25 8.00] microwave g vg g p [5.25 7.25] landfill f vp vp f [2.00 3.00] a grey-based assessment model to evaluate health-care waste treatment alternatives in libya 101 c4 incineration g vg g f [6.00 7.75] steam sterilization g g vg vg [7.00 9.00] microwave g vg vg p [5.75 7.75] landfill g vp p f [2.75 4.25] c5 incineration p vp vp g [1.75 3.25] steam sterilization vg vg g g [7.00 9.00] microwave vg vg vg p [6.25 8.25] landfill f vp g g [4.00 5.50] the next step is to calculate the weights of the criterion using equation (5); by grey multiplication of weights assigned to criterion with the corresponding elements of normalized grey decision matrix. the grey possibility degree of the waste treatment techniques for every criterion is determined with reference to the ideal technique . the is obtained as shown below: every technique is compared with the to determine the final crisp value (grey possibility degree). the different values of grey possibility degree of the four different techniques were denoted by incineration, landfilling, microwave, and steam respectively. the result of the comparison is as follows: = 0.758 =0.719 =0.717 =0.884 the final step is to sort the techniques according to their grey possibility degree in descending order: closer to the centre point (i.e., zero), better the rank order. according to the probability degree obtained in last step, the rank order will be as follows: 5. discussion the evaluation of four hcw treatment alternatives for libya using a grey based decision making approach yields to microwave as the best treatment method. the microwave is the preferred alternative treatment method for the case study since it minimizes the impact on the environment and demonstrates a commitment to public health. it has also relatively low investment and operating cost when compared with other treatment alternatives. it can be said that medical waste management in the libyan hospitals and health centers is in a very bad situation. even though they often have incinerators to incinerate these wastes, this does not seem to be effective in fact. most of these incinerators have, in reality, been abandoned or used for short periods of time and badi et al./oper. res. eng. sci. theor. appl. 2 (3) (2019) 92-106 102 then neglected. people dealing with these incinerators are usually janitors who are mostly not qualified in this field. moreover, maintenance work is almost nonexistent, often with insufficient maintenance plans and shortages of spare parts. it should also be noted that appropriate types of incinerators are not selected on the basis of their size and absorption of the waste quantities expected to be generated at hospitals, or the temperatures they can reach. choosing small and inadequate incinerators for waste quantities generated has resulted in the exhaustion of these incinerators, due to their overuse, combined with a lack of maintenance. with the increase in complaints from residents living near hospitals about these incinerators plus the causes mentioned above, hospital officials are led to resort to the easiest solutions, which would be to transport medical waste along with municipal solid waste and dump them at open dumping, with consequent significant environmental risks. in fact, studies state that municipal solid waste dumps are often beyond control and waste is treated by burning, burying, or even left in open air without taking any action (badi et al., 2019). inappropriate ways of handling solid wastes have resulted in many environmental and health problems, in terms of proliferation of diseases by viruses and micro-organisms, as well as contamination of ground water by untreated medical waste in landfills. therefore, the problems associated with treatment of hcw should be solved in a manner that minimizes the risks to the public health and human well-being, and the damage to the environment. the results obtained in this paper are consistent with those produced by dursun et al (dursun et al., 2011b). as is pointed out in (dursun et al., 2011b), non-incineration alternative technologies, such as steam sterilization and microwave, are placed in the first and second rankings in view of the fact that they appear to emit fewer pollutants and generate non-hazardous residues. furthermore, abd el-salam indicated that incineration is not an accepted treatment method for solid medical waste due to the risks associated with (el-salam, 2010). this paper highlights a standard model that decision makers in the country may benefit from, as it can help them make appropriate resolutions about these issues by choosing, from a range of methods, the most appropriate treatment technology. this conclusion has been reached on the basis of opinions provided by a group of experts in the field of environment and management of medical waste. finally, this standard model can be generalized especially for those countries with similar circumstances to ours. the outcome of the work has been analysed to provide the decision makers with valuable tool to select the best technique. according to the results in equation error! reference source not found., microwave is the most preferred technique, because it has the lowest weight, while steam sterilization is the next recommended technique. the difference between weights of microwave and steam sterilization is small, so it is possible to use either one of them. 6. conclusion health-care waste management problem has been increasing fast caused by the development of urbanization, particularly in developing countries. the aim of this paper is, for the first time, a methodology using a grey based decision making approach is used for evaluating hcw treatment alternatives in libya. this is an important and urgent decision needs to be taken, while the only way for treatment methods now is to dump and burn the wastes in open spaces. in this regard, a a grey-based assessment model to evaluate health-care waste treatment alternatives in libya 103 systematic decision making technique with an emphasis on opinion of experts who work in health care and environment sectors was conducted. the results of this study show that microwave is the 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(2016). hybrid multiple criteria decision making methods: a review of applications in engineering. scientia iranica, 23, 1-20. © 2019 by the authors. submitted for possible open access publication under the terms and conditions of the creative commons attribution (cc by) license (http://creativecommons.org/licenses/by/4.0/). operational research in engineering sciences: theory and applications vol. 5, issue 3, 2022, pp. 194-209 issn: 2620-1607 eissn: 2620-1747 doi: https://doi.org/10.31181/oresta221122151h * corresponding author. zahrahassanzadeh.s@gmail.com (z. hassanzadeh), irajarashrediffmail.com (i. mahdavi), ali_tajdin@yahoo.com (a. tajdin), h.fazl@du.ac.ir (h. fazlollahtabar) designing a sustainable logistics model with a heterogeneous collaboration approach zahra hassanzadeh1, iraj mahdavi1, ali tajdin1, hamed fazlollahtabar 2* 1 department of industrial engineering, mazandaran university of science and technology, babol, iran 2 department of industrial engineering, school of engineering, damghan university, damghan, iran received: 17 august 2022 accepted: 14 november 2022 first online: 22 november 2022 research paper abstract: this paper aims at designing a sustainable logistics model with a heterogeneous collaboration approach. in this regard, we worked on a logistics system by transmitting raw materials to a factory and then sending various products to consumption centers. accordingly, three logistics layers of supply, production, and consumption were designed and the parameters of collaboration within and between the logistics layers were evaluated. after that, as novelty of our paper, the interactions of sustainability indicators with the logistics network and their effects on the collaboration were analyzed through productivity. in this paper, we use two objectives includes minimizing the supply chain costs and maximizing the productivity of the collaboration parameter affecting the sustainability indicators at different levels. finally, the developed mathematical model is solved and validated in gams optimization software to analyze the performance of the proposed approach using epsilon constraint method. key words: sustainable logistic model, heterogeneous collaboration, epsilon constraint method, multi-level model 1. introduction today, rapid developments and changes have led organizations to research logistics and supply chain to overcome their uncertain environment. supply chain management is a two-way interaction with new technologies such as outsourcing, lean logistics, virtual logistics, etc. this volume of theory shows that different organizations consider the major significance of supply chain and logistics (shafizadeh, 2004). in 2021, the global logistics industry that hit from covid-19 designing a sustainable logistics model with a heterogeneous collaboration approach 195 pandemic, recovered with market size of 8.43 trillion euros approximately. by 2027, the logistics industry scale is forecasted to exceed 13.7 billion euros that is very huge value (data gathered from statista1). logistics is a big part of the supply chain, which includes matters related to supply, transportation, storage, distribution, etc. logistics and supply chain variables can be used to assess the logistics status of an organization (david et al., 2004). figure 1 show the north american net revenue of leading logistics companies in the united states in 2021. figure 1the north american net revenue of leading logistics companies in the united states in 2021 today, with improvements in production processes, many industry executives have realized that improving internal processes and flexibility in just the company's capabilities is not enough to stay in the market. rather, suppliers of parts and materials must produce the required supplies with the best quality and lowest cost; in addition, distributors of products must be closely related to the development policies of the producer market (kazimieras zavadskas et al., 2020). with such an attitude, logistics, supply chain, and supply chain management approaches have emerged. logistics is a planning orientation and a framework that seeks to create a unique program for the production and flow of information through businesses. the concept of supply chain management is presented after this approach and seeks to create the link and coordination between the processes of other organizations in this 1 https://www.statista.com/ hassanzadeh et al./oper. res. eng. sci. theor. appl. 5(3)2022 194-209 196 linking line (zakeri et al., 2015). logistics processes directly or indirectly affect almost all areas of activity in the industry sector. in this regard, coordination is a strategic response to the challenge posed by supply chain partners. coordination is the act of controlling the institutions' affiliations by working together to achieve mutually defined goals. the benefits of coordination include better use of resources, reduced operating costs, increased profits, improved customer satisfaction, and increased productivity in developing productions (kassami et al., 2022). the concept of collaboration is both linked to supply chain coordination and seen as a complementary aspect of a comprehensive concept of coordination. collaboration can be between members of a supply chain or between multiple supply chains. it occurs when several organizations and companies work together and engage in normal business relationships. it is the response to the fact that organizations and companies cannot separately solve common problems to achieve the expected performance indicators (nu et al., 2004). the concept of sustainability led to the formation of a new approach to designing logistics networks. evidently, there are sustainability dimensions that lead to the formation of differences when comparing general logistics networks. it is the use of various resources to meet the needs of the present generation industries without jeopardizing the ability of the next generation. sustainable supply chain management comprises all dimensions of sustainability, including economic, environmental, and social dimensions. these processes include the entire life cycle of an organization or factory supply chain from the purchase of raw materials to the stage of product design and development, storage and distribution, and finally, the delivery of the final product. the important features of sustainable supply chain management are the sustainability based on environment and social responsibility (hassanpour and pamucar, 2019). therefore, by taking the sustainability of the supply chain and financial profitability into account, disadvantageous environmental effects and social effects can be decreased. the most important aspects of sustainability are the economic dimension, which deals directly with cost and benefit parameters. in logistics networks, economic decision-making concerning costs leads to a profitable optimal design. another important dimension of sustainability is the environmental dimension, which is generally focused on clean air and land, as well as the reduction of any pollution or encroachment on nature. the main difference between general logistics networks and sustainable logistics networks is the focus on the pollution caused by the transport fleet. accordingly, in a sustainable logistics network, transmission routes and the location of logistics facilities in nature are designed with an environmental approach. another dimension is the social factor which includes partner satisfaction, coordination, and collaboration leading to greater sustainability. on the other hand, in today's business world, influenced by the globalization of markets, there is a basic need to understand customers’ changes to maintain the sustainability of systems. as a result, companies are constantly looking for new strategies to improve their logistics performance and ensure their competitiveness in today's market (allaoui, et al., 2020), especially in the distribution network of their goods, which represents a key component in all supply chains (williamser et al., 2019). in this regard, logistics collaboration is deemed as one of the most effective mechanisms for companies that want to increase their logistic efficiency and achieve their goals of economic, environmental, and social sustainability (vanovermeire, & designing a sustainable logistics model with a heterogeneous collaboration approach 197 sörensen, 2017; jouida et al., 2014). collaboration is critical to the success of sustainable logistics operations. modern logistics systems are under increasing pressure to achieve environmental goals, reduce rush hours, and make parking spaces and vehicles accessible. for example, regulations on the timing, access, and size of cars, areas, timing, and size of vehicles restrict cargo delivery. similarly, tax relief policies may encourage people to use vehicles consuming clean energy or apply methods of distributing energy-efficient goods. under these circumstances, it seems that collaboration is a logical and performable strategy for many logistics systems to create sustainability and achieve operational performance as well as successfully achieve environmental goals (soysal et al., 2018). accordingly, the concepts of collaboration and sustainability are very important in supply chain and logistics networks. therefore, this study aims at designing a sustainable multilevel logistics model with a heterogeneous participation approach based on the uncertainty approach. in order words, in this study we use two objectives includes minimizing the supply chain costs and maximizing the productivity of the collaboration parameter affecting the sustainability indicators at different levels. in this study, coordinated sustainable logistics is taken into account in terms of economic factors (time and cost), social factors (general consumer satisfaction and 3pl system satisfaction), and environmental factors (co2, vehicle depreciation, and less damage to natural resources). also, in this study, collaboration is considered between members of the supply chain and between layers of the supply chain. the parameters of collaboration in this research include communication, bargaining power, and opportunism. the research design consists of different sections including section 2, in which previous studies will be reviewed and the research gap will be illustrated. then, in section 3, the research problem is stated. in section 4, the developed model will be reviewed and in the next section, i.e., section 5, the operation of the model will be examined and analyzed using a real example in gamz software, and sensitivity analysis will be performed. finally, in section 6, the research results will be discussed. 2. literature review liotta et al. (2014) developed a new solution method based on optimization and simulation for multilevel production and transportation problems with precise dynamic distribution schemes under the influence of demand uncertainty. the objective function of the optimization model, the costs of supply, production, transportation, and emission of co2 as well as collaboration in a multilevel network are all taken into account. in this research, the computational experiments are based on real samples. the results showed that the developed approach can be effectively used for co2 emission swap analysis, the effects of demand uncertainty, and joint distribution strategies on the economic and environmental function of supply chains. reverse logistics (rl) can be applied as a proper tool and technique to achieve loyalty and satisfaction of customer and also decrease operating costs with maximizing the used products recovery. nowadays, industries face different problems that is as a barrier to suitable implementation of rl, including lack of financial constraints, capabilities, facilities, and market constraints. basiri et al. (2017) examined the subject of green channel coordination in a twostage supply chain (sc). demand for the products is a function of the retail price, the hassanzadeh et al./oper. res. eng. sci. theor. appl. 5(3)2022 194-209 198 green quality of the products, and the efforts of the retailer. both the retail price and the amount of effort for selling the green product are determined by the retailer, while the green quality of the product is a variable of the manufacturer. three decision scenarios are modeled and compared: (1) a non-integrated scenario in which each member decides independently based on their benefits, (2) an integrated scenario in which there is one decision-maker in the system, and (3) a participatory scenario in which the goal is to increase the channel's overall profit provided that pareto is improved for each member. numerical studies showed that the proposed collaboration model can increase sc profit almost close to the integrated model; it also guarantees higher profits for both channel members than that of the nonintegrated decision-making scenario. vargas et al. (2020) proposed a freight share laboratory platform (fslp) and introduced its embedded business model intending to facilitate and encourage horizontal collaboration in transportation logistics. the idea of fslp is to create collaborative clusters of transport operators and related joint operational plans, through specialized decision support algorithms and multi-fleet optimization. in addition, a profit-sharing business model embedded in fslp algorithms guarantees that participants, mainly logistics service providers and transport operators, can maintain their profit margins and fairly share the profits of the partnership. a case study focusing on a major uk transport operator is presented to evaluate key fslp algorithms in a real-world context. the results show the potential for significant financial and environmental benefits to industry and society. aloui et al. (2019) proposed a joint decision-making method for planning of the sustainable supply chain. this structure improves the development of multilateral partnerships across a network in order to improve the sustainability of the offered products. the platform supports the new ict system and creates an insightful platform for infrastructure. the proposed decision support system simultaneously offers collaboration and sustainability capabilities that are not available in many supply chain planning systems. konstantakopoulos et al. (2021) describe a sustainable approach in which logistics companies collaborate in routing and scheduling operations by sharing fleets and resources. to estimate the improvement in the system, in terms of pollution and cost reduction, the state in which companies operate independently is compared to the state of partnership. the data used in their study are derived from the daily distribution cases encountered by third-party logistics companies in greece. these are examined daily by a meta-heuristic algorithm, either separately to study how they work today, or jointly to determine common benefits. given that sustainability in different aspects has become increasingly important in today's supply chain, emamian et al. (2021) presented an integrated model for production routing in the sustainable closed-loop supply chain. a three-objective mathematical model is also proposed for minimizing supply chain costs, maximizing social responsibility, and ultimately minimizing environmental emissions. the data of proposed method analyzed for different scales groups with considering the bco technique. also, the results of this mentioned method eventually compared with the experimental results of nsga-ii technique for different features for example quality, variability, and distance as well as execution time to solution. mancini et al. (2021) investigated a centrally organized multi-period partnership automobile routing problem in which telecommunications companies could exchange customers who regularly need services. in addition, telecommunications companies may only be willing to cooperate if a minimum market share can be guaranteed. to consider all designing a sustainable logistics model with a heterogeneous collaboration approach 199 these issues, the matter of common automobile routing was proposed while considering the sustainability of time and service. an iterative local search algorithm was used to solve the developed model. they showed that both methods reach nearoptimal solutions in very short computational times. ding et al. (2018) develop a model for examining the opportunity to outsource a pollutant reduction service to overcome environmental constraints. the service supply chain consists of a coal-fired power plant (end user) and a pollution reduction service provider that the former outsources the services to the latter. they studied the profit improvement policy of this service supply chain according to which, profit allocation is made through outsourcing price negotiations between the two partners. the results showed that the price of outsourcing green services is related to the government's incentive policy that defines the shares of two partners. finally, they hey examined the integration of complex factors affecting supply chain cooperation, such as green services, profitsharing and etc. the concept of emergency energy supply chain collaboration has become a business necessity with various energy trading organizations so that its problems could be solved in consensus. jiang (2020), developed an intelligent model for emergency power supply chain cooperation, which bridges the gap between optimizing emergency supply chain collaboration with consensus decision-making and reinforcement learning. the simulation results show that the proposed model has a significantly less running time of 40%, reducing the minimum cost of energy recovery by 7% and co2 emissions by an average of 10.8%. the two-tier supply chain model consists of two separate components with different purposes. yaldim et al. (2022), provided a model of a two-tier supply chain consisting of a supplier, a retailer, and a product in a drug supply chain (p-sc). the main goal of their proposed model is to maximize the profit of whole of the supply chain. akbari-kasgari et al. (2022) designed a new supply chain based on resilience and sustainable concepts in copper industry. aloui et al. (2022) proposed the integrated planning problem to design two-echelon green logistics model based on collaborative and non-collaborative conditions. they assess the benefits of collaboration between different layers in integrated transportation optimization. anes et al. (2022) developed a new model for evaluating risk value in logistics companies with considering collaborative networks. proposed model increases the sustainability of collaborative model in the logistics network by reducing reputational risk. in another research, mishra et al. (2022) investigated a new structure to environmental collaboration between logistic network layers to consider sustainability in production. the sale takes place in a drug retailer and the demand is random and the order periods are determined by the number of visits by the drug supplier. by considering these visits, the drug retailer follows a periodic review inventory model. for the retailer, the decision variable is the safety factor, which is determined by the level of the announced order. the problem stated in this paper was optimized with two different scenarios and two different models: the traditional sc model and the two-tier supply chain model. table 1 presents the studies conducted by research indicators. hassanzadeh et al./oper. res. eng. sci. theor. appl. 5(3)2022 194-209 200 table 1. literature review author(s) year logistics mathematical model collaboration sustainability singlepurpose multipurpose environmental economic social 1 lyut et al. 2014    2 basiri et al. 2017    3 vargas et al. 2020      4 alvi et al. 2019     5 constantako -poulos et al. 2021      6 imams et al. 2021      7 mansini et al. 2021    8 ding et al. 2018      9 jiang et al. 2020      10 yildet al. 2022    11 akbarikasgari et al. 2022      12 aloui et al. 2022      13 anes et al. 2022     14 mishra et al. 2022     15 present study       according to the studies given in table (1), it is recognized that collaboration and sustainability in all dimensions have been less addressed simultaneously. also, due to the importance of collaboration in logistics systems and its impact on sustainability in economic, social, and environmental dimensions, the previous research has not addressed the role of intra-layer and inter-layer collaboration at all levels. also, the gap of studied research show that the collaboration parameter affecting the sustainability indicators are not considered at different levels of supply chain. therefore, in the present study, it is dealt with designing a sustainable logistics network with a heterogeneous participation approach in which the issue of intralayer and inter-layer collaboration at different levels of the supply chain and its impact on supply chain sustainability have been considered under conditions of uncertainty. 3. statement of the problem logistics is a planning orientation and framework that seeks to create a unique program for the production and flow of information through a business. supply chain management is created after this framework and aims at achieving links and coordination between the processes of other organizations in this link line. logistics processes directly or indirectly affect almost all areas of human activity. one of the important subjects of logistics processes is coordination within the overall structure of the supply chain. coordination is the act of controlling the dependencies of an institution by working together to achieve mutually defined goals. supply chain coordination can be supported through functions such as forecasting, production management, maintenance management, distribution, and transportation management, product design, and upstream and downstream interfaces. it may also be related to simple activities. collaboration can be between members of the supply chain or between layers of the supply chain. such collaboration occurs when several organizations and companies work together and engage in normal business designing a sustainable logistics model with a heterogeneous collaboration approach 201 relationships. it is the answer when organizations and companies alone cannot find solutions for common problems to achieve the expected performance indicators. on the other hand, the concept of sustainability led to the formation of a new paradigm in the design of logistics networks. clearly, there are sustainability dimensions that lead to the formation of differences compared to general logistics networks. the most important dimension of sustainability is the economic dimension, which deals directly with cost and benefit parameters. in logistics networks, economic decision-making concerning costs leads to a profitable optimal design. another important dimension is the environmental one, which is generally focused on clean air and land and the reduction of any pollution or encroachment on nature. one of the differences between general logistics networks and sustainable logistics networks is the special focus on the pollution of the transport fleet. additionally, the design of transport routes and location of logistics facilities in nature is created with an environmental approach in a sustainable logistics network. another dimension is the sustainability of the social factor, including the satisfaction of partners, coordination, and collaboration that leads to greater sustainability. the proposed model in the present study deals with the design of a sustainable logistics network with a heterogeneous collaboration approach. in other words, due to the necessity to reduce environmental hazards such as greenhouse gas emissions, use of natural resources, energy consumption, costs such as transportation, and delay in operations, and also to increase access to facilities, the concept of designing a sustainable multilevel logistics network with a heterogeneous collaboration approach is investigated. accordingly, the logistics system is designed based on sending raw materials to the factory and then sending different products to consumption centers. the main purpose of this study is to investigate the effect of the collaboration parameter on sustainability indicators for nodes within a layer and between different layers of the supply chain. the proposed model has two objectives, the first target function includes minimizing the supply chain costs and the second one is to maximize the productivity of the collaboration parameter affecting the sustainability indicators at different levels. in this study, coordinated sustainable logistics is taken into account in terms of economic factors (time and cost), social factors (general consumer satisfaction and 3pl system satisfaction), and environmental factors (co2, vehicle depreciation, and less damage to natural resources). also, the parameters of collaboration in this research include communication, bargaining power, and opportunism. communication indicator ensures that tasks are augmented and transferred from one point to the other without delay. in addition, the bargaining power index refers to the pressure that suppliers can put on different firms by decreasing the availability of their products, increasing their prices, or lowering their quality. the opportunism index also is defined as behavior that is self-interest seeking with guile. it is manifested in behaviors such as stealing, cheating, dishonesty, and withholding information. essentially, these concepts lead institutions to cooperate (doodi et al., 2016). hassanzadeh et al./oper. res. eng. sci. theor. appl. 5(3)2022 194-209 202 4. the developed mathematical model in this section, the developed model will be described. 4.1. indices: index for nods 1, ...,i i 1, ...,j j , 1, ...,i i  index for layer 1, ...,k k  , 1, ...,k k index for collaboration parameter 1, ...,w w index for sustainability indices 1, ...,s s 4.2. variables: 1 : 0 ws x ikjk    if collaboration parameter w is established about sustainability index s with node i in layer k and node j in layer k’ 1 : 0 ws y ii k    if node i with node i’ in layer k has a collaboration parameter w about sustainability index s 4.3. parameters: ws b budget available to establish the collaboration parameter w affecting the sustainability index s ws ii k p  the efficiency of collaboration parameter w affecting the sustainability index s between nodes i and i’ in layer k ws ikjk p  the efficiency of collaboration parameter w affecting the sustainability index s from node i in layer k to node j in layer k’ w s ik a the degree of collaboration w affecting the sustainability index s for node i in layer k ws ii k ca  collaboration capacity of collaboration parameter w affecting the sustainability index s between nodes i and i’ in layer k ws ikjk ca  collaboration capacity of collaboration parameter w affecting the sustainability index s from node i in layer k to node j in layer k’ ws ii k c  cost of creating the collaboration parameter w affecting the sustainability index s between nodes i and i’ in layer k ws ikjk c  cost of creating the collaboration parameter w affecting the sustainability index s from node i in layer k to node j in layer k’ 4.4. mathematical model: 1 1 1 1 1 1 1 min . . i k j k i i k i k j k i i k ws wsws ws z c cx yikjk ii kikjk ii k                    (1) 2 1 1 1 1 1 1 max . . i k j k i i k i k j k i i k ws wsws ws z p px yikjk ii kikjk ii k                    (2) designing a sustainable logistics model with a heterogeneous collaboration approach 203 s.t. 1 , ' 1 ws k k k kx ikjks wi j i          (3) 1 ws ky ii ks wi i i       (4) ,. . 1 ws ws ws wsws b w sx yc cikjk ii ki j i ii kk k kk k i iikjk                 (5) ,. ' 1 ' 1 ws ws ws ca w sx ikjkaiki j ikjkk k k k i k k j k k               (6) ,. ' ws wsws w sy caii kaiki iii k ik ki         (7) 1 , ,. '' 1 ws ws i k k wx y ikjksjk k i ii k        (8) 0 ' ws x ikjk  kkjiwsk  ',,,,,1 (9)  , 0,1 ws ws x yikjk ii k   (10) 4.5. model description: this research consists of a two-objective mathematical model. the first target function represents the minimization of the total costs created by the collaboration parameter effective on the sustainability index between and within the different mentioned layers. the second target function represents the maximization of productivity resulting from the collaboration parameter affecting the sustainability index. equation (3) shows that between each of the two different layers and according to the collaboration and sustainability, at least one connection between different nodes of the mentioned layers should be selected. equation (4) shows that between two nodes in a particular layer, at least one connection between different nodes should be selected concerning collaboration and sustainability. equation (5) is the total costs incurred by the collaboration parameter affecting the sustainability index from one node to another in each layer with the costs incurred by the collaboration parameter affecting the sustainability index between different layers that should be less than the total budget available for establishing a collaboration parameter. equations (6) and (7) indicate that the amount of collaboration between and within different layers should not exceed the collaboration capacity of the collaboration parameter. equation (8) shows that for each layer and its corresponding node, there is exactly one collaboration parameter for each sustainability index. equation (9) ensures that communication between the two layers is done sequentially. equation (10) shows the type of decision variables. hassanzadeh et al./oper. res. eng. sci. theor. appl. 5(3)2022 194-209 204 5. solution methodology in this paper, a bi-objective sustainable logistic model presented based on a heterogonous collaboration approach. the first objective function represents the minimization of the total costs created by the collaboration parameter effective on the sustainability index between and within the different layers. the second objective function represents the maximization of productivity resulting from the collaboration parameter affecting the sustainability index. to reformulating bi-objective mathematical model to a single one, we used epsilon-constraint method. finally, the developed model of the present study was encoded using gamz 24.1.2 software and the program was written by a computer with 2.3 ghz processor specifications, core i7 with 4gb ram memory. 6. numerical study in this section we present a numerical example to illustrate and analyze the performance of proposed bi-objective model based on problem goals. as mentioned, the proposed model was solved by gamz 24.1.2 software. after solving the proposed model, with regarding to 3237 repetitions, the model reached its optimal value and the time to achieve the optimal answer took 3.00 seconds. some of the used data and parameters are applied in the model using real data that are shown in table (2). other data are generated to handle the optimization model. also, the validity of the model was performed by analyzing the sensitivity of some effective parameters in the model and the efficiency of the model was evaluated. in the developed model, sustainability with index s = 1,2,3 includes three economic, social, and environmental indices. also, the parameter of collaboration with index w = 1,2,3 includes communication, bargaining power, and opportunism. table (2) shows the available budget for establishing the collaboration parameter w affecting the sustainability index s ( ws b ). table 2. budget available for the establishment of collaboration ( ws b ) ws b s 1 2 3 w 1 787 579 647 2 523 577 574 3 663 566 753 after solving the developed model using the values defined for the problem parameters, the model achieves the optimal answer and the values of the variables ws x ikjk (if the collaboration parameter w is established in relation to the sustainability index s with node i in layer k with node j in layer k’) and ws y ii k (if node i with node i’ in layer k has parameter collaboration w in relation to the sustainability index s) which are equal to 1 and shown in tables (3) and (4). designing a sustainable logistics model with a heterogeneous collaboration approach 205 table 3. operation of the developed model and the optimal value of the objective function the results of table (3) show that the optimal value of the weighted integrated objective function of the developed model after running in gams software with 1265 repetitions, the value of 269,000 has been obtained. the results also show that the running time of the model to achieve the optimal answer was 3 seconds. the results related to the optimal values of the developed model variables including and ws x ikjk are shown in table (4). this table shows the establishment of collaboration parameters with respect to sustainability indices in the interlayer mode and between different layers. for example, the value obtained 13 211y shows that between nodes 2 and 1 in the first layer, the collaboration parameter 1 (communication parameter) affects the sustainability index 3 (environmental index) that reduces system costs and increases the efficiency resulted from the collaboration parameter affecting the sustainability index. also, the value obtained 21 3223x shows that between node 3 from the second layer and node 2 from the third layer, the collaboration parameter 2 (bargaining power parameter) affects the sustainability index 1 (economic index) that reduces the cost of the entire system and increases the efficiency of the cooperation. table 4. optimal values of the variables in the developed model variable y(1,1,3,1,1) 1 y(1,2,1,3,3) 2 y(1,2,2,3,2) 3 y(1,2,3,1,2) 4 y(1,3,1,2,1) 5 y(1,3,1,3,2) 6 y(1,3,2,1,1) 7 y(2,1,3,2,1) 8 y(2,2,1,3,1) 9 y(2,2,2,1,2) 10 y(2,2,3,1,2) 11 y(2,3,1,3,2) 12 y(2,3,2,3,1) 13 y(3,3,1,2,1) 14 y(3,3,1,2,2) 15 y(3,3,2,1,1) 16 y(3,3,2,1,2) 17 y(3,3,3,1,2) 18 y(3,3,3,2,1) 19 x(1,1,3,1,1,2) 20 x(1,2,2,2,2,3) 21 total solver iterations extended solver steps gams obj time 3237 268 291.000 3.00 hassanzadeh et al./oper. res. eng. sci. theor. appl. 5(3)2022 194-209 206 x(1,2,3,2,1,3) 22 x(1,3,1,1,1,2) 23 x(1,3,1,2,2,3) 24 x(1,3,2,1,3,2) 25 x(2,1,3,1,3,2) 26 x(2,2,1,1,1,2) 27 x(2,2,2,2,2,3) 28 x(2,2,3,2,1,3) 29 x(2,3,1,2,3,3) 30 x(2,3,2,1,2,2) 31 x(3,3,1,1,3,2) 32 x(3,3,1,2,1,3) 33 x(3,3,2,1,1,2) 34 x(3,3,2,2,1,3) 35 x(3,3,3,1,3,2) 36 x(3,3,3,2,3,3) 37 also, the results of the proposed model based on the optimal values of the variables and are shown in fig. 2 and 3. in these figures, collaboration parameters and sustainability indicators are shown with symbols w and s, respectively. also, layers 1 to 3 including nodes within layers 1 to 3 are considered for each layer. with respect to the fig. 2 and 3, the relations of collaboration parameters and sustainability indices in different layers and nodes are shown with arrows and they are assigned to each other based on the optimal values obtained for the mentioned variables. figure 2. optimal values of the variable in the developed model designing a sustainable logistics model with a heterogeneous collaboration approach 207 figure 3. optimal values of the variable in the developed model 7. conclusion in this paper, a model is developed to evaluate the sustainability interaction with inter-layer and intra-layer collaboration of a two-tier logistics network. first, indices of economic, social, and environmental sustainability along with the parameters of collaboration, communication, bargaining power, and opportunism on different layers of logistics were examined. according to the capacity of collaboration and the cost required to establish collaboration, the problem was modeled and solved with the objectives of minimizing costs and maximizing 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(2015). carbon pricing versus emissions trading: a supply chain planning perspective. international journal of production economics, 164, 197-205.. doi:10.1016/j.ijpe.2014.11.012. zavadskas, e. k., turskis, z., stević, ž., & mardani, a. (2020). modelling procedure for the selection of steel pipes supplier by applying fuzzy ahp method. operational research in engineering sciences: theory and applications, 3(2), 39-53. https://doi: 10.31181/oresta2003034z. © 2022 by the authors. submitted for possible open access publication under the terms and conditions of the creative commons attribution (cc by) license (http://creativecommons.org/licenses/by/4.0/). https://doi.org/10.1016/j.ejor.2020.12.064 https://doi.org/10.1016/j.jclepro.2022.130619 http://dx.doi.org/10.1080/13675567.2018.1513467 https://doi.org/10.1016/j.cor.2016.02.003 https://doi.org/10.1016/j.ejor.2014.04.015 http://dx.doi.org/10.3390/su12166627 http://dx.doi.org/10.1016/j.ijpe.2014.11.012 https://doi:%2010.31181/oresta2003034z https://doi:%2010.31181/oresta2003034z designing a sustainable logistics model with a heterogeneous collaboration approach zahra hassanzadeh1, iraj mahdavi1, ali tajdin1, hamed fazlollahtabar 2* 1. introduction 2. literature review 3. statement of the problem 4. the developed mathematical model 4.1. indices: 4.2. variables: 4.3. parameters: 4.4. mathematical model: 4.5. model description: 5. solution methodology 6. numerical study 7. conclusion references operational research in engineering sciences: theory and applications first online issn: 2620-1607 eissn: 2620-1747 doi: https://doi.org/10.31181/oresta171122136u * corresponding author. anilutku@munzur.edu.tr (a. utku) deep learning based cirrhosis detection anıl utku * department of computer engineering, munzur university, tunceli, turkey received: 26 august 2022 accepted: 11 october 2022 first online: 17 november 2022 research paper abstract: cirrhosis is a liver disease caused by long-term liver damage. scar tissue caused by cirrhosis prevents the liver from working properly. with the hepatitis c virus, 130-150 million people are infected in the world and 350-500 thousand deaths, and 34 million new cases are reported every year due to liver disease. in 2030, it is predicted that there will be 40 percent increase in compensated cirrhosis due to the hepatitis c virus, 60 percent increase in decompensated cirrhosis, and 70 percent increase in liverrelated deaths. although it is difficult to diagnose cirrhosis in the early stages, it is very important step for its treatment. blood tests, imaging tests, and biopsy methods are used to detect cirrhosis. due to the costs of these tests and the inability to get the test results immediately, the treatment of the patients cannot be started immediately. in this study, a mlp-based deep learning model has been developed for the prediction of cirrhosis. the developed model has been compared with dt, knn, lr, nb, rf, and svm. experimental studies using the accuracy, precision, recall, and f1-score showed that the developed model was more successful than the compared models. experimental results showed that the developed model had 80.48% accuracy, 85.71% precision, 85.71% recall, and 85.71% f1-score. experimental results showed that the developed model had a prediction accuracy of over 80% and f1-score of over 85% in cirrhosis detection from blood tests. the developed model can be used in real-world applications to alleviate the workload of healthcare professionals and to develop early diagnosis systems. keywords: cirrhosis detection, deep learning, machine learning, mlp. 1. introduction cirrhosis, also called chronic liver disease, causes severe damage to the liver (arroyo et al., 2016). different levels of damage to the liver can occur due to various diseases. as a result, various deteriorations occur in the structural functions of the liver and it cannot perform its normal functions (garcia‐martinez et al., 2013). this is mailto:anilutku@munzur.edu.tr utku/oper. res. eng. sci. theor. appl. first online the beginning of the cirrhosis process. as a result of the decrease in liver cells that continue to function, the liver begins to harden and shrink. the flow of blood to the hardened tissues becomes difficult and new vascular pathways are formed due to the inability of the blood to reach the tissue. all these events aggravate the cirrhosis table by affecting the liver more negatively (mozos, 2015). as a result, the liver begins to fail to function and liver failure occurs. cirrhosis is a long-lasting and progressive disease (vranjkovic et al., 2019). in the early stages, the findings may be very mild. as the damage to the liver increases, the symptoms worsen (younossi and henry, 2015). the most common symptoms in the early period are; loss of appetite, weight loss, nausea, weakness, and fatigue. these findings get worse in the future. in this process, water accumulation in the body, edema in the legs, swelling in the abdomen, muscle wasting, rapid bruising on the skin, tendency to bleeding, excessive itching, and jaundice are observed (pinto et al., 2015). the liver is the body's factory. all the foods taken are used in the liver to make useful and necessary products for the body. one of them, albumin, keeps the fluids in the blood vessels. when liver functions are impaired, albumin synthesis is also affected (van zutphen et al., 2016). when the albumin level decreases, the fluids cannot be kept in the vascular bed and leak into the tissues (guerci et al., 2019). as a result, edema occurs in the legs. likewise, fluid accumulates in the abdominal cavity. in these patients, bruises may occur on the skin, or the tendency to bleed increases with the slightest impact (amitrano et al., 2002). the reason for this is that the substances necessary for coagulation cannot be produced as much as they should due to the damage in the liver. again, as a result of liver failure, some substances accumulate in the blood and severe itching and encephalopathy may occur. longterm use of alcohol, viral hepatitis b/c, diabetes, obesity, obstruction and inflammation of the biliary tract, chronic heart failure, history of liver disease, and unprotected sex cause cirrhosis (ginès et al., 2021). blood tests, imaging tests such as mri or ultrasound, and biopsy methods are used to detect cirrhosis (acharya et al., 2015). the costs of these tests and the inability to get the test results immediately highlight the use of artificial intelligence technologies in the cirrhosis detection. artificial intelligence methods are used successfully in many applications in the field of medicine. systems for the diagnosis of diseases can be developed by using artificial intelligence methods. in the literature, there is no study on the detection of cirrhosis using artificial intelligence methods. in this section, studies in the literature in which artificial intelligence methods are used in the field of medical diagnosis are examined. goceri (goceri, 2019) presented a deep learning-based comparative analysis for the detection of skin diseases. u-net, inceptionv3, inceptionresnetv2, vggnet and resnet models were compared. experimental results showed that resnet was the most successful model with 80% accuracy, while u-net was the most unsuccessful model with 0.74 accuracy. che azemin et al. (che azemin et al., 2020) presented a resnet-101-based model for detecting covid-19 cases using chest radiography images. the developed model had 0.82 auroc, 77.3% sensitivity, 71.8% specificity, and 71.9% accuracy. deep learning based cirrhosis detection jain et al. (jain et al., 2021) developed a deep learning-based model for detecting covid-19 from medical images. in the study, resnext, inception v3 and xception models were compared. experimental results showed that the xception model was more successful than the compared models with 97.97% accuracy. ismael and şengür (ismael and şengür, 2021) proposed a deep learning-based model for detecting covid-19 from x-ray data. resnet18, resnet50, resnet101, vgg16 and vgg19 were used for feature extraction. support vector machine (svm) with different kernel functions is used to classify features. a dataset consisting of 380 x-ray images was used. experimental results showed that resnet50 and svm with linear kernel function outperform other models with 94.7% accuracy. mostafa et al. (mostafa et al., 2021) presented comparative analysis of ann, rf and svm for hepatitis c detection from blood test values. the dataset used consists of blood test results of 615 patients. experimental results showed that rf, ann and svm had 98.14%, 88.89% and 96.75% classification accuracy, respectively. allugunti (allugunti, 2022) aims to classify patients as cancer and non-cancerous using mammography images. in the study, the results of the convolutional neural network (cnn), random forest (rf) and svm classification models were compared. experimental results showed that cnn has 99.65% accuracy, svm has 89.84% accuracy, and rf has 90.55% accuracy. terlapu et al. (terlapu et al., 2022) presented comparative analysis of the probabilistic neural network (pnn), svm, k nearest neighbours (knn), rf, decision tree (dt), and naïve bayes (nb) for hepatitis c detection. experimental results showed that pnn outperformed machine learning models with 99.6% accuracy. rf was the most successful model among machine learning models with 97.5% accuracy. almadhoun and abu-naser (almadhoun and abu-naser, 2022) presented a deep learning-based comparative analysis for brain tumor detection. using a dataset of 10,000 images, the proposed model, inception, vgg16, mobilenet, and resnet models were compared. experimental results showed that the vgg16 outperformed the compared models with 99.86% accuracy. luetkens et al. (luetkens et al., 2022) presented deep learning-based comparative analysis for cirrhosis detection from liver mr images. the dataset used consists of 465 patient data. experimental studies using the resnet50 and densenet121 models showed that resnet50 had 0.823 precision. pasyar et al. (pasyar et al., 2022) developed a hybrid deep learning model for detecting liver diseases such as hepatitis and cirrhosis from ultrasound images. transfer learning has been applied to the resnet and alexnet architectures. the voting method was used to weight the results obtained by each model. experimental results showed that the hybrid resnet50 model had classification accuracy of over 86%. cirrhosis does not usually cause symptoms in the early stages. however, as the degree of the disease progresses and the level of damage to the liver increases, the symptoms and the severity of these symptoms increase. liver diseases cause other diseases in the body and can pose great dangers to the body. for this reason, diagnosis and treatment of liver diseases such as cirrhosis at an early stage are vital utku/oper. res. eng. sci. theor. appl. first online for the human body. blood tests are mainly used to diagnose liver diseases. however, cirrhosis diagnosis made with traditional methods. these methods have limitations in terms of cost, time, and accuracy compared to artificial intelligence methods. especially in hospitals where these tests are carried out intensively, limitations in terms of the decision-making phase and time come to the fore in terms of the human factor. the motivation of this study is to offer a solution to the limitations of traditional methods used in cirrhosis detection. in this study, a deep learning model was developed to detect cirrhosis patients from blood test values. it was aimed to provide a pre-diagnosis system for the detection of cirrhosis by easing the workload of healthcare professionals. the main contributions of this study to the literature can be summarized as follows: this is the first study in the literature on cirrhosis detection using artificial intelligence methods. in this study, multilayer perceptron (mlp) based deep learning model were developed for cirrhosis detection. the developed model were compared with dt, knn, logistic regression (lr), nb, rf and svm using accuracy, precision, recall and f1-score. experimental results showed that the developed model was more successful than the compared models with 80.48% classification accuracy. 2. deep learning based cirrhosis detection many diseases cause people to die as a result of late diagnosis. for this reason, experts recommend that it is appropriate to perform screening tests at regular intervals. despite this recommendation of experts, many people do not care about health screenings and do not go to the doctor without any symptoms. artificial intelligence is used for the effective use of human resources, rapid diagnosis, and treatment, supporting healthcare professionals in many ways. artificial intelligence is used in the diagnosis and treatment of diseases, in determining the appropriate tools for treatment and in medical decision support systems. in this study, it was aimed to determine whether people had cirrhosis according to their demographic characteristics and blood test results. for this purpose, mlp-based deep learning model was developed. the developed model was compared with dt, knn, lr, nb, rf and svm using accuracy, precision, recall, and f1-score. 2.1. dataset the dataset used in this study consists of patients' demographic information and blood test values. the dataset is publicly available via https://www.kaggle.com/datasets/fedesoriano/cirrhosis-prediction-dataset. the dataset consists of blood test data from a total of 418 pbc patients. the dataset consists of 19 attributes. ‘id’ is a unique sequence number of patients. ‘n_days’ represents the number of days from the patient's registration date to the date of the transplant, the date of the patient's death, or july 1986. ‘status’ refers to deep learning based cirrhosis detection the patient's status as c (censored), cl (censored due to liver transplant), or d (death). 'drug' refers to the type of drug, either d-penicillamine or placebo. 'age' refers to the patient's age in days. sex denotes gender as m for males and f for females. 'acid' refers to the presence of acid as n for no and y for yes. 'hepatomegaly' refers to the presence of hepatomegaly as n for no and y for yes. 'spiders' refers to the presence of spiders as n for no and y for yes. 'edema' refers to the presence of edema as n (no edema and no diuretic therapy for edema), s (existing edema without diuretics or edema resolving with diuretics), or y (edema despite diuretic therapy). 'bilirubin' refers to the amount of serum bilirubin in mg/dl. 'cholesterol' means the amount of cholesterol in mg/dl. 'albumin' refers to the amount of albumin in mg/dl. 'copper' refers to the amount of copper in the urine in µg/day. 'alk_phos' refers to the amount of alkaline phosphatase in u/liter. 'sgot' refers to the sgot value in u/ml. 'triglycerides' refers to the triglycerides value in mg/dl. 'platelets' refers to the platelet's value per cubic ml/1000. 'prothrombin' refers to the prothrombin time in seconds. 'stage' refers to the stage of the disease as 1, 2, 3, or 4. in the dataset, missing data (na) of the features are filled with the mean values of the relevant column. the categorical features in the dataset were replaced with a numeric value. the categorical values of the 'sex' attribute were changed to 0 for 'm' and 1 for 'f'. the categorical values of the 'ascites' attribute were changed to 0 for 'n' and 1 for 'y'. the categorical values of the 'drug' attribute were changed to 0 for 'dpenicillamine' and 1 for 'placebo'. the categorical values of the 'hepatomegaly' attribute were changed to 0 for 'n' and 1 for 'y'. the categorical values of the 'spiders' attribute were changed to 0 for 'n' and 1 for 'y'. the categorical values of the 'edema' attribute were changed to 0 for 'n', 1 for 'y', and -1 for 's'. the categorical values of the 'status' attribute were replaced with 0 for 'c', 1 for 'cl', and -1 for 'd'. the distribution of the patients according to the disease stages is shown in fig 1. figure 1. the distribution of the patients according to the disease stages the heatmap showing the relationships of the features in the dataset is shown in fig. 2. the heatmap was used for feature selection. utku/oper. res. eng. sci. theor. appl. first online figure 2. the heatmap used for feature selection the distributions of the features are shown in fig. 3. deep learning based cirrhosis detection figure 3. the distributions of the features the attributes with categorical values in the dataset are shown in figure 4. utku/oper. res. eng. sci. theor. appl. first online figure 4. the attributes with categorical values in the dataset relationships between features other than blood values are shown in fig. 5. figure 5. relationships between features other than blood values the density graphs of the features obtained from the blood tests and the age feature according to their classes are shown in fig. 6. deep learning based cirrhosis detection figure 6. the density graphs of the features obtained from the blood tests and the age feature 2.2. developed model mlp has a structure in which many neurons with non-linear activation functions are hierarchically connected. mlp consists of an input, one or more intermediate, and an output layer. the input layer receives the input strings to be processed. inputs are forwarded to the network using the weights between the input layer and the hidden layers. in hidden layers, activation functions such as relu, sigmoid, and tanh are used. input sequences processed in hidden layers are transmitted over the network with the help of these activation functions. these processes are repeated as many times as the number of hidden layers in the network structure. the output layer performs tasks such as regression or classification. in the output layer, activation functions are used according to the type of problem. for example, sigmoid is used for binary classification and softmax activation functions are used for multiclass classification problems. the neurons in the mlp are trained using the backpropagation algorithm. the developed mpl-based model takes the blood test data of the patients as input and predicts whether the patient has cirrhosis. the architecture of the developed model is shown in fig. 7. utku/oper. res. eng. sci. theor. appl. first online figure 7. the architecture of the developed mlp-based model the developed model consists of an input layer in which demographic data of the patients and blood test data are presented as input. there are 2 hidden layers for the model to calculate. hyperparameter analysis studies were carried out using gridsearchcv to determine the number of neurons and epochs in the hidden layers. relu activation function is used in the input layer. in hidden layers, relu activation function is used to sort the layers and make nonlinear calculations. since the binary classification is done, the sigmoid activation function is used in the output layer. 2.3. evaluation metrics classification algorithms aim to predict categorical values with two or more classes. accuracy, precision, recall, and f1-score metrics are used to measure the performance of classification algorithms. these metrics are calculated using the confusion matrix. the confusion matrix is used to interpret the results of classification models and evaluate the relationship between actual values and predicted values. the confusion matrix is shown in table 1. table 1. confusion matrix actual values positive (1) negative (0) p re d ic te d v a lu e s positive (1) tp fp negative (0) fn tn tp is the number of patients that are actually cirrhosis and the classifier also predicts cirrhosis. tn is the number of cases that are actually non-cirrhosis and the classifier also predicts non-cirrhosis. fp is the number of patients that the classifier predicts as cirrhosis, but non-cirrhosis. fn is the number of patients that the classifier predicts as non-cirrhosis, but cirrhosis. deep learning based cirrhosis detection accuracy is calculated as the ratio of the number of samples classified correctly by the model to the total number of samples, as seen in eq. (1). tp+tn accuracy = tp+fp+fn+tn (1) precision refers to how many of the positively predicted values are actually positive. precision is calculated using eq. (2). tp precision = tp+fp (2) recall is a metric that shows how many of the samples that should be predicted positively are correctly predicted. recall is calculated using eq. (3). tp recall = tp+fn (3) the f1-score is calculated using precision and recall values. f1-score is calculated as seen in eq. (4). 2.precision.recall f1 score = precision+recall − (4) 3. experimental results in this study, mlp-based deep learning model was developed to detect cirrhosis patients. the experimental results of the developed model were extensively compared with dt, knn, lr, nb, rf and svm. the accuracy, precision, recall, and f1score obtained for each model were compared. parameter analysis studies were conducted using gridsearchcv to determine the parameters of models. cross validation has been used to eliminate the overfitting problem and to increase the quality of the models. cross-validation has been made by choosing the k value as 10. all models were run on 10 randomly generated datasets using crossvalidation, and the results obtained were averaged. the confusion matrix and experimental results for dt are shown in table 2 and table 3. table 2. confusion matrix for dt actual values cirrhosis (1) non-cirrhosis (0) p re d ic te d v a lu e s cirrhosis (1) 20 6 non-cirrhosis (0) 8 7 as seen in table 2, tp is 20, fp is 6, fn is 8, and tn is 7. experimental results showed that dt correctly detected 20 of 28 cirrhosis patients and 7 of 13 non utku/oper. res. eng. sci. theor. appl. first online cirrhosis patients. of the 41 patients in the dataset, 27 patients were correctly classified and 14 patients were misclassified. table 3. accuracy, precision, recall and f1-score values for dt accuracy precision recall f1-score 0.6585 0.7692 0.7142 0.7406 as seen in table 3, the accuracy of dt is 0.6585, the precision is 0.7692, the recall is 0.7142, and the f1-score is 0.7406. the confusion matrix and experimental results for knn are shown in table 4 and table 5. table 4. confusion matrix for knn actual values cirrhosis (1) non-cirrhosis (0) p re d ic te d v a lu e s cirrhosis (1) 18 9 non-cirrhosis (0) 10 4 as seen in table 4, tp is 18, the fp is 9, fn is 10, and tn is 4. experimental results showed that knn correctly detected 18 of 28 cirrhosis patients and 4 of 13 non cirrhosis patients. of the 41 patients in the dataset, 22 patients were correctly classified and 19 patients were misclassified. table 5. accuracy, precision, recall and f1-score values for knn accuracy precision recall f1-score 0.5365 0.6666 0.6428 0.6544 as seen in table 5, the accuracy of knn is 0.5365, the precision is 0.6666, the recall is 0.6428, and the f1-score is 0.6544. the confusion matrix and experimental results for lr are shown in table 6 and table 7. table 6. confusion matrix for lr actual values cirrhosis (1) non-cirrhosis (0) p re d ic te d v a lu e s cirrhosis (1) 20 7 non-cirrhosis (0) 8 6 as seen in table 6, tp is 20, fp is 7, fn is 8, and tn is 6. experimental results showed that lr correctly detected 20 of 28 cirrhosis patients and 6 of 13 non cirrhosis patients. of the 41 patients in the dataset, 26 patients were correctly classified and 15 patients were misclassified. deep learning based cirrhosis detection table 7. accuracy, precision, recall and f1-score values for lr accuracy precision recall f1-score 0.6341 0.7407 0.7142 0.7272 as seen in table 7, the accuracy of lr is 0.6341, the precision is 0.7407, the recall is 0.7142, and the f1-score is 0.7272. the confusion matrix and experimental results for nb are shown in table 8 and table 9. table 8. confusion matrix for nb actual values cirrhosis (1) non-cirrhosis (0) p re d ic te d v a lu e s cirrhosis (1) 15 11 non-cirrhosis (0) 13 2 as seen in table 8, tp is 15, fp is 11, fn is 13, and tn is 2. experimental results showed that nb correctly detected 15 of 28 cirrhosis patients and 2 of 13 non cirrhosis patients. of the 41 patients in the dataset, 17 patients were correctly classified and 24 patients were misclassified. table 9. accuracy, precision, recall and f1-score values for nb accuracy precision recall f1-score 0.4146 0.5769 0.5357 0.5555 as seen in table 9, the accuracy of nb is 0.4146, the precision is 0.5769, the recall is 0.5357, and the f1-score is 0.5555. the confusion matrix and experimental results for rf are shown in table 10 and table 11. table 10. confusion matrix for rf actual values cirrhosis (1) non-cirrhosis (0) p re d ic te d v a lu e s cirrhosis (1) 22 5 non-cirrhosis (0) 6 8 as seen in table 10, tp is 22, fp is 5, fn is 6, and tn is 8. experimental results showed that rf correctly detected 22 of 28 cirrhosis patients and 8 of 13 non cirrhosis patients. of the 41 patients in the dataset, 30 patients were correctly classified and 11 patients were misclassified. utku/oper. res. eng. sci. theor. appl. first online table 11. accuracy, precision, recall and f1-score values for rf accuracy precision recall f1-score 0.7317 0.8148 0.7857 0.7999 as seen in table 11, the accuracy of rf is 0.7317, the precision is 0.8148, the recall is 0.7857, and the f1-score is 0.7999. the confusion matrix and experimental results for svm are shown in table 12 and table 13. table 12. confusion matrix for svm actual values cirrhosis (1) non-cirrhosis (0) p re d ic te d v a lu e s cirrhosis (1) 22 5 non-cirrhosis (0) 6 8 as seen in table 12, tp is 22, fp is 5, fn is 6, and tn is 8. experimental results showed that svm correctly detected 22 of 28 cirrhosis patients and 8 of 13 non cirrhosis patients. of the 41 patients in the dataset, 30 patients were correctly classified and 11 patients were misclassified. table 13. accuracy, precision, recall and f1-score values for rf accuracy precision recall f1-score 0.7317 0.8148 0.7857 0.7999 as seen in table 13, the accuracy of svm is 0.7317, the precision is 0.8148, the recall is 0.7857, and the f1-score is 0.7999. the confusion matrix and experimental results for developed model are shown in table 14 and table 15. table 14. confusion matrix for developed model actual values cirrhosis (1) non-cirrhosis (0) p re d ic te d v a lu e s cirrhosis (1) 24 4 non-cirrhosis (0) 4 9 as seen in table 14, tp is 24, fp is 4, fn is 4, and tn is 9. experimental results showed that the developed model correctly detected 24 of 28 cirrhosis patients and 9 of 13 noncirrhosis patients. of the 41 patients in the dataset, 33 patients were correctly classified and 8 patients were misclassified. deep learning based cirrhosis detection table 15. accuracy, precision, recall and f1-score values for developed model accuracy precision recall f1-score 0.8048 0.8571 0.8571 0.8571 as seen in table 15, the accuracy of proposed model is 0.8048, the precision is 0.8571, the recall is 0.8571, and the f1-score is 0.8571. comparative experimental results according to accuracy, precision, recall and f1score values for dt, knn, lr, nb, rf, svm and developed model are shown in table 16 and fig. 8. table 16. comparative experimental results model accuracy precision recall f1-score dt 0.6585 0.7692 0.7142 0.7406 knn 0.5365 0.6666 0.6428 0.6544 lr 0.6341 0.7407 0.7142 0.7272 nb 0.4146 0.5769 0.5357 0.5555 rf 0.7317 0.8148 0.7857 0.7999 svm 0.7317 0.8148 0.7857 0.7999 developed model 0.8048 0.8571 0.8571 0.8571 as seen in table 16 and fig. 8, the developed model has more successful results than the other models compared. figure 8. comparative experimental results as can be seen in table 16 and fig. 8, the developed model showed better classification performance in detecting cirrhosis patients compared to other models. after the developed model, rf, svm, dt, lr, knn and nb are the models with the successful results, respectively. experimental results showed that the developed model had a classification accuracy of over 80% and an f1-score close to 86%. the obtained results showed utku/oper. res. eng. sci. theor. appl. first online that the developed model can be successfully applied in the cirrhosis detection and can be used in early diagnosis systems. the accuracy/loss graphs of the developed model during the training and validation are shown in fig. 9. figure 9. the accuracy/loss graphs of the developed model during the training and validation experimental results showed that the proposed model was more successful than other models compared according to accuracy, recall and f1-score metrics. the accuracy value is important because it shows the number of correctly classified patients. precision value is important because it shows how many patients with predicted cirrhosis have cirrhosis. the recall value is important because it shows how many of the patients who should have been predicted as cirrhosis were correctly predicted. f1-score is a harmonic mean value calculated according to precision and recall values. in other words, successful models are expected to have a higher f1-score value. roc and precision-recall curve graphs of the developed model are shown in fig. 10.a and fig. 10.b. deep learning based cirrhosis detection figure 10. roc and precision-recall curve graphs of the developed model the roc curve is a very important performance measure for classification problems. roc is a probability curve. auc is the area under the curve and represents the degree or measure of discrepancy. in the roc curve, there is false positive rate (fpr) on the x axis and true positive rate (tpr) on the y axis. as the area under the curve increases, the discrimination performance between classes increases. tpr is the recall value. in other words, it is the detection rate of cirrhosis patients. fpr is the rate of erroneous prediction for non-cirrhosis patients. 4. conclusions cirrhosis is an advanced chronic liver disease. different levels of damage occur in the liver due to different diseases. depending on these reasons, the cirrhosis process begins with the development of structural changes in the liver. as a result, the number of functional liver cells decreases, and the liver hardens and shrinks. the resistance to the blood that has to pass through increases. when the blood cannot flow from here, the intravascular pressure increases in the areas where the blood comes from. the blood, which cannot reach the liver due to the increased pressure, looks for other ways to reach the liver and creates new vascular pathways. as a result, liver functions gradually deteriorate and signs of liver failure occur. artificial intelligence technologies are used in medical application areas such as disease diagnosis, surgery, drug development, analysis of radiological images and lesions, and personalized therapy. in this study, mlp-based deep learning model was developed for cirrhosis detection. the developed model was compared with dt, knn, lr, nb, rf, and svm. experimental studies using the accuracy, precision, recall, and f1-score showed that the developed model was more successful than the compared models. experimental results showed that the developed model has 80.48% accuracy, 85.71% precision, 85.71% recall and 85.71% f1-score. the fact that rf is more successful than dt can be interpreted by the bagging technique of rf. rf creates multiple decision trees. it evaluates the results of these trees using the voting method. the fact that rf is more successful than knn can be explained as random samples selected from the dataset. knn only tries to include the closest instances in the same class. however, in this case, samples outside of local similarity will not be classified correctly by knn. utku/oper. res. eng. sci. theor. appl. first online the fact that rf is more successful than nb can be interpreted as nb's inability to represent the complex behavior of models due to the small model size. on the other hand, the size of rf is very large. rf can adapt to the dynamic structure and change of data. the fact that svm is more successful than rf can be interpreted as the presence of numerical and categorical features in the dataset. rf works with a mixture of numerical and categorical features. rf is advantageous when features are of various scales. svm maximizes the margin between different points and calculates the distance between points. in the classification problem, rf gives the probability of belonging to the class, while svm gives the points closest to the boundary between classes. due to the categorical and numerical coexistence of the features in the data, rf performed better than svm. the fact that the developed model is more successful than other models can be interpreted as a large number of input data presented to the network. the more inputs presented to the network, the network learns better and makes better predictions. but basically machine learning methods require fewer input data. studies in the literature have generally focused on hepatitis c and liver diseases detection. disease detection is made from blood test values with ultrasound or mr images. to the best of our knowledge, there is no study in the literature for cirrhosis detection using this dataset. therefore, the experimental results could not be compared with the studies in the literature. the size of the dataset used is one of the limitations of this study. the dataset consists of 418 pvc patient data and 19 attributes. making more different measurements in 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(2015). systematic review: patient‐reported outcomes in chronic hepatitis c‐the impact of liver disease and new treatment regimens. alimentary pharmacology & therapeutics, 41(6), 497-520. https://doi.org/10.1111/apt.13090 © 2022 by the authors. submitted for possible open access publication under the terms and conditions of the creative commons attribution (cc by) license (http://creativecommons.org/licenses/by/4.0/). https://doi.org/10.1002/ima.22746 https://doi.org/10.1016/j.jhep.2016.05.046 https://doi.org/10.3389/fimmu.2019.01926 https://doi.org/10.1111/apt.13090 deep learning based cirrhosis detection anıl utku * 1. introduction 2. deep learning based cirrhosis detection 2.1. dataset 2.2. developed model 2.3. evaluation metrics 3. experimental results 4. conclusions plane thermoelastic waves in infinite half-space caused operational research in engineering sciences: theory and applications vol. 1, issue 1, 2018, pp.29-39 issn: 2620-1607 eissn: 2620-1747 doi: https://doi.org/10.31181/oresta19012010129s * corresponding author. e-mail addresses: dstanujkic@tfbor.bg.ac.rs (d. stanujkić), darjankarabasevic@gmail.com (d. karabašević) an extension of the waspas method for decision-making problems with intuitionistic fuzzy numbers: a case of website evaluation dragiša stanujkić1*, darjan karabašević2 1 technical faculty in bor, university of belgrade, bor, serbia 2 faculty of applied management, economics and finance, university business academy in novi sad, belgrade, serbia received: 16 september 2018 accepted: 01 november 2018 published: 19 december 2018 original scientific paper abstract: the use of fuzzy sets in classical multiple criteria decision-making methods has led to forming fuzzy multiple criteria decision-making that has enabled solving of a significantly larger number of decision-making problems. however, the membership function introduced in the fuzzy set theory has some limitations. unlike the fuzzy set theory, the intuitionistic fuzzy set theory introduces non-membership function. therefore, the intuitionistic fuzzy set theory, as an extension of the fuzzy set theory, can provide for some advantages in solving complex decision-making problems. the waspas method is a newly-proposed, widely-used multiple criteria decision-making method for which numerous extensions have already been proposed. in order to enable the use of the waspas method for solving a significantly larger number of decisionmaking problems, a new extension based on the use of intuitionistic fuzzy numbers is proposed in this article. compared to similar extensions, the proposed extension is based on the use of the hamming distance for the purpose of ranking alternatives. efficiency and usability of the proposed approach are considered on the example of website evaluation. based on the successfully conducted numerical example of the website evaluation it can be concluded that the proposed extension of the waspas method based on the use of single-valued intuitionistic fuzzy sets and of the hamming distance has proven to be very effective and applicable when it comes to website evaluation. besides, usability of the proposed extension is demonstrated on the example of website evaluation. in doing so, the same order ranking order of the considered alternatives is obtained using the proposed ranking procedure and the procedure based on the score function, which confirms the correctness of the proposed procedure. key words: waspas, intuitionistic fuzzy set, single-valued intuitionistic fuzzy number, hamming distance, website evaluation stanujkić and karabašević/oper. res. eng. sci. theor. appl. 1 (1) (2018) 29-39 30 1. introduction in recent decades, the multiple criteria decision making (mcdm) has successfully been applied for the purpose of solving numerous decision-making problems. significant progress in the mcdm was made after zadeh (1965) had proposed his fuzzy sets theory on the basis of which bellman and zadeh (1970) also proposed the fuzzy multiple criteria decision making, thus enabling the solving of many real-world problems in a much more adequate manner. evident progress was also made after atanasov (1986) had proposed the intuitionistic fuzzy sets (ifs) theory as an extension of the fuzzy sets theory, which additionally introduces not belonging to a given set. up to now, the ifs has been successfully used to solve many decision-making problems such as: szmidt and kacprzyk (1996), atanassov et al. (2002, 2017), wei (2011), xu (2011), shen et al. (2015), xu and liao (2015), oztaysi et al. (2017); besides, it has also got significant extensions. moreover, there is a number of mcdm methods adapted for the use of ifs such as topsis (tan, 2011), vikor (devi, 2011).), promethee (krishankumar et al. 2017), waspas (zavadskas, 2014), and so on. the weighted aggregated sum product assessment (waspas) method was proposed by zavadskas et al. (2012) for solving different problems such as: contractor selection (zavadskas et al. 2015), construction site selection (stević et al. 2018; turskis et al. 2015), supplier selection (stojić et al. 2018; keshavarz ghorabaee et al. 2016), logistics (sremac et al. 2018; keshavarz ghorabaee et al. 2017), garage location selection (bausys, juodagalviene, 2017), telecommunications (mishra et al. 2018; peng, dai, 2017) manufacturing decision-making (chakraborty, zavadskas 2014; jahan, 2018), personnel selection (urosevic et al. 2017) and so on. also, a systematic and comprehensive review of the application of the waspas method is given by mardani et al. (2017). a number of extensions of the waspas method have also been proposed. for example, zavadskas et al. (2015a, 2015b) have proposed neutrosophic and grey extensions of the waspas method. zavadskas et al. (2014) also proposed an extension that allows the use of interval-valued intuitionistic fuzzy numbers. in order to enable the use of the waspas method for solving a significantly larger number of decision-making problems, an extension based on the use of intuitionistic fuzzy numbers is proposed in this article. compared to similar extensions, the proposed extension is based on the use of the hamming distance for the purpose of ranking alternatives. on the other hand, websites could have a very important role in modern companies; that is why their evaluation is chosen to demonstrate efficiency and usability of the proposed approach. because of their growing importance, there has been an increasing attention paid to evaluation of their quality. one of the increasingly used methods for evaluating their quality is the approach based on the use of the mcdm method. some of those approaches can be mentioned here, such as: pamučar et al. (2018), abdel-basset et al. (2018), chou et al. (2012), and bilsel et al. (2016). therefore, this paper is organized as follows: in section 2 some basic elements of the ifss theory as well as some elements relevant to the proposed approach are discussed. in section 3, the waspas method is presented and one extension adapted an extension of the waspas method for decision-making problems with intuitionistic fuzzy numbers: a case of website evaluation 31 for use ifss is proposed, and in section 4, efficiency and usability of the proposed approach are considered on an example of a website evaluation problem. finally, the conclusions are given. 2. preliminaries in this section some basic definitions and notations relevant for the proposed approach are discussed. 2.1 the basic concepts of intuitionistic fuzzy sets atanassov intuitionistic fuzzy sets. an ifs a ~ in x can be defined as follows:        xxxxxa aa )(),( , ~  (1) where: )(xa and )(xa denote the degree of the membership and the degree of the non-membership of the element x to set a, respectively; ]1 ,0[: xa and ]1 ,0[: xa , with the following condition .1)()(0  xx aa  (2) 2. 2 intuitionistic fuzzy numbers the ifss theory proposes several shapes of intuitionistic fuzzy numbers (ifns). triangular and trapezoidal shapes can be mentioned as significant ones. in addition to the above mentioned shapes, the singleton (single-valued) shape can be pointed out as a characteristic one. a single-valued ifn a ~ , aaa  , ~ , shown in fig. 1, is defined with membership )(x a  and non-membership )(x a  function, respectively, as follows:      ;0 ,1 )( otherwise ax x (2)      ;0 1 )( otherwise ax x (3) where: parameter a indicates the most promising value that describes belonging to a set, parameter a' indicates the most promising value that describes not-belonging to a set stanujkić and karabašević/oper. res. eng. sci. theor. appl. 1 (1) (2018) 29-39 32 fig. 1 a singleton ifn basic operations on ifns. let aaa  , ~ and bbb  , ~ be two ifns. the operations of addition and multiplication on ifns are as follows (atanassov 1994): baabbaba  , ~~ (4) babaabba  , ~~ (5)   aaa  ,)1(1 ~ (6)  )1(1 , ~ aaa  (7) score function of ifns. let be a single-valued ifn. then, the score is as follows aas a ~ , (8) where ]1 ,1[~  a s . the hamming distance of ivifns. let aaa  , ~ and bbb  , ~ be two ifns. then, the hamming distance dh is as follows |)||(| 2 1 ) ~ , ~ ( bababadh  (9) intuitionistic weighted arithmetic mean operator of single-valued ifns. let jjj aaa  , ~ be a collection of n single valued ifns. then, the intuitionistic weighted arithmetic mean (iwam) operator is as follows (tikhonenko-kędziak, kurkowski, 2016):     n j w j n j w j jj aaiwam 11 )(,)1(1 (10) 1 1 0 x )( x )( x a a an extension of the waspas method for decision-making problems with intuitionistic fuzzy numbers: a case of website evaluation 33 where: j w denote weight of j-th element of collection, ]1 ,0[jw and 11   n j jw . intuitionistic fuzzy weighted geometric operator of ifss. let jjj aaa  , ~ be a collection of n single-valued ifns. then, the intuitionistic fuzzy weighted geometric (ifwg) operator is as follows (tikhonenko-kędziak, kurkowski, 2016):    n j w j wn j j jj aaifwg 11 )1(1,)( (11) where: j w denote weight of j-th element of collection, ]1 ,0[jw and 11   n j jw . 3. waspas method the basic idea of the waspas method is that it integrates two well-known approaches: weighted sum (ws) and weighted product (wp). the computational procedure of the waspas method for a decision-making problem involving only the beneficial criteria can be presented as follows: step 1 determine the optimal performance rating for each criterion as follows: ij i j xx max0  (12) where jx0 denotes the optimal performance rating of j-th criterion, ijx denotes the performance rating of i-th alternative in relation to the j-th criterion. step 2 construct the normalized decision matrix, as follows: j ij ij x x r 0  (13) where ijr denotes the normalized performance rating of i-th alternative in relation to the j-th criterion. step 3 calculate the importance of each alternative based on ws method ws iq as follows:   n j ijj ws i rwq 1 (14) step 4 calculate the importance of each alternative based on wp method wp iq as follows:   n j w ij wp i jrq 1 (15) stanujkić and karabašević/oper. res. eng. sci. theor. appl. 1 (1) (2018) 29-39 34 step 5 calculate the overall importance of each alternative iq as follows: )(5.0 wp i ws ii qqq  (16) 3.1 an extension of waspas method based on the application of ifn and group decision-making one extension of the waspas method proposed with the aim to enable the use of ifn in a group environment is presented in this section. at the very beginning, it can be said that normalization is not necessary in this approach. the normalization process, in mcdm methods, is used for the following reasons:  to transform performance ratings in the interval (0,1], and  to transform performance ratings of cost criteria into adequate beneficial criteria. however, as has already been stated, the values of ifn already belong to [0, 1] interval, which makes no need for normalization in this extension of the waspas method. therefore, the procedure of the proposed extension could be precisely presented by using the following steps: step 1 form a group decision-making matrix based on individual decisionmaking matrices, which can be carried out using eq. (10). step 2 determine the group criteria weights. in the scientific literature, a number of methods for determining criteria weights are proposed, and each of them can be used in this approach. step 3 calculate the importance based on the ws approach, for each alternative, by using eq. (10). step 4 calculate the importance based on the wp approach, for each alternative, by using eq. (11). step 5 calculate the overall importance of each alternative iq ~ . in this step, iq ~ is calculated by using eq (5). however, taking into account that the values of ws iq ~ and wp iq ~ are ifns, the calculation must be carried out by using eqs. (4) and (7). step 6 rank the alternatives and select the most acceptable one. ranking of ifns can be done based on the value of their score functions, which is an often used approach. however, the use of the hamming distance is recommended in this approach, where the distance of each alternate is determined in relation to the ideal point <1, 0>. finally, the alternative that has the least distance from the ideal point is the most acceptable one. an extension of the waspas method for decision-making problems with intuitionistic fuzzy numbers: a case of website evaluation 35 4. a numerical example in order to provide for a detailed explanation of the proposed approach an example of websites evaluation, borrowed from stanujkic et al. (2015), is considered. in this example, three websites are evaluated based on the following criteria:  environment (e),  content (c),  graphics (g), and  authority (a). the ratings obtained from three respondents are shown in tables 1, 2 and 3. table 1 ratings obtained from the first of three respondents criteria alternatives en co gr au a1 <0.625,0.125> <0.625,0.375> <0.625,0.250> <0.375,0.250> a2 <0.625,0.375> <0.750,0.125> <0.625,0.125> <0.500,0.250> a3 <0.750,0.125> <0.500,0.125> <0.625,0.375> <0.375,0.125> table 2 ratings obtained from the second of three respondents criteria alternatives en co gr au a1 <0.875,0.125> <0.625,0.375> <0.625,0.250> <0.375,0.250> a2 <0.750,0.250> <0.750,0.250> <0.625,0.125> <0.500,0.250> a3 <0.750,0.125> <0.500,0.125> <0.500,0.250> <0.375,0.125> table 3 ratings obtained from the third of three respondents criteria alternatives en co gr au a1 <0.625,0.125> <0.625,0.375> <0.500,0.250> <0.375,0.250> a2 <0.250,0.375> <0.750,0.125> <0.500,0.125> <0.500,0.250> a3 <0.625,0.250> <0.500,0.125> <0.625,0.375> <0.250,0.375> the group ratings, determined by using eq. (10), and criteria weights are shown in table 4. in this calculation, the following weights were assigned to the respondents: 0.35, 0.34, 0.31. the importance of the considered alternatives based on the ws approach, calculated by using eq. (10), are shown in table 5. the importance of the considered alternatives based on the wp approach, calculated by using eq. (11), are also shown in table 5. stanujkić and karabašević/oper. res. eng. sci. theor. appl. 1 (1) (2018) 29-39 36 table 4 group ratings and criteria weights criteria en co gr au weights alternatives 0.28 0.25 0.24 0.23 a1 <0.742,0.125> <0.625,0.375> <0.590,0.250> <0.375,0.250> a2 <0.595,0.327> <0.750,0.158> <0.590,0.125> <0.500,0.250> a3 <0.717,0.155> <0.500,0.125> <0.586,0.327> <0.339,0.176> table 5 overall ratings and ranking order of alternatives ws wp iq ~ hd rank a1 <0.609,0.229> <0.572,0.253> <0.591,0.241> 0.325 3 a2 <0.622,0.202> <0.604,0.222> <0.613,0.212> 0.300 1 a3 <0.562,0.181> <0.522,0.198> <0.543,0.190> 0.323 2 the overall importance of the considered alternatives, calculated by using eqs. (4) and (7), as well as ranking order of the considered alternatives, are also shown in table 5. as can be seen from table 5, the most appropriate alternative is alternative denoted as a2. for the purpose of verifying the proposed approach, the result of ranking alternatives based on the use of score function is shown in table 6. table 6 values of the score function and the ranking order of alternatives si rank a1 0.190 3 a2 0.210 1 a3 0.190 2 as can be seen from table 6, the results obtained by using the hamming distance and the score function are identical, which confirms accuracy of the proposed approach. 5. conclusions in this article, an extension of the waspas method that allows the use of single-valued intuitionistic fuzzy numbers and the hamming distance is proposed. due to the use of intuitionistic numbers, the proposed extension allows the formation of multiple criteria decision-making models using a smaller number of criteria, which can be more appropriate in some cases. in numerous extensions of many multiple criteria decision-making methods, the ranking of intuitionistic fuzzy numbers is mainly based on the use of the score function. therefore, a ranking based on the hamming distance is suggested in the proposed extension of the waspas method. usability of the proposed extension is demonstrated on an example of website evaluation. in doing so, the same order ranking order of the considered alternatives an extension of the waspas method for decision-making problems with intuitionistic fuzzy numbers: a case of website evaluation 37 was obtained using the proposed ranking procedure and the procedure based on the score function, which confirms the correctness of the proposed procedure. the proposed approach is based on the intuitionistic set theory, which is a generalization of the fuzzy logic. therefore, there are currently no significant limitations in the application of the proposed approach. the only real limitation that is observed is the gathering of the interviewees' realistic attitudes, which can be overcome by preparing interviewees or by using interactive questionnaires. on the other hand, with the adjusted set of evaluation criteria, the proposed model can be applied to solving similar problems. references abdel-basset, m., zhou, y., mohamed, m., & chang, v. 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(2012). optimization of weighted aggregated sum product assessment. elektronika ir elektrotechnika, 122(6), 3-6. © 2018 by the authors. submitted for possible open access publication under the terms and conditions of the creative commons attribution (cc by) license (http://creativecommons.org/licenses/by/4.0/). plane thermoelastic waves in infinite half-space caused operational research in engineering sciences: theory and applications vol. 2, issue 2, 2019, pp. 55-71 issn: 2620-1607 eissn: 2620-1747 doi:_ https://doi.org/10.31181/oresta1902039p * corresponding author. e-mail addresses: dpamucar@gmail.com (d. pamucar), dbozanic@yahoo.com (d. bozanic). selection of a location for the development of multimodal logistics center: application of single-valued neutrosophic mabac model dragan pamučar 1*, darko božanić 2 1 department of logistics, military academy, university of defence in belgrade, serbia 2 military academy, university of defence in belgrade, serbia received: 16 may 2019 accepted: 05 august 2019 first online: 18 august 2019 original scientific paper abstract. logistics center (lc) is unique technological, spatial, organizational and economic unity that brings together different providers and users of logistics services. by selecting the optimal lc location, transport costs are reduced and business performance, competitiveness and profitability are improved. in order to achieve the overall optimum, it is necessary to perform adequate evaluation and selection of the optimal location for the construction of a lc. in this paper is performed the evaluation of potential locations based on new approach in the field of logistics. weight coefficients of criteria are determined using objective model integrated in single-valued neutrosophic (svnn) multi-attributive border approximation area comparison (mabac) model. in order to determine the stability of the model, the svnn mabac model is compared with other representative multi-criteria models. in the final part of the model validation, statistical correlation between the svnn mabac model and other mcdm approaches (svnn waspas, svnn vikor, svnn topsis and svnn codas) is performed. key words: single-valued neutrosophic sets, mabac, logistics center, multi-criteria decision making. 1. introduction a logistics center (lc) location selection presents the process of selecting one of several possible solutions. a large number and heterogeneity of location factors clearly indicate that location issues are interdisciplinary and often require the application of complex procedures when searching for a solution. there are numerous methodologies and procedures that are available concerning this issue (kaboli et al, 2007; lai et al, 2010; sun, 2012; zare at al, 2013; rahmaniani et al, 2013). the problem pamučar and božanić/oper. res. eng. sci. theor. appl. 2 (2) (2019) 55-71 56 of location selection for the development of a logistics center can be considered as a special case within general facility location problem. there are different studies associated with location selection decisions that have been commonly carried out by using multi-criteria decision-making (mcdm) techniques, such as distribution centre selection with weighted fuzzy factor rating system (ou & chou, 2009), selection of distribution centres with three-stage hierarchy of selection (vinh & devinder, 2005), distribution location problem with qfd (chuang, 2002), location problem with fuzzy-ahp (kaboli et al, 2007), location problem with moora and copras method (rezaeiniya et al, 2012), select distribution centers for a firm and location choice of distribution centers with promethee method (fernández-castro and jiménez, 2005), logistic centre selection with dynamic dualdiamond model (cao yunzhong, 2009), logistics distribution location based on genetic algorithms and fuzzy comprehensive evolution (shao et al, 2009), intermodal freight hub location decision with multi-objective evaluation model (sirikijpanichkul & ferreira, 2005; 2006), location selection of logistics centre based on fuzzy ahp and topsis (wang & liu, 2007), selection of logistics centre location with fuzzy topsis based on entropy weight (chen & liu, 2006), facility or plant location selection with multiple objective decision making (farahani & asgari, 2007), facility location selection with ahp and electre (yang & lee, 1997), convenience store location with fuzzy-ahp (kuo et al, 2002), port selection with ahp and promethee (ugboma et al, 2006), reverse logistics location selection with moora (kannan et al, 2008), selecting a site for a logistical centre on factor and methods (chen & liu, 2006), logistic centre selection with fuzzy-ahp and electre method (ghoseiri & lessan, 2008) and multimodal hub location (ashayeri & kampstra, 2002). the research shown in the previous section show that in the process of selecting a lc location, moora, copras, topsis, electre and promethea methods are often used in fuzzy or crisp environment. however, multi-criteria decision-making models that contain qualitative or quantitative attribute values can not always be expressed with crisp numbers. in traditional multi-criteria models (mcdm), the weight of every attribute and rank of alternatives are presented with crisp numbers. though, in reality a decision maker may prefer attribute assessment using linguistic variables, instead of crisp values, due to partial knowledge of attributes or lack of information from the domain of the problem. a fuzzy set presented by zadeh (1965) is one of the tools used to present such imprecision in mathematical form. nevertheless, a fuzzy set can not present the degree of non-affiliation and the degree of imprecision of imprecise parameters. in order to partially overcome the difficulties in defining imprecise parameters atanassov (1986) introduced intuitionistic fuzzy sets (ifs) characterized with the degree of affiliation and non-affiliation simultaneously. however, in the ifs, the sum of the degree of affiliation and the degree of non-affiliation of the imprecise parameter is less than a unity. that is why smarandache (1999) presented the concept of neutrosophic sets (ns) in order to deal with unspecified or inconsistent information that usually exist in reality. the concept of neutrosophic set is a general platform that extends the concepts of classic sets, fuzzy sets (zadeh, 1965), intuitionistic fuzzy sets (atanassov, 1986) and interval valued intuitionistic fuzzy sets (atanassov and gargov, 1989). unlike intuitionistic fuzzy sets and interval valued intuitionistic fuzzy sets, in neutrosophic set uncertainty is explicitly characterized. the neutrosophic set (ns) has three basic components: (1) the truth function t, (2) the indeterminacy function i and selection of a location for the development of multimodal logistics center: application of single-valued neutrosophic mabac model 57 (3) the falsity function f. each of these components in the neutrosophic set is defined independently. however, so defined neutrosophic set hardly finds application in real scientific and engineering field. that is why wang and others developed the concept of interval-valued neutrosophic sets (ivns) (wang et al, 2005) and the concept of single-valued neutrosophic sets (svns) (wang et al, 2010). due to the large presence of uncertainty, imprecision and inconsistency in subjective assessments, and due to simple application in practical problems, ivns and svns have quickly become widely applied in reality (ye, 2013). in this paper, the lc location selection is performed by using single-valued neutrophic multi-attributive border approximation area comparison (mabac) method (svnn mabac). within the svn mabac algorithm, objective approach has been implemented to determine weight coefficients of criteria based on single-valued neutrosophic numbers (svnn). this paper has several goals. the first goal is to develop new multi-criteria model that integrates the svnn concept with objective approach for determining weight coefficients and the mabac method and improves the field of multi-criteria decision making. the second goal of the paper is to form completely new methodology to enable decision-makers to evaluate potential locations for a lc development in the case of partially known values and uncertain values of the decision attributes. the paper is organized in the following way. after the introduction, in the second section is presented single-valued neutrosophic concept and basic arithmetic operations with the svnn. the model for evaluating potential locations for lc development using the svnn mabac model is formed in the third section. the fourth section shows the application of the svnn mabac model and validation of the results obtained. finally, the fifth section provides final conclusions. 2. single-valued neutrosophic set according to the definition of neutrosophic set, neutrosophic set a is universal set x characterized by membership function used to describe truth (truth-membership function) ta(x), membership function used to describe indeterminacy (indeterminacymembership function) ia(x) and membership function used to describe falsity (falsitymembership function) fa(x), where ta(x), ia(x) and fa(x) are real standard or non standard subsets ranging in the interval [-0,1+], so that each of the three neutrosophic components meets the condition where ta(x)→ [-0,1+], ia(x)→ [-0,1+] and fa(x)→ [-0,1+]. the set ia(x) can be used not only to present indeterminacy, but also to present uncertainty, inaccuracy, imprecision, error, contradiction, undefined, unknown, incomplete, redundancy, etc.. (ghaderi et al, 2012; biswas et al, 2016). in order to cover all the unclear information, indeterminacy-membership degree can be divided in subcomponets, such as "contradiction", "uncertainty" and ''unknown'' (smarandache, 2005). sum of these three membership functions of the neutrosophic set ta(x), ia(x) and fa(x) should meet the following condition (biswas et al, 2016) 0 ( ) ( ) ( ) 3 a a a t x i x f x − +  + +  . the component of the neutrosophic set a for all the values of is determined with ac so that ( ) 1 ( )ca at x t x + = − , ( ) 1 ( )ca ai x i x + = − and ( ) 1 ( ) c a a f x f x + = − . neutrosophic set a is contained in another neutrosophic set b (respectively a b ) if and only if for every value x x the following conditions are x x pamučar and božanić/oper. res. eng. sci. theor. appl. 2 (2) (2019) 55-71 58 met: inf ( ) inf ( ) a b t x t x , sup ( ) sup ( ) a b t x t x , inf ( ) inf ( ) a b i x i x , sup ( ) sup ( ) a b i x i x , inf ( ) inf ( ) a b f x f x and sup ( ) sup ( ) a b f x f x . the svns are a special case of neutrophysic sets that can be successfully used in real scientific and engineering applications. the following section provides some basic definitions, operations and properties of the svns (deli and şubaş, 2017). definition 1. let x be universal point (objects) space with generic element x marked with x. then, single-valued neutrosophic set ~ n x is presented with ~ ( ) n t x truth membership function, ~ ( ) n i x indeterminacy membership function and ~ ( ) n f x falsity membership function with the condition  ~ ~ ~( ), ( ), ( ) 0,1 n n n t x i x f x  for every x x . next we can mark svns in a simplified manner as   ~ , ( ), ( ), ( ) |n x t x i x f x x x=  (1) in this paper, for the sake of simplicity the svns   ~ , ( ), ( ), ( ) |n x t x i x f x x x=  will be presented with the simplified expression   ~ ( ), ( ), ( ) |n t x i x f x x x=  . the sum of truth membership function ~ ( ) n t x , indeterminacy membership function ~ ( ) n i x and falsity membership function ~ ( ) n f x of svns meets the following relation ~ ~ ~0 ( ) ( ) ( ) 3, n n n t x i x f x x x + +    (2) when x is continuous object space, then single-valued neutrosophic set ~ n can be presented as ~ ~ ~ ~ ( ), ( ), ( ) | , n n n x n t x i x f x x x x=   (3) when x is discrete object space, then single-valued neutrosophic set ~ n can be presented as ~ ~ ~ ~ ( ), ( ), ( ) | , n n n x n t x i x f x x x x=   (4) therefore, final svnc can be presented as follows ( ) ( ) ~ ~ ~ ~ ~ ~ ~ 1 1 1 1 , ( ), ( ), ( ) ,..., , ( ), ( ), ( ) ; , 1, 2,..., n n n n n n n n n n i n x t x i x f x x t x i x f x x x i n =   = (5) definition 2. let  ~ ~ ~ ~ ( ), ( ), ( ) a a a a t x i x f x= and  ~ ~ ~ ~ ( ), ( ), ( ) b b b b t x i x f x= present two svns, and then the following operations can be defined on the mentioned svns (wang et al, 2010): (1) ~ ~ a b if and only if for every value of x x are met the following conditions ~ ~( ) ( ) a b t x t x , ~ ~( ) ( ) a b i x i x , ~ ~( ) ( ) a b f x f x . (2) ~ ~ a b= if and only if for every value of x x is met that ~ ~ a b and ~ ~ b a . (3)  ~ ~ ~ ~ | ( ),1 ( ), ( ), | , c a a a a x f x i x t x x x x x= −    . selection of a location for the development of multimodal logistics center: application of single-valued neutrosophic mabac model 59 (4) ( ) ( ) ( )~ ~ ~ ~ ~ ~ ~ ~ max ( ), ( ) , min ( ), ( ) , min ( ), ( ) , a b a b a b a b t x t x i x i x f x f x x x =   . (5) ( ) ( ) ( )~ ~ ~ ~ ~ ~ ~ ~ min ( ), ( ) , max ( ), ( ) , max ( ), ( ) , a b a b a b a b t x t x i x i x f x f x x x =   . let  ~ ~ ~ ~ ( ), ( ), ( ) a a a a t x i x f x= and  ~ ~ ~ ~ ( ), ( ), ( ) b b b b t x i x f x= present two svns, and then the operations with ~ a and ~ b are defined with the following expressions (smarandache, 2016): (1) addition svns "+" ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ( ) ( ) ( ) ( ), ( ) ( ) ( ) ( ), ( ) ( ) ( ) ( ) a b a b a b a b a b a b t x t x t x t x a b i x i x i x i x f x f x f x f x + −  + = + −  + −  (6) (2) subtraction svns "‒" ~ ~ ~ ~ ~ ~ ~ ~ ~ ( ) ( ) ( ) ( ) , , 1 ( ) ( ) ( ) a b a a b b b t x t x i x f x a b t x i x f x − − = − (7) where ~ ~ ~( ), ( ), ( ) a a a t x i x f x ,  ~ ~ ~( ), ( ), ( ) 0,1 b b b t x i x f x  with the limitation of ~ ( ) 1 b t x  , ~ ( ) 0 b i x  and ~ ( ) 0 b f x  . (3) multiplication svns "×" ~ ~ ~ ~ ~ ~ ~ ~ ( ) ( ), ( ) ( ), ( ) ( ) a b a b a b a b t x t x i x i x f x f x =    (8) (4) division svns "÷" ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ( ) ( ) ( ) ( ) ( ) , , ( ) 1 ( ) 1 ( ) a a b a b b b b t x i x i x f x f x a b t x i x f x − −  = − − (9) where ~ ~ ~( ), ( ), ( ) a a a t x i x f x ,  ~ ~ ~( ), ( ), ( ) 0,1 b b b t x i x f x  with the limitation of ~ ( ) 0 b t x  , ~ ( ) 1 b i x  and ~ ( ) 1 b f x  . (5) scalar multiplication svns where ( ) ( ) ( )~ ~ ~ ~ 1 1 ( ) , ( ) , ( ) k k k a a a k a t x i x f x = − − (10) (6) svns power, where ( ) ( ) ( )~ ~ ~ ~ ( ) ,1 1 ( ) ,1 1 ( ) k k k k a a a a t x i x f x= − − − − (11) definition 3 (euclidean distance). let ( ) ( ) ~ ~ ~ ~ ~ ~ ~ 1 1 1 1 , ( ), ( ), ( ) ,..., , ( ), ( ), ( ) n n n n a a a a a a a x t x i x f x x t x i x f x= and ( ) ( ) ~ ~ ~ ~ ~ ~ ~ 1 1 1 1 , ( ), ( ), ( ) ,..., , ( ), ( ), ( ) n n n n b b b b b b b x t x i x f x x t x i x f x= be two svns where ( ) 1, 2,...,ix x i n  = . then, euclidean distance between the two svns ~ a and ~ b is defined as follows: 0k  0k  pamučar and božanić/oper. res. eng. sci. theor. appl. 2 (2) (2019) 55-71 60 ( ) ( ) ( )~ ~ ~ ~ ~ ~ 2 2 2~ ~ 1 ( , ) ( ) ( ) ( ) ( ) ( ) ( ) n eu i i i i i i a b a b a b i d a b t x t x i x i x f x f x =   = − + − + −     (12) normalized euclidean distance between two svns ~ a and ~ b is obtained with the application of the following expression ( ) ( ) ( )~ ~ ~ ~ ~ ~ 2 2 2~ ~ 1 1 ( , ) ( ) ( ) ( ) ( ) ( ) ( ) 3 n n eu i i i i i i a b a b a b i d a b t x t x i x i x f x f x n =   = − + − + −     (13) definition 4. let  ~ ~ ~ ~ ( ), ( ), ( ) a a a a t x i x f x= be single valued neutrosophic number, and then the score function ~ ( )s a can be determined as crisp value by applying the following expression (zavadskas et al, 2015) ~ ~ ~~ 3 ( ) 2 ( ) ( ) ( ) 4 a a a t x i x f x s a + − − = (14) where the score function is defined in the interval   ~ ( ) 0,1s a  . such defined score function allows obtaining crisp values ranging in the same interval as ~ a . definition 5. let  ~ ~ ~ ~ ( ), ( ), ( ) a a a a t x i x f x= and  ~ ~ ~ ~ ( ), ( ), ( ) b b b b t x i x f x= be any of the svns. then, if the condition ~ ~ ( ) ( )s a s b is valid, single valued neutrosophic number ~ a is smaller than single valued neutrosophic number ~ b , respectively ~ ~ a b . definition 6. the fuzzification of the svns  ~ ~ ~ ~ ( | ( ), ( ), ( ) ) | n n n n x t x i x f x x x=  can be defined as the process of mapping ~ n in the fuzzy set  ~ ~ | ( ) | f f x x x x=  , respectively ~ ~ f n f= → for x x . representative degree of membership to the fuzzy function  ~ ( ) 0,1 f x  of the vector  ~ ~ ~( | ( ), ( ), ( ) ) | n n n x t x i x f x x x is defined as follows ( ) ( ) ( )~ ~ ~ ~ 2 2 2 ( ) 1 1 ( ) ( ) ( ) 3 f n n n x t x i x f x   = − − + +    (15) 3. single valued neutrosophic mabac method step 1. forming initial decision-making matrix (n). the evaluation of alternatives by criteria is performed by m experts  1 2, ,..., me e e with the assigned weight coefficients 1 2 { , ,..., } m    , 0 1, ( 1, 2,..., ) e e m  = , 1 1 m e e  = = . with the aim of final ranking of alternatives i a a ( 1, 2,..,i b= ), every expert e e ( 1, 2,...,e m= ) evaluates alternatives by the defined set of criteria  1 2, ,... nc c c c= . therefore, for every expert is formed related initial decision-making matrix selection of a location for the development of multimodal logistics center: application of single-valued neutrosophic mabac model 61 ( ) ( ) ( ) 11 12 1 ( ) ( ) ( ) ( ) ( ) 21 22 2 ( ) ( ) ( ) 1 2 ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 11 11 11 12 12 12 1 1 1 ( ) ( ) 11 11 11 ... ... ... , , , , ... , , , , e e e n e e e e e n ij b n e e e b b bn e e e e e e e e e n n n e e n t i f t i f t i f t i f                              = =         = ( ) ( ) ( ) ( ) ( ) ( ) ( ) 22 22 22 2 2 2 ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 1 1 1 , , ... , , , , , , ... , , e e e e e e e n n n e e e e e e e e e b b b bn bn bn bn bn bn t i f t i f t i f t i f t i f                               (16) where the elements of the matrix ( )en ( ( )e ij  ) present svn numbers from the predefined neutrosophic linguistic scale. final aggregated decision-making matrix n is obtained by averaging the elements ( ) ( ) ( ) ( ), ,e e e e ij ij ij ij t i f     = of the matrix (16) by applying the expression (18). 11 12 1 21 22 2 1 2 11 11 11 12 12 12 1 1 1 11 11 11 22 22 22 2 2 2 1 1 1 ... ... ... , , , , ... , , , , , , ... , , , , , , ... n n ij b n b b bn n n n n n n b b b bn bn bn bn n t i f t i f t i f t i f t i f t i f t i f t i f t                                           = =         = , , bn bn i f                  (17) where the elements , , ij ij ij ij t i f     = are obtained by applying the svnn weighted average operator (swnswaa) , with the expression (18) ( ) ( ) ( ) (1) ( 2) ( ) (1) 1 ( ) ( ) ( ) 1 1 1 ( , ,.., ) 1 1 , , e e e m m ij ij ij ij e ij b m m m e e e ij ij ij b b b svnswaa t i f             = = = = = = = − −     (18) where e  the weight coefficients, 0 1, ( 1, 2,..., ) e e m  = , 1 1 m e e  = = . step 2. normalization of initial decision-making matrix (n). by normalization of the matrix elements (17), it is obtained the matrix ^ ^ ^ ^ ^ , , ij ij ij ij b n b n n t i f          = =        . the elements of the matrix ^ n are obtained by applying the expression (19) , , , ; ,1 , , ; jij ij ij ij jij ij ij t i f if c b f i t if c c           =   −   (19) where b and c, respectively, present the sets of criteria of benefit and cost type. step 3. determining weight coefficients’ values. determining weight coefficients values is based on maximum deviation model (mdm). after the normalization of pamučar and božanić/oper. res. eng. sci. theor. appl. 2 (2) (2019) 55-71 62 expert correspondent matrices, aggregated normalized decision-making matrix is obtained ^ ^ ^ ^ ^ , , ij ij ij ij b n b n n t i f          = =        . aggregated normalized decision-making matrix ^ n is further transformed into the weighted matrix * * ij b n n    =   , * ij j ij w =  . in the matrix can be calculated the degree of elements’ deviation kj  ( 1 k b  ) in relation to other elements ij  within the criteria j c ( 1, 2,...,j n= ) * * 1 1 ( ) ( , ) ( , ) b b ij j kj ij kj ij j k k w d d w     = = = =  (20) where ( , ) kj ij d   present the distance between kj  ( 1 k b  ) and ij ( 1, 2,...,j n= ). from the expression (19) it can be clearly noted that for higher values of ( ) ij j d w the alternative i a ( 1, 2,...,i b= ) is better. the mdm model is based on the following starting points: (1) in case there are small deviations between the value of kj ( 1 k b  ) and the value of ij within the criterion jc ( 1, 2,...,j n= ), then the criterion has low influence to the rank of alternatives and small value of the weight coefficient jw ; (2) contrary to the mentioned, if there are significant deviations between the value of kj ( 1 k b  ) and the value of ij within the criterion jc ( 1, 2,...,j n= ), then the criterion has high influence to the rank of alternatives and large value of the weight coefficient jw ; (3) if all the values of ij are identical within the criterion jc ( 1, 2,...,j n= ), then the criterion has no influence to the rank of alternatives and has the value of the weigh coefficient 0 j w = . after that, it is calculated the degree of deviation between all the elements within the observed criterion jc ( 1, 2,...,j n= ). step 3.1. calculation of the degree of deviation between all the elements within the observed criterion jc ( 1, 2,...,j n= ) 1 1 1 ( ) ( ) ( , ) b b b j j ij j kj ij j i i k w w d w    = = = = =  (21) respectively, calculation of total deviation of all alternatives by criteria 1 1 1 1 ( ) ( ) ( , ) n n b b j j kj ij j j j i k w w d w    = = = = = =  (22) step 3.2. the weight coefficients jw are obtained by solving optimization model which is based on maximum deviation 1 1 1 2 1 max ( ) ( , ) . . 1; 0 1; 1, 2,..., n b b ij uj j j i u n j j j d w d w s t w w j n   = = = = =  =     =   (23) with the aim of solving the model (23), it is introduced the lagrange function n selection of a location for the development of multimodal logistics center: application of single-valued neutrosophic mabac model 63 2 1 1 1 1 ( , ) ( , ) 1 2 n b b n ij uj j j j i u j l w p d w w    = = = =   = + −      (24) after partial deviation by w , and then by p are obtained two equations ( ) 0 j d w pw+ = i 2 1 1 n jj w = = , where ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 1 1 1 2 1 1 1 1 1 3 1 3 uj ij uj ij uj uj ij uj ij uj b b pij p t q t q t r t r i u j n b b pij p t q t q t r t r j i u f s f s f s f s f s f s w f s f s f s f s f s f s         − − − − = = − − − − = = =    − + − + −      =      − + − + −            (25) step 3.3. calculation of final values of weight coefficients. by normalization of the values (25) are obtained final values of weight coefficients. 1 j j n j j w w  = =  (26) where j present optimal values of weight coefficients. step 4. calculation of the elements of the border approximate area matrix (g). the elements of the matrix 1 j n g g   =   are obtained by applying the expression (27) ( ) ( ) ( ) ( ) 1/ 1/ 1/ 1/ 1 1 1 1 ,1 1 ,1 1 b b b b b b b b j ij dij dij dij i i i i g d t i f = = = = = = − − − −    (27) step 5. calculation of the matrix of the distance of alternatives from the border approximate area (s). the elements of the matrix ij b n s s   =   are obtained by applying the expression (28) ( , ), ; 0, ; ( , ), . eu ij j ij j ij ij j eu ij j ij j d d g if d g s if d g d d g if d g    = =  −  (28) where the distance is determined by applying the expression(13). step 6. ranking alternatives. based on the values of the criteria functions of alternatives i q ( 1, 2,...,i b= ), it is performed ranking of alternatives. criteria functions are obtained by applying the expression (29), 1 , 1, 2,..., ; 1, 2,..., . n i j j q s i b j n = = = = (29) rank of alternatives is determined based on the value i q , where it is more favorable for alternative to have as high as possible value of the criteria function i q . 4. application of the svnn mabac model in this paper, a case study of location selection for a multimodal lc is presented. as an example, eight potential locations for the development of a multimodal lc on the danube river in the territory of serbia are considered. based on the recommendations eu d pamučar and božanić/oper. res. eng. sci. theor. appl. 2 (2) (2019) 55-71 64 of zecevic (2006), nine criteria are identified based on which the selection of the location of a multimodal lc is done, as in the table 1. table 1. criteria for the evaluation of multimodal lc locations mark criteria name criteria description c1 connectivity to multimodal transport the criterion presents traffic and logistic characteristics of the environment and the connection of the location with other modes of transport. this criterion expresses the possibility of approach, accepting and dispatching of the means of external transport. it belongs to the group of "benefit" criteria. c2 assessment of infrastructure construction this criterion shows the regulation of infrastructure to adequately serve the demands of goods flows in the lc. every location has certain limitations, some of which can be eliminated by investing material resources, while some present limiting factors for the development and exploitation of the lc. the criterion belongs to the group of "benefit" criteria. c3 influence to the environment this criterion is descriptive and presents the impact of the location to environmental pollution through the emission of gases, noise and vibration. it belongs to the group of "cost" criteria. c4 compliance with spatial plans and economic development strategy the criterion shows the compliance of the lc development with spatial plans and the strategy of economic development. it belongs to the group of "benefit" criteria. c5 existing intermodal transport units this criterion is an estimate of the existing transport flows towards the lc. it is expressed through an estimate of the number of itus per year (itu / year). it belongs to the group of "benefit" criteria. c6 loading capacities of the lc this criterion presents the loading capacities of the lc. the lc loading capacities express the maximum number of itus that can be unloaded within one hour (itu / h). it belongs to the group of "benefit" criteria. c7 available area for future development and lc capacity expansion based on the requirements of material flows and preliminary estimation of the required area for certain subsystems, it is determined the minimal required total area for the development of the lc. when designing, additional area is planned for the expansion and development of terminals in the future. the criterion belongs to the group of "benefit" criteria. c8 distance of the users from the lc the criterion is descriptive and presents an estimate of the distance of the lc location from the potential users of services. it belongs to the group of "cost" criteria. c9 traffic safety the criterion presents the regulation of the location of the lc from the aspect of traffic safety (regulation of traffic signalization, number of traffic accidents on access roads, regulation of road and rail crossings). the criterion is descriptive and belongs to the group of "benefit" criteria. in model testing participated four experts from the field of transport which are assigned weight coefficients we1=0.2864, we2=0.2741, we3=0.2170 and we4=0.1673. selection of a location for the development of multimodal logistics center: application of single-valued neutrosophic mabac model 65 table 2. aggregated initial decision-making matrix experts evaluated the criteria by applying linguistic scale: very important – vi (0.90,0.10,0.10); important – i (0.75,0.25,0.20); medium – m (0.50,0.50,0.50); unimportant – ui (0.35,0.75,0.80); very unimportant – vu (0.10,0.90,0.90). step 1: in the first step, the experts evaluated eight alternatives (locations) in relation to the nine evaluation criteria marked with c1 to c9. thus, for every expert, one correspondent matrix is formed. evaluation of the alternatives is made using predefined set of the svn linguistic variables. therefore, for every expert, a correspondent initial decision-making matrix is defined, which by using swnswaa (18) is aggregated into the initial decision-making matrix, as in the table 2. table 3. deviations between the criteria in the initial decision-making matrix criteria a1 a2 a3 a4 a5 a6 a7 a8 c1 0.693161 0.729263 0.711873 0.673599 0.64468 0.854589 0.670868 0.873455 c2 0.658016 0.678004 0.661235 0.7689 0.726337 0.80292 0.721386 0.691708 c3 0.649877 0.812623 0.656083 0.646737 0.669801 0.866943 0.590643 0.604452 c4 0.620961 0.728282 0.548415 0.614471 1.016261 0.743172 0.654049 0.545849 c5 0.639613 0.718458 0.681562 0.750361 1.218171 0.889591 0.75045 0.872205 c6 0.675299 0.623921 0.72922 0.80159 0.626706 0.658559 0.673925 0.589811 c7 0.779089 0.738575 0.715328 0.717412 0.779176 0.777315 0.701796 0.665741 c8 0.843699 0.894391 0.769733 0.772811 0.672498 0.770101 0.769027 0.818187 c9 0.839894 0.942952 0.857972 0.860605 0.95581 0.731635 0.689946 0.725356 sum 5.851 5.709 5.497 5.471 6.520 5.379 5.874 6.310 crit a1 a2 a3 a4 a5 a6 a7 a8 c1 (0.54,0.3,0.28) (0.53,0.34,0.35) (0.52,0.37,0.28) (0.5,0.33,0.29) (0.41,0.33,0.29) (0.63,0.37,0.38) (0.52,0.29,0.23) (0.59,0.34,0.47) c2 (0.51,0.29,0.24) (0.53,0.31,0.25) (0.5,0.34,0.26) (0.56,0.31,0.39) (0.47,0.33,0.4) (0.55,0.46,0.3) (0.49,0.38,0.35) (0.51,0.36,0.3) c3 (0.47,0.27,0.33) (0.57,0.4,0.34) (0.46,0.32,0.31) (0.5,0.27,0.26) (0.49,0.34,0.29) (0.59,0.38,0.42) (0.41,0.3,0.19) (0.45,0.28,0.24) c4 (0.44,0.27,0.25) (0.47,0.34,0.35) (0.37,0.25,0.15) (0.41,0.34,0.15) (0.63,0.42,0.48) (0.51,0.32,0.35) (0.39,0.4,0.19) (0.33,0.24,0.24) c5 (0.41,0.28,0.23) (0.52,0.31,0.29) (0.44,0.19,0.34) (0.52,0.33,0.36) (0.56,0.75,0.47) (0.62,0.33,0.44) (0.53,0.35,0.32) (0.58,0.42,0.41) c6 (0.51,0.33,0.31) (0.48,0.24,0.28) (0.51,0.36,0.36) (0.52,0.41,0.4) (0.45,0.32,0.28) (0.5,0.31,0.31) (0.52,0.31,0.3) (0.43,0.25,0.25) c7 (0.56,0.3,0.44) (0.53,0.39,0.31) (0.55,0.27,0.36) (0.54,0.32,0.37) (0.53,0.39,0.41) (0.58,0.37,0.37) (0.5,0.32,0.38) (0.49,0.29,0.32) c8 (0.59,0.4,0.43) (0.6,0.49,0.41) (0.55,0.43,0.32) (0.56,0.39,0.36) (0.47,0.3,0.26) (0.57,0.42,0.25) (0.48,0.42,0.39) (0.61,0.41,0.33) c9 (0.61,0.42,0.37) (0.66,0.47,0.43) (0.58,0.35,0.48) (0.62,0.42,0.4) (0.65,0.5,0.44) (0.45,0.38,0.35) (0.47,0.28,0.31) (0.48,0.29,0.38) pamučar and božanić/oper. res. eng. sci. theor. appl. 2 (2) (2019) 55-71 66 step 2: in the second step by applying the expression (19) it is normalized the aggregated matrix, which is further in the step three used for determining objective values of the weights of criteria. step 3: after determining normalized initial decision-making matrix, by applying the expressions (20)-(24) are calculated the deviations between the elements of the aggregated matrix. thus, for the criteria (c1-c9) are obtained the deviations presented in the table 3. by applying the expressions (25) and (26) are obtained optimal values of the weigh coefficients of criteria (0.1100,0.1073;0.1033;0.1028;0.1225;0.1011;0.1104;0.1186;0.1241) j w = . step 5: the calculation of the elements of border approximate area matrix (baa). by applying the expression (27) are obtained the elements of border approximate area matrix, as in the table 4. table 4. border approximate area matrix criteria baa c1 (0.10,0.11,0.12) c2 (0.11,0.11,0.13) c3 (0.13,0.12,0.10) c4 (0.17,0.12,0.12) c5 (0.08,0.13,0.15) c6 (0.14,0.10,0.10) c7 (0.08,0.11,0.08) c8 (0.06,0.09,0.08) c9 (0.07,0.09,0.11) step 6: the calculation of the matrix of alternatives distance from border approximate area. by applying the expression (28) is determined the distance of alternatives from the baa, as in the table 5. table 5. distance of alternatives from border approximate area criteria a1 a2 a2 a4 a3 a6 a4 a8 c1 0.833 -0.500 -0.500 0.500 -0.333 -0.667 0.167 0.500 c2 0.500 0.500 -0.500 0.667 -0.333 0.333 -0.667 0.333 c3 0.167 -0.333 0.500 0.833 0.500 0.667 0.833 0.167 c4 0.167 -0.167 0.333 -0.667 0.333 -0.500 0.333 0.167 c5 -0.333 -0.500 0.333 0.667 -0.100 -0.167 0.500 0.333 c6 0.333 0.500 0.500 0.833 -0.333 0.333 -0.667 0.167 c7 -0.333 -0.500 -0.333 -0.833 -0.500 0.500 -0.833 0.667 c8 0.500 -0.667 0.333 0.833 0.500 0.333 -0.667 0.833 c9 -0.667 0.167 0.500 -0.833 -0.667 0.667 0.167 0.333 step 7: selection of a location for the development of multimodal logistics center: application of single-valued neutrosophic mabac model 67 ranking alternatives. based on the distance of alternatives from border approximate area (table 5), by applying the expression (29) are obtained final values of the criteria functions of alternatives and final rank of alternatives, as in the table 6. table 6. criteria functions and rank of alternatives alternative qi rank a1 1.167 4 a2 -1.500 8 a3 1.160 5 a4 2.000 2 a5 -0.933 7 a6 1.499 3 a7 -0.834 6 a8 3.500 1 the validation of the svnn mabac model is carried out in this part. the validation of the svnn mabac model is made by comparison with other multi-criteria svnn models from bibliography. for these purposes, the following methods are used: svnn waspas (zavadskas et al, 2015), svnn vikor (pouresmaeil et al. 2017), svnn topsis (pouresmaeil et al. 2017) i svnn codas (peng & dai, 2018). 1 2 3 4 5 6 7 8 svnn mabac svnn waspas svnn vikor svnn topsis svnn codas a1 a2 a3 a4 a5 a6 a7 a8 figure 1. comparison of the results of the svnn mabac model with other mcdm models the figure 1 shows that the eighth location is the best solution in all scenarios formed, respectively, in the application of all the other methods mentioned above. the location four in four models is in the second position, using svnn mabac, svnn waspas, svnn topsis and svnn codas, while using the svnn vikor model it is in the third place. this is due to the significant differences between the svnn vikor methodology and other mcdm models considered. the second location is on the eighth position four times, while in the svnn topsis model it is in the seventh pamučar and božanić/oper. res. eng. sci. theor. appl. 2 (2) (2019) 55-71 68 position. considering these are only the worst alternatives, these changes in ranks have no impact on the final decision. since there is no complete consensus in the results between the models considered, statistical comparison of the ranks is performed in the following part and the correlation of the ranks is done using spearman’s coefficient (tian et al., 2018; pamucar et al., 2019). in the table 7 it is presented spearman's coefficient of rank correlation between the models observed. table 7. spearman's coefficient of correlation for rank location using different methods methods svnn mabac svnn waspas svnn vikor svnn topsis svnn codas svnn mabac 1.000 1.000 0.999 0.999 1.000 svnn waspas 1.000 0.999 0.999 1.000 svnn vikor 1.000 0.997 0.999 svnn topsis 1.000 0.999 svnn codas 1.000 based on the total calculated statistical coefficient of correlation (0.990), it can be concluded that the ranks are in high correlation in all formed scenarios. observing the overall ranks and correlation coefficients, it can be concluded that the model obtained is very stable, and that the ranks are in high correlation. since all the values are significantly greater than 0.90, according to pamucar et al. (2018) these present very high correlation of ranks. 5. conclusion this paper presents the application of the svnn mabac model in the process of selecting the location of multimodal logistic center on the danube river. the svnn mabac model additionally enriches the field of multi-criteria decision making. the model presented allows making more objective decisions through respecting subjectivity and uncertainty in the decision-making process. the third contribution of the paper is the improvement of the methodology for evaluating and selecting optimal location for the development of multimodal lc through new approach to dealing with imprecision, since the application of this or similar approach has not been observed in the literature that examines the subject area. with the application of the developed approach, it is possible to consider the evaluation of a lc construction sites systematically, which have significant impact on the efficiency achievement of the entire supply chain. the svnn mabac model is also applicable for solving other logistic problems, such as supplier evaluation, selection of means of transport in other areas. the flexibility of the model is reflected in the fact that its upgrade can be carried out by integrating other methods of multi-criteria decision-making. the results of the research shown in this paper indicate that the svnn mabac model presents a useful and reliable tool for rational decision-making. basic recommendation for further use of this method is simple mathematical apparatus, stability (consistency) of the solution, as well as the possibility of combining it with other methods, especially concerning the determination of the weights of criteria. selection of a location for the development of multimodal logistics center: application of single-valued neutrosophic mabac model 69 references ashayeri, j., & kampstra, p. 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(2006). robni terminali i robno-transportni centri. saobraćajni fakultet univerziteta u begradu (only in serbian). operational research in engineering sciences: theory and applications vol. 5, issue 3, 2022, pp. 131-152 issn: 2620-1607 eissn: 2620-1747 doi: https:// https://doi.org/10.31181/oresta051022061d * corresponding author. doductrung@haui.edu.vn (d. t. do) application of fuca method for multi-criteria decision making in mechanical machining processes duc trung do hanoi university of industry, vietnam received: 12 august 2022 accepted: 29 september 2022 first online: 05 october 2022 research paper abstract: multi-criteria decision making (mcdm) is a very useful tool to find the best solution among many solutions. for most mcdm methods, the data must be normalized. however, the data normalization method has a significant influence on the results of ranking solutions. choosing the right data normalization method is sometimes complicated. in many mcdm methods, fuca is known as the method without using normalize the data. however, the fuca method has a small limitation. all publications that were applied this method have not mentioned this limitation. in this study, this limitation was overcome and then used for multi-criteria decision making in some cases in the mechanical processing field. the ranked results of the solutions when determined by the fuca method are compared with those ones when using other mcdm methods. the sensitivity analysis was also performed. the results show that the fuca method can be used for multi-criteria decision making in mechanical machining. it is also expected to be successful when applying in other fields. the works in the future were mentioned in the last section of this article as well. keywords: mcdm, fuca method, mechanical machining 1. introduction the decision to choose one of many solutions always happens in many situations in many different fields. each solution is described by different criteria, in which, there are criteria as the larger the better such as machining productivity, tool life, and product quality, etc. conversely, there are also criteria as the smaller the better such as cost, energy consumption, etc. in these cases, the decision making to select a solution is known as “multi-criteria decision making” (zopounidis & doumpos, 2017). over the years, mcdm methods have received more and more attention from many scholars. a common feature of most mcdm methods is the need to perform the data normalization (zopounidis & doumpos, 2017). the criteria with different dimensions d. t. do /oper. res. eng. sci. theor. appl. 5(3)2022 131-152 132 are converted to the same dimensionless form as the basis for ranking options, which is the goal of data normalization (wen et al. 2020; krishnan, 2022). however, the data normalization method in each mcdm method is not exactly the same, which leads to different ranking results of the mcdm methods (aytekin, 2021; ersoy, 2021; palczewski & sałabun, 2019; lakshmi & venkatesan, 2014). the rank inversion phenomenon can also occur if the selected data normalization method is not suitable with the mcdm method (trung, 2022). currently, many mcdm methods have been proposed by reseachers, it is quite difficult for decision makers to choose one of them in ranking process. fuca is known as a multi-criteria decision making method without using data normalization (fernando et al., 2011). simple steps to implement decision making using this method, its limitations as well as improvements to overcome those limitations will be presented in the next sections of this paper. baydas (2022) simultaneously used three methods including moora, mabac, and fuca to assess the rankings of companies in the period before and after the covid 19 pandemic. the author showed that the fuca method gives more effective than the other two methods. in another study, baydas (2022) used two methods fuca and wsa to evaluate the financial performance of companies. the results of this study show that the fuca method is better than the wsa method in finding the best solution. in another study, baydas & pamucar (2022) also used the fuca method to evaluate the financial performance of companies. in addition to the fuca method, in this study, six other methods were used simultaneously including promethee, copras, topsis, saw, codas, and moora. their results showed that fuca and promethee were equally effective in finding the best solution, and that these two methods were better than the other five ones. baydas et al. (2022) one time again used simultaneously ten multicriteria decision making methods including fuca, promethee, topsis, gra, s-, wsa, saw, copras, moora, and linmap to evaluate the financial performance of twentythree companies. the authors concluded that the two methods fuca and promethee were equally effective and better than other eight methods. ouattara et al. (2022) used two methods topsis and fuca to make multi-criteria decisions in the selection of chemical manufacturing processes. they confirmed that the fuca method is better than the topsis method. the analysis results from some of the above studies show that the fuca method has been successful in ranking the solutions in the economic and chemical manufacturing fields. it has also been determined to be better or equivalent to other mcdm methods. however, the number of studies that have applied this method is very limited. this method has never been applied to multi-criteria decision making in the field of mechanical processing. the application of fuca method in multi-criteria decision-making in mechanical processing is a novelty and is also the first reason to conduct this study. it is important to note that the fuca method has a small limitation. this limitation has not been considered in any published studies. that limitation occurs when a certain criterion has equal value in two or more solutions. the detailed analysis of this limitation of the fuca method as well as the improvement to overcome this limitation will be presented in section 2 of this paper. this is also the second reason for doing this study. from the above analysis, the structure of the next sections of this paper includes: (1) discovering the limitation of the fuca method and improving this method to overcome the limitation; (2) apply fuca method for multi-criteria decision making for some common mechanical machining processes. in each example, the data were https://ieeexplore.ieee.org/author/37087868293 https://www.sciencedirect.com/science/article/abs/pii/s0098135411002870?via%3dihub#! application of fuca method for multi-criteria decision making in mechanical machining processes 133 referenced from published studies. the ranking results of the solutions when using fuca method were compared to that ones when using other mcdm methods. the sensitivity analysis in each case was also performed for different scenarios; (3) discussing about the achieved results; and (4) conclusion of this study and proposal of the further studies are the closing content of this paper. 2. fuca method the fuca method performs the ranking of solutions in just three simple steps as follows (fernando et al. 2021): step 1. rank the solutions for each criterion (rij). suppose there are m solutions, the best value will be ranked 1, otherwise the worst value will be ranked m. if there are n criteria, perform n ranking times for each criterion. however, at this step, we have noticed a limitation of the fuca method that when a certain criterion has the same value in two or more solutions, how will the ranking of the solutions (for each criterion) be implemented? to clarify this issue, a simple example is presented as below. suppose there are four solutions including a1, a2, a3, and a4, each of which is described by three criteria c1, c2, and c3, where c1 and c2 are the criteria as the larger the bettere, and c3 is the criterion as the smaller the better as shown in table 1. table 1. example of a certain criterion having equal value in several solutions no. criteria c1 c2 c3 a1 4 3 4 a2 6 5 2 a3 2 5 4 a4 8 7 4 the ranking of alternatives for each criterion will be conducted as follows. for criterion c1 (the larger the better): a4 ranked 1, a2 ranked 2, a1 ranked 3, and a2 ranked 4. for this criterion, its values in the four solutions are different. so the ranking process is performed easy. for criterion c2 (the larger the better): because c2 at a4 is the largest, so a4 ranked 1, c2 at a1 is the smallest, so a1 ranked 4. however, c2 at a2 and a3 are equal. so, what is the ranking order of a2 and a3? a simple proposal that a2 and a3 should have the same rank, and equal to 2.5 (the average of 2 and 3). for criterion c3 (the smaller the better): because c3 at a2 is the smallest, so a2 is ranked 1. c3 has the same value in three solutions a1, a3, and a4, so all three solutions ranked 3 (the average of 2, 3, and 4). from above analyzed results, a table of the ranking results of the solutions for the data in table 1 was presented in table 2. https://ieeexplore.ieee.org/author/37087868293 d. t. do /oper. res. eng. sci. theor. appl. 5(3)2022 131-152 134 table 2. the ranked results of the solutions according to the data in table 1 no. rank c1 c2 c3 a1 3 4 3 a2 2 2.5 1 a3 4 2.5 3 a4 1 1 3 step 2. calculate the score of each solution according to the eq. (1). 𝑣𝑖 = ∑ 𝑟𝑖𝑗 . 𝑤𝑗 𝑛 𝑗=1 (1) where wj is the weight of the criterion j. step 3. rank the solutions by the value of vi. the solution with the smallest vi is the best one, and vice versa. the discovery of the limitation of the fuca method as well as the proposed method to overcome that limitation were performed. to evaluate the effectiveness of this remedial method, in the next sections of this study, the proposed method will be applied to multi-criteria decision making in some cases in the mechanical processing field. because the main purpose of this study is the application of the fuca method for multi-criteria decision making in mechanical machining processes, the data are therefore all referenced from the published studies, the number of criteria in each case is not the same. two main reasons for performing this content include: first, not spending too much effort on conducting the experiments; and second, published studies have used other mcdm methods to rank solutions. the ranking results of the solutions when using those mcdm methods are used to compare to those ones when using the fuca method. in each case, first, the weight of the criteria that was used was the value in the published studies. then, in each case, the sensitivity analysis was also performed for different scenarios by varying the weights of the criteria. the number of the generated scenarios in each case also varies. the implementation of examples in different mechanical processing processes, the number of criteria in different situations, the number of different scenarios aim to draw the most general conclusions. 3. applying the fuca method for multi-criteria decision making in several cases 3.1. multi-criteria decision making in milling process (example 1) this case used the experimental data of the milling process of ti-6al-4v alloy by nguyen et al. (2021). in that study, they conducted nine experiments, each of which changed three parameters including cutting speed, feed rate, and depth of cut. two criteria were measured in each experiment including surface roughness (c1) and material removal rate (c2). the experimental data are presented in table 3. in which application of fuca method for multi-criteria decision making in mechanical machining processes 135 c1 is the smaller the better criterion, c2 is the larger the better criterion. in addition, in that study, they used the entropy method to determine the weights for the criteria, and the determined weights of c1 and c2 were 0.2906 and 0.7094, respectively. that study also used the topsis method for multi-criteria decision making with the aim of determining the solution ai (with i = 1 ÷ 9) with simultaneously ensuring the smallest c1 and the largest c2. table 3. experimental data when milling process of alloy ti-6al-4v (nguyen et al. 2021). no. criteria c1 (m) c2 (cm3/min) a1 0.281 5.42 a2 0.337 1.08 a3 0.737 16.25 a4 0.328 21.67 a5 0.321 10.83 a6 0.507 2.17 a7 0.359 32.5 a8 0.412 43.33 a9 0.636 16.52 the ranking of the solutions according to the fuca method will be performed as follows. step 1. rank the solutions for each criterion. in this case, both criteria c1 and c2 have different values for all solutions, so the ranking of solutions according to the fuca method is conducted normally. the results are presented in the table 4. table 4. ranking the solutions for each criterion (example 1) no. rank (rij) c1 c2 a1 1 7 a2 4 9 a3 9 4 a4 3 3 a5 2 6 a6 7 8 a7 5 2 a8 6 1 a9 8 5 step 2. calculate the score of each solution according to eq (1). first of all, the weights of the selected criteria are the same as their values in the referenced literature, i.e., the weights of c1 and c2 are 0.2906 and 0.7094, respectively (nguyen et al. 2021). the calculated results are presented in table 5. d. t. do /oper. res. eng. sci. theor. appl. 5(3)2022 131-152 136 table 5. the vi score of each solution (example 1) no. rij. wj vi c1 c2 a1 1 7 5.2564 a2 4 9 7.5470 a3 9 4 5.4530 a4 3 3 3.0000 a5 2 6 4.8376 a6 7 8 7.7094 a7 5 2 2.8718 a8 6 1 2.4530 a9 8 5 5.8718 step 3. ranking the solutions according to the value of vi, the calculated results are presented in table 6. the ranking results of the solutions when using the topsis method are also presented in this table. table 6. ranking the solutions for example 1 no. rank fuca topsis a1 5 7 a2 8 9 a3 6 4 a4 3 3 a5 4 6 a6 9 8 a7 2 2 a8 1 1 a9 7 5 the calculated results from table 6 show that when using the improved fuca method, it was determined that a8 is the best solution. this result is also similar to the result when ranking solutions by topsis method (nguyen et al. 2021). in addition, the second ranked solution (a7) and the third ranked solution (a4) also coincide when using both improved fuca and topsis methods. thus, in this case, it is seen that when using the same set of weight values, two methods including improved fuca and topsis are considered to be equally effectiveness. however, in order to evaluate the effectiveness of a certain mcdm method in each case, the last work that needs to be done is the sensitivity analysis (bozanic et al. 2021; muhammad et al. 2021). many studies have performed the sensitivity analysis by changing the weighted values of the criteria and using sperman's rank correlation coefficient (bobar et al. 2020; pamucar et al. 2021; dimic et al. 2019; le et al. 2022; lamba et al. 2019). in this study, the sensitivity analysis was also performed in the same way. the sperman's rank correlation coefficient is determined according to eq. (2). 𝑆 = 1 − 6 ∑ 𝐷𝑖 2𝑛 𝑖=1 𝑛(𝑛2 − 1) (2) application of fuca method for multi-criteria decision making in mechanical machining processes 137 where di presents the difference of the rank according to the given scenario and the rank in the corresponding scenario, and n is the number of ranked elements. six different scenarios were created by randomly changing the weights of the criteria as presented in table 7. in which, s4 is the scenario just implemented above. table 7. weight of criteria in different scenarios (example 1) criteria scenarios s1 s2 s2 s4 s5 s6 c1 0.2 0.22 0.25 0.2906 0.3 0.35 c2 0.8 0.78 0.75 0.7094 0.7 0.65 the ranked results solutions according to six different scenarios are presented in table 8. we see that in all six given scenarios, a8 is still the best solution. table 8. ranking the solutions in different scenarios (example 1) no. scenarios s1 s2 s3 s4 s5 s6 a1 7 7 6 5 5 5 a2 9 9 9 8 8 8 a3 4 4 5 6 6 6 a4 3 3 3 3 3 2 a5 5 5 4 4 4 4 a6 8 8 9 9 9 9 a7 2 2 2 2 2 3 a8 1 1 1 1 1 1 a9 6 6 7 7 7 7 table 9 presents the values of the spearman coefficients calculated according to formula (2) for comparison between scenarios as well as comparison of the initial ranking si. table 9. the values of sperman’s rank correlation coefficients (example 1) si s1 s2 s3 s4 s5 s6 si 1 1 1.000 0.958 0.900 0.900 0.883 s1 1 1.000 0.958 0.900 0.900 0.883 s2 1 0.958 0.900 0.900 0.883 s3 1 0.975 0.975 0.958 s4 1 1.000 0.983 s5 1 0.983 s6 1 the calculed results in table 9 show that the sperman's rank correlation coefficient of the solution is in the range s  [0.883, 1]. it means the degree of correlation is very high. this shows that the change in rankings is not significant even though the weight of the criteria changed with a relatively large degree (the weight of c1 changed from 0.2 to 0.35, the weight of c2 changed from 0.8 to 0.65). one great thing that was achieved is that solution a8 is always determined to be the best one of all scenarios. d. t. do /oper. res. eng. sci. theor. appl. 5(3)2022 131-152 138 thus, a solid conclusion is drawn that the fuca method was successful in solving the problem in this example. 3.2. multi-criteria decision making in turning process (example 2) singh et al. (2019) conducted twenty-seven experiments when turning ti-6al-4v steel. in each experiment, the input parameters were adjusted in each experiment including cutting speed, feed rate, and depth of cut. the criteria that were used to evaluate each solution included tool wear (c1), surface roughness (c2), cutting heat (c3), and cutting force (c4). all four of these criteria are the smaller tha better criteria. the values of the criteria at the solutions are as presented in table 10. table 10. experimental data when turning process of steel (singh et al. 2019) no. criteria c1 (m) c2 (m) c3 (0c) c4 (n) a1 70 0.5 405 310 a2 85 0.53 410 315 a3 95 0.55 420 323 a4 110 0.62 440 295 a5 135 0.68 445 300 a6 120 0.6 435 298 a7 195 0.76 503 290 a8 180 0.72 490 280 a9 190 0.74 495 285 a10 118 0.62 438 296 a11 125 0.66 443 295 a12 132 0.69 455 305 a13 175 0.75 485 283 a14 180 0.73 490 289 a15 190 0.75 500 292 a16 65 0.52 410 314 a17 90 0.56 415 321 a18 98 0.57 425 325 a19 168 0.73 485 288 a20 175 0.74 497 284 a21 188 0.78 501 290 a22 92 0.54 415 328 a23 100 0.55 420 320 a24 105 0.57 425 332 a25 115 0.62 448 302 a26 130 0.63 450 308 a27 140 0.65 447 310 in that study, the ranking of the solutions by topsis and saw methods was also performed. in which, the weights of c1, c2, c3, and c4 were determined by the ahp method, and those values were 0.5846, 0.2570, 0.1088, and 0.0556, respectively. the application of the fuca method to ranking solutions is similar to the example in section 3.1. however, in this case, the value of each criterion is equal in some application of fuca method for multi-criteria decision making in mechanical machining processes 139 solutions. therefore, the ranking of the solutions for each criterion will have to consider the proposed solution. the specific steps are as follows. for criterion c1, the ranks from rank 1 to rank 19 are ranked normally. because c1 at a13 and a20 are equal to each other, both a13 and a20 ranked 20.5 (average of 20 and 21); c1 at a8 and a14 are equal each other, both a8 and a14 ranked 22.5 (average of 22 and 23); c1 at a9 and a15 are equal each other, both a9 and a15 ranked 25.5 (average of 25 and 26). for criterion c2, the ranks from rank 1 to rank 4 are ranked normally. because c2 at a3 and a23 are equal, both a3 and a23 ranked 5.5 (average of 5 and 6); c2 at a18 and a24 are equal each other, both a18 and a24 ranked 8.5 (average of 8 and 9); ect. for the remaining criteria (c3 and c4), the ranking of solutions was performed similarly to this method. the ranking results of the solutions for each criterion are presented in table 11. table 11. ranking the solutions for each criterion in example 2 no. criteria rank (rij) c1 c2 c3 c4 c1 c2 c3 c4 a1 70 0.5 405 310 2 1 1 18.5 a2 85 0.53 410 315 3 3 2.5 21 a3 95 0.55 420 323 6 5.5 6.5 24 a4 110 0.62 440 295 10 12 12 10.5 a5 135 0.68 445 300 17 17 14 14 a6 120 0.6 435 298 13 10 10 13 a7 195 0.76 503 290 27 26 27 7.5 a8 180 0.72 490 280 22.5 19 21.5 1 a9 190 0.74 495 285 25.5 22.5 23 4 a10 118 0.62 438 296 12 12 11 12 a11 125 0.66 443 295 14 16 13 10.5 a12 132 0.69 455 305 16 18 18 16 a13 175 0.75 485 283 20.5 24.5 19.5 2 a14 180 0.73 490 289 22.5 20.5 21.5 6 a15 190 0.75 500 292 25.5 24.5 25 9 a16 65 0.52 410 314 1 2 2.5 20 a17 90 0.56 415 321 4 7 4.5 23 a18 98 0.57 425 325 7 8.5 8.5 25 a19 168 0.73 485 288 19 20.5 19.5 5 a20 175 0.74 497 284 20.5 22.5 24 3 a21 188 0.78 501 290 24 27 26 7.5 a22 92 0.54 415 328 5 4 4.5 26 a23 100 0.55 420 320 8 5.5 6.5 22 a24 105 0.57 425 332 9 8.5 8.5 27 a25 115 0.62 448 302 11 12 16 15 a26 130 0.63 450 308 15 14 17 17 a27 140 0.65 447 310 18 15 15 18.5 d. t. do /oper. res. eng. sci. theor. appl. 5(3)2022 131-152 140 after ranking the solutions for each criterion, apply eq. (1) to calculate the value of i. first, the weights of the selected criteria are the same as their values in the references, i.e., the weights of c1, c2, c3, and c4 are 0.5846, 0.2570, 0.1088, and 0.0556, respectively (singh et al. 2019). the ranked results of the solutions by fuca method and two other methods (including topsis and saw) are presented in table 12. table 12. ranking the solutions for example 2 no. fuca topsis saw a1 1 1 1 a2 3 3 3 a3 6 5 6 a4 10 11 11 a5 16 17 17 a6 12 10 10 a7 27 26 26 a8 20 19 20 a9 24 23 24 a10 11 13 12 a11 14 16 15 a12 17 18 18 a13 21 24 23 a14 23 21 21 a15 26 25 25 a16 2 2 2 a17 5 7 5 a18 8 8 8 a19 19 20 19 a20 22 22 22 a21 25 27 27 a22 4 4 4 a23 7 6 7 a24 9 9 9 a25 13 12 13 a26 15 14 14 a27 18 15 16 the calculated results in table 12 show that using the fuca method, a1 was identified as the best solution. this result is also consistent with cases using two methods including topsis and saw. in addition, all three methods jointly identify that a16 solution ranked 2, and a2 solution ranked 3. seven different scenarios were generated by randomly varying the weights of the criteria as presented in table 13. where s7 is the scenario that was performed above. application of fuca method for multi-criteria decision making in mechanical machining processes 141 table 13. weight of criteria in different scenarios (example 2) criteria scenarios s1 s2 s3 s4 s5 s6 s7 c1 0.1 0.2 0.3 0.3 0.3 0.4 0.5846 c2 0.2 0.1 0.2 0.1 0.3 0.4 0.2570 c3 0.3 0.4 0.1 0.3 0.1 0.1 0.1088 c4 0.4 0.3 0.4 0.3 0.3 0.1 0.0556 the ranking results of the solutions according to different scenarios are presented in table 14. the calculated results show that in all 7 scenarios, it is always determined that a1 is the best solution, a16 ranked 2, a2 ranked 3, and a7 ranked 27. table 14. ranking the solutions in different scenarios (example 2) no. scenarios s1 s2 s3 s4 s5 s6 s7 a1 1 1 1 1 1 1 1 a2 3 3 3 3 3 3 3 a3 12 9 11 7 7 6 6 a4 4 6 4 5 5 10 10 a5 16 15 19 17 18 16 16 a6 5 8 6 10 9 11 12 a7 27 27 27 27 27 27 27 a8 10 18 10 18 15 20 20 a9 20 24 21 24 24 24 24 a10 6 10 5 9 10 12 11 a11 9 11 8 11 13 14 14 a12 24 23 23 21 21 18 17 a13 13 16 15 15 19 21 21 a14 19 22 18 23 22 22 23 a15 25 26 26 26 26 25 26 a16 2 2 2 2 2 2 2 a17 7 4 7 4 4 5 5 a18 17 12 17 12 11 8 8 a19 14 17 14 16 16 19 19 a20 18 21 16 20 20 23 22 a21 26 25 25 25 25 26 25 a22 11 5 12 6 6 4 4 a23 8 7 9 8 8 7 7 a24 21 13 22 14 14 9 9 a25 15 14 13 13 12 13 13 a26 22 19 20 19 17 15 15 a27 23 20 24 22 23 17 18 eq. (2) is used to calculate the spearman’s rank correlation coefficients. table 15 presents the values of the spearman coefficients when comparing between scenarios as well as the initial rank si. d. t. do /oper. res. eng. sci. theor. appl. 5(3)2022 131-152 142 table 15. the values of sperman coefficients (example 2) si s1 s2 s3 s4 s5 s6 s7 si 1 1 0.904 0.988 0.907 0.897 0.752 0.751 s1 1 0.904 0.988 0.907 0.897 0.752 0.751 s2 1 0.886 0.991 0.980 0.947 0.946 s3 1 0.901 0.901 0.744 0.747 s4 1 0.988 0.938 0.941 s5 1 0.946 0.948 s6 1 0.998 s7 1 the calculated data in table 15 show that the sperman's rank correlation coefficients of the solutions is in the range s  [0.747, 1], this value represents a very high degree of correlation. this shows that the change in rankings is not significant even though the weight of the criteria changed with a relatively large degree. specifically, although c1 changed 5.846 times, c2 and c3 changed 4 times, and c4 changed 7.19 times, the solutions ranked 1st, 2nd, 3rd, and 27th are all same to each other in all seven scenarios. thus, for each criterion, when ranking solutions with equal value in several solutions was implemented according to the proposed method, the fuca method was also successful in solving the problem of this example. 3.3. multi-criteria decision making in drill process of magnesium az91 material (example 3) varatharajulu et al. (2021) performed the drilling process of magnesium az91 in seventeen different experiments. in each experiment the input parameters are changed including spindle speed and feed rate. six criteria that were used to evaluate each experiment included drilling time (c1), entry burr height (c2), exit burr height (c3), entry burr thickness (c4), exit burr thickness (c5), and surface roughness (c6). all six of these criteria are the smaller the better criteria. the data on the criteria for the seventeen experiments is presented in table 16. the multi-criteria decision-making that was performed to find a solution that ensures simultaneously all six criteria to be the same minimum values using topsis and copras methods (varatharajulu et al. 2021). in which, the weights of c1 and c6 were chosen to be 0.3 and the weights of all the remaining four criteria were chosen to be 0.1. the application of the fuca method to rank solutions was performed similarly to the example in section 3.1. it is note with the cases that one certain criterion is equally valid in several solutions. this process was presented follows. the values of criterion c1 are different in all seventeen solutions, so ranking of the solutions for this criterion is performed normally. for criterion c2: c2 at a15 is the smallest, so a15 ranked 1st; c2 at a8, a9, and a12 are equal to each other, so all three solutions are ranked 3 (the average of 2, 3, and 4); c2 at a4 is equal to c2 at a7, so both solutions ranked 5.5 (average of 5 and 6); c2 at a10, a11, and a16 are equal to each other, so all three solutions ranked 11 (average of 10, 11, and 12), ect. application of fuca method for multi-criteria decision making in mechanical machining processes 143 table 16. experimental data when drilling process of magnesium material (varatharajulu et al. 2021) no. criteria c1 (s) c2 (mm) c3 (mm) c4 (mm) c5 (mm) c6 (m) a1 14.03 0.051 0.058 0.105 0.21 0.479 a2 7.59 0.053 0.058 0.155 0.245 1.211 a3 7.34 0.035 0.06 0.165 0.215 0.916 a4 4.06 0.033 0.075 0.18 0.215 0.535 a5 5.4 0.048 0.078 0.25 0.195 0.601 a6 5.5 0.05 0.084 0.185 0.185 0.703 a7 2.81 0.033 0.058 0.185 0.185 0.466 a8 2.62 0.028 0.048 0.2 0.19 0.577 a9 2.88 0.028 0.05 0.18 0.15 0.417 a10 2.75 0.043 0.051 0.23 0.195 0.675 a11 2.84 0.043 0.055 0.165 0.205 0.418 a12 1.59 0.028 0.074 0.145 0.17 0.601 a13 1.88 0.038 0.064 0.185 0.175 0.563 a14 3.44 0.049 0.066 0.19 0.185 0.391 a15 2.04 0.023 0.059 0.16 0.18 0.493 a16 2.1 0.043 0.05 0.235 0.185 0.675 a17 1.25 0.04 0.049 0.44 0.19 0.65 table 17. ranking the solutions when drilling process of magnesium material no. rank (rij) rank c1 c2 c3 c4 c5 c6 fuca topsis copras a1 17 16 8 1 14 5 13 17 17 a2 16 17 8 3 17 17 17 16 16 a3 15 7 11 5.5 15.5 16 15 15 15 a4 12 5.5 15 7.5 15.5 7 11 12 12 a5 13 13 16 16 11.5 10.5 14 13 13 a6 14 15 17 10 6.5 15 16 14 14 a7 8 5.5 8 10 6.5 4 4 5 6 a8 6 3 1 13 9.5 9 6 7 7 a9 10 3 3.5 7.5 1 2 2 2 2 a10 7 11 5 14 11.5 13.5 12 10 11 a11 9 11 6 5.5 13 3 7 6 5 a12 2 3 14 2 2 10.5 3 4 3 a13 3 8 12 10 3 8 5 3 4 a14 11 14 13 12 6.5 1 9 8 8 a15 4 1 10 4 4 6 1 1 1 a16 5 11 3.5 15 6.5 13.5 10 9 9 a17 1 9 2 17 9.5 12 8 11 10 the ranking of the remaining criteria (c3, c4, c5, c6) was also conducted in a similar way. the ranked results of the solutions for each criterion are presented in table 17. the data in table 17 show that the fuca method indicates that a15 is the best solution. this result is also similar to the results when using topsis and copras d. t. do /oper. res. eng. sci. theor. appl. 5(3)2022 131-152 144 methods. in addition, all three methods fuca, topsis, and copras identified that a9 ranked 2. eight different scenarios were also generated by randomly varying the weights of the criteria as shown in table 18, where s5 scenario was the just analyzed above. table 18. weight of criteria in different scenarios (example 3) criteria scenarios s1 s2 s3 s4 s5 s6 s7 s8 c1 0.2 0.2 0.25 0.28 0.3 0.32 0.33 0.35 c2 0.15 0.1 0.15 0.2 0.1 0.1 0.15 0.15 c3 0.2 0.1 0.15 0.2 0.1 0.1 0.1 0.1 c4 0.2 0.2 0.15 0.2 0.1 0.1 0.15 0.1 c5 0.15 0.15 0.2 0.1 0.1 0.1 0.1 0.15 c6 0.1 0.25 0.1 0.02 0.3 0.28 0.17 0.15 the ranking results of the solutions according to the different scenarios are presented in table 19. it is seen that in all eight scenarios, a15 is always determined to be the best solution. table 19. ranking the solutions in different scenarios (example 3) no. scenarios s1 s2 s3 s4 s5 s6 s7 s8 a1 11 10 13 13 13 13 13 13 a2 15 17 16 15 17 17 15 17 a3 14 14 14 12 15 15 14 14 a4 13 12 12 11 11 11 12 12 a5 17 16 17 17 14 14 16 15 a6 16 15 15 16 16 16 17 16 a7 5 4 6 7 4 5 7 7 a8 4 7 5 4 6 6 5 5 a9 2 2 3 3 2 2 3 3 a10 10 13 10 10 12 12 11 11 a11 8 6 9 9 7 7 8 9 a12 3 3 2 2 3 3 2 2 a13 6 5 4 6 5 4 4 4 a14 12 8 11 14 9 9 10 10 a15 1 1 1 1 1 1 1 1 a16 9 11 8 8 10 10 9 8 a17 7 9 7 5 8 8 6 6 eq. (2) is again used to calculate the sperman coefficients. table 20 presents the values of the sperman coefficients when comparing between scenarios as well as the initial rank si. the data in table 20 show that the sperman's rank correlation coefficients of the solutions is in the range s  [0.853, 1], which means that the correlation level in this case is very high. this shows that the change in rankings is not significant even though the weight of the criteria changed with a relatively large degree. specifically, the weight of c1 changed from 0.2 to 0.35, the weight of four criteria c2, c3, c4, and c5 all changed from 0.1 to 0.2. in particular, the weight of c6 changed from 0.02 to 0.3. in all application of fuca method for multi-criteria decision making in mechanical machining processes 145 scenarios, a15 is always determined to be the best solution. one time again, the fuca method was confirmed as a successful applied method in this example. table 20. the values of sperman’s rank correlation coefficients (example 3) si s1 s2 s3 s4 s5 s6 s7 s8 si 1 1 0.931 0.978 0.966 0.946 0.944 0.971 0.961 s1 1 0.931 0.978 0.966 0.946 0.944 0.971 0.961 s2 1 0.924 0.853 0.973 0.971 0.929 0.924 s3 1 0.968 0.953 0.958 0.985 0.988 s4 1 0.897 0.900 0.961 0.956 s5 1 0.998 0.961 0.963 s6 1 0.968 0.971 s7 1 0.990 s8 1 3.4. multi-criteria decision making with the qualitative criteria (example 4) the analyzed results in the three examples that were performed above confirmed that the fuca method was successfully applied when used in each example. however, in all those examples, the the criteria are the quantitative ones. in this example, both qualitative and quantitative criteria will be considered. to implement the content of these cases, the authors of this paper were conducted the surface grinding process of suj2 steel with some basic parameters of the experimental system and the experimental conditions as summarized follows: the grinding machine was the apsg820/2a machine, grinding wheel was the wa46j7v1a-180-13-31.5, workpiece material was suj2 steel; workpiece dimensions (length x width x height) were 60 mm x 40 mm x 10 mm, respectively. the workpiece was heat treated to reach a hardness of 62 hrc, the coolant was 10% emulsion oil with the flow of 4.6 l/min. eight experiments were carried out with the values of the changed cutting conditions in each experiment as listed in table 21. two quantitative criteria include the surface roughness (c1) and material remove rate (c2). the values of c1 and c2 at each experiment are also summarized in table 21. in addition, in this study, another criterion is used which is the number of the grinding grains adhered in the surface of the part (c3). the number of grinding grains adhered in the surface of the part after grinding has a great influence on the workability of the part. if there are a large number of the grinding grains adhered in the surface of the part of the part, these grinding grains will scratch the surfaces when they contact with each other. it makes the level of wear happening quickly, especially in the initially wear stage. thereby it will rapidly reduce the life of the product (malkin & guo, 2018; marinescu et al. 2006). therefore, creating a surface after grinding with a small number of the grinding grains adhered in the surface of the part is always desirable. however, it is very difficult to determine the exact number of the grinding grains adhered in the surface of the part. instead, we can only evaluate them at the qualitative level, i.e., through the observation (using specialized equipment) to evaluate the number of the grinding grains adhered more or less in the surface of the part. it means that according to this measurement method, c3 is in the form of a qualitative criterion. the evaluation of c3 in this study was performed through the observation of workpiece surface micrographs after grinding (figure 1). d. t. do /oper. res. eng. sci. theor. appl. 5(3)2022 131-152 146 table 21. experimental data when surface grinding process of suj2 steel no. criteria c1 (m) c2 (mm3/min) c3 (in fig. 1) a1 0.278 325 (1) a2 0.844 1625 (2) a3 1.041 975 (3) a4 1.548 1300 (4) a5 0.502 1950 (5) a6 0.225 650 (6) a7 1.059 2925 (7) a8 1.542 3900 (8) (1) (2) (3) (4) (5) (6) (7) (8) figure 1. the surface of workpiece in surface grinding process of suj2 steel observation of figure 1 shows that: in the photo (8) corresponding to the a8, the number of the grinding grains adhered in the surface of the part is the least, thus, c3 at a8 ranked 1. as observed the c3 at a3 and a7 is quite the same and only more that that one at a8, so, both a3 and a7 rated 2.5 (the average of 2 and 3). for the remaining solutions, c3 decrease in order a5, a6, a4, a1, and a2. therefore, the ranks of a5, a6, a4, a1, and a2 are rank 4, rank 5, rank 6, rank 7, and rank 8, respectively. the ranked results of the solutions for all three criteria are listed in table 22. application of fuca method for multi-criteria decision making in mechanical machining processes 147 table 22. ranking the solutions for each criterion when surface grinding of suj2 steel no. criteria rank (rij) c1 (m) c2 (mm3/min) c3 (in figure 1) c1 c2 c3 a1 0.278 325 (1) 2 8 7 a2 0.844 650 (2) 4 4 8 a3 1.041 975 (3) 5 6 2.5 a4 1.548 1300 (4) 8 5 6 a5 0.502 1950 (5) 3 3 4 a6 0.225 650 (6) 1 7 5 a7 1.059 2925 (7) 6 2 2.5 a8 1.542 3900 (8) 7 1 1 the score of each solution was calculated according to eq. (1) with six randomly selected different weight sets of the criteria (table 23). the calculated results are presented in table 24. the ranked results of the solutions according to the fuca method as presented in table 25. table 23. weight of criteria in different scenarios (example 4) criteria scenarios s1 s2 s3 s4 s5 s6 s7 s8 c1 0.2 0.25 0.28 0.3 0.32 1/3 0.35 0.38 c2 0.3 0.25 0.37 0.4 0.42 1/3 0.35 0.32 c3 0.5 0.4 0.35 0.3 0.26 1/3 0.3 0.3 table 24. the vi score of each solution (example 4) no. scenarios s1 s2 s3 s4 s5 s6 s7 s8 a1 6.300 6.100 5.970 5.900 5.820 5.667 5.600 5.420 a2 6.000 5.600 5.400 5.200 5.040 5.333 5.200 5.200 a3 4.050 4.350 4.495 4.650 4.770 4.500 4.600 4.570 a4 6.100 6.150 6.190 6.200 6.220 6.333 6.350 6.440 a5 3.500 3.400 3.350 3.300 3.260 3.333 3.300 3.300 a6 4.800 4.700 4.620 4.600 4.560 4.333 4.300 4.120 a7 3.050 3.200 3.295 3.350 3.410 3.500 3.550 3.670 a8 2.200 2.500 2.680 2.800 2.920 3.000 3.100 3.280 table 25. ranking the solutions according to the improved fuca (example 4) no. scenarios s1 s2 s3 s4 s5 s6 s7 s8 a1 8 7 7 7 7 7 7 7 a2 6 6 6 6 6 6 6 6 a3 4 4 4 5 5 5 5 5 a4 7 8 8 8 8 8 8 8 a5 3 3 3 2 2 2 2 2 a6 5 5 5 4 4 4 4 4 a7 2 2 2 3 3 3 3 3 a8 1 1 1 1 1 1 1 1 d. t. do /oper. res. eng. sci. theor. appl. 5(3)2022 131-152 148 the data in table 25 shows that solution a8 is always determined to be the best solution for all scenarios. seven of the eight scenarios identified a4 as the worst solution (except for s1). the ranking results for all solution are the same in the five scenarios s4, s5, s6, s7, and s8. the two scenarios s2 and s3 also give the same ranking results. in addition, there is only a small difference in ranking results between scenario s1 and the rest. eq. (2) is again used to calculate the sperman coefficients. table 26 presents the value of the sperman coefficients when comparing between scenarios as well as the initial rank si. table 26. the values of sperman’s rank correlation coefficients (example 4) si s1 s2 s3 s4 s5 s6 s7 s8 si 1 1 0.943 0.943 0.829 0.829 0.829 0.829 0.829 s1 1 0.943 0.943 0.829 0.829 0.829 0.829 0.829 s2 1 1 0.886 0.886 0.886 0.886 0.886 s3 1 0.886 0.886 0.886 0.886 0.886 s4 1 1 1 1 1 s5 1 1 1 1 s6 1 1 1 s7 1 1 s8 1 the calculated results in table 26 show that the sperman’s rank correlation coefficients of the solutions are in the range s  [0.886, 1]. this represents a very high degree of correlation in this case. thus, in this example, once again the fuca method was successfully applied. although the four examples that were performed belonging to different machining processes (milling, turning, drilling, and grinding). the number of solutions, number of criteria, and number of scenarios that used in each case also were different. however, in each case, the obtained results confirmed the successful application of the fuca method in multi-criteria decision making. from the obtained results, it can be concluded that the proposed method to overcome the limitations of the fuca method is an accurate one. so, the application of fuca method completely ensures the reliability when using for multi-criteria decision making, firstly in the mechanical processing field. 4. conclusion having to choose a certain mcdm method to combine with a certain data normalization method to ensure the accuracy of multi-criteria decision making is a relatively complicated work with a lot of time consumption of decision makers. fuca is a multi-criteria decision making method without requirement of data normalization. when using this method, the first mission is ranking the solutions for each criterion. however, the case with a certain criterion having equal value in several solutions has not considered in any published studies. in that case, the decision maker will not be able to rank the solutions. this is the first study to discover that limitation and to propose a method to overcome that one. with the additional use of the proposed method, the fuca one was used for multi-criteria decision making for four different application of fuca method for multi-criteria decision making in mechanical machining processes 149 cases in the mechanical processing field. in each of those cases, the number of solutions, the number of criteria, and the type of criteria (qualitative, quantitative) are also not the same. the sensitivity analysis in ranking process was also performed with different scenarios for each case. although there are many differences in the examples, the obtained results confirm that the fuca method was successfully applied in the mentined cases. the discovery of the limitation of the fuca method and the improvement of this method to overcome its limitation extends the application scope of this method. it was not only successful applied in multi-criteria decision making in the field of mechanical machining as done in this study, but it also promises to be successful applied in other fields as well. the method to overcome the limitation of the fuca one that was proposed in this study has not been presented in the form of a general mathematical formula. this limitation needs to be implemented in the next time. in addition, this study as well as the published studies that applied the fuca method only considered the case the values of each criterion at each solution as a unique quantity. the case these values as a fuzzy set have been not considered in any studies. this gap also needs to be filled in the further studies. in this study, the weighted values of the criteria were selected according to the studies that this study references (in those references, the weights were determined by the entropy, ahp method, ect.), or were selected according to random values without considering the importance of the criteria. the use of weighting methods considering the importance of criteria, such as the piprecia method (stanujkic et al. 2017) in combination with the fuca method are also the contents of works to be done in the future. refercences aytekin, a. 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(2017). multiple criteria decision making applications in management and engineering. springer. https://doi.org/10.1007/978-3-31939292-9 © 2022 by the authors. submitted for possible open access publication under the terms and conditions of the creative commons attribution (cc by) license (http://creativecommons.org/licenses/by/4.0/). https://www.sciencedirect.com/science/article/abs/pii/s0098135411002870?via%3dihub#! https://www.sciencedirect.com/science/article/abs/pii/s0098135411002870?via%3dihub#! https://www.sciencedirect.com/science/article/abs/pii/s0098135411002870?via%3dihub#! https://www.sciencedirect.com/science/article/abs/pii/s0098135411002870?via%3dihub#! https://www.sciencedirect.com/science/article/abs/pii/s0098135411002870?via%3dihub#! https://www.sciencedirect.com/journal/computers-and-chemical-engineering https://www.sciencedirect.com/journal/computers-and-chemical-engineering https://doi.org/10.1016/j.compchemeng.2011.09.016 https://doi.org/10.1016/j.procs.2019.09.378 https://doi.org/10.1016/j.jclepro.2020.125302 https://doi.org/10.1108/wje-06-2019-0170 https://doi.org/10.1016/j.jma.2021.05.006 https://doi.org/10.15388/20-infor417 https://doi.org/10.1007/978-3-319-39292-9 https://doi.org/10.1007/978-3-319-39292-9 d. t. do /oper. res. eng. sci. theor. appl. 5(3)2022 131-152 152 abbreviations mcdm: multi-criteria decision making fuca: faire un choix adéquat (in french) make an adequate choice moora: multiobjective optimization on the basis of ratio analysis mabac: multi-attributive border approximation area comparison wsa: weighted sum approach promethee: preference ranking organization method for enrichment of evaluations copras: complex prroportional assessment topsis: technique for order of preference by similarity to ideal solution s-: negative ideal separation saw: simple additive weighting codas: combinative distance-based assessment gra: grey relational analysis linmap: linear programming technique for multidimensional analysis of preference ahp: analytic hierarchy process copras: complex proportional assessment piprecia: pivot pairwise relative criteria importance assessment 3.1. multi-criteria decision making in milling process (example 1) 3.2. multi-criteria decision making in turning process (example 2) 3.3. multi-criteria decision making in drill process of magnesium az91 material (example 3) 3.4. multi-criteria decision making with the qualitative criteria (example 4) baydas, m. (2022). comparison of the performances of mcdm methods under uncertainty: an analysis on bist sme industry index. opus – journal of society research, 19(46), 308-326. https://doi.org/10.26466/opusjsr.1064280 bobar, z., bozanic, d., djuric, k., & pamucar, d. (2020). ranking and assessment of the efficiency of social media using the fuzzy ahp-z number model fuzzy mabac. acta polytechnica hungarica, 17(3), 43-70. bozanic, d., milic, a., tesic, d., sałabun, w., & pamucar, d. (2021). d numbers – fucom – fuzzy rafsi model for selecting the group of construction machines for enabling mobility. facta universitatis mechanical engineering, 19(3), 447 – 471. https:/... dimic srđan, h., & ljubojevic srđan, d. (2019). decision making model in forest road network management. military technical courier, 67(1), 93-115. https://doi.org/10.5937/vojtehg67-18446 lamba, m., munjal, g., & gigras, y. (2022). a mcdm-based performance of classification algorithms in breast cancer prediction for imbalanced datasets. international journal of intelligent engineering informatics, 9(5), 425-454. https://doi.org/10.1504... le, h.a., hoang, x.t., trieu, q.h., pham, d.l., & le, x. h. (2020). determining the best dressing parameters for external cylindrical grinding using mabac method. applied scicences, 12(16), 8287. https://doi.org/10.3390/app12168287 muhammad, l.j., badi, i., haruna, a.a., & mohammed, i.a. (2021). selecting the best municipal solid waste management techniques in nigeria using multi criteria decision making techniques. reports in mechanical engineering, 2(1), 180-189. https://doi.o... ouattara, a., pibouleau, l., azzaro-pantel, c., domenech, s., baudet, p., & yao, b. (2022). economic and environmental strategies for process design. computers & chemical engineering, 36, 174-188. https://doi.org/10.1016/j.compchemeng.2011.09.016 pamucar, d., behzad, m., bozanic, d., & behzad, m. (2021). decision making to support sustainable energy policies corresponding to agriculture sector: case study in iran's caspian sea coastline. journal of cleaner production, 292, 125302. https://doi.... operational research in engineering sciences: theory and applications vol. 5, issue 3, 2022, pp. 230-243 issn: 2620-1607 eissn: 2620-1747 doi: https://doi.org/10.31181/oresta121222211j * corresponding author. shjin@cju.ac.kr (s. jin), jmchoi@cju.ac.kr (j. choi) optimal load scheduling of home appliances considering operation conditions sukho jin*, jeongmi choi college of business, cheongju university, s. korea received: 14 september 2022 accepted: 22 november 2022 first online: 12 december 2022 research paper abstract: to reduce energy consumption arising from increasing energy efficiency in response to energy depletion around the world, energy price rises, climate change, and accidents of electric power are cooperating simultaneously. recognizing the seriousness of the above-mentioned problems, feasible and effective policies for reducing greenhouse gas have been promoted in developed countries since the 2000s. moreover, industry and academia are actively researching to develop energy-efficient and eco-friendly technologies, respectively. this study proposes an optimal model for scheduling home appliances that minimizes power costs by assuming a smart-home environment with smart metering and advanced metering infrastructure. in addition, a case-study was performed using actual data from south korea, and sensitivity analysis was performed according to changes in parameters. the experiment considered possible real-life situations, such as an increase and decrease in power cost and a limitation in power usage, and proved that the proposed model was excellent to establish a power schedule for home appliances. this research result seems to serve as a guideline in relation to the control of home appliances to reduce power and smart homes. key words: load scheduling, house appliances scheduling, smart home, mixed-integer linear programming (milp) 1. introduction nowadays, as the severity of energy resource depletion increases, various studies on energy utilization methods are conducted. in particular, measures to efficiently manage power usage are emerging very quickly. for instance, research related to the construction of next-generation intelligent power networks, called smart grids, not to mention the development of related technologies is becoming an issue. the meaning of smart grids is defined differently depending on each country or institution. institute of electrical and electronics engineers (ieee) has defined smart grid as follows. "smart grids have come to illustrate the next generation of power systems optimal load scheduling of home appliances considering operation conditions 231 represented by the increasing use of communication and information technology in the generation, transmission and consumption of electrical energy." according to australian energy market operator, shabanzadeh and moghaddam (2013) defined smart grid as “smart grid creates opportunities for consumers to change their energy consumption at short notice in response to a variety of signals that include price.” various discussions around the world regarding the introduction of the smart grid system have been underway since the early 2000s. in north america, the u.s., canada, and europe, all member states and asian regions especially around japan and china, are focusing on fostering industries and revitalizing early markets, not only at the level of governments, but also private companies to secure the lead in next-generation energy technology competition. in south korea, a smart grid demonstration complex was established in jeju island in 2009, related technologies were commercialized, and export industrialization began. in january 2010, the smart grid national roadmap was announced, and a plan was established to build the smart grid in three stages by 2030. to this end, a total of 27.5 trillion krw (korean won) of investment in the smart grid technology will be implemented at the private and public levels, resulting in 230 billion tons reduction in greenhouse gas, 47 trillion krw reduction in energy income, and 3.2 trillion krw reduction in new power plant construction costs. in order for the smart grid system to operate, it is essential to introduce smart metering technology and advanced metering infrastructure (ami) facilities that exchange real-time power information in both directions using a communication network. smart metering is the most basic facility technology for smart grids, allowing intelligent measurement, monitoring, and controlling of overall power grids such as user power consumption, distributed energy production, power loss, and power interruption. in the united states, smart metering technology is introduced to restore reliability in the power supply (due to large-scale power outages) and increase people's awareness of energy saving. ami is an infrastructure facility that actively saves energy through demand response between end consumers and energy suppliers based on smart meters of smart grids. in other words, information and services are provided so that power companies and consumers can use energy efficiently through integrated management of demand-side power resources and efficient operation and distribution thereof. this information is the means for mutual recognition based between power suppliers and receivers and includes functions of various types of distribution power systems and power distribution intelligence systems. it also supports advanced time-based plans such as time-of-usage, critical peak pricing, and real-time pricing, which encourage consumers to participate in active energy savings. if ami infrastructure and smart metering technology are used, various applications can be used at home; for example, in response to real-time power charges, a schedule of home appliances can be established to save energy, and power consumption patterns and overall energy monitoring can be performed. this study proposes a schedule plan for home appliances in use to minimize power cost in an environment that introduces ami and smart metering technology. in addition, the sensitivity analysis of major parameters, such as power charge and power usage, was conducted through a case-study using real data in south korea. the sections of this study are as follows. in section 2, existing literature on smart metering, ami optimization research considering the environment, and scheduling of home appliances are fixed. section 3 proposes an optimal model for scheduling home jin and choi/oper. res. eng. sci. theor. appl. 5(3)2022 230-243 232 appliances. section 4 verifies the effectiveness of the proposed model by performing model verification and experimental analysis using real data from korea. finally, section 5 presents conclusions and future research contents. 2. literature review in this section, studies using optimization methods were investigated and summarized, focusing on keywords such as application scheduling, smart metering, and demand response. adika and wang (2014) conducted clustering analysis related to power consumption patterns and power loads for each device used. based on the analysis results, a linear programming was developed to save consumers' electricity bills. zhu et al. (2012) established a mathematical model based on the integer programming method for the purpose of balancing electricity use by time zone. the latter model proposed a power load balancing mechanism that minimizes the maximum power load per hour, and it was argued that it is essential to prepare a plan to induce voluntary participation of consumers as a way to reduce the power peak load. althaher et al. (2015) designed a model in consideration of the increase in consumer satisfaction while minimizing power cost. beaudin and zareipour (2015) designed a model by classifying the characteristics of the device in detail. heterogeneity, consumer considerations, and uncertainties were considered, and optimization models and heuristic methods were presented to solve the problem. in addition, this study also presented evaluation criteria for home energy management systems. samadi et al. (2015) solved problems related to power load scheduling and electric power transaction under a system with a high penetration rate of renewable energy. it is assumed that the excess power produced by the user can be sold to enterprises or other users, and sellers participate in price competition. besides, a game theory approach is adopted to model interactions between producers, and utilize approximate dynamic programming to represent different types of device operations. sou et al. (2011) reflected the power consumption by step considering the characteristics of home appliances and proposed a mixed-integer linear programming that aims to minimize power costs. a case-study was conducted by constructing a scenario based on actual data, and the computational complexity and scalability of the research model were discussed. the integer and mixed-integer linear programming methods are efficient methods for deriving an optimal solution within an appropriate time when the problem size is small. however, this process takes a lot of time as the problem size increases. there are also studies that have adopted complex methods to solve these problems. morales-españa et al. (2022) summarized and classified the demand response in detail, focusing on the power system. furthermore, an optimization model was developed in this study to perform flexible load management. research using heuristic methods has been actively conducted to reduce the problem complexity and resolution time of load scheduling. alham et al. (2016) and gupta et al. (2016) developed and utilized heuristic methods for optimal power use. alham et al. (2016) approached the problem with the aim of minimizing energy use cost and carbon emission. to simultaneously consider cost aspects and eco-friendly factors, objective-functions were defined linearly, and branch and bound method and genetic algorithm were used in consideration of the increase in problem complexity as the problem size grew. gupta et al. (2016) developed a mixed-integer linear optimal load scheduling of home appliances considering operation conditions 233 programming model with the aim of minimizing consumer power cost. in addition, heuristic methods such as genetic algorithms, are utilized to compensate for the limitations of mixed-integer linear programming methods in which computational time increases exponentially as the size of the problem grows. bharathi et al. (2017) divided the power peak hours into industrial, commercial, and residential areas, and developed a model that effectively distributes available power in other areas and minimizes power use during the power peak hours. the developed model solved the problem through a genetic algorithm and proved the superiority of the results compared to evolution algorithms. chakraborty (2013) proposed an intelligent economic operation model that considers wind and solar powers in a smart grid environment. the model was developed based on fuzzy logic and the quantum inspired evolutionary algorithm was used to solve the problem. the model was verified through case-studies considering multiple heat devices, electric vehicles, thermal and wind power plants. excellent results were derived to reduce production cost and carbon emission at the same time. ma et al. (2016) presented a cost-effective, efficiency-based residential power load scheduling framework that increase the economic efficiency of residential power consumption, rather than minimize power charges that have been primarily used for purposes. in addition, the power bidding process and real-time pricing mechanism were reflected to make the smart grid environment more realistic, and a load scheduling algorithm based on the quadratic optimization program was proposed. chakraborty et al. (2020) proposed a power load scheduling-based management plan to reduce peak load. it was assumed that the user could set the desired operating time for each home appliance, and a two-dimensional strip problem-based heuristics model was developed to solve the problem. load scheduling is also being actively conducted in studies related to smart-home or smart-building. wang et al. (2016) used an optimization method to establish a schedule plan for home appliances that can operate in a smart-home environment. each home appliance reflected the presence or absence of automation, the possibility of stopping during operation, the use of hot water, and the setting according to the change in the ambient temperature as constraints. the integer programming method was constructed, and the minimization of consumers' electricity bills was defined as an objective function. in addition, as computational complexity increases and decreases, the problem was solved by utilizing particle swarm optimization. ogunjuyigbe et al. (2017) developed a model that can manage the power load of the home within the budget set by the user. the developed model aims to maximize user convenience while reducing power consumption cost, and the problem is solved through genetic algorithm. in addition, various implications were derived through scenario analysis based on variables such as satisfaction and budget. nazemi et al. (2021) presented the intensive-based multi-objective nonlinear optimization approach for load scheduling problems in smart-building. this study aims to minimize the total power cost, maximize incentives allocated to each customer, minimize customer inconvenience, and consider electronics, electric vehicles, heating sulfur, and air conditioning systems. foroozandeh et al. (2021) proposed a multi-objective mixed-binary linear programming to minimize the total energy consumption cost and peak load for residential builds. this model is considered the electric vehicles and battery energy storage system, and the performance of the model was compared and analyzed through scenario analysis. nezhad et al. (2021) proposed a scheduling problem considering solar photovoltaic power supply and jin and choi/oper. res. eng. sci. theor. appl. 5(3)2022 230-243 234 home energy management systems. this study considered the uncertainty of photovoltaic power generation and established it for the optimal schedule plan of home applications based on mixed-intermediate programming to minimize the daily bill. korkas et al. (2022) proposed a distributed feedback-based optimization method based on principles of approximate dynamic programming for grid-connected builds. this model was considered to be user-convenience. electric vehicles, energy storage systems, and robustness evaluation were performed through various experimental designs. foroozandeh et al. (2022) assumed the customers have flexible contract systems in smart-buildings. in this study, a mixed binary optimization problem was proposed considering photovoltaic power generation, electric vehicles, and battery energy storage systems. scenario analysis was conducted to prove the excellence of the proposed model, and the experimental results showed that the electricity cost was reduced by about 47%. 3. mathematical model 3.1. assumptions this study aims to establish a schedule for home appliances to minimize total power usage at home. the type and power consumption of home appliances were set based on periodical data published by the korea electric power exchange (2019). the operating level of the home appliance was composed of three stages, and the conditions that consumers can set are divided into three as follows. condition #1: operate the home appliance at a definite time. condition #2: the home appliance is set to a range time and operates in consideration of the power charge. however, it is not necessary to operate continuously. condition #3: the home appliance is set to a range time and operates in consideration of the power charge. however, it must be operated continuously. it is assumed that electricity charges are measured under circumstances in which seasonal and hourly rate systems are applied. this is a plan that induces users to use power at a low cost because the high rate unit price is applied during the time of the day when power demand is high, and the low rate unit price is applied during the day time. since its introduction in south korea in 1977, the criteria for seasonal and time-of-day classification have been changed according to changes in conditions, and it is being applied to large-capacity users such as general industrial use nationwide. in addition, the demand power is obtained by dividing the amount of power used within the demand time by the usage time. in south korea, the demand time is applied as 15 min. accordingly, this study also assumed that it can be set every 15 min. 3.2. model description the following notation is used to formulate the proposed model. the indices, parameters, and variables used to formulate the model are described below. indices optimal load scheduling of home appliances considering operation conditions 235 i = index of appliances (i = 1, … , i) l = index of appliance levels (l = 1, … , l) t = index of time periods (t = 1, … , t) parameters over t p = power charge corresponding to punitive charge (super user) in period t over t l = amount of electricity used applied to punitive charge (super user) in period t t p = power charge in period t fix ilt s = 1 if the consumer sets to the appliance i to level l in period t, zero otherwise max il tdc = maximum value of the operation time if the consumer sets the appliance i to condition 2 status and level l min il tdc = minimum value of the operation time if the consumer sets the appliance i to condition 2 status and level l ,var dc il s = operation time if the consumer sets to the appliance i to condition 2 status and level l max il tc = maximum value of the operation time if the consumer sets the appliance i to condition 3 status and level l min il tc = minimum value of the operation time if the consumer sets to the appliance i to condition 3 status and level l ,c il var s = 1 if the consumer sets the appliance i to condition 3 and level l, zero otherwise il cot = continuous operation time if the consumer sets to the appliance i to condition 3 status and level l il ec = power consumption operated to the appliance i to level l variables ilt c = cost of operating appliances i to level l in period t cum t c = cumulative charging to the period t over t c = excess cost of the t period following the introduction of a punitive charge over t u = the amount of excess electricity in period t according to the introduction of the electric power peak jin and choi/oper. res. eng. sci. theor. appl. 5(3)2022 230-243 236 ilt x = 1 if appliance i is set to condition 1 and level l in the period t, zero otherwise dc ilt y = 1 if appliance i is set to condition 2 and level l in the period t, zero otherwise c ilt y = 1 if appliance i is set to condition 3 and level l in the period t, zero otherwise cont ilt y = 1 if appliance i is set continuously by condition 3 and level l in the period t, zero otherwise ilt z = 1 if appliance i is set to level l in the period t, zero otherwise based on the notation described, the model for the load scheduling of home appliances is formulated as follows: objective function cum t t minimize c  (1) subject to 1 1 , l ilt l z i t    (2) , , fix ilt ilt s x i l t  (3) , , min max il il l dc var dc ilt il tdc t tdc y s i l     (4) , , min max il il l c var c ilt il tc t tc y s i l     (5) 1 ' ' , , ( 1) ilt cot c cont il ilt ilt il t t cot y y i l t t t cot         (6) , , 3 dc cont ilt ilt ilt ilt x y y z i l t     (7) 1 1 i l over over il ilt t t i l ec z l u t      (8) , , ilt il l ilt c ec p z i l t  (9) over over over t t t c p u t  (10) optimal load scheduling of home appliances considering operation conditions 237 1 1 i l cum over t ilt t i l c c c t      (11-1) 1 1 1 i l cum cum over t t ilt t i l c c c c t        (11-2) , , , , {0,1} dc c cont ilt ilt ilt ilt ilt x y y y z  (12) , , , 0 cum over over ilt t t t c c c u  (13) equation (1) is an objective function, and aims to minimize the total power cost incurred in all periods. constraint equation (2) means that all home appliances can only set one operation per hour. constraint equation (3) is an equation for a definitive operation setting of a home appliance. that is, when the home appliance, the operating level, and the operating time are set, ilt x is calculated accordingly. constraints (4) and (5) are indicating that the home appliance is set as a range time. constraint equation (4) is a case where discontinuity is allowed, and constraint equation (5) is a case where continuous operation is required. constraint equation (6) means that when the home appliance is set to the range time, it must be operated for a set time based on the operation start time. constraint equation (7) means that only one of the definitive setting, range setting (continuous and discontinuous) is possible. constraint equation (8) is a restriction for determining whether the power usage corresponds to an excessive power consumption layer (super consumers). constraints (9) and (10) represent the costs for power consumption. constraint equation (9) refers to the cost of general power consumption thatis calculated by multiplying the power consumption of the home appliance, the power charge of the corresponding time, and whether it is operational or not. constraint equation (10) is a formula for calculating the amount of power used when corresponding to superuser. constraint equations (11-1) and (11-2) calculate the accumulated power usage amount in period t. constraint (12) represents the binary variables, and constraint (13) indicates the non-negative variables. 4. experiment results and discussion 4.1. input data in order to conduct the experiment of the mathematical model proposed in sections 3-2, actual data operated by jeju island of south korea was used. jeju island uses seasonal and hourly rate systems (korea electric power corporation (2021), basic terms of supply enforcement detailed rules) to induce users to use low-rate power by applying high rates during high power demand times of the day or low rates during low power times. that is, power charges vary by season and time, and detailed data are presented in table 1. in addition, if the monthly power consumption exceeds 1000 kwh in summer (from june 1 to august 31) and winter (from november 1 to the end of february of the following year), it will be classified as a super user, and the unit price of 704.5 krw per kwh will be applied to the excess usage. in addition, household appliances and power consumption in regular jin and choi/oper. res. eng. sci. theor. appl. 5(3)2022 230-243 238 publications published by the korea electric power exchange (2019) were used, and data on household appliances are presented in table 2. the power usage according to the level of home appliances was set based on the second stage, and it was assumed that the first stage decreases by 20% whereas the third stage increases by 20%. ibm ilog cplex 22.1, a commercial optimization package conducted on a pc (amd ryzen 5600x, cpu 3.7 ghz), was used to conduct experiments on the optimization model. table 1. energy charge for seasonal and hourly in jeju island basic rate (krw/kw) energy charge (krw/kwh) a time zone spring, fall summer, winter 4310 light-load (22:00–08:00) 99.0 111.9 heavy-load (08:00–16:00) 127.0 157.9 overload (16:00–22:00) 145.6 193.7 table 2. data and experimental settings for appliances appliance number of level power rating (kw) operation setting condition setting operating time (min) minimum start time maximum start time tv 3 0.1515 #1 420 17:00 22:00 refrigerator 3 0.0422 #1 1440 00:00 24:00 washing machine 3 0.9043 #3 120 07:00 22:00 air conditioner 3 1.5 #2 300 12:00 20:00 vacuum cleaner 2 1.2 #3 30 07:00 22:00 microwave 2 1.1615 #2 30 06:00 07:00 water purifier 2 0.5775 #1 1440 00:00 24:00 induction heating cooking heater 2 1.3745 #3 30 18:00 20:00 toaster 2 0.9157 #3 30 05:00 07:00 blender 2 0.7276 #3 30 05:00 07:00 air purifier 1 0.0491 #2 120 18:00 24:00 computer 1 0.3119 #1 360 18:00 24:00 stereo 1 0.1015 #1 300 18:00 23:00 dryer 1 1.5061 #2 15 06:00 07:00 iron 1 1.3748 #3 30 17:00 22:00 4.2. experimental results the results of the experiment are shown in figure 1. the experimental results showed that a flexible operation was set during light and heavy-load times when power charges were low by avoiding the maximum load time, except for the appliance set to condition 1. in addition, as shown in figure 2, it can be seen that the cost in the heavy-load time period has increased rapidly due to the power usage transfer to the heavy-load time period in the overload time period. optimal load scheduling of home appliances considering operation conditions 239 figure 1. experimental results by conditions figure 2. cumulative cost according to time period 4.3. additional experimental design and results in this study, sensitivity analysis was conducted to analyze the change in the result value according to the change in the input data value. the new light-load power rate and overload power charge were calculated using the power charges and weight factors in the light-load, heavy-load, and overload times presented in table 1. weight factors were taken to be 0.5, 0.8, 1.0, 1.2 1.5, respectively. the experimental results are as illustrated in figure 3, and it is confirmed that reducing the difference in power charge according to load increases the power usage cost during light load time, whereas increasing the difference in power charge increases the power usage cost during overload time. jin and choi/oper. res. eng. sci. theor. appl. 5(3)2022 230-243 240 new light-load power charge = heavy-load power charge (heavy-load power charge light-load power charge) · weight factor new overloaded power charge = heavy-load power charge + (overload power charge heavy-load power charge) · weight factor figure 3. total costs based on power rate weight factor and time zone by rate in the second experiment, we added constraints on the instantaneous maximum used amount. in south korea, when power consumption is high, such as in summer or winter, instantaneous power consumption cannot exceed contract demand. therefore, the following constraint formula (14) was added in consideration of this situation, and the experiment was conducted assuming that the power use limitations were 2.6, 3.0, and 3.4 kw/h, respectively. 1 1 i l il ilt i l ec z ce t     (14) figure 4 shows the rate of change in power cost compared to the basic experimental result value for each light-load, heavy-load, and overload time zone. the experimental results show that, when the instantaneous power use limit is 3.4 kw, the same cost is incurred as in the basic experiment. at 3.0 kw, the power use cost increased in heavy-load time, and in the case of limitation to 2.6 kw, the power usage cost increased in overload time. it can be seen that as the restriction on instantaneous power use became stronger, the schedule plan of home appliances was moved to a section where costs gradually increased. optimal load scheduling of home appliances considering operation conditions 241 figure 4. amount of change in total power cost for instantaneous power usage 5. conclusion this study proposed a mathematical model for optimal scheduling for home appliances to minimize electricity charges assuming an environment to introduce smart metering, which is rapidly being promoted in the power market. this study also proved the superiority of the model using actual data in jeju island of south korea. in addition, sensitivity analysis was conducted to find the change in decision variables and objective function as the parameter values were changed, and as a result, it was confirmed that the decision-making was made by changing the load time to lower the total power charge. furthermore, two sensitivity analyses were conducted to find out the changes in decision variables and objective functions according to the changes in parameters. the first sensitivity analysis compared and analyzed the case where the difference in power prices according to the light-load period, the heavy-load period, and the overload period increased or decreased, the second sensitivity analysis was performed by considering the instantaneous maximum usage so that instantaneous power consumption cannot exceed the contract demand when the power consumption is high, such as in summer or winter. looking at the results of the two sensitivity analyses, it was found that the decision was made by reducing the total power cost and varying the load time to satisfy the additional constraints and circumstances. this study result could help establish schedule plans for home appliances to save power and serve as a guideline for development and operation related to smart homes. the limitations of this study and future research directions are as follows. the electricity rate system applied not only to each region of south korea but also to each country is different. in this study, input data was prepared using actual data from jeju island located in south korea, but the latter can be changed according to country, timing, policy, and situation. therefore, in future studies, it will be necessary to analyze power rate systems in various countries and establish a mathematical model for scheduling accordingly. other limitations of this study include considering only commonly used home appliances, not considering detailed operations such as step jin and choi/oper. res. 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(2012). an integer linear programming based optimization for home demand-side management in smart grid. paper presented at the 2012 ieee pes innovative smart grid technologies (isgt). © 2022 by the authors. submitted for possible open access publication under the terms and conditions of the creative commons attribution (cc by) license (http://creativecommons.org/licenses/by/4.0/). https://doi.org/10.1016/j.enbuild.2021.111676 https://doi.org/10.1016/j.ijepes.2015.11.099 https://doi.org/10.1016/j.energy.2021.122544 https://doi.org/10.3390/buildings11060237 https://doi.org/10.1016/j.ijepes.2021.107230 https://doi.org/10.1016/j.apenergy.2016.11.071 https://doi.org/10.1109/tsg.2015.2435708 https://doi.org/10.1016/j.enbuild.2016.08.082 optimal load scheduling of home appliances considering operation conditions sukho jin*, jeongmi choi 1. introduction 2. literature review 3. mathematical model 3.1. assumptions 3.2. model description 4. experiment results and discussion 4.1. input data 4.2. experimental results 4.3. additional experimental design and results 5. conclusion references operational research in engineering sciences: theory and applications vol. 3, issue 1, 2020, pp. 57-71 issn: 2620-1607 eissn: 2620-1747 doi: https:// doi.org/10.31181/oresta2001057m * corresponding author. vladimir.markovic@spu.ba (v. marković), danijelamaksimovic89@gmail.com (d. maksimović), mladenrgajic@gmail.com (m. gajić) ranking banks by applying the multilevel i– distance methodology vladimir marković 1*, danijela maksimović 2, mladen gajić 3 1* slobomir p university, faculty of economics and management, bijeljina, bosnia and herzegovina 2 ernst and young, fra anđela zvizdovića 1, 71000 sarajevo, bosnia and herzegovina 3 public health institution, hospital “sveti apostol luka”, doboj, bosnia and herzegovina received: 11 march 2020 accepted: 06 april 2020 first online: 06 april 2020 research paper abstract: banks in the republic of srpska are one of the most important drivers of the economy and household savings. the activity of the financial market of the republic of srpska is low and banks are still the main source of funding. the question of the objective ranking of banks based on business results is an important element in the business decisions made by companies and the population. a bank’s position and quality would depend on the criteria to be included in the analysis. the professional literature recommends that banks’ liquidity, profitability, efficiency and solvency should be monitored. in most cases, whether to rank banks based on liquidity or adequacy or on another indicator is doubtful. the best picture of the state of the banks is obtained when all indicators are involved in such ranking. the aim of this study is to define and rank the banks headquartered in the republic of srpska by following a total of four indicators. in this paper, the calculation of banks’ liquidity, efficiency, profitability and solvency based upon the publicly presented audit reports for the years 2013 and 2014 is given. then, the statistical model that absorbs information and generates the final ranking of banks in the rs is defined. the subject of the study is the banks that operate and are headquartered in the rs. the hypothesis is to determine their rankings based on their business performance. keywords: bank, ranking list, i-distance, criteria. 1. introduction the quality evaluation of banks’ success includes monitoring a bank from different perspectives and measuring its quality from different aspects. successful marković et al./oper. res. eng. sci. theor. appl. 3 (1) (2020) 57-71 58 banks are those banks that do not have a problem with liquidity and solvency, thereby achieving the optimal amount of the profit. these aspects are the main principles of banking operations, well-known as the “golden rules” of banking. performance analysis is closely related to liquidity, efficiency, profitability, and solvency (capital adequacy). 1.1. liquidity the liquidity of a bank is a complex concept, usually interpreted as a bank's ability to meet its obligations upon maturity. a bank's management are required to continuously monitor its liquidity from the static and dynamic aspects. by disrupting the liquidity of only one bank, the survival of the entire financial system may be brought into question. if a bank is unable to service its obligations, general confidence in the financial system is lost, which leads to the erosion of the monetary assets of all banks. the following indicators are used both in theory and in practice to assess liquidity: • l1 = cash and pledged marketable securities / business assets, • l2 = total deposits / borrowings, • l3 = variable funds / liquid assets, • l4 = total loans / total deposits, • l5 = liquid assets / operating assets (ćurčić, 1995). during the management of a bank's liquidity, the indicators l1, l2 and l5 need to be maximized, i.e. a higher value of these ratios shows the presence of better liquidity. the indicators l3 and l4 have a completely opposite meaning, i.e. a low value of these indicators implicates high liquidity, and vice versa. when analyzing a bank, it should not be forgotten that too high liquidity causes low profitability. 1.2. efficiency efficiency is defined by the phrase “do things right” and, in a specific case, it is indicative of the fact that banks must manage their assets by implementing the best possible strategy. a bank’s efficiency is achieved when the bank produces bigger effects with as-low-as-possible costs, increasing its productive assets by placing liabilities in the best way under current circumstances (ćurčić, 1995). productive assets bring interest income, after which banks increase capital, provided that they have achieved a positive financial result. the indicators providing information about effectiveness are as follows: • e1 = interest expense / interest income • e2 = provisions / net interest income, • e3 = interest income / total number of employees (sinkey, 1989). the data for this calculation are taken from the income statement, and banks tend to minimize the indicators e1 and e2 – a lower value rejects greater efficiency, and vice versa. the indicator e3 has an alternative explanation, i.e. the maximum value increases efficiency. ranking banks by applying the multilevel i–distance methodology 59 1.3. profitability profitability indicators are crucial for business analysis and are defined as a bank’s earning ability, i.e. its ability to receive income from invested assets and increase them during business cycles. they are used to evaluate a bank’s profitability in a given time, usually at the end of the accounting period (roman et al., 2015): • p1 = profit before tax / equity, • p2 = profit before tax / business assets • p3 = profit before tax / interest income. higher values of the profitability indicators signal a greater earning power, and thus there is a possibility of increasing share capital. caution should be exercised when interpreting the profitability indicators, because numbers may distort the true picture. the profitability indicators are maximized as a result of an increase in a net profit before tax, not under the influence of a reduction in capital, assets or income from interest and the like. 1.4. solvency the solvency, or capital adequacy, of a bank is an indicator which should be paid more attention to in the banking practice. to support this indicator, there is the statutory rate of the minimum capital adequacy ratio of 12%, which represents a bank's ability to eventually fulfill all of its obligations, even from its bankruptcy estate. “a bank is considered insolvent when its liabilities exceed the value of its assets, or when realized losses exceed its equity capital.” in that case, the bank does not have enough capital to cover the incurred losses, and a part of the assets are nonperforming loans, receivables and loans, and there is no possibility for the bank to fulfill all of its obligations (ćurčić, 1995; garcia et al., 2010). the criteria used to test the solvency (capital adequacy) of the bank are: • s1 = total liabilities / equity; • s2 = total deposits / equity; • s3 = venture capital / total risk-weighted assets; • s4 = shareholders' equity / business assets; • s5 = shareholders' equity / risk-weighted assets; • s6 = shareholders' equity / total deposits; • s7 = shareholders' equity / loans (dragašević, 2010). when managing solvency, a bank should tend to minimize the indicators s1 and s2 and have the values of the other indicators as high as possible. instead of total assets and total resources, operating assets and business assets are included in the calculation of these indicators. banks are for-profit organizations and business assets, which represent the funds arising from operations, participate directly in making a profit and are fully justifiably included in the calculation. the confirmation for this is the fact that total assets represent a sum of operating assets and offbalance assets, where the off-balance sheet positions are sureties, guarantees, acceptances, bills of exchange and other forms of guarantees, uncovered letters of marković et al./oper. res. eng. sci. theor. appl. 3 (1) (2020) 57-71 60 credit, irrevocable, approved but undrawn loans and so forth. it is characteristic of the off-balance sheet positions that they are potential liabilities or claims, and that there is an amount of uncertainty regarding whether and when those contingent liabilities and receivables would be implemented. banks often use off-balance sheet transactions in order to earn additional income, accomplished through commission fees. to conclude, off-balance sheet (assets) are excluded from the calculation, because the research is aimed at showing the real rank and position of the banks operating in the republic of srpska’s banking sector based on their core business. 2. methods there are numerous methods and ways for ranking certain units within a set or a sample. in particular, it is possible to use various multicriteria ranking methods for banks, such as electre, promethee, camels, and so on. in this paper, however, we decided to apply the i-distance method. the i-distance method was originally introduced and defined in professor branislav ivanović’s publications in the 1960s and the 1970s. professor ivanović designed this method so as to rank countries by the development level, which he described by means of various socio-economic indicators (jeremić et al., 2013). the relative position of a unit in relation to another within the units of a dataset can be determined by using this method. the linear (clustered and non-clustered) and quadratic distances were worked out in the method, and further research in this field has led to the development of a multistage i-distance, which will be used in this paper (ivanović, 1977; jeremić et al., 2013; jovanović–milenković et al., 2015). the process of the construction of the i-distance is iterative (jeremić et al., 2013), the number of iterations depending on the number of the indicators to be included in the analysis. if observing a set of indicators , which in this case describe the quality of a certain field of operations, the i-distance between the two observed units (i.e. banks in this case) and is calculated by applying the following equation: (1) where: di(r,s) is the distance between the units er and es for the indicator ci; σi is the standard deviation for the value of all the units as per indicator ci; rji.12…j-1 represents a partial correlation coefficient between the indicators ci and cj (marković et al., 2020; radojičić et al., 2012). it was pointed out that the calculation of the i-distance is a procedure consisting of several iterations. the process, first, involves the entire discriminatory effect of the indicator x1, i.e. the indicator with the most information about the level of the “quality” of the unit. after that, the part of the discriminatory effect of the second indicator not involved in the discriminatory effect of the first indicator is added. in a fashion similar to the previous one, the part of the information provided by the third ranking banks by applying the multilevel i–distance methodology 61 indicator not involved in the discriminatory effect of the first two is added. the whole process continues, so that the level of the “quality” of the unit ej, defined by a set of the indicator x, might finally be as follows: ji n i j dd  = = 1 (2) if the variables have a different (either positive or negative) sign resulting in the occurrence of a negative correlation coefficient between the variables, it is necessary to use the square i-distance (jeremić et al., 2013) in the analysis. the inclusion of the indicators with less information is greater in the square distance than in the plain distance, which is another reason why the square i-distance should be used when there is a large number of indicators. the square i-distance is calculated as follows: (3) in this paper, the ranking of the banks will be performed by means of the square i-distance, because of the occurrence of the negative partial correlation coefficients between the observed indicators for the ranking. it is, however, necessary to say that, due to the specific problem being solved, the two-stage method of the i-distance will be applied. this method involves the calculation of the i-distance for units in the set in several stages, i.e. in two stages in this particular case. the results of the i– distance will be obtained within each segment and the measurement of the banks’ performances (liquidity, profitability, efficiency, solvency), after which the same method will be applied again to the obtained results in order to obtain the final ranking of the banks in the rs. this method will allow us to determine the bestperforming banks for each of these segments, and the most successful one among them (marković et al., 2020; jovanović – milenković et al., 2015). apart from the final ranking, this method also allows the determination of weight coefficients for each indicator individually, also establishing the relative importance of bank performance indicators (liquidity, profitability, efficiency, solvency) and giving a picture of the quality assessment of each bank individually (dobrota et al., 2015). 3. research results the research study includes all the banks headquartered in the rs. it is aimed at forming the final ranking, which realistically reflects the quality of the operations of the banks by the observed indicators. the years the survey was conducted for are 2013 and 2014, the data having been taken from the official financial and audit reports of the included banks. table 1 shows the quantitative indicator values expressed for the observed banks in 2013. marković et al./oper. res. eng. sci. theor. appl. 3 (1) (2020) 57-71 62 table 1. the indicators of the banks' performance in 2013 ind. nova bank nlb unicredit hypo sberba nk komer cijalna banka srpske pavlov. banka mf bobar i liq. l1 0.059 0.103 0.030 0.052 0.062 0.046 0.082 0.104 0.052 0.066 l2 0.834 0.863 0.844 0.902 0.881 0.878 0.712 0.948 0.657 1.001 l3 5.695 2.451 6.534 4.242 4.287 6.236 4.339 3.594 12.64 4.634 l4 0.950 0.861 1.161 1.055 1.158 1.096 1.108 0.822 1.330 0.901 l5 0.170 0.396 0.150 0.225 0.229 0.158 0.208 0.261 0.078 0.209 ii effic. e1 0.492 0.385 0.203 0.445 0.348 0.307 0.487 0.353 0.398 0.456 e2 0.031 0.038 0.013 2.241 0.020 0.118 1.564 0.177 0.055 0.751 e3 124714 102893 128527 104789 116425 100021 58208 55980 77257 97697 iii prof. p1 0.103 0.113 0.128 0.000 0.039 0.006 0.000 0.024 0.016 0.043 p2 0.008 0.011 0.020 0.000 0.006 0.001 0.000 0.003 0.002 0.006 p3 0.009 0.013 0.023 0.000 0.007 0.002 0.000 0.004 0.002 0.007 iv sol. s1 11.80 8.89 5.54 4.82 5.76 3.07 7.80 6.17 6.36 6.18 s2 9.42 7.32 4.60 3.71 4.95 2.64 5.19 5.79 3.97 5.26 s3 0.130 0.186 0.226 0.202 0.128 0.255 0.142 0.133 0.186 0.143 s4 0.064 0.052 0.103 0.134 0.093 0.228 0.156 0.092 0.171 0.124 s5 0.082 0.039 0.171 0.190 0.099 0.317 0.202 0.117 0.225 0.151 s6 0.087 0.071 0.147 0.210 0.128 0.351 0.265 0.114 0.316 0.169 s7 0.092 0.054 0.126 0.199 0.110 0.320 0.239 0.159 0.238 0.187 all indicators were calculated as stated in the introductory part, the example of the calculation being the method for the calculation of the criteria l1 and l2 for nova banka. l1 = cash and pledged marketable securities / business assets l1 = 103,560,819/ 1,737,567,592 = 0.059 l2 = total deposits / borrowings l2 = 1,074,122,000/1,288,604,269=0.834 the results show the performance of the ten banks, only one of which (banka srpske) is a bank in the majority ownership of the state. the following is the final ranking combining all the aspects of the banking operations of the analyzed banks in 2013. table 2. the ranking of the banks according to performance indicators in the rs in 2013 number bank i-distance (total) 1 unicredit 14.2327838 2 komercijalna bank 11.610584 3 nlb 3.56011666 4 sberbanka 2.13446858 5 pavlović 1.78470972 6 mf 1.70531188 7 hypo 1.3461246 8 nova banka 1.30309752 9 banka srpske 0.96692585 10 bobar 0.83768652 ranking banks by applying the multilevel i–distance methodology 63 according to the performance results in 2013, the most successful bank was unicredit bank inc. banja luka, only to be followed by komercijalna bank, while bobar bank inc. bijeljina ranked the last. the market verification and justification of the use of the method was confirmed by the data analysis. in 2014, bobar bank lost its banking license, which confirmed the results obtained by the ranking method, because it is exactly that bank that was identified as the worst. also, an additional analysis was performed, which included the ranking of the banks by each individual criterion, and the results are presented below. the first to have been analyzed is the liquidity criterion, the ranking results being presented in table 3. the above-described indicators (l1 to l5) were used for the ranking. table 3. the ranking of the banks by the liquidity criterion (2013) number bank i-distance (total) 1 nlb 16.8738237 2 pavlović 15.0160139 3 bobar 8.5174958 4 nova banka 5.6421245 5 hypo 4.05662494 6 banka srpske 3.75091339 7 sberbank 3.054496 8 komercijalna 1.86807697 9 unicredit 1.33231758 10 mf banka 0 the results indicate that nlb bank had the best liquidity in 2013, only to be followed by pavlović bank and bobar bank. on the other hand, mf bank and unicredit bank had the lowest liquidity. given the fact that unicredit bank was previously seen to be the best-ranked in general, this indicates that they had no problem with the placement of their funds, and the following criteria will show that they are doing it the right way. after liquidity, the banks were also analyzed according to the profitability criterion, which included the three aforementioned and explained indicators. the ranking results for this criterion are given in the following table. table 4. the ranking of the banks by the profitability criterion (2013) number bank i-distance (total) 1 unicredit 17.23932 2 nlb 6.275044 3 nova banka 4.048731 4 bobar 1.651467 5 sberbank 1.455483 6 pavlović 0.523299 7 mf banka 0.188562 8 komercijalna 0.089404 9 hypo 0 10 banka srpske 0 marković et al./oper. res. eng. sci. theor. appl. 3 (1) (2020) 57-71 64 by far, the most profitable bank is unicredit, only to be followed by nlb bank, and nova banka being in the 3rd place. hypo and banka srpske are the banks ranked the worst, with the lowest values in all the observed indicators. the next ranking criterion was efficiency, which included a total of three indicators. the results are given in the following table. table 5. the ranking of the banks by the efficiency criterion (2013) number bank i-distance (total) 1 unicredit 25.381683 2 sberbank 6.9713765 3 nova banka 6.6322243 4 komercijalna 4.4184533 5 nlb 3.2628914 6 hypo 3.2233851 7 bobar 2.8586987 8 mf banka 1.2178958 9 pavlović 0.6498732 10 banka srpske 0.0025168 unicredit bank, which has shown a dramatically better score than the secondranked sberbank, ranked the highest. the three worst banks were bobar, mf bank and pavlović bank. the last criterion observed was solvency, including a total of seven individual indicators. table 6. the ranking of the banks by the solvency criterion (2013) number bank i-distance (total) 1 komercijalna 32.93711 2 banka srpske 15.234933 3 mf banka 14.380753 4 hypo 12.070788 5 bobar 8.7877177 6 unicredit 6.5899765 7 pavlović 4.1813884 8 sberbank 2.4290309 9 nova banka 0.8491772 10 nlb 0.2067228 it can be noticed here that the most solvent were komercijalna and banka srpske, whereas the lowest solvency was that of nova and nlb banks. the same complete analysis for the year 2014 was also performed. in addition to the final rankings, the individual rankings of the banks in all the selected performance criteria were also given. the quantitative indicators of the banks’ business success for the year 2014 are given in the following table. ranking banks by applying the multilevel i–distance methodology 65 table 7. the banks' performance indicators in 2014 ind. nova banka nlb unicred it hypo sberba nk komerc ijalna banka srpske pavlovi ć mf i liq. l1 0.053 0.176 0.087 0.078 0.108 0.039 0.083 0.102 0.032 l2 0.861 0.884 0.872 0.916 0.907 0.857 0.743 0.929 0.754 l3 6.201 2.077 4.307 4.149 3.859 6.332 2.889 3.230 15.383 l4 0.935 0.932 1.032 0.964 0.930 1.141 1.054 0.886 1.167 l5 0.155 0.468 0.228 0.228 0.256 0.156 0.326 0.287 0.064 ii effic. e1 0.465 0.369 0.240 0.455 0.352 0.282 0.577 0.359 0.435 e2 0.060 0.043 0.014 0.948 0.015 0.246 0.141 0.155 0.165 e3 139110 103618 131912 79899 122774 96497 44440 65204 88029 iii prof. p1 0.107 0.133 0.121 0.000 0.038 0.002 0.012 0.027 0.032 p2 0.008 0.014 0.018 0.000 0.005 0.001 0.001 0.004 0.004 p3 0.009 0.016 0.021 0.000 0.006 0.001 0.001 0.005 0.004 iv sol. s1 11.823 8.338 5.761 4.256 6.585 3.142 8.614 5.121 7.609 s2 9.703 7.034 4.928 3.262 5.834 2.644 6.138 4.707 5.461 s3 0.1250 0.1710 0.1990 0.255 0.1421 0.2590 0.1220 0.13 0.1388 s4 0.064 0.052 0.089 0.131 0.091 0.224 0.142 0.108 0.139 s5 0.084 0.036 0.152 0.252 0.118 0.320 0.149 0.130 0.178 s6 0.085 0.070 0.122 0.210 0.118 0.351 0.222 0.140 0.219 s7 0.091 0.075 0.118 0.218 0.127 0.308 0.210 0.158 0.188 in 2014, there were nine banks headquartered in the rs, of which only banka srpske was in the majority ownership of the state. when speaking about the banks' liquidity, the following table provides an overview of the performance of the banks' liquidity criterion. table 8. the ranking of the banks by the liquidity criterion (2014) number bank i-distance (liquidity) 1 nlb 23.0679518 2 pavlović 12.2169568 3 sberbank 10.1900486 4 hypo 7.50696812 5 unicredit 5.50971948 6 banka srpske 4.53137136 7 nova banka 4.09852271 8 komercijalna 2.11820058 9 mf bank 0.01845142 the bank with the best liquidity was nlb bank, only to be followed by pavlović bank and sberbank, while the last place was occupied by mf bank, which had significantly poorer liquidity than the other banks included in the survey. the next criterion according to which the banks were ranked was profitability, which included three individual indicators. according to this criterion, the success achieved by the banks is given in the following table. marković et al./oper. res. eng. sci. theor. appl. 3 (1) (2020) 57-71 66 table 9. the ranking of the banks by the profitability criterion (2014) number bank i-distance (profitability) 1 unicredit 9.646974 2 nlb 5.556958 3 nova banka 1.802034 4 sberbank 0.742712 5 pavlović 0.598086 6 mf bank 0.384051 7 banka srpske 0.039267 8 komercijalna bank 0.013401 9 hypo 0 based on the data, the best-ranked is unicredit bank, only to be followed by nlb bank and nova bank. the three banks with very poor profitability are banka srpske, komercijalna bank and hypo bank. the third criterion is efficiency, which includes three individual indicators. table 10. the ranking of the banks by the efficiency criterion (2014) number bank i-distance (efficiency) 1 unicredit 23.528331 2 sberbank 13.591869 3 nova bank 7.9688431 4 komercijalna bank 7.6410548 5 nlb 5.1772631 6 pavlović bank 2.242352 7 mf bank 2.1212785 8 hypo 1.3832248 9 banka srpske 0.0561461 according to the previous criterion, the best-ranked bank is unicredit bank, only to be followed by sberbank and nova bank, whereas banka srpske is ranked the last again, being far behind the other banks in terms of efficiency. the final performance criterion to be analyzed was capital adequacy (solvency), which included a total of seven single indicators, and the classification of the banks according to this criterion is as follows: table 11. the ranking of the banks by solvency criterion (2014) number bank i-distance (solvency) 1 komercijalna bank 27.191051 2 hypo 13.274755 3 mf bank 6.067496 4 banka srpske 5.90802 5 pavlović bank 3.3239149 6 unicredit 2.9352242 7 sberbank 1.8211099 8 nova bank 0.4040932 9 nlb 0.0739856 ranking banks by applying the multilevel i–distance methodology 67 the best bank is komercijalna bank, only to be followed by hypo bank and mf bank. the worst banks in terms of solvency are nova bank and nlb bank. finally, the survey included all the criteria in the joint ranking list and all the aspects of the business performance of the banks in the final ranking of the banks headquartered in the rs for the year 2014. table 12. the ranking of the banks by the performance indicators in the rs in 2014 number bank i-distance (total) 1 unicredit 13.82901 2 nlb 11.99673 3 komercijalna bank 10.09697 4 hypo 3.149554 5 sberbank 3.100193 6 pavlović bank 2.499681 7 nova bank 1.170214 8 banka srpske 0.757758 9 mf bank 0.517659 according to the results given in the tables (above), it can be concluded that unicredit bank was the best-ranked, only to be followed by nlb bank, whereas komercijalna bank was the third. banka srpske and mf bank ranked the last, significantly lagging behind the leading banks. before the discussion of the obtained results, it is important to note that the application of this method allows for the calculation of the importance of individual criteria and indicators. based on the correlation coefficients, the weight coefficients were determined not only for each individual indicator, but also for the criteria, and these data are clearly specified in the figure below (maričić et al., 2014). the calculation was performed in such a manner that the correlation coefficients between each of the indicators and the values of the i-distance for the corresponding criterion were first determined. subsequently, the correlation coefficients of the individual indicators were put into relation to the total sum of the correlation coefficients, thus the relative importance of each indicator being obtained individually. the identical calculation method was applied to all the main criteria, as well as the corresponding sub-criteria. the following is an example of the calculation of the weighting coefficients for the individual indicators within the profitability criteria (2014): r31=0.977; r32=0.953; r33=0.869; sum (r)=2.797 w31*=0,977/2,797=0.348; w32*=0.953/2,797=0.341; w33*=0,869/2,797=0.311 after this round of the calculation, the values obtained were multiplied by the weighting factor of the profitability criterion, which was calculated in the identical manner, but with the correlation coefficients obtained from the values of all the main criteria and the final value of the i-distance. in this case, the value of the weight coefficient w3 was 0.4; therefore, w31 = 0.14; w32 = 0.14; w33 = 0.12 (rounded to two decimal places), exactly as is shown in figure 1. marković et al./oper. res. eng. sci. theor. appl. 3 (1) (2020) 57-71 68 figure 1. the relative importance of the criteria and the individual indicators in the literature and in practice, throughout the territory of the republic of srpska and a wider environment, capital adequacy (solvency) was taken as the primary indicator of the ranking of the banks. applying the described model, completely different data were obtained. as can be seen in figure 1, the most important criterion in the analysis was profitability, whose significance is 0.40, which is only followed by efficiency, with the importance of 0.32, then liquidity, with 0.19, and ultimately solvency (capital adequacy), with 0.09. such an order is justified in terms of successful business, so that the banks may increase assets effectively and also service their obligations on a regular basis. the main goal for the banks is to be solvent and fulfill their obligations, even from their bankruptcy estate. 4. discussion it should be taken into consideration that banks are supposed to operate indefinitely, for which reason a conclusion can be drawn that the importance of individual the indicators was fairly evenly distributed within the criteria and the distances of the individual indicators had a very short range, namely: liquidity (0.03:0.05), profitability (0.12:0.14), efficiency (0.10:0.12) and solvency (0.011:0.014). the model also included the arithmetic mean of all the parameters individually. the arithmetic mean presents the average, the minimum value of the banking sector in the rs. all the banks headquartered in the rs that had not reached the minimum value were classified into the group of the banks with risky business. the ranking of the banks according to the liquidity criterion in 2014 is shown in table 4 of the previous section, according to which the most liquid was nlb ranking banks by applying the multilevel i–distance methodology 69 development bank, whereas the worst-ranked was mf bank. it is important to note that the average value of the liquidity criterion in the banking sector in the rs was 5.403 for the year 2014. banka srpske, nova bank, komercijalna bank and mf bank were in the so-called gray, alarming business zone. the average value of profitability was 1.084, and only three banks achieved profitability above the minimum required value, the first being unicredit bank, only to be followed by nlb development bank and nova bank, whereas the other four banks (pavlović bank, mf bank, banka srpske, komercijalna bank and hypo bank) had the profitability value below the average. the final ranking list of the banks' profitability indicator is shown in table 5. table 6 accounts for the order of the banks starting from the most efficient to the least efficient bank in the rs. the average value for the efficiency indicator of the banks in the rs was 4.533. in 2014, pavlović bank, mf bank, hypo bank and banka srpske failed to reach the minimum threshold of the average value. the ranking of the banks according to the last indicator, i.e. solvency, with the least significance for the ranking of the banks is presented in table 7. the average value of the solvency for the banks in the rs was 4.49. pavlović international bank, unicredit bank, sberbank, nova bank and nlb development bank were in the gray business zone when solvency is concerned. the list of the final ranking of the banks in the rs according to all the tested indicators is given in table 8 of the previous section. the average value of all the indicators, here used as the landmark when companies enter into the gray business area, was 2.34. according to that criterion, nova bank, banka srpske and mf bank were the banks with “problematic” business in 2014. according to the criterion with the greatest significance for the ranking, i.e. the profitability criterion, and also based on the efficiency and solvency criteria, banka srpske ranked the worst. if the fact that these three indicators account for 79% of the overall significance of the model is taken into account, then it is can be concluded that banka srpske had a worse ranking than mf bank, regardless of the final ranking. banka srpske was betterranked than mf bank only according to the liquidity criterion, which means that it had not used resources at its disposal as it should have. attention should be paid to the worst-ranked banks in 2013. banka srpske was slightly better than bobar bank in 2014. banka srpske still holds the same position (the penultimate place). if mf bank, which is quite a young and small bank in relation to the other banks, were omitted, then banka srpske could be said to have ranked the worst in 2014. this is supported by the abstained audit opinions for banka srpske in the year 2013, and a negative audit opinion for the year 2014. mf bank received an unqualified audit opinion for both periods. 5. conclusion the model for ranking the banks is based on the official data obtained from the financial statements and the annually valorized indicators. the results show that bobar bank was the worst and had the lowest business indicators of all the banks in the overall ranking in the rs in 2013. the audit report in which the auditors refrained from expressing an opinion was a confirmation of this. in the model for marković et al./oper. res. eng. sci. theor. appl. 3 (1) (2020) 57-71 70 ranking the banks in 2013, the worst-ranked bank confirmed its low indicators and risky business by the loss of the banking license in 2014. the indicators in the statistical model pointed out the weakening market position and were a signal for change in the bank’s business policy. according to the criteria of the established model, mf bank was the worst-ranked in 2014, although it must be noted that mf bank has been operating for eight years now, that it is a small bank, and that it has not been firmly established on the financial market. also, the results obtained by using the i-distance method in relation to the data obtained by analyzing the financial and audit reports indicate that mf bank was the worst-ranked, but there was a high business risk for banka srpske. it can be expected that mf bank and banka srpske will change positions in the forthcoming period and that the indicators of the i-distance will point to the fact that banka srpske is the least reliable. in a time period shorter than a fiscal year, high-risk businesses change indicators much faster. for that reason, it is recommended that they should be observed in shorter intervals, for example on a monthly basis. calculations in shorter intervals provide more objective indicator values than average values do annually. monthly performance results indicate reliable positioning through the ranking indicator of business performance, thereby enabling high-quality information for the immediate effect on business indicators, both internally and externally. references ćurčić u., (1995.) bankarski portfolio mendažment – strategijsko upravljanje bankom, bilansom i portfolio rizicima banke. novi sad: fejton; dobrota, m., bulajic, m., bornmann, l., & jeremic, v. (2016). a new approach to the qs university ranking using the composite i‐distance indicator: uncertainty and sensitivity analyses. journal of the association for information science and technology, 67(1), 200-211. dragašević z., (2010). modeli višekriterijumske analize za rangiranje banaka. podgorica: doctoral dissertation garcía, f., guijarro, f., & moya, i. (2010). ranking spanish savings banks: a multicriteria approach. mathematical and computer modelling, 52(7-8), 1058-1065. ivanovic b., (1977) classification theory. belgrade: institute for industrial economics; jeremić, v., jovanović-milenković, m., radojičić, z., & martić, m. (2013). el profesional de la información, 22(5).. el profesional de la información 22, 474-480. milenkovic, m. j., brajovic, b., milenkovic, d., vukmirovic, d., & jeremic, v. (2016). beyond the equal-weight framework of the networked readiness index: a multilevel i-distance methodology. information development, 32(4), 1120-1136. maricic, m., & kostic-stankovic, m. (2016). towards an impartial responsible competitiveness index: a twofold multivariate i-distance approach. quality & quantity, 50(1), 103-120. marković, v., stajić, l., stević, ž., mitrović, g., novarlić, b., & radojičić, z. (2020). a novel integrated subjective-objective mcdm model for alternative ranking in order to achieve business excellence and sustainability. symmetry, 12(1), 164. radojicic, z., & jeremic, v. (2012). quantity or quality: what matters more in ranking higher education institutions?. current science, 158-162. ranking banks by applying the multilevel i–distance methodology 71 roman a., saragu a. c., (2015). the impact of bank-specific factors on the commercial banks liquidity: empirical evidence from cee. 7th international conference on globalization an higher education in economics and business administration geba 2013, procedia economics and finance, 20, 571 – 579. sinkey j., (1989.) commercial bank financial management in the financial services industry. 3th ed. new york: macmillan publishing company; upustvo za kompiliranje idikatora finansijskog zdravlja. ccbh; 2012: paragraph ii, article 28. © 2020 by the authors. submitted for possible open access publication under the terms and conditions of the creative commons attribution (cc by) license (http://creativecommons.org/licenses/by/4.0/). ranking banks by applying the multilevel i–distance methodology vladimir marković 1*, danijela maksimović 2, mladen gajić 3 1. introduction 1.1. liquidity 1.2. efficiency 1.3. profitability 1.4. solvency 2. methods 3. research results 4. discussion 5. conclusion references plane thermoelastic waves in infinite half-space caused operational research in engineering sciences: theory and applications vol. 2, issue 3, 2019, pp. 77-91 issn: 2620-1607 eissn: 2620-1747 doi: https:// 10.31181/oresta1903077l * corresponding author. ilazarevic@grf.bg.ac.rs using the electre mlo multi-criteria decision-making method in stepwise benchmarking – application in higher education ivan lazarević faculty of civil engineering, university of belgrade, serbia received: 08 october 2019 accepted: 01 december 2019 first online: 16 december 2019 research paper abstract. the purpose of this paper reflects in a study of an optimal development path in the electre-based stepwise benchmarking context. in the paper, multi-criteria decision-making is first described as a tool for stepwise benchmarking, where the electre mlo ranking method is used. in order to make the problem of finding the optimal path easier and significantly reduce the number of the paths that have to be considered, we are proving the theorem showing that it is better to make gradual progress than “skip steps”. as an illustration of these considerations, the electre mlo method is applied to the benchmark teaching assistants of one faculty of belgrade university, according to the marks given by their students. we are looking for an optimal development path by using our theorem that substantially reduces the number of cases. we are also checking that the paths with no steps skipped are superior to the paths in which steps are skipped, in accordance with the theoretical result we have obtained. thus, we are demonstrating that one should first look up to the colleague who is a little better than him/her, and then gradually improve until he/she has reached the level of the individual given the best mark. key words: multi-criteria decision-making, electre, benchmarking, evolution path, higher education 1. introduction benchmarking is a management tool representing a systematic process of measuring the quality of products or services against the best representative ones in the field of interest. this process includes comparison with the direct competitor and comparison against the given benchmark, or standard one strives to achieve. in this paper, an example of the teaching assistants of one faculty of belgrade university, in which the teaching assistants are compared with one another according to the marks they have received from students, is used as an illustration. the marks are based on a total of ten criteria. lazarević/oper. res. eng. sci. theor. appl. 2 (3) (2019) 77-91 78 benchmarking is mostly used for the purpose of comparing the state policies at the international level. benchmarks are always provided by the most developed countries. there are a lot of studies on this topic; see (arrowsmith et al.,2004; petrović et al., 2012; p. hong et al., 2012; petrović et al., 2014; brehmer et al., 2019; m. petrović et al., omega, 2018; petrović et al., journal of sustainable business and management solutions in emerging econo, 2018). the socioeconomic, geostrategic and cultural influences of one country are often neglected during a mutual comparison, so the question is whether the measures transferred from other countries are always applicable; see (dolowitz and marsh, 1996; bauer, 2010; lundvall and tomlison, 2012). in spite of the differences, it is clear that country leaders, especially the leaders of those in the same region, in the european union, or those tending to enter the european union, can follow one another (rose 1991). international benchmarking is broadly applied even in information and communication technologies. the benchmarking process includes making different decisions, ranging from the manner of choosing the most relevant statistical data, all the way to the role model which is considered as the best to improve certain characteristics. the main question is as follows: who or what should we look up to in order to become better? to learn from the best in a certain field is not always the best of options. one should also be realistic when assessing abilities. the main purpose of this paper is to more closely examine this topic and particularly answer the question of whether it is better to make gradual progress or “skip steps”. the answer is provided as the central theorem of this paper. there are many studies on striving towards slightly better, gradual progress; see (moore, 1999; hambelton and gross, 2008; lim et al., 2011). we look for someone or something who/which is a bit better, i.e. for an appropriate benchmark in each step of such progress, thus coming to the so-called evolution of progress. at this point, the most important thing is to choose the best evolution path. in chapter 3 herein, an example of the teaching assistant who obtained the worst marks is presented. he should first look up to the colleague who is a little better than him, after which he should gradually improve until he has reached the level of the teaching assistant who has received the best marks. if uniform progress is made, then the ideal evolution path is obtained, which is difficult to achieve in practice because a non-uniform benchmark distribution is typical for situations in which we deal with realistic data. the dea (data envelope analysis) method is one of the popular operational research methods often used in benchmarking; see (ramon et al., 2018; ji et al., 2019; de blas et al., 2018; gidion et al., 2019). it is based on linear programming and was created in the paper (charnes et al., 1981). in this paper, a modification of the electre i method developed in order to serve as a benchmarking tool is used. this is the electre mlo method that first appeared in the study (petrović et al., 2012). the electre i method was introduced by roy b., in the paper (roy 1968). the method is now only of a historical interest as the method representing the base on which other, more useful methods have been created. the most popular and the most frequently used modifications of electre i are electre iv (figueira et al., 2005) and electre is (roy and skalka, 1987). the family of the electre methods solve the following three very important problems, namely: making a choice (hassan. et al., 2018; wang y and xeo., 2018; tavassoli et al., 2018), ranking (dias et al., 2018; harsoyo and jati, 2018) and sorting (pereira et al, 2019; pereira and ishizaka, 2019; ishizaka et al., 2019; singh, 2019). the methods which solve the alternatives ranking problem are especially important using the electre mlo multi-criteria decision-making method in stepwise benchmarking – application in higher education 79 for benchmarking. the electre iii method deals with these issues; see (bouysson and roy, 1986; papadopulos and karagiannidis, 2008; ishizaka and giannoulis, 2010; hashemi et al., 2016; la fata et al., 2019). over time, modifications of electre iii have developed; see (galo et al., 2018; doumpos and figueira, 2019). before the electre mlo method appeared, the alternatives forming a cycle had been thought to be indifferent and had been ranked at the same hierarchical level. this approach can lead to obtaining imprecise levels (i.e. levels containing many more alternatives than other levels). in the paper (petrović et al., 2012), the problem of cycles for the electre mlo method is solved based on an important result obtained in the study (anic and larichev, 1996) which solved the problem of cycles for the original electre method. the problem of cycles is solved by introducing a modified concordance index and the ast (absolute significance threshold), which represent its limit, above which no cycle will appear in a graph. the electre mlo method will help us find the best evolution path. by this method, alternatives are ranked into levels, so that we can clearly see a hierarchy between them. by applying this method, a tree (a graph without a cycle) is obtained. the best alternative, i.e. the one being a benchmark to all other alternatives, is on top of the tree. the worst candidate needs to make progress gradually towards the top, choosing the best benchmark every step of the way. he looks for the optimal path, the path which is closest to the ideal one. although benchmarking is mostly used in foreign policies, its specific application in higher education is demonstrated in chapter 3. benchmarking is applied in higher education; see (ganushchak-yefimenko et al., 2017; padro and sankey, 2012; placek et al., 2017; paliulis and labanaskis, 2015). various studies on the quality of lectures, the lecturer’s capability and the students’ evaluation of their lecturers in higher education have been carried out; see (millis and cottell, 1997; ramsden, 2003; wei, 2007; spehl et al., 2019). they have been aimed at improving the quality of higher-education facilities. the paper (wachtel, 1998) provides the arguments “for” and “against” students’ evaluation of their lectures. the authors of the paper (sullivan and skanes, 1974) pay special attention to the characteristics of the lecturers with succesful academic carriers who were given excellent marks by their students. in the methodology chapter of this paper, our main result is proven. in chapter 3 of this paper, the theorem is applied to a concrete example of benchmarking the teaching assistants of one faculty of belgrade university, and how to choose an optimal development path and make gradual progress towards the top is illustrated. 2. methodology as stated in the introduction, electre mlo is a good benchmarking tool. electre mlo (multi-level outranking) first appeared in the study (petrović et al, 2012) as a tool in stepwise benchmarking; it is a modification of electre i. the result of the application of electre mlo to realistic data is a hierarchical structure of alternatives (e.g. in figure 1 of chapter 3). the sets of the criteria gij+, gij-, gij= are now defined for two alternatives, ai and aj, in the following manner: lazarević/oper. res. eng. sci. theor. appl. 2 (3) (2019) 77-91 80 gij+={gk |gk(ai)>gk(aj)}, gij-={gk |gk(ai)<gk(aj)}, (1) gij=={gk |gk(ai)=gk(aj)}; where gk(ai) are marks for the alternative ai and the criterion k, and the ωk is a weight factor for the criterion k. let the i1,…,im be a set of marks for any criteria and |ik|=maxik-minik be a scaled score range of the criterion k. allow us to define the normalized value of the marks and the normalized value of the weight factor, as follows: (2) for the electre i method, the concordance and discordance indices are defined in the following manner: (3) (4) the given concordance index is modified by applying the following equation: (5) let us then define the parameter (i, j), applying the following equation: (6) theorem 1 (anić, larichev): the parameter λ is chosen, so that, for each arranged pair of alternatives: {( ) s s } holds inequality: (7) at this point, s is a binary relation, where s implies that is at least as good as the alternative this theorem provides a sufficient condition for the construction of a relationship when cycles do not appear. the parameter λ is the limit value of the modified concordance index, an there is no cycle. alternatives are not indifferent, either. the following equation defines the ast: using the electre mlo multi-criteria decision-making method in stepwise benchmarking – application in higher education 81 ast= . (8) = for each criterion k, the difference between the scores of the alternatives from adjacent levels of performance is as follows: (9) the ideal step is as follows: (10) for each criterion k on the path π, the variation measuring the mean-squared difference from the increment step is depicted, thus obtaining the distance from the ideal path: (11) the overall value of the variation for all criteria is as follows: (12) the value is the worst path, where the total difference between the scores of the alternatives and the target for each criterion k is obtained when only moving by one level. the number is the relative measure of the evolution path π. (13) now, the difference between the scores of the alternatives from the two concrete levels are subjected to examination: = (14) = (15) =c (16) (17) the following inequalities read as follows: ultimately, the main result of our study is formulated and proven. theorem 2: if alternatives are compared according to one single criterion, it is always better to follow the order of events and move one level at a time than move on to the next level only to immediately have a “break” after that. lazarević/oper. res. eng. sci. theor. appl. 2 (3) (2019) 77-91 82 proof: invoking the previously said, the next inequality must be proven: (18) from the right-hand side of the inequality, the addendum represents the skipped step and the pause of the value . the rest of the left-hand and the right-hand sides is the same; so, after canceling out, the following is obtained: (19) now, the theorem is proven. remark 1: that the step skipped at the j-th moment is equivalent to the step skipped at any other moment has been proven. 3. application human resources allow us to understand the sum of all the knowledge and skills of a certain group of people. these skills and knowledge should be a product of one’s, especially higher, education in today’s developed world. it is very important that, during their education process, students should be taught by high-quality lecturers, who will prepare them for making further progress. the students of one faculty of belgrade university evaluated their teaching assistants according to a total of 10 criteria (regularity of practice, regularity of consultation, comprehensibility and manner of presentation, encouraging students to be more active, importance of practice, providing useful information, assistant responds to students’ questions, being professional and ethical in communication, being objective and impartial in evaluation, general impression) on a scale from 1 to 5. the evaluation was anonymous. we accessed and used the data, the average marks given for the teaching assistants according to each of the 10 criteria. the teaching assistants of this faculty were generally given good marks, so that the normalization of those marks was performed by giving the value 1 to the marks below 3 and creating a uniform integer scale from 2 to 9 for the values ranging from 3 to 5. using the electre mlo multi-criteria decision-making method in stepwise benchmarking – application in higher education 83 the example only included the teaching assistants who were evaluated by more than fifty students, for the reason of which fact the marks can be considered as realistic. table 1 shows the evaluation criterion, the weight factor for the criterion and the obtained normalized marks for the teaching assistants. each criterion is given an appropriate weight factor according to its importance (table 1). since the faculty at which our research study was carried out is a technical science faculty and the teaching assistants hold practical classes, the order of the most important criteria is as follows: encouraging students to be more active, importance of practice, comprehensibility and manner of presentation. regularity of practice and regularity of consultation is a duty on the part of all those employed at the faculty, but it does not affect much the quality of the lecturers. table1. the marks obtained (after the normalization) for teaching assistant of the faculty of belgrade university which is the subject matter of the research. c1 c2 c3 c4 c5 c6 c7 c8 c9 c10 ω 1 1 4 5 4 3 3 2 2 3 a1 7 7 7 6 7 7 7 6 7 6 a2 7 7 5 6 6 6 6 6 6 6 a3 8 7 7 6 7 6 6 6 7 7 a4 7 7 3 4 4 4 5 5 5 4 a5 6 7 4 4 4 5 5 5 6 5 a6 6 4 3 2 2 2 3 3 3 2 a7 8 7 7 7 7 7 7 7 7 7 a8 9 8 8 7 8 8 8 8 8 8 a9 8 7 6 3 5 4 5 5 5 4 a10 8 7 7 6 7 7 7 7 7 6 a11 9 9 8 8 8 8 8 8 8 8 a12 9 9 9 9 9 9 9 9 9 9 a13 9 8 4 6 5 6 6 7 7 6 a14 6 6 5 4 5 4 5 4 5 5 a15 9 9 9 8 8 8 9 9 9 9 a16 9 9 8 8 9 8 8 8 8 8 a17 9 8 8 7 8 8 8 7 8 8 a18 6 5 3 3 3 3 3 3 3 3 a19 6 6 5 5 5 5 6 5 5 5 a20 8 8 6 5 4 7 5 6 6 6 specialized software applied the electre mlo ranking method to these data. the value of the modified concordance index of 0.85 was chosen. the ast was 0.75. the tree in figure 1 is a result of the application of the electra mlo method. the hierarchy amongst the alternatives and a possible development path for each alternative can clearly be seen. weaker candidates have the aim to make the most possible uniform progress. since the data are realistic, the ideal evolution path is non-existent. the candidates, however, need to choose the optimal evolution path in order to achieve the level of the teaching assistant who has received the highest of marks. lazarević/oper. res. eng. sci. theor. appl. 2 (3) (2019) 77-91 84 in every educational institution, cooperation among colleagues is advisable. evolution paths were considered for alternative 5. for each of those paths (figure 2), was calculated and the example of the calculation is given at the end of this chapter. the effect of skipping steps, either one step or two at a time, was also considered. that skipping does not improve the evolution paths (in the cases of the the two paths in figure 2, they are clearly worse, because is greater of the first four paths in figure 2) is clearly seen (the bottom of figure 2), which is in accordance with theorem 2. that the same value ρ was obtained for the two paths should not be a surprise, either, given the fact that they only differ in one alternative, a15 replacing a16 (these two alternatives have the marks that only differ from each other in a few criteria, and these two alternatives are at same tree level). so, the teaching assistant number 5 should choose one of these two best paths (the first and the second paths in figure 2). the suggestion for the teaching assistant number 5 implies that he should first look up to the colleague who is a little better than him, and that is the teaching assistant number 2 or the teaching assistant number 20, after which he should start gradually improving until he has reached the level of the teaching assistant given the best of marks. in our opinion, it is very important for the faculty and with respect to the quality of knowledge that the said teaching assistant should be making gradual progress. we suggest that the teaching assistants should be attending each other’s practical classes so as to be able to take the advantage of learning from a better-evaluated colleague. workshops without students could be organized for the teaching assistants in order to enable them to improve their personal teaching methods. figure1. the result of the application of the electre mlo method to the realistic data. using the electre mlo multi-criteria decision-making method in stepwise benchmarking – application in higher education 85 figure 2. the evolution paths for the alternative a5, without “skipped steps” (paths 1, 2, 3, and 4), and with “skipped steps” (paths 5 and 6). for example, we calculated according to the equations given in the methodology chapter for the first path in figure 2 (a5-a2-a1-a10-a7-a17-a8-a11-a15-a12) in the following manner: for the regularity of practice criterion (k=1), the marks of the alternatives of these paths are as follows: 6-7-7-8-8-9-9-9-9-9 and for this criterion is calculated as follows: = + + it is clear that, if the marks of the adjacent alternatives for the criterion k are equal, then we obtain for the regularity of consultation criterion (k=2), the marks for the teaching assistant of these paths are as follows: 7-7-7-7-7-8-8-9-9-9; now, is calculated as for the previous criterion, ; lazarević/oper. res. eng. sci. theor. appl. 2 (3) (2019) 77-91 86 for the comprehensibility and manner of presentation criterion (k=3), the normalized marks are as follows: 4-5-7-7-7-8-8-8-9-9; and for the encouraging students to be more active criterion (k=4), the following marks were obtained: 4-6-6-6-7-7-7-8-8-9; and for the importance of practice criterion (k=5), the obtained normalized marks are as follows: 4-6-7-7-7-7-8-8-8-9; and 5-6-7-7-7-8-8-8-8-9 ; and for the assistant responds to students’ questions criterion (k=7), the following marks were obtained and the dpv was calculated in a manner similar to the previous one: 5-6-7-7-7-8-8-8-9-9; ; after the calculation, we obtained for the teaching assistants are professional and ethical in communication criterion (k=8), the obtained marks are as follows: 5-6-6-7-7-7-8-8-9-9 ; after the calculation, we obtained for the objective and impartial in evaluation criterion (k=9), the obtained normalized marks are as follows: 6-6-7-7-7-8-8-8-9-9 ; after the calculation, we obtained for the general impression criterion (k=10), the obtained normalized marks are as follows: 5-6-6-6-7-8-8-8-9-9 ; after the calculation, we obtained the sum of the weight factors for all the criteria concerned is 28. according to this equation: now, the worst dpv is calculated for this concrete path: for the regularity of practice criterion (k=1): = using the electre mlo multi-criteria decision-making method in stepwise benchmarking – application in higher education 87 for the regularity of consultation criterion (k=2): and for the comprehensibility and manner of presentation criterion (k=3) : and in following example, the dpv is calculated in the same manner as the previous one was. for the encouraging students to be more active criterion (k=4), the following was obtained: and for the importance of practice criterion (k=5), the following was obtained: and ; for the providing useful information criterion (k=6), the following was obtained: and ; for the assistant responds to students’ questions criterion (k=7), the following was obtained: and ; for the teaching assistants are professional and ethical in communication criterion (k=8), the following was obtained: and ; for the objective and impartial in evaluation criterion (k=9), the following was obtained: and ; for the general impression criterion (k=10), the following was obtained: and according to the equation in the methodology chapter, the same calculation was performed in the other five paths shown in figure 2. it was concluded that one of the first two paths is the best choice for the teaching assistant a5. lazarević/oper. res. eng. sci. theor. appl. 2 (3) (2019) 77-91 88 4. conclusion and discussion there is a saying, according to which if you do not become better, you will become worse. there is an existent constant tendency of people to make progress. this research study has shown that the electre mlo ranking method is a good tool in stepwise benchmarking. in the methodology chapter, a detailed description of the electre methods of multi-criteria decision-making, especially the electre mlo ranking method, which is a good stepwise benchmarking tool is given. it prescribes how to pick the best evolution path of all possible paths in the graph by calculating ρ, which is very important for everyday practice. people very often want to make progress as fast as they can so as to become the best in a certain field. the main contribution of this paper rests on theorem 2, which shows how one should behave in order to make general progress. according to this theorem, “skipping steps” is a worse choice than making progress gradually. the best thing to do is always to learn from a colleague who is slightly better than us. the electre mlo ranking method helps us to plan our progress, i.e. “who or what we should look up to in order to become better”. the decision-making based on the application of this method has been illustrated on an example pertaining to higher education, based on the data obtained from one faculty of belgrade university. in this example, it is concluded that there is a suggested development path for every teaching assistant. all possible evolution paths for the teaching assistant number 5 (a5) were considered as well. the best evolution path was chosen after the calculation of . the effect of skipping steps on this concrete example was also considered, and a conclusion is drawn that it is in accordance with our theorem 2. since we are dealing with the realistic data, our research has resulted in two equally good evolution paths because they only differ in one alternative (i.e. a15 or a16), with very similar marks for all the criteria. the same calculation (described in detail in chapter 2) can also be applied to any other teaching assistant. this model and approach to the problem could also be useful in other business progress planning fields. 5. acknowledgement the author would hereby like to thank professors vladimir božin and ivan anić for their encouragement and support during his work on this paper. references anić, i., larichev. o. 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(2007). dilemma of the criteria and anxiety for the reality: reflections on the current system for evaluation of college teachers' classroom teaching [j]. journal of zhejiang normal university (social sciences), 3, 025. © 2019 by the authors. submitted for possible open access publication under the terms and conditions of the creative commons attribution (cc by) license (http://creativecommons.org/licenses/by/4.0/). operational research in engineering sciences: theory and applications vol. 3, issue 1, 2020, pp. 89-102 issn: 2620-1607 eissn: 2620-1747 doi:https://doi.org/10.31181/oresta2001089p * corresponding author adispuska@yahoo.com (a. puška), ilija.stojanovic@teol.net (i. stojanović), a.maksimovic22@gmail.com (a. maksimović), nasihao@yahoo.com (n. osmanović) project management software evaluation by using the measurement of alternatives and ranking according to compromise solution (marcos) method adis puška 1*, ilija stojanović 2, aleksandar maksimović 1, nasiha osmanović 2 1 institute for scientific research and development, brčko district of bosnia and herzegovina 2 al ghurair university dubai, united arab emirates received: 27 february 2020 accepted: 28 march 2020 first online: 07 april 2020 original scientific paper abstract: every organization needs to invest in order for it to grow, and investments are made through projects. thus, investment management is performed by applying project management techniques. different project management software programs are used to manage multiple projects. there is a lot of project management software on the market, and four pieces of the software were selected and analyzed. in this paper, the best management software rated by the beneficiaries of these projects in the united arab emirates are explored. the research required for this study was conducted in the united arab emirates. the marcos method was used to evaluate the program. the results showed that smartsheet had been rated the best by users. this paper provides an overview of how multicriteria analysis methods can be used when ranking project management programs. keywords: project management, software, united arab emirates, marcos method 1. introduction every organization is required to invest. in order to implement their project investments, it is necessary for such organizations to apply the project management techniques that enable the smooth implementation of project investments. a project is a very complex undertaking, especially when organizational constraints and elements used, resources and costs involved, a large number of people working on it, as well as the other elements that further complicate the project, are concerned (puška, 2013). due to project complexity and its importance for any organization, a puška et al./oper. res. eng. sci. theor. appl. 3 (1) (2020) 89-102 90 project requires special it support for its implementation. market demand in this field has led to the development of a broad range of it software solutions supportive of the creation, monitoring and implementation of projects in order to meet set investment goals. the task of project management software is to facilitate the business operations of the company pertaining to project management. these pieces of software are used to plan, monitor and control projects (sajad et al., 2016). however, project management software often does not efficiently facilitate project work and failures in project management occur. the failure status of project management software programs has not changed much today, some projects still being delayed, overbilling or not meeting customer expectations (hassan et al., 2018). all these software solutions are different, so it is necessary to choose the software that best suits the appropriate project in a company. on the market, there are several tools for automated project program management, and these projects are steadily increasing in number. given the ongoing process of change, it is not possible to provide a list of all project management programs (kostalova and tetrevova, 2014). each tool specializes in the different fields of project management, so some programs are used in specific project lifecycles, whereas others are used throughout the project. the purpose of this study is to rank different software solutions intended for the project management implementation based on the evaluations provided by project managers in the united arab emirates (uae). this will provide information on which software features are best-suited for the project manager in the uae. this allows software companies to find out the gaps within their software solutions which need to be addressed so as to make them more user-friendly. for this study, a comparison was made between the four pieces of software that are very much appreciated globally among practitioners, namely smartsheet, asana, microsoft project and basecamp, based on a total of six criteria. since software evaluation was based on multiple criteria, the logical choice is to use multicriteria analysis methods. the contribution of this study reflects in the application of the measurement of alternatives and ranking according to compromise solution (marcos) method in project management software ranking. this multicriteria analysis method is a new method developed by stević et al. (2020) and has only just begun to be put into practice. this method has shown excellent results in the sustainable selection of suppliers (stević et al., 2020) and has shown a certain advantage over other multicriteria analysis methods, which is why this method was chosen. this paper is divided into six sections, excluding the literature. the introductory section sets out the purpose and contribution of this paper. the second section is dedicated to the application of multicriteria methods in project management software ranking, and the theoretical foundations of the marcos method are presented. in the third section, the model is presented and the research methodology is explained. the fourth section is focused on processing the results of the survey. in the fifth section, the results of the sensitivity analysis performed are shown, and the obtained results are confirmed. in the sixth selection, the most important results, shortcomings and recommendations for future research are presented. project management software evaluation by using the measurement of alternatives and ranking according to compromise solution (marcos) method 91 2. the application of multicriteria analysis methods in project management multicriteria analysis methods are concerned with decision-making taking into consideration multiple criteria. these criteria may be different. some criteria are numerical, some are quantitative, some have units of measurement, and so on. certain criteria can solely be obtained through a subjective attitude, whereas other criteria can be measured and determined (erdogan et al., 2019). the basic features of the application of multicriteria analysis are: (rifle, 2013) it often happens that one alternative is better than another in one criterion, while the other is better than the first in the second criterion. it is not always the case that one alternative is better than another in all criteria, so there is no optimal solution in a strict mathematical sense in that case. a solution to the problem implies finding a compromise solution. different methods have been used in different studies on project management. alencar and almeida (2010) used the promethee vi method in the selection of project management members. zavadskas et al. (2012) applied the ahp and aras methods in the evaluation of project managers. chang et al. (2012) applied a fuzzy approach in order to evaluate which criterion is the most important in improving the project team performance by using the dematel, anp, and vikor methods. górecka (2013) applied the electra and promethee methods when choosing the best alternative for road construction. wang et al. (2014) applied a hybrid model by using the dematel, anp and vikor methods in the estimation and improvement of the six sigma projects so as to reduce the performance differences in each criterion. jafarnejad chaghooshi et al. (2016) made a choice of the project manager by using the fuzzy dematel method and the fuzzy vikor method. puška et al. (2017) used the topsis method to examine the impact of subjective judgments on project management decision-making. khoshnava et al. (2018) used the dematel and fuzzy anp methods to improve green project management. erdogan et al. (2019) used the ahp method when designing a sustainable construction in project management. piengang et al. (2019) selected project management programs by using the ahp and vikor methods. based on this brief overview of the research studies carried out so far, it can be seen that different multicriteria analysis methods have been used for project management purposes. in the following section, the marcos method used in the paper in order to rank software intended for project management is explained. 2.1. the measurement of alternatives and ranking according to compromise solution (marcos) method the marcos method is based on defining the relationship between alternatives and reference values (ideal and anti-ideal alternatives) (stević et al., 2020). decisionmaking preferences are defined based on utility functions. a utility function is the position of an alternative in relation to the ideal and anti-ideal solutions (stanković puška et al./oper. res. eng. sci. theor. appl. 3 (1) (2020) 89-102 92 et al., 2020). the best alternative is that closest to the ideal point and farthest from the anti-ideal point. the marcos method is implemented through the following steps (stević, et al, 2020): step 1. the formation of the initial decision matrix. step 2. the formation of an extended initial matrix. this step defines the ideal and anti-ideal solutions. the ideal solution is an alternative with the best alternative for certain criteria, whereas the anti-ideal solution is the worst alternative for certain criteria. this is based on the following equations: min maxij ij j j aai x if j b and x if j c=   (1) max minij ij jj ai x if j b and x if j c=   (2) where b stands for the criteria to be maximized, and c stands for the criteria to be minimized. step 3. the normalization of the extended initial matrix. normalization is performed by using the following equations: ai ij ij x n if j c x =  (3) ij ij ai x n if j b x =  (4) where the elements ijx and aix represent the elements from the initial decision matrix. step 4. the determination of a weighted matrix. aggravation is performed by multiplying normalized matrix values by corresponding weights. step 5. the calculation of the utility degree of the alternatives ki. the utility degree is determined by applying the following equations: i i aai s k s − = (5) i i ai s k s + = (6) where is (i=1,2,..,m) represents the sum of the elements of a difficult matrix: 1 n i ij i s v = =  (7) step 6. the formation of the utility function of the alternatives f(ki). the utility function is calculated by using the following equation: project management software evaluation by using the measurement of alternatives and ranking according to compromise solution (marcos) method 93 ( ) ( ) ( ) ( ) ( ) ; 1 1 1 i i i i i i i k k f k f k f k f k f k + − + − + − + = − − + + (8) where f(k-i) is the utility function versus the anti-ideal solution, while f(k+i) is the utility function versus the ideal solution. the utility functions are calculated by using the following equations: ( ) ii i i k f k k k + − + − = + (9) ( ) ii i i k f k k k − + + − = + (10) step 7. ranking the alternatives. a rank is formed based on the final value of the utility function. it is desirable that the alternative should have the greatest value of the utility function (stević and brković, 2020). 3. model and methodology the methodology used in this research study consists of the following stages: • phase 1. defining the research problem and goal • phase 2. defining the criteria and alternatives, and the creation of the models • phase 3. drafting a survey questionnaire and data collection • phase 4. the selection of multicriteria analysis methods • phase 5. data processing and preparation for analysis • phase 6. the analysis of the collected data • phase 7. conducting a sensitivity analysis the initial stage in this study is focused on the definition of the research problem. the problem of this research is how to choose the software for project management needs that best meets the needs of managers in the uae. based on this problem, the aim of the research is presented, which is highlighted in the introductory part of the paper. the most important project management software ranking criteria are related to human, technical and managerial factors (chatzoglou et al., 2007). many authors have used these software rankings. gharaibeh (2014) used the following criteria in his ranking of project management software: accuracy, affordability, ease of use and ability to handle complexity. ahmad and laplante (2006) used the following criteria: task scheduling, resource management, collaboration, time tracking, puška et al./oper. res. eng. sci. theor. appl. 3 (1) (2020) 89-102 94 estimating, risk assessment, change management, reporting/charts, file attachment, e-mail notification, process/methodology and portfolio management. rouhani and zare ravasan (2016) identified a total of the 48 criteria that may be used to evaluate project management software. due to a large number of different criteria, these criteria were systematized in this paper into six criteria, each including several sub-criteria. in order to rank project management implementation software, it is necessary to, first, define the criteria and determine the alternatives that will be ranked. in this study, those six criteria were defined as follows: • the tasks (c1) criterion evaluated how tasks can be created and assigned with software, what is done from identified activities, and how to set agreed dates in the project, how to prioritize the project, and how to determine the project to-do lists. • the collaboration (c2) criterion assessed how collaborative joint project planning is, how comments can be made, how documents can be uploaded and downloaded. • the projects criterion (c3) evaluated support for individual projects in terms of the project map design, respectively the gantt map, what the calendar view of the planned activities is, what support for the activity display is, how the project is budgeted for individual activities and for the entire project, and how the implementation of certain activities is monitored. • the portfolio management (c4) criterion assessed the coordination of the projects that a particular company owns, how those projects are budgeted, how the what-if scenarios are developed, the workflow for individual activities, how project request management is monitored, how support for cost tracking and return on investment (roi) calculations is implemented, various project projections, and how project risk analysis is performed through software. • the resource management (c5) criterion evaluated the bases used to store the data, how resources could be allocated, how the workload of the project workers is monitored, and the time spent in the project execution. • the platform (c6) criterion evaluated support for the project alerts, mobile access to these programs, user management, roles and access, the integration of the application programming interface, reporting on and the monitoring of these programs, how the program is adjusted to users, how reliable the software is and how fast it runs. after the criteria for the evaluation of the project management software had been defined, the software that will be evaluated was determined. in this study, globally recognized software solutions (i.e. smartsheet (a1), asana (a2), microsoft project (a3) and basecamp (a4)) and their applicability in the uae were evaluated. smartsheet is a cloud-based platform, which allows organizations of all sizes to plan, capture, manage, automate and report on work across the business, empowering you to move faster, drive innovation, and achieve more. asana is a web and mobile application, designed to help teams organize, track and manage their work. asana is the work management platform that teams use to stay focused on the goals, projects project management software evaluation by using the measurement of alternatives and ranking according to compromise solution (marcos) method 95 and daily tasks that grow business. microsoft project is a project management software product developed and sold by microsoft. it is so designed to assist a project manager in developing a schedule, assigning resources to tasks, tracking progress, managing the budget and analyzing workloads. basecamp is focused on the development of a simple interface, in which users can create projects, document progress and manage tasks. it is a web-based piece of software, allowing users to sign in anywhere, anytime, either through a web browser or through applications compatible with many mobile devices. based on the defined criteria and the alternative in the study, the research model was created, which is shown in figure 1. in order to choose the best characteristics of project management software, it is necessary the weight of the criteria should, first, be determined, after which the value of the alternatives should be determined according to all the criteria. based on this, two questionnaires were formed. the first survey questionnaire refers to the determination of the weight of the criteria representing a certain feature of the software indicated as important for practitioners in the uae. in this questionnaire, the experts were asked to anonymously rate the importance of individual criteria, which ranged from 1 to 5, the questionnaire resulting in the experts’ ratings (table 1). for the second questionnaire, the secondary data drawn from the g2.com user community were used. this web portal monitors how different software solutions are accepted by users. on the platform, they ask users daily to evaluate the software they use. these data represent the evaluations of different project management software solutions from global users and practitioners. they rated the selected programs with the grades ranging from 1 to 10. based on their grades, a mean value was formed for each criterion for the individual alternatives (table 2). in this way, the data needed to conduct the research were collected. figure 1. the project management software selection model once the data were collected, it was necessary to select a multicriteria analysis method. since the focus of this research is on the marcos method, the weights of the criteria were calculated by applying a simple sum of ratings from the experts and converting those ratings into the percentage that, in fact, is the weight of each criterion. the marcos method was selected for ranking the alternatives. after the data had been collected, they were processed and prepared for the research. based on the data collected, the initial decision-making tables were the selection of programs for the project management tasks (c1) collaboration (c2) projects (c3) portfolio management (c4) resource management (c5) platform (c6) microsoft project (a3) smartsheet (a1) asana (a2) basecamp (a4) puška et al./oper. res. eng. sci. theor. appl. 3 (1) (2020) 89-102 96 formed; the first table was for the determination of the value of the criteria weights (table 1), and the second was for the determination of the ranking of the alternatives (table 2). once the decision tables were formed, the defined analysis were carried out and the research results were obtained. in order to confirm the results obtained, a sensitivity analysis was also conducted. the sensitivity analysis was aimed at examining the dependence of the results on the change in the weights of the criteria. the details on stages 6 and 7 are given in chapter 4. 4. results this chapter provides a more detailed elaboration on the manner in which the research results were generated. first, the weights of the criteria used in the decision model were calculated and presented. the ratings given by the experts on an anonymous basis are presented in table 1. they determined the rating based on the subjective assessment of the importance of certain criteria, where the score 1 represents a value of little or no importance, whereas the score 5 represents a value of a very important criterion. after the criteria had been collected by the experts, all the individual criteria were summed up. based on the total value of the criteria, a percentage of the importance of the individual criteria expressed in decimals was formed. these values represent the weight of each criterion. table 1. the experts’ evaluation of the importance of the criteria c1 c2 c3 c4 c5 c6 expert 1 5 4 5 5 4 2 expert 2 5 4 5 4 3 2 expert 3 4 4 5 5 4 4 expert 4 5 4 5 5 4 3 expert 5 5 4 5 5 4 3 sum 24 20 25 24 19 14 weight 0.190 0.159 0.198 0.190 0.151 0.111 based on the results obtained, it can be observed that the criterion c3 – projects (w = 0.198) has the highest importance according to the experts, whereas the criterion c6 – platform (w = 0.111) has the lowest importance. based on all the other values, it can be concluded that the criteria c1 and c4 were assigned high values, whereas the criteria c2 and c5 were assigned mean values. this means that the criteria c1, c3 and c4 are the most important for the evaluation of individual software, the criteria c2 and c5 are of medium importance, while the criterion c6 is the least important. once the weights were established for the criteria, it was necessary to determine the rankings for the selected alternatives. based on the data collected, an initial decision matrix for the observed alternatives was formed (table 2). forming an initial decision matrix is the first step in all multicriteria analysis methods. in order to determine the ranking of the alternatives, it was necessary to normalize the data so as to make them be uniform. simple linear normalization (equation 3) was applied to the marcos method. it was necessary to determine the maximum value of project management software evaluation by using the measurement of alternatives and ranking according to compromise solution (marcos) method 97 the criteria, since it is desirable for all criteria that the values of the alternatives should be maximized. the normalization of the initial decision matrix is step 3 of the marcos method. table 2. the initial decision matrix c1 c2 c3 c4 c5 c6 smartsheet 8.675 8.433 8.000 7.800 8.025 8.043 asana 8.825 8.600 7.420 7.463 7.825 8.229 microsoft project 8.325 7.600 8.040 7.700 7.925 7.600 basecamp 8.525 8.667 7.180 7.375 7.750 8.071 max 8.825 8.667 8.040 7.800 8.025 8.229 the results of the normalized decision matrix (table 3) show that the alternatives a1 and a2 have two maximum values of the criteria each, while the alternatives a3 and a4 have one maximum value of the criteria. based on this, it was necessary that a compromise solution should be made, since there was no optimal solution, speaking in a strictly mathematical sense. in these cases, multicriteria analysis methods were applied, because one alternative had all the best indicators and there was no need to rank them, because the best alternative was known. table 3. the normalized decision matrix c1 c2 c3 c4 c5 c6 smartsheet 0.983 0.973 0.995 1.000 1.000 0.977 asana 1.000 0.992 0.923 0.957 0.975 1.000 microsoft project 0.943 0.877 1.000 0.987 0.988 0.924 basecamp 0.966 1.000 0.893 0.946 0.966 0.981 weight 0.190 0.159 0.198 0.190 0.151 0.111 after the normalization of the data in the decision matrix, these values needed to be aggravated by the weighting coefficients. this was the fourth step in the marcos method. the fifth step in the marcos method was to calculate the utility degree. in order to perform this step, it was first necessary to determine the ideal and anti-ideal solutions. the ideal solution represents the maximum value of a certain criterion, whereas anti-ideal values represent the minimum value of a specific criterion. then, the values for the individual alternatives and for the ideal and anti-ideal solutions were summed up and the utility degrees were calculated (equations 5 and 6). table 4. the aggravated normalized decision matrix c1 c2 c3 c4 c5 c6 sum smartsheet 0.187 0.154 0.197 0.190 0.151 0.109 0.989 asana 0.190 0.158 0.183 0.182 0.147 0.111 0.971 microsoft project 0.180 0.139 0.198 0.188 0.149 0.103 0.957 basecamp 0.184 0.159 0.177 0.180 0.146 0.109 0.955 ideal 0.190 0.159 0.198 0.190 0.151 0.111 1.000 anti-ideal 0.180 0.139 0.177 0.180 0.146 0.103 0.924 puška et al./oper. res. eng. sci. theor. appl. 3 (1) (2020) 89-102 98 the sixth step of the marcos method was to form the utility function of the alternatives. the utility function was calculated by using equation 8. in order to calculate the utility function of the alternatives, it was necessary to calculate the utility function in relation to the ideal and anti-ideal solutions. these functions are the same for all the values and their values: f (ki-) = 0.520 and f (ki +) = 0.480. the inclusion of these values generated the final value for the alternatives (table 5) and determined the ranking of the alternatives. table 5. the ranking of the alternatives. kiki+ f(ki) rank smartsheet 1.070 0.989 0.685 1 asana 1.051 0.971 0.673 2 microsoft project 1.035 0.957 0.663 3 basecamp 1.033 0.955 0.661 4 the survey results show that smartsheet received the highest ratings, while the basecamp ranked the worst among the selected pieces of software. according to these results, there was a very small difference between the final values for the alternatives based on the marcos method calculation. microsoft project received slightly over 0.002 more value than basecamp, while asana was better than microsoft project by 0.01, and smartsheet was better than asana by 0.012. based on all the foregoing, the difference between the first-ranked and the last-ranked software is 0.024, which leads to the conclusion that neither software deviates from the others according to the estimates made by the experts through their anonymous responses. the original normalized decision matrix also shows that all the selected pieces of software have the best grades for certain criteria. in order to confirm these results, a sensitivity analysis was carried out. 5. sensitivity analysis a sensitivity analysis was performed in such a manner that the weights of the criteria varied, and it was observed that the change made in the weights influenced the ranking of the alternatives (puška et al., 2018). seven scenarios were used for this purpose. in the first six scenarios, an individual criterion was assumed to be five times as significant as the other criteria, and it was assigned a weight of 0.5, while the other criteria were assigned a weight of 0.1 (table 6). the seventh scenario assumed that the validity of all the criteria was the same, and the assigned weight was 0.167. the aim of the sensitivity analysis was to avoid the subjective evaluation of the criteria by the experts. using these criteria, the results of the study were tested so as to understand whether they were sensitive to changing weights. this enabled us to confirm or deny the results. in addition, this analysis shows the advantages and disadvantages of different software solutions according to certain criteria. project management software evaluation by using the measurement of alternatives and ranking according to compromise solution (marcos) method 99 table 6. the scenarios for sensitivity analysis c1 c2 c3 c4 c5 c6 scenario 1 0.5 0.1 0.1 0.1 0.1 0.1 scenario 2 0.1 0.5 0.1 0.1 0.1 0.1 scenario 3 0.1 0.1 0.5 0.1 0.1 0.1 scenario 4 0.1 0.1 0.1 0.5 0.1 0.1 scenario 5 0.1 0.1 0.1 0.1 0.5 0.1 scenario 6 0.1 0.1 0.1 0.1 0.1 0.5 scenario 7 0.167 0.167 0.167 0.167 0.167 0.167 the research study provided an opportunity to explore the opinion of the users of these programs. they provided the grades from 1 to 10, and this interval was the basis for the evaluation of these software solutions. these ratings were, then, ranked by using the defined scenarios. the results of the survey show that smartsheet achieved the best results in six scenarios, whereas only in scenario 6 it ranked the second. this shows that asana has better c6 – platform criterion than smartsheet, according to the users’ ratings, so it did not rank the first in this scenario. the same situation is with asana, which was the third in scenario s3, in which microsoft project achieved better results than this software solution. microsoft project achieved the worst results in four scenarios, whereas the basecamp achieved the worst results in three scenarios. based on the results of the sensitivity analysis, a conclusion can be drawn that smartsheet achieved the best results in the user-made evaluation, whereas microsoft project and basecamp showed the worst results. table 7. the ranking of the project management software by scenarios rank (s1) rank (s2) rank (s3) rank (s4) rank (s5) rank (s6) rank (s7) smartsheet 1 1 1 1 1 2 1 asana 2 2 3 2 2 1 2 microsoft project 4 4 2 3 3 4 4 basecamp 3 3 4 4 4 3 3 6. conclusion project management is very important for any organization. an organization may deal with multiple and very complex projects, so they need to be managed appropriately. in such cases, project management is performed with the support of it software. there are many software solutions on the market. in this paper, four pieces of software were selected. the selection was made through the evaluation provided by the g2.com user community for different software features and whether these features were relevant in the united arab emirates or not was evaluated. these findings led to the results implicative of user preferences in the uae for using a certain software solution. only an overview of whether the software features for the selected software solutions were relevant for users in the uae or not was presented. the weights of the criteria were determined in collaboration with the experts. using the marcos method, the selected project management software was ranked. the puška et al./oper. res. eng. sci. theor. appl. 3 (1) (2020) 89-102 100 research results show that the smartsheet features are the most relevant in the experts’ opinions. still, this does not reflect the fact that this solution is the most used solution, but rather that its futures are most apricated by the experts. the disadvantage of this research study is that only a limited number of software solutions were included in the evaluation. another disadvantage of this research study is the use of the six criteria according to which the pieces of software were evaluated. this number of the criteria were used due to the availability of the secondary data provided by the g2.com user community about different software solutions in project management. however, the respondents were instructed to perceive the sub-criteria through the basic criteria and provide a cumulative rating for the software they are using. in this manner, more criteria were considered than the stated. future research may be focused on presenting the ratings of the subcriteria by going deeper into the main criteria. it is also necessary to conduct a research study on the importance that criteria have for users in order to enable them to obtain the necessary information about the criteria which they should pay attention to when ranking different software options. the purpose of each evaluation is to see how a particular solution suits the user, so it is necessary to obtain all the necessary information from users. this study has presented a new approach to how to evaluate project management software by using the newly-introduced macros method. in future research, this model and this methodology should be applied, because they are very simple and can be applied to other decision problems as well. references ahmad, n., & laplante, p. 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(2014). applying a hybrid mcdm model for six sigma project selection. mathematical problems in engineering, 2014, 1-13. doi:10.1155/2014/730934 zavadskas, e. k., vainiūnas, p., turskis, z., tamošaitienė, j. (2012). multiple criteria decision support system for assessment of projects managers in construction. international journal of information technology & decision making, 11(02), 501– 520. doi:10.1142/s0219622012400135 © 2020 by the authors. submitted for possible open access publication under the terms and conditions of the creative commons attribution (cc by) license (http://creativecommons.org/licenses/by/4.0/). project management software evaluation by using the measurement of alternatives and ranking according to compromise solution (marcos) method adis puška 1*, ilija stojanović 2, aleksandar maksimović 1, nasiha osmanović 2 1. introduction 2. the application of multicriteria analysis methods in project management 2.1. the measurement of alternatives and ranking according to compromise solution (marcos) method 3. model and methodology 4. results 5. sensitivity analysis 6. conclusion references operational research in engineering sciences: theory and applications vol. 3, issue 1, 2020, pp. 41-56 issn: 2620-1607 eissn: 2620-1747 doi: https:// doi: 10.31181/oresta2002041s * corresponding author. marko.subotic@sf.ues.rs.ba (m. subotić), biljana.jeremic47@gmail.com (b. stević), bojana.ristic@sf.ues.rs.ba (b. ristić), sanja.simic@sf.ues.rs.ba (s. simić) the selection of a location for potential roundabout construction – a case study of doboj marko subotić*, biljana stević, bojana ristić, sanja simić university of east sarajevo, faculty of transport and traffic engineering doboj, bosnia and herzegovina received: 25 february 2020 accepted: 13 march 2020 first online: 17 march 2020 original scientific paper abstract: the increase in the number of traffic accidents, as well as the development of modern traffic signaling, have influenced realistic traffic solutions at intersections to be aimed at constructing roundabouts, which has increased the capacity and safety of traffic participants. this paper has several goals that refer to the development of methodology for evaluating potential locations for roundabout construction. the subject of this research is based on the development of a model for the construction of a roundabout in doboj using the integrated bwm (best worst method) and mabac (multi-attributive border approximation area comparison) approach. taking into account the fact that doboj is a transport hub where many roads intersect and that it is a very important transit point, the necessity of constructing roundabouts is justified. therefore, as part of the paper, an adequate methodology has been developed for an optimal selection of a potential location for the construction of a roundabout. key words: roundabout, location, sustainable traffic, bwm, mabac, 1. introduction in european countries, experts believe that roundabouts reduce the number of accidents and cause capacity increase, making their usage attractive since the 1980s. in the netherlands, france, norway, denmark and other european countries, the number of roundabouts has been increasing progressively. in the netherlands (vasilyeva and sazonova, 2017), turbo-roundabouts are being introduced with 20 to 30% higher speeds of movement in them and with greater safety. at intersections regulated by light signals, the problem occurs since pedestrian and vehicle flows intersect, which adversely affects pedestrians as a "vulnerable" category. this case is especially dominant at russian signalized intersections, where drivers often drive under the influence of alcohol or pass the crossroad on red light. (vasilyeva and mailto:marko.subotic@sf.ues.rs.ba mailto:biljana.jeremic47@gmail.com mailto:bojana.ristic@sf.ues.rs.ba mailto:sanja.simic@sf.ues.rs.ba subotić et al./oper. res. eng. sci. theor. appl. 3(1) (2020) 41-56 42 sazonova, 2017) according to the research (møller and hels, 2007), the performance of roundabouts was considered by the criteria of road properties, capacity and location. their research consists of observing two types of roundabouts, with and without pedestrian crossings and cycle paths. the trend of constructing roundabouts has also shifted to smaller urban areas, so when looking at the territory of the republic of srpska it is possible to see a constant increase of roundabouts in urban areas. urban areas bijeljina, derventa, trebinje, prnjavor and others are an example of that. to solve traffic congestion and increase safety on main roads, roundabouts are being constructed extensively. when it comes to the territory of the city of doboj and the main roads passing through the city, the number of roundabouts is zero. taking into account the fact that doboj is a transport hub where many roads intersect and that it is a very important transit point, the necessity of constructing roundabouts is justified. the subject of this paper is to define potential locations for the construction of roundabouts in the area of the city of doboj. the main objective of the paper is to identify priority intersections on the entire street network of the city of doboj. a roundabout falls into the category of at-grade intersections, where all entering streams flow in and exiting streams flow out of usually one-way traffic flow around the central island of the intersection. based on this, it has been formed a hypothetical assumption which implies that the introduction of a roundabout on the current street network is functionally dependent on traffic conditions and their effects on the current traffic infrastructure in the urban area of the city of doboj. in addition, the location of a roundabout in doboj depends on the potential urban-planning and technical conditions for the implementation of the intersection, and any potential solution can influence the change in modernity of the traffic infrastructure. after the introduction, the second section presents an overview of the situation in the field of interest with a brief review of multi-criteria decision-making methods. the third section provides the algorithms of the methods used in this paper: mabac, best worst. the fourth section is a case study of selecting a location for the construction of a roundabout in the city of doboj using the bwm-mabac model. the paper ends with conclusions presenting contributions of the paper and directions for future research. 2. brief literature review increasing capacity in road engineering according to (li et al., 2014) has become an important way of solving traffic problems, and roundabouts, in addition to a large number of benefits, also cause the increase in traffic capacity (prateli, 2006), and higher traffic flow rate (retting et al. 2006). a properly constructed roundabout, according to (prateli et al., 2018), can have a significant impact on increasing traffic safety, which is also confirmed by (antov et al., 2009), who find that the construction of roundabouts is an efficient measure to increase safety. depending on the type of location problem, different methods are used as shown above. in the last decade, multi-criteria decision-making (mcdm) methods have been applied widely in addressing location problems (chauhan and singh, 2016; nie et al., 2017; samanlioglu and ayag, 2017; zhao et al., 2018; nazari et al., 2018). zhao et al. (2018) use a combination of ahp and topsis methods to develop a metro-integrated logistics system. using the topsis method, they performed a significance evaluation the selection of a location for potential roundabout construction – a case study of doboj 43 for each metro station. nazari et al. (2018) conducted a study to select a suitable site for photovoltaic installation in iran. 3. methods psychology provides an explanation why individuals frequently make irrational decisions, while economics proposes normative theories (morselli, 2015). according to (triantaphyllou and mann, 1995), multi-criteria decision-making plays an important role in real-life problems since there are many everyday decisions to be made that involve a large number of criteria, whereas, according to (chen et al., 2015), multi-criteria decision-making is an efficient, systematic and quantitative method of solving vital real-life problems in the presence of a large number of alternatives and several (opposing) criteria. the best worst (rezai, 2015) method was used to determine the weight values of criteria, while the mabac method was used to evaluate the intersection locations for the construction of a roundabout. in addition, to determine model validity through a sensitivity analysis, four other multi-criteria decision-making methods were used: aras (zavadskas and turksis, 2010) waspas (zavadskas and turksis, 2012), saw (macrimon, 1968), and edas (ghoarabaee et al., 2016). 3.1. best – worst method the following section presents the algorithm of the bw method based on interval rough numbers. determining the weight coefficients of evaluation criteria using the irn-bw method includes the following steps: step 1. determining a set of evaluation criteria. in this step, we consider a set of evaluation criteria c = {c1, c2, .... cn}, where n represents the total number of criteria. step 2. determining the most significant (most influential) and worst (least influential) criterion. if there are two or more criteria that are best, i.e. worst, it is arbitrary to choose the best, i.e. the worst criterion. step 3. determining the preferences of the most significant (most influential) criterion in a set c over all other criteria in a defined set. the scale of numbers in the interval of 1-9 is used to determine the preferences. as a result, the best-to-others (bo) vector is obtained: 𝐴𝐵 = (𝑎𝐵1, 𝑎𝐵2,…..,𝑎𝐵𝑛 ) (1) where 𝑎𝐵𝑗 represents the influence (preference) of the best criterion b over the criterion j, while 𝑎𝐵𝐵 = 1 . step 4. determining the preferences of all criteria in a set c over the worst (least influential) criterion in a defined set. to determine the preferences, as in step 3, a scale of numbers in the interval of 1-9 is used. the result is obtaining the others-to-worst (ow) vector: 𝐴𝑊 = (𝑎1𝑊 , 𝑎2𝑊 , . . . , 𝑎𝑛𝑊 ) (2) where bj a represents the influence (preference) of the criterion j over the worst criterion w, while 𝑎𝐵𝐵 = 1. subotić et al./oper. res. eng. sci. theor. appl. 3(1) (2020) 41-56 44 step 5. calculation of optimal values of the weight coefficients of the criteria in a set c, (𝑤1 ∗, 𝑤2 ∗, … . , 𝑤𝑛 ∗ ). the aim is to determine the optimal values of the evaluation criteria, which should satisfy the condition that the maximum absolute gaps (3) w b a bjw j and w j a jwww − − (3) for all values of j be minimized. in order to satisfy these conditions, a solution that satisfies the maximum gaps by absolute value b bj j w a w − and j jw w w a w − should be minimized for all values of j. this condition can be shown through the following minmax model: 1 . . 1 0 min max , n j j j s t w w j ww jb a a bj jwj w wwj =           =   − −  (4) the presented model (4) is equivalent to the following model: 1 1 0 min . . , , n j j j j w w j s t w b a j bjw j w j a jwww    =  =   −   −   (5) by solving the system of equations and inequations of model (5), we obtain the optimal values of the weight coefficients of the evaluation criteria (𝑤1 ∗, 𝑤2 ∗, . . . , 𝑤𝑛 ∗ ) and 𝜉∗ . the selection of a location for potential roundabout construction – a case study of doboj 45 definition 1. the criterion comparison is consistent when the condition that 𝑎𝐵𝑗 × 𝑎𝑗𝑊 = 𝑎𝐵𝑊 is fulfilled for all criteria j, where 𝑎𝐵𝑗 , 𝑎𝑗𝑊 and 𝑎𝐵𝑊 respectively represent the influence (preference) of the best criterion over the criterion j, the influence (preference) of the criterion j over the worst criterion, and preference of the best criterion over the worst criterion. however, when comparing criteria, it may be that for some pairs of criteria j, the comparisons are not fully consistent. therefore, the following section defines a consistency ratio (cr) that provides information on the consistency of the bo and ow comparisons. to show the determination of cr, we start from the calculation of the minimum consistency in the comparison of criteria, which is explained in the following section. as noted above, pair-wise comparisons of criteria are made on the basis of the scale 𝑎𝑖𝑗 ∈ {1,2, . . . , 𝑎𝐵𝑊 }, where the highest value from scale 𝑎𝐵𝑊 is a value of 9 or any other maximum value of a scale defined by the decision-maker. the consistency of the comparison decreases when 𝑎𝐵𝑗 × 𝑎𝑗𝑊 is lower or higher than 𝑎𝐵𝑊 , i.e. when 𝑎𝐵𝑗 × 𝑎𝑗𝑊 ≠ 𝑎𝐵𝑊. it is clear that the greatest inequality occurs when 𝑎𝐵𝑗 and 𝑎𝑗𝑊 have maximum values that are equal to 𝑎𝐵𝑊 , which further affects the values of 𝜉. based on the relations defined above, we can conclude that there is a relation as follows: (𝑤𝐵 𝑤𝑗⁄ ) × (𝑤𝑗 𝑤𝑊⁄ ) = 𝑤𝐵 𝑤𝑊⁄ (6) since the greatest inequality occurs when 𝑎𝐵𝑗 and 𝑎𝑗𝑊 have maximum values (𝑎𝐵𝑊 ), then the value of 𝜉 needs to be subtracted from 𝑎𝐵𝑗 and 𝑎𝑗𝑊 and added to 𝑎𝐵𝑊 . thus, we obtain expression (7): (𝑎𝐵𝑗 − 𝜉) × (𝑎𝑗𝑊 − 𝜉) = (𝑎𝐵𝑊 + 𝜉) (7) since the minimum consistency implies the equality that 𝑎𝐵𝑗 = 𝑎𝑗𝑊 = 𝑎𝐵𝑊, expression (7) is presented as follows: ( ) ( ) ( ) ( ) ( )2 2 1 2 0a a a a a abw bw bw bw bw bw    −  − = +  − − + − = (8) for different values of 𝑎𝐵𝑊 ∈ {1,2, . . . ,9} based on expression (8), we obtain maximum values of  (max ξ). table 1 presents the maximum values of ξ (consistency index) for different values of 𝑎𝐵𝑊 ∈ {1,2, . . . ,9}. table 1. consistency index (ci) values bw a 1 2 3 4 5 6 7 8 9 ci ( max ) 0.00 0.44 1.00 1.63 2.30 3.00 3.73 4.47 5.23 based on ci (table 2), we obtain a consistency ratio (cr) 𝐶𝑅 = 𝜉∗ 𝐶𝐼 (9) cr takes values from the interval 0,1 , where values closer to zero show high consistency, while cr values closer to one show low consistency. subotić et al./oper. res. eng. sci. theor. appl. 3(1) (2020) 41-56 46 the solution space of model (5) includes all positive values of 𝑤𝑗 (𝑗 = 1,2, . . . 𝑛) that satisfy two conditions: (1) the sum of all weight coefficients should be equal to one and (2 ) the ratio of the weighted coefficients of the criteria which are compared should be at most equal to 𝜉. 3.2. mabac method the mabac (multi-attributive border approximation area comparison) method is a recent method. the mabac method was developed by dragan pamučar at the center for defense logistics research at the university of defense in belgrade and was first introduced to the scientific community in 2015 (pamučar and ćirović, 2015). so far, it has found wide application and modification in solving various problems in the field of multi-criteria decision-making. the basis of the mabac method is seen in the definition of the distance of the criterion function of each alternative from the border approximation area. the following section shows the process of implementing the mabac method, consisting of six steps: step 1. formation of the initial decision matrix (x). ... 1 2 ... 11 12 11 21 22 22 ... ... ... ...... ... 1 2 c c cn x x xa n x x xa nx x x xa mnm m m       =         (10) step 2. normalization of the elements from the initial matrix (x). ... 1 2 ... 11 12 11 21 22 22 ... ... ... ...... ... 1 2 c c cn t t ta n t t ta nn t t ta mnm m m       =         (11) the elements of the normalized matrix (n) are determined by applying the following expressions: for benefit-type criteria (higher criterion value is preferable) x x ij i t ij x x i i − − = + − − (12) for cost-type criteria (lower criterion value is preferable) x x ij i t ij x x i i + − = − + − (13) the selection of a location for potential roundabout construction – a case study of doboj 47 where 𝑥𝑖𝑗 , 𝑥𝑖 +i 𝑥𝑖 − are the elements of the initial decision matrix (x), where 𝑥𝑖 + and 𝑥𝑖 − are defined as follows: 𝑥𝑖 + = max (𝑥1, 𝑥2, . . . , 𝑥𝑚 ) and represents the maximum values of the observed criterion by alternatives. step 3. calculation of the elements from the weighted matrix (v). 𝑣𝑖𝑗 = 𝑤𝑖 ⋅ 𝑡𝑖𝑗 + 𝑤𝑖 (14) where 𝑡𝑖𝑗 represents the elements of the normalized matrix (n), 𝑤𝑖 represents the weight coefficients of criteria. by applying expression (14), we obtain the weighted matrix v. 11 12 1 21 22 2 1 2 ... 1 11 1 2 12 2 1 ... 1 21 1 2 22 2 2 ... ... ... ... ... 1 1 1 2 2 2 ... ... ... ... ... ... n n m m mn w t w w t w w t wn nn w t w w t w w t wn nn w t w w t w w t wn mn nm m v v v v v v v v v v  +  +  +  +  +  +  +  +  +         = =            where n represents the total number of criteria, m represents the total number of alternatives. step 4. determining the border approximation area matrix (g). 1/ 1 m m g v i ij j   =    =  (15) where 𝑣𝑖𝑗 represents the elements of the weighted matrix (v), m represents the total number of alternatives. after calculating the values of 𝑔𝑖 by criteria, a border approximation area matrix g (16) of the form 𝑛 𝑥 1 is created (n represents the total number of criteria by which the offered alternatives are selected). ... 1 2 ... 1 2 c c cn g g g gn  =   (16) step 5. calculation of matrix elements of alternative distance from the border approximation area (q). ... 11 12 1 21 22 2 ... ... ... ... ... 1 2 q q q n q q q nq q q qmnm m       =         (17) the distance of alternatives from the border approximation area (𝑞𝑖𝑗 ) is determined as the difference of the weighted matrix elements (v) and the values of the border approximation areas (g) subotić et al./oper. res. eng. sci. theor. appl. 3(1) (2020) 41-56 48 ... 11 12 1 21 22 2 ... 1 2... ... ... ... ... 1 2 v v v n v v v nq v g g g gn v v vmnm m        = − = −          (18) ... ... 11 1 12 2 1 11 12 1 ... 21 1 22 2 2 21 22 2 ... ... ... ... ... ... ... ... ... ... 1 1 2 2 1 2 v g v g v g q q qnn n v g v g v g q q qnn nq v g v g v g q q qmn n mnm m m m − − −        − − −    = =           − − −     (19) where 𝑔𝑖 represents the border approximation area for the criterion 𝐶𝑖 , 𝑣𝑖𝑗 represents the elements of the weighted matrix (v), n represents the number of criteria, m represents the number of alternatives. the alternative 𝐴𝑖 can belong to the border approximation area (g), the upper approximation area (𝐺 +) or the lower approximation area (𝐺 −), i.e. 𝐴𝑖 ∈ {𝐺 ∨ 𝐺 + ∨ 𝐺 −} the upper approximation area (𝐺 +) represents the area where the ideal alternative (𝐴+) is located, while the lower approximation area (𝐺 −) represents the area where the anti-ideal alternative (𝐴−) is located. the affiliation of the alternative 𝐴𝑖 to the approximation area (𝐺, 𝐺 + or 𝐺 −) is determined on the basis of expression (20) g if q g ij i a g if q g i ij i g if q g ij i +     =  −   (20) in order for the alternative 𝐴𝑖 to be selected as the best alternative of the set, it should belong to the upper approximation area (𝐺+) by as many criteria as possible. for instance, if the alternative belongs to the upper approximation area by five criteria (out of a total of six criteria), and to the lower approximation area (𝐺 −) by one criterion, it means that the alternative is close or equal to the ideal alternative by five criteria, while it is close or equal to the anti-ideal alternative by one criterion. if the value of 𝑞𝑖𝑗 > 0, i.e. 𝑞𝑖𝑗 ∈ 𝐺 +, then the alternative 𝐴𝑖 is close or equal to the ideal alternative. the value of 𝑞𝑖𝑗 < 0, i.e. 𝑞𝑖𝑗 ∈ 𝐺 −, indicates that the alternative 𝐴𝑖 is close or equal to the anti-ideal alternative. step 6. ranking alternatives. the calculation of the values of criterion functions by alternatives (21) is obtained as the sum of the distances of alternatives from the border approximation area (𝑞𝑖). by summing the elements of the matrix 𝑄 by rows, we obtain the final values of the criterion functions of alternatives , 1, 2,..., , 1, 2,..., 1 n s q j n i m i ij j = = = = (21) the selection of a location for potential roundabout construction – a case study of doboj 49 where n represents the number of criteria, m represents the number of alternatives. 4. a case study in the city of doboj – description of the situation in the city of doboj the selection of the location for the construction of a roundabout consists of several stages that are described in detail below. the first stage implies the formation of a multi-criteria model based on the realistic needs for traffic infrastructure in the city of doboj. the second stage implies the collection of data on the basis of measurements of traffic indicators and other sources, such as the ministry of interior, where data on the number of traffic accidents at the locations for roundabout construction were obtained. the third stage refers to the expert evaluation of the significance of criteria as the first step and the determination of the weights of the criteria using the bwm method as the second step. the fourth stage is the evaluation of the locations based on the mabac method. this paper will analyze six potential locations for the introduction of a roundabout intersection in the city of doboj, where no roundabout has been constructed so far. as already mentioned, the city of doboj, by its geographical position, is located at the crossroads of the most important main and regional roads in the republic of srpska and bosnia and herzegovina. this research involved traffic experts. they are on average 50 years old and there were 62 respondents. the 105 main road (m1) passes in the north-south direction and, in the east, it is connected to the 110 main road from (m1) the direction of tuzla (federation of bih). the most frequent part of the 105 main road (m1) is on the šešlije doboj karuše federation of bih route. the intersections of city streets with access to the main roads are not well resolved in the city, which significantly hinders a normal flow of traffic, especially at peak hours. taking into account the transport significance of the city of doboj, as well as the fact that nearby towns, such as modriča, derventa, teslić and many other smaller towns and municipalities already have roundabouts, six potential intersections have been selected for the construction of a roundabout in the city, as well as on the 105 main road (m1). the following table gives an overview of the potential coordinates for the roundabout. table 2. coordinates for the roundabout location a1 a2 a3 a4 a5 a6 coordinates 44.743443 18.095140 44.735776 18.096611 44.733405 18.096111 44.726579 18.091869 44.713155 18.080535 44.730244 18.081451 4.1. forming a multi-criteria model six locations, out of which one is located in the very center of the city, four locations representing the connection between the streets for the entrance into/exit from the city and the first-order main road, and one location where the first-order main roads intersect, are evaluated on the basis of a total of eight criteria presented in table 3. subotić et al./oper. res. eng. sci. theor. appl. 3(1) (2020) 41-56 50 table 3. criteria in a multi-criteria model and their description no. criterion criterion description 1 flow of vehicles the number of vehicles passing through the observed road intersection in a unit of time in both directions 2 flow of pedestrians the number of pedestrians crossing the observed intersection at the point for pedestrian movement (pedestrian crossing, zebra, etc.) at a given time interval 3 traffic safety indicator the number of traffic accidents on the observed section of road 4 cost of construction and exploitation cost estimation (construction, exploitation and maintenance) 5 type of intersection three-way or four-way intersections 6 average vehicle intensity per access arm the limit intensity is the intensity at the entry arm into the intersection of 360 pa/h 7 functional criterion of spatial fitting what is the primary role of the intersection observed? this section analyzes what type of intersection is the most acceptable due to its role in traffic 8 public opinion it implies a survey of local people who have chosen one of the offered locations as a priority for the construction of a roundabout. the criteria were selected according to the current needs of the city of doboj and relevant literature that considered similar studies (day et al., 2013; benekohal and atluri, 2009; deluka-tibljaš et al., 2010; steiner et al., 2014). in all the aforementioned studies, the criteria are organized into several categories: traffic criteria, safety criteria, functional criteria, performance, cost, etc. the criteria used in this study are the most commonly used criteria in croatia: functional criterion, spatially-urbanistic criterion, traffic flow criterion, design and technical criterion, traffic safety criterion, capacity criterion, environmental criterion, economic criterion; in serbia and slovenia: functional criterion, capacity criterion, spatial criterion, design and technical criterion, traffic safety criterion and economic criterion (kozić et al., 2016). the results provided by the study (retting et al., 2007) indicate that public support increases with time since traffic participants become more familiar and comfortable with this form of traffic control. considering this, the use of the last criterion in this research has its justification. 4.2. evaluating and ranking the locations for roundabout construction using the mabac method flow measurement was performed at the sampling level in the period septembernovember 2017. the data collected for each location based on established criteria are presented in table 4. the selection of a location for potential roundabout construction – a case study of doboj 51 table 4. values of alternatives according to criteria c1 c2 c3 c4 c5 c6 c7 c8 a1 1256 8 2 3 3 419 7 85 a2 2194 4 2 9 3 731 5 89 a3 1037 5 4 7 3 346 3 45 a4 2878 32 3 7 4 720 5 8 a5 1052 2 4 5 4 263 5 27 a6 4197 124 1 3 4 1050 7 74 table 4 shows the values for all the locations by established criteria. it can be noticed that the highest intensity of traffic flows of vehicles and pedestrians belongs to the sixth location with 4197 vehicles and 124 pedestrians in one hour. locations 4 and 2 have slightly less intensity regarding vehicle flows, while the intensity of pedestrians is 32 for the fourth, and only four for the second location. the remaining locations have double less intensity than the two previously mentioned locations, and almost four times less than the sixth location. if the sixth and fourth locations are excluded, the flows of pedestrians are very low. the reason is that the sixth location is in the city center, and the fourth location represents the connection between entering the city and the railway station. regarding the number of traffic accidents, the largest number of accidents occurred at locations 3 and 5, four accidents per each, while the lowest number of accidents occurred at the sixth location. the average vehicle intensity per an arm (table 4) is the largest at the sixth location, 1050, while for the second and fourth location it is almost identical, 731 and 720, respectively. the minimum intensity per an arm is at the fifth location since this location has four arms and an additional arm that is not presented in the paper as an arm, as it is a side road with no frequent traffic. based on the public opinion survey for potential locations, the largest number of citizens have characterized the first two locations as a priority for the construction of a roundabout, and as the third one, they designated the sixth location. after obtaining the matrix q, it is necessary to sum the elements by rows and rank them. table 5 shows the final values of roundabout locations using the mabac method. table 5. final values and ranking the alternatives values rank a1 -0.042 5 a2 0.010 4 a3 -0.043 6 a4 0.074 3 a5 0.132 2 a6 0.167 1 5. sensitivity analysis in order to validate the model and test the results obtained by applying the mabac method, a sensitivity analysis consisting of the application of the aras (table 6), edas (table 7), saw (table 8), and waspas (table 9) methods is performed in the paper. subotić et al./oper. res. eng. sci. theor. appl. 3(1) (2020) 41-56 52 5.1. ranking the locations using the aras method compared to mabac and other methods used in this paper, the initial matrix for the aras method is slightly different. it is reflected through the formation of an additional row that represents the optimal alternative. this alternative consists of the best values depending on the type of criteria. if it is a criterion belonging to the benefit group, the maximum value is taken, while for the criteria belonging to the cost group, the minimum value is taken. after forming the optimal alternative, the initial matrix is as shown in table 6. table 6. ranking the locations using the aras method si ki rank a1 0.111 0.519 6 a2 0.134 0.626 3 a3 0.122 0.573 5 a4 0.131 0.614 4 a5 0.144 0.673 2 a6 0.144 0.675 1 ao 0.214 1.000 5.2. ranking the locations using the edas method table 7. results obtained using the edas method spi nsi nspi nsni asi rank a1 0.080 0.177 0.233 0.462 0.348 6 a2 0.167 0.118 0.488 0,.642 0.565 1 a3 0.189 0.210 0.554 0.363 0.459 5 a4 0.149 0.144 0.435 0.563 0.499 4 a5 0.253 0.201 0.740 0.390 0.565 2 a6 0.342 0.329 1.000 0.000 0.500 3 5.3. ranking the locations using the saw method table 8. ranking the locations using the saw method values rank a1 0.547 6 a2 0.634 3 a3 0.595 5 a4 0.633 4 a5 0.694 2 a6 0.694 1 5.4. ranking the locations using the waspas method this method, as already mentioned in the paper, contains the previously applied saw method in its steps, so that the normalization, weighting of the normalized matrix, and summarizing the values by alternatives are identical as by the saw method, thus there is no need to display those matrices. the selection of a location for potential roundabout construction – a case study of doboj 53 table 9. ranking the locations using the waspas method wpm qi rank a1 0.508 0.528 6 a2 0.615 0.624 2 a3 0.522 0.558 5 a4 0.564 0.599 4 a5 0.576 0.635 1 a6 0.514 0.604 3 based on the presented calculation, it can be noticed that the location under the number 6 is best and a priority for the construction of a roundabout. since it is the location that has the largest traffic flow of pedestrians, an alternative solution for this location is the installation of traffic lights at this intersection, which has been done in the meantime, as it is well-known that if there is a high rate of pedestrians at a roundabout, alternative solutions are used. the intensity of pedestrians at this location for the period of one hour is 124 and, according to the authors’ opinion, it is not a limitation for the roundabout construction. location 6 represents the location in the city center. the second priority location for the construction of a roundabout is location 5 representing the last exit from the city towards sarajevo and which is a fourway intersection with an additional side road. there is often traffic congestion at this intersection where city streets are its arms, so there is often a situation where drivers carelessly merge onto the main road, as evidenced by a number of accidents. considering the above, the priority for the construction of a roundabout at this location is justified. since there is a change in the ranks of the alternatives, it is necessary to make a statistical comparison of the ranks, i.e. to determine their correlation. table 10 shows spearman's correlation coefficient of the ranks of the alternatives for all the methods used. table 10. spearman's correlation coefficient of the ranks of the alternatives for all the methods used methods mabac aras waspas saw edas average mabac 1.000 0.886 0.657 0886 0.543 0.794 aras 1.000 0.829 1.000 0.771 0.900 waspas 1.000 0.829 0.943 0.924 saw 1.000 0.771 0.886 edas 1.000 1.000 overall average 0.901 based on the total calculated statistical correlation coefficient (0.910), it can be concluded that the ranks are in a high correlation in all the created scenarios. regarding the rank correlation of mabac with other methods, there is a high correlation with aras and saw methods, while there is a lower correlation with the other two methods, with waspas 0.657 and with edas 0.543. aras has the total correlation with the saw method (1.000), with waspas (0.829), while it has the lowest correlation of 0.771 with edas. waspas and edas have the highest correlation between each other, when considering these two methods, and it is 0.943. by observing the overall ranks and correlation coefficients, it can be concluded that the model obtained is very stable and the ranks are in a high correlation since all values subotić et al./oper. res. eng. sci. theor. appl. 3(1) (2020) 41-56 54 higher than 0.80 according to (keshavarz ghorabaee et al., 2016) represent a very high correlation of ranks. 6. conclusion the developed model that includes the integration of bwm and mabac methods has been applied in a case study of selecting the location for the construction of a roundabout in the city of doboj, which is one of the important factors for increasing the mobility and functional sustainability of the city. taking into account the geographical position of doboj, it is imperative to construct roundabouts on the territory covered by this urban area. its location affects a significant share of transit flows, increasing negative externalities to traffic sustainability. the solution is certainly the construction of roundabouts that significantly eliminate or reduce current negative effects. the hypotheses set out in the paper have been proven through the development of the integrated model and analysis of all necessary parameters, which can be seen from the results obtained. the paper considers six potential locations, which have been evaluated using the integrated multi-criteria model. based on the obtained results, it can be concluded that the sixth location is best in terms of the defined optimization criterion and represents a priority location for the construction of a roundabout. location 6 represents the location that is in the city center. the second priority location for the construction of a roundabout is location 5 representing the last exit from the city towards sarajevo and a four-way intersection with an additional side road. there is frequently traffic congestion at this intersection where city streets are its arms. taking into account the above, the priority for the construction of a roundabout at the mentioned locations has been evaluated as justified. the model stability was verified throughout a sensitivity analysis in which the scenarios were created by applying different approaches. when observing the current state in the field of interest and infrastructure construction that involves smaller local projects, it is often one or two criteria considered when building infrastructure. the development of such a model as in this research creates the possibility of comprehensive consideration of all the important factors for infrastructure construction, which is one of the contributions of this research. in addition to the traffic flows of vehicles that are the main criterion, it is necessary to take into account the number of traffic accidents that occurred at the considered locations, pedestrian traffic flows, the economic aspect of construction and other factors covered in detail throughout the paper. future research with respect to this paper refers to the development of a model that will enable the 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(2010). a new additive ratio assessment (aras) method in multicriteria decision‐making. technological and economic development of economy, 16(2), 159-172. zhao, l., li, h., li, m., sun, y., hu, q., mao, s., ... & xue, j. (2018). location selection of intra-city distribution hubs in the metro-integrated logistics system. tunnelling and underground space technology, 80, 246-256. © 2020 by the authors. submitted for possible open access publication under the terms and conditions of the creative commons attribution (cc by) license (http://creativecommons.org/licenses/by/4.0/). the selection of a location for potential roundabout construction – a case study of doboj marko subotić*, biljana stević, bojana ristić, sanja simić 1. introduction 2. brief literature review 3. methods 3.1. best – worst method 3.2. mabac method 4. a case study in the city of doboj – description of the situation in the city of doboj 4.1. forming a multi-criteria model 4.2. evaluating and ranking the locations for roundabout construction using the mabac method 5. sensitivity analysis 5.1. ranking the locations using the aras method 5.2. ranking the locations using the edas method 5.3. ranking the locations using the saw method 5.4. ranking the locations using the waspas method 6. conclusion references operational research in engineering sciences: theory and applications vol. 3, issue 2, 2020, pp. 74-86 issn: 2620-1607 eissn: 2620-1747 doi: https://doi.org/10.31181/oresta2003074m * corresponding author. dragan.marinkovic@tu-berlin.de (d. marinković), manfred.zehn@tu-berlin.de (m. zehn), ana.pavlovic@unibo.it (a. pavlović) highly efficient fe simulations by means of simplified corotational formulation dragan marinković 1*, manfred zehn 1, ana pavlović 2 1 berlin institute of technology, department of structural analysis, germany 2 department industrial engineering, alma mater studiorum university of bologna, italy received: 14 june 2020 accepted: 15 july 2020 first online: 15 july 2020 original scientific paper abstract: finite element method (fem) has deservedly gained the reputation of the most powerful numerical method in the field of structural analysis. it offers tools to perform various kinds of simulations in this field, ranging from static linear to nonlinear dynamic analyses. in recent years, a particular challenge is development of fe formulations that enable highly efficient simulations, aiming at real-time dynamic simulations as a final objective while keeping high simulation fidelity such as nonlinear effects. the authors of this paper propose a simplified corotational fe formulation as a possible solution to this challenge. the basic idea is to keep the linear behavior of each element in the fe assemblage, but to extract the rigid-body motion on the element level and include it in the formulation to cover geometric nonlinearities. this paper elaborates the idea and demonstrates it on static cases with three different finite element types. the objective is to check the achievable accuracy based on such a simplified geometrically nonlinear fe formulation. in the considered examples, the difference between the results obtained with the present formulation and those by rigorous formulations is less than 3% although fairly large deformations are induced. key words: structural analysis, co-rotational fem, geometric nonlinearity, solid, shell 1. introduction structural analysis is an important engineering discipline encountered in various fields of mechanical and civil engineering. reliable, accurate and efficient predictions of structural behavior in general, and deformations in particular, are of crucial importance for successful design and optimization of structures, testing their functionality, prediction of their load-carrying capacity and life-time, etc. recently, this aspect started gaining in importance in some modern fields as well, such as highly efficient fe simulations by means of simplified corotational formulation 75 interactive simulations, where physics-based simulation are supposed to increase the realism of various applications. until several decades ago, computations in the field of structural analysis were performed mainly analytically by implementing significant simplifications. those simplifications have made the models mathematically tractable, but seriously affected the accuracy of the obtained results and therewith their reliability. however, the development of modern hardware tools has set the ambient for development of modern numerical methods for this purpose and the development of computer aided engineering (cae) software packages skyrocketed. those programs offered a great assistance to engineers in the previous decades. among different methods, the finite element method (fem) has established itself as the method of choice for all problems characterized by complex domains, arbitrary boundary conditions and described by partial differential equations. problems in the field of structural analysis fit perfectly well into this description and this is why structural analysists have initiated the development of this powerful method and made the very first steps (turner et al., 1956). its general applicability to many other engineering fields was later recognized and richly used. initial developments of fem were done for the least complicated but quite often encountered problems of structural analysis, namely the linear static problems. those problems are characterized by slowly increasing loads of constant direction, constant geometric boundary conditions and quite small deformations, so that the initial and deformed structural configurations are almost identical. those assumptions imply that the balance can be considered over the initial configuration (bathe, 1996). it is a straightforward task to extend the fe formulations from linear static to linear dynamic cases and it basically comes down to extending the equations by including inertial and damping effects. however, high level of structural optimization implies exploitation of structures to the levels quite close to their limits. in such cases, structural deformations are not small any more and more sophisticated fe formulations were needed to meet the objectives. total lagrange and updated lagrange formulations have set the standards in commercially available fe codes. the essential difference between the two lies in the choice of the reference configuration. principally it could be any configuration between the initial one and the last determined one, but the common sense choice would be to use either the initial one (total lagrange formulation) or the last determined one (updated lagrange formulation). different strain and stress measures are used in those two formulations and building the tangential stiffness matrix also reflects those differences, but numerics of the two formulations is essentially the same and the choice between the two is basically a matter of taste. another interesting formulation, namely the corotational fe formulation, appeared several decades ago. related to fem the term ‘corotational’ was used for the first time in a paper by belytschko and hseih (1979). the idea to cover geometric nonlinearities by attaching a corotational frame to single elements was introduced by horrigmoe and bergan (1978). the work in this direction continued under the supervision of bergan and the developments were summarized in a survey article by nygard and bergan (1989). crisfield (1990, 1997) and crisfield & moita (1996) introduced “consistent cr formulation” by developing the stiffness matrix as the marinković et al./oper. res. eng. sci. theor. appl. 3 (2) (2020) 74-86 76 actual variation of the internal force. rankin and brogan (1986) proposed the concept of element independent corotational formulation. a high-quality survey of these developments and a detailed analysis of their properties was provided by felippa and haugen (2005). this paper suggests a corotational (cr) fe approach that offers a trade-off between numerical efficiency and achievable accuracy by simplifying the rigorous corotational fe formulation. the idea is to offer a fe formulation that would be of high interest for specific applications such as multi-body system dynamics, where parts exhibit large rigid-body deformations but small strains, or applications involving real-time simulations. in this paper, the achievable accuracy will be tested with a few basic solid and shell elements in cases involving large local rigid-body rotations. 2. simplified cr formulation and implemented elements 2.1. basic principles of the simplified cr formulation while the linear fe formulations offer very efficient and stable computations, the nonlinear formulations are very time consuming and prone to computational stability issues, as they might not necessarily produce converged solutions. on the other hand, linear formulations are accurate only for small deformations, but geometrically nonlinear formulations offer engineering accuracy for large deformations involving arbitrarily large rigid-body rotations. while one would wish to have advantages of both formulations in one formulation, it is certainly not possible to have all the advantages to the full extent. but a formulation may offer a kind of trade-off or a compromise between those. the formulation that will be explained here follows the idea of element-based cr formulation. hence, the basic concept is to attach a coordinate system to an element and keep the linear fe formulation of the element with respect to this coordinate system. the attached coordinate system follows the element in its rigid-body motion. as the elastic behavior of the element remains linear with respect to the attached coordinate system, this implies that the element matrices are computed only once for this coordinate system. as deformation proceeds, it is necessary to determine the motion of the attached coordinate system, or, in other words, to determine the element rigid-body motion. once this is described by the element rotational matrix, re, the related element matrices and vectors can be rotated to the current configuration and the assemblage of the global matrices and vectors can be done for further computation. hence, the element elastic behavior is described as linear with respect to the attached corotational frame and the element stiffness matrix with respect to this frame is not updated. in this manner, the local element deformation and the stress state is neglected from the consideration of geometrically nonlinear effects, thus simplifying the formulation significantly compared to the rigorous nonlinear formulations. the formulation keeps the very important aspect of geometric nonlinearity, namely the rigid-body rotation that is accounted for on the element level. in continuum every point exhibits its own rigid-body rotation, generally speaking. obviously, this aspect is described here in a coarser way, as it is always the highly efficient fe simulations by means of simplified corotational formulation 77 case with methods that apply discretization. but one may arbitrarily adjust the ‘resolution’ of accounting for rigid-body rotation by performing finer or coarser fe meshing. hence, assuming the element rigid-body rotation between the initial and the current configuration is known and given as the rotation matrix re, the element stiffness matrix, ke, is update with respect to the global coordinate system in a straightforward manner: tt0tt eeee rkrk = , (1) where the left superscript denotes the moment in time at which the term is given. this simple way of updating the element stiffness matrix is where the efficiency of the method resides. not only is the tangential stiffness matrix efficiently updated, but also its condition number does not change dramatically in this manner, so that the stability of computation is kept to a large extent. this is not always the case with rigorous nonlinear fe formulations in which single elements may suffer significant deformations, and, as a consequence, the solution may not converge. in order to perform nonlinear computations, one needs the tangential stiffness matrix, the update of which was elaborated above, and the internal forces. in order to determine the internal forces, deformational displacements and rotations are required. those are obtained when the rigid-body rotation is removed from the overall element displacements. this procedure is best explained using figure 1. in this figure, a tetrahedron element is shown in its original and an arbitrarily deformed configuration. again, it is assumed that the rigid-body rotation of the element is known. it is sufficient to rotate the deformed element back to the original element configuration. by comparing so obtained element configuration with the initial one, one obtains deformational displacements. figure 1. extraction of deformational displacements for a tetrahedron element hence, the expression for the deformational displacements reads: eee xxru 0ttt r t 0 −= , (2) where xe denotes the element configuration, i.e. those are the nodal coordinates of all element nodes. with the known deformational displacements, one may simply multiply those with the element stiffness matrix for the initial configuration to obtain the internal forces with respect to the initial configuration. the internal forces are marinković et al./oper. res. eng. sci. theor. appl. 3 (2) (2020) 74-86 78 the rotated to the current configuration. those steps are summarized in the following expression: eeeeeeeeee xkrxrkrfrf 00tttt0tt 0 tt t −== , (3) if finite elements contain rotational degrees of freedom, the procedure is essentially the same for rotations, as illustrated in figure 2. figure 2. extraction of deformational rotations for a shell element with the incremental nodal rotations, t-ti1, t-ti2 and t-ti3, the element nodal normals are updated by means of the rotation matrix qi (argyris, 1982): ( ) ( ) 2 i tδt 2 i tδt i tδt t i tδt i tδt i tδt 2/γ 2/γsin 2 1 γ γsin ssiq − − − − − −         ++= , (4) where 2 3i tδt2 2i tδt2 1i tδt i tδt θδθδθδγ −−−− ++= , (5)           − − − = −− −− −− − 0θδθδ θδ0θδ θδθδ0 1i tδt 2i tδt 1i tδt 3i tδt 2i tδt 3i tδt i tδt s , (6) so that i tδttδt i t nqn −− = . (7) after rotating the element from the current to initial orientation, it is a straightforward task to compute the internal moments and rotate them again to the current configuration in an analogous manner as done above with the forces. 2.2. finite elements implemented into the formulation so far three finite elements have been implemented into the proposed simplified cr formulation – two solid elements and one shell element. highly efficient fe simulations by means of simplified corotational formulation 79 the solid elements are the linear tetrahedron element and the quadratic hexahedron element. the linear tetrahedron element is notorious for its too stiff behavior and is, therefore, often avoided in modeling. however, it has two nice properties. it is numerically very efficient and can discretize any geometry. actually, the second advantage makes it often inevitable in fe models in order to model some figure 3. linear tetrahedron element (left) and quadratic hexahedron element (right) areas of the model that are otherwise too difficult to discretize. in addition, this element is characterized by unambiguity of the rotation matrix. there is a single, unique rotation matrix describing the rigid-body rotation of this element, which is not the case with most of the finite elements. for any two given configurations of the element there is a unique matrix that transforms the element from one configuration to the other one. this is due to the fact that the element employs the linear shape functions, so that the deformation gradient has a constant value over the whole element domain. polar decomposition of this transformation matrix yields the rotation matrix. in order to obtain reasonable results with this element, a quite fine discretization is required. but this also increases the “resolution” of accounting for the rigid-body rotation, which is a positive aspect regarding the corotational fe approach. nguyen et al. (2016) have used this element in combination with a corotational fe approach that implements the projector matrix for the sake of better result convergence. the quadratic hexahedron element is in most aspects the opposite of the linear tetrahedron element. it offers the best accuracy among solid elements (apart from those that use special techniques), but is numerically very demanding and requires partitioning of complex geometries for successful meshing, whereby the ‘corners of the geometry’ will still require tetrahedron elements. the rotational matrix is not unique for the element, i.e. it differs for different points within the element domain. hence, it is ambiguous and one has to decide what strategy to use in order to determine it. it may be determined by local coordinate systems defined in a special ways by using the current nodal positions. a better option would be to use the deformational gradient at some point of the element, whereby the element centroid appears to be a natural choice – exactly this option was applied in this work. the best, but also the most demanding option would be to obtain some kind of average rotational matrix of the element. it is so far, however, an open question with respect to what criteria the averaging is to be performed. the implemented shell element is a linear triangular shell element (figure 4) recently developed (rama et al., 2018, 2018a, 2018b, marinkovic et al., 2019). essentially, the element is a combination of a plate element and a membrane element. it implements the mindlin-reissner kinematics and uses the discrete shear marinković et al./oper. res. eng. sci. theor. appl. 3 (2) (2020) 74-86 80 gap (dsg) method (li et al., 2019) in combination with the strain smoothing technique to alleviate the notorious shear locking. the membrane part of the element is actually the andes membrane formulation developed by felippa and militello (1992). similarly to the linear tetrahedron element, this one also has a unique rotational matrix, can discretize any surface geometry and is numerically highly efficient. due to the flat shape of the element, the discretized geometry is actually faceted, which affects the achievable accuracy. figure 4. linear triangular shell element 3. numerical examples in what follows, three examples of large deformations, each for one type of implemented elements, will be considered in order to investigate the achievable accuracy by means of the proposed corotational fe formulation. the major purpose is the comparison of computed displacements obtained by rigorous geometrically nonlinear fe formulation (computed in abaqus) and those obtained by the presented development. in accordance with this objective, all quantities will be given as dimensionless. the selected examples are of academic nature involving structures of rather simple geometry. sufficiently large loading will be chosen to produce geometrically nonlinear deformations, i.e. those that significantly differ from deformations computed by the linear formulation. 2.1. solid elements the same structure, which may be referred to as a block, with dimensions 10101.5 and clamped over one surface with dimensions 101.5 will be discretized with both tetrahedron and hexahedron element. the geometry with kinematic boundary conditions is depicted in figure 5, left. the material is linear elastic with the following properties: young’s modulus e=21011 and poisson ration =0.3. the load cases are chosen to be different for the discretization with the tetrahedron element and for the discretization with the hexahedron element. in both cases the force is set to be f=1010 in order to produce sufficiently large, geometrically nonlinear deformations. as shown in figure 5, middle, in the case of discretization with the tetrahedron element, the force acts only at one corner of the structure so as to bend and twist it at the same time. figure 5, right, shows discretization with the hexahedron element and the load case with a pair of oppositely oriented forces that cause twisting of the considered structure. highly efficient fe simulations by means of simplified corotational formulation 81 figure 5. block structure: geometry and kinematic boundary conditions (left), load cases and discretization with tetrahedrons (middle) and hexahedrons (right) in order to visualize the deformations and get the feeling for the magnitude of deformation, the unscaled deformations (i.e. scale factor set to 1) are depicted in figures 6 (the fe model with tetrahedron elements and one force) and 7 (the fe model with hexahedron elements and two forces) together with the undeformed structure. the structure is shown from different perspectives. obviously, the magnitude of deformation is well beyond the realm of linearity. figure 6. deformed and undeformed block structure under single force load, discretization with tetrahedron elements, three different perspectives figure 7. deformed and undeformed block structure under force couple load, discretization with hexahedron elements, three different perspectives as a representative point to follow its displacements with the gradually increasing loading, the point at which the force acts in figure 5, middle, is selected. its displacements in all three global directions are considered in both cases and compared with the linear and geometrically nonlinear results from abaqus. the marinković et al./oper. res. eng. sci. theor. appl. 3 (2) (2020) 74-86 82 results are given in figure 8, for the case shown in figure 5, middle, and figure 9, for the case shown in figure 5, right. one may notice that the results for the same global displacements show a similar trend in both considered cases. comparing the displacements in the same directions in those two cases, one would notice that the major distinction is in the relative difference between linear and geometrically nonlinear results. there is actually a significant difference between the linear and geometrically nonlinear results, and it goes even up to 50%. this was expected and, figure 8. model with tetrahedron elements – displacements in three global directions figure 9. model with hexahedron elements – displacements in three global directions in fact, the loading was chosen with this objective. on the other hand, there is also a good agreement between the nonlinear results by abaqus and present formulation. the difference is observable in the last 30-40% of the loading but stays in the limits of up to 2%, which is an acceptable result for many different applications. in addition, the highest difference is at the full loading, where local element deformations start to kick in and this is an effect not accounted for by the present formulation. as long as this effect is not present, the difference in the results is practically negligible. 2.2. shell element the example considered for the shell element is a typical benchmark case used in development of shell elements for geometrically nonlinear analysis. it a straight beam, with one end clamped, while the free end is exposed to a bending moment of such a magnitude that the beam bends into a circle. the moment required to produce such a deformation can be computed analytically assuming beam kinematics and is given as m = ebh3/6l (bathe and bolourchis, 1979), where e is the young’s modulus, while b, l and h are the width, length and thickness of the beam, respectively. in this highly efficient fe simulations by means of simplified corotational formulation 83 case, the young’s modulus is the same as in the previous cases with solid elements, while poisson ratio is set to zero, so that the shell element reproduces the beam behavior (poisson effect is neglected over the beam’s cross-section). dimensions of the beam can be seen in figure 10, left, while figure 10, right, shows the fe mesh applied. figure 10. beam model and discretization with triangular shell elements interestingly, abaqus encounters a problem to complete the computation with its 3-node shell element. the computation runs until approximately 95% of the load, and when this level is reached, a converged solution is not found any more (automatic stepping was used to facilitate the computation). figure 11 shows the initial and deformed configuration as computed by abaqus. the relatively coarse mesh is the reason for the faceted deformed geometry and could be one of the reasons for the computational issues encountered by abaqus. figure 11. beam model – deformed (abaqus) and undeformed configuration the results for the displacements along the xand y-axes are given in figure 12. the diagrams include only nonlinear results as the large difference between those and linear results would make the inclusion of linear results unreasonable. the computation with the proposed corotational formulation proceeds till 100% of the load. one may notice a good agreement of the results up to the load level computed by abaqus. marinković et al./oper. res. eng. sci. theor. appl. 3 (2) (2020) 74-86 84 figure 12. beam model – free end displacements in the xand y-directions 4. conclusions the paper elaborates a simplified corotational fe formulation in which the element local behavior is described as linear, but the element rigid-body rotation is accounted for. hence, it neglects the effect of the element pure deformation and element stress state on the element tangential stiffness matrix. this is where the numerical savings are made, thus rendering the formulation very efficient in terms of computational effort and also numerically stable. at the same time, this means that it delivers results that are an approximation compared to the results delivered by the rigorous geometrically nonlinear fe formulations, such as total and updated lagrange formulation, or the rigorous corotational fe formulation. the examples were focused on accuracy of predicting the structural displacements, which is equivalent to the accuracy of predicting the deformed structural configuration. it was shown in the considered examples that the discrepancy between the rigorous results and those obtained by the proposed formulation is only a few percent for fairly large deformations. of course, the achievable accuracy certainly depends on the nature of the deformation and is expected to be better in cases where local rigid-body rotation dominates. furthermore, this means that the formulation can successfully be used for certain engineering simulations where this level of accuracy is acceptable. for instance, it can be a very attractive alternative for consideration of elastic bodies in multi-body system (mbs) simulations, which is currently mainly done based on the modalsuperposition technique thus covering only linear deformations with respect to the local frame of the whole structure. the proposed formulation would offer better accuracy and fidelity of the full-scale fe model, while keeping the numerical effort in acceptable limits. another interesting field of application would be virtual reality (vr) where physics-based real-time simulations have always played a challenging task (marinkovic et al., 2018, marinkovic & zehn, 2019, zehn & marinkovic , 2019). in this field, the presented formulation can be successfully used for various types of simulators such as surgery (marinkovic & zehn, 2018), assembly planning and practicing assembling of various complex products, thus improving the productivity, etc. highly efficient fe simulations by means of simplified corotational formulation 85 references argyris, j. (1982). an excursion into large rotations. computer methods in applied mechanics and engineering, 32(1-3), 85-155. bathe, k. j. (1996). finite element procedures. new york : prentice hall. bathe, k. j., & bolourchis, s. (1979). large displacement analysis of threedimensional beam structures. international journal of numerical methods in engineering 14(7), 961-986. belytschko, t., & hsieh, b. j. (1979). application of higher order corotational stretch theories to nonlinear finite element analysis. computers & structures, 11, 175–182. crisfield, m. a. (1990). a consistent corotational formulation for nonlinear threedimensional beam element. comp. meths. appl. mech. engrg., 81, 131–150. crisfield, m. a. (1997). nonlinear finite element analysis of solids and structures. vol. 2: advanced topics. chichester: wiley. crisfield, m. a., & moita, g. f. (1996). a unified co-rotational for solids, shells and beams. int. j. solids struc., 33, 2969–2992. felippa, c., & haugen, b. 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(2018). corotational finite element formulation for virtual-reality based surgery simulators. physical mesomechanics, 21(1), 15-23. marinkovic, d., & zehn, m. (2019). survey of finite element method-based real-time simulations. applied sciences, 9(14), art. no. 2775. marinkovic, d., zehn, m., & rama, g. (2018). towards real-time simulation of deformable structures by means of co-rotational finite element formulation. meccanica, 53(11-12), 3123-3136. nguyen, v. a., zehn, m., & marinkovic, d. (2016). an efficient co-rotational fem formulation using a projector matrix. facta universitatis, series: mechanical engineering, 14(2), 227-240. nygard, m. k., & bergan, p. g. (1989). advances in treating large rotations for nonlinear problems. in a. k. noor, & j. t. oden (eds.), state-of the art surveys on computational mechanics (pp. 305–332). new york: asme. rama, g., marinkovic, d., & zehn, m. (2018). efficient three-node finite shell element for linear and geometrically nonlinear analyses of piezoelectric laminated structures. journal of intelligent material systems and structures, 29(3), 345-357. marinković et al./oper. res. eng. sci. theor. appl. 3 (2) (2020) 74-86 86 rama, g., marinkovic, d., & zehn, m. (2018a). a three-node shell element based on the discrete shear gap and assumed natural deviatoric strain approaches. journal of the brazilian society of mechanical sciences and engineering, 40(7), art. no. 356. rama, g., marinkovic, d., & zehn, m. (2018b). high performance 3-node shell element for linear and geometrically nonlinear analysis of composite laminates. composites part b: engineering, 151, 118-126. rankin, c. c., & brogan, f. a. (1986). an element-independent corotational procedure for the treatment of large rotations, asme j. pressure vessel technology, 108, 165– 174. turner, m. j., clough, r. w., martin, h. c., & topp, l. j. (1956). stiffness and deflection analysis of complex structures, j. aeronaut. sci., 23, 805-824. zehn, m.w., marinkovic, d. (2019). chances of real-time simulation in fe analyses with conventional hardware. advances in engineering materials, structures and systems: innovations, mechanics and applications proceedings of the 7th international conference on structural engineering, mechanics and computation, 2019, cape town, south africa, pp. 531-536. © 2020 by the authors. submitted for possible open access publication under the terms and conditions of the creative commons attribution (cc by) license (http://creativecommons.org/licenses/by/4.0/). highly efficient fe simulations by means of simplified corotational formulation dragan marinković 1*, manfred zehn 1, ana pavlović 2 1. introduction 2. simplified cr formulation and implemented elements 2.1. basic principles of the simplified cr formulation 2.2. finite elements implemented into the formulation 3. numerical examples 2.1. solid elements 2.2. shell element 4. conclusions references operational research in engineering sciences: theory and applications vol. 3, issue 2, 2020, pp. 24-38 issn: 2620-1607 eissn: 2620-1747 doi: https://doi.org/10.31181/oresta2003024s * corresponding author. saryanto.01@yahoo.com (saryanto). humiras.hardi@mercubuana.ac.id (purba, h. h.), aristrimarjoko@gmail.com (trimarjoko, a) ah.fuadf@gmail.com (fatahillah, f) quality improvement of remanufacturing lift arm using six sigma methods in the heavy-duty industry in indonesia: a case study saryanto*, humiras hardi purba, aris trimarjoko , fuad fatahillah department of industrial engineering, mercu buana university, jakarta, indonesia received: 11 april 2020 accepted: 02 june 2020 first online: 12 june 2020 original scientific paper abstract: the high remanufacturing forecast reaching 160 billion dollars/year in the world of the equipment industry (heavy duty) is a promising business opportunity. however, the remanufacturing industry has a higher risk of product failure compared to original equipment products. the remanufacturing of the heavy-duty industry in indonesia in carrying out its production has a product failure rate of 834586,47 dpmo and is at 1.91 sigma with copq idr 650,800,000.00 six sigma method is used in this research and is successful in reducing remanufacturing defective product for lift arm to 140762,5 dpmo, is at the level of 2.43 sigma and copq idr. 135,000,000.00 or decreased 78.71% from the previous condition. key words: quality improvement, remanufacturing, six sigma, product failure 1. introduction 1.1. general the remanufacturing industry has been around for at least 28 year and provide significant economic, social and environment benefit. strategy 3r ( reduce, reuse and recycle ) ,system was founded in the usa and remanufacturing operation have grown substantially and become common practice in many industries. in development countries, the remanufacturing engineering also developed rapidly and has been applied to industry. the united states environment protection agency (epa) implemented a comprehensive procurement guidelines (cpg) program to enact waste reduction and resource conservation through the reuse of used materials and ensuring recycling programs for certain materials can be made into materials to create new products. reman world magazine, march/april edition, 2018 states the remanufacturing industry is spreading in various countries with a total forecast of $ 160 billion/year with spread: the usa $ 100 billion, europe $ 32, asia $ quality improvement of remanufacturing lift arm using six sigma methods in the heavyduty industry in indonesia: a case study 25 27 billion and brazil $ 1.4 billion. the asian region (including indonesia) ranks third in the distribution of the remanufacturing industry. the high remanufacturing forecast reaching 160 billion dollars/year in the remanufacturing industry is a promising business opportunity. however, the remanufacturing industry has a higher risk of product failure compared to original equipment products. in indonesia, the remanufacturing industry, which is engaged in the heavy-duty equipment industry, supports the repair of mining equipment and vehicles both in open pit and underground in running its production, experiencing a product failure rate of 834586.47 dpmo if the capability of the process is measured at the level of 1.91 sigma and the cost of poor quality must be borne by usd. 43386.57 for january ~ may 2019. valles et al., 2009 state that six sigma is a strategy of continuous organizational improvement to find and eliminate the causes of errors, damage, and delays in business organization processes. gijo et al., 2014 with the application of the six sigma method resulted in a reduction intolerance related to problems and increased yield values from 85% to more than 99%. get a total savings of us $70,000 per year. hassan, 2013 shows that, for the calculation of the yield value of 95.75%, from this result, the sigma level was calculated and found an initial sigma value of 3.22 and a dpmo of 42,500. using a target of a 2% defect rate, the target sigma value is calculated to be 3.55 and the dpmo value is 20.000. the results achieved 98.24%, according to the sigma level of 3.6 and the dpmo value of 17.600. referring to various studies on problem-solving with the help of six sigma methods showing positive results that are marked by decreasing product failure rates and increasing sigma levels, then in this study, six sigma methods are expected to be used in the failure of remanufacturing lift arm products in the heavy-duty industry in indonesia to be reduced so that the process capability is getting better, copq can be suppressed and will certainly increase company profits. 1.2. motivating of research the companies engaged in manufacturing tools in indonesia that support the repair of mining equipment and vehicles both in the open pit or underground. companies are required to make innovation efforts so as not to lose their market share. consumers always want innovative products, because their tastes and needs tend to change with the changing times. products that consumers want are products that are not only able to meet their needs but are also able to provide satisfaction for their users. the activity carried out is to suppress as little as possible the name of the product defect to zero defect. in line with the principle of zero defects, remanufacturing companies engaged in heavy equipment, have full attention to this matter. evidenced by improvement activities carried out by all company employees to reduce product defects. lower-level employees (operators) to the top level of management, improvement activities carried out continuously. this research was conducted to examine the level of disability in the machine rebuild section with the machining and welding process in the company. the section is the final section of the process in the production process, where the level of disability is still high based on the 2018 machining and welding quality reports. based on internal data of the 2018 machining and welding product defects, 1.99% with types of defective products as follows: lift arm (73.5%), bucket (7.9%), front frame (3.3%), rear frame (3.3%), tilt lever (3.3%), tilt link (2.6%), cabin (2.0%) and others (4.0%). based on the 2018 defect product data, this study is motivated to reduce the lift arm saryanto et al./oper. res. eng. sci. theor. appl. 3 (2) (2020) 24-38 26 product failure of the machining and welding process which has the highest accumulation of defective products by 73.5%, with the hope that lift arm quality can be improved to meet customer satisfaction and provide a more optimal company advantage. 2. literature review 2.1. quality improvement the purpose of quality control is to make the final product produced according to product specifications and standard sets (james, 2012). speaking of quality, of course, there is no definite understanding of quality and quality has a broad scope and has a different understanding (suwendra, 2014. quality in terms of producers is the fulfillment of quality standards that have been owned (purba, 2017). in addition there are several objectives for quality control, namely: (1) to improve the uncontrolled process, (2) to control the finished product, in this case it is done by taking the sample of the receipt, (3) to produce quality products, (4) work for inspection or inspection cost to minimize, (5) strives to reduce the cost of product design and processes using certain production quality, and (6) make sure the cost of production is minimized as low as possible (cullison et al., 2013). for some of the widely used quality features, among others : (a) quality is compliance with requirements or claims, (b) quality is a match with use, (c) quality is continuous improvement and improvement, (d) quality is an effort to meet the needs of consumers from the beginning and at all times, (e) quality is something that can satisfy the user (chunxioa et al., 2013). quality can generally be interpreted as a measure of quantity that indicates the stage of the good of a product, or can be interpreted as the best condition within certain limits in accordance with the will of the consumer. in general, the conditions required by consumers as the most important are product prices and product benefits. the two things are related: a. specification of operating characteristics, b. product age and reliability, c. manufacture of product, d. the condition in which the product is made, e. installation and maintenance of products and facilities in the field (milln et al., 2013). so briefly the quality can be defined as satisfaction in the use of products that include aspects of: product quality: the quality of the product or service cost quality: quality of cost, delivery quality: quality delivery products, safety quality: safety quality, utility of spirit: quality in serving customers (pylväs et al., 2015). referring to the definition of quality, the improvement of product quality to increase customer satisfaction is an important attribute in a business organization (nugroho, 2015). 2.2. remanufacturing industry in 2005 the remanufacturing industry began when the united states environmental protection agency (epa) implemented a comprehensive procurement guidance program (cpg) to enact waste reduction and resource conservation guidelines through the reuse of waste materials and ensuring recycling programs for certain materials can be made into materials to create new products. in 2004, the epa established several remanufactured vehicle parts. remanufacturing is to use a portion of its original form and replace or rebuild damaged parts. the testing quality improvement of remanufacturing lift arm using six sigma methods in the heavyduty industry in indonesia: a case study 27 process follows the same specification process as the new product manufacturing process (https://www.epa.gov/). the remanufacturing industry is an industry that uses a portion of its original form/original equipment to rebuild damaged parts and replace it with new equipment through the testing process following the same specifications as the new product manufacturing process. the quality of re-manufacturing products has the same standard as the manufacturing of new products (ijomah, 2008; ijomah and childe, 2010). one of the complicating characteristics in remanufacturing is the stochastic and sporadic nature in the condition and quantity of the returned cores which impacts on many levels in the planning and control (junior et al., 2012). returned products can range from minor scratches to extensive damage and thus inspection and sorting procedures are required to filter the valuable cores. high quality returns are preferred as the quality of the returns determines the level of the remanufacturing effort required, the processing time, the rate of remanufacturing success, the process sequence used, the amount of cost savings, and the amount of cores being scrapped (ortegon et al., 2013). the extent to which remanufacturing is done and the definition of sufficient quality depend on the type of remanufacturers and the business model; independent remanufactures try to repair as many parts as possible, whereas oem remanufacturers can be more selective on the cores to accept. reliable engineering expertise and capabilities is the backbone to a successful remanufacturing facility. remanufacturing depends extensively on the skills of the technicians and the knowledge base related to the cores and their restoration (ijomah. 2009). 2.3. six sigma quality six sigma is a business strategic management which originally developed by motorola in 1986 in order to enhance the quality of products through decreasing of product variations on manufacturing operations as they face compete in semiconductor industries. through the application of the six sigma method, motorolla has acknowledged an award of malcolm baldrige in 1988 as the first american’s company which won its prestigious quality’s award (parsana et al. 2014). quality in terms of producers is the fulfillment of quality standards that have been owned (purba, 2017. according to these facts, by considering an obtained quality level for only 99 percent or 1 percent of defect levels on such cases in manufacturing industries or services can potentially lead to fatalities. hence, for gaining the target of quality level of 99.9996 percent or free-defects, an organization requires both flexibility and discipline in solving problems using statistical approach rather than using simple intuition or by trial and error; wider usage of statistical treatments is one of the benefits of six sigma method (pacheco, 2014). application of six sigma’s method is more valuable due to its contribution to the science and practice for particularly reduces waste and provides added values. six sigma allows users to identify waste and hidden costs, eliminates defects, increases profit margin, satisfies customers, encourages employee commitment and satisfaction as well as expands businesses (patil et al, 2015). six sigma as a management system is applied to ensure that efforts and critical opportunities for improvement are well developed through metric methodology and an applied level is inline with its business strategy. six sigma enables an organization to improve quality process by identifying and eliminating the causes of defects and error terms through minimizing variability in saryanto et al./oper. res. eng. sci. theor. appl. 3 (2) (2020) 24-38 28 manufacturing and business processes (mittal, 2014). the stages for improve process ability (process capability) regarding six sigma method are specifically allowing the standard steps such as define, measure, analyze, improve, and control for interlinked statistical tests. for a particular project within organization of applied of six sigma the stage is typically consists of a step-by-step requires for obtain measurable target values i.e. reduces cycle time, decreases air pollution, reduces costs, improves customer satisfaction, and increases profits (mittal, 2014). it is inevitable, in order to gain benefits, as a results of six sigma’s application in an organization or company, would require relatively high of initial investment, but might be offer benefits in long terms including cost savings, generated profits, improved consistency of quality processes, better employee performance, and better service quality and products. those elements particularly would lead an organization or company to provide a higher customer satisfaction as well as to gain the ultimate goal of organization (mittal, 2014). by applying dmaic using a statistical approach, the root causes of the problem can be found and can improve the production process. the results of the six sigma improvement show the process capability increased from 2.2 to 3.1 sigma, saving $18,394.2 per month (syafwiratama et al., 2017). six sigma is a systematic, flexible, measurable and effective method in solving various problems in the industrial world (trimarjoko et al., 2019). seeing the results of the studies mentioned above, the six sigma method is used in improving the quality of remanufacturing lift arm in the heavy-duty equipment industry in indonesia to be better to meet customer satisfaction and provide better company benefits. 3. research methodology the research methodology is a systematic description of the steps taken by the author from the beginning to the end of the study so that the implementation of the research becomes clear and focused following the research objectives. through the following principal steps: (1) describe the issue that is happening (2) measure baseline performance or sigma level as an initial standard re-manufacturing the lift arm process. (3) analyzing the cause of product failure factors in the lift arm remanufacturing process. (4) determine the improvement efforts that can be done to improve the quality of the re-manufacturing lift arm process, (5) evaluate and control the results of repairs. the 5 stages are following the rules of problem-solving using the six sigma method namely the dmaic phases (define, measure, analyze, improvement and control). the research methodology used in this study is shown in figure 1. quality improvement of remanufacturing lift arm using six sigma methods in the heavyduty industry in indonesia: a case study 29 define sipoc diagram, identifikasi ctq (pareto diagram) measure sigma level, four block diagram, copq measurement analyze brainstorming, fish bone diagram improve 5w 1h method control sigma level, four block diagram, copq measurement, standardization defect lift arm 73.5% in welding and machining process literature study quality improvement remanufacturing process data collection internal of data company processing data analysis : six sigma start result, discussion and recomendation finish dmaic phases figure 1. research methodology of problem solving lift arm in welding and machining process 4. processing and analysis processing and analysis in this study using the six sigma (dmaic) method based on previous research studies six sigma is a systemic, flexible, measurable and effective method, with a combination of methods and other tools proven to be able to reduce defective products, reduce errors, reduce customer complaints and improve process capability in maintaining company sustainability and can improve company competitiveness. six sigma has structured steps known as dmaic phases (define, measure, analyze, improve, control). 4.1. define phase at the stage of defining activities carried out to identify problems that occur based on consumer needs and determination of goals (reduction of product failure). the initial step of the define stage is to identify the sequence of activities that occur in the welding and machining process that aims to find out at which stage the problem is. as for the sequence of activities intended in the sipoc diagram as in table 1. table 1 sipoc diagram of remanufacturing lift arm. supplier input process output customer disassembly area scope of work schedule material damage part consumable welding consumable machining welding process machining process part finish process remanufacturing ok tag from quality control assembly area saryanto et al./oper. res. eng. sci. theor. appl. 3 (2) (2020) 24-38 30 the welding and machining process is critical in this research. the next step is to find out the critical to quality in the lift arm welding dam machining process is carried out the production data collection and welding and machining lift arm product failure in january ~ may 2019 with the percentage and types of product failure as in pareto diagram figure 2. figure 2 pareto chart of product failure welding and machining process lift arm refer to the pareto diagram as in figure 3. can be interpreted that 6 types of defective products occur in the welding process and machining lift arm, namely: miss alignment (68.5%), porosity (18.9%), crack (4.5%), oversize (2.7%) scratches (2.7%) and others (2.7%). based on the concept of pareto product failure that has an accumulation of 80% into the improvement priority in problem-solving, then ctq in this study there are 2 types are miss alignment and porosity product failure with cumulative 68.5% + 18.9% = 87.4%. research focuses on solutions to eliminate these two defects 4.2. measure phase the measuring stage is the second stage in the quality improvement program with the six sigma method in this stage, the capability process/sigma level measurement is used to determine the ability of the process before improvement, plotting the ability of the process into 4 block diagrams to determine the improvement direction from the control side of technology and also carried out measurements cost of poor quality (copq) to determine the financial losses caused by defective products. 4.2.1. capability process/sigma level measurement based on the collection of production data and product failure (defects) in the remanufacturing lift arm process from january to may 2019 obtained from the report of the production department and quality control total production 266 part, and total defect 111 part, the calculation of the process capability/sigma level is shown in table 2. quality improvement of remanufacturing lift arm using six sigma methods in the heavyduty industry in indonesia: a case study 31 table 2. measurement of level sigma current condition that representative of before improvement item value total production 266 total product failure (defect) 111 ctq ( control to quality ) 2 dpmo ( defect per million opportunity ) 834586,47 level of sigma 1,91 4.2.2. four block diagram four block diagram is a description of a process and states improvement direction that leads to two sides of improvement, namely technology and control which is a description of the ability of the process (z) of an ongoing process. based on sigma level 1.91, it can be calculated zshif value as a reflection of control ability and zst value which reflects the ability of technology and then plots it in four block diagrams that show the capability of the ongoing process (z). the zshif and zbench.lt calculations in the four-block diagram are as follows: zst = zbench.lt + 1.5 1.91 = zbench.lt + 1.5 z bench.lt = 1.91 – 1.5 = 0.41 zshift = zbench.st – zbench.lt = 1.91– 0.41 = 1.50 the next step is after knowing the value of z shif (control ability) and zst (sigma level) then it can be done by making four block diagrams to illustrate the current process condition (current condition), as for the four block diagrams referred as in figure 3. figure 3. four block diagram product failure (defect) welding and machining process lift arm looking at the four block diagram above(figure 4), it is known that from the control side it is good and still lacking in technology, meaning that improvements are saryanto et al./oper. res. eng. sci. theor. appl. 3 (2) (2020) 24-38 32 needed so that both sides are expected in the category of proper control and technology. 4.2.3. cost of poor quality (copq) mesurement in addition to measuring the baseline performance of the remanufacturing lift arm process, a cost analysis is also carried out due to poor quality, in this case, the cost of losses caused by product failure. the company's internal source costs must be borne due to product failure resulting in rework. cost of poor quality us$ 390,87 per pcs. as a result, the costs of losses due to product failure in january may 2019 are as follows: table 3. calculation of cost of poor quality january may 2019 no month product failure (pcs) copq (usd) 1 january 2019 22 8599.14 2 february 2019 18 7035.66 3 march 2019 22 8599.14 4 april. 2019 23 8990.01 5 may 2019 26 10162.62 total 111 43386.57 table 3. shows the cost of losses resulting from product failure from january to may 2019 cost of poor quality of usd 43386.57. 4.3. analyze phase analyze phase is the third stage of the dmaic method. in this stage, what needs to be done is to analyze why deviations or product failures occur by looking for the causes that cause these product failures. in this case, a defect analysis arises in the remanufacturing lift arm process which consists of 2 types of product failure eg alignment and porosity fishbone diagram (cause and effect diagram) as in figures 4 and 5. method needed 3 step to finish the machining process measuring manually is done with a combination of 3 measuring tools, string, caliper and ruler there is no standard jig or fixture for machining and inspection man different operator skills different enviorement material machine shaft portable line boring is not straight the process cannot be done on one machine because shibhaura's machine table is shorter than the part's length condition of bending parts the condition of welding results in the previous process is not evenly distributed the condition of the workshop is hot, dusty and miss allighment figure 4. cause and effect diagram of product failure miss alignment quality improvement of remanufacturing lift arm using six sigma methods in the heavyduty industry in indonesia: a case study 33 method welding position that is difficult for the inside welding manually no standard welding parameters there is no pre-heat standard before welding not closed when finished welding (post heat) man different welder skills welders are not disciplined in checking the results of welding enviorement material machine the machine is dead or stuck when welding argon hp runs out when welding runs no welding is carried out before welding dirty and oilcontaminated surface, grease moist welding wind and humidity and porosity figure 5. cause and effect diagram of product failure porosity from the cause and effect diagram, in figure 4 the root cause of miss alignment in the remanufacturing lift arm process is: (1) the process cannot be done in a cnc machine because parts are longer than the machine table. (2) if done with a portable line boring machine, the machining and inspection process is done manually so that it depends on the operator's skill. (3) different parts condition when received such as bending, crack, and welding results from the previous process are uneven. (4) there is no standard process using jigs and fixtures. (5) the absence of standard parameters, methods for the machining process. from the cause and effect diagram, in figure 5. the root cause of porosity in the remanufacturing lift arm process is (1) dirty, oil-contaminated, grease and inconsistent surface cleaning by grinding before welding. (2) the welding process is carried out without jigs, fixtures, parameters, and procedures as well as the inconsistency of checking after welding. (3) humid winds and conditions in the welding area. (4) difficult welding for inner diameter. (5) uneven welder skill. 4.4. improve phase improve stage is determining the proposed improvement of the root causes that have been done at the analyze stage. the improvement plan is carried out using the 5w + 1h method that contains plans and corrective actions for each of the factors causing product failure miss alignment and porosity that have accumulated 80% of the largest product failures from the overall product failures that occur in the welding and machining process. 4.4.1. improve plan product failure of miss alignment miss alignment product failure that occurs in the machining process is a major problem in the machining process based on joint discussion with the 5w + 1h method. miss alignment problem is reconditioned: the machining process changes from a manual process with 3 settings to 1 time setting with "jig". this changes from the previous process of series per 1-2 holes into 10 holes directly in 5 different places. the inspection or checking process can also be reduced by saryanto et al./oper. res. eng. sci. theor. appl. 3 (2) (2020) 24-38 34 eliminating the alignment checking/alignment from using the meter, caliper, ruler, thread and pendulum become unnecessary because the jig hole size has been adjusted to the part specifications. quality control focuses on checking dimensions with bore gauge and caliper and visual smoothing of machining results. the process is faster than the previous 4 days to 2 days so that it can increase the capacity of workshops that were previously 13-14 units to 24-25 units per month. the engine parameters with a speed of 200 rpm, feeding rate. 1,2 and feeding 0.5 1 mm per step. from the operator side, this process will change from grade 4 or multi-skill cnc operator to grade 2 semi-automatics. the jig referred to above is as in figure 6. 4.4.2. improve plan product failure of porosity product porosity failure that occurs in the welding process is a major problem in the machining process based on joint discussion with the 5w + 1h method. miss alignment problem is reconditioned: the welding process for inside diameter or the inner hole is replaced from before the manual process becomes semi-automatic by modifying the machine and making jigs and fixtures. with this process, a change occurred before welder did welding to just run the machine correlated with jigs and fixtures so that the welding results will be standard, even and the operator can prepare other parts in the queue. the making of welding procedure standard starts from the cleaning process with chemical and grinding, preheat up to a temperature of 120º celsius, welding and pwht with glass wool after finishing. in the surrounding area of welding made a cover or screen to keep the wind and humidity. the improvements to the welding process in question are shown in figure 7. 4.4. control phase this stage is the final phase of the dmaic phase. what is done at this stage is monitoring and controlling the results after improvement. process capability/sigma level, mapping sigma level into four blocks are salted and the calculation of the cost of poor quality (copq) is again carried out to determine the effectiveness of the results of improvements, in addition to the process of standardization of new processes that are also carried out to avoid similar failure products occurring in the future. figure 6. jig machining process design figure 7. jig semi automatic welding process design quality improvement of remanufacturing lift arm using six sigma methods in the heavyduty industry in indonesia: a case study 35 4.5.1. capability process/sigma level measurement (after improvement) based on data taken from the production and quality control department with a duration from the first week of july 2019 to the fourth week of november 2019, the total production for lift arm is 341 units with a total of 24 units of product failure, with a percentage of 7.03%. the calculation of process capability/sigma level is presented in table 4. table 4. calculation of process capability/sigma level after improvement item value total production 341 total product failure (defect) 24 ctq ( control to quality ) 2 dpmo ( defect per million opportunity) 140762,5 sigma level 2,43 table 4. shows that the capability of the welding and machining process after improvement is at 2.4 sigma with dpmo 140762.50 better than the conditions before improvement 1.91 sigma with dpmo 834586.47. 4.5.2. four block diagram (after improvement) referring to table 3 above and the same calculation as in the measure phase, the sigma level after improvement (2.43) can be mapped in the four-block diagram as in figure 8. figure 8. four block diagram product failure (defect) welding and machining process lift arm (after improvement) 4.5.3. calculation of cost of poor quality (copq) after improvement just as in the measuring stage, the calculation of the cost of poor quality (copq) is a calculation of the company's losses that must be borne by the product failure that occurs. cost of poor quality us$ 390,87 per pcs. the copq calculations after improvement can be seen in table 5. saryanto et al./oper. res. eng. sci. theor. appl. 3 (2) (2020) 24-38 36 table 5. calculation of cost of poor quality after improvement no month product failure (pcs) copq (usd) 1 july 2019 5 1954.35 2 august 2019 5 1954.35 3 september 2019 5 1954.35 4 october 2019 5 1954.35 5 november 2019 4 1563.48 total 24 9380.88 table 5. above can be interpreted that the loss that must be borne by the company due to product failure after improvement as much as usd 9380.88 decreased from before improvement usd 43386.57 equivalent to 78.37%. 4.5.4. standardization to avoid similar failure products, namely miss alignment and porosity lift arm in the process of welding and machining in the indonesian remanufacturing industry, socialization of the results of improvement to all relevant levels and the creation of new standards in the form of operational procedure standards (sop) related to welding and machining processes. 5. conclusion referring to the entire stages of this research, it can be concluded that improving quality by using the six sigma method in this study can reduce lift arm failure products in the welding and machining process and can increase company profits due to decreased product failure. this study generally strengthens previous studies that the six sigma method is effective in identifying and analyzing product failures, and can improve the capability/level of sigma to get better quality products. seeing the positive results contained in this study, it is recommended for further studies the use of the six sigma method in combination with other tools of quality can be used in improving quality in the other remanufacturing industries. to increase the repertoire of research using the six sigma method becomes more varied. acknowledgment: the authors would like to thank the master of the industrial engineering program at the mercu buana 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international journal of industrial engineering: theory, applications and practice, 16(3), 171-181. © 2020 by the authors. submitted for possible open access publication under the terms and conditions of the creative commons attribution (cc by) license (http://creativecommons.org/licenses/by/4.0/). http://creativecommons.org/licenses/by/4.0/ quality improvement of remanufacturing lift arm using six sigma methods in the heavy-duty industry in indonesia: a case study saryanto*, humiras hardi purba, aris trimarjoko , fuad fatahillah 1. introduction 1.1. general 1.2. motivating of research 2. literature review 2.1. quality improvement 2.2. remanufacturing industry 2.3. six sigma 3. research methodology 4. processing and analysis 4.1. define phase 4.2. measure phase 4.2.1. capability process/sigma level measurement 4.2.2. four block diagram 4.2.3. cost of poor quality (copq) mesurement 4.3. analyze phase 4.4.1. improve plan product failure of miss alignment 4.4.2. improve plan product failure of porosity 4.4. control phase 4.5.1. capability process/sigma level measurement (after improvement) 4.5.2. four block diagram (after improvement) 4.5.3. calculation of cost of poor quality (copq) after improvement 4.5.4. standardization 5. conclusion references plane thermoelastic waves in infinite half-space caused operational research in engineering sciences: theory and applications vol. 3, issue 1, 2020, pp. 1-15 issn: 2620-1607 eissn: 2620-1747 doi: https:// doi: 10.31181/oresta200101t * corresponding author. suncicat@uns.ac.rs (s. kocić-tanackov), ilijat@uns.ac.rs (i. tanackov), lmojovic@tmf.bg.ac.rs (lj. mojović), jpejin@uns.ac.rs (j. pejin), feta.sinani@unite.edu.mk (f. sinani) synergy effects of natural fungal inhibitors calculated by queuing model sunčica kocić-tanackov 1, ilija tanackov 2*, ljiljana mojović 3, jelena pejin 1, feta sinani 4 1 university of novi sad, faculty of technology, serbia, 2 university of novi sad, faculty of technical sciences, serbia, 3 university of belgrade, faculty of technology and metallurgy, serbia, 4 faculty of applied sciences, state university of tetovo, republic of north macedonia received: 24 october 2019 accepted: 28 january 2020 first online: 06 february 2020 original scientific paper abstract. model is based on the fungal birth and death processes. model is suited for petri dish. growth of fungal colony diameter in petri dish is described with exponential function. the value of diameter is declared as integer variable. integer variable with 1 mm increment is a discrete state of the system. time in the system is continuously. discrete states, continuous time and exponential growth are basis for the application of queuing systems in the petri dish. queuing system clearly separated the intensity of birth and death. difference between the birth intensity and death intensity is declared as the fungal life cycle. fungal life cycle variable is extra sensitive to the inhibitors effects. the procedures for parameters calculation are mathematically explained, as well as the significance of the obtained parameters. application of the model is performed for f. verticilloides in control conditions and at 16% concentration of basil and clove essential oils. life cycle minimum is the synergetic inhibition maximum. for f. verticilloides, synergetic inhibition maximum is at 42% of basil and 58% of clove in 16% essential oil concentration. key words: fungi, synergy, inhibition, essential oil, natural extract 1. introduction exponential probability distribution has exceptional constitutive characteristics such as maximum entropy, constant hazard function and it is memoryless. if the random evolution of a system is exponentially distributed, then this system is memoryless. in memoryless system, future state depends only on its present state, and not on any past states. the exponential distribution is the only distribution that kocić-tanackov et al./oper. res. eng. sci. theor. appl. 3 (1) (2020) 1-15 2 has memoryless property. also, exponential function with the base e = 2.718281, f(x)=ex has one unique feature. function f(x)=ex and her arbitrary derivation are identical, f(x)= f(x)  =…= f(x)(n)= ex. this feature is the basis of memoryless. mycelium growth (kang et al., 2003, vargas-arispuro et al., 2005; boyraz and özcan, 2006, judith et al., 2008, villa et al., 2009), hifae growth (larralde-corona et al., 1997 ; kampichler et al., 2004; diéguez-uribeondo et al., 2004), spore count (wagner et al., 2001) and fungal germination under extreme conditions (onofri et al., 2007) have exponential properties. alteration of the fungal colony diameter (roller and covill, 1999; tzortzakis and economakis, 2007; taniwaki et al., 2009, tang et al., 2009), fungal colonies in the presence of bacteria (brule et al., 2001), the development of fungal biomass (damar et al., 2006), the influence of various inhibitors (collopy-junior et al., 2006), essential nutritienats (ramirez et al., 2004) and the impact of radiation on the fungal growth (maity et al., 2008) can be described with exponential distribution. indirect evidence about exponential fungal dynamics we can find in the fungal degradation process (kim et al., 2000; schober and trösch, 2000; mal-nam et al., 2000; ruiz-aguilar et al., 2002; ishii et al., 2007, 2008; wakaizumi et al., 2009; tanaka et al., 2009, elsherbiny et al., 2017). fungal growth occurs in the system of self-replicator species (scheuring and szathmáry, 2001; chertov et al., 2004; milne, 2008; boswell, 2008). self-replicator growth system is the basis of analogy between fungal growth and exponential function. indirectly, through an exponential distribution, fungal systems are memoryless. analogously, the fungal growth is the markovian process. management of microbiological systems has significant economic, environmental and health aspects. the microbiological control of foods is particularly significant. in the case of fungi, control of growth by using inhibitors is based on compromise. inhibition need to meet the requirements of microbiological quality and in the same time, to preserve the nutritional, health and organoleptic properties of food. the intensity of fungal inhibition is commonly investigated with the agar plate method, based on the measurement of the colony diameter, in the presence of essential oil or herbal extract during the time. (nielsen and rios, 2000; guynot et al., 2003; suhr and nielsen, 2003; benkeblia, 2004; pereira, et al., 2006; sheng-hsien et al., 2007; lopez-malo et al., 2007; fung and zheng, 2007; tullio et al., 2007; soylu et al., 2007; viuda-martos et al., 2007, 2008; tzortzakis, 2009; reddy et al., 2009; tatsadjieu et al., 2009, tanackov s. et al., 2014; badea et al., 2016; llana-ruiz-cabello et al., 2016 tancinová et al., 2018, 2019). inhibitors can be synthetic and natural. use of synthetic inhibitors is not always desirable, especially in food. essential oils and plant extract are the main natural inhibitors. a special analytical challenge is the potential synergic effects in the application of inhibitors. synergy inhibitors may improve the composition of the combinatorial selection of inhibitors with greater antifungal effect and more acceptable organoleptic characteristics. the inhibition intensity is determined by the comparative method a posteriori. this method is based on determining the initial birth rate without inhibition. in the presence of inhibitors, a reduced birth rate is obtained. the comparison (difference) synergy effects of natural fungal inhibitors calculated by queuing model 3 of these two intensities represents the difference in the birth intensity, again. the intensity of dying due to inhibitory effects remains unknown. individual inhibitor intensities can be estimated by standard procedure, but the synergistic effect of two or more inhibitors is difficult to describe by existing models. considering the growth of colonies as a stochastic system opens up the possibility of applying a queuing system (qs). the birth and death intensities in microbiology analysis are analogous to the intensities of clients arrivals and clients servicing from queueing systems. the capacity of qs models has been proven in many fields of research (fazlollahtabar anf gholizadeh, 2019a; fazlollahtabar and gholizadeh, 2019b; tanackov i. et al, 2019a, tanackov i. et al, 2019b) 2. materials and methods 2.1. experimental setup for the antifungal activity testing, commercially available, food grade clove and basil extract was provided from etol “tovarna arom in eteričnih olj” d.d., celje, slovenia. as test microorganisms, the following fungal strain from the genus fusarium was used: f. verticillioides (sacc.) nirenberg (syn. f. moniliforme sheld.). the fungal culture were isolated from cakes and maintained on potato dextrose agar (pda) at 4c as a part of the collection of the laboratory for food microbiology at the faculty of technology, university of novi sad, serbia. the agar plate method was applied in the testing of the antifungal activity of extracts. the basic medium for the antifungal tests was pda. the medium was divided into equal volumes (150 ml), poured into erlenmeyer (250 ml) flasks and autoclaved at 121ºc for 15 min. concentrations 0 i 0.16% (v/v) were tested self-contained extracts, and basil-clove combinations: 50%:50%; 75%:25% i 25%:75%. the extracts were added to medium after cooling to 45c. the culture medium was then poured into sterile petri dishes (9 cm), 12 ml into each plate. to prepare the conidial suspension dispute we used the seven-day culture f. verticillioides grown on pda. suspension of fungi prepared in a medium which contained 0.5% tween 80 and 0.2% agar dissolved in distilled water and were adjusted to provide initial spore count of 106 spores/ml by using a haemocytometer. for each extract dose and fungi species, including the controls were centrally inoculated by spreading 1 µl of spore suspension (103 spores/ml) using an inoculation needle. after inoculation, the petri plates were closed with parafilm. the efficacy of the treatment was evaluated by daily measurement of the diameter of radial colony growth during 14 days of incubation at 25 2ºc (table 1.). 2.2. markovian process in petri dish exponential parameter (whitt, 2018; tanackov et al., 2019) of fungal growth  is a function of the intensity of birth  and death , =f(,), provided . in petri dish queuing system, number of microorganisams determines the state of the system. description with markovian birth-death process is based on the exponential intensity of birth  and death . if the initial state of the system is defined with zero kocić-tanackov et al./oper. res. eng. sci. theor. appl. 3 (1) (2020) 1-15 4 microorganisms, then the initial intensity of death  is also equal to zero. the system goes into a state one microorganism with intensity . simultaneously with the transition to a state one microorganism, death process with intensity  is started. in the same time with the transition to a state with one microorganism, process of death with intensity  start. from the state with one microorganism, system exceeds to the state with two microorganisms by the same intensity of the birth, . if the system implemented another birth with intensity , and the first micro-organism has not finished the process of dying, the system exceeds in to the state two microorganisms. the dying process of the first microorganism is not complited and the second microorganism begins the process of dying. therefore, the intensity of death in a state two microorganisms is equal 2. system with the same birth intensity exceeds in the next state, and with multiplicity intensity of death exceeds to a previous state. if the number of microorganisms is equal to k in the system, then all k microorganisms are in the process of dying. therefore, the intensity of dying in system with k microorganisms is equal to k. system with k microorganisms cannot realize (k +1) intensity of the death. this relationship between the intensity of birth  and intensity of death , can be described with exponential development of fungal colonies in petri dish (fig. 1). figure 1. fugal colony, exponential development at asymptote diameter, the intensity of birth and k multiplicated death are identical, =k. the value of the colony diameter is equal to asymptote value which is maximal colony diameter dmax. this point have a crucial importance for solving the explicit form of the function =f(,). the solution to the intensity of dying is now synergy effects of natural fungal inhibitors calculated by queuing model 5 available, initially in steady-state mode. if necessary, the intensity of dying can be considered as non-stationary in time, and additional possibilities are consideration of non-stationary intensity of dying in conditions of different temperatures, humidity, initial inoculation or other important microbiological parameters. 2.3. petri dish queuing system marcovian processes in the system are determined with the time and state of the system. time in the system can be discretely and continuously. state of the system can be discrete and continuous, also. consecutive time intervals for fungal colony diameter measurements were determined by si unit, time. these intervals are discrete, usually 1 day. measurement of fungal colony diameters in petri dish, are recorded in the si unit of length, in millimetres or centimetres. development of fungal colonies declared this dimension as a variable. diameters values are represent in the time series. the time is independent variable, and the diameter is dependent variable. due to the nature of the fungal colony development, the total number of fungi cannot be precisely determined. all elements of the fungal colony development are synthesized in the diameter. diameter is a generalized variable of the system. the state of the fungal colony is continuous variable. fungal colony diameter (d0, d1, d2, d3, …, dk), f(ti)=di time series in petri dish, for discrete time intervals t, (t0, t1, t2, t3, …, tk), t(i+1) = ti+t , k0, 1, 2, … , n have a form of exponential function: )e1(dd)t(f k t m axkk − −== k0, 1, 2, … , n (1) a high approval of empirical and theoretical data is necessary condition for regular description of the fungal colony diameter with the exponential function. this agreement can be expressed with the correlation coefficient. the linear regression of empirical and theoretical data must be described with fulfil values of parameters a1 and b0, in addition to the high value of correlation coefficient r1. a fulfilment of these conditions gives a representative description of the empirical time series with exponential theoretical function. discrete values of colony diameter can be obtained with integer function values from representative function.    )e1(dint)t(f)t(s tmax −−== (2) approximation of f(t) with the function s(t) depends from the increment size. smaller increment has a better approximation. for fungal colony diameter measuring in millimetres, integer increment 1 mm gives a satisfactory approximation. with discrete values of the colony diameter, are fulfilment conditions for the application of markovian process with continuous time. continuous time with discrete states of the system allows the petri dish to formation markovian queuing system (fig. 2). kocić-tanackov et al./oper. res. eng. sci. theor. appl. 3 (1) (2020) 1-15 6 figure 2. petri dish markovian queuing system explicit form of the function =f(,) have two unknown variables,  and . for the calculation of their values, it is necessary to define a system of two equations. the first equation is obtained from initial conditions. at the beginning of growth, at t=0, the intensity of death is equal to zero, =0. intensity of birth  is equal to: dmax(1−e−t)t=0 = (dmaxe−t) t=0 =    = dmax (3) the second equation can be obtained from the development of state and calculation of the average number of clients in the markovian system (fig. 3). figure 3. development of markovian’s system mold colonies in petri dishes differential equations of queuing states in the stationary mode, with constant values of birth and death intensity (t)= =const and (t)==const, are: 01100 pppp0)t(p   =+−== 0 2 220 2 21101 p 21 1 ppp0p2ppp0)t(p          =+   −=+−−== 0 3 3202 3 21112 p 321 1 pp3p 2 0p3pp2p0)t(p          =+   −=+−−== synergy effects of natural fungal inhibitors calculated by queuing model 7 . . . . . 0 k k1kkk1kk p !k 1 ppppp0)t(p         =−−−== +− . . . . . 0 n nn1nn p !n 1 ppnp0)t(p         =−+== − (4) in the n previous equations we have (n +1) unknown variables, k0, 1, 2, … , n. equation needed to solve this system of equations, we can obtaine from the basic requirements of probability states: 1p !n 1 ...p !k 1 ...pp1pp...ppp 0 n 0 k 00n1n210 =        ++        ++   +=+++++ − from these (n +1) equations, probability of state p0 is:          ==         =        ++        ++   + = = n 0k k0 n 0k k 0 nk 0 0 !k 1 1 p1 !k 1 p !n 1 ... !k 1 ...1(p (5) recurrent equation for calculating the probabilities of the queuing system states is obtained from (4) and (5):                  =        = = n 0k k k k0 k k !k 1 !k 1 pp !k 1 p (6) the average number of clients in the system is obtained from the (6):                   −          =                  =                  =  = = − = = = = = n 0k k n 1s 1s n 0s n 0k k s n 0s n 0k k s n 0s s !k 1 )!1s( 1 !k 1 !s s !k 1 !s 1 sps (7) the exponential function   e may be written as a taylor series: kocić-tanackov et al./oper. res. eng. sci. theor. appl. 3 (1) (2020) 1-15 8    = =+         +         +         +         =         e !3!2!1!0!n 3210 0n n  1 e e !k 1 )!1s( 1 lim 0k k 1s 1s n ==                   −      =  = − → for a large enough n, we can adopt 1 !k 1 )!1s( 1 n 0k k n 1s 1s                    − = = − average number of clients in the system is equal:   =  = n 0s sps (8) in stationary mode of ergodic marcovian queuing system, this value (8) is equal to the average diameter of the fungal colony dave. from birth intensity initial conditions and from average number of clients, the value of death intensity  is: ave aveave d dd dd  =   =   = maxmax (9) values dmax,  and dave we can calculated from experimental measurements of petri dish. dmax is the parameter of the fungal colony asymptote.  is the parameter of the exponential function.  is calculated by the heuristic search of the colony diameter time series d0, d1, d2, d3, … , dk, parameter dave is equal to:  ++++ == = k i k iave k dddd d k d 0 210 ...1 (10) in a long time of measurement, average diameter dave converge to asymptote of fungal colony dmax. max 210 ...limlim d k dddd d k k ave k = ++++ = →→ (11) also, the intensity of death converges to the growth rate. =  = ++++  = →→→ max max 210 max lim ... limlim d d k dddd d kkkk (12) synergy effects of natural fungal inhibitors calculated by queuing model 9 therefore, entry in to the deep asymptotic region should be limited. the introduction of another diameter dk+1 from time series in to the dave calculation (11), should be stopped because of small differences between successive diameter, dkdk+1. significance of this difference, p= (1−q) can be directly set and calculated from the integral equation (13): qeed t t eddted kk k k tt k kt t t t −== − ++ + −−+−− )()1( 11 1 max 1 maxmax (13) adding and subtracting the value of 1, we relate the diameter and significance (14): qeedeed kkkk tttt −−−−=−+−− ++ −−−− ))1(1()11( 11 maxmax (14) successive diameters are )e1(dd k t m axk  −= i )e1(dd 1k t m ax1k + + −= , and limit of the diameter difference dend is equal to (15) : endkkkk d d q ddqddd =  −−− ++ max 11max )()( (15) equation (14) provides reliable intensity of birth  and death , with the required significance p. 2.4. results the calculation of all relevant parameters is given in table 2. calculated limit difference dend for significance p=0.95 satisfies all the requirements of measuring up to 14 days. empirical results of measuring diameter and theoretical exponential functions linear regression parameters a and b were a1 and b0, in control conditions and 16% concentration for all compositions of basil and clove essential oils. the correlation coefficient is high r2 0.99, for all conditions, also. calculation of the parameters  i dmax is valid. parameter dave is obtained from (11) as the average diameter of fungal colonies. birth intensity  is obtained form (3), and death intensity  is obtained from (9) 3. discusion in this example, approximated diameter converges to value 120.154 mm for 50% basil and 50% clove in 16% essential oil concentration. this value is larger than the approximated diameter for control conditions, 117.176 mm. from diameter comparation, synergetic stimulation off fungal growth is deduced by classic approach. however, the diameter does not express explicit morphological changes. morphological changes are contained in the parameter of the life cycle. the life cycle of fungi represent the subtraction between birth intensity and death intensity. subtraction between birth intensity in control conditions control=9,608 mm/day and the death intensity in control conditions control=2,058 mm/day is the life cycle of fungi f. verticilloides in control conditions control=7,594 mm/day. life cycle control value is constant for all range of concentration and arbitrary inhibitors kocić-tanackov et al./oper. res. eng. sci. theor. appl. 3 (1) (2020) 1-15 10 relation. intensity of birth and death values, basil clove i basil clove respectively, at 16% concentration for different relations basil and clove, do not have a constant value. these values are functions of relations between basil and clove. the calculations of the f. verticilloides life cycles in control condition and basil-clove synergetic conditions are given in table 3. graphic presentation of the results in table 3 is given in fig. 4. figure 4. f. verticilloides life cycle dynamic from fig. 4 is the apparent dynamics of birth and death process for the f. verticilloides. birth process intensity basil clove on the 16% concentration has pronounced variations of value. birth intensity at 100% basil in 16% essential oil concentration (8.850 mm/day) have higher birth intensity from 100% clove in 16% essential oil concentration (6,197 mm/day). with the increasing participation of clove in 16% essential oil concentration, come to a sudden fall of the birth intensity. minimum intensity birth is about 60% basil and 40% clove participation. with further increase participation of clove, comes an increase in the intensity of birth. stabilization of about 75% of clove participation, remains constant until the end of the domain. the intensity of the death basil clove at 16% concentration has not pronounced variations. death intensity have basil clove are less than the death intensity in control conditions. lacking the expected death intensity increase. however, reducing the intensity of growth directly reduces the quantity of the system, and thus the intensity of dying. birth intensity minimum is at 50% basil and 50% clove. death intensity minimum is at 25% basil and 70% clove. approximate function of the life cycle basil clove = basil clove − basil clove , has a minimum at 42% basil and 58% clove. f. verticilloides life cycle minimum is the maximum basil-clove synergetic inhibition (fig. 4.). synergy effects of natural fungal inhibitors calculated by queuing model 11 equilibrium line eq gets points through 100% of the selected concentrations of two inhibitors. equilibrium line is a set of values that is linearly proportional to the inhibitor participation in a 16% essential oil concentration. the synergetic stimulation zone (ss) is above from equilibrium line the synergetic inhibitona zone (si) is below from equilibrium line. area from equilibrium line to the life cycle control level line is the synergic stimulation area. the values of the life cycle can vary about equilibrium line. in such variations, values above the equilibrium line are synergistic stimulation, even though they are less from the control level value. synergetic inhibition values are below the equilibrium line. in the shown case, for 16% concentration of essential oil relationships basil and clove, all values of the life cycle are under equilibrium line. selection of essential oils have a distinct inhibiting effect of synergy in the whole area, with a pronounced minimum of 42% basil and 58% clove. standard models based on the difference in growth intensity between non-inhibited and inhibited sample, cannot directly express the maximum synergistic effect of the two inhibitors. the formation of the two-dimensional function of the action of two inhibitors using standard models requires an incomparably larger number of experiments with different concentrations, and one post-process application of some heuristic model. the results show that the qs model is more accurate, reliable and less expensive for research. 4. conclisuions queuing model has a high sensitivity. the basis of sensitivity is in intensity differentiation. these intensities are obtained from growth rate. at the same time, it is necessary to percieve a clear distinction between growth rate and life cycle. growth rate is a feature of the of birth and death process. the life cycle is a feature of the birth and death intensitys. the queuing model has limitations. in the case of higher concetrations, application of inhibitors may delay the start of fungal growth. during the asymptotic inhibition, birth intensity is equal to zero. changes in diameter does not correspond to exponential function. this period lasts until the beginning of delayed growth. start of growth changes the value of the birth intensity. existence of two values for the same intensity is a 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(2009). acrylamide degradation by filamentous fungi used in food and beverage industries, journal of bioscience and bioengineering, 108, 391-393. © 2020 by the authors. submitted for possible open access publication under the terms and conditions of the creative commons attribution (cc by) license (http://creativecommons.org/licenses/by/4.0/). operational research in engineering sciences: theory and applications vol. 3, issue 1, 2020, pp. 72-88 issn: 2620-1607 eissn: 2620-1747 doi: https:// doi.org/10.31181/oresta2001072v * corresponding author. veskos@sf.bg.ac.rs (s. vesković), s.milinkovic@sf.bg.ac.rs (s. milinković), borna.abramovic@fpz.unizg.hr (b. abramović), ivica.ljubaj@fpz.unizg.hr (i. ljubaj) determining criteria significance in selecting reach stackers by applying the fuzzy piprecia method slavko vesković 1*, sanjin milinković 1, borna abramović 2, ivica ljubaj 2 1 university of belgrade, faculty of transport and traffic engineering, serbia 2 university of zagreb, faculty of transport and traffic sciences; croatia received: 12 march 2020 accepted: 01 april 2020 first online: 06 april 2020 original scientific paper abstract: handling facilities play the essential role in the work of the complete transport chain, especially when performing operations at ports or container terminals. in this paper, a list of 15 criteria for the evaluation and selection of a reach stacker for the container terminal in belgrade were formed in a double hierarchical structure, with an equal number of the elements. there are three main groups of the criteria: economic, technological and technical, each containing a total of the five sub-criteria. the survey involved 15 decision-makers, who evaluated all the criteria. to determine the individual significance of each criterion, the fuzzy pivot pairwise relative criteria importance assessment (i.e. fuzzy piprecia) method was applied. the results showed that the most essential criteria belong to the technology group. key words: reach stacker, container terminal, fuzzy piprecia 1. introduction “railway integral transport” (rit) limited liability company (žit d.o.o.) belgrade was founded in 1983 as a subsidiary of železnice srbije (jsc serbian railways), when a container terminal was built in the area of the former belgrade central railway station. during 2016, the rit terminal has been relocated to the new location at the belgrade marshalling yard. one of the company’s primary activities is the provision of terminal services in the international container transportation of cargo, such as the handling, loading and containerization of goods, and the transportation of loaded and empty containers. due to limited space, the maximum dispatch and distribution capacity of the terminal is about 15,000 intermodal units (containers) annually determining criteria significance in selecting reach stackers by applying the fuzzy piprecia method 73 the main technological process of the transhipment of containers from the rail mode to the road transportation mode and vice versa, as well as the storage of loaded and empty containers in the area of the terminal itself, is carried out by the reachstacker-type container handlers belloti (the load capacity being 45 t) and kalmar (the load capacity being 42 t). it should be noted that both reach stackers are over 20 years old. in order to perform the primary operations at the terminal, two tracks of a length of 250 m and a shunting track for shunting units of 250 m in length are available. at the terminal, there are also three tracks in the shunting and dispatching groups of the belgrade marshalling yard used by cranes and for the movements of trains from the terminal, as well as the storage of spare wagons. the construction of the phase 2 of the container terminal, i.e. the expansion to the fifth marshalling group of the belgrade marshalling yard, would enable the conditions for the rit terminal to process over 80,000 containers per year, or about 120,000 teu units. according to the analysis conducted in the period from 2016 to 2019, the rit terminal processes about 40% of all the containers arriving by rail, which is about 15% of all the containers arriving in serbia. of this, about 90% of the containers processed by the rit terminal come from the rijeka – belgrade–rijeka line (three trains running on that route weekly). the completion of the phase 1 of the new terminal is expected to introduce the fourth pair of trains, and the fifth pair of trains in the year 2021. this paper aims to evaluate and determine the significance of the criteria by which the reach stacker selection will be made. all of the above data indicate the need to expand the range of the handling equipment, for which reason buying at least one reach stacker is a necessity. the rest of the paper is structured into several chapters. in chapter two, a brief description of the volume of business at the container terminal and some forecasts for this year and for next year are given. in chapter three, the fuzzy piprecia method applied in the paper in order to determine the significance of the criteria is presented in detail. chapter fur of the paper deals with a case study, detailing the input parameters and the calculation procedure. in chapter five, the conclusion concerning the continuation of this research is presented. 2. a short description of the extent of work for the terminal taking into account the expected increase in the scope of work (figure 1), it is necessary that new reach stackers should be purchased, since the installation of a bridge crane for the transhipment of intermodal units is not foreseen in the first phase of the construction and operation of the terminal. given the state of the existing two reach stackers, it is necessary to procure two new ones so as to ensure the reliability and continuity of the performance of the basic technological operations at the terminal. vesković et al./oper. res. eng. sci. theor. appl. 3 (1) (2020) 72-88 74 figure 1. the achieved and the planned scopes of work at the rit terminal by constructing a large logistics centre (figure 2), which is planned to be operated in the makiš field, the workload might also double. figure 2. the plan for the construction of the new rit terminal determining criteria significance in selecting reach stackers by applying the fuzzy piprecia method 75 3. methods 3.1. operations on fuzzy numbers a fuzzy number a on r to be a tfn if its membership function ( ) a x : r→[0,1] is equal to the following equation (1): ( ) 0 a x l l x m m l u x x m x u u m otherwise  −   −  − =   −   (1) from equation (1), l and u denote the lower and the upper bounds of the fuzzy number a , and m is the modal value for a . the tfn can be denoted by ( , , )a l m u= . the operational laws of tfn 1 1 1 ( , , )a l m u= and 2 2 2 ( , , )a l m u= are displayed as the following equations. addition: 1 1 1 ( , , )a l m u= 1 2 1 1 1 2 2 2 1 2 1 2 1 2 ( , , ) ( , , ) ( , , )a a l m u l m u l l m m u u+ = + = + + + (2) multiplication: 1 2 1 1 1 2 2 2 1 2 1 2 1 2 ( , , ) ( , , ) ( , , )a a l m u l m u l l m m u u =  =    (3) subtraction: 1 2 1 1 1 2 2 2 1 2 1 2 1 2 ( , , ) ( , , ) ( , , )a a l m u l m u l u m m u l− = − = − − − (4) division: 1 1 1 1 1 1 1 2 2 2 2 2 22 ( , , ) , , ( , , ) a l m u l m u l m u u m la   = =     (5) reciprocal: 1 1 1 1 1 1 1 1 1 1 1 1 ( , , ) , ,a l m u u m l − −   = =     (6) vesković et al./oper. res. eng. sci. theor. appl. 3 (1) (2020) 72-88 76 3.2. the fuzzy pivot pairwise relative criteria importance assessment (i.e. fuzzy piprecia) method the piprecia method in a crisp form has been developed in (stanujkić et al., 2017). the fundamental advantage of the piprecia method lies in the fact that it allows criteria to be evaluated without their prior sorting by importance, which is not the case with the fuzzy swara method. today, the largest number of the problems of multicriteria decision-making are solved by applying group decisionmaking. in such cases, especially with an increase in the number of the decisionmakers involved in the fuzzy model, piprecia achieves its advantages. the fuzzy piprecia method consists of the 11 steps that are shown below (stević et al., 2018; đalić et al. 2020). step 1. forming the required benchmarking set of criteria and forming a decisionmaking team. sorting the criteria according to the marks from the first to the last, which means that they need to be sorted unclassified. therefore, their significance does not play any role at all in this step. step 2. in order to determine the relative importance of the criteria, each decisionmaker individually evaluates the pre-sorted criteria by starting from the second criterion, as in equation (7). 1 1 1 1 1 1 j j r j j j j j if c c s if c c if c c − − −    = = =    (7) where r j s denotes the criteria assessment made by the decision-maker r. in order to obtain a matrix j s , it is necessary to perform the averaging of the matrix r j s by using the geometric mean. the decision-makers evaluate the criteria by applying the scales defined in tables 1 and 2. the second and third steps of the developed method are closely dependent on one another, and new fuzzy scales are defined in order to meet the second and third steps of the fuzzy piprecia method. if the facts that the nature of fuzzy number operations and that, in the third step, the values js are subtracted from number two are taken into consideration, then it is required that these scales be defined. it is important to note that, by defining these scales, the appearance of number two is avoided, which might cause difficulties and lead to wrong results in the case of calculation. therefore, no other previously developed fuzzy scales, but only the scales defined in this paper, may be used. determining criteria significance in selecting reach stackers by applying the fuzzy piprecia method 77 table 1. the criteria assessment scale 1-2 scale 1-2 l m u dfv an almost equal value 1 1.000 1.000 1.050 1.008 slightly more significant 2 1.100 1.150 1.200 1.150 moderately more significant 3 1.200 1.300 1.350 1.292 more significant 4 1.300 1.450 1.500 1.433 much more significant 5 1.400 1.600 1.650 1.575 dominantly more significant 6 1.500 1.750 1.800 1.717 absolutely more significant 7 1.600 1.900 1.950 1.858 when a criterion has greater importance concerning the previous one, an assessment is made by using the above scale (table 1). in order to make it easier for the decision-makers to evaluate the criteria, the table shows the defuzzified value (dfv) for each comparison. table 2. the criteria assessment scale 0-1 scale 01 l m u dfv 0.667 1.000 1.000 0.944 slightly less significant 0.500 0.667 1.000 0.694 moderately less significant 0.400 0.500 0.667 0.511 less significant 0.333 0.400 0.500 0.406 really less significant 0.286 0.333 0.400 0.337 much less significant 0.250 0.286 0.333 0.288 dominantly less significant 0.222 0.250 0.286 0.251 absolutely less significant when a criterion is of less importance compared to the previous one, an assessment is made by using the above scale (table 2). step 3. determining the coefficient jk : 1 1 2 1 j j if j k s if j = = =  −  (8) step 4. determining the fuzzy weight jq : 1 1 1 1 jj j if j qq if j k − = =  =     (9) step 5. determining the relative weight of the criterion j w : vesković et al./oper. res. eng. sci. theor. appl. 3 (1) (2020) 72-88 78 1 j j n j j q w q = =  (10) in the following steps, the inverse methodology of the fuzzy piprecia method needs to be applied. step 6. performing the assessment of the above-defined applied scale, this time starting from the penultimate criterion. 1 1 1 1 ' 1 1 j j r j j j j j if c c s if c c if c c + + +    = = =    (11) where ' r j s denotes the criteria assessment made by the decision-maker r. it is, again, necessary to perform the averaging of the matrix r j s by applying a geometric mean. step 7. determining the coefficient 'jk : 1 ' 2 ' j j if j n k s if j n = = =  −  (12) where n denotes the total number of the criteria. specifically, in this case, it means that the value of the last criterion is equal to the fuzzy number one. step 8. determining the fuzzy weight 'jq : 1 1 '' ' jj j if j n qq if j n k + = =  =     (13) step 9. determining the relative weight of the criterion 'jw : 1 ' ' ' j j n j j q w q = =  (14) step 10. in order to determine the final weights of the criteria, it is first necessary to perform the defuzzification of the fuzzy values jw and 'jw as follows: determining criteria significance in selecting reach stackers by applying the fuzzy piprecia method 79 1 '' ( ') 2 j j j w w w= + (15) step 11. checking the results obtained by applying the spearman and pearson correlation coefficients. 4. determining criteria significance when selecting a reach stacker by applying the fuzzy piprecia method for the evaluation and selection of a reach stacker, a total of the 15 criteria formed into the two levels of the hierarchical structure were applied. as it is essential to obtain objective results, the hierarchical structure should be balanced. this means that each major criterion has an equal number of criteria. this problem was to some extent addressed in (markovic et al., 2020), where it was found that it was necessary to form a hierarchical structure with an equal number of the elements at the lower levels of the hierarchy. therefore, this paper approached the formation of a group of criteria in this manner, with the three main criteria inclusive of the five sub-criteria in each group. ce economic: ce1 – the cost ce2 – the supply of spare parts ce3 – fuel consumption when manipulating one hour of operation ce4 – the tire type and price ce5 – maintenance costs cth technological: cth1 – life expectancy cth2 – the capacity cth3 – the number of the teus processed as per unit of time, cth4 – manipulative abilities, cth5 – the lift height ctr technical solutions: ctr1 – the engine type ctr2 – the gross mass (the net mass) ctr3 – the engine power ctr4 – the lift speed ctr5 – the driving speed vesković et al./oper. res. eng. sci. theor. appl. 3 (1) (2020) 72-88 80 as already pointed out, the three main criteria are economic (ce), technological (cth) and applied technical solutions (ctr). these three criteria cover the whole aspect of the operation of a reach stacker, i.e. the performance of the necessary technological activities at the terminal. the first set of the economic criteria, which describe the financial and economic aspects of the acquisition and exploitation of a reach stacker, include the following sub-criteria: • the purchase price on the market (ce1) is expressed as a numerical value. the goal of every terminal operator is to achieve the top-notch performance of a reach stacker for minimum investment. ce1 → min. • the supply of spare parts (ce2) is essential for the reliable operation of a reach stacker and the quality maintenance system. this parameter is represented as a linguistic variable, and the same can be wrong, good, very good or excellent. ce2 → max. • manipulation fuel consumption (ce3) is expressed as per hour of operation. this parameter directly affects the exploitation cost. ce3 → min. • the tire type (ce4) directly influences its price, and as such is classified into this parameter group. the purchase and replacement of tires are a significant source of the operation cost. ce4 → min. • maintenance costs, if the result of the technological process of the maintenance process can significantly affect the choice of a type of a reach stacker. they cover all the aspects of the maintenance process (both current and investment) and are expressed every year. ce5 → min the second group consists of the technological criteria, which describe the technological parameters and characteristics of a reach stacker, the sub-criteria being as follows: • the expected service life (cth1) is expressed as a numerical value. the manufacturer proposes the expected service life in quality maintenance conditions, but the value of this parameter is also determined by customers’ experience at the terminals. cth1 → max. • the reach stacker capacity (cth2), i.e. the maximum payload declared by the manufacturer, is essential for operators, as it may be a limiting factor in processing certain types and intermodal units and their loads. cth2 → max. • the number of the teus processed as per unit of time (cth3) represents the output, i.e. the processing power of a reach stacker, thus determining the processing power and capacity of the terminal. cth3 → max. • manipulative abilities (cth4) are an essential parameter for the operation of a reach stacker, especially so in confined spaces. this parameter is presented as a linguistic variable, and the same can be weak, satisfactory, good and excellent. cth4 → max. • the lift height (cth5) is a parameter declared by the manufacturer and expressed in meters or in the number of the containers that can stack the height for the first and second stack orders. cth45 → max. determining criteria significance in selecting reach stackers by applying the fuzzy piprecia method 81 the third group is represented by the applied technical solutions in a reach stacker, namely including the following sub-criteria: • the motor type (ctr1) is expressed as a linguistic value. usually, diesel engines are the euro3, euro4 or euro5 type. the engine type affects fuel consumption, thus also making an influence on the environment. the negative impact of this parameter by engine type is high, medium and low, while the lowest negative environmental impact is desirable. ctr1 → min. • the reach stacker gross mass (ctr2) is a parameter declared by the manufacturer. it is desirable that this parameter should be as high as possible for the purpose of the stability of operation, i.e. for the purpose of lifting heavy intermodal units. ctr2 → max. • the engine power (ctr3) is a parameter declared by the manufacturer. it is desirable for this parameter to be as high as possible, because of the reliability of the work, i.e. the low load of a reach stacker. ctr3 → max. • the lifting speed (ctr4) is a parameter declared by the manufacturer. this parameter is expressed in m/s and is given for the following lifting conditions: empty/full. in the model, the value of lifting a full container is considered. ctr4 → max. • the driving speed (ctr5) is a parameter declared by the manufacturer. this parameter is expressed in km/h and is given for the conditions of the movement of a reach stacker with empty/full intermodal units. in the model, the value of the maximum driving speed with full intermodal units is considered. ctr5 → max. ctr5 – the travel speed (km/h) empty/full the evaluation of the criteria was performed by using a linguistic scale involving quantification into fuzzy triangle numbers. table 3 shows the evaluation of the criteria for fuzzy piprecia and inverse fuzzy piprecia carried out by the decisionmaker. there are a total of 15 decision-makers, whose structure is viewed from the following three aspects: • the profession, i.e. what activity (function) the expert performs, • the expert’s competence field, • the expert’s work experience. when the expert’s occupation is in question (figure 3), three occupational groups are covered. the largest number of the experts, i.e. 47% of them in total, belong to the group of traffic and mechanical engineering university professors, only to be followed by those employed in the economic sector (practitioners), accounting for 33%, and finally, the employed in design institutions in the transportation field, accounting for 20%. vesković et al./oper. res. eng. sci. theor. appl. 3 (1) (2020) 72-88 82 figure 3. the structure of the experts by occupation the structure of the experts in the competence field is shown in figure 4. the survey included 47% of the experts in railway transport, 20% of the experts employed in logistics and mechanical engineering, and 13% of the experts working in road transportation. figure 4. the structure of the experts by the competence field the last analysis refers to the experience (the experts’ work experience) and is shown in figure 5. the largest number of the experts included in the survey, i.e. 40% of them, have a work experience ranging from 21 to 30 years; a total of 27% have a determining criteria significance in selecting reach stackers by applying the fuzzy piprecia method 83 work experience ranging from 11 to 20 years, and 20% of the experts have a work experience exceeding 30 years. the smallest number of the experts, actually 13% of them, have a work experience of less than ten years. figure 5. the structure of the experts by work experience table 3. the criteria ratings for fuzzy piprecia and inverse fuzzy piprecia for the main criteria pipr. c2 c3 pipr-i c2 c1 dm1 1.200 1.300 1.350 0.250 0.286 0.333 dm1 1.500 1.750 1.800 0.400 0.500 0.667 dm2 1.000 1.000 1.000 1.000 1.000 1.000 dm2 1.000 1.000 1.000 1.000 1.000 1.000 dm3 1.200 1.300 1.350 0.286 0.333 0.400 dm3 1.400 1.600 1.650 0.400 0.500 0.667 dm4 1.000 1.000 1.000 1.200 1.300 1.350 dm4 0.400 0.500 0.667 1.000 1.000 1.000 dm5 1.200 1.300 1.350 0.286 0.333 0.400 dm5 1.400 1.600 1.650 0.400 0.500 0.667 dm6 1.000 1.000 1.000 0.400 0.500 0.667 dm6 1.200 1.300 1.350 1.000 1.000 1.000 dm7 1.400 1.600 1.650 1.000 1.000 1.000 dm7 1.000 1.000 1.000 0.286 0.333 0.400 dm8 1.300 1.450 1.500 1.100 1.150 1.200 dm8 0.500 0.667 1.000 0.333 0.400 0.500 dm9 1.300 1.450 1.500 1.000 1.000 1.000 dm9 1.000 1.000 1.000 0.333 0.400 0.500 dm10 1.000 1.000 1.000 1.000 1.000 1.000 dm10 1.000 1.000 1.000 1.000 1.000 1.000 dm11 1.100 1.150 1.200 0.250 0.286 0.333 dm11 1.500 1.750 1.800 0.500 0.667 1.000 dm12 1.200 1.300 1.350 0.500 0.667 1.000 dm12 1.100 1.150 1.200 0.400 0.500 0.667 dm13 1.500 1.750 1.800 1.000 1.000 1.000 dm13 1.000 1.000 1.000 0.250 0.286 0.333 dm14 1.100 1.150 1.200 1.000 1.000 1.000 dm14 1.000 1.000 1.000 0.500 0.667 1.000 dm15 1.300 1.450 1.500 0.286 0.333 0.400 dm15 1.400 1.600 1.650 0.333 0.400 0.500 av 1.187 1.280 1.317 0.704 0.746 0.806 av 1.093 1.194 1.251 0.542 0.610 0.727 note: as has been shown in the method steps, it ranges from the second criterion for the fuzzy piprecia method, and the penultimate criterion for the inverse fuzzy piprecia method, i.e. c2 in the first column and also c2 in the third column. based on the evaluation of the criteria and equation (7), the matrix sj is formed. vesković et al./oper. res. eng. sci. theor. appl. 3 (1) (2020) 72-88 84 applying equation (8), these values are subtracted from number two. following the rules of operations with the fuzzy numbers of the kj matrices, the following is obtained: according to equation (8), the value 1 (1.000, 1.000, 1.000)k = applying equation (9) to the value of qj the following is obtained: 1 (1.000,1.000,1.000)q = after that, the values for qj are summed up and the following are obtained: 3.178; 3.496 and 3.689, respectively. applying equation (10), the relative weights are calculated in the following manner: then, the following equation must be applied: 4 6 crisp l m u df + + = so as to get crisp value: 0.288; 0.397 and 0.318 in order to determine the final weights of the criteria, it is necessary to apply equations (11)-(15) and the methodology of the inverse fuzzy piprecia method. the matrix sj' was obtained from the decision-maker. applying equation (12), the values of the matrix kj' are obtained as follows: determining criteria significance in selecting reach stackers by applying the fuzzy piprecia method 85 3 ' (1.000,1.000,1.000)k = applying equation (13), the following values are obtained: 3 ' (1.000,1.000,1.000)q = after that, the values for qj are summed up and the values obtained are as follows: 3.178, 3.496 and 3.689, respectively. after that, it is necessary to apply equation (14) so as to obtain the relative weights for the fuzzy inverse piprecia method. then, the equation 4 6 crisp l m u df + + = must be applied in order to obtain the crisp values 0.288, 0.396 and 0.320, after which the obtained wj values are aggregated and the final weighted values for the main criteria are obtained: 0.288, 0.397 and 0.319. the results of the methodology applied are presented in table 4. table 4 shows the complete previous calculation, and the last column shows the deficient values of the relative weights of the criteria. vesković et al./oper. res. eng. sci. theor. appl. 3 (1) (2020) 72-88 86 table 4. the calculation of the weights and values of the main criteria p sj kj qj wj df rang c1 1.000 1.000 1.000 1.000 1.000 1.000 0.271 0.286 0.315 0.288 3 c2 1.187 1.280 1.317 0.683 0.720 0.813 1.230 1.389 1.463 0.333 0.397 0.460 0.397 1 c3 0.704 0.746 0.806 1.194 1.254 1.296 0.949 1.107 1.225 0.257 0.317 0.386 0.318 2 sum 3.178 3.496 3.689 p – i sj kj qj wj c1 0.542 0.610 0.727 1.273 1.390 1.458 0.757 0.893 1.049 0.224 0.285 0.367 0.288 3 c2 1.093 1.194 1.251 0.749 0.806 0.907 1.103 1.241 1.335 0.326 0.396 0.467 0.396 1 c3 1.000 1.000 1.000 1.000 1.000 1.000 0.296 0.319 0.350 0.320 2 sum 2.860 3.135 3.384 the spearman correlation coefficient (erceg et al., 2019) for the obtained ranks is 1.00, which means that these ranks are in absolute correlation. the pearson correlation coefficient (stevic et al., 2018) was also calculated for the criterion weights of 0.985. table 5 presents the final weight results by using the fuzzy piprecia method. as can be seen from the application of the complete methodology and the results obtained in table 5, the technological criteria group represents the most important group for the selection of a reach stacker, because the three priority criteria belong to this group: cth4 – manipulative abilities, cth5 – the lift height and cth3 – the number of the processed teu in the unit of time. of the economic criteria group, the most important is ce4 – the tire and price types, which ranks fourth in the overall ranking. determining criteria significance in selecting reach stackers by applying the fuzzy piprecia method 87 table 5. the criteria ranking by applying the fuzzy piprecia method economic local value global value rank ce1 0.184 0.043 19 ce2 0.187 0.049 17 ce3 0.228 0.061 13 ce4 0.152 0.073 4 ce5 0.281 0.071 7 technological cth1 0.150 0.059 15 cth2 0.171 0.068 10 cth3 0.211 0.084 3 cth4 0.253 0.100 1 cth5 0.246 0.098 2 technical ctr1 0.228 0.073 6 ctr2 0.185 0.059 16 ctr3 0.214 0.068 9 ctr4 0.206 0.066 11 ctr5 0.195 0.062 12 5. conclusion in this paper, the fuzzy piprecia method for the determination of the significance of the reach stacker selection criteria for a rail container terminal is presented. a total of 15 criteria were considered, those criteria being divided into the three groups: economic, technological and technical. the survey involved 15 decision-makers of different structures, which is presented in detail in the paper. the results show that the most essential criteria belong to the technology group. continued research would imply drafting a list of potential reach stackers, collecting quantitative and qualitative data and evaluating those data. some of the classical mcdm methods can be applied for evaluation and selection (stevic et al., 2020; zavadskas and turskis, 2010; pamučar and ćirović) individually or in combination with uncertainty theories (stojić et al., 2018; stanujkić and karabašević, 2018; stevic et al., 2019; kahraman et al., 2017). references đalić, i., stević, ž., karamasa, c., & puška, a. (2020). a novel integrated fuzzy piprecia–interval rough saw model: green supplier selection. decision making: applications in management and engineering, 3(1), 126-145. erceg, ž., starčević, v., pamučar, d., mitrović, g., stević, ž., & žikić, s. (2019). a new model for stock management in order to rationalize costs: abc-fucom-interval rough cocoso model. symmetry, 11(12), 1527. kahraman, c., keshavarz ghorabaee, m., zavadskas, e. k., cevik onar, s., yazdani, m., & oztaysi, b. (2017). intuitionistic fuzzy edas method: an application to solid waste vesković et al./oper. res. eng. sci. theor. appl. 3 (1) (2020) 72-88 88 disposal site selection. journal of environmental engineering and landscape management, 25(1), 1-12. marković, v., stajić, l., stević, ž., mitrović, g., novarlić, b., & radojičić, z. (2020). a novel integrated subjective-objective mcdm model for alternative ranking in order to achieve business excellence and sustainability. symmetry, 12(1), 164. pamučar, d., & ćirović, g. (2015). the selection of transport and handling resources in logistics centers using multi-attributive border approximation area comparison (mabac). expert systems with applications, 42(6), 3016-3028. pamučar, d., stević, ž., & sremac, s. (2018). a new model for determining weight coefficients of criteria in mcdm models: full consistency method (fucom). symmetry, 10(9), 393. stanujkić, d., & karabašević, d. (2018). an extension of the waspas method for decision-making problems with intuitionistic fuzzy numbers: a case of website evaluation. operational research in engineering sciences: theory and applications, 1(1), 29-39. stanujkic, d., zavadskas, e. k., karabasevic, d., smarandache, f., & turskis, z. (2017). the use of the pivot pairwise relative criteria importance assessment method for determining the weights of criteria. infinite study. stević, ž., durmić, e., gajić, m., pamučar, d., & puška, a. (2019). a novel multi criteria decision-making model: interval rough saw method for sustainable supplier selection. information, 10(10), 292. stević, ž., pamučar, d., puška, a., & chatterjee, p. (2020). sustainable supplier selection in healthcare industries using a new mcdm method: measurement of alternatives and ranking according to compromise solution (marcos). computers & industrial engineering, 140, 106231. stević, ž., stjepanović, ž., božičković, z., das, d., & stanujkić, d. (2018). assessment of conditions for implementing information technology in a warehouse system: a novel fuzzy piprecia method. symmetry, 10(11), 586. stojić, g., stević, ž., antuchevičienė, j., pamučar, d., & vasiljević, m. (2018). a novel rough waspas approach for supplier selection in a company manufacturing pvc carpentry products. information, 9(5), 121. zavadskas, e. k., & turskis, z. (2010). a new additive ratio assessment (aras) method in multicriteria decision‐making. technological and economic development of economy, 16(2), 159-172. © 2020 by the authors. submitted for possible open access publication under the terms and conditions of the creative commons attribution (cc by) license (http://creativecommons.org/licenses/by/4.0/). determining criteria significance in selecting reach stackers by applying the fuzzy piprecia method slavko vesković 1*, sanjin milinković 1, borna abramović 2, ivica ljubaj 2 1. introduction 2. a short description of the extent of work for the terminal 3. methods 3.1. operations on fuzzy numbers 3.2. the fuzzy pivot pairwise relative criteria importance assessment (i.e. fuzzy piprecia) method 4. determining criteria significance when selecting a reach stacker by applying the fuzzy piprecia method 5. conclusion references plane thermoelastic waves in infinite half-space caused operational research in engineering sciences: theory and applications vol. 1, issue 1, 2018, pp. 13-28 issn: 2620-1607 eissn: 2620-1747 doi: https://doi.org/10.31181/oresta19012010113n e-mail address: zdravko.nunic@sf.ues.rs.ba evaluation and selection of the pvc carpentry manufacturer using the fucom-mabac model zdravko nunić university of east sarajevo, faculty of transport and traffic engineering doboj, bosnia and herzegovina received: 14 september 2018 accepted: 29 october 2018 published: 19 december 2018 original scientific paper abstract: solving real-life problems using multi-criteria decision-making methods is now an everyday challenge. these methods represent a very useful tool and support for decision-making in all areas. therefore, this paper comprises evaluation and selection of the pvc carpentry manufacturers using a combined multi-criteria model. five potential manufacturers are evaluated on the basis of seven criteria. for the determination of criteria weights, the fucom (full consistency method) is used, while the multiattributive border approximation area comparison (mabac) method is used for evaluating and selecting the pvc manufacturer. the results show that the third alternative is the most suitable solution, as demonstrated by the sensitivity analysis. four other methods are used in the sensitivity analysis, namely, aras (additive ratio assessment), waspas (weighted aggregated sum product assessment), edas (evaluation based on distance from average solution), and saw (simple additive weighting). the obtained results using all the methods show the complete correlation of the ranks obtained using the mabac method. key words: pvc manufacturer, fucom, mabac, criteria weights 1 introduction in solving real-life problems, there is a large number of influencing factors that can affect the final decision. in the case of a larger number of criteria involved in the decision-making process, according to zavadskas et al. (2018), it is practically impossible to avoid the use of multi-criteria decision-making (mcdm) methods. according to kumar, (2010) the mcdm can be perceived as a process of evaluating real-world situations based on various qualitative/quantitative criteria in certain/uncertain/risky environments in order to find a suitable course of action/choice/strategy/policy among several available options. according to chen et al. (2015), the mcdm is an effective systematic and quantitative way of dealing with vital real-life problems in the presence of a number of alternatives and several usually conflicting criteria. a great number of works applying diverse mcdm nunić/oper. res. eng. sci. theor. appl. 1 (1) (2018) 13-28 14 techniques for engineering problems have recently been published (zavadskas et al. 2016). everyday use of mcdm methods (petrović et al. 2016; shetwan et al. 2018; eshtaiwi et al. 2018; karabašević et al. 2018) has certainly contributed to the rise in popularity of this area. the main objective of the paper is to evaluate and select the pvc carpentry manufacturer using the fucom-mabac model. the way of reaching the given goal is by satisfying a number of criteria such as: selection of a high-quality manufacturer at the lowest possible price, a short time for delivery and montage, possibility of deferred payment and a longer warranty period with the manufacturer's reliability. in addition to the introduction, the paper is structured through four more sections. the second section (section 2) presents the fucom and mabac methods with their detailed steps. in the third section (section 3), a multi-criteria model is formed and the previously described methods for evaluating and selecting pvc manufacturers are applied. the fourth section (section 4) presents a sensitivity analysis in which the stability of the applied model is proved. the paper ends with the conclusions along with the guidelines for future research. 2 methods 2.1 full consistency method fucom this method is a new mcdm method proposed in (pamučar et al. 2018). the problems of multi-criteria decision-making are characterized by the choice of the most acceptable alternative out of a set of the alternatives presented on the basis of the defined criteria. a model of multi-criteria decision-making can be presented by a mathematical equation      1 2max , ,..., , n 2nc x c x c x    , on the condition that  1 2, ,..., mx a a a a  ; where n represents the number of the criteria, m is the number of the alternatives, jc represents the criteria ( 1,2,...,ј n ) and a represents the set of the alternatives ai ( 1, 2,...,i m ). values ijf of each considered criterion jc for each considered alternative ia are known, namely    , , ; 1, 2,..., ; 1, 2,...,ij j if c a i j i m j n    . the relation shows that each value of the attribute depends on the jth criterion and the ith alternative. real problems do not usually have the criteria of the same degree of significance. it is, therefore, necessary that the significance factors of particular criteria should be defined by using appropriate weight coefficients for the criteria so that their sum is one. determining the relative criteria weights in multi-criteria decision-making models is always a specific problem inevitably accompanied by subjectivity. this process is very important and has a significant impact on the final decision-making result since the weight coefficients in some methods crucially influence the solution. therefore, particular attention in this paper is paid to the problem of determining the criteria weights, and the new fucom model for determining the weight coefficients of criteria is proposed. this method enables precise determination of the values of the weight coefficients of all of the elements evaluation and selection of manufacturer pvc carpentry using fucom-mabac model 15 mutually compared at a certain level of the hierarchy, simultaneously satisfying the conditions of the comparison consistency, too. in real life, pairwise comparison values /ij i ja w w (where aij shows the relative preference of criterion i to criterion j) are not based on accurate measurements, but rather on subjective estimates. there is also a deviation of values ij a from ideal ratios /i jw w (where iw and jw represent criteria weights of criterion i and criterion j). if, for example, it is determined that a is of much greater significance than b, b of greater importance than c, and c of greater importance than a, there is inconsistency in the problem solving and the reliability of the results decreases. this is especially true when there is a large number of pairwise comparisons of criteria. the fucom reduces the possibility of errors in comparison to the least possible extent due to: (1) a small number of comparisons (n-1) and (2) the constraints defined when calculating the optimal values of criteria. the fucom provides the ability to validate the model by calculating the error value for the obtained weight vectors by determining dfc. on the other hand, in the other models for determining criteria weights (the bwm, the ahp models), the redundancy of the pairwise comparison appears, which makes them less vulnerable to errors in judgment, while the fucom methodological procedure eliminates this problem. in the following section, the procedure for obtaining the weight coefficients of criteria by using the fucom is presented. step 1 in the first step, the criteria from a predefined set of the evaluation criteria  1 2, ,..., nc c c c are ranked. the ranking is performed according to the significance of the criteria, i.e. starting from the criterion which is expected to have the highest weight coefficient down to the criterion of the least significance. thus, the criteria ranked according to the expected values of the weight coefficients are obtained: (1) (2) ( ) ... j j j k c c c   (1) where k represents the rank of the observed criterion. if there is a judgment of the existence of two or more criteria with the same significance, the sign of equality is placed instead of “>” between these criteria in expression (1). step 2 in the second step, comparison of the ranked criteria is carried out and the comparative priority ( / ( 1)k k   , 1, 2,...,k n , where k represents the rank of the criteria) of the evaluation criteria is determined. the comparative priority of evaluation criteria ( / ( 1)k k   ) is an advantage of the criterion of the ( )j k c rank compared to the criterion of the ( 1)j k c  rank. thus, the vector of the comparative priorities of the evaluation criteria is obtained, as in expression: (2)  1/ 2 2 / 3 / ( 1), ,..., k k     (2) where / ( 1)k k   represents the significance (priority) of the criterion of the ( )j k c rank in comparison with the criterion of the ( 1)j k c  rank. nunić/oper. res. eng. sci. theor. appl. 1 (1) (2018) 13-28 16 the comparative priority of the criteria is defined in one of the two ways defined in the following part: a) pursuant to their preferences, the decision-makers define comparative priority / ( 1)k k   among the observed criteria. thus, for example, if two stones a and b, which, respectively, have the weights of 300 a w  grams and 250 b w  grams are observed, comparative priority ( /a b  ) of stone a in relation to stone b is / 300 / 250 1.2 a b    . also, if weights a and b cannot be determined precisely, but a predefined scale is used, e.g. from 1 to 9, then it can be said that stones a and b have weights 8 a w  and 7 b w  , respectively. then comparative priority ( /a b  ) of stone a in relation to stone b can be determined as / 8 / 7 1.14 a b    . this means that stone a in relation to stone b has a greater priority (weight) by 1.18 (in the case of precise measurements), i.e. by 1.14 (in the case of application of measuring scale). in the same manner, the decision-makers define the comparative priority among observed criteria / ( 1)k k   . when solving real problems, the decision-makers compare the ranked criteria based on internal knowledge so that they determine comparative priority / ( 1)k k   based on subjective preferences. if the decision-maker thinks that the criterion of the ( )j k c rank has the same significance as the criterion of the ( 1)j k c  rank, then the comparative priority is / ( 1) 1 k k    . b) based on a predefined scale for comparing criteria, the decision-makers compare the criteria and thus determine the significance of each individual criterion in expression (1). the comparison is made with respect to the first-ranked (the most significant) criterion. thus, the significance of criteria ( ( )j kc  ) for all of the criteria ranked in step 1 is obtained. since the first-ranked criterion is compared with itself (its significance is (1) 1 jc   ), the conclusion can be drawn that the n-1 comparison of the criteria should be performed. for example: a problem with three criteria ranked as c2>c1>c3 is being subjected to consideration. suppose that scale   ( ) 1, 9 j kc   is used to determine the priorities of the criteria and that, based on the decision-maker’s preferences, the following priorities of criteria 2 1 c   , 1 3.5 c   and 3 6 c   are obtained. on the basis of the obtained priorities of the criteria and condition / ( 1) 1 k k k k w w     we obtain the following calculations 2 1 3.5 1 w w  , i.e. 2 1 3.5w w  , 1 3 6 3.5 w w  i.e. 1 3 1.714w w  . in that way, the following comparative priorities are calculated: 2 1/ 3.5 / 1 3.5 c c    and 1 3/ 6 / 3.5 1.714 c c    (expression (2)). as we can see from the example shown in step 2b, the fucom model allows the pairwise comparison of the criteria by means of integer, decimal values or values from the predefined scale for the pairwise comparison of the criteria. evaluation and selection of manufacturer pvc carpentry using fucom-mabac model 17 step 3 in the third step, the final values of the weight coefficients of evaluation criteria  1 2, ,..., t n w w w are calculated. the final values of the weight coefficients should satisfy two conditions, namely: (1) that the ratio of the weight coefficients is equal to the comparative priority among observed criteria ( / ( 1)k k   ) defined in step 2, i.e. that the following condition is met: / ( 1) 1 k k k k w w     (3) (2) in addition to the condition (3), the final values of the weight coefficients should satisfy the condition of mathematical transitivity, i.e. that / ( 1) ( 1)/ ( 2) / ( 2) k k k k k k          . since / ( 1) 1 k k k k w w     and 1 ( 1) / ( 2) 2 k k k k w w       , that 1 1 2 2 k k k k k k w w w w w w       is obtained. thus, yet another condition that the final values of the weight coefficients of the evaluation criteria need to meet is obtained, namely: / ( 1) ( 1) / ( 2) 2 k k k k k k w w         (4) full consistency, i.e. minimum dfc (  ) is satisfied only if transitivity is fully respected, i.e. when the conditions of / ( 1) 1 k k k k w w     and / ( 1) ( 1) / ( 2) 2 k k k k k k w w         are met. in that way, the requirement for maximum consistency is fulfilled, i.e. dfc is 0  for the obtained values of the weight coefficients. in order for the conditions to be met, it is necessary that the values of weight coefficients  1 2, ,..., t n w w w meet the condition of / ( 1) 1 k k k k w w       and / ( 1) ( 1)/ ( 2) 2 k k k k k k w w           , with the minimization of value  . in that manner the requirement for maximum consistency is satisfied. based on the defined settings, the final model for determining the final values of the weight coefficients of the evaluation criteria can be defined. ( ) / ( 1) ( 1) ( ) / ( 1) ( 1) / ( 2) ( 2) 1 min . . , , 1, 0, j k k k j k j k k k k k j k n j j j s t w j w w j w w j w j                          (5) nunić/oper. res. eng. sci. theor. appl. 1 (1) (2018) 13-28 18 by solving the model (5), the final values of evaluation criteria  1 2, ,..., t n w w w and the degree of dfc (  ) are generated. 2.2 mabac method the mabac method (multi-attributive border approximation area comparison) was developed by pamučar and ćirović, (2015). the basic setting of the mabac method is reflected in defining the distance of the criterion function of each observed alternative from the boundary approximation domain. in the following section, the implementation procedure for the mabac method consisting of 6 steps is shown. step 1 forming initial decision matrix (x) as the first step, m alternatives are evaluated by n criteria. alternatives are shown with vectors ai=(xi1, xi2,…, xin, where xij is the value of i-… alternative by j-… criteria (i=1,2,…,m; j=1,2,…,n) ... 1 2 ... 11 12 11 21 22 22 ... ... ... ...... ... 1 2 x c c cn x x xa n x x xa n x x xa mnm m m                 (6) where m denotes the number or alternative, while n is the total number of criteria. step 2 normalization of the elements of starting matrix (x) ... 1 2 ... 11 12 11 21 22 22 ... ... ... ...... ... 1 2 n c c cn t t ta n t t ta n t t ta mnm m m                 (7) the elements of normalized matrix (n) are determined using the expression: for the criteria belonging to a "benefit" type (greater value of criteria is more desirable): x x ij i t ij x x i i       (8) for the criteria belonging to a "cost" type (lower value of criteria is more desirable) evaluation and selection of manufacturer pvc carpentry using fucom-mabac model 19 x x ij i t ij x x i i       (9) where xij, x+ and x are representing elements of the starting matrix of making decision (x), where xij , x+ and xare defined as: xj+ =max (x1, x2, .., xn) and representing maximal values of observed criteria by alternatives; xj=min (x1, x2, .., xm) and representing minimal values of observed criteria by alternatives. step 3 calculation of the element of weighted normalized matrix (v) elements of weighted normalized matrix (v) are being calculated on the base of expression (10): v w t w ij i ij i    (10) where tij are representing the elements of normalized matrix n, wi represents weighting coefficients of criteria. step 4 determining the matrix of bordering approximative fields (g) bordering approximative field (gao) is determined by expression (11): 1/ 1 m m g v i ij j         (11) with vij representing the elements of weighted matrix v, m represents the total number of alternatives. matrix of bordering approximative fields is being formed according to criteria g (12) in format n x 1. ... 1 2 ... 1 2 c c cn g g g gn     (12) step 5 the calculation of the distance matrix element is an alternative to boundary approximative area (q): ... 11 12 1 21 22 2 ... ... ... ... ... 1 2 q q q n q q q nq q q qmnm m                (13) distance of alternatives from boundary approximative area (quid) is determined as a difference of elements of heavier matrix (v) and values of bordering approximative areas (g). nunić/oper. res. eng. sci. theor. appl. 1 (1) (2018) 13-28 20 ... 11 12 1 21 22 2 ... 1 2... ... ... ... ... 1 2 v v v n v v v nq v g g g gn v v vmnm m                     (14) where qij represents the bordering approximative areas for criterion ci, vij represents elements of weighted matrix (v), n represents number of criteria, m represents number of alternatives. alternative ai may belong to bordering approximative area (g), upper bordering approximative area (g) or lower bordering approximative area (g-). upper approximative area (g) represents the area in which ideal alternative (a+) is located, while lower approximative area (g-) represents the area in which anti-ideal alternative is located (a). g if q g ij i a g if q g i ij i g if q g ij i           (15) in order for an alternative ai to be selected as the best from a given set, it is necessary for it to belong to the upper approximating field by as many criteria as possible (g). if, for example, an alternative ai belongs to the upper approximative area by 5 criteria (out of 6 in total), and to the lower approximative area by one criterion, (g-) that means that, by 5 criteria, this alternative is close to or equal with the ideal alternative, while by one criterion it is close to or equal to anti-ideal alternative. if value 0 ij q  , i.e. ij q g   , then alternative ai is close or equal to the ideal alternative. value 0 ij q  , i.e. ij q g   , shows that alternative ai is close or equal to the anti/ideal alternative. step 6 alternatives ranking calculation of values of the criteria functions by alternatives is obtained as the sum of distance of the alternatives from bordering approximative fields ( ) i q . by summarizing the elements of q matrix by rows, we obtain the final values of the criterion functions of alternatives (16) where n represents the number of criteria, and m represents the number of alternatives. , 1, 2,..., , 1, 2,..., 1 n s q j n i m i ij j     (16) 3 evaluation of pvc carpentry manufacturer on today’s market, according to stević et al. (2018), there is a large number of pvc carpentry manufacturers that bid a very diverse offer from their wide range of production. the research in this paper has led to the selection of five manufacturers, evaluation and selection of manufacturer pvc carpentry using fucom-mabac model 21 all located at the maximal distance of 70 km. the surface of apartment which requires the selection of the most suitable manufacturer of pvc carpentry is 64 m2 and fig. 1 shows dimensions of all the apartment surfaces in need of pvc carpentry. in addition, a selection of six-chamber pvc profiles with thermal insulation glasses of 24 mm was carried out in advance. from fig. 1 it can be seen that, according to the wishes of buyers who are also decision-makers, a montage of carpentry together with window blinds and mosquito nets is needed. only position 5 is without mosquitoes nets, and it is necessary to install internal and external benches. position 1 as a single-hung window with position 2 (a double-hung window) makes a corner window in the living room. also, position 3 is a single-hung window belonging to the living room. position 4 of the single-hung window belongs to the bedroom, while position 5 of the single-hung window and position 6 of the balcony door belong to the dining room. the criteria formulated in this research representing the basis for decisionmaking of those who select the most favorable manufacturer are: product quality, product price, timeframe guarantee, manufacturer’s reliability, delivery time, payment methods and the possibility of walls treatment after the montage of new carpentry, marked hereinafter as c1–c7, respectively. the second criterion is a cost criterion that needs to be minimized, while the rest belongs to benefit criteria that are of maximizing type. fig. 1 dimensions of elements needed for montage table 1 presents the criteria used to evaluate and select the manufacturer, while table 2 shows the scale for assessing qualitative criteria. some of these criteria nunić/oper. res. eng. sci. theor. appl. 1 (1) (2018) 13-28 22 can be successfully applied to evaluation of suppliers in the companies manufacturing pvc carpentry, which is confirmed by the research carried out in (stojić et al. 2018). table 1 criteria used in the research mark of criteria name of criteria c1 product quality c2 product price c3 timeframe guarantee c4 manufacturer’s reliability c5 delivery time c6 payment methods c7 treatment of walls after the montage of new carpentry table 2 linguistic scale for evaluating the benefit criteria (stević et al. 2017) linguistic scale for criteria max type (benefit criteria) very poor (vp) 1 poor (p) 3 medium (m) 5 good (g) 7 very good (vg) 9 table 2 shows only the benefit criteria scale since the only cost criterion is the product price that is quantitatively expressed. in addition to this criterion, the warranty period is also displayed through its real values. the criterion of delivery time could not be quantified because certain manufacturers display, as this criterion, time by agreement. therefore, this criterion is qualitative and benefit. 3.1 determining criteria weight using the fucom method step 1 in the first step, the decision-makers perform the ranking of the criteria: c1> c2> c5> c3=c6>c4>c7. step 2 in the second step (step 2b), the decision-maker perform pairwise comparison of the ranked criteria from step 1. the comparison is made with respect to the first-ranked c2 criterion. the comparison is based on the scale  1, 9 . thus, the priorities of criteria ( ( )j kc  ) for all of the criteria ranked in step 1 are obtained (table 3). table 3 priorities of criteria criteria c1 c2 c5 c3 c6 c4 c7 ( )j kc  1 1.3 2 2.5 2.5 2.8 3.5 based on the obtained priorities of the criteria, the comparative priorities of the criteria are calculated: 1 2/ 1.3 / 1 1.3 c c    , 2 5/ 2 / 1.3 1.54 c c    , evaluation and selection of manufacturer pvc carpentry using fucom-mabac model 23 5 3/ 2.5 / 2 1.25 c c    , 3 6/ 2.5 / 2.5 1 c c    , 6 4/ 2.8 / 2.5 1.12 c c    and 4 7/ 3.5 / 2.8 1.25 c c    . step 3 the final values of the weight coefficients should meet the following two conditions: a) the final values of the weight coefficients should meet the condition (3), i.e. that 1 2 1.3 w w  , 2 5 1.54 w w  , 5 3 1.25 w w  , 3 6 1 w w  , 6 4 1.12 w w  and 4 7 1.25 w w  . b) in addition to the condition (3), the final values of the weight coefficients should meet the condition of mathematical transitivity, i.e. that 1 5 1.3 1.54 2 w w    , 2 3 1.54 1.25 1.82 w w    , 5 6 1.25 1 1.25 w w    , 3 4 1 1.12 1.12 w w    and 6 7 1.12 1.25 1.34 w w    . by applying expression (5), the final model for determining the weight coefficients can be defined as: 5 3 61 2 4 2 5 3 6 4 7 5 3 61 2 5 3 6 4 7 7 1 min 1.30 , 1.54 , 1.25 , 1.00 , , 1.12 , 1.25 , . . 2.00 , 1.92 , 1.25 , 1.12 , 1.34 , 1, 0, j j j w w ww w w w w w w w w w w ww w s t w w w w w w w j                                                 by solving this model, the final values of the weight coefficients  0.266, 0.207, 0.134, 0.108, 0.108, 0.098, 0.079 t and dfc of the results 0.018  are obtained. the value of the criteria according to the marks given at the beginning is shown in table 4. the model is solved using the lingo17 software. table 4 criteria weights criteria c1 c2 c3 c4 c5 c6 c7 j  0.266 0.207 0.108 0.098 0.134 0.108 0.079 from table 4 it can be concluded that the most important criterion for the selection of the pvc carpentry manufacturer is the first one, i.e. product quality, followed by product price and guarantee period, while the other criteria have somewhat less significance. nunić/oper. res. eng. sci. theor. appl. 1 (1) (2018) 13-28 24 3.2 evaluation of the manufacturer pvc carpentry using the mabac method the initial matrix presented in table 5 consists of five alternatives that are presented in detail at the end of the previous subsection and seven criteria. evaluation of the alternative is performed on the linguistic scale shown in table 2. upon request for the production and montage of pvc carpentry, as noted earlier, five manufacturers have been selected and their locations are located at a distance of up to 70 km. table 5 initial matrix c1 c2 c3 c4 c5 c6 c7 a1 7 5776.000 5 5 5 3 5 a2 7 8252.780 2 3 5 3 1 a3 7 3490.030 5 5 5 3 7 a4 3 4355.000 5 3 3 3 1 a5 5 5795.000 0 3 1 1 1 normalization is performed as follows: for criteria c1, c3, c4, c5, c6, and c7 that belong to the benefit criteria, the normalization is carried out using equation (8) 7 3 1.00 11 7 3 t     for criterion c2, belonging to the cost criteria the normalization is carried out using equation (9) 5776 8252.780 0.52 12 3490.030 8252.780 t     a complete normalized matrix is shown in table 6. table 6 normalized matrix c1 c2 c3 c4 c5 c6 c7 a1 1 0.52 1 1 1 1 0.667 a2 1 0 0.4 0 1 1 0 a3 1 1 1 1 1 1 1 a4 0 0.818 1 0 0.5 1 0 a5 0.5 0.516 0 0 0 0 0 after normalization, the normalized matrix is weighted by applying equation (10): v w t w ij i ij i    and the weighted normalized matrix is obtained and shown in table 7. evaluation and selection of manufacturer pvc carpentry using fucom-mabac model 25 table 7 weighted normalized matrix v c1 c2 c3 c4 c5 c6 c7 a1 0.532 0.315 0.216 0.196 0.268 0.216 0.132 a2 0.532 0.207 0.151 0.098 0.268 0.216 0.079 a3 0.532 0.414 0.216 0.196 0.268 0.216 0.158 a4 0.266 0.376 0.216 0.098 0.201 0.216 0.079 a5 0.399 0.314 0.108 0.098 0.134 0.108 0.079 the next step is to obtain a matrix of 1x7 boundary approximative values (table 8) by applying the geometric mean or equation . table 8 matrix of boundary approximative areas g 0.437 0.317 0.175 0.129 0.220 0.188 0.101 the next step is to determine the q matrix shown in table 9 which represents the difference between the two previous matrices and is obtained by applying equation (14): 0, 532 0, 437 0, 095 11 q   table 9 matrix of bordering approximative field q=v-g c1 c2 c3 c4 c5 c6 c7 a1 0.095 -0.002 0.041 0.067 0.048 0.028 0.031 a2 0.095 -0.110 -0.024 -0.031 0.048 0.028 -0.022 a3 0.095 0.097 0.041 0.067 0.048 0.028 0.057 a4 -0.171 0.060 0.041 -0.031 -0.019 0.028 -0.022 a5 -0.038 -0.003 -0.067 -0.031 -0.086 -0.080 -0.022 the results obtained using the fucom-mabac model are shown in table 10, where it can be noted that the alternative of the three is the best solution. table 10 results of the fucom-mabac model a1 0.307 2 a2 -0.016 3 a3 0.433 1 a4 -0.115 4 a5 -0.327 5 characteristics of the selected manufacturer are as follows:  pvc positions are made of the german six -chamber inoutic pvc profile of prestige system with three grey seals ,  depth of construction is 76 mm white colored with 1.5 mm reinforcement ,  dimensions of window frame are 76/85 mm and blinds of 84 mm in height,  window blinds made of pvc system inoutic protex with aluminum cover,  box dimensions of 205x185 mm, except on the balcony door and the nunić/oper. res. eng. sci. theor. appl. 1 (1) (2018) 13-28 26 corresponding window of dimensions 205x205 mm,  all positions are with internal opening and integrated roller mosquitoes nets except position 5 which is without mosquitoes net,  frame roto nt, and  glass: izo flot 24 mm thick (4+16+argon+4low-e). 4 sensitivity analysis an important feature of the multi-criteria decision-making method is the sensitivity analysis of the applied model, and at the same time, the decision-maker enables testing of different sets of alternative solutions. the sensitivity analysis shows the relations of changing the priority of the alternative as a function of the significance of the attributes, that is, the criteria. in order to check the stability of the applied model, the sensitivity analysis is performed. it represents, beside the mabac method, application of the following methods: aras (zavadskas and turskis, 2010) saw (maccrimmon, 1968), waspas (zavadskas et al. 2012) and edas (keshavarz ghorabaee et al. 2015). the results of the applied fucom-mabac model are shown in table 11. table 11 results of sensitivity analysis mabac saw waspas aras edas a1 0.307 2 0.961 2 0.942 2 2.287 2 2.287 2 a2 -0.016 3 0.748 3 0.699 3 1.519 3 1.519 3 a3 0.433 1 1.065 1 1.058 1 2.410 1 2.410 1 a4 -0.115 4 0.686 4 0.648 4 1.479 4 1.479 4 a5 -0.327 5 0.487 5 0.243 5 1.270 5 1.270 5 on the basis of the results shown in table 11 it can be concluded that the model is very stable and that the ranks obtained by the fucom-mabac model are in complete correlation with those obtained by means of the other four methods. 5 conclusions this paper presents the results of the research which again demonstrates the applicability of multi-criteria decision-making methods in making everyday decisions. making such decisions can be of significant importance to each individual. solving the problem of the selection of the pvc carpentry manufacturer has included all the relevant criteria which are of influence upon the final decision. the objective was to obtain the most suitable offer, that is, the one which involves high quality, which means high quality, the lowest possible price, short times for delivery and montage, possibility of deferred payment, a longer warranty period with the manufacturer’s reliability but it is not necessary to ignore other relevant facts that may have an impact on the formation of a final decision. finally, when the final decision is made on the basis of the obtained results, it can be freely stated that the third manufacturer truly represents the most favorable solution since all the essential criteria that are mentioned above are satisfied to a great extent. regarding the practical aspect, the contribution of this research is to the solving real-life problems by using the fucom-mabac model. from the scientific aspect, the contribution of the evaluation and selection of manufacturer pvc carpentry using fucom-mabac model 27 applied model can be to the integration of the fucom and mabac methods, which was first used in this paper in the literature. future research is related to the application of the fucom method in combination with other methods and the taking of a larger set of relevant criteria for evaluation of a multi-criteria model. references chen, n., xu, z., & xia, m. 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(2012). optimization of weighted aggregated sum product assessment. elektronika ir elektrotechnika, 122(6), 3-6. http://dx.doi.org/10.5755/j01.eee.122.6.1810 © 2018 by the authors. submitted for possible open access publication under the terms and conditions of the creative commons attribution (cc by) license (http://creativecommons.org/licenses/by/4.0/). operational research in engineering sciences: theory and applications vol. 3, issue 2, 2020, pp. 111-126 issn: 2620-1607 eissn: 2620-1747 doi: https://https://doi.org/10.31181/oresta2003111m * corresponding author. salih.memis@giresun.edu.tr (s.memiş), edemir@pirireis.edu.tr (e.demir), ckaramasa@anadolu.edu.tr (ç. karamaşa), selcuk.korucuk@giresun.edu.tr (s.korucuk) prioritization of road transportation risks: an application in gi̇resun province salih memiş 1, ezgi demir 2, çağlar karamaşa* 3, selçuk korucuk 1 1 giresun university, department of international trade and logistics, giresun, turkey 2 piri reis university, department of management information systems, i̇stanbul, turkey 3 anadolu university, department of business administration, eskişehir, turkey received: 25 june 2020 accepted: 25 july 2020 first online: 27 july 2020 research paper abstract: the purpose of this study is to determine and rank the road transportation risk factors that are crucial for effective and economic supply chain management. road transportation risk factors can be defined as equipment related risks, risk to be lost and disappearance, risks related to delivery and packaging, inadequacy of qualified personnel and technical equipment, risks caused from incompatibility to logistic information system/technology, security risk, compulsory reasons, risks originated from regulations and arrangements, risks related to waiting at customs gate and transport infrastructure based risks. accordingly, fuzzy piprecia as a multi-criteria ranking method was used to prioritize the risk factors. according to the results, while the transport infrastructure based risks criterion was found as the most important, the risk to be lost and disappearance factor was obtained as the least important one. keywords: road transportation, road transportation risk factors, piprecia, fuzzy sets. 1. introduction goods, money and documents that are subject to commerce are started to circulate in market after globalization happened in 21th century. companies try to find new methods in order to be competitive and reduce risks in related markets with globalization and the rapid development of information technologies. circulation of goods is possible with suitable risk management plan under controlled, in time and most economical manner. memiş et al./oper. res. eng. sci. theor. appl. 3 (2) (2020) 111-126 112 international transportation becomes crucial in parallel with the development of international commerce due to consumers’ habits in recent years. it is a requirement of transporting related goods and raw materials from one point to another because of rising needs and globalized commerce. economic growth leads to the increased demand for freight shipment especially. observed advancements in the communication between transportation and information technologies contribute to the circulation of goods. in this context, local and global commerce can be possible via the assurance of transportation activities. each process of international trade contains various risks. transportation risk can be considered as the most crucial and critical one due to including damages for goods that are subject to international trade. risks related to transportation activities include not only driver based accidents in a transportation process, but also error based accidents in goods traffic. in other words, transportation risk can be defined as issues such as driver errors, missing and incorrect operations related to goods subject to trade in packaging and loading processes. it is not possible to develop and generalize international trade without bringing transportation sector based risks that are drivers of commerce and goods circulation under control. risk and risk management concepts are started to gain importance, while international trade makes progress from exchange periods to virtual worlds. each step of international trade includes different risks too. therefore, globalization increased risks in the international trade. transportation risks in the logistic activities need to be evaluated thoroughly due to having direct impact on the goods subject to trade. risks happened in transportation activities can cause loss of property and material damage. hence, transportation risk can be described as damage risk too. however, issues observed in transportation can cause loss of lives apart from material damage. additionally, a time concept is handled as an essential risk element because incompatibility in arrangements related to good transport lead to material damage. risk management in transportation activities can be differentiated for each mode and include related people identification, determination of danger and related risk, taking a risk control process into account according to the dangers, reviewing process and taking additional precautions for the risk control process. road transportation is one of the mostly preferred transportation types due to low cost, delivery time and transport. general transportation and authorization rules are possible for each country. additional rules can be applied according to the countries involved in a transportation process. that condition creates a risk element as obligation for obeying the rules related to road transportation regulations and arrangements. accordingly, road transportation risk factors can be stated as equipment related risks, risk to be lost and disappearance, risks related to delivery and packaging, inadequacy of qualified personnel and technical equipment, risks caused from incompatibility to logistic information system/technology, security risk, compulsory reasons, risks related to waiting at customs gate and transport infrastructure based risks (pezier, 2002; cavinato, 2004; tang, 2006; manuj and mentzer, 2008; enyinda et al., 2010; hoffman et al., 2013; ho et al., 2015; kara and fırat, 2015; koban and keser, 2015; korucuk and erdal, 2018; korucuk and memiş, 2018). prioritization of road transportation risks: an application in giresun province 113 in this way, aforementioned road transportation risk factors are important for all stakeholders and have a direct impact on a business competitive level via cost minimization. in this context, the purpose of this study is to rank the road transportation risk criteria. a case study is made in girusen province, turkey. piprecia as a multi-criteria decision-making method is used for prioritization under fuzzy environment in order to better represent decision-makers’ judgments. other parts of the study are presented as follows: studies for transportation and related risk factors are explained in the second part. fuzzy piprecia is introduced in the third section. case study applied in giresun province and findings are presented in the fourth part. conclusions and future suggestions are made in the last section. 2. literature review transportation and transportation risk factors related studies can be presented as below: lazar et al. (2001) made risk evaluation in hazardous waste transportation via geographical information systems. chen et al. (2003) made overall evaluation related to transportation risks in radioactive substance and waste under normal and accident conditions. erkut and ingolfsson (2005) examined transportation risk models in dangerous goods carriage and proposed new ones after a revision process. xin et al. (2007) evaluated routing, inventory, planning, managementorganization and external factors under logistic risks context. ghazali (2009) examined the operational risks for highway projects in malaysia. risks are defined as wage scales, traffic congestion, road network change and excess load carriage. adams (2010) searched a transportation risk based model and proposed a human behaviour based model. wang (2011) used ahp model for ranking logistical risk factors according to carriage, technology, process, management, decision-making and environment contexts. khan (2013) considered the risk factors in employee life cycle and presented various risk analysis methods. zeng and song (2015) made fuzzy based risk assessment in order to ensure road safety in project carriage. govindan and chaudhuri (2016) applied dematel method for evaluating risk factors in third party logistical service providers. prakas et al. (2017) proposed supply chain network design structure and model related to supply chain and logistical risks. furthermore, they observed the efficiency of supply chain risk design in risk evaluation. i̇zer (2017) investigated new risk reduction technologies for cold chain logistics. korucuk and erdal (2018) ranked logistical risk factors for firms in cold chain transportation and found the most ideal risk management tool. noriega et al. (2018) examined risk factors related to livestock carriage in mexico. korucuk and memiş (2018) measured the risk factors for the supply chain via ahp and found quality risk as the most essential one. budzynski et al. (2019) examined tramway transportation risks and made propositions for increasing transportation quality and security. according to the depth literature review, there is not enough study in order to determine the importance levels for road transportation risk factors and that shows memiş et al./oper. res. eng. sci. theor. appl. 3 (2) (2020) 111-126 114 the originality and novelty of this concept. in addition, authors anticipate the contribution of this study to literature from method and application area viewpoint. 3. methodology 3.1. fuzzy pivot pairwise relative criteria importance assessmentfuzzy piprecia method the fuzzy piprecia method was developed by stević et al. (2018). it consists of 11 steps shown below. step 1. forming the required benchmarking set of criteria and forming a team of decision-makers. sorting the criteria according to marks from the first to the last, which means they need to be sorted unclassified. therefore, in this step, their significance is irrelevant. step 2. in order to determine the relative importance of criteria, each decisionmaker individually evaluates the pre-sorted criteria by starting from the second criterion, equation (1). 1 1 1 1 1 1 j j r j j j j j if c c s if c c if c c − − −    = = =    (1) r j s denotes the evaluation of the criteria by a decision-maker r. in order to obtain a matrix js , it is necessary to perform the averaging of matrix r j s using a geometric mean. decision-makers evaluate the criteria by applying the linguistic scales developed and defined in stević et al. (2018). step 3. determining the coefficient jk 1 1 2 1 j j if j k s if j = = =  −  (2) step 4. determining the fuzzy weight jq 1 1 1 1 jj j if j qq if j k − = =  =     (3) step 5. determining the relative weight of the criterion jw prioritization of road transportation risks: an application in giresun province 115 1 j j n j j q w q = =  (4) in the following steps, it is necessary to apply the inverse methodology of the fuzzy piprecia method. step 6. evaluation of the applying scale defined above, but this time starting from a penultimate criterion. 1 1 1 1 ' 1 1 j j r j j j j j if c c s if c c if c c + + +    = = =    (5) ' r j s denotes the evaluation of the criteria by a decision-maker r. it is again necessary to average the matrix r j s by applying a geometric mean. step 7. determining the coefficient 'jk 1 ' 2 ' j j if j n k s if j n = = =  −  (6) n denotes a total number of criteria. specifically, in this case, it means that the value of the last criterion is equal to fuzzy number one. step 8. determining the fuzzy weight 'jq 1 1 '' ' jj j if j n qq if j n k + = =  =     (7) step 9. determining the relative weight of the criterion ' j w 1 ' ' ' j j n j j q w q = =  (8) step 10. in order to determine the final weights of the criteria, it is first necessary to perform the defuzzification of the fuzzy values jw and 'jw memiş et al./oper. res. eng. sci. theor. appl. 3 (2) (2020) 111-126 116 1 '' ( ') 2 j j j w w w= + . (9) step 11. checking the results obtained by applying spearman and pearson correlation coefficients. 3.2. the evaluation of criteria using the fuzzy piprecia method in this study, ten criteria are handled for evaluating road transportation risks by eight decision-makers. criteria related to road transportation risks are presented in table 1. table 1. criteria related to road transportation risks criteria mark risk to be lost and disappearance c1 equipment related risks c2 risks related to delivery and packaging c3 inadequacy of qualified personnel and technical equipment c4 risks caused from incompatibility to logistic information system/technology c5 security risk c6 compulsory reasons c7 risks originated from regulations and arrangements c8 risks related to waiting at customs gate c9 transport infrastructure based risks c10 the evaluation of the criteria has been performed using a linguistic scale that involves quantification into fuzzy triangular numbers. figure 1 and figure 2 shows the evaluation of the criteria for fuzzy piprecia and inverse fuzzy piprecia by decision-makers and the average values (av) which are used for further calculation. it is important to note that, compared to the original method developed, the average value (av) is used here to average decision-makers' preferences (đalić et al., 2020; vesković et al., 2020; tomašević et al., 2020; stanković et al., 2020), which in this specific case contributed to the more accurate input parameters of the model. whether a geometric mean or an average value is applied depends directly on a particular case. both methods of averaging are valid. prioritization of road transportation risks: an application in giresun province 117 figure 1. evaluation of criteria by eight dms for the fuzzy piprecia figure 2. evaluation of criteria by eight dms for inverse fuzzy piprecia memiş et al./oper. res. eng. sci. theor. appl. 3 (2) (2020) 111-126 118 based on the evaluation of the criteria and their averaging, equation (1), a matrix sj is formed as in figure 3. figure 3. sj form applying equation (2), those values are subtracted from number 2. following the rules of operations with fuzzy numbers, the kj matrix is obtained as in figure 4. figure 4. kj form applying equation (3), the value qj is obtained as in figure 5. prioritization of road transportation risks: an application in giresun province 119 figure 5. qj form applying equation (4), the relative weights are acquired as in figure 6. figure 6. wj form after that, it is necessary to defuzzify obtained values by using the expression 4 6 crisp l m u df + + = obtaining the number crispdf 0.036, 0.037, 0.058, 0.056, 0.060, 0.251, 0.196, 0.335, 0.513, 0.698 respectively. in order to determine the final weights of the criteria, it is necessary to apply equations (5)–(9) or the methodology of the inverse fuzzy piprecia method. based on the evaluation by the decision-makers and the application of the average value, the matrix sj' is obtained as in figure 7. memiş et al./oper. res. eng. sci. theor. appl. 3 (2) (2020) 111-126 120 figure 7. sj form applying equation (6), the values of matrix kj' are obtained as in figure 8. applying equation (7), the following values are obtained as in figure 9. figure 8. kj form figure 9. qj form after that, it is necessary to apply equation (8) to obtain relative weights for the fuzzy inverse piprecia method as in figure 10. prioritization of road transportation risks: an application in giresun province 121 figure 10. wj form after that, it is necessary to defuzzify obtained values by using the expression 4 6 crisp l m u df + + = obtaining the number crispdf , 0.040, 0.045, 0.062, 0.064, 0.070, 0.118, 0.094, 0.133, 0.174, 0.220 respectively. applying equation (9), the final weights of road transportation risk criteria and rank of them are obtained as in figure 11. figure 11. final weights it has been shown in figure 12 the complete previous calculation, and the last column shows the defuzzified values of the relative weights of the criteria in terms of fuzzy piprecia method. memiş et al./oper. res. eng. sci. theor. appl. 3 (2) (2020) 111-126 122 figure 12. calculation and results obtained by the application of fuzzy piprecia for road transportation risk criteria accordingly, calculation and results obtained by the application of inverse fuzzy piprecia for road transportation risk criteria are presented in figure 13. prioritization of road transportation risks: an application in giresun province 123 figure 13. calculation and results obtained by the application of inverse fuzzy piprecia for road transportation risk criteria figure 14 shows the final results of the procedure for determining the individual significance of each of the road transportation risk criteria. as explained above, based on the personal preferences of the eight experts, the significance of the observed criteria was obtained using the fuzzy piprecia method. then, the defuzzification of the values was carried out to obtain the final weights of all the road transportation risk criteria, and, based on them, we can determine that the most significant criterion is c10 (transport infrastructure based risks) with a weight coefficient of 0.459, followed by the ninth criterion c9 (risks related to waiting at customs gate) with a weight of 0.343. as opposed to that, c1 (risk to be lost and disappearance) was found as the least important criterion with a weight of 0.038. memiş et al./oper. res. eng. sci. theor. appl. 3 (2) (2020) 111-126 124 scc for the ranks obtained with fuzzy piprecia and inverse fuzzy piprecia is 0.988, which means that these ranks are nearly to complete correlation. additionally, pearson's correlation coefficient has been calculated for the weights of the criteria obtained using these approaches and is 0.956. figure 14. final values of the road transportation risk criteria obtained using the fuzzy piprecia method 4. conclusion the aim of the present study is 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selçuk korucuk 1 1. introduction 2. literature review 3. methodology 3.1. fuzzy pivot pairwise relative criteria importance assessmentfuzzy piprecia method 3.2. the evaluation of criteria using the fuzzy piprecia method 4. conclusion references operational research in engineering sciences: theory and applications first online issn: 2620-1607 eissn: 2620-1747 doi: https://doi.org/10.31181/oresta241122166s * corresponding author. sahamech90@gmail.com (s. saha) saikatjumtech@gmail.com (s.r. maity), infodrsudip@gmail.com (s. dey) comparative analysis of metaheuristic optimizers in the performance optimization of wire electric discharge machining processes subhankar saha 1, 2, saikat ranjan maity 1*, sudip dey 1 1 department of mechanical engineering, national institute of technology silchar, india 2 department of mechanical engineering, st. martin’s engineering college, telangana, india received: 25 july 2022 accepted: 29 october 2022 first online: 24 november 2022 research paper abstract: wedm is an intricate process whereby improper selection of machine parameters often leads to undesirable performances. therefore, the extraction of optimal machining parameters is pivotal for achieving better performances in wedm. metaheuristic optimizers have gained immense popularity due to their capability of providing global optimal solutions. the application of recently reported metaheuristic optimizers in non-traditional machining processes is rarely being explored. in light of the above, the current paper examines the use of six recently reported metaheuristic optimizers, namely the ant lion optimization (alo), chimp optimization algorithm (choa), moth flame optimization (mfo), spotted hyena optimization (sho), harris hawk optimization algorithm (hho), marine predator algorithm (mpa) to optimize wedm performances in three wedm processes. particle swarm optimization (pso) and teaching learning-based optimization (tlbo), two well-known existing optimization approaches, are also included in this study to enable a reasonable comparison of the algorithms' performance. the algorithms are compared with parameters such as the quality of optimal solutions, convergence behavior, and average computational time. hho algorithm is found to be robust amongst the eight competitors in terms of culminating the global optimal solution and propensity to quickly converge to the global optimal solution which corroborates the high exploration and exploitation capability of the algorithm. therefore, hho optimizer can be exploited in future to determine the optimal operating conditions for other manufacturing processes. key words: wedm, optimization, metaheuristic algorithms, two sample t-test, sensitivity analysis saha et al./oper. res. eng. sci. theor. appl. first online 1. introduction in the era of technological advancements, there is a growing demand for advanced materials which are hard and difficult-to-machine. the machining of such advanced materials with high geometrical accuracy using traditional machining approaches is an impossible task. as a result, a number of non-traditional machining (ntm) techniques are available to meet the requirement for high geometrical accuracy. wedm is a non-traditional machining approach that has garnered a lot of interest in the industry because of its ability to create intricate curves with high geometrical accuracy [majumder & maity, 2018]. the material removal in the wedm process commences when an electric spark emerges amid the wire-workpiece interface. the spark liquidifies the material, and subsequently the molten debris is cleaned by the dielectric fluid injected from the top and bottom nozzles. the simplified view of the wedm procedure is portrayed in figure 1. figure 1. simplified view of wedm process the performance attributes in wedm are not always acquired at the envisioned level due to the process's intrinsic nature and a number of processing parameters (pulse duration, pulse interval, servo voltage, wire feed, wire speed, and so on), i.e., each process performance enhancement comes at the expense of another. as a result, machining under optimal operating conditions guarantees that a trade-off between the process performances is adequately maintained. in light of the preceding, researchers looked at several optimization techniques for selecting the best combination of process attributes. the next section provides a concise description of the optimization techniques that have been reported in wedm operation, the importance of metaheursitic optimization algorithms and the advantages and limitations of different metaheuristic optimizers. 2. literature review mandal et al. (2016) derived the optimal operating conditions by the desirability function while processing nimonic c-263 superalloy through wedm. in a recent investigation, the research group adopted a hybrid strategy i.e., signal-to-noise ratio and the taguchi methodology to optimize the performance variables of the wedm comparative analysis of metaheuristic optimizers in the performance optimization of wire electric discharge machining processes process concurrently (ramakrishnan & karunamoorthy, 2008). a group of researchers optimized the performances using rsm in wedm of inconel 718 (tonday & tigga, 2019). khan et al. (2014) implemented grey relational strategy to optimize microhardness and surface roughness simultaneously during the wedm process. it is worth pointing that conventional techniques such as the taguchi approach and grey relational analysis do not guarantee global optimum solutions as they commence the optimization with the specific level of process parameters. as a result, researchers are intrigued to adopt metaheuristic algorithms in wedm process since they provide global optimum solutions or the best solutions. metaheuristic algorithms are algorithms that are used in tackling a spectrum of complicated optimization problems without requiring to substantially adapt to each problem. the greek word "meta," which appears in the term, denotes that these algorithms are "higher level" heuristics, as contrary to problem-specific heuristics. metaheuristic algorithms are commonly used to address problems for which no appropriate problem-specific algorithm exists. the following traits are shared by almost all metaheuristics: they are nature-inspired; they use stochastic components (involving random variables); they do not evaluate the gradient or hessian matrix of the objective function. the research community has been using metaheuristic algorithms in wedm for the past thirty years. one pioneer contribution is the proposition of the simulated annealing method in wedm to discover the optimal operating condition for the cutting rate and surface roughness (tarng et al. 1995). in a similar manner, sadeghi et al. (2011) explored the tabu-search algorithm for optimizing the performance parameters. in wedm of inconel-690, a modified version of cuckoo search algorithm is proposed to assess the optimal outcomes (rao & venkaiah, 2017). a group of two researcher performed optimization of the performance parameters employing bat algorithm in taper formation in inconel 718 exploiting wedm. in a research effort, nsga methodology is executed to track the various optimal parametric combinations (pareto set) for two performance parameters in wedm of ti6al4v (nayak & mahapatra, 2016). in a similar manner, garg et al. (2012) found a set of pareto optimal solutions in wedm of ti6al-4v alloy employing the nsga-ii algorithm. in view of the above, it is observed that there are limited research in wedm which have documented the use of metaheuristic optimizers in wedm processes. it is worth emphasizing that the no-free-lunch (nfl) theorem asserts that one specific algorithm cannot solve all sorts of optimization problems (wolpert & macready, 1997). furthermore, previous studies have not documented the use of recently developed metaheuristic optimizers in wedm. as a result, we plan to investigate the algorithmic performance of six recently reported metaheuristic optimizers, as well as two popular state-of-the-art metaheuristic optimizers, while optimizing wedm performances either individually (single-objective) or collectively (multi-objective) for three wedm processes. the six recently reported metaheuristic optimizers are ant lion optimization (alo), chimp optimization algorithm (choa), moth flame optimization (mfo), spotted hyena optimization (sho), harris hawk optimization (hho), and marine predator algorithm (mpa). whereas, the two popular metaheuristic optimizers are particle swarm optimization and teaching learningbased optimization. we discussed the typical characteristics of each representative algorithm as follows to support the decisions made during the algorithm selection process. the pso optimizer is simpler (lee & park, 2006). however, the main saha et al./oper. res. eng. sci. theor. appl. first online loophole of this optimizer is the quick convergence of all solutions which undermines the diversity in the population (juneja & nagar, 2016). the tlbo optimizer has fewer tuning parameters than other optimizers, doesn't get stuck in local optima like other optimizers, and provides an accurate global optimal solution in minimum time (uzlu et al., 2014). the limitation of this optimizer is that it ends with near-optimal solution in minimum iterative step (sultana & roy, 2014). sho requires a low computational effort when tackling problems with high dimensions (krishna et al., 2021). however, it is found that the problem space remains partially explored using sho because of the concentrated search around the current optimal solution which might be a local optimum (sabahno & safara, 2021). choa has ample of advantages such as high exploration, a semi-deterministic feature of chaotic maps assists in high exploitation, local optima avoidance is very high, few parameters to tune, ease in implementation due to the parallel structure of independent groups (khishe & mosavi, 2020). in contrary, it has few limitations such as premature convergence, a slow rate of convergence, discovering local minima rather than global minima, and a low balance between exploitation and exploration (kaur et al., 2021). the advantage of using mfo is that it is simple, and can be easily hybridized with other algorithms (shehab et al., 2021). but, it may easily fall into the local optima because it emphasizes on exploitation more than exploration which causes premature convergence, and the search ability is insufficient (shan et al. 2021). population diversity, strong optimization ability, and fewer adjustment factors are the typical advantages of alo algorithm (yao et al. 2021). due to the roulette wheel selection technique, alo algorithm suffers from rapid convergence (abualigah et al., 2021). mpa optimizer has limited number of algorithmic variables. moreover, the procedures are simple and converge fast with the added benefits of flexibility, and robustness (yakout et al. 2021). however, it exhibits premature convergence in complex and high dimensional problems, and falls in local optima (houssein et al., 2021). hho optimizer is simple and has a few exploratory and exploitative mechanisms (mansoor et al., 2020). but it has the major limitation of displaying finite exploration behavior as the exploration behavior depends on the equal perching chance, and in the mid-flight, the escape energy gets limited within unity (naik et al., 2021). in the present study, the goal is to compare the considered algorithms' performances based on several parameters such as the quality of optimal solutions, convergence behavior, and average computing time. the motive behind the comparative analysis is to find the most reliable optimization algorithm. performance stability of the optimizers are retrieved exploiting the sensitivity analyses. lastly, we tested the performance of the eight competing optimizers on benchmark test functions (i.e., the sphere function and the generalized rastrigin's function) to determine the robust algorithm. the strategy adopted to accomplish the goal of the current research is delineated with a flowchart (see in figure 2). comparative analysis of metaheuristic optimizers in the performance optimization of wire electric discharge machining processes figure 2. flowchart showing the strategy adopted for the present work 3. metaheuristic optimization algorithms 3.1. teaching learning based optimization (tlbo) the fundamental concept of tlbo is to simulate a two-stage learning process in a traditional classroom setting (rao et al., 2011). the communication of knowledge between a teacher and students occurs in the first stage, known as the teacher phase. the amount of knowledge gained by students is proportional to the amount of teacher's knowledge. however, in practice, the likelihood of the teaching to become successful is distributed according to gaussian law. only a small percentage of students can comprehend everything indicated by the right end of the gaussian distribution. however, the chances of learning new things aren't entirely eliminated. saha et al./oper. res. eng. sci. theor. appl. first online a student can understand from the fellow students at the second stage, known as the learner phase. overall, the amount of knowledge conveyed to a student is determined by his or her teacher and by peer learning exchanges. 3.1.1. teacher phase in this phase, a teacher intends to improve the average performance in the subject being taught. the teaching job is first assigned to the best individual in the population teacher x , after which the algorithm improves other individuals i x by adjusting their positions towards that of the teacher teacher x . the current mean value of the individuals mean x is used to create each individual's position, which symbolizes the traits of all learners in the current generation. the disparity amid the teacher's knowledge and the students’ knowledge is simulated in eq. (1), which shows how the difference in student performance is affected by the difference in teacher’s knowledge and the students’ knowledge.   new i teacher f meanx x r x t x   (1) the f t in eq. (1) refers to a teaching factor which depicts the altered mean value, and r refers a random number in [0,1]. 3.1.2. learner phase increasing an individual's knowledge  ix is done in this phase through peer learning from any student ii x and interaction amid the individual and other learners. two states can arise based on the relative knowledge levels of these two students: if ii x is better than i x , i x will move towards iix (shown in eq. (2)), and if iix is worse than i x , ix will be moved away from iix (shown in eq. (3). student will be allowed into the population if he or she performs better by using eq. (2), and eq. (3). the algorithm will iterate till the end condition is reached.  new i ii ix x r x x   (2)  new i i iix x r x x   (3) 3.2. particle swarm optimization pso is led by swarm intelligence behavior which takes advantage of the social information sharing model. individuals (i.e., particles) fly across a higherdimensional search space in pso (poli et al. 2007). the individuals' tendency to imitate the success of others in population leads to changes in particle positions within the search space (called swarm). the knowledge, of a particle's surroundings thereby affects its modification within the swarm. the search characteristic of a particle is affected by the search characteristic of other particles in the swarm. the particle keeps track of its location in the problem space, which is related to its best solution so far, known as best p , and the overall best value is the best value recorded by the particle swarm optimizer when globally treated. furthermore, its current comparative analysis of metaheuristic optimizers in the performance optimization of wire electric discharge machining processes location, as determined by any particle in the population, is known as best g . each particle's velocity is changed as it moves toward its best p and bestg positions in the particle swarm optimization process. separate random values are created for acceleration towards the best p and bestg positions, which are weighted by random terms. the pso method adjusts the particle's velocities and positions as shown in the equations below.          1 1 2 2 2 1 2 2 1 , , 2 4 where , 4 ii i best i best i vel t vel t c r p z t c r g z t c c                        (4)      1 1i i iz t z t vel t    (5) where, c1 and c2 are the positive constants which represent the cognitive learning factor, and social learning factor respectively, r1 and r2 are random numbers in range [0,1].  1 2 dim, ,..., t i i i i z z z z depicts the ith particle position in the search space of dimension dim, and,  1 2, ,..., t i i i in vel vel vel vel depicts the ith particle velocity. 3.3. spotted hyena optimizer spotted hyena optimizer is a new bio-inspired optimization algorithm, which simulates the collaborative behavior of a group of spotted hyenas during encircling, hunting, and attacking the prey (dhiman & kumar, 2017). 3.3.1. prey encircling during prey encircling, the target prey is assumed to be the best solution, and the other spotted hyenas change their positions by following the best solution. this behavior is mathematically modeled as follows.     prey . h sh d a p t p t  (6)     prey 1 . sh h p t p t b d   (7) where h d denotes the separation between the spotted hyena and prey, t denotes the present iteration, a and b are co-efficient vectors, prey p represent prey’s position vector, and sh p represent spotted hyena’s position vector. 12 a r  (8) 22b s r s   (9) 5 5 maxiter s t         (10) where s reduces linearly from 5 to 0, and 1r , and 2r randomly changes between 0 and 1. saha et al./oper. res. eng. sci. theor. appl. first online 3.3.2. prey hunting and prey searching during prey hunting, the hunting strategy adopted by spotted hyenas in the sho algorithm is modeled mathematically as follows: . h kbsh d a p p  (11) k bsh h p p b d   (12) 1 .... k k k mh c p p p       (13) where, bsh p is the initial best position of spotted hyena, k p represents the position of other spotted hyenas, and m represents the number of spotted hyenas (shown in eq.(13)).   1 2 ,, , .....bsh bsh bsh bshm count p p p p r   (14) r randomly varies between 0.5 and 1, and h c is a cluster of m number of optimal solutions. during prey hunting, spotted hyenas attack the prey in a way that is mathematically expressed below:  1 hsh c p t m   (15) where,  1shp t  saves the best solutions, and the positions of the remaining spotted hyenas' changes relative to the best-spotted hyena’s position. during prey searching, the vector a in eq. (11) provides random values during the iteration process, which aids in exploration. 3.4. chimp optimization algorithm the chimp optimization algorithm, a metaheuristic optimizer, is motivated by the intelligence behavior exhibited by the chimps during hunting in their communities (khishe & mosavi, 2020). there are four categories of chimps, i.e., attacker, chaser, barrier, and driver, with different capabilities. the chaser, barrier, and driver lead the exploration process while the function of the attacker leads the exploitation process. the behavior of chimps modeled as follows:     prey chimp . . d c p t o p t  (16)     chimp prey 1 .p t p t a d   (17) where prey p and chimp p indicate the position vectors of the prey and the chimp respectively. the co-efficient vectors c, o, and a are determined as follows: 1 2. . a g r g  (18) 2 2. c r (19) o = chaotic_value (20) where g diminishes from 2.5 to 0 through the iteration process, o is a chaotic vector determined using chaotic maps. the generation of stochastic population of chimps is the initial step in the chimp optimization algorithm. then in the next step, chimps are classified into four varying categories: driver, barrier, attacker, and chaser. the best comparative analysis of metaheuristic optimizers in the performance optimization of wire electric discharge machining processes chimps are the initial attacker, barrier, driver, and chaser as they are aware of the prey's position. therefore, amongst the entire set of best solutions, four best solutions are used to represent them. the rest of the chimps are compelled to change their locations on the basis of the best chimp locations. this behavior can be mathematically expressed as below: attacker attacker1 1 . ( ) . d c p t o p  (21)   barrier barrier2 2 . . d c p t o p  (22)   chaser chaser 3 3 . . d c p t o p  (23)   driver driver4 4 . . d c p t o p  (24)   attacker attacker1 1 . p p t a d  (25)   barrier barrier2 2 . p p t a d  (26)   chaser3 3 . chaser p p t a d  (27)  4 4. driver driverp p t a d  (28)    1 2 3 41 / 4p t p p p p     (29) where, attacker d , barrier d , chaser d , and driver d analogs with d in eq. (16). for updating the location of the chimps during the searching period, a probability of 50% is chosen between two alternatives, i.e., the usual updating rule and the chaotic model, which is mathematically expressed below:     prey chimp . if 0.5 1 chaotic_value if 0.5 p t a d p t          (30) 3.5. moth flame optimization transverse orientation for navigation of moths at night using moonlight forms the motivation of this mfo algorithm (mirjalili, 2015). in the mfo algorithm, the candidate solutions are the moths and the problem variables refers to their positions in the search space. the set of moths is represented as a matrix with n moths and dim dimensions which is shown below: 1,1 1,2 1,dim 2,1 2,2 2,dim ,1 ,2 ,dim n n n m m m m m m m m m m                (31) we further suppose that the fitness values for all the moths are stored in an array, as follows: 1 2 = n om om om om             (32) saha et al./oper. res. eng. sci. theor. appl. first online another key part of the mfo algorithm is flames. the following is a matrix that is identical to the moth matrix: 1,1 1,2 1,dim 2,1 2,2 2,dim ,1 ,2 ,dim n n n f f f f f f f f f f                (33) where n is the number of moths and dim is the dimension. the dimension of the flame matrix is the same as the dimension of the moth matrix. both the moth and the flame are solutions, but the moth is the search agent and the flame is the moth's best position. flames are the flags that moths drop during the search process, and the moths travel around the flags and update accordingly. as a result of this, the moths never lose their best solution. according to the equation below, moths update their position in relation to flame.  = ,i i jm s m f (34) where i m represents the ith moth, j f represents the jth flame, and the spiral function is represented by s. the logarithmic spiral motion of the moth is given below:    , . .cos 2bti j i js m f d e r f  (35) where, i j i d f m  (36) b is a constant that determines the form of spiral motion, r refers to random number within [-1, 1]. flame gets updated over the course of iterations as follows: 1 flame no = round maxiter n n t        (37) where n is the maximum number of flame. 3.6. ant lion optimization ant lion optimizer is a metaheuristic optimizer which is conceptualized based on the chasing strategy of antlions in catching their prey (mirjalili, 2015). the ant lions hide underneath the base of the cone-shaped cavities in the sand and then wait for the ants to get captured in the hole. they throw sand at the tip of the trap so that the ants fail to escape and slide down to the bottom of the trap. in this manner, the ants get captured by the ant lions. the pits are rebuilded to capture other ants. the positions of the ants are stored in the matrix ant m (shown in eq. (38)) which is employed during the optimization. 11 1dim 1 dim ant n n a a m a a            (38) where n refers to the quantity of ants, and dim refers to the dimension of the problem. fitness function f is utilized for the evaluation of the fitness of each ant during optimization; the fitness values are stored in the matrix oant m as shown below: comparative analysis of metaheuristic optimizers in the performance optimization of wire electric discharge machining processes       1,1 1,2 1,dim 2,1 2,2 2,dim ,1 ,2 ,dim f ,..., f ,..., f ,..., oant n n n a a a a a a m a a a                          (39) apart from ants, the ant lions also have their hideouts in the search domain. the matrices antlion m and oantlion m save the positions and fitness values of the ant lions, respectively. 1,1 1, ,1 , m antlion n n m a a m a a            (40)       1,1 1,2 1, 2,1 2,2 2, ,1 ,2 , m m oantlion n n n m f al al al f al al al m f al al al                          (41) while searching for food, ants move in a stochastic fashion; thus, a random walk is selected to simulate ants’ movement as below:           1 20, csum 2 1 , csum 2 1 ..., csum 2 1maxiterx t r t r t r t      (42) where csum reveals the cumulative sum, t reveals the random walk steps, and  r t is a stochastic function which is enumerated as follows:   1 if rand 0.5 0 if rand 0.5 r t     (43) to limit the movement within the search space in a random fashion, eq. (42) is normalized exploiting the eq. (44).       t t i i i it i it i i x a b c x c d a       (44) eq. (45), and eq. (46) show how ants’ slide down into pits. t t c c i  (45) t t d d i  (46) saha et al./oper. res. eng. sci. theor. appl. first online when the ant reaches the pit bottom, the antlion snatches it and consumes it. to improve its chances of obtaining new prey, an antlion must update its position to the most recent position of the chased ant. eq. (47) represents this procedure.    t i t tj i i jantlion ant if f ant > f antlion  (47) in every step, elitism is employed to keep the best solutions. the fittest antlion is treated as elite, which is the best antlion achieved. in every step, the elite should have an impact on the antlion (random movement). for this, every ant is assumed to associate with an antlion by roulette wheel and elite, which eq. (48) gives. t t t a e i r r ant 2   (48) t a r , and ter represent the random walk around the selected antlion and elite at t th iteration respectively. 3.7. marine predator algorithm (mpa) the marine predator algorithm is a novel nature-inspired metaheuristic algorithm that replicates the biological interaction between marine predators and prey (faramarzi et al., 2020). predators are inspired in this algorithm to use the widespread foraging methods known as the brownian and levy random movement in the marine ecosystem. predators utilize the brownian approach if there exists a large concentration of prey in the hunting region, and the levy method when there is a low concentration of prey. however, environmental factors namely eddy generation and the effects of fish aggregating devices (fads) are among the elements that influence marine predator behavior. the steps of the algorithm are enumerated as follows: 3.7.1. initialization both the prey (p) and elite (e) matrices are formed during the initialization phase. in accordance with the survival of the fittest argument, the skilled foragers are the top predators in nature. thus, in order to construct the elite matrix, the fittest solution is designated as a top predator. prey is another matrix with the same dimension as elite, and predators use it to update their positions. 3.7.2. phase 1 this phase commences during the one-third of iterations and is implemented by a large velocity ratio  10v  for an adequate exploration ability, wherein the movement of the prey is faster than the predator. the prey moves quickly to guard their food. whereas the fittest predators are stationary during this stage. this stage is mathematically illustrated with the help of equations (eq. 49 & eq. 50). maxiter while t 3     1, 2,....,ii b i bs r e r p i n     (49)  0.5i i ip p r s   (50) comparative analysis of metaheuristic optimizers in the performance optimization of wire electric discharge machining processes where i s indicate the step size of the predator, b r is the random vector based on normally distributed brownian motion, r indicate a uniformly distributed random variable, and n indicates the search agents per population. the notation  indicate entry-wise multiplications. 3.7.3. phase 2 in this phase, there is a transient transformation from exploration to exploitation. here, the velocity ratio of unity (v ≈ 1) indicates that both the predator and the prey moves at an identical speed. maxiter 2 while < t < maxiter 3 3 the first half population gets updated based on levy strategy as follows:    1, 2,...., / 2ii l i ls r e r p i n     (51)  0.5i i ip p r s   (52) where l r is a uniformly distributed random vector based on levy motion. on contrary, the second half population is updated using brownian strategy as follows (shown in eq. (53) & eq. (54):    / 2,....,ii b b is r r e p i n n     (53)  0.5i i ifp e x s   (54) where f x is a variable that monitor the predator’s step size and is evaluated by the following eq. (55)   2 / 1 t maxiter f t x maxiter            (55) 3.7.4. phase 3 this phase is usually marked with a high level of exploitation capacity. this phase is marked by a low velocity ratio (v = 0.1), in which the predator runs past the prey. this phase is based on levy movement which is mathematically expressed as follows: 2 while t maxiter 3     1, 2,....,ii l b is r r e p i n     (56)  0.5i i ifp e x s   (57) 3.7.5. finishing after each iteration, the best solutions gets stored in the elite (e) matrix. the final solution is then achieved after the last iteration. saha et al./oper. res. eng. sci. theor. appl. first online 3.8. harris hawk optimization harris hawk optimization (hho) is a new nature-inspired optimizer that imitates the chasing trait of harris hawks in order to catch their prey (rabbit), which are the best solutions in the search space (heidari et al., 2019). hho goes through two stages: the first is looking for prey with a group of hawks, and this stage is referred to as the exploration phase in the algorithm. the second stage involves hunting the prey in order to catch it, which is depicted in the optimization algorithm as the exploitation phase. the balance between exploitation and exploration of search space is determined by the rabbit's energy escape, with hawks having the potential to explore for large energy and exploitation for small energy. in the exploration phase, the hho algorithm employs two alternative search strategies. these strategies are chosen based on α; if α is greater than 0.5, the first strategy is employed to search near one of the other hawks at random, but if α is lesser than 0.5, the second strategy, stated in eq. (59) is employed for the search operation.         1 21 2 0.5rand randx t x t s x t s x t      (58)           3 41 0.5rabbit mx t x t x t s lb s ub lb        (59)     1 1 where n m i i x t x t n    the mathematical model to demonstrate the mechanism which is exploited to get transformed from the exploration phase to the exploitation phase is shown in eq. (60). 0 2 1 t e e t        (60) the algorithm arrives the exploration phase when 1e  whereas the algorithm arrives the exploitation phase when 1e  . e diminishes when the iteration count increases. in the exploitation phase, the hho algorithm utilizes four different ways to conduct optimization operations. if e is greater than 0.5, two techniques are used: besiege and soft besiege with increasing quick dives. if e is less than 0.5, two techniques are used: besiege and hard besiege with progressive quick dives. the illustration of the strategies can be found in the literature. 4. wedm performance optimization to assess the efficacy of the eight metaheuristic optimization techniques, single and multiple objective optimization is carried out for two wedm processes (elaborated in case 1, and case 2). the codes for the eight optimizers are built in matlab r2018a and executed on windows 10 os, intel(r) core™ i5 processor, and 8.00 gb ram. for unprejudiced comparison amid the performances of the considered optimizers, population size, and maximum generation is kept at 50 and 100 respectively for all the considered algorithms. comparative analysis of metaheuristic optimizers in the performance optimization of wire electric discharge machining processes 4.1. case 1 performance optimization in wedm of a286 superalloy we assessed the wedm performances such as material removal rate (mrr, in mm2/min) and surface roughness (sr in µm) for an a286 superalloy. machining of the samples are accomplished using an ultra cut f1 model, a variant of the wedm machine tool. twenty-seven sets of experiments are undergone under the l27 scheme. five parameters are tuned in three subsequent levels (depicted in table 1) within the stipulated bounds while machining. finally, multiple performances are optimized simultaneously using a multi-objective evolutionary algorithm and a decision making tool (saha et al., 2021). in this research, we use the eight different metaheuristic optimizers to optimize individual performances as well as two performances at the same time. the goal is to compare the performances of the optimizers. to accomplish the task, we intend to exploit the mathematical expressions used for devising the correlation between the response variables and the explanatory variables in the previous investigation (saha et al., 2021). the mathematical models are shown below: 2 2 1 2 3 4 5 1 2 2 2 2 3 4 5 1 2 1 3 1 4 1 5 2 3 2 4 2 5 3 4 4 5 567 20.39 2.91 102.8 28.4 2.83 0.0497 0.0354 8.192 0.037 0.0302 0.0117 * 0.858 * 0.1511 * 0.0034 * 0.244 * 0.1140 * 0.0196 * 0.326 * 0.145 * mrr x x x x x x x x x x x x x x x x x x x x x x x x x x x x                     (61) 2 2 1 2 3 4 5 1 2 2 2 2 3 4 5 1 2 1 3 1 4 1 5 2 3 2 4 2 5 3 4 177.3 0.59 0.889 27.26 1.82 0.110 0.00276 0.00934 1.2656 0.0323 0.00642 0.00014 * 0.0177 * 0.0157 * 0.0034 * 0.244 * 0.1140 * 0.0196 * 0.326 * 0.14 sr x x x x x x x x x x x x x x x x x x x x x x x x x x                      3 5 5 *x x (62) table 1. process variables and levels process variables level 1 level 2 level 3  1x pulse on period (μs) 120 125 130  2x pulse off period (μs) 48 52 56  3x peak current (a) 10 11 12  4x wire feed rate (m/min) 5 7 9  5x servo voltage (v) 30 35 40 4.1.1. single-objective optimization the optimization of mrr and sr is accomplished under a set of constraints i.e., 1 120 130,x  2 48 56x  , 3 10 12,x  35 9,x  and 430 40x  . the results of the different optimizers for the two performance attributes is demonstrated in table 2. it is evident that choa, mfo, hho, mpa, and pso are able to produce the optimized mrr of 37.527 mm2/min which is close to the maximum mrr present in the experimental dataset (saha et al., 2021). however, alo, sho, and tlbo produces saha et al./oper. res. eng. sci. theor. appl. first online optimized mrr of 35.701 mm2/min, 29.614 mm2/min and 6.718 mm2/min respectively, which is relatively poor. figure 3. convergence behavior of alo, choa, hho, mfo, mpa, pso, sho, and tlbo for mrr for sr, unlike the sho, we detect that all the algorithms have produced similar results, but better than all the results reported in the previous investigation (saha et al., 2021). to realize the convergence traits of the optimizers, we plotted the convergence history of the competing optimizers while optimizing the response mrr (shown in figure 3). it is noted that hho algorithm rapidly converges to the global optimal solution which exposes the algorithm’s outstanding exploitation capability. table 2. single-objective optimization outcomes. optimizer response optimal value pulse on period pulse off period peak current wire feed rate servo voltage alo mrr 35.701 130 48 11.51 5.01 31.14 sr 0.4776 120 56 10 5 40 choa mrr 37.527 130 48 11.63 7 30 sr 0.4776 120 56 10 5 40 mfo mrr 37.527 130 48 11.59 7 30 sr 0.4776 120 56 10 5 40 sho mrr 29.614 130 48 12 5 30 sr 0.5320 120 56 10 9 40 mpa mrr 37.527 130 48 11.59 7 30 sr 0.4776 120 56 10 5 40 hho mrr 37.527 130 48 11.59 7 30 sr 0.4776 120 56 10 5 40 pso mrr 37.527 130 48 11.59 5 30 sr 0.4776 120 56 10 5 40 tlbo mrr 6.718 120 56 10 9 40 sr 0.4776 120 56 10 5 40 comparative analysis of metaheuristic optimizers in the performance optimization of wire electric discharge machining processes 4.1.2. multiple objective optimization to perform optimization of the two performance attributes (mrr and sr) simultaneously, we formed the objective function using weighted-sum method as follows:       1 2 min max sr mrr min sr mrr y y y w w  (63) where 1 w and 2 w are the preference weights assigned to sr and mrr, respectively. here, equal weights for all the responses are considered, i.e., 1 2 0.5w w  . min sr is the minimum surface roughness and max mrr is the maximum material removal rate, which are procured from the single-objective optimization outcomes. table 3 shows the optimal mrr and sr values recommended using the eight competitor techniques (alo, mfo, choa, mpa, sho, hho, pso, and tlbo). hho portrays the superior performance i.e., it produces the global optimal responses of mrr and sr at minimal value of the combined fitness function (y = 0.306708). the corresponding optimal process parameters are pulse on period = 130 s, pulse off period = 52 s, peak current = 10 a, wire feed rate = 5 m/min, and servo voltage = 30 volt. figure 4 analyzed the convergence traits of the eight competing algorithms. the objective function of the hho algorithm approaches the least fitness value (global optimum) in the fewest generations possible, demonstrating the algorithm's excellent exploitation capability. table 4 shows the average computing time (seconds) consumed by the optimizers while optimizing the multiple performances. as seen in table 4, tlbo has the shortest average computation time. table 3. multiple objective optimization outcomes. optimizer response optimal value y pulse on period pulse off period curre nt wire speed servo voltag e saha et al. (2021) mrr 36.04 130 52 10 5 30 sr 3.49 alo mrr 1.51 0.47 967 120 56 10 5 39 sr 0.96 mfo mrr 1.20 0.47 984 120 56 10 5 40 sr 0.79 sho mrr 1.20 0.47 984 120 56 10 5 40 sr 0.79 pso mrr 1.20 0.47 984 120 56 10 5 40 sr 0.79 tlbo mrr 1.20 0.47 984 120 56 10 5 40 sr 0.79 hho mrr 36.04 0.30 670 130 52 10 5 30 sr 3.49 mpa mrr 1.20 0.47 984 120 56 10 5 40 sr 0.79 choa mrr 1.20 0.47 984 120 56 10 5 40 sr 0.79 saha et al./oper. res. eng. sci. theor. appl. first online figure 4. convergence behavior of alo, choa, mfo, sho, hho, mpa, pso, and tlbo for multi-objective function. table 4. average computation time for the eight optimizers optimizer average computational time (secs) alo 2.20241 choa 1.83478 mfo 1.53465 sho 1.85662 hho 2.53421 mpa 1.25715 pso 1.23427 tlbo 1.20124 4.2. case 2 performance optimization in wedm of ti-6al-4v alloy devarajaiah & muthumari, (2018) conducted wedm machining on ti-6al-4v employing wire edm machine tool of model: dk 7732. the machine tool used in this work is based on reusable wire technology and doesn't need air-conditioning below 40 degrees centigrade. molybdenum wire electrode (diameter of 0.18 mm) is employed as wire electrode. four parameters, i.e., pulse duration, pulse off period, applied current, and wire-speed, were selected as control variables. the levels considered for the four control variables are revealed in table 5. two vital process performance measures were considered as responses (i.e., material removal rate (mrr in g/min) and power consumption (pc in kw)). the experimental trials were carried out as per taguchi l16 design, and each trial is repeated thrice to capture the variability in the wedm responses. furthermore, regression analysis was employed comparative analysis of metaheuristic optimizers in the performance optimization of wire electric discharge machining processes by devarajaiah & muthumari, (2018) to correlate the performance measures with the control variables. the regression models for mrr and pc are shown below (eq. (64) & eq. (65)): 2 1 2 3 4 1 2 2 2 3 1 4 2 3 0.00249 0.0056 0.0151 0.000011 0.000065 0.00039 0.00008 0.000001 0.00088 mrr x x x x x x x x x x x          (64) 2 1 2 3 4 1 2 2 2 3 0.756 0.002 0.0569 0.0133 0.000045 0.000036 0.00273 0.002 pc x x x x x x x         (65) table 5. process variables with levels process variables level 1 level 2 level 3 level 4  1x pulse on period (μs) 13 20 27 36  2x pulse off period (μs) 4 6 8 10  3x current (a) 1 2 4 5  4x wire speed (rpm) 350 700 1050 1400 4.2.1. single objective optimization in this case, two responses, i.e., mrr and pc, are optimized separately engaging the eight metaheuristic optimization algorithms. in other words, we intend to discover the optimal parametric condition for both the responses separately using the competing algorithms. the goal is to maximize the mrr and minimize the pc subjected to the imposed constraints as follows: 1 13 36,x  2 4 10x  , 3 1 5,x  and 4 350 1400x  . table 6 exhibits the single objective optimization solutions derived by the eight metaheuristic optimizers. it is observed that all the competing optimizers furnished improved optimal mrr than the optimal mrr derived by (devarajaiah & muthumari, 2018). unlike the sho algorithm, all the algorithms have drastically improved the mrr from its initial value of 0.0647gm/min (devarajaiah & muthumari, 2018). from the optimal pc values as registered by the eight competitor algorithms (shown in table 6), it is worth pointing that all the algorithms deliver almost similar performance. besides, the optimal pc provided by the optimizers are found to be relatively better than the optimal pc endorsed by (devarajaiah & muthumari, 2018). when the convergence traits of the eight competitor algorithms are analyzed (shown in figure 5), it is noted that hho, and tlbo have accelerated tendency to converge faster to global optimal solution implying better exploitation potential of the two algorithms. saha et al./oper. res. eng. sci. theor. appl. first online table 6. single objective optimization outcomes. optimizer response optimal value pulse duration pulse off period current wire speed (devarajaiah & muthumari, 2018). mrr 0.0647 27 4 4 1400 pc 0.589 27 8 1 700 alo mrr 0.0825 29.92 4 5 1400 pc 0.523 13 10 1 350 choa mrr 0.0825 29.92 4 5 1400 pc 0.523 13 10 1 350 hho mrr 0.0825 29.92 4 5 1400 pc 0.523 13 10 1 350 mpa mrr 0.0825 29.92 4 5 1400 pc 0.52313 13 10 1 350 sho mrr 0.0669 21.17 4 5 350 pc 0.52313 13 10 1 350 mfo mrr 0.0825 29.92 4 5 1400 pc 0.52313 13 10 1 350 pso mrr 0.0825 29.92 4 5 1400 pc 0.52313 13 10 1 350 tlbo mrr 0.0825 29.92 4 5 1400 pc 0.52313 13 10 1 350 figure 5. convergence behavior of alo, choa, mfo, sho, hho, mpa, pso, and tlbo for mrr. 4.2.2. multiple objective optimization for multiple performance optimization, eq. (66) is exploited as the objective function which is displayed below: comparative analysis of metaheuristic optimizers in the performance optimization of wire electric discharge machining processes       1 2 min max pc mrr y pc mrr y y min w w  (66) where 1 w and 2w are the preference weights to pc and mrr respectively. in the present paper, we have assigned equal weights to pc and mrr, respectively. min pc is the minimum power consumption, and max mrr is the maximum material removal rate. the values are attained from the single-objective optimization results. table 7 reported the findings of multiple performance optimization exploiting eight metaheuristic optimization algorithms. alo, mfo, choa, hho, tlbo, and mpa have been discovered to seek the best trade-off condition for both the performance attributes as corroborated when compared with the reported results by (devarajaiah & muthumari, 2018). substantial improvement in mrr with a marginal decrement in the performance of pc is evident utilizing these algorithms. conversely, sho and pso algorithms are found to deliver mediocre optimal performances. when the convergence traits of the eight competing algorithms are compared, it is discovered that the hho algorithm rapidly converges to the minimal function value at minimal generation (as shown in figure 6), confirming the hho algorithm's exceptional exploitation capability. the comparison of average computational time for the eight algorithms for multiple performance optimization is exhibited in table 8. it is noted from table 8 that the tlbo algorithm requires the least computational time to reach the optimality condition. table 7. multiple-objective optimization outcomes optimizer response optimal value y pulse on time pulse off time current wire speed (devarajaiah & muthumari, 2018) mrr 0.0348 20 6 2 1050 pc 0.625 alo mrr 0.049 0.53072 16.12 6.71 5 350 pc 0.670 mfo mrr 0.048 0.53228 16.09 6.77 5 350 pc 0.669 choa mrr 0.049 0.53072 16.12 6.71 5 350 pc 0.670 hho mrr 0.049 0.53072 16.12 6.71 5 350 pc 0.670 sho mrr 0.044 0.53089 15.75 6.40 5 350 pc 0.676 pso mrr 0.0255 0.53199 16.12 10 2.88 350 pc 0.572 tlbo mrr 0.049 0.53072 16.12 6.71 5 350 pc 0.670 mpa mrr 0.049 0.53072 16.12 6.71 5 350 pc 0.670 saha et al./oper. res. eng. sci. theor. appl. first online figure 6. convergence behavior of alo, choa, mfo, sho, hho, mpa, pso, and tlbo for multi-objective function. table 8. average computation time for the eight optimizers optimizer average computational time (secs) alo 5.070851 choa 1.664359 mfo 1.119026 hho 1.052527 mpa 0.720689 sho 0.1390570 pso 0.2506701 tlbo 0.3054067 5. statistical and sensitivity analysis to summarize the robustness and performance stability of the metaheuristic optimizers, we retrieved the statistical data evaluated for all the optimizers while dealing with multi-objective optimization problems in the two considered cases. the statistical metrics such as the mean and co-efficient of variation are evaluated after the execution of the optimizers for 30 number of runs. comparative analysis of metaheuristic optimizers in the performance optimization of wire electric discharge machining processes figure 7. bar plots revealing mean value of objective function derived using optimizers for the two cases. case-1 performance optimization in wedm of a286 superalloy; case2 performance optimization in wedm of ti-6al-4v superalloy the mean value of objective function procured using the optimizers for the two cases are plotted in the form of 3d bar plots in figure (7). from figure (7), it is clear that hho provides the least mean value of objective function for all the cases corroborating the robustness of hho over the other competing algorithms in terms of tracking the global optimal solution. figure (8) portrays the coefficient of variation procured using the optimizers for the two cases in the form of 3d bar plots. it is noted that hho exhibits the least coefficient of variation for all the cases corroborating that hho optimizer has the maximum stability over its other competitors. to summarize, it can also be inferred that hho exhibits robustness in bolstering an adequate balance between two phases (i.e., exploration and exploitation). figure 8. bar plots revealing coefficient of variation derived using optimizers for the two cases. case-1 performance optimization in wedm of a286 superalloy; case-2 performance optimization in wedm of ti-6al-4v superalloy saha et al./oper. res. eng. sci. theor. appl. first online 6. performance of optimizers on benchmark test functions as corroborated from the different cases investigated in wedm on the superiority of hho over the other competing algorithms, we further intend to investigate the robustness of hho by comparing its performance with the other competing optimizers on standard test functions. the details of the standard test functions can be found in the literature (zhu & kwong, 2010). the standard test functions considered in the present work are the sphere function, and the generalized rastrigin’s function, respectively. sphere function is a unimodal function which contains only one optimum point. whereas generalized rastrigin’s function is a multimodal function which contains many local optima but only one global optimum. the mathematical description of the functions is illustrated below: sphere function dim 30 2 1 ( ) -100 100 i i i f x x x      (67) where dim denotes the dimension of the solution space, and -100 100 i x  depicts the initial range of i x . generalized rastrigin’s function     dim 30 2 1 10 cos 2 10 -5.12 5.12 i i i i f x x x x          (68) where dim refers the dimension of the solution space, and -5.12 5.12 i x  depicts the initial range of i x . table 9 depicts the results (average ± standard deviation) of the eight optimizers on the optimization of benchmark test functions. hho algorithm is found to be superior over the other optimizers in terms of robustness. table 9. performance comparison on benchmark test functions optimizer alo choa mfo hh o mpa sho pso tlbo sphere function 5.30e09 ±3.4035 e-09 2.60e06 ±6.43 e-06 3.38e -13 ±5.21 e-13 0 ± 0 2.76e -21 ±3.66 e-21 6.61 e100 ±1.5 e-99 3.39e-07 ±8.40871 e-07 2.83e -89 ±6.78 e-89 generalize d rastrigin’s function 23.4809 8± 12.6612 3 10.63 647 ± 10.56 995 20.70 2215 ± 11.50 4771 2 0 ± 0 0 ± 0 0 ± 0 12.43697 ± 6.52438 2.45e +00 ± 2.154 3798 09 comparative analysis of metaheuristic optimizers in the performance optimization of wire electric discharge machining processes 7. conclusions wedm is a complicated machining process. machining in wedm at any parametric combination does not result in enhanced performance outcomes. for improved performances in wedm, machining must be carried out in compliance with the optimal parametric settings. metaheuristic optimizers have grown in prominence due to their potential to provide global optimal solutions. however, the use of recently reported metaheuristic optimizers in non-traditional machining techniques has received little attention. the novelty of the present article is to explore the six recently reported metaheuristic optimizers namely the ant lion optimization (alo), chimp optimization algorithm (choa), moth flame optimization (mfo), spotted hyena optimization (sho), harris hawk optimization algorithm (hho), and marine predator algorithm (mpa) in the optimization of wedm performances for two wedm processes. two well-known existing optimization approaches (i.e., pso and tlbo), are also included in this study to allow a fair evaluation of the algorithms' performance. the comparison between the eight algorithms are carried out in terms of the optimal solutions, convergence rate, and average computational time. the goal of the comparative analyses is to select the robust optimizer. it is observed that the hho algorithm is extremely robust in yielding global optimal solutions. moreover, hho algorithm surpasses other competitors in terms of rapid convergence. thus, hho portrays high exploration and exploitation potential. tlbo algorithm shows the least average computation time. future research might focus on the exploitation of hho to determine the optimal operating condition in other areas of manufacturing. acknowledgment s saha is grateful for the financial support from moe, india, during this work. references abualigah, l., shehab, m., alshinwan, m., mirjalili, s., & elaziz, m.a. 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(2010). gbest-guided artificial bee colony algorithm for numerical function optimization. applied mathematics and computation, 217, 31663173. https://doi.org/10.1016/j.amc.2010.08.049 © 2022 by the authors. submitted for possible open access publication under the terms and conditions of the creative commons attribution (cc by) license (http://creativecommons.org/licenses/by/4.0/). https://doi.org/10.1016/j.measurement.2019.04.003 https://doi.org/10.1016/0890-6955(95)00019-t https://doi.org/10.1016/0890-6955(95)00019-t https://doi.org/10.1016/j.energy.2014.07.078 https://doi.org/10.1109/4235.585893 https://doi.org/10.1109/jsen.2021.3091619 https://doi.org/10.1016/j.aej.2021.11.011 https://doi.org/10.1016/j.amc.2010.08.049 comparative analysis of metaheuristic optimizers in the performance optimization of wire electric discharge machining processes subhankar saha 1, 2, saikat ranjan maity 1*, sudip dey 1 1. introduction 2. literature review 3. metaheuristic optimization algorithms 3.1. teaching learning based optimization (tlbo) 3.1.1. teacher phase 3.1.2. learner phase 3.2. particle swarm optimization 3.3. spotted hyena optimizer 3.3.1. prey encircling 3.3.2. prey hunting and prey searching 3.4. chimp optimization algorithm 3.5. moth flame optimization 3.6. ant lion optimization 3.7. marine predator algorithm (mpa) 3.7.1. initialization 3.7.2. phase 1 3.7.3. phase 2 3.7.4. phase 3 3.7.5. finishing 3.8. harris hawk optimization 4. wedm performance optimization 4.1. case 1 performance optimization in wedm of a286 superalloy 4.1.1. single-objective optimization 4.1.2. multiple objective optimization 4.2. case 2 performance optimization in wedm of ti-6al-4v alloy 4.2.1. single objective optimization 4.2.2. multiple objective optimization 5. statistical and sensitivity analysis 6. performance of optimizers on benchmark test functions 7. conclusions operational research in engineering sciences: theory and applications vol. 5, issue 3, 2022, pp. 108-130 issn: 2620-1607 eissn: 2620-1747 doi: https://doi.org/10.31181/oresta051022076a * corresponding author. lazim_m@umt.edu.my (l. abdullah), harish.garg@thapar.edu (h. garg), azzah@tmsk.uitm.edu.my (n.a. awang), mherrini@yahoo.com (h.m. pauzi), hazwanihashim@uitm.edu.my (h. hashim) non-pharmaceutical intervention strategies to respond to the covid-19 pandemic: preference ranking method lazim abdullah1*, harish garg 2,3,4, noor azzah awang 5, herrini mohd pauzi1, hazwani hashim 65 1 management science research group, faculty of ocean engineering technology and informatics, university malaysia terengganu, malaysia 2 school of mathematics, thapar institute of engineering and technology, (deemed university), punjab, india 3 department of mathematics, graphic era deemed to be university, dehradun, india 4 applied science research center, applied science private university, amman, jordan 5 college of computing, informatics and media studies, university of technology mara, malaysia 6 faculty of computer and mathematical sciences, university of technology mara, malaysia received: 22 august 2022 accepted: 03 october 2022 first online: 05 october 2022 research paper abstract: one of the hot topics of discussion today is coronavirus disease 2019 (covid19). the disease is easily transmitted from one person to another person. however, there are no specific drugs that can alleviate the disease thus non-pharmaceutical intervention strategies is a good option. this paper aims to apply the preference ranking organization method for enrichment evaluation (promethee) method to outrank the intervention strategies. a case study is presented where five experts were invited to rate ten alternatives and ten criteria using linguistic scales. spreadsheet software and promethee-gaia software were employed to establish outranking results and to provide evidence on the vigorousness of the outranking results. the final outranking indicates that the most and the least preferred intervention strategies are alternative a1 (lockdown/quarantine) and alternative a10 (practice of hand hygiene) respectively. the outranking results are further analyzed with distribution analysis and weights sensitivity analysis where these analyses provide evidence on the vigorous of the outranking results. it is found that these analyses confirm the position of a1 as the most preferred intervention strategy to curtail the covid-19 transmissions. the findings would be beneficial for public health authorities to deal with multiple challenges to curb the spread of covid-19. key words: preference function; decision making; covid-19, public health; weight sensitivity non-pharmaceutical intervention strategies to respond to the covid-19 pandemic: preference ranking method 109 1. introduction one of the deadliest diseases of late 2019 was coronavirus disease 2019 (covid19). according to the world health organization (who), covid-19 was detected in wuhan, hubei province, china, in december 2019. covid-19 is a contagious disease caused by a novel coronavirus called sars-cov-2 and is also familiar with 2019-ncov (zhang et al., 2020). the virus of covid-19 can spread from one person to another through respiratory droplets when an infected individual sneezes or coughs. the covid-19 symptoms can make someone experience shortness of breathing, fever, dryness, cough, myalgia, diarrhea, fatigue, headache, rhinorrhea, or severe symptoms (larsen, 2021). in some cases, people can die, and it will start appearing within two and fourteen days, with a median of five days after someone gets infected (who 2020). according to rismanbaf (2020), there are still no specific treatments for covid-19 patients. for people at increased risk for severe cases such as pneumonia and septic shock, the patients will refer to additional treatment that includes intubation or mechanical ventilation. initially, it may seem that the person involved with an infected animal or who eats the kind of animal in that market could be infected. however, the rapid transmission of 2019-ncov from person to a person gives the result on such a large scale. the rise of covid-19 supports these confirmed cases, and more proof that comes to light with the new clusters between a close person and family members has affirmed the likelihood of person-to-person transmission (chan et al. 2020; chen et al. 2020; phan et al. 2020; rothe et al. 2020). the covid-19 virus spreads initially through inhaling when an infected person coughs or sneezes (rothan & byrareddy, 2020). some claim that symptomatic humans are likely the most persistent cause of spreading 2019ncov. china's public health is finding three major transmission tracks of 2019-ncov: droplet spreading, close contact transmission, and respiratory transmission (adhikari et al. 2020). a great deal of work has been involved in suggesting measures to stop the transmission of covid-19. these include important measures, which are avoiding close contact with infected people, physical distancing, practicing good hygiene, isolation, and additional treatments (güner et al. 2020). recently, there is still no cure and specific drugs available (cao et al. 2020). despite the fact that there are still many tests to be done, as of this writing, the who has proclaimed covid-19 to be a global pandemic that has spread quickly around the world. as the ongoing pandemic of covid-19 has rapidly spread to the global community, it is crucial for countries, such as their policymakers, governors, and individuals that are responsible for this spread to understand the risk factors and provide responses to the covid-19 pandemic. countries around the world have suffered disruption from this pandemic. ten million people have been infected, and as a result of this, social and economic structures have been badly affected (ahlstrom & wang 2021). therefore, it is crucial to understand the response that may take to prevent this unnecessary suffering. mahmud & al-mohaimeed (2020), in response to this problem, examined the effectiveness of local and international covid-19 epidemic control measures and proposed the best global pandemic prevention and control techniques. in a different study, maqbool & khan (2020) identified the challenges of using social and public health interventions to stop the spread of covid-19. countries need adequate l. abdullah et al./oper. res. eng. sci. theor. appl. 5(3)2022 108-130 110 devising to hinder mass transmission and disaster, and efficient planning might help flatten the curve of a graph in the spike of the outbreak pandemic. however, samanlioglu & kaya (2020) indicate that research about evaluating strategies is insufficient. some academics have assessed non-pharmaceutical strategies for the covid-19 pandemic based on a combined expert opinion to prepare for it and other pandemics of a similar nature (aledort et al. 2007). a study on preventive strategies, for example, was conducted by merler & ajelli (2010). they used a survey approach to evaluate the diffusion of pandemic influenza and developed stochastic mathematical modeling. data were collected from a large number of respondents which involved households’ groups, workers, and students that highly been exposed to close contacts within europe. similar survey approaches were also adopted by kohlhoff et al. (2012) and russell et al. (2016) where data at hospitals and schools were used respectively to identify strategies in preventing the spread of high-scale pandemic influenza and transmission of influenza virus. the approaches were also used to assess the magnitude of an individual’s condition, both physically and mentally, such as depression and anxiety as the consequences of the lockdown prevention strategy (ahorsu et al. 2020). coccia (2020) studies environmental elements that speed up the spread of covid-19 using data from a sample of fifty-five italians. she also offers a solution for dealing with covid-19-like pandemic concerns in the future. three series of statistical analyses were conducted to meet the research objectives. preliminary statistical analysis such as mean and standard deviation was implemented followed by correlation and linear regression. these analyses are the typical basic statistics used in analyzing cause-effect relations between the factors and their effect on the diffusion of covid-19. it can be seen that these statistical approaches were disregarded the collection of data through expert opinion. in contrast to the methodology based on statistical analysis, this paragraph provides some light on multi-criteria decision-making approaches used in dealing with the covid-19 pandemic of which research gaps between these reviews and the current approach used in this study can be filled in. the covid-19 disease appeared in the world in late 2019 and since then numerous research has been conducted to investigate this pandemic from non-pharmaceutical preventing approaches perspectives. in order to determine the most effective course of action, saeidpour & rohani (2022) created an intervention policy model that included the relative human, implementation, and healthcare costs of non-pharmaceutical pandemic solutions. maqbool & khan (2020) for example, conducted research regarding analyzing barriers to implementing public health and social measures to prevent the transmission of the covid-19 disease. they applied the decision-making trial and evaluation laboratory (dematel) method to suggest the barriers that prevent the implementation of public health and social measures in india. they suggested that the efficient execution of public health and social initiatives is dependent on the availability of appropriate resources such as medical facilities, the healthcare system, and financial relations. this research extends further in evaluating the barrier through similar work or using other decision-making methods in different countries. the method of dematel was also applied by altuntas & gok (2021) to suggest a method on how to lower the impact of the covid-19 pandemic on domestic tourism in turkey. about the similar approach as maqbool and khan (2020), they suggested that quarantine resolution is the most influential strategy to slow down the spread of the covid-19 disease. similar multi-criteria decision-making was also extended in non-pharmaceutical intervention strategies to respond to the covid-19 pandemic: preference ranking method 111 the field of the hospitality industry and quarantine disease. yang et al. (2020) introduced a novel method to propose the decision support algorithm for selecting an antivirus mask to widen the use of masks in the era of the covid-19 pandemic. they also developed a multi-criteria decision-making method based on bonferroni mean operator in selecting medical consumer products during the covid-19 outbreak, which is for selecting the antivirus masks over the covid-19 era. recently, upadhyay et al. (2021) applied the multi-criteria analysis fuzzy-analytical hierarchical process method to identify the critical barriers in social isolation in india amid the covid-19 outbreak. unlike survey and statistical approaches where huge data collection is involved, the current study intends to undertake a non-statistical approach where data are collected via expert judgment and the analysis is made using a preference based on level criterion function. non-pharmaceutical strategies for preventing the spread of the covid-19 pandemic are investigated from the perspective of multi-criteria decision making owing to the understanding that multiple strategies in preventing the spread are associated with multiple criteria. specifically, this study aims to obtain the ranking of non-pharmaceutical intervention strategies in combating the covid19 using a preferred method. the preference ranking organization method for enrichment evaluation (promethee) method is applied to suggest the most viable intervention strategies in combating the covid-19 pandemic. in addition, the sensitivity of the ranking results is investigated based on a variety of weights of the criteria. in summary, this study provides several significant contributions to methodology and findings. first, this study suggests the method based on preference order to rank the non-pharmaceutical approaches in preventing the spread of the covid-19. the method employs linguistic evaluation elicited from a group of experts in public health. accordingly, the level criterion preference function of promethee provides a convenient way to compute linguistic information from experts. second, the findings are derived from the multi-criteria decision aid promethee method of which the optimal solution in searching the non-pharmaceutical approaches is obtained through experts’ opinions. the ranking results can provide a better understanding of the measures needed to curb the infectivity. finally, the findings are affirmed with a sensitivity test of weight where the variations in weights of criteria are observed against the robustness of preference order of alternatives. this paper is structured as follows. a brief review on the use promethee in various fields is presented in section 2. the methodology of this research is given in section 3. the implementation of the case which includes detailed computational steps is presented in section 4. section 5 adds an analysis of the sensitivity of weight towards the final preference results. section 6 concludes the outcomes of the study. 2. related research this section presents a brief literature review of promethee and its applications. the promethee is one of the most often used methods in preference method selection analysis, which has recently attracted a lot of interest from decision making researchers (arcidiacono et al. 2018). therefore, the use of promethee in various applications is not something new and is increasingly growing. this pattern of growth l. abdullah et al./oper. res. eng. sci. theor. appl. 5(3)2022 108-130 112 can be noticed since the day it was published in 1985 (brans & vincke, 1985). the promethee has been effectively utilized in solving numerous decision making problems. a non-exhaustive list of scientific materials related to promethee method and its applications has been published since 2010 (behzadian et al. 2010). it is primarily used in a wide range of decision-making scenarios and has a specific use in decision-making. in business and management related research, the pomethee has been used in bankruptcy prediction (hu & chen, 2011), and recently used in measuring key performance indicators (demirdöğen, et al. 2022). by utilising promethee ii, mousavi & lin (2020) expanded the use of expert systems to anticipate business credit risk and financial distress. in a corporate governance study, guney et al. (2020) used promethee method and econometric analysis to obtain a relationship between firm performance and corporate governance quality. recently, kuncova & seknickova (2021) evaluated the order of regions regarding economic indices using weighted promethee combines with preferences functions. not only the use of promethee in business and management research, this preference-based decision making method was also used in very specific or niche research areas. for example, nassereddine et al. (2019) conducted research in evaluating emergency response systems. the interaction synergy of criteria and alternatives in the system was investigated using the promethee. the competitiveness of tourist destinations is a crucial topic in the tourism business since it allows destinations to understand their position or ranking in relation to other destinations. to solve this issue, lopes et al. (2018) applied the promethee method to rank eight tourism destinations in the northern region of portugal. about the similar application of promethee can be seen in the education sector (de smet and lidouh, 2013; murat et al., 2015; ningsih et al., 2019), in green building research (hermoso-orzáez et al., 2019), and biomass and biofuel energy research (schröder et al., 2019; mofijur et al., 2022; genç et al., 2022). in industry-based research, promethee was used by aydemir et al. (2019) to identify the mechanical, thermal, and morphological characteristics of heat-treated wood-polypropylene polymer composites and choose the composites with the best characteristics. durin and nad (2018) applied promethee in selecting the most appropriate variant of solar photovoltaic water supply systems. turning now to an application of promethee in health sciences where a group of researchers in uruguay identified and ranked alternatives used in the national food mouth disease program illustrated using promethee (corbellini et al., 2020). in healthcare education, recently, saboktakin et al., (2021) used pomethee to educate hospitalized cardiovascular disease patients about lifestyle and behavior modification. in animal healthcare research, very recently, guétin‐poirier et al., (2022) used promethee as a tool to aid decision-makers in choosing the appropriate protocol to apply to a group animal while considering the technical and socio-economic facets of the problem. as we can see, despite the considerable amount of research has been carried out on promethee and its various applications, to the best of the authors’ knowledge, there has been little attention has been devoted to conclude the most preferred invention strategies in combating the spread of covid-19. non-pharmaceutical intervention strategies to respond to the covid-19 pandemic: preference ranking method 113 3. methodology this section describes how this study is implemented. the first subsection explains the criteria and alternatives employed in this study. these criteria and alternatives are evaluated by a group of experts using five linguistic scales. subsection 3.2 presents profiles of experts and the rating scales used in this study. more importantly, the computational procedures of the promethee method are presented in the final subsection. 3.1. criteria and alternatives in this section, the criteria and alternatives are selected and retrieved from the work of maqbool & khan (2020). in their research, they used the term barriers instead of criteria to make it consistent with the term normally used in public health. these barriers are identified using a systematic literature review and, in the analysis, they employed the dematel method to categorize the ten barriers. their study's main objective is to classify the obstacles to putting social and public health measures in place to stop the spread of covid-19. unlike this objective, our current study aims to rank the barriers according to expert judgment using the promethee method. in the methodology of this study, we use the term criteria instead of barriers to fit with the conceptual definition of the promethee method. the ten criteria are adopted in this study where these criteria are believed to represent the factors to respond to the covid-19 pandemic. these criteria and their brief descriptions are listed below. i. failure of safety engagement (c1): the acknowledgment and awareness about covid-19 from the public. ii. failure of safety practice (c2): this criterion indicates that refer to safety practices to help from exposure to covid-19 iii. failure of bureaucratic and governmental commitment at society (c3): this criterion focuses on commitment from the government how to discover the opportunities to simplify the progress of lockdown, social distancing, and mass events. iv. poor of strict requirement of who regulation (c4): the attribute that focuses on guidelines from who regulations because who is the only one that states regarding covid-19 v. inadequate resources for public health (c5): this criterion indicates the capacity of public health in handling the covid-19 cases in erecting the critical care or place for those who have severe cases of covid-19. vi. lack of medical equipment (c6): the demand for medical facilities due to the rise in infection of covid-19. vii. lack of insight from government policies (c7): this refers to government policies that require them to provide new update details of covid-19 accurate, rational, timely according to human rights principles. viii. non-implementation of domestic instruction during quarantine (c8): the criteria refer to non-fixed conditions for movement due to shortage of groceries and daily basis. l. abdullah et al./oper. res. eng. sci. theor. appl. 5(3)2022 108-130 114 ix. public censure (c9): the statement and judgment from the public about a person who is infected with covid-19 lead to someone enclosing and hiding their condition or illness. x. lack of appropriate information from public health (c10): the awareness from public health regarding the importance and seriousness of covid-19 to the public. the community needs an efficient and systematic way to ascertain the best strategy to be implemented amid the covid-19 outbreak. these strategies are retrieved from samanlioglu & kaya (2020) and aledort et al. (2007) where it appraises the non-pharmaceuticals that are normally used in public health for pandemic influenza. for the purpose of tailoring with the promethee method used in this study, the words intervention strategies and alternatives are interchangeably used. the list of alternatives is given below. i. lockdown/quarantine (a1): the alternative centers on everything from required geographic restrictions to optional rules that urge everyone in the nation to stay at home, shut down specific companies, and prohibit large-scale gatherings. closure borders within a country (a2): this alternative indicates keeping the measures by the closure of borders within the country. ii. physical distancing (a3): this indicates limiting a massive group of people and keeping a particular distance from other people. iii. contact monitoring/tracing (a4): this attribute focuses on a person who has close contact with someone that is infected with covid-19. iv. isolation of infected patients (a5): the alternative indicates that a person who got infected from covid-19 must be quarantined in hospitals, other facilities, and in their own homes. v. school closure (a6): the shutdown of schools and other educational institutions. vi. restraint of nonessential business (a7): this refers to discontinuing and closing the operation of their business. vii. prohibition/ban of internal and domestic travel (a8): the alternative represents someone is not allowed to go out of the country. viii. abortion of group events and mass gatherings (a9): the alternative represents the density of people that are involved in the limited space and recognized in other living areas. ix. practice of hand hygiene (a10): this is the capacity to prevent the transmission of covid-19 that is highly supposed to be used with an alcohol-based solution. the criteria and alternatives are the main variables of this study in which their relationship and dependency in decision-making are evaluated by a group of experts. the relationships and dependency of the alternatives and criteria are illustrated in figure 1. non-pharmaceutical intervention strategies to respond to the covid-19 pandemic: preference ranking method 115 figure 1. the dependency structure of alternatives and criteria expert judgment of alternatives with respect to criteria is guided by rating and linguistic scales. this type of evaluation is typically applied at the project planning stage, where decisions are made based on abilities, specializations, or knowledge in a given field. an individual's expertise may be based on their training, educational background, professional experience, or knowledge of a particular field. for instance, a nurse's professional judgment typically depends on the experience and knowledge of the nurse who is currently on duty (burstein et al. 2006). the following subsection describes a brief biography of experts and linguistic ratings. 3.2. experts and linguistic scales the alternatives and criteria are evaluated by a group of experts. five experts are invited to rate the importance of alternatives with respect to criteria using the rating scale as shown in table 1. table 1. five-point likert scale and its linguistic scale. rating linguistic scale 0 certainly low importance (cli) 1 low importance (li) 2 moderate importance (mi) 3 high importance (hi) 4 very high importance (vhi) the brief biography of experts is summarized in table 2. l. abdullah et al./oper. res. eng. sci. theor. appl. 5(3)2022 108-130 116 table 2. biographical data of experts expert biodata expert 1 (d1) expert 2 (d2) expert 3 (d3) expert 4 (d4) expert 5 (d5) field of experts biomedicine nursing nursing public health critical care position senior lecturer senior staff nurse staff nurse senior medical officer medical officer academic qualification doctorate in biomedicine bachelor of nursing bachelor of nursing mbbs, mph mbbs years of experience 7 17 8 15 6 the data that was collected via experts’ judgments are gathered and then analyzed using the computational procedural of promethee. the detailed steps of computational procedures are given as follows. 3.3 computational procedures primarily, the promethee method proposed by mousavi & lin (2020) is used as the computational procedure tool in this research. this method is relatively new and is considered the latest version of promethee. the computational procedures begin with the degree of importance of criteria and a criterion-based evaluation of alternatives. these numerical data represent the relative importance of criteria and the difference between two alternatives using a preference function. the importance of criteria and the difference of two alternatives are aggregated to become a preference index. the whole computational procedures consist of nine steps of which the first step and second step are adopted from bagherikahvarin et al. (2019). the first two steps are meant to ensure the correct fraction and normalization of data. the rest of the computational procedures remained as mousavi & lin (2020) where these authors applied the computational procedures to predict distress in finance. this study is the maiden attempt to solve the problem about alternatives and criteria of non-pharmaceutical approach in combating the covid-19 pandemic. given qualitative linguistic data used in this study, the type iv preference function is adopted while the indifferences between alternatives are set on an interval. the flow chart of the methodology is illustrated in figure 2. non-pharmaceutical intervention strategies to respond to the covid-19 pandemic: preference ranking method 117 figure 2. flowchart of the proposed method details of the computational procedures are described as follows. step 1: define fraction and normalized data fraction data xi is defined as quotient, in which responded scale is divided by largest scale whereas normalized data yi is the ratio of xi to a total of xi , step 2: aggregate weight of the criteria w where  1 m j j w (1) where j w is the weight of the criteria j=1,2,…,m. step 3: obtain ratings of alternatives from experts, ij r aggregate the scale that represents expert judgment using equation (2). | min( ) | , =1,2,..., 1, 2,..., | max( ) min( ) | ij ij ij ij ij x x r i n j m x x       (2) where ij x denoted the evaluation values provided by the experts =1,2,...,i n and the number of criteria j=1,2,…,m. the average weight and average rating as shown below: l. abdullah et al./oper. res. eng. sci. theor. appl. 5(3)2022 108-130 118 average weight of criteria = 0 m ji i c m   (3) average rating = 0 m ji i r m   (4) step 4: determine the deviations between the evaluations of a and b on each of the criterion using pairwise comparisons using equation (5) ( , ) ( ) ( ) j j j d a b m a m b  (5) where j d is the deviations while  jm a and  jm b are the evaluations of a and b on each criterion, respectively. step 5: obtain threshold value and deviations between two alternatives     , ,j j jp a b f d a b , j=1,2,…,m (6) where  ,jp a b represent the difference function between the alternative b of evaluations in each of the criterion into a degree 0 to 1. fj is type iv, level criterion function where the domain q(x) is given as 0, 1 ( ) , 2 1, q x        for x r for x x r s for x r s       step 6: calculate the aggregated preference index.           1 1 , , m m j j j j j a b p a b w w (7) where j w > 0 are the weights associated with each criterion. the symbol   ,a b indicates the degree of a is preferred to b over all the criteria.   , 0a b implies a weak preference of a over b.   , 1a b implies a strong preference of a over b. step 7: promethee i can be used to obtain partial ranking; if complete ranking is required, promethee ii must be used for one more step in the computation. determine the leaving and the entering outranking flows i. leaving the (positive) flow ath alternatives,  (a) non-pharmaceutical intervention strategies to respond to the covid-19 pandemic: preference ranking method 119 1 1 ( , ) ( ) 1 n k a b a b n      (8) ii. entering the (negative) flow ath alternatives,  (a) 1 1 ( , ) ( ) 1 n k b a a b n      (9) where k is alternative and n is the number of alternatives. step 8: calculate the net outranking flow of each alternative ( ) ( ) ( )a a a       (10) where ( )a is net outranking flow. step 9: determine the ranking of all the considered alternatives depending on the value ( ) net a . the higher leaving flow and the lower entering flow show the best alternative performance. in accordance with the computational procedures, this study attempts to implement it in the case of the selection of alternatives of responses to the covid-19 pandemic. 4. implementation in this section, data analysis using the promethee method is presented. these computations are implemented using spreadsheet software and promethee-gaia software of which the alternatives or prevention strategies of the covid-19 pandemic are evaluated. the following notation are used for a set of ten criteria:  1 2 3 4 5 6 7 8 9 10, , , , , , , , ,c c c c c c c c c c , a set of experts:  1 2 3 4 5, , , ,d d d d d and a set of alternatives:  1 2 3 4 5 6 7 8 9 10, , , , , , , , ,a a a a a a a a a a . in accordance with the computational procedures given in section 3, these computations are implemented as follows. step 1: fraction and normalization of the data of criterion. fraction xi = ri-1 / max{ 1}ix  . for example, ix = 3-1/5-1= 0.5, and normalized data 10 1 i i i i x y x    . for example, 1 0.5 0.090909 0.5 0.5 ... ... ... ... ... ... 0.75 0.5 y            the fractioned and normalized data of each criterion given by experts are shown in table 3 and table 4, respectively. l. abdullah et al./oper. res. eng. sci. theor. appl. 5(3)2022 108-130 120 table 3. fractioned data of criteria given by experts 1 d 2 d 3d 4d 5d c1 0.5 0.5 0.5 0.5 0.5 c2 0.5 0.5 0.5 0.75 0.75 c3 0.5 0.5 0.25 0.5 0.5 c4 0.5 0.5 0.25 0.75 0.75 c5 0.5 0.5 0.5 0.75 0.5 c6 0.5 0.5 0.5 0.75 0.25 c7 0.75 0.5 0.25 0.75 0.75 c8 0.5 0.5 0.25 0.75 0.5 c9 0.75 0.5 0.25 0.75 0.75 c10 0.5 0.5 0.5 0.5 0.75 table 4. normalized data of criteria and experts 1 d 2 d 3d 4d 5d c1 0.090909 0.10 0.133333 0.074074 0.083333 c2 0.090909 0.10 0.133333 0.111111 0.125 c3 0.090909 0.10 0.066667 0.074074 0.083333 c4 0.090909 0.10 0.066667 0.111111 0.125 c5 0.090909 0.10 0.133333 0.111111 0.083333 c6 0.090909 0.10 0.133333 0.111111 0.041667 c7 0.136364 0.10 0.066667 0.111111 0.125 c8 0.090909 0.10 0.066667 0.111111 0.083333 c9 0.136364 0.10 0.066667 0.111111 0.125 c10 0.090909 0.10 0.133333 0.074074 0.125 step 2: utilizing equation (1), aggregate each criterion's weight. table 5 summarizes the aggregated weight of the criteria. table 5. aggregated weight of criteria criteria aggregate weight c1 0.09633 c2 0.112071 c3 0.082997 c4 0.098737 c5 0.103737 c6 0.095404 c7 0.107828 c8 0.090404 c9 0.107828 c10 0.104663 step 3: rating of alternatives. the rating of alternatives uses an averaging equation (see equation (3)) and normalization by using equation (4). the evaluations of these alternatives (a1,…,a10) corresponds to all criteria are shown in table 6. non-pharmaceutical intervention strategies to respond to the covid-19 pandemic: preference ranking method 121 table 6. rating of alternatives with respect to criteria c1 c2 c3 c4 c5 c6 c7 c8 c9 c10 a1 0.7 0.6 0.6 0.65 0.6 0.6 0.6 0.45 0.65 0.6 a2 0.6 0.55 0.5 0.45 0.6 0.5 0.55 0.4 0.6 0.6 a3 0.55 0.55 0.5 0.6 0.65 0.6 0.55 0.4 0.55 0.65 a4 0.65 0.6 0.55 0.5 0.7 0.5 0.55 0.45 0.6 0.65 a5 0.45 0.45 0.35 0.4 0.55 0.65 0.6 0.35 0.65 0.7 a6 0.45 0.5 0.45 0.55 0.55 0.6 0.45 0.25 0.35 0.3 a7 0.55 0.55 0.4 0.65 0.65 0.55 0.55 0.4 0.5 0.45 a8 0.55 0.55 0.6 0.6 0.6 0.6 0.6 0.55 0.5 0.45 a9 0.65 0.45 0.5 0.6 0.5 0.65 0.55 0.45 0.35 0.6 a10 0.55 0.45 0.35 0.45 0.55 0.45 0.35 0.35 0.4 0.45 step 4: determination of deviation pairwise comparison the computation comprises utilizing equation (5) to calculate the differences between the criteria value of ai and other alternatives. table 7 displays a summary of the deviations. table 7. deviation of two alternatives with respect to criteria c1 c2 c3 c4 c5 c6 c7 c8 c9 c10 a1a2 0.1 0.05 0.1 0.2 0 0.1 0.05 0.05 0.05 0 a1a3 0.15 0.05 0.1 0.05 -0.05 0 0.05 0.05 0.1 -0.05 a1a4 0.05 0 0.05 0.15 -0.1 0.1 0.05 0 0.05 -0.05 a1a5 0.25 0.15 0.25 0.25 0.05 -0.05 0 0.1 0 -0.1 a1a6 0.25 0.1 0.15 0.1 0.05 0 0.15 0.2 0.3 0.3 a1a7 0.15 0.05 0.2 0 -0.05 0.05 0.05 0.05 0.15 0.15 a1a8 0.15 0.05 0 0.05 0 0 0 -0.1 0.15 0.15 a1a9 0.05 0.15 0.1 0.05 0.1 -0.05 0.05 0 0.3 0 a1a10 0.15 0.15 0.25 0.2 0.05 0.15 0.25 0.1 0.25 0.15 a2a1 -0.1 -0.05 -0.1 -0.2 0 -0.1 -0.05 -0.05 -0.05 0 a2a3 0.05 0 -0.1 -0.15 -0.05 -0.1 0 0 0.05 -0.05 a2a4 -0.05 -0.05 0 -0.05 -0.1 0 0 -0.05 0 -0.05 a2a5 0.15 0.1 0.1 0.05 0.05 -0.15 -0.05 0.05 -0.05 -0.1 a2a6 0.15 0.05 -0.05 -0.1 0.05 -0.1 0.1 0.15 0.25 0.3 a2a7 0.05 0 -0.15 -0.2 -0.05 -0.05 0 0 0.1 0.15 a2a8 0.05 0 -0.1 -0.15 0 -0.1 -0.05 -0.15 0.1 0.15 a2a9 -0.05 0.1 -0.1 -0.15 0.1 -0.15 0 -0.05 0.25 0 a2a10 0.05 0.1 0.05 0 0.05 0.05 0.2 0.05 0.2 0.15 step 5: obtain threshold value the level function (type iv) is used to propose threshold values. the level function consists of indifference and preference thresholds where q represents the most significant value below sufficient to generate a full preference. in contrast, the preference threshold (p) indicates the smallest number above sufficient to generate a full preference. these values are selected based on their judgment and based on experts’ evaluation in this study. the threshold value for all criteria is 0.1p and 0.05q . these threshold values will determine a deviation between two alternatives with respect to criteria. l. abdullah et al./oper. res. eng. sci. theor. appl. 5(3)2022 108-130 122 step 6: calculate the preference index the index is calculated by using equation (7). for example, 1 2 ( , )a a  10 1 (0.5* 0.09633 0 * 0.11207 0.5* 0.083 1* 0.09874 0 * 0.10374 0.5* 0.0954 0 * 0.10783 0 * 0.0904 0 * 0.10783 0 * 0.10466) 0.2361 j            step 7: find the alternative's positive and negative outranking flows (promethee i partial ranking). the positive outranking is computed using equation (8) such as   ( 1a ) = 6(1 0.236105 0.191745 0.14644 0.43534 0. 95455 0.39182 0.30882 0.31327 0.85 )19 06          similarly, the negative outranking is computed using equation (9)   ( 1a ) = 2 1 3( 0 0 0.05187 0.05 3 0 0 0. 2 ) 9 045 0 0        step 8: find the alternatives' net outranking flow (promethee ii). the net flows are obtained using equation (10). table 8 shows the positive and negative outranking obtained using promethee i and the net flow of alternatives using promethee ii. table 8. results of promethee i and the net flow (promethee ii) alternatives positive outranking   ( i a ) negative outranking   ( i a ) net flow ranking a1 0.396673 0.0166 0.380073 1 a2 0.172916 0.138937 0.033978 4 a3 0.251328 0.052654 0.198673 3 a4 0.320057 0.085821 0.234236 2 a5 0.195939 0.288839 -0.0929 8 a6 0.058355 0.468532 -0.41018 9 a7 0.182466 0.184657 -0.00219 7 a8 0.286343 0.132887 0.153457 5 a9 0.225944 0.205606 0.020338 6 a10 0.02735 0.54284 -0.51549 10 based on the value of net flow, the ranking of alternatives is finalized as in the last column of table 8. the alternative with the highest net flow value, ϕ(a) which is a1 is the most preferred intervention strategy. as shown in table 8, the alternative a1 (lockdown/quarantine) is the most preferred intervention strategy in response to covid-19. the other strategies are arranged as a4 ≺ a3≺ a8≺ a2≺ a9 ≺ a7 ≺a5 ≺ a6 ≺ a10 based on the degree of preference where ≺ represents ‘is less preferred than’ the complete ranking results are further analyzed as these results are short in visualizing the distribution of the alternatives. the results are also not sufficient to non-pharmaceutical intervention strategies to respond to the covid-19 pandemic: preference ranking method 123 demonstrate the effect of weights of criteria toward the alternatives. in response to these limitations, the complete ranking results are further analyzed using the gaia plane and weight analysis. detailed elucidations of these two analyses are given in the following section. 5. distribution and sensitivity the outranking results obtained from the promethee are further discussed from the perspective of correlations between alternatives and the decision axis. this analysis provides some extend of distribution of alternatives and criteria and how these two variables correlate with the decision axis. the distribution of the criteria is analyzed to see the convergence of every criterion with respect to the decision axis. the variability of weights of criteria and how it affects the alternatives are also discussed in this section. the distribution and weight are two different analyses where their purposes of analyses are distinctive. the analysis of weight is meant to check the sensitivity of the weights of criteria toward the alternatives. these two analyses are further described in the following subsections. 5.1 distribution of criteria and alternatives the recognition of correlations, strengths and weaknesses of alternatives can be seen from the output of the gaia plane. lines on the plane reflect the criteria, whereas dots on the plane represent the alternatives. figure 3 shows the position or distribution of alternatives and the criteria. figure 3. gaia plane the gaia plane’s distribution of criteria allows for a better understanding of the competitive panorama and the analysis of criteria concordance. they all have the l. abdullah et al./oper. res. eng. sci. theor. appl. 5(3)2022 108-130 124 same length, meaning they have a similar power of discrimination. we can observe that the alternative a1 is ranked first. furthermore, it occupies a distinct position from the other alternatives. this owes its position, 'lockdown/quarantine strategy’ in the most preferred intervention strategies to be implemented during the covid-19 pandemic. the figure also depicts the modeled plane indicating the decision axis ( ) (the red line) where most of the criteria are converged to the quadrant. as can be seen in the figure, a1 has established a high position, scoring in all measures of lockdown/quarantine from the origin to the direction of the decision axis. the criteria c10 is noted as the conflicting criterion with c9 and c5 because they are aligned entirely in opposite directions. the other criteria are c6, c4, c7, c3 with either c8 or c1 with c2, indicating that these criteria have the same effect on priority sequencing rule selection. furthermore, the longer axis in blue lines of c4, c9, and c10 demonstrate that they have greater strength in distinguishing all options or strategies. the criteria c8 has a comparatively shorter length as compared to the preferred measures, showing low distinguishing power between the alternatives. the distribution of criteria and alternatives and also their correlations with the decision axis provide supportive evidence of the outranking results obtained from the complete ranking of promethee ii. 3.3 sensitivity of weights weights of criteria used in this study are normally assumed to be almost equal. in other words, the weight of the importance of failure of safety engagement (c1) for example, is assumed to be similar to the other nine criteria. it seems that this assumption warrants further investigation as weights of criteria is intuitively unequal in our daily life. this different treatment of weights is hypothesized to affect the outranking of alternatives. therefore, in this analysis the variability of weights and how it affects the outranking is investigated. in section 4, the outranking results are given as a1≺ a4 ≺ a3≺ a8≺ a2≺ a9 ≺ a7 ≺a5 ≺a6 ≺ a10. this outranking is obtained using the nine-step computation where the weights of criteria are computed using equation (10) (see table 8). figure 4 depicts the outranking results and the weights of criteria. figure 4. outranking of alternatives and weights of criteria this figure includes two bar charts where the top chart depicts the net-flow values of promethee ii while the bottom chart depicts the weight of the criteria. it can be non-pharmaceutical intervention strategies to respond to the covid-19 pandemic: preference ranking method 125 seen that the weight distribution is almost equal where a1 dominates the others, while a10 remains at the bottom of the list. the results of promethee ii will be reviewed in accordance with the weights of criteria. the variability of weight is a sensitivity analysis technique for determining the effects of criterion weight on the final priority sequencing rule selection choice (bari and karande 2021). in the following analysis, we increase the weight of importance in c10 by 25% and this could lead to major changes in rankings of alternatives. figure 5 illustrates the changes in weights and how it affects the ranking. figure 5. weights of criteria and ranking of alternatives the above figure demonstrates that increasing weight of c10 by 25% does not affect the first ranking of alternatives (a1). however, the weights of other criteria have been changed by various percentages thereby the ranking of alternatives also has been changed accordingly. it is good to note that the change of weight of one criterion has little effect on the weights of other criteria. however, the ranking of alternatives has changed completely. in this context, the final ranking results are very sensitive to the weight of each criterion thereby should be dynamically and proportionally vigilant. this result provides evidence on the significance of the weight of criteria in the evaluation of alternatives. in this case study, when the weights of the criteria are changed, then the outranking of alternatives is also changed except a1 (lockdown/quarantine). in addition, the spearman’s rank correlation coefficient is also conducted to see the correlations between the net flow of alternative before and after the changes in criteria weights. figure 6 shows the analysis of spearman’s rank correlation coefficient using the statistical package for the social sciences (spss) software. l. abdullah et al./oper. res. eng. sci. theor. appl. 5(3)2022 108-130 126 figure 6. spearman’s rank correlation coefficient results the correlation coefficient between the net flow of alternatives before and after the modification of the criterion weights is 0.794, an indication of a substantial relationship. since the significant value is 0.006 which is less than 0.01 tested value, we can say that the test is significant and there is a significant relationship between the net flow of alternatives before and after the changes of the criterion weights. therefore, the changes of criterion weights do not have much effect on the outranking of alternatives. 6. conclusion in this study, the promethee method is introduced to determine the best intervention strategies during the covid-19 pandemic by experts’ judgments. to the best of authors’ knowledge, this is the first application of the promethee method and its affiliated analysis to the case of non-pharmaceutical intervention strategies in dealing with the covid-19 pandemic. final results have shown that the proposed method has its own benefits. the promethee method has been successfully identified the alternative a1 (lockdown/quarantine) as the most preferred intervention strategy in response to the covid-19 pandemic. further analysis of the promethee method strengthens the outranking results where distribution analysis indicates the alternative a1 is located at the distinct position from the other alternatives. the weighted analysis also adds another evidence on the optimized preference a1 when the first ranking remains despite changes in weights of criteria. therefore, we can conclude that the promethee method can be attributed to the identification of the best nonpharmaceutical intervention strategies in dealing with the contagious covid19 disease. however, the results of the current study are subjected to limitations and scope of this study. the evaluation model promethee used in this study employs the level non-pharmaceutical intervention strategies to respond to the covid-19 pandemic: preference ranking method 127 criterion function (type iv) where its outcomes (domains) rely on the proposed threshold values. different preference functions and threshold values might give different outcomes of indifferences between two alternatives. the results obtained using the promethee method also very much depend on the weight of the criteria. from the analysis, we can see that the weight of the criterion has a direct impact on the findings. this vulnerability of weights could undermine this study but more importantly this limitation may open a new opportunity in exploring weights. as for future research, different settings of the corresponding parameters such as preference functions and threshold value can be applied in order to discover different ability of the method. yet, the value of weight also could be written in the continuous interval. in this way, an in-depth investigation could be implemented to discover how sensitivity of weights could affect the complete outranking. acknowledgment the authors would like to thank the research student nur alia syazana mh for her assistance in data collection and analyses that have led to the completion of this article. references adhikari, s. p., meng, s., wu, y., mao, y., ye, r., wang, q., sun, c., sylvia, s., rozelle, s., raat, h., zhou, h. 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(2020). new understanding of the damage of sars-cov-2 infection outside the respiratory systems, biomedicine & pharmacotherapy, 127, 110195 (2020). https://doi.org/10.1016/j.biopha.2020.110195. © 2022 by the authors. submitted for possible open access publication under the terms and conditions of the creative commons attribution (cc by) license (http://creativecommons.org/licenses/by/4.0/). non-pharmaceutical intervention strategies to respond to the covid-19 pandemic: preference ranking method lazim abdullah1*, harish garg 2,3,4, noor azzah awang 5, herrini mohd pauzi1, hazwani hashim 65 1. introduction 2. related research 3. methodology 3.1. criteria and alternatives 3.2. experts and linguistic scales 3.3 computational procedures 4. implementation 5. distribution and sensitivity 5.1 distribution of criteria and alternatives 3.3 sensitivity of weights 6. conclusion references operational research in engineering sciences: theory and applications vol. 3, issue 1, 2020, pp. 28-40 issn: 2620-1607 eissn: 2620-1747 doi: https:// doi: 10.31181/oresta200134s * corresponding author herrysupriyatna86@gmail.com (h. supriyatna), widykunia1@gmail.com (w. kurniawan), humiras.hardi@mercubuana.ac.id (h. hardi purba) occupational safety and health risk in building construction projects: a literature review herry supriyatna*, widy kurniawan, humiras hardi purba school of engineering, mercu buana university, jakarta, indonesia received: 13 december 2019 accepted: 03 february 2020 first online: 09 february 2020 review paper abstract. construction building projects have the highest accident rates compared to other industrial projects. for this reason, special attention needs to be paid to all stakeholders, starting from management, contractors and the government to reduce the number of work accidents, occupational diseases, especially in the field of construction. based on the background of the problem and the results of the literature review sourced from journals collected and reviewed discussing occupational safety and health in construction projects in this paper concludes that there are two sources of risk that are very influential namely risks originating from internal and external, both viewed technically and non-technically. technical results can be seen from the use of 4d-bim technology, the use of personal protective equipment, the use of construction tools according to their permits and the nontechnical results, namely awareness to work safely, knowledge and culture about occupational safety and health, construction building projects have the highest accident rates compared to other industrial projects. for this reason, special attention needs to be paid to all stakeholders, starting from management, contractors and the government to reduce the number of work accidents, occupational diseases, especially in the field of construction. based on the background of the problem and the results of the literature review sourced from journals collected and reviewed discussing occupational safety and health in construction projects in this paper concludes that there are two sources of risk that are very influential namely risks originating from internal and external, both viewed technically and non-technically. technical results can be seen from the use of 4d-bim technology, the use of personal protective equipment, the use of construction tools according to their permits and the non-technical results of awareness to work safely, knowledge and culture about occupational safety and health, incentives or gifts given by management and support from the government regarding commitments and supervision for occupational safety and health in construction building projects. key words: occupational safety and health, construction management, risk management, building construction. supriyatna et al./oper. res. eng. sci. theor. appl. 3 (1) (2020) 28-40 29 1. introduction with the rapidly increasing construction projects in the last few decades, the challenges of occupational safety and health in the construction industry have become even greater. the safety record of the construction industry is always bad, it remains one of the most dangerous industries to work. the magnitude of the risk of accidents that occur depends also on the number of risks or hazards identified. factors that influence include task complexity, organizational factors such as giving incentives or bonuses, personal factors such as fatigue, work environment such as work pressure, and external factors such as weather (hallowell and gambatese, 2009). however, the most recognised occupation safety and health hazards on construction sites have been working at height, working underground, working in confined spaces and proximity to falling materials, handling load manually, handling hazardous substances, noises, dusts, using plant and equipment, fire, exposure to live cables, poor housekeeping and ergonomics (okoye, 2018). occupational safety and health not only target construction workers from the local area but also need to provide protection to migrant workers (bust et al. 2008). the reasons construction is risky and prone to occupational safety and health risks are because of the physical environment of the work, nature of the construction work operations, construction methods, construction materials, heavy equipment used, and physical properties of the construction project itself (laryea and mensah 2010). to overcome work accidents, efforts are also being made using technology, namely the ongoing bim safety research project, which aims to develop and test solutions for planning and safety management of construction sites using a more dynamic 4d site model where the aim of the bim safety research project is to develop procedures and use of bim technology for safety planning, management and communication part of 4d construction planning (sulankivi et al. 2010). hazards in the workplace also when combined with task requests, organizational factors, work environment, personal factors, and external factors can produce unacceptable safety risks in the field of personnel and can cause severe injuries at work for that is an important form of approach this behavior is the application of an incentive safety program. safety incentive programs, if carefully chosen and implemented correctly, can create high safety awareness that leads to reduced risk taking and enhanced behavior safety culture. safety incentive programs are usually associated with rewards, either extrinsic or intrinsic, given to workers to encourage safe actions and behavior (karakhan and gambatese, 2018). 2. methodology writing this article is ba sed on a literature review obtained online from a trusted source that discusses risk identification (figure 1)and management of occupational safety and health risks which is then reviewed and synthesized to provide the latest information. occupational safety and health risk in building construction project: literature review 30 figure 1. the method to identify risk 3. result and discussion the review of the publication of scientific articles was carried out from several sources, namely: google scholar, asce, science direct, researchgate, springer, proquest, etc. the list of selected articles is analyzed from aspects of identifying occupational safety and health risks in building construction projects as shown in table 1. supriyatna et al./oper. res. eng. sci. theor. appl. 3 (1) (2020) 28-40 table 1: review of identifying occupational safety and health risks in building construction projects 31 no paper identity risk identification results internal external t nt t nt 1 hallowell and gambatese, (2009) ✓ x x x results indicate that there are 13 major activities required to construct concrete formwork and the highest risk activities are applying form oil, lifting and lowering form components, and accepting materials from a crane. 2 okoye, (2018) ✓ x x x the study found that masonry, carpentry (including formwork and roofing), and iron bending and steel fixing are common building trades associated with high risks; whereas electrical fitting and installation, painting, tiling, and plumbing are medium risk build ing trades. 3 bust et al. (2008) x ✓ x x the challenge of converting the health and safety systems to accommodate a multi national/ cultural workforce is being addressed using initiatives such as, translation of health and safety materials, use of interpreters and an increased use of visual methods for communica ting health and safety messages. 4 laryea and mensah (2010) x ✓ x x the primary reasons are a lack of strong institutional framework for governing construction activities and poor enforcement o f health and safety policies and procedures. 5 kahkonen et al. (2014) ✓ x x x providing more illustrative site layout and safety plans, providing methods for managing and visualizing up-to date plans and site status information, as well as by supporting safety communication in various situations, such as informing site staff about c oming safety arrangements or warning about risks 6 karakhan and gambatese, (2018) x ✓ x x incentives are motivations associated with future rewards, either extrinsic or intrinsic, that are contingent upon the fulfil lment of future conditions determined ahead of time before the start of work operations. 7 lin mills, (2000) x ✓ x x existing government safety regulations place considerable pressure on all firms, to protect the construction workforce. 8 cooke et al. (2008) ✓ x x x the toolshed™ ds tool addresses an issue of emerging importance, i.e. the need to address ohs in construction design. the potenti al to reduce ohs risks during the design stage of buildings and other structures has gained considerable recognition among industry policy-makers and legislators. 9 pinto et al. (2011) ✓ x x x this knowledge should be further extended to support a more in-depth risk analysis and modeling in the construction industry 10 johnstone et al. (2014) x ✓ x x situations where the legal responsibilities of employers are more ambiguous and attenuated.while subcontracting and the leasing of workers had been a long-term feature of the some industries (like construction), the expansion of these practices to other industries creates additio nal logistical demands on often already stretched inspectorates. 11 baxendale and jones (2000) x ✓ x x the cdm regulations are aimed at improving the overall management and coordination of health and safety throughout all stages of a cp with the aim of reducing the number of serious and fatal accidents and causes of ill health that occur in the industry. 12 manu, et al. (2017) x ✓ x x while the study has shown that in each country there are practices that are not commonly implemented by contractors (and hence need attention from contractors and relevant bodies/ institutions in the countries). 13 holmes et al. (1999) ✓ x x x the risk of occupational skin disease is perceived to be unknown and associated with delayed effects. the risk of falling from height is perceived to be highly relevant to the work of small business construction firms. 14 fortunato iii et al. (2012) ✓ x x x the results indicate that (1) workers on leed construction projects are exposed to work at height, with electrical current, near unstable soils, and near heavy equipment for a greater period of time than workers on traditional projects; (2) workers are exposed to new high -risk tasks such as constructing atria, installing green roofs, and installing photovoltaic (pv) panels; and (3) some credits result in a positive impact on construction worker safety and health when low volatile organic compound (voc) adhesives and sealants are specified. 15 windapo, (2013) x ✓ x x regulatory requirements by contractors because of cost implications will lead to unsafe work condition, injuries and fatalities on construction sites 16 yuan, et al. (2018) ✓ x x x the results of performing sem indicated that the direct impacts of construction workers’ p&m health on work efficiency and productivity were identified to be much more important than that of the snc. in addition, construction workers’ social capital can indirectly i nfluence the work efficiency and productivity by affecting the construction workers ’ p&m health. 17 wu et al. (2018) x ✓ x x this study contributes to the current stress-management research by developing a reliable factor structure of construction workers’ job stress, including the job itself, family-work conflict, career development, organizational style, interpersonal relationship, and role management. 18 wachter and yorio, (2014) x ✓ x x results indicate the following: there is a significant negative relationship between the presenceof ten individual safety management practices, as well as the composite of these practices, with accidentrates; there is a significant negative relationship between the level of safety-focused worker emotionaland cognitive engagement with accident rates; safety management systems and worker engagementlevels can be used individually to predict accident rates; safety management systems can be used topredict worker engagement levels; and worker engagement level s act as mediators between the safetymanagement system and safety performance outcomes (such as accident rates). occupational safety and health risk in building construction project: literature review 32 19 cheung, et al. (2004) x ✓ x x the combined effect of these components results in a system that enables speedy performance assessment of safety and health a ctivities on construction sites. with the cshm’s built-in functions, important management decisions can theoretically be made and corrective actions can be taken before potential hazards turn into fatal or injurious occupational accidents. 20 zhou et al. (2012) x ✓ x x bringing these strands of literature together suggests new kinds of interventions, such as the development of tools and processes for using digital models to promote mindfulness through multi-party collaboration on safety. 21 howard et al. (2017) ✓ x ✓ x this paper describes the four major uses of uavs, including their use in construction, the potential risks of their use to workers, appr oaches for risk mitigation, and the important role that safety and health professionals can play in ensuring safe approaches to the their use in the workplace. 22 badri, et al. (2012) x ✓ x x a new concept called risk factor concentration along with weighting of risk factor categories as contributors to undesirable events are used in the analytical hierarchy process multi-criteria comparison model with expert choice software. 23 ringen et al. (1995) x ✓ x x potential solutions are in labor-management site safety and health planning and management. education and training of workers and supervisors, new technologies, federal regulation, workers' compensation law, medical monitoring, and occupational health delivery. 24 idoro, (2011) x ✓ x x thus, the results reveal the challenges facing nigerian contractors and other stakeholders working to improve the ohs performance of the industry. the findings indicate the need for effective risk management and regulation and control of ohs in the nigerian construction industry. 25 martinez-aires, et al. (2018) ✓ x ✓ x the main result shows that the growing implementation of bim in the architecture, engineering and construction (aec) industry is changing the way safety can be approached. potential safety hazards can be automatically identified and corresponding prevention methods c an be applied using an automated approach. 26 badri, et al. (2018) x ✓ x ✓ as major changes are implemented, previous gains in preventive management of workplace health and safety will be at risk. if we are to avoid putting technological progress and ohs on a collision course, researchers, field experts and industrialists will have to collaborate on a smooth transition towards industry 4.0. 27 carter and smith, (2006) x ✓ x ✓ a max. of only 6.7% of the method statements analyzed on these projects managed to identify all of the hazards that should h ave been identified, based upon current knowledge. maximum hazard identification levels were found to be 0.899 _89.9%_ for a cp. 28 rahmawati et al. (2019) ✓ ✓ x x project safety review, safety inspection, installation project signs, safety morning, personal protective equipment, safety n et installation, installation of safety line, installation of lighting to clean up the project area is the application of the k3 program that is carried out. 29 astiningsih et al. (2018) x ✓ x x there was an association between safety inspection and the use of ppes (p = 0,024; α=0,05); safety supervision and the use of ppes (p = 0,024; α=0,05); safety morning and the use of ppes (p = 0,043; α=0,05). 30 hidayat, (2018) x ✓ x x k3 risk is known to be levelneach risk is 1 risk classified as high risk, 41 risk classified as medium, and 9 risks classifie d as low risk. 31 bria and loden, (2017) x ✓ x x alternative risk controls that can carried out at the risk of workers falling, controlling the risk is a daily k3 inspection f or the use of ppe (personal protective equipment) complete, tightening management supervision of workers who do not wear personal protective equipment, provide and complete the signs safety in construction projects if none o incomplete. 32 atmaja et al. (2018) ✓ ✓ ✓ x construction site of cronbach’s values alpha count obtained by 0.908 means that it can it is said that for characteristic variables reliable site construction because of the alpha value between 0.61 0.80. could concluded the consistency of the questions for the sub-variables is necessary training on the importance of osh in a the project is very consistent and very appropriate. 33 suparman and fitriani, (2016) ✓ ✓ x x there are 64 occupational injury risks, i.e., 13 low risk, 47 medium risk, and 4 high risk. it can be concluded that the high est risk factor for the workers is inhaled the welding smoke with the risk index of 16. 34 endroyo, (2010) x x x ✓ educational factors correlated 0.30 (significance: 0.048) contribute to attitude of k3, and was another factor correlations w ere not significant. all these factors have only to give efectif contribution about to 0.213 (21.3%) of the attitude factor k3. it means that about of 78.7% which can not be explained and is a problem to be studied again. 35 wijaya and paing, (2018) x ✓ x ✓ dominant factor affecting k3 there are 5 namely change workers must be responsible for k3, k3 regulations and procedures are very in need, k3 regulations are easily applied consistently, the results of the work are fulfilling standard quality and the absence of work accidents in the work environment for certain reasons. 36 sutrisno, et al. (2000) x ✓ x ✓ measurement of the influence of the safety climate on the most influential safety behavior on variable x (climate safety) of the y variable (safety behavior), namely communication, perception of someone's involvement in k3 and accidents / incidents/ nearmi ss. 37 pradipta, et al. (2015) ✓ ✓ x x the most determining factor for the lack of completeness of k3-l is the factor handling of work accidents where workers do not apply implementation of standard operating procedure (sop) at work and less implementation of health insurance implementation. 38 milen, et al. (2012) x ✓ x x all the three project cases has a medium risk due to accident caused by ignoring the safety standards and procedure are obvio us. supriyatna et al./oper. res. eng. sci. theor. appl. 3 (1) (2020) 28-40 33 39 novianto and sri, (2016) x ✓ x x free variables occupational safety (x1) and health (x2) against k3 problem simultaneously and partial positive and significant inf luential variable against the performance of construction workers on the project construction of the fly over palur, where the infl uence of variable x1 amounted to 1,903 (54,38%) and x2 of 1,098 (45,62%) 40 hakim, (2017) x ✓ x x in the risk matrix analysis there are 3 jobs that are categorized as high risk include worker falls from height at reinforcem ent, formwork and parapet, full electric shock on electrical installation work, and materials falls from a height and hit the worker in erectio n work. 41 sanjaya et al. (2012) x ✓ x x that the connection of factors that influence k3 to implementation of k3 in building construction was high (0.614), determination coefficient about 0.377 that showed the mean of k3 in building construction about 37.7 % which were determined by three factor s that influenced k3, while 62.3 % were determined by the other factors. the result of relative distribution counting showed that supervising factor gave bigg est influence to k3 in building construction. 42 hartanto and siahaan, (2018) x ✓ x x the five independent variables of this order of magnitude of influence are caused by osh management system (x2) 73,4%, self prote ctive equipment mechanism (x3) 60,9%, definition and initiation osh (x1) 42,6%, osh risk (x5) 7,9% and osh facility and infrastruct ure (x4) 3,5% so that which needs to be handled by the project leader is based on the order of the percentage. 43 kani, et al. (2013) x ✓ x x that there are still many workers who do not know about k3. what is meant by k3, how to apply k3, and so forth. this shows that there is still a lack of attention or commitment from the contracting company to implement the k3 program well. 44 munang, et al. (2018) x x x ✓ assessing railway double rail project has identified 19 unexpected risks as a high risk and 12 unacceptable risks that are required risk mitigation to reduce the impact. 45 triaswati et al. (2014) x ✓ x ✓ from the k3 management system it is planned that a risk control fee of rp 310,266,500.00 is obtained be a reference in suppressing the accident rate. 46 soputan, et al. (2014) x ✓ x x a high risk value is obtained, i.e. the material is dropped from height and override workers with a risk index of 20 and risk classification to very high risk. for risk classification at the high risk level as many as 21 variables can be endangering workers and jobs, while for classification a t the medium risk level obtained as many as 18 variables. 47 indah, (2017) ✓ ✓ x x the level of k3 implementation on aspects of the personal protective equipment (60%), the role of emergency condition (75%), structural work, scaffolding and ladder (66.7%), use of toxic and dangeorus materials ( 62.9%), health and hygiene of work environmental (89.2 %). 48 handayani and prihatiningsih, (2018) x ✓ x x it is found that the cause of risk in ohs for construction sector is dominated by structure criterion (44%), followed by preparation criterion (17%), sub-structure criterion (21%) and finishing criterion (19%). the biggest cause of occupational accidents is human factor by 77%, 49 tannya et al. (2017) x ✓ x x the most influential inhibiting factor is the lack of knowledge about smk3 from the company and its employees. of the inhibit ing factors that have been obtained, it is suggested several alternative solutions note: √ (discussed), x (not discussed), t – technical, nt nontechnical occupational safety and health risk in building construction project: literature review 34 3.1. internal technical risk results indicate that there are 13 major activities required toconstruct concrete formwork and the highest risk activities are applying form oil, lifting and lowering form components, and accepting materials from a crane (hallowell and gambatese, 2009). the study found that masonry, carpentry (including formwork and roofing), and iron bending and steel fixing are common building trades associated with high risks; whereas electrical fitting and installation, painting, tiling, and plumbing are medium risk building trades. it also found that the rate of occurrence and magnitude of impact of different safety risk factors differ across the building trades, which could be attributed to the differences in activities and modes of operation in different building trades (okoye, 2018). the main objective of the bim safety research project is to develop procedures and use of bim technology for safety planning, management, and communications, as part of the 4d-construction planning (sulankivi et al. 2010). developed to help construction designers to integrate the management of ohs risk into the design process (cooke et al. 2008). for the construction industry, discussing their limitations and pointing advantages of using fuzzy sets approaches to deal with ill-defined situations (pinto et al. 2011). the results indicate that (1) workers on leed construction projects are exposed to work at height, with electrical current, near unstable soils, and near heavy equipment for a greater period of time than workers on traditional projects; (2) workers are exposed to new high-risk tasks such as constructing atria, installing green roofs, and installing photovoltaic (pv) panels; and (3) some credits result in a positive impact on construction worker safety and health when low volatile organic compound (voc) adhesives and sealants are specified. it is expected that these results can be used by practitioners to focus attention and resources on new highrisk work environments (fortunato iii et al. 2013). this review explores relationships between construction safety and digital design practices with the aim of fostering and directing further research. it surveys state-of-the-art research on databases, virtual reality, geographic information systems, 4d cad, building information modeling and sensing technologies, finding various digital tools for addressing safety issues in the construction phase, but few tools to support design for construction safety (yhou et al. 2012). using uavs in carrying out planned or reactive maintenance inspections of tall structures, such as skyscrapers, bridges, and towers where access can be costly and pose a risk to workers of falling from a great height, appears to be a clear benefit for construction managers and workers (howard et al. 2012). the main result shows that the growing implementation of bim in the architecture, engineering and construction (aec) industry is changing the way safety can be approached. potential safety hazards can be automatically identified and corresponding prevention methods can be applied using an automated approach (martinez-aires et al. 2018). the use of appropriate methods of implementation, weak supervision of construction implementation in the field, not yet fully implementing the regulations regarding existing k3, weak supervision of the implementation of k3, inadequate both in the quality and quantity of the availability of personal protective equipment (ppe) availability (rahmawati et al. 2019). technical equipment factors, factory ugliness problems, equipment used, machines that are no longer suitable for use (atmaja et al. 2018). the factors assessed by respondents are still not fulfilling k3l completeness, namely lack of fire fighting equipment, no medical equipment / first aid kit at the project location, signs not properly installed, and lack of data collection for workers who experience illness or work accidents (milen, 2012). the constraints to applying ohs in general are budget constraints, the culture of workers who are not supriyatna et al./oper. res. eng. sci. theor. appl. 3 (1) (2020) 28-40 35 familiar with the application of ohs and the impact of the application on the cost and selling price of property construction (handayani and prihatiningsih, 2018). 3.2. internal non technical risk this context we argue that it is crucial to identify the sorts of (audio)visual narratives and forms that can effectively communicate about health and safety in ways that are meaningful and relevant to construction workers employed in multicultural contexts (bust et al. 2008). the primary reasons are a lack of strong institutional framework for governing construction activities and poor enforcement of health and safety policies and procedures (laryea and mensah, 2010). the results show that the major factors influencing safety performance were; company size, and management and employee commitment to ohs (lin andmills, 2001). the efforts by osha to make prime contractors take responsibility for their subcontractors would place pressure on them to take control of subcontractors in a way that threatens this distancing and the manipulation of legal forms it entails (johnstone et al. 2000). the cdm regulations are aimed at improving the overall management and coordination of health and safety throughout all stages of a construction project with the aim of reducing the number of serious and fatal accidents and causes of ill health that occur in the industry (baxendale and jones, 2000). overall, the findings offer an opportunity for contractors and key industry stakeholders (e.g. state authorities) to reflect on their approach/initiatives to improving h&s management in construction (manu et al. 2018). social, economic and cultural factors of workers and lack of discipline among workers in complying with k3 provisions, including the use of ppe for work accidents (rahmawati et al. 2019). the workforce still lacks understanding of ppe knowledge (astiningsih et al. 2018; munang et al. 2018). 1 variable with a high level of risk (high risk) in casting jobs, namely workers falling from a height, fall of equipment / material, injured workers will be in direct contact with tools, workers exposed to dust, workers slip, until workers are exposed to electrical contact (hidaya, 2018; soputan et al. 2014; indah, 2017). from the multiplication of risk frequency and risk impact, it is also obtained the criteria for the highest causes of work accidents are human beings with risk level l (low) by 56% and subc criteria for the highest causes of accidents is not using ppe with risk level l (low) by 56% (bria and loden, 2017; handayani and prihatiningsih, 2018). human factor it means that workers do not know safe procedures or dangerous actions: unable to meet work requirements so that actions occur below standard, knowing all the rules and work requirements but not complying with them (altmaja et al. 2018). the highest risk obtained in the palembang musi vi bridge construction project is risk factor 17.e is absorbed by welding fumes with a risk index of 16 (suparman and fitriani, 2016). factors that influence occupational safety and health on the performance of construction work construction projects in surabaya are communication between the contractor and the owner (wijaya and paing, 2018). based on the partial regression test (backward method enter method), the x variable which influences y variable is communication, perception of someone's involvement in k3, accident/incident/nearmiss (sutrisno et al. 2000). the most decisive factor for the lack of completeness of k3-l on the hotmix road project of the sumbawa regency public works office is the factor in handling of work accidents where workers do not implement the standard operating procedure (sop) at work and lack the implementation of health insurance (milen, 2012). the highest and most frequent risk is the x.15 variable, where workers do not use ppe in the field as an accident factor that occurs in construction projects (novianto et al. 2016). the independent variable occupational safety and health risk in building construction project: literature review 36 occupational health safety (x1) and occupational health (x2) on k3 problems simultaneously and partially have a significant and positive effect on the performance variable of construction workers on the fly over palur development project, where the influence of variable x1 is 1,309 (54.38%) and x2 of 1,098 (45.62%) (hakim, 2017). the highest risk index is known, that is, the variable of workers falls from height in construction, formwork and parapet work with a total risk index of 13.8. the lowest risk index is found in the variable workers exposed to respiratory disorders due to compressors on road markings with a total risk index of 5.5 (sanjaya et al. 2014). the factor which gives the biggest influence/contribution to k3 on building construction projects is the supervision factor (hartanto and siahaan, 2018). the results of these five independent variables in order of magnitude of influence are caused by the k3 management system (x2) 73.4%, the mechanism of personal protective equipment (x3) 60.9%, the definition and initiation of the k3 (x1) 42.6%, the k3 risk (x5) 7.9% and k3 facilities and infrastructure (x4) 3.5% (kani et al. 2013). work accidents on construction projects are caused by human factors that neglect work safety by behaving unsafe at work (soputan et al. 2014). k3 management plays a very important role in accident prevention in construction projects. the role starts from planning, organizing, implementing, monitoring. furthermore, it can also be viewed from human components, materials, money, machines / tools, work methods, information. the final results of this study are: the order of the top 3 (three) of the factors that influence the implementation of the k3 work system namely (costs for ppe providers, joking while doing work, lack of knowledge of workers on the dangers and risks of the work done) (sihombing et al. 2014). 3.3. external technical risk using uavs in carrying out planned or reactive maintenance inspections of tall structures, such as skyscrapers, bridges, and towers where access can be costly and pose a risk to workers of falling from a great height, appears to be a clear benefit for construction managers and workers (howard et al. 2018). the main result shows that the growing implementation of bim in the architecture, engineering and construction (aec) industry is changing the way safety can be approached. potential safety hazards can be automatically identified and corresponding prevention methods can be applied using an automated approach (martinez-aires et al. 2018). work environment factors, the physical environment of the workplace and the wider psychological social environment (atmaja et al. 2018). 3.4. external non technical risk researchers, field experts and industrialists will have to collaborate on the implementation of measures based on a comprehensive vision of managing change in order to ensure a smooth and safe transition to the new paradigm. acknowledgments the authors thank the natural sciences and engineering research (badri et al. 2018). this is achieved using a central safety database that contains knowledge relating to safety that exists within the organization as a whole, that is construction tasks, hazards, and the relationships between them (carter and smith, 2006).there is no significant relationship between internal factors (level of education, experience, certification) and external (level of commitment of the company) with the attitude of k3 (keselamatan et al. 2010). while from the education factor also said there were differences between employees with the level of junior high, high school and bachelor supriyatna et al./oper. res. eng. sci. theor. appl. 3 (1) (2020) 28-40 37 education (sutrisno et al. 2000). the results showed that the construction of a double track railway project had a high risk because it directly intersected with an active train line so that there were identified 19 unexpected risks (triaswati et al. 2014). 4. conclusion and recommendation this paper concludes that there are two sources of risk that are very influential namely risks originating from internal and external, both viewed technically and nontechnically. technical results can be seen from the use of 4d-bim technology, the use of personal protective equipment, the use of construction tools according to their permits and the non-technical 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(2012). construction safety and digital design: a review. automation in construction, 22, 102-111. © 2020 by the authors. submitted for possible open access publication under the terms and conditions of the creative commons attribution (cc by) license (http://creativecommons.org/licenses/by/4.0/). https://www.researchgate.net/publication/228640694 operational research in engineering sciences: theory and applications vol. 3, issue 3, 2020, pp. 1-12 issn: 2620-1607 eissn: 2620-1747 doi: https://doi.org/10.31181/oresta2030301b * corresponding author. tapasbiswasmckv@gmail.com (t. biswas), cd_manik@rediffmail.com (m. das) selection of the barriers of supply chain management in indian manufacturing sectors due to covid-19 impacts tapas kumar biswas*, manik chandra das department of automobile engineering, mckv institute of engineering, howrah-711204, india received: 22 june 2020 accepted: 10 august 2020 first online: 29 august 2020 research paper abstract. the coronavirus (covid-19) pandemic is having a clear impact on the supply chains of virtually all manufacturers. whether frozen foods and grocery items or emergency items, or even the services, the supply chain has been facing multiple obstacles. for manufacturing industries with complex supply chains, it is indeed critical to identify strategies to deal with such a crisis. with demand high and supply unavailable, some products became more desirable causing price hikes and price extorting because the manufacturing sectors are facing some barriers during lockdown. this research has identified the five essential barriers of supply chain such as lack of man power, local laws enforcement, lack of transportation, scarcity of raw materials and deficiency in cash flow for indian manufacturing sectors during lockdown. this paper proposed a methodology based on a fuzzy analytical hierarchy process (fuzzy-ahp) with use of triangular fuzzy numbers for the pairwise comparison matrices. it has been seen that lack of man power is a higher weight barrier than others. moreover, the managerial implication about the results is also provided, which will be useful for manufacturing sectors to take suitable decisions to overcome these obstacles. keywords: covid-19, manufacturing sectors, barriers, fuzzy ahp, scm 1. introduction at present time, the world is facing the coronavirus disease known as covid-19. the first case of the coronavirus was reported in december, 2019 in the wuhan city of china which is known as the major transportation hub of china (mayo clinic, 2020). many countries have shut down their sea docks and airports after the spread of the virus. they have banned the import and export activities. world health organization (who) has declared the covid-19 outbreak as a global pandemic on march 11, 2020 (cucinotta & vanelli, 2020). the virus has affected the lives of many biswas & das/oper. res. eng. sci. theor. appl. 3 (3) (2020) 1-12 2 people and also affecting the global economy more than that happened during the outbreak of severe acute respiratory syndrome (sars) (who, situation report-92, 2000). the first case of covid-19 in india was reported in january 30, 2020. on 23rd of march, 2020, the government of india has declared the lockdown in the whole country to minimize the spread of covid-19 (jamwal et al., 2020). within a month, unemployment has risen from 6.7% on 15 march to 26% on 19 april (vyas, 2020). during the lockdown, estimated 140 million people lost employment while salaries were cut for many others (goyal, 2020). more than 45% of households across the nation have reported an income drop as compared to the previous year (research, centre for policy, 2020). since the last couple of months, the fast spread of the covid-19 disease is creating huge uncertainty and indefinable disruptions in the global supply chain. according to who (2020), the global supply chain is experiencing a big challenge to keep smooth supplies of food and medical instruments including masks and medicine highly required to the treatment, protection, and control of the pandemic. in india, the supply chain (sc) has also been put under stress with the lockdown restrictions which disrupted the sc across the nation (chaudhry, 2020). major companies in india such as larsen & toubro, bharat forge, ultratech cement, grasim industries, aditya birla group, bhel and tata motors have temporarily suspended or significantly reduced operations. young startups have been impacted as funding has fallen (singh, 2020). fast-moving consumer goods companies in the country have significantly reduced operations and are focusing on essentials. the indian express, 2020 showed that stock markets in india posted their worst losses in history on 23 march 2020. almost all two-wheeler and four-wheeler companies put a stop to production till further notice. hindustan unilever, itc and dabur india shut manufacturing facilities except for factories producing essentials (mudgill, 2020). foxconn and wistron corp, iphone producers, suspended production following the 21-day-lockdown orders (wu, 2020). following the lockdown, certain essential supply chains (scs) broke down. britannia industries, supporting the lockdown, urged the government to ensure inter-state movement of the raw material for the food processing industry was not hampered. during the lockdown, inter-state logistics has been banned, it does not apply to essentials, and in places like maharashtra, the state police are yet to streamline the process and disrupt the scs. (parth, 2020). vidya krishnan writes in the atlantic that due to the lockdown, even movement of medical goods were affected (krishnan, 2020). on 29 march, 2020, the government of india permitted the movement of all essential goods across the country during the lockdown. the milk and newspaper scs are also allowed to function. chemicals, automotive, electronics and other industries are shut down due to supply disruption and restriction of logistics/shipment (kumar et al., 2020). on another note, the pandemic control measures taken by countries worldwide have interrupted flows of finished goods and raw materials from plants to many parts of the world. for instance, wuhan, the epicenter of the covid-19 outbreak, is an automobile factory hub with global brands such as general motors, hyundai, and toyota (yu & aviso, 2020). aside from these car manufacturing plants, multinational companies such as apple, alphabet, starbucks, mcdonald’s, and proctor & gamble have closed production facilities. presently, the country is suffering from recession in the third quarter of fiscal year (fy) 2020. the economic impact of the 2020 coronavirus pandemic in india has been largely disruptive. india's growth in the fourth quarter of the fy 2020 went down to 3.1% according to the ministry of statistics. in india, manufacturing industry is selection of the barriers of supply chain management in indian manufacturing sectors due to covid-19 impacts 3 totally hampered due to lack of man power, logistics and sc due to lockdown restrictions. although many companies are embracing more online shopping activities to deal with low foot traffic and extensive closure of many showrooms completely by trying to meet car buyer needs virtually. changes in business models and the use of innovative practices and technologies also lead to changes in existing sc structures and relationships. micro, small and medium-sized enterprises (msme), the united nations industrial development organization in india, communicated 85 enterprises and enquired about the challenges they are facing and their expectations and plans for the revival of their businesses once the lockdown is lifted. the survey was conducted by telephone during the period 9-13 april, 2020 and included enterprises engaged in the automotive components, bicycle, paper, textile, ceramic, foundry, tea and rice milling sectors (rice milling sector where production has reportedly dropped by half) in clusters across the country. some communications, sales, administrative and other support activities are being undertaken from home but on a limited scale. workers who come from different states of india have returned in large numbers to their hometowns. in this situation, some manufacturers are involved in the manufacturing of ventilators, but small quantities and small fraction of its regular workforce. the movement of materials (raw materials/finished goods) is standstill. the disruption of the flow of materials and goods is having negative implications on other aspects of business, in particular an abrupt end to incoming cash flows and the migration of workforce across all skill levels. the blockage of people and material movement disrupted every sc. there are different critical barriers found out which affected the scs in india during this period. it is expected that this paper will be helpful to the manufacturing sectors to overcome this issue. covid-19 pandemics suddenly projected those sc change scenarios onto a level of dramatic uncertainty. the susceptibility to which regional and global scs are subjected to extreme events raises several concerns in terms of analysis and transport and logistics scenarios. irrespective of significant benefits, the implementation of supply chain management (scm) is stimulating, and industries continue to meet barriers that prevent them from implementing effective scm (meehan & muir, 2008). benefits of scm execution can be achieved when companies are able to identify and overcome these barriers to stay competitive in today’s changing environment (stank et al., 2011). these barriers are complex in nature, and thus it is crucial for industries to understand them well. therefore, multi criteria decision making (mcdm) techniques may be used in selecting the best one among criteria. in the present paper, quality of performance of five critical barriers of scm such as lack of man power, local laws enforcement, lack of transportation, scarcity of raw materials and deficiency in cash flow in indian manufacturing sectors has been analyzed using a modified fuzzy ahp method (shaw et al., 2012), (arikan, 2013) for their subsequent ranking. in this paper, we use the fuzzy ahp method to determine the weights associated with criteria under study. the paper is organized as follows: after the introduction and barriers of scm in manufacturing environment, section 3 presents the fuzzy ahp methodology with mathematical formulation of the method. section 4 contains the application of fuzzy ahp method for calculating the weights. section 5 presents the discussion and concluding remarks, and directions for future research is presented in section 6. biswas & das/oper. res. eng. sci. theor. appl. 3 (3) (2020) 1-12 4 2. barriers of supply chain management (scm) due to covid-19 as reported in literature (moktadir et al., 2018), (sirisawat & kiatcharoenpol, 2018), scm barriers are lack of top management commitment and support, an unclear organizational objective, employee empowerment and training, insufficient funds, poor corporate culture, mistrust among employees and sc partners, lack of education and training to employees and suppliers, poor information and communication technology infrastructure, unwillingness to implement sc practices, lack of integration among sc partners, lack of collaboration among sc partners, lack of responsiveness, lack of customer satisfaction index, etc. these barriers are complex in nature, and thus it is crucial for decision makers to understand them well, so that the barriers can be curtailed. it has been seen that supply chains are always influenced by some barriers. now in india, covid-19 has disrupted the supply chain in manufacturing sectors. the barriers for the indian sc caused by the covid-19 are found out with the discussion with academic experts and industrial experts and they sort out many barriers of scm in manufacturing sectors like lack of man power, lack of raw materials, unavailability of imported goods, a bottleneck in last mile delivery, lack of transportation, slow movements of goods, restriction on overseas transportation, lack of buyers, lack of cash flow, slow credit flow from the financial sectors and local laws enforcement. in this study, five serious barriers are considered which are further discussed in table 1 because these five barriers are the most important in this pandemic situation and these five barriers are directly or indirectly connected with all other barriers. the five barriers are lack of man power, local laws enforcement, lack of transportation, scarcity of raw materials and deficiency in cash flow in the market, found out as critical in the scs in india. it is expected that this study will be helpful for the researchers to develop the conceptual models to overcome this issue. these barriers have a great influence on indian sc. although these issues in the sc are very generalized, which needs further study, the prioritization of these barriers will help the industries to overcome the sc issues due to the covid-19. table: 1 description of the barriers barriers description of the variables lack of man power man power in any sectors is defined by the supply of people who are able to work. any sector suffers from a lack of man power. this is an important variable or criterion for any industry or service sectors and it directly affects the productivity, which reduces the revenue and profit. local laws enforcement government of india is taking all necessary steps against the spread of corona virus 19. the most important factor in preventing the spread of the virus locally is to empower the citizens with the right information and taking precautions as per the advisories being issued by government. in india, the government has decided a nationwide lockdown to battle the spread of the covid-19 virus. lack of transportation due to covid 19, india has restricted or stopped the transport system in the country and globally, which https://www.sciencedirect.com/science/article/abs/pii/s0360835218300214#! selection of the barriers of supply chain management in indian manufacturing sectors due to covid-19 impacts 5 directly affects the sc of manufacturing sectors. scarcity of raw materials industries in the country are facing shortages of raw materials because of the graded lifting of the ongoing nationwide lockdown. due to restricted capacity at the main ports in india, both for sea and air freight, industries are facing a scarcity of import of material for which a locally-produced alternative is extremely difficult to find. deficiency in cash flow in the market a lockdown of this magnitude puts immediate pressure on the cash flow and pandemic has significantly impacted the cash flow at organizations. 3. methodology there are a number of multiple criteria decision making (mcdm) tools, such as ahp, entropy, critic (saaty, 1980), (biswas et al., 2019), (biswas et al., 2020), etc., available for prioritization of criteria in a set. in this paper, the fuzzy ahp method has been used to determine the weights/performance evaluation of the different barriers. this method works with the development of pairwise comparison matrix to determine the subjective weights or relative importance of each criterion. to capture the vagueness or imprecision in the judgments rendered by decision makers, triangular fuzzy membership function has been used (chang, 1996) with ahp theory. there are a good number of advantages of this method such as: it is simple to understand and comprehend, it can capture imprecision in judgments, it can return to a crisp value at the end, etc. a fuzzy scale as proposed by chang (1996) has been considered for pairwise comparisons of one criterion over another and the same is shown in table 2. table 2. fuzzy scale preference of pairwise comparisons fuzzy numbers equal (1,1,1) moderate (0.67,1,1.5) strong (1.5,2,2.5) very strong (2.5,3,3.5) extremely strong (3.5,4,4.5) in this work, the extent fuzzy ahp (chang, 1996) is utilized for defuzzification. 4. data and computation in order to rank the different barriers of scm due to covid-19 for indian manufacturing sectors, 15 respondents were contacted and their demographic information was collected. it has been seen that the majority of the respondents are bachelor degree, master’s degree or phd degree holders. all the respondents comprised are in manufacturing sectors, sc sectors and professors/associate biswas & das/oper. res. eng. sci. theor. appl. 3 (3) (2020) 1-12 6 professors in colleges/universities. all the academicians involved in the survey either teach engineering or management and by virtue of their profession, they have practical experiences in dealing with sc activities in indian manufacturing industries. it has been observed that all the respondents have working experiences of 5 years or more. so, overall, it can be concluded that all the respondents participated in the present survey have sufficient expertise in sc management. after identification of evaluation barrier, with the help of expert committee, fuzzy linguistic values are used to determine weights of criteria. 4.1 priority of criteria considering the feedback of the experts from various fields, we form a pairwise comparison matrix of 5 criteria to get their relative weight over others. table 3 shows the fuzzy evaluation of the criteria. table 3. pairwise comparison matrix criteria lack of man power local laws enforcement lack of transportation scarcity of raw materials deficiency in cash flow in the market lack of man power (1,1,1) (1.5,2,2.5) (0.67,1,1.5) (2.5,3,3.5) (0.67,1,1.5) local laws enforcement (0.4,0.5,0.67) (1,1,1) (0.67,1,1.5) (0.67,1,1.5) (1.5,2,2.5) lack of transportation (0.67,1,1.5) (0.67,1,1.5) (1,1,1) (0.67,1,1.5) (2.5,3,3.5) scarcity of raw materials (0.29,0.33,0.4) (0.67,1,1.5) (0.67,1,1.5) (1,1,1) (1.5,2,2.5) deficiency in cash flow in the market (0.67,1,1.5) (0.4,0.5,0.67) (0.29,0.33,0.4) (0.4,0.5,0.67) (1,1,1) using the steps of extent fuzzy ahp mentioned in the literature (chang, 1996) and fuzzy evaluation values in table 3, we determine the triangular fuzzy number (tfn) values of five criteria as follows: s1(lack of man power) =(6.33,8.00,10.00)  (1/37.30,1/29.17,1/22.94) =(0.17,0.27,0.44) s2(local laws enforcement) =(4.23,5.50,7.17)  (1/37.30,1/29.17,1/22.94) =(0.11,0.19,0.31) s3(lack of transportation) =(5.50,7.00,9.00)  (1/37.30,1/29.17,1/22.94) =(0.15,0.24,0.39) s4(scarcity of raw materials) =(4.12,5.33,6.90)  (1/37.30,1/29.17,1/22.94) =(0.11,0.18,0.30) s5(deficiency in cash flow in the market) =(2.75,3.33,4.23)  (1/37.30,1/29.17,1/22.94) selection of the barriers of supply chain management in indian manufacturing sectors due to covid-19 impacts 7 =(0.07,0.11,0.18) similarly as mentioned in literature (chang, 1996), the degree of possibility of sj=(lj,mj,uj)≥si=(li,mi,ui) can be computed by comparing the values of si as determined above. table 4 shows the values of v(sj≥si). table 4. values of v(sj≥si) v(sj≥si) value v(sj≥si) value v(sj≥si) value v(s1≥s2) 1.000 v(s2≥s1) 0.636 v(s3≥s1) 0.880 v(s1≥s3) 1.000 v(s2≥s3) 0.762 v(s3≥s2) 1.000 v(s1≥s4) 1.000 v(s2≥s4) 1.000 v(s3≥s4) 1.000 v(s1≥s5) 1.000 v(s2≥s5) 1.000 v(s3≥s5) 1.000 v(s4≥s1) 0.590 v(s5≥s1) 0.059 v(s4≥s2) 0.950 v(s5≥s2) 0.467 v(s4≥s3) 0.714 v(s5≥s3) 0.187 v(s4≥s5) 1.000 v(s5≥s4) 0.500 calculate the minimum degree of possibility d´ (i) of v (sj≥si) for i,j=1,2,3,….k. d´(1)=min v(s1≥s2,s3,s4,s5) = min (1.000, 1.000, 1.000, 1.000)=1.000 d´(2)= min v(s2≥s1,s3,s4,s5) = min (0.636, 0.762, 1.000, 1.000)=0.636 d´(3)= min v(s3≥ s1,s2,s4,s5)= min (0.880, 1.000, 1.000, 1.000)=0.880 d´(4)= min v(s4≥ s1,s2,s3,s5)= min (0.590, 0.950, 1.000, 1.000)=0.590 d´(5)= min v(s5≥ s1,s2,s3,s4)= min (0.059, 0.467, 0.187, 0.500)=0.059 therefore, the weight vector becomes w´= (1.000, 0.636, 0.880, 0.590, 0.059)t normalizing the weight vector, we get w= (0.316, 0.201, 0.278, 0.186, 0.019)t therefore, the final weights of lack of man power, local laws enforcement, lack of transportation, scarcity of raw materials and deficiency in cash flow in the market become 0.316, 0.201, 0.278, 0.186 and 0.019 respectively. the relative weights which are non-fuzzy numbers are described in the following figure (figure 1). biswas & das/oper. res. eng. sci. theor. appl. 3 (3) (2020) 1-12 8 figure 1: relative weights for evaluation of barriers 5. result and discussion as mentioned above, the five essential barriers of scm implementation in different manufacturing sectors were identified and subsequently validated by academicians and practitioners in order to see the importance of the different barriers of scm in manufacturing sectors. the majority of the expert respondents belongs to either academic or industry area. all the academicians involved in the survey are aware of operations management and marketing management by virtue of their profession, and they have practical experiences in dealing with sc activities. so, overall, it can be concluded that all the respondents participated in the present survey have sufficient expertise in sc management. the figures also show the priorities of the factors compared. for clarity purpose, the five barriers and their corresponding priorities and ranks are shown in fig. 1. it is observed that the five most critical barriers are (arranged in a descending order of criticality) the following: 1. lack of man power, 2. lack of transportation, 3. local laws enforcement, 4. scarcity of raw materials, 5. deficiency in cash flow in the market. from figure 1, it is found that the most serious barrier is “lack of man power” and the least critical barrier is “deficiency in cash flow in the market”. this does not mean that ‘deficiency in cash flow in the market’ is not serious; it merely shows that the other barriers considered are more serious compared to it because deficiency in cash flow directly or indirectly depends on logistics and scm. lack of man power affects production directly. presently, the production level is already low due to unavailability of the raw materials because of the irregular transportation system. in selection of the barriers of supply chain management in indian manufacturing sectors due to covid-19 impacts 9 this present scenario, local law enforcement has played a major role in implementation of “the lockdown”. so, the entire distribution channel is hampered and does not meet the demand supply equation. as a result, there is a scarcity of raw material items in the market. these emergency items are unnecessarily being stocked by some classes of people as they are thinking that there may be a crisis in the near future. therefore, it widens the gap between demand and supply in the local market. as most of the businesses were entirely stopped due to the lockdown countering this pandemic, it resulted in the downfall of the economy and an increase in the unemployment level as well. it has been noticed that many people had lost their jobs in different sectors and some employees did not get their remuneration fully. due to the loss of job, these people are having difficulties to meet their necessities. consequently, all the above mentioned points directly affect the cash flow. it has been observed from the literature review that manufacturing industry has been hit in many ways due to the corona effect. to begin with, lower production due to lack of raw materials, employees stop coming in to work due to government directives, thereby reducing the scale of operations, with a consequent effect on quality, cost and production volumes. over a period, this adversely affects the turnover, which slows down to a drop. the uncertainties in the logistics leads to a flowing effect; transporters struggle to not only place vehicles for loading; they also are under pressure to adjust their quotes for carrying goods, as it also faced lower attendance, with their operational risks increasing steeply. another side, the slower rate of banking operations, shorter working hours and jammed & overloaded communication lines lead to delayed money transactions, thereby elevating monetary risks. hence, the main challenges for restarting manufacturing industries can be started, although covid-19 will remain around and create a high degree of uncertainty in all aspects in manufacturing sectors. in particular, the need to avoid the further spread of covid-19 in the workplace or through the movement of people and materials may result in further restrictions and a potential return to lockdown. when restrictions are lifted, the market is expected to be very tight and extremely cash-constrained. this is largely due to extreme uncertainties with regard to demand for manufacturing and consequent low or non-existing business income while expenses for labor, energy, rent and other business inputs will still be suffered. now, the different indian govt. organizations (msme, confederation of indian industry) may consider the followings: 1. manpower will be a constraint due to maintaining social distancing, therefore some percentage of workers have to bring back from their hometowns due to uncertainties of job and loss of income during the lockdown. now, it will be a challenge to convince staff to return or to hire new staff for operation. even though engagement with industrial training institutes and hiring of temporary workers on walk-in basis. 2. machinery and stocks of raw materials, work in progress and final products become tainted. it needs to undertake outstanding maintenance and service, and clean out wasted stocks, before they can resume operations, at a significant cost and with likely write-offs of stocks currently trapped on-site. biswas & das/oper. res. eng. sci. theor. appl. 3 (3) (2020) 1-12 10 3. ensuring timely supplies of essential inputs without price hikes is a matter of concern. those are sometimes critically dependent on specialized parts from other states or from abroad express concerns about their susceptibility to supply shortages. 4. some emergency product industries had already started pre-lockdown with some measures for covid-19 infection prevention and control, particularly through awareness-raising and communication (on hygiene, physical distancing, etc.) and, in some cases, the provision of hand sanitizers, masks and gloves. this forms the basis for stepping up preventive measures for post-lockdown. common measures under consideration are health checks at the factory entrance, the provision of personal protective equipment (ppe), staggering of shifts and break times to minimize congestion of people, maintaining physical distancing during work and compulsory use of aroygya setu app (covid-19 contact tracing app launched by the government). 5. currently, the most immediate concerns are cash flow and working capital. most are concerned that survival is only possible with a substantive financial and/or fiscal support package from the government. 6. build digital sc & logistics and mandate and further drive digital payments. 6. conclusion the panic-stricken country has come to a standstill with nationwide lockdowns, mandatory quarantine, home confinement, job losses and economic woes. however, these restrictions have a severe impact on scm in indian manufacturing sectors. notably, the restrictions disrupted the raw materials and finished goods sc that in turn made to experience huge losses and growth of market are facing too much problems. adding to that, immense post losses due to shortage of labors and transportation bottlenecks were observed. in this paper, we have focused on five main barriers of scm in manufacturing sectors and used the fuzzy-ahp model to evaluate the weightage of different barriers due to covid-19. it has been seen that lack of man power is the most serious barrier and the least weightage barrier comparing to others is deficiency in cash flow in the market because it depends upon the other barriers. this study can be extended by considering the other barriers with different multi-criteria decision making approaches. the proposed paper provides some useful information to manufacturing sectors in checking out the action plans in order to overcome those barriers. once the barriers are overcome, the manufacturing sectors can start their production and continue in contributing to the country’s gdp substantially. references arikan, f., (2013). an interactive solution approach for multiple objective supplier 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(2020). modelling the economic impact and ripple effects of disease outbreaks. process integr optim sustain. https://doi.org/10.1007/s41660-020-00113-y. © 2020 by the authors. submitted for possible open access publication under the terms and conditions of the creative commons attribution (cc by) license (http://creativecommons.org/licenses/by/4.0/). https://www.sciencedirect.com/science/article/abs/pii/s0360835218300214#! https://www.sciencedirect.com/science/article/abs/pii/s0360835218300214#! https://www.sciencedirect.com/science/journal/03608352 https://www.sciencedirect.com/science/journal/03608352 https://www.sciencedirect.com/science/journal/03608352/117/supp/c https://indianexpress.com/article/business/market/bse-sensex-nse-nifty-stock-market-live-updates-coronavirus-global-markets-6327415/ https://indianexpress.com/article/business/market/bse-sensex-nse-nifty-stock-market-live-updates-coronavirus-global-markets-6327415/ https://www.cmie.com/kommon/bin/sr.php?kall=warticle&dt=2020-04-21%2010:40:01&msec=873 https://www.bloomberg.com/news/articles/2020-03-25/iphone-makers-suspend-india-production-due-to-lockdown https://www.bloomberg.com/news/articles/2020-03-25/iphone-makers-suspend-india-production-due-to-lockdown https://doi.org/10.1007/s41660-020-00113-y selection of the barriers of supply chain management in indian manufacturing sectors due to covid-19 impacts tapas kumar biswas*, manik chandra das 1. introduction 2. barriers of supply chain management (scm) due to covid-19 3. methodology 4. data and computation 4.1 priority of criteria 5. result and discussion 6. conclusion references operational research in engineering sciences: theory and applications vol. 3, issue 2, 2020, pp. 39-53 issn: 2620-1607 eissn: 2620-1747 doi: https://doi.org/10.31181/oresta2003034z * corresponding author. edmundas.zavadskas@vgtu.lt (e. k. zavadskas), zenonas.turskis@vgtu.lt (z. turskis), zeljkostevic88@yahoo.com and zeljko.stevic@sf.ues.rs (ž. stević), mabbas3@liveutm.onmicrosoft.com (a. mardani) modelling procedure for the selection of steel pipe supplier by applying the fuzzy ahp method edmundas kazimieras zavadskas 1, zenonas turskis 1, željko stević 2*, abbas mardani 3,4 1, vilnius gediminas technical university, institute of sustainable construction, faculty of civil engineering, lithuania 2 university of east sarajevo, faculty of transport and traffic engineering doboj, bosnia and herzegovina 3 informetrics research group, ton duc thang university, vietnam 4 faculty of business administration, ton duc thang university, vietnam received: 22 may 2020 accepted: 03 july 2020 first online: 03 july 2020 original scientific paper abstract: the objective of this study is the supplier evaluation and selection by applying the fuzzy multi-criteria analysis. the study used the fuzzy analytic hierarchy process (fahp) to choose the most suitable supplier for the purchase of materials necessary for the production of pre-insulated pipes. decision-makers selected among five suppliers based on nine criteria. effective execution of procurement, in this case, the procurement of material needed for the production logistics subsystem, influences the overall efficiency of the business. results show that it is very important to perform the right ranking in the process of supplier selection. good decisions can ensure lower costs and higher quality of the production and therefore a better position in the market. also, applied methodology and the rank show that supplier a is the most suitable solution. keywords: fuzzy ahp, optimization, supplier selection 1. introduction lately, the area of multi-criteria analysis is rapidly developing, thanks to the large number of publications dealing with the adoption of individual decisions based on the applied methods that belong to the specified field. for example, fallahpour et al. (2020) introduced a new integrated mcdm approach under uncertainty by integrating fuzzy preference programming as a modification of fuzzy analytic hierarchy process, with fuzzy inference system as a fuzzy rule-based expert system. zavadskas et al./oper. res. eng. sci. theor. appl. 3 (2) (2020) 39-53 40 the ahp method is one of the most common methods, among the dozens of approaches proposed, to solve complex multi-level decision-making problems. the importance of this method is the fact that there are conferences dedicated only to the method of the analytic hierarchy process. however, despite this fact, there is a constant strive to create better opportunities and more accurate problem-solving. for this reason, there is an enlargement of the ahp method, and creation of a fuzzy approach that allows a more precise definition of the most favourable alternative, or decision. ahp is often used in integration with other approaches, as can be seen in the study (stević et al., 2015) where this method is integrated with topsis. for this study, the extended fuzzy ahp method based on triangular fuzzy numbers (tfn) was used, where extended analysis of the target was performed for each object. in addition to this one, some other methods can be applied as well, such as maxmax, maxmin, saw, electre, promethee, topsis, but for the issues addressed in this paper, it is much better to apply the ahp method. methods minmax, maxmin and saw are straightforward methods of multi-criteria analysis, of which only the saw method takes the importance of criteria into account, and as such are not applied frequently in solving complex problems. methods electre and promethee have several versions and based on the authors’ knowledge stemming from the extensive review of the literature, we cannot say that these methods are not applied, they are, but to a much lesser extent than the ahp method, especially when it comes to the field of choice of suppliers. due to its simple concept, the topsis method has become very popular and is applied in many areas of decision-making procedures (zavadskas et al., 2016). however, despite that, this method is often criticized because there is no possibility for adequate handling of uncertainty and imprecision at the moment when the decision-maker wants accurate results. when compared to other methods, the ahp method has frequently shown features that are more practical, which is of great importance. some of the advantages of this method are outstanding problem structuring from the highest to the lowest level, pointing to the subjectivity that exists with the decision-makers, less susceptibility to errors in assessing thanks to the redundancy of comparison in pairs, use for complex decisionmaking and the like. as the most common shortcomings of this method stand out that there are not enough measures in the saaty scale to compare pairs of elements of specific decision-making problems with quite many criteria. however, a combination with fuzzy logic can somehow eliminate or reduce the disadvantage. chapter 3 presents it in detail. applying the ahp method enables more accurate interpretation of results because all values are the sum of an alternative one as a contrast to other methods where it is not the case, and thus it is possible to see how exactly the optimum solution is better than other estimated solutions. the primary reason for the ahp method application would be its ability to handle quantitative and qualitative criteria equally. in current business conditions, for one company to achieve the market position that makes it competitive, and to keep it, continuous measuring and monitoring of performance is necessary. if there is a deviation (which is often the case) from the planned values, it is necessary to undertake specific corrective measures to ensure the achievement of higher values. however, a better route by which it is possible to achieve efficient business management is a proactive way, where business results are not expected, but they are managed instead. thanks to the constant changes to which the market is exposed and to increasingly stringent requirements placed on modelling procedure for the selection of steel pipes supplier by applying the fuzzy ahp method 41 the market, it is undoubtedly a challenge to maintain a competitive position. it can be achieved if there is an adequate production, which means as low product cost as possible, as higher product quality as possible, high accuracy of delivery to final users, reliability, response to specific requirements set by users, i.e. flexibility and cooperation that can be accomplished with both – customers and suppliers. the research carried out in this paper connects the first two logistics stages: the procurement and production, which, with their consolidation, are making logistics of materials-effective execution of activities related to the system. the inclusion of the selection of the best suppliers significantly affects the price and quality of the final product. these are some of the most important factors determining success in the market. the correct choice of suppliers from the start provides the ability for timely, continuous and efficient production, which enables achieving the above-described benefits and makes that production competitive. the researched company is engaged in the production of pre-insulated pipes for heating and their application and installation in all heating systems. to be able to carry out the production smoothly, one of the necessary materials that need to be procured is steel pipes. in the market, there are many potential suppliers of the material mentioned above, and it is necessary to set aside those who particularly stand out based on their characteristics and based on criteria of the company that is the subject of research. after a thorough market analysis carried out by experts from the commercial service, the choice was reduced to five suppliers representing variants of which three are located in the domestic and the other two on the international market, which includes the territory of neighbouring countries. a similar issue is treated in (bronja and bronja, 2015; chatterjee and stević, 2019), where it can be seen the exact significance of the expert team, which, in addition to the selection of potential solutions, created a total of nine quantitative and qualitative criteria based on which it is necessary to evaluate potential suppliers. based on the current market needs and demands, as well as on the knowledge, skills and abilities acquired over the years in the same business, an expert team has evaluated criteria, bringing out the different weight value. the most significant aim and the contribution of this study is performing the optimization of the purchasing process through the proposed model for the application of fuzzy ahp method to this problem, and the possibility of establishing a long-term collaboration with the chosen supplier, which would enable additional benefits for the company. the paper is structured in several sections. in the introduction, aims and motivation for research are described. the second section shows a brief literature review with an emphasis on the fuzzy ahp method and the problem of supplier selection. the third section shows steps used in the fuzzy ahp method, while in the fourth section, an empirical study is shown. the paper ends with a conclusion and future tasks. 2. brief literature review there are many criteria to evaluate suppliers but the question is how to choose the right one from a given set, which will help to choose the best option. some authors have tried to answer this question, so webber (1991) investigated the zavadskas et al./oper. res. eng. sci. theor. appl. 3 (2) (2020) 39-53 42 criteria for the selection of suppliers in the manufacturing and retail environment in the 74 documents published from 1966 to 1991. he concluded that quality, delivery and price are prevailing as the dominant criteria. besides, geographical location, financial position and production capacity fall to the second group of factors. verma and pullman (1998) conducted a study among 139 managers whose aim was to examine how to make a compromise when selecting suppliers. their work indicated that the managers are paying the greatest attention to quality as the most critical attribute of suppliers, followed by delivery and price. karpak et al. (2001) took delivery reliability as a criterion for selection, while bhutta and huq (2002) used four criteria to evaluate suppliers: price, quality, technology and service. many researchers use multi-criteria decision-making (mcdm) methods and differently control target alternatives (turskis et al., 2019). different researchers developed different models to select the best supplier in a competitive market environment. keshavarz ghorabaee et al. (2016) extended the edas method for fuzzy multi-criteria decision-making. later, keshavarz ghorabaee et al. (2017) presented a novel model based on interval type-2 fuzzy sets and edas method. aouadni et al. (2017) presented a model based on the meaningful mixed data topsis (topsis-mmd) method. recently, yazdani et al. (2019) developed a grey combined compromise solution (cocoso-g) method for supplier selection. the criteria that are a base for the choice of suppliers were selected based on two factors: the most commonly used criteria in the same or similar research, and current needs of the company and demands that it might face in the market. as mentioned in the introduction, the company’s expert team selected the criteria set. the ahp method was addressed to the problem of supplier selection, in many types of research (galankashi et al., 2016; chen et al., 2006; jain et al., 2018; stević et al., 2016) the choice of supplier in the industry, where the general purpose of the model is applied to the leading electro motor manufacturer of turkey (barbarosoglu and yazgac, 1997), the choice of supplier in textile company (ertugrul and karakasoglu, 2006), where the focus is on the identification and discussion of criteria which make up an essential part of the decision. it is the price, quality, service level and profile of suppliers (chan and kumar, 2007). then, the choice of supplier among manufacturers of tft-lcd, where the applied model can identify strengths, opportunities on the one, and the cost and risk on the other hand (lee 2009). the ahp method has a wide application in practical research in a wide range of areas, thus contributing to the improvement of the entire management system (erdogan et al., 2017; hashemkhani zolfani et al., 2011). in the supply chain, decisions based on this method provide the proper choice of suppliers that affects the formation of a more efficient flow of further chain. decision-makers used many methods, which do not belong to the field of multi-criteria analysis, to solve similar problems. however, they frequently combined them with the ahp method. 3. the fuzzy ahp the creator of the ahp method is thomas saaty (1977; 1980). according to (saaty, 1990), the ahp is a measurement theory, which is dealing with comparing modelling procedure for the selection of steel pipes supplier by applying the fuzzy ahp method 43 pairs and which relies on expert opinion in order to perform the priority scale. fuzzy ratings and scales provide decision-makers possibilities to express better the level of their knowledge accuracy (zemlickienė & turskis, 2020; turskis et al., 2015). various approaches of fuzzy ahp method were developed as an extended fuzzy ahp method based on triangular fuzzy numbers (setyohadi & suyoto, 1977; saaty, 1978, 1982; van laarhoven & pedrycz, 1983; chang, 1996; zhu et al., 1999). zadeh (1965) introduced the theory of fuzzy sets. its application enables dms to deal with uncertainties effectively. fuzzy sets used generally triangular, trapezoidal and gaussian fuzzy numbers, which convert uncertain fuzzy numbers. more details can be found in (xu and liao, 2014). the authors use chang’s (1996) extent analysis method in this study. steps of the approach application are relatively simple and easy, requiring less time than many other fuzzy extensions of the ahp method. at the same time, it can eliminate the shortcomings of the classical ahp method. assume that x = {x1, x2, ..., xn} is a number of objects, and u = {u1, u2,...,um} is a number of aims. for each object, an extended goal analysis is performed. values of the extended analysis "m" for each object can be shown: (1) where are tfns. steps of fuzzy ahp are: step 1: the value of fuzzy synthetic extent si for the i-th criterion is as follows: (2) to obtain equation (3), (3) we need to perform additional fuzzy operations with "m" values: (4) (5) then it is necessary to calculate: (6) zavadskas et al./oper. res. eng. sci. theor. appl. 3 (2) (2020) 39-53 44 step 2: the sets of weight values for each criterion are calculated by decisionmakers according to the principle of comparing fuzzy numbers. for example, for two fuzzy numbers sb and sa,, the decision-makers define the possibility degree of sb ≥ sa as follows: (7) where sup represents the supremum and when a pair (x, y) exists such that x ≥ y and µsb (x) =µsa (y) = 1, it follows that v(sb ≥ sa) =1 and v(sa ≥ sb) = 0. since sb and sa are convex fuzzy numbers defined by the tfns (l1, m1, u1) and (l2, m2, u2) respectively, it follows that: (8) where iff represents “if and only if” and d is the ordinate of the highest intersection point between the µsb and µsa tfns and xd is the point on the domain of µsb and µsa where the ordinate d is found. the term hgt is the height of fuzzy numbers on the intersection of sb and sa. (9) where "d“ is the ordinate of the largest cross-section in point d between μsa and μsb, as shown in figure 1. figure 1. intersection between sb and sa the decision-makers need both values v(s1 ≥ s2) and v(s2 ≥ s1) to compare s1 and s2. step 3: the level of possibility for a convex fuzzy number to be greater than "k" convex number si (i =1, 2, ..., k) can be defined as follows: (10) (11) the following expression gives the weight vector: modelling procedure for the selection of steel pipes supplier by applying the fuzzy ahp method 45 (12) step 4: through normalization, the weight vector is reduced to the expression: (13) where w represents a crisp number. through its application, the fuzzy ahp method alleviates the main disadvantage of the classical ahp method, and that is, as previously mentioned, an insufficiently big comparison scale. to this end, various scales have been developed based on comparing the fuzzy triangular numbers, where the decision-maker can evaluate the significance of criteria or alternatives much closer and easier, and thus reducing his/her subjectivity that is present in solving these problems to a minimum. 4. numerical example the following criteria are applied in this study: the price of materials, pipe length, delivery time, way of payment, transport distance, quality, reliability, flexibility and relationship with customers that are still in operation, which are marked with c1-c9 respectively. therefore, there are four criteria, quantitatively expressed and five qualitative criteria, as shown in figure 2. detailed explanation of used criteria in this study can be found in (stević et al. 2016). as mentioned in the introduction, the panel selected a set of criteria for evaluating suppliers. these selected critical criteria are the same as those most widely used in practice. consideration of them and their share in the selection of suppliers achieves a significant overall business performance. the level of meeting the needs of end-users and the requirements of strict standards and norms is well reflected in the company's profit. figure 2. the hierarchical structure of the proposed model table 1. values of triangular fuzzy scale linguistic scale triangular fuzzy triangular fuzzy zavadskas et al./oper. res. eng. sci. theor. appl. 3 (2) (2020) 39-53 46 scale reciprocal scale just equal (1, 1, 1) (1, 1, 1) equally important (1/2, 1, 3/2) (2/3, 1, 2) weakly more important (1, 3/2, 2) (1/2, 2/3, 1) strongly more important (3/2, 2, 5/2) (2/5, 1/2, 2/3) very strongly more important (2, 5/2, 3) (1/3, 2/5, 1/2) absolutely more important (5/2, 3, 7/2) (2/7, 1/3, 2/5) one of the main features of mcdm process is that the different criteria cannot have the same significance, so following the methodology described for decision making which applies the extended ahp method, i.e. fuzzy ahp to get the required results, it is necessary to perform criteria comparison based on tfns, as shown in table 2. the comparison was made based on the scale shown in table 1 (chang, 1996). by comparing them, weight values of criteria are determined. the criteria weights have a large significance in the further application of methods because, on the base of these values, the best solution is determined. if a variant is better according to criteria that are very important when deciding, it increases the possibility to have exactly this variant as an optimum. table 2. comparison of criteria on the base of triangular numbers c1 c2 c3 c4 c5 c1 (1,1,1) (2/3,1,2) (1/2,2/3,1) (1/2,1,3/2) (1/2,1,3/2) c2 (1/2,1,3/2) (1,1,1) (2/3,1,2) (1,3/2,2) (1,3/2,2) c3 (1,3/2,2) (1/2,1,3/2) (1,1,1) (3/2,2,5/2) (3/2,2,5/2) c4 (2/3,1,2) (1/2,2/3,1) (2/5,1/2,2/3) (1,1,1) (1,1,1) c5 (2/3,1,2) (1/2,2/3,1) (2/5,1/2,2/3) (1,1,1) (1,1,1) c6 (1/2,1,3/2) (1,1,1) (2/3,1,2) (1/2,1,3/2) (1,3/2,2) c7 (1,1,1) (2/3,1,2) (1/2,2/3,1) (1/2,1,3/2) (1/2,1,3/2) c8 (1,1,1) (2/3,1,2) (1/2,3/2,1) (2/3,1,2) (1/2,1,3/2) c9 (2/3,1,2) (2/3,1,2) (2/5,1/2,2/3) (1,1,1) (2/3,1,2) c6 c7 c8 c9 c1 (2/3,1,2) (1,1,1) (1,1,1) (1/2,1,3/2) c2 (1,1,1) (1/2,1,3/2) (1/2,1,3/2) (1/2,1,3/2) c3 (1/2,1,3/2) (1,3/2,2) (1,3/2,2) (3/2,2,5/2) c4 (2/3,1,2) (2/3,1,2) (1/2,1,3/2) (1,1,1) c5 (1/2,2/3,1) (2/3,1,2) (2/3,1,2) (1/2,1,3/2) c6 (1,1,1) (1/2,1,3/2) (1/2,1,3/2) (1,3/2,2) c7 (2/3,1,2) (1,1,1) (1,1,1) (1,1,1) c8 (2/3,1,2) (1,1,1) (1,1,1) (2/3,1,2) c9 (1/2,2/3,1) (1,1,1) (1/2,1,3/2) (1,1,1) by applying the equation (4), (5) and (6), the following values are obtained: s1=(6.333;8.667;12.5)x(1/120;1/84.5;1/61.364)=(0.053; 0.103;0.204) s2=(6.667;10;14) x(1/120;1/84.5;1/61.364)=(0.056;0.118; 0.228) s3=(9.5;13.5;17.5)x(1/120;1/84.5;1/61.364)=(0.079;0.160;0.285) s4=(6.4;8.167;12.167) x(1/120;1/84.5;1/61.364)=(0.053;0.097; 0.198) modelling procedure for the selection of steel pipes supplier by applying the fuzzy ahp method 47 s5=(5.9;7.833;12.167) x(1/120;1/84.5;1/61.364)=(0.049; 0.093; 0.198) s6=(6.667;10;14)x(1/120;1/84.5;1/61.364)=(0.056;0.118;0.228) s7=(6.833;8.667;12)x(1/120;1/84.5;1/61.364)=(0.057;0.103;0.196) s8=(6.667;9.5;13.5)x(1/120;1/84.5;1/61.364)=(0.056;0.112;0.220) s9=(6.4;8.167;12.167)x(1/120;1/84.5;1/61.364)=(0.053;0.097. 0.198) after completion of the calculation using the equation (9), values are obtained as described in step three to the amounts: v(s1≥s2)=v(s1≥s6)=0.908;v(s1≥s3)=0.687;v(s1≥s4)=(s1≥s5)=v(s1≥s7)=v(s1≥s9)=1;v( s1≥s8)=0.943 v(s2≥s1)=v(s2≥s4)=v(s2≥s5)=v(s2≥s6)=v(s2≥s7)=v(s2≥s8)=v(s2≥s9)=1;v(s2≥s3)=0.78 v(s3≥s1)=v(s3≥s2)=v(s3≥s4)=v(s3≥s5)=v(s3≥s6)=v(s3≥s7)= v(s3≥s8)= v(s3≥s9)=1 v(s4≥s1)=0.960; v(s4≥s2)=v(s4≥s6)=0.871; v(s4≥s3)= 0.654; v(s4≥s5)=v(s4≥s9)=1; v(s4≥s7)=0.959; v(s4≥s8) =0.904 v(s5≥s1)=0.935; v(s5≥s2)= v(s5≥s6)=0.850; v(s5≥s3)= 0.640; v(s5≥s4)= v(s5≥s9)=0.973; v(s5≥s7)=0.934; v(s5≥s8)=0.882 v(s6≥s1)=v(s6≥s2)=v(s6≥s4)=v(s6≥s5)=v(s6≥s7)=v(s6≥s8)=v(s6≥s9)=1;v(s6≥s3)=0.78 v(s7≥s1)=v(s7≥s4)=v(s7≥s5)=v(s7≥s9)=1; v(s7≥s2)= v(s7 ≥s6)=0.903; v(s7≥s3)=0.672; v(s7≥s8)=0.934 v(s8≥s1)=v(s8≥s4)=v(s8≥s5)=v(s8≥s7)=v(s8≥s9)=1; v(s8≥s2)= v(s8≥s6)=0.965; v(s8≥s3)=0.746 v(s9≥s1)=0.960; v(s9≥s2)=0.871; v(s9≥s3)=0.654; v(s9 ≥s4)=v(s9≥s5)=1; v(s9≥s6)=0.871; v(s9≥s7)=0.959; v(s9≥s8)=0.904. then, using the equation (10) and (11), the values shown below are obtained. d'(a1)=minv(s1≥s2,s3,s4,s5,s6,s7,s8,s9)=0.687 d'(a2)=minv(s2≥s1,s3,s4,s5,s6,s7,s8,s9)=0.780 d'(a3)=minv(s3≥s1,s2,s4,s5,s6,s7,s8,s9)=1 d'(a4)=minv(s4≥s1,s2,s3,s5,s6,s7,s8,s9)=0.654 d'(a5)=minv(s5≥s1,s2,s3,s4,s6,s7,s8,s9)=0.640 d'(a6)=minv(s6≥s1,s2,s3,s4,s5,s7,s8,s9)=0.780 d'(a7)=minv(s7≥s1,s2,s3,s4,s5,s6,s8,s9)=0,672 d'(a8)=minv(s8≥s1,s2,s3,s4,s5,s6,s7,s9)=0,746 d'(a9)=minv(s9≥s1,s2,s3,s4,s5,s6,s7,s8)=0,654 after the equation (12) is applied, criteria weights are obtained, and from the equation (13), normalized weights of criteria are determined: w'=(0.687;0.780;1;0.654;0.640;0.780;0.672;0.746;0.654) zavadskas et al./oper. res. eng. sci. theor. appl. 3 (2) (2020) 39-53 48 w=(0.104;0.118;0.151;0.099;0.097;0.118;0.102;0.113;0.099) on the basis of the procedure and obtained results, the most significant criterion in this study is the third criterion, delivery time, which has importance of 15.1%, then the quality and pipe length have the same importance with a share of 11.8 %, while the other criteria have lower values. these three most significant criteria in a large number of practical examples dealing with similar tasks have large importance. a crisp value from table 2 is taken to calculate the level of consistency cr = 0.01. after these values were obtained in order to reach a ranking, and then after making the choice of the suitable variant, it is necessary to compare suppliers in relation to each criterion individually as already described, depending on whether the criteria are quantitative or qualitative. comparison of suppliers with respect to the first criterion, the cost of materials, is shown in table 3. table 3. comparison of suppliers with respect to the first criterion c1 sa sb sc sd se sa (1,1,1) (1,3/2,2) (3/2,2,5/2) (2,5/2,3) (5/2,3,7/2) sb (1/2,2/3,1) (1,1,1) (1/2,1,3/2) (1,3/2,2) (3/2,2,5/2) sc (2/5,1/2,2/3) (2/3,1,2) (1,1,1) (1/2,1,3/2) (1,3/2,2) sd (1/3,2/5,1/2) (1/2,2/3,1) (2/3,1,2) (1,1,1) (1/2,1,3/2) se (2/7,1/3,2/5) (2/5,1/2,2/3) (1/2,2/3,1) (2/3,1,2) (1,1,1) by applying the equation (4), (5) and (6), the following values are obtained: sa=(8;10;12)x(1/38.234;1/28.734;1/21.919)=(0.209;0.348;0.547) sb=(4.5;6.617;8)x(1/38.234;1/28.734;1/21.919)=(0.118; 0.215; 0.365) sc=(3.567;5;7.167)x(1/38.234;1/28.734;1/21.919)=(0.093;0.174;0.327) sd=(3;4.067;6) x(1/38.234;1/28.734;1/21.919) =(0.078; 0.142; 0.274) se=(2.852;3.5;5.067) x(1/38.234;1/28.734;1/21.919)=(0. 075;0.122;0.231) after the application of eq. (7), values are obtained as described in step three to the amounts: v(sa≥sb)=v(sa≥sc)=v(sa≥sd)=v(sa≥se)=1 v(sb≥sa)=0.540; v(sb≥sc)=v(sb≥sd)=v(sb≥se)=1 v(sc≥sa)=0.404;v(sc≥sb)=0.836; v(sc≥sd)=v(sc≥se) =1 v(sd≥sa)=0.240;v(sd≥sb)=0.681;v(sd≥sc)=0.850;v(sd ≥se)=1 v(se≥sa)=0.089;v(se≥sb)=0.549; v(se≥sc)=0.726;v(se ≥sd)=0.884 then, by applying the equation (8), the following values are obtained: d'(aa)=minv(sa≥sb,sc,sd,se)=1 d'(ab)=minv(sb≥sa,sc,sd,se,)=0.540 d'(ac)=minv(sc≥sa,sb,sd,se)=0.404 d'(ad)=minv(sd≥sa,sb,sc,se)=0.240 modelling procedure for the selection of steel pipes supplier by applying the fuzzy ahp method 49 d'(ae)=minv(sd≥sa,sb,sc,sd,)=0.089 by applying the equation (10), criteria weight values are computed, and applying equation (11), normalized weight values of criteria are as follow: w'=(1; 0.540; 0.404; 0.240; 0.089) w=(0.404; 0.237; 0.178; 0.106; 0.039) it shows that, according to the first criterion, material prices, the best solution is supplier a. in the same way, values are obtained for suppliers for the remaining eight criteria, whose final values are shown in the table below. table 4. final values for suppliers according to each criterion c1 c2 c3 c4 c5 c6 c7 c8 c9 0.104 0.118 0.151 0.099 0.097 0.118 0.102 0.113 0.099 sa 0.440 0.241 0.280 0.090 0.169 0.285 0.242 0.214 0.264 sb 0.237 0.241 0.280 0.436 0.133 0.236 0.169 0.170 0.121 sc 0.178 0.132 0.194 0.161 0.242 0.146 0.242 0.258 0.264 sd 0.106 0.187 0.246 0.090 0.242 0.146 0.214 0.179 0.264 se 0.039 0.199 0 0.223 0.214 0.186 0.133 0.179 0.087 figure 3. values of suppliers in relation to criteria suppliers’ values based on each criterion are shown in fig. 3, where it is clearly visible which supplier is the best solution, and based on which criteria. supplier a according to the first criterion and supplier b according to the fourth criterion reach the greatest values. zavadskas et al./oper. res. eng. sci. theor. appl. 3 (2) (2020) 39-53 50 in order to choose the best solution and the best supplier, obtained values for suppliers from table 4 should be multiplied by the values of the criteria in the following way: aa=wk1*waa+wk2*waa+wk3*waa+wk4*waa+wk5*waa+wk6*waa+wk7*waa+wk8 *waa+wk9*waa ab=wk1*wab+wk2*wab+wk3*wab+wk4*wab+wk5*wab+wk6*wab+wk7*wab+wk8 *wab+wk9*wab ac=wk1*wac+wk2*wac+wk3*wac+wk4*wac+wk5*wac+wk6*wac+wk7*wac+wk8* wac+wk9*wac ad=wk1*wad+wk2*wad+wk3*wad+wk4*wad+wk5*wad+wk6*wad+wk7*wad+wk 8*wad+wk9*wad ae=wk1*wae+wk2*wae+wk3*wae+wk4*wae+wk5*wae+wk6*wae+wk7*wae+wk8 *wae+wk9*wae application of previously described methodology leads to results shown in figure 4. figure 4. ranking alternatives since suppliers a and b have the maximum values according to the first and fourth criterion, when it comes to comparison of alternatives against the criteria, modeling the results in the best way possible can be done by a change of their values. obtained results in which supplier a is the most suitable solution are valid if the lower limit of the first criterion is 0.063 and the upper limit of the fourth criterion is 0.140. given the fact that, based on the great number of criteria, the selected supplier stands out as the best or equally best solution, which can be seen in table 4, to change the obtained results, except for the previous modeling, it is necessary to change the weight value largely. modelling procedure for the selection of steel pipes supplier by applying the fuzzy ahp method 51 5 . conclusion making decisions based on overview of great number of different criteria that largely are influencing efficiency of day–to–day business is certainly a challenge because multiple criteria are to be satisfied, which sometimes may be opposed. procurement logistics in today's modern age is a very important factor in a complete supply chain, so its optimization can ascertain a certain effect on the entire logistics system. it is necessary to take into account a number of criteria that could affect the formation of the final price of the product, and therefore the position company achieves in the market. application of fuzzy ahp method makes decisions possible, by taking into account the importance of criteria and their relative priority that reflects market demands and needs. by using the fuzzy ahp method in this study, it can be concluded that the purchase of steel pipes for the production of pre-insulted pipes should be done from supplier a. after the sensitivity analysis, it can be concluded that the model is stable because, in the case of changing the importance of the criteria up to 30%, results remain the same and the chosen solution remains first ranked. this means that a change of results obtained requires large turbulences in the market, both in terms of suppliers and their characteristics, as well as from the aspect of user requirements. depending on market trends where demands and needs change frequently, it is necessary to apply the methods of multi-criteria analysis more often to adopt appropriate decisions that 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(1999). a discussion on extent analysis method and applications of fuzzy ahp. european journal of operational research, 116(2), 450456. © 2020 by the authors. submitted for possible open access publication under the terms and conditions of the creative commons attribution (cc by) license (http://creativecommons.org/licenses/by/4.0/). modelling procedure for the selection of steel pipe supplier by applying the fuzzy ahp method edmundas kazimieras zavadskas 1, zenonas turskis 1, željko stević 2*, abbas mardani 3,4 1. introduction 2. brief literature review 3. the fuzzy ahp 4. numerical example 5 . conclusion references plane thermoelastic waves in infinite half-space caused operational research in engineering sciences: theory and applications first online issn: 2620-1607 eissn: 2620-1747 doi: https://doi.org/10.31181/oresta241222001s * corresponding author ilija.stojanovic@aue.ae (i. stojanović), adispuska@yahoo.com (a. puška), marko.selakovic@spjain.org (m. selaković), iisyedashafiaii@gmail.com (s. shafia), mshamout@sharjah.ac.ae (m. shamout), ercegdajana1994@gmail.com (d. erceg) selection of viable suppliers for project organizations during the long-term disruption of supply chains using imf swara ilija stojanovic1, adis puška2*, marko selakovic3, syeda shafia4, mohamed shamout5, dajana erceg6 1 american university in the emirates, dubai, united arab emirates 2 government of brčko district of bosnia and herzegovina, brčko, bosnia and herzegovina 3 freelance author, dubai, united arab emirates 4 sp jain school of management, dubai, united arab emirates 5 university of sharjah, sharjah, united arab emirates 6 university of east sarajevo, faculty of business economics, bosnia and herzegovina received: 30 october 2022 accepted: 24 december 2022 first online: 24 december 2022 research paper abstract: the covid 19 pandemic has led to long-term disruption in the supply chain. therefore, refocusing on the supplier selection process was a logical sequence. the new approach of viable suppliers appears as a solution to long-term disruption. this research aims to determine the importance of criteria in selecting suppliers within the viable supplier framework. based on the questionnaire, the opinion of companies with different profiles on the importance of the viable suppliers' criteria was collected. the ranking of the importance of the criteria in selecting viable suppliers was done with the imf swara (improved fuzzy stepwise weight assessment ratio analysis) method. based on the analysis, the criteria were ranked and the most important criterion is the finance criterion. the findings can be a valuable basis for making public policies that will support project organizations to survive the long-term disruption of supply chains. the core contribution of this paper is about determining the importance of criteria in the selection of viable suppliers as a new approach to their selection. a significant amount of research has been done in the field of choosing sustainable suppliers, but this is one of the first works related to defining the significance of the criteria of viable suppliers using the mdcm method, which represents the novelty of this paper. keywords: viable suppliers, long-term disruption, selection of suppliers, imf swara stojanovic et al./oper. res. eng. sci. theor. appl. first online 1. introduction the supply chain concept can be linked with an organized business that enables the supply of products and services to customers (kumar, 2001). suppliers and customers were connected through historical trade routes such as the silk route even in ancient times. during ancient times, supply chains faced many challenges, including inadequate transport infrastructure, robberies on transport routes, and wars (sénquiz-díaz, 2021). seland (2015) highlighted the issue of the non-existence of trade route maps necessary for better navigation of traders who were transporting goods at that time. in the modern era, apart from similar challenges that one can find in the past for supply chains, new challenges are on the horizon (bairagi, 2022). the biggest issues are the legal access to the market caused by trade barriers (dymond & hart, 2008), bioterrorism as a new form of war (gummow, 2010), climate change and sustainability issues (gummow, 2010; garcia & you, 2015; barbosa-póvoa et al., 2018). stadtler (2005) tried to frame different challenges related to business micro, business macro, and technical challenges. nowadays, the covid-19 pandemic become a great challenge to supply chains (remko, 2020; aday & aday, 2020; chowdhury et al., 2021). supply chains have faced many challenges and pressures in the last few years. the global supply chain pressure index introduced by the federal reserve bank of new york showed intensive pressure on supply chains during the period of the covid 19 pandemic. this pressure caused delays in the delivery of raw material subcomponents across supply chain networks. figure 1. global supply chain pressure index (source: benigno et al., 2022) different challenges have caused supply chain disruption (puška, et al., 2018) which differs in size, length, and severity causing negative effects on consumers. wu et al. (2007) highlighted uncertainty as the main trigger for supply chain disruptions that can be considered unexpected events in supply chains (jokić et al., 2021). no one could predict the covid-19 pandemic and its unprecedented long-term disruption effects on supply chains that have led to delays of ongoing projects and rising project delivery costs. the covid-19 pandemic supply chain disruption is completely selection of viable suppliers for project organizations during the long-term disruption of supply chains using imf swara different from others in size, length, and severity. the agreed project delivery terms began to be extended for a long period, and the costs of project deliverables began to rise sharply. the covid-19 pandemic has influenced the re-shifting of orientation in the selection of suppliers. instead of focusing on the criteria that can be associated with the short-term resilience of suppliers, agility of suppliers, or sustainability of suppliers, the covid-19 pandemic highlighted the need to select viable suppliers, those who are capable to survive long-term disruptions (ivanov, 2020). in this study, we investigated the priority criteria in selecting viable suppliers to understand how can the effects of long-term disruption of supply chains be overcome or at least mitigated. although ivanov (2020) proposed a framework for the selection of viable suppliers, we assume that companies will have different weights for different criteria. thus, the initiation of this study enables the analysis of priorities in the selection of suppliers to respond to problems in the period of longterm disruption of supply chains. particular research interest is given to the analysis of priorities in selecting viable suppliers with the characteristics of supply chains in mind. this paper is composed of six sections. after the introduction section, the second section provides the relevant literature about the evolution in a selection of suppliers’ approaches. a special review is given to the literature on the selection of viable suppliers in response to the long-term disruption of the supply chain that occurred during the covid 19 pandemic. the third section is a description of the research methodology and how the criteria for the selection of viable suppliers were prioritized. the findings are presented in the fourth section with the presentation of weights and prioritization of viable suppliers’ selection criteria. in the first section, the findings are discussed in terms of their meaning for the theory and practice. finally, in the sixth section, a conclusion is given on the results of the study and the possible implications of the results. 2. literature review a proper selection of suppliers is one of the most important aspects of any organization, but determining the appropriate approach for selecting suppliers can be one of the most challenging tasks (jauhar et al., 2014). patil (2014) indicated a change in the orientation of supplier selection. the previous approach in which price played a fundamental role in supplier selection has been replaced by a multi-criteria approach. based on his overview, scholars used many criteria in supplier selection. thiruchelvam (2011) argued that companies must have multiple decision-making criteria to select suppliers using qualitative and quantitative approaches. for every purchasing organization, a supplier determines the firm’s purchasing costs (mešić, et al., 2022), ameliorates net profits, minimizes lead times, and enhances csat (customer satisfaction score). de boer (1998) proposed a supplier selection model, which acclimatizes to suit different situations. purchasing activities on one axis and actual steps of purchasing on another. the purchasing process is divided into a matrix comprising problem description, development criteria, and choice on the stojanovic et al./oper. res. eng. sci. theor. appl. first online vertical plane. on the horizontal axis, new task, modified rebuy, straight, rebuy, and strategic straight rebuy. pal et al. (2013) identified the mathematical programming selection methods as linear programming, goal programming, and multi-objective linear programming with data envelopment analysis as a prequalification. cheraghalipour et al. (2017) used a hybrid multi-criteria decision-making (mcdm)-method and mixed integer linear programming (milp) in their study of collection center selection. a very interesting study is conducted by cheraghalipour (2018) in which they used the bwm-vikor approach to supplier selection. ghoushchi et al. (2021) applied swarawaspas framework in landfill site selection for medical waste. ivanov (2020) provided an overview of the historical evaluation of supply chain management and the focus on the supplier selection process. he noticed that different triggers affected changes in approaches to supplier selection. he noticed well several triggers affecting re-shifting the supplier selection approach: • responsiveness that shifted focus on leagility; • natural and man-made disasters that shifted focus on resilience; • climate changes, society, and economics that shifted focus on sustainability; • global pandemics that shifted focus on viability. agarwal et al. (2006) highlighted the necessity of supply chains to be adaptable to changes in the business environment and proactively address needs. they highlighted the importance of combining two concepts, leanness and agility in managing supply chains. according to them, the main determinants for leagile supply chains are managing lead time, costs, quality, and service level. leagility is a supply chain approach that combines cost efficiency, time responsiveness, and a hybrid of the two, or a lean and agile approach (soni & kodali, 2012). leagility (lean-agile) is an essential supply chain strategy for an organization's competitiveness (galankashi & helmi, 2016; li & lu, 2020). galankashi & helmi (2016) proposed a new assessment tool for leagility including different drivers such as facility layout, facility location, inventory, transportation, sourcing, pricing, and information. li & lu (2020) indicated several criteria important for the selection of suppliers including raw material costs, increasing quality, delivery, customer satisfaction, and improving reactions to market changes as per ivanov (2020), natural and man-made disasters triggered changes in the focus of supply chains to the concept of resilience. rajesh & ravi (2015, p.343) state that “resilience that stands for the adaptive capability to respond to disruptions and recover from it needs to be considered in supplier selection.” the vulnerability of supply chains to catastrophic events was discussed by sahu et al. (2016) who indicated the effects of different man-made events (e.g., terrorist attacks) and environmental (e.g., earthquakes). thus, effective supplier selection is the key to the survival of supply chains in these conditions. hosseini & barker (2016) discussed different resilience-based supplier selection criteria. they especially put focus on absorptive, adaptive, and restorative capacities. with the re-shifting of the economic focus to the concept of sustainability, sustainable suppliers become a very hot topic in the literature. the focus of selection of viable suppliers for project organizations during the long-term disruption of supply chains using imf swara sustainable supply chains is on collaborating with suppliers to balance economic, social, and environmental issues (gimenez & sierra, 2013). puška et al. (2021) highlighted the importance of selecting sustainable suppliers for achieving sustainability in business. puška & stojanović (2022) used the fuzzy mabac, marcos, and cardis techniques to select green suppliers in the example of an agrifood company in bosnia and herzegovina. with the covid-19 pandemic, fully new challenges appear in supply chain management. at the beginning of the pandemic, remko (2020) highlighted that the lack of preparedness for long-term disruption and the shortcomings of risk response strategies are major concerns for supply chain resilience in the long run. this opens new research opportunities in the arena of supply chain management (puška, et al., 2020). within just two years, a great amount of the literature discussed the issue of long-term disruption and the selection of suppliers. polyviou et al. (2022) conducted a scenario-based role-play experiment on 286 sourcing professionals. it was revealed that sourcing professionals encounter high levels of feeling of culpability during two situations. firstly, when responsible for selecting a disrupted supplier. secondly, they reckon that the supply disruption was controllable, however, the supplier thought vice versa. hence, the emotions of guilt led many sourcing professionals to select less risky though more advantageous suppliers for new sourcing decisions. supply disruptions have carryover effects on future sourcing decisions in unrelated situations. mdcm (multi-criteria decision making) criteria were proposed to control the product development cycle and to dispense firms with a structured way to grade risks and select suppliers. a study by ilyas et al. (2021) proposed supplier selection criteria to include pandemic-related risks. after analyzing the covid-19 risks, the authors calculated the criteria weights using the best-worst method. furthermore, ftopsis (fuzzy technique for order of preference by similarity to ideal solution)was then applied to categorize and prioritize risks affecting suppliers. the following methods were used in real case studies of the automotive industry and can be extended to other industries as well. a fuzzy rough decision-making approach for the supply chain in the healthcare sector was proposed by pamucar et al. (2022). considering the high uncertainty during covid-19, the study used the “measuring attractiveness through categoricalbased evaluation technique” macbeth (measuring attractiveness through a categorical-based evaluation technique) approach. it’s a distance-based assessment method to address supplier selection problems during covid-19. fuzzy sets and rough numbers were utilized as superior uncertainty sets. multiple-stage multiple-objective organization model, proposed by shao et al. (2022), can be applied to different stages of covid development and the intensity of the pandemic spread. the model's objective is to solve problems related to sustainable supplier selection and order allocation during pandemics like covid-19. the study utilizes a novel nra-nsga-ii (the non-dominated sorting genetic algorithm ii) algorithm to solve the multiple-stage multiple-objective organization model. the case has experimented on a multinational company. the advantages of the algorithm used are as follows: could be used for high dimensional optimization, stojanovic et al./oper. res. eng. sci. theor. appl. first online provide a non-dominated set and reflect t priorities of decision-makers in different situations ivanov (2020) introduced the concept of "viability" which is a concept that balances agility, resilience, and sustainability. “viability is a system ability to meet the demands of surviving in a changing environment” (ivanov & dolgui, 2020, p.2906). additionally, ivanov (2020) highlighted three main features of the dynamically adaptable and structurally changeable viable supply chain: agility reaction, resilience to negative events, and survival in long-term disruptions by adjusting capacities utilizations. based on ivanov (2020) there are 5 main indicators of a viable supply chain: • organizational structure; • informational structure; • technological structure; • financial structure; • process-functional structure. this study aims to assess the importance of these indicators and sub-indicators while selecting viable suppliers. 3. methodology for this study, the following phases were applied used: • phase 1. data collection • phase 2. data processing • phase 3. determination of criteria weights • phase 4. comparison of weights by company location and company supplier the first phase of this research is data collection. based on the theoretical model proposed by ivanov, d. (2020), a questionnaire was prepared that included the proposed criteria for viable suppliers. ivanov (2020) made a significant contribution to the development of the concept of viable suppliers and he proposed criteria for their selection. this study enables further investigation of the significance of criteria and subcriteria suggested by this author. the questionnaire made it possible to identify the importance of criteria by companies in the field of supply chain management, as well as project organizations. the criteria are divided into five main criteria, each into sub-criteria (table 1). table 1. criteria for selecting viable suppliers id criteria description c1 organization c11 back-up suppliers reserve suppliers in case of long-term disruption c12 back-up subcontractors reserve sub-contractors in case of long-term disruption c13 facility fortification preventive measures within your company that protects the process in a period of long-term selection of viable suppliers for project organizations during the long-term disruption of supply chains using imf swara disruption (e.g., social distancing methods) c14 workforce resilience the level of workforce readiness to continue working under the situation of disruption (e.g., vaccinated workforce) c2 information c21 digital twins computerized supply chain models of real state network or virtual supply chain replica that consists of hundreds of assets, warehouses, logistics, and inventory positions used for prediction c22 data analytics processes organizations use to gain insight and extract value from the large amounts of data associated with the procurement, processing, and distribution of goods c23 visibility tools real-time tracking of shipments with integrated operations and analytics capabilities c24 supplier portals a platform for buyers and suppliers to connect with each other and exchange data c25 blockchain technology access to the same information, potentially reducing communication or transfer data errors c3 technology c31 additive manufacturing digital manufacturing technology enables companies to rethink their supply chain design c32 robotics automate the process of storing and moving goods as they make their way through the supply chain c33 smart manufacturing and warehousing help store managers keep track of all inventoryrelated activities c34 industry 4.0 tools global networks of machines in a smart factory setting capable of autonomously exchanging information and controlling each other c4 finance c41 liquidity reserves available cash and cash equivalents during long-term disruption c42 business-government collaboration two or more autonomous organizations from the public and private sectors working jointly to plan and execute supply chain operations c43 revenue management use of pricing to increase the profit generated from a. limited supply of supply chain assets c5 process-functional c51 inventory and capacity buffers the level of inventory that is taken to address disruption of supply chains (e.g., safety stocks) c52 flexibility capacities and sourcing the capability of the buying firm and its processes to respond or react rapidly to changing supply requirements, and the possibility to respond to shortterm changes in demand or supply situations. of other external disruptions together with the adjustment to strategic and structural shifts in the environment c53 omni-channel omni-channel supply chains also serve customers across different channels and it is fully integrated to provide a seamless customer experience c54 product diversification and substitution increasing choices when to order what supplies and from whom to bring products to the market stojanovic et al./oper. res. eng. sci. theor. appl. first online a survey questionnaire was sent to the companies, that were supposed to evaluate the importance of a particular criterion when choosing viable suppliers (vs). the grades ranged in value from 1 to 7 in which grade one is the lowest grade and indicates that the criterion has no importance for the company, while grade seven is the highest and indicates that the criterion has great importance for the company. other values are formed about the importance of the criterion for the company. the 7-grade scale was used to enable respondents with more freedom of expression about the importance of specific criteria and sub-criteria for the selection of viable suppliers. having in mind the volume of different sub-criteria used, a wider scale enables better understanding of the importance of individual subcriteria. after the data was collected from the companies, using the surveysparrow online survey software, it was necessary to convert the data for analysis. the conversion was done by transferring all the data to microsoft excel. this program was then used to determine the weights of the vs criteria. weight calculation was done as follows. based on the company information, the average rating was determined. if the difference between criteria is 0.1, one criterion is considered to be slightly less significant, if the difference is 0.2, one criterion is considered to be moderately less significant, etc. according to the scale of values used in the imf swara (improved fuzzy stepwise weight assessment ratio analysis) method. the imf swara method represents a modification of the swara method developed by keršuliene, et al. (2010). imf swara modifies the fuzzy swara (stepwise weight assessment ratio analysis) method (vrtagić, et al., 2021). this method uses the same steps as the swara method except that it uses a different scale of values (table 2) table 2. scale for the evaluation of the criteria linguistic variable abbreviation tfn scale absolutely less significant als 1 1 1 dominantly less significant dls 1/2 2/3 1 much less significant mls 2/5 1/2 2/3 really less significant rls 1/3 2/5 ½ less significant ls 2/7 1/3 2/5 moderately less significant mdls 1/4 2/7 1/3 weakly less significant wls 2/9 1/4 2/7 equal significant es 0 0 0 the basis of imf swara, like all swara methods, has the following steps (stanujkić, et al., 2021): step 1. identification and selection of criteria step 2. sorting the criteria according to their importance from the most to the least important step 3. determining the relative importance of criteria. here, the criterion that has the greatest importance takes the value of one (1), while the value of the other criteria is determined by their importance. selection of viable suppliers for project organizations during the long-term disruption of supply chains using imf swara step 4. calculation of the coefficient value kj,, based on expression: 𝑘𝑗 = { 1 𝑖𝑓 𝑗 = 1 𝑠𝑗 + 1 𝑖𝑓 𝑗 > 1 (1) step 4. calculation of significance values 𝑞𝑗 , based on expression: 𝑞𝑗 = { 1 𝑖𝑓 𝑗 = 1 𝑞𝑗−1 𝑘𝑗̅̅ ̅ 𝑖𝑓 𝑗 > 1 (2) step 5. calculating the weight of criteria 𝑤𝑗 , based on expression: 𝑤𝑗 = 𝑞𝑗 ∑ 𝑞𝑘 𝑛 𝑗=1 (3) more details about this procedure will be given in the results section. after the weight for the criteria and sub-criteria were determined for all observed companies in total, the weights were determined for certain companies divided by their main location and by the location of suppliers. after companies were subgrouped, criteria and sub-criteria weights were calculated for those groups, and a comparison of those weights was conducted. the obtained weights were compared by correlation person analysis for weights correlation and spearman for rank correlation. 4. results a prepared survey questionnaire was sent to the addresses of 273 companies, with which companies assessed the importance of criteria for selecting valid suppliers. a total of 67 companies filled out the questionnaire, while 64 completed questionnaires were suitable for analysis. companies from different parts of the world participated in the research, most of them from europe (figure 2) figure 2. respondent profile: main location stojanovic et al./oper. res. eng. sci. theor. appl. first online bearing in mind the specificity of the research problem, it was interesting to see if there are different perceptions about the importance of the vs criteria among companies that have suppliers from the local and national markets, compared to companies that mainly deal with suppliers outside national borders. figure 3 shows the percentage of participation of companies in the research from the aspect of the location of their suppliers. figure 3. respondent profile: location of suppliers the results presented in table 3 were obtained based on the completed questionnaires. the results showed (table 3) that criterion c2 has the highest overall score (sum = 265) and the highest average score (mean = 5.80), while sub-criterion c25 has the lowest overall score. grade (sum = 192) and the lowest average grade (mean = 4.39). regarding the deviation of grades from the mean value of the largest deviation, sub-criterion c14 (sd = 1.87) has the corresponding highest dispersion of grades, while sub-criterion c12 (sd = 1.06) has the smallest dispersion of grades. this deviation calculated by the indicator of standard deviation shows that if the value of this indicator is higher, the higher the score deviates from the average score and vice versa. the maximum value of all criteria is 7, while the minimum score for criteria is 1, that is, for criteria c2 and c4, the lowest score is 3. after the data were collected, they were processed to calculate the weights of the criteria and sub-criteria. using the example of the main criteria, the method of determining the weight of the criteria is explained. the importance of the criteria was determined based on the aggregate evaluation. the main criterion with the highest sum was placed first, then the criterion with the next highest number of marks. in this way, the criteria are ordered by their importance (table 3). value 𝑠𝑗 was formed in this way by subtracting the total scores of the information criterion from the total scores of the finance criterion. selection of viable suppliers for project organizations during the long-term disruption of supply chains using imf swara table 3. descriptive research results criteria overall score mean standard deviation maximum score minimum score c1 247 5,47 1,33 7 1 c11 247 5,42 1,28 7 1 c12 238 5,22 1,05 7 1 c13 211 4,78 1,67 7 1 c14 208 4,81 1,87 7 1 c2 265 5,80 1,06 7 3 c21 208 4,81 1,54 7 1 c22 221 5,02 1,45 7 1 c23 235 5,31 1,41 7 1 c24 221 4,95 1,52 7 1 c25 192 4,39 1,54 7 1 c3 255 5,56 1,31 7 1 c31 230 5,02 1,56 7 1 c32 203 4,61 1,71 7 1 c33 221 4,98 1,64 7 1 c34 213 4,80 1,61 7 1 c4 260 5,66 1,13 7 3 c41 256 5,55 1,32 7 1 c42 230 5,06 1,33 7 1 c43 230 5,13 1,28 7 1 c5 243 5,39 1,28 7 1 c51 239 5,36 1,25 7 1 c52 242 5,39 1,32 7 1 c53 223 4,95 1,27 7 1 c54 239 5,25 1,15 7 1 after the data were collected, they were processed to calculate the weights of the criteria and sub-criteria. using the example of the main criteria, the method of determining the weight of the criteria is explained. the importance of the criteria was determined based on the average evaluations of the criteria. the main criterion that had the highest average score was placed first, then the criterion that had the next highest average score was placed in second place, etc. in this way, the criteria were ordered by their importance (table 3). the value 𝑠𝑗 was formed in such a way that the average evaluations of the criteria were observed. for example, the difference from the average ratings of the information and finance criteria is 0.1, and then the weakly less significant (wls) value is taken from the value scale. if the difference is 0.2, it is a value moderately less significant (mdls). in this way, the values for all differences were determined and the value for 𝑠𝑗 was formed. the value 𝑘𝑗 was formed by adding one (1) to the value 𝑠𝑗 (expression 1). the value 𝑞𝑗 was formed based on expression 2. for the information criterion, the value was overwritten, and the value one (1) was overwritten, for the finance criterion, the value 𝑞𝑗 of the previous criterion (in this case, the information criterion) was divided by the value 𝑘𝑗 of that criterion. the 𝑞𝑗 values for all criteria stojanovic et al./oper. res. eng. sci. theor. appl. first online were formed in the same way. then all 𝑞𝑗 values were added. the value of 𝑤𝑗 was formed by dividing the individual values of 𝑞𝑗 by the aggregate value of 𝑞𝑗 (expression 3). the results obtained in this way show that the information criterion (w = 0.27) received the highest weight value, while the process-functional criterion (w = 0.11) received the lowest value (table 4) table 4. calculation of weights for the main criteria criteria 𝑠𝑗 𝑘𝑗 𝑞𝑗 𝑤𝑓 𝑤𝑗 information 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 0.28 0.27 0.25 0.272 finance 0.22 0.25 0.29 1.22 1.25 1.29 0.82 0.80 0.78 0.23 0.22 0.20 0.217 technology 0.22 0.25 0.29 1.22 1.25 1.29 0.67 0.64 0.60 0.19 0.18 0.15 0.174 organization 0.22 0.25 0.29 1.22 1.25 1.29 0.55 0.51 0.47 0.15 0.14 0.12 0.139 processfunctional 0.22 0.25 0.29 1.22 1.25 1.29 0.45 0.41 0.37 0.12 0.11 0.09 0.111 sum 3.48 3.36 3.22 in the same way, the decision matrices for the sub-criteria were formed and the weights of the sub-criteria were calculated (table 5). in the organization criterion, sub-criterion c11 (w = 0.347) received the highest weight, while sub-criterion c13 and c14 (w = 0.192) received the lowest weight. for the information criterion, subcriterion c23 (w = 0.286) received the highest weight value, while sub-criterion c25 (0.119) had the lowest value. in the technology criterion, sub-criterion c31 and c33 (w = 0.296) received the highest weight, while sub-criterion c32 (w = 0.179) received the lowest weight value. in the finance criterion, sub-criterion c41 (w = 0.413) received the highest weight value, while sub-criterion c42 and c43 (w = 0.294) received the lowest weight value. for the process-functional criterion, subcriterion c51 and c52 (0.294) received the highest weight value, while sub-criterion c53 (w = 0.176) received the lowest weight value. table 5. calculation of weights of sub-criteria criteria 𝑠𝑗 𝑘𝑗 𝑞𝑗 𝑤𝑓 𝑤𝑗 c11 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 0.32 0.33 0.35 0.347 c12 0.25 0.29 0.33 1.25 1.29 1.33 0.80 0.78 0.75 0.26 0.26 0.26 0.269 c13 0.25 0.29 0.33 1.25 1.29 1.33 0.64 0.60 0.56 0.21 0.20 0.20 0.192 c14 0.00 0.00 0.00 1.00 1.00 1.00 0.64 0.60 0.56 0.21 0.20 0.20 0.192 sum 3.08 2.99 2.88 criteria 𝑠𝑗 𝑘𝑗 𝑞𝑗 𝑤𝑓 𝑤𝑗 c23 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 0.27 0.29 0.30 0.286 c21 0.29 0.33 0.40 1.29 1.33 1.40 0.78 0.75 0.71 0.21 0.21 0.22 0.214 c22 0.00 0.00 0.00 1.00 1.00 1.00 0.78 0.75 0.71 0.21 0.21 0.22 0.214 c24 0.25 0.29 0.33 1.25 1.29 1.33 0.62 0.58 0.54 0.17 0.17 0.16 0.166 c25 0.33 0.40 0.50 1.33 1.40 1.50 0.47 0.42 0.36 0.13 0.12 0.11 0.119 sum 3.64 3.50 3.32 criteria 𝑠𝑗 𝑘𝑗 𝑞𝑗 𝑤𝑓 𝑤𝑗 c31 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 0.29 0.30 0.30 0.296 c33 0.00 0.00 0.00 1.00 1.00 1.00 1.00 1.00 1.00 0.29 0.30 0.30 0.296 selection of viable suppliers for project organizations during the long-term disruption of supply chains using imf swara c34 0.25 0.29 0.33 1.25 1.29 1.33 0.80 0.78 0.75 0.23 0.23 0.23 0.230 c32 0.25 0.29 0.33 1.25 1.29 1.33 0.64 0.60 0.56 0.19 0.18 0.17 0.179 sum criteria 𝑠𝑗 𝑘𝑗 𝑞𝑗 𝑤𝑓 𝑤𝑗 c41 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 0.40 0.41 0.43 0.413 c42 0.33 0.40 0.50 1.33 1.40 1.50 0.75 0.71 0.67 0.30 0.29 0.29 0.294 c43 0.00 0.00 0.00 1.00 1.00 1.00 0.75 0.71 0.67 0.30 0.29 0.29 0.294 sum 2.50 2.43 2.33 criteria 𝑠𝑗 𝑘𝑗 𝑞𝑗 𝑤𝑓 𝑤𝑗 c51 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 0.29 0.29 0.30 0.294 c52 0.00 0.00 0.00 1.00 1.00 1.00 1.00 1.00 1.00 0.29 0.29 0.30 0.294 c54 0.22 0.25 0.29 1.22 1.25 1.29 0.82 0.80 0.78 0.24 0.24 0.23 0.235 c53 0.29 0.33 0.40 1.29 1.33 1.40 0.64 0.60 0.56 0.18 0.18 0.17 0.176 sum 3.45 3.40 3.33 the global values of those sub-criteria were calculated based on certain weights for the main criterion and its sub-criteria. these values were calculated in such a way that the weight values of the sub-criteria were multiplied by the weight values of the corresponding criterion. in this way, the weights of the sub-criteria for svs were formed (table 6). sub-criterion c41 (w = 0.0896) has the highest weight, followed by sub-criterion c23 (w = 0.0778), while sub-criterion c53 (w = 0.0195) has the lowest weight. these results showed that the sub-criteria of the finance criterion received the highest weight values. table 6. weights of sub-criteria of viable suppliers criteria local value global value rank organization 0.139 c11 0.347 0.0482 9 c12 0.269 0.0374 12 c13 0.192 0.0267 17 c14 0.192 0.0267 17 information 0.272 c21 0.214 0.0582 5 c22 0.214 0.0582 5 c23 0.286 0.0778 2 c24 0.166 0.0452 10 c25 0.119 0.0324 15 technology 0.174 c31 0.296 0.0515 7 c32 0.179 0.0311 16 c33 0.296 0.0515 7 c34 0.230 0.0400 11 finance 0.217 c41 0.413 0.0896 1 c42 0.294 0.0638 3 c43 0.294 0.0638 3 process-functional 0.111 stojanovic et al./oper. res. eng. sci. theor. appl. first online c51 0.294 0.0326 13 c52 0.294 0.0326 13 c53 0.176 0.0195 20 c54 0.235 0.0261 19 in the same way, as sub-criteria weights were determined for all companies in total, criteria weights were determined for two sub-groups of companies that operate within national borders and outside national borders considered global companies. first, the companies were divided into those operating within national borders and those operating on the international market, and then weights were determined for these companies. as with the aggregate weights, the sub-criteria of the finance criterion received the highest weights in this scenario (table 7). by observing those weights using correlation analysis, it was determined that there is a good connection (r = .634). however, when the rankings between these companies were observed using the spearman correlation coefficient, the correlation value was lower than when the weight of the criteria was observed (r = .333). based on that, it can be determined that the weights did not change significantly, but the ranking orders did change. even then there was no significant statistical difference between the observed ranking orders of the sub-criteria weights. the obtained results show us that there is still a difference, which is not statistically significant, between the importance of subcriteria for companies according to their business location. the first criterion is in favor of companies operating in the global market, and the second sub-criterion is in favor of companies operating in the local market. the highest weight value for companies operating in the local market is for sub-criterion c41, while the lowest weight is for sub-criterion c14. when looking at companies operating on the global market, sub-criterion c41 has the highest weight, while subcriterion c25 has the lowest weight. the biggest change in rankings was in subcriteria c14 and c31, where the ranking changed by 15. table 7. value of the criteria about the main location of the company criteria local value global value rank local value global value rank national borders global company organization 0.1498 0.2141 c11 0.3838 0.0575 8 0.2814 0.0603 6 c12 0.2979 0.0446 11 0.2302 0.0493 12 c13 0.1768 0.0265 17 0.2302 0.0493 12 c14 0.1414 0.0212 20 0.2968 0.0636 5 information 0.3019 0.2478 c21 0.1611 0.0486 10 0.2293 0.0568 8 c22 0.2152 0.0650 6 0.2293 0.0568 8 c23 0.2877 0.0868 2 0.2818 0.0698 3 c24 0.2152 0.0650 6 0.1713 0.0424 16 c25 0.0710 0.0214 19 0.1217 0.0302 20 technology 0.1874 0.1708 c31 0.3511 0.0658 3 0.2091 0.0357 18 c32 0.1646 0.0308 14 0.2091 0.0357 18 selection of viable suppliers for project organizations during the long-term disruption of supply chains using imf swara c33 0.2726 0.0511 9 0.3313 0.0566 10 c34 0.2118 0.0397 12 0.2617 0.0447 15 finance 0.2412 0.2141 c41 0.4578 0.1104 1 0.4132 0.0885 1 c42 0.2711 0.0654 4 0.2521 0.0540 11 c43 0.2711 0.0654 4 0.3244 0.0695 4 processfunctional 0.1198 0.2141 c51 0.2523 0.0302 15 0.3446 0.0738 2 c52 0.3157 0.0378 13 0.2781 0.0595 7 c53 0.1809 0.0217 18 0.1677 0.0359 17 c54 0.2523 0.0302 15 0.2159 0.0462 14 the following analysis was taken into account the location of suppliers. thus, companies were divided into two sub-groups: those whose suppliers are within national borders and those whose suppliers are outside of national borders. the results showed (table 8) that when we use this structure of a grouping of companies, the sub-criteria of the finance criterion had the highest weight values. observing the connection between the values of the weights of the sub-criteria, there is a greater connection than was the case with the sub-grouping companies by their main location (r = .636). looking at the ranking of the alternatives using the spearman correlation coefficient, there is a greater connection (r = .355). the highest weight in the sub-criteria for companies that use a global supplier is c22, while the lowest weight is in sub-criteria c32. when looking at companies with suppliers from the global market, the highest weight is in sub-criterion c41, while the lowest is in sub-criteria c13 and c14. when looking at the rankings, the biggest change was in sub-criterion c34, where the change was in favor of companies that use global suppliers. table 8. value of the criteria about the location of suppliers criteria local value global value rank local value global value rank national suppliers global suppliers organization 0.2069 0.1262 c11 0.3540 0.0732 4 0.3641 0.0459 12 c12 0.2649 0.0548 8 0.2908 0.0367 15 c13 0.1693 0.0350 16 0.1726 0.0218 19 c14 0.2118 0.0438 12 0.1726 0.0218 19 information 0.2765 0.2542 c21 0.2183 0.0604 5 0.1553 0.0395 14 c22 0.2732 0.0755 1 0.2075 0.0527 7 c23 0.2183 0.0604 5 0.3134 0.0796 2 c24 0.1745 0.0482 10 0.2075 0.0527 7 c25 0.1158 0.0320 18 0.1164 0.0296 17 technology 0.1549 0.2542 c31 0.3473 0.0538 9 0.2988 0.0759 3 c32 0.1675 0.0259 20 0.1788 0.0454 13 c33 0.2697 0.0418 13 0.2988 0.0759 3 stojanovic et al./oper. res. eng. sci. theor. appl. first online c34 0.2156 0.0334 17 0.2236 0.0568 6 finance 0.2069 0.2031 c41 0.3572 0.0739 2 0.5000 0.1016 1 c42 0.2855 0.0591 7 0.2500 0.0508 9 c43 0.3572 0.0739 2 0.2500 0.0508 9 process-functional 0.1549 0.1624 c51 0.1973 0.0306 19 0.2830 0.0460 11 c52 0.2469 0.0382 14 0.3542 0.0575 5 c53 0.2469 0.0382 14 0.1510 0.0245 18 c54 0.3089 0.0478 11 0.2118 0.0344 16 5. discussion viable suppliers become a very important tool in sustaining project business during long-term disruptions. thus, the framework for the selection of viable suppliers proposed by ivanov (2020) seems very suitable for long-term disruptions such as the covid-19 pandemic, or similar events that can cause long-term disruptions. this study aimed to rank the main criteria and sub-criteria based on this framework. as per the findings, the most important criterion for selecting viable suppliers is the financial criterion. the characteristics of the effects of long-term disruptions on project business can justify this. the first visible effect of the covid 19 pandemic was the delay in delivering projects. keeping in mind contractual obligations in terms of delivering dates caused penalties for project organizations and delays in charges for carrying out projects. additionally, the costs of raw materials and sub-components that should be included in project deliverables increased. putting it all together and considering the duration of the supply chain disruption, this affected great challenges in managing cash flow for project organizations, putting them into a serious situation that brought many project organizations to the brink of survival. therefore, the result of the study, which places the financial criterion in the first place in the selection of suppliers, is quite justified. similar findings are provided by zamani et al. (2020) who showed two major issues; operational and financial including late payment increased cost of the project and declining number of projects. payments are made as the project phase completes. during the covid 19 pandemic, the payments were delayed when government operations were impeded. as a result, companies suffered from working capital problems. additionally, due to increased demand and reduced supply of materials, the cost of materials rose. in addition, among the other 20 sub-criteria, the sub-criterion liquidity reserves from the finance main criterion is ranked as the most prominent, which further gives the impression of the importance of available cash and cash equivalents during longterm disruption. as a secondly ranked sub-criterion was inventory and capacity buffers from the process-functional criterion. this sub-criterion refers to the inventory level taken to address the disruption of supply chains (e.g., safety stocks). as per this finding, just in time approach should not be the focus of the procurement strategy of project organizations. selection of viable suppliers for project organizations during the long-term disruption of supply chains using imf swara delays in delivering projects and issues with the rising costs of raw materials raise the issue of availability of raw materials during disruptions, thus safety stocks are necessary regardless of additional inventory costs that they raise. as the third sub-criterion is the additive manufacturing from the technology main criterion which is about digital manufacturing technology enables companies to rethink their supply chain design. due to preventive measures that were taken during covid 19 pandemic, it is necessary to find an additional solution for supply channels that will replace the one under disruption. thus, the technology that enables fast redesign is appreciated by project organizations. the revenue management sub-criterion is ranked in fourth place. it refers to the use of pricing to increase the profit generated from a limited supply of supply chain assets. rising costs of raw materials that occur during longterm disruptions increase the cost for project organizations. those project organizations that had fixed-cost contractual relations with their customers felt all the negativity of this kind of relationship in the period of long-term disruption. thus, the tools of revenue management should be reconsidered carefully to address these types of challenges. katsaliaki et al. (2021), while analyzing the operational and financial impact of supply chain disruptions, found a correlation with the increased globalization of businesses. a big challenge for project companies is their previous full orientation to cost reduction which has been achieved through the offshoring and outsourcing of many manufacturing and r&d (research and development) facilities, especially in emerging markets and underdeveloped nations. for these supply chain operations to be successful, the economy and business environment must be stable. however, due to globalization, economies have become interconnected, leading to supply chain operations being vulnerable to global disruptions. for instance, us retailers reported a massive $700 million loss from production and transportation shortages due to coronavirus. katsaliaki (2021) highlighted also that hindrances in cargo movement, infection prevention control, and labor shortage accumulated supply disruption. however, we should not think only on covid 19 pandemic as a cause of long-term disruptions. there are many other causes. although wars occur in developing and underdeveloped economies, their effects penetrate global supply chains, endangering the global supply of metals, energy, and agrarian commodities supplied by war zones. according to jola-sanchez & serpa (2021), a typical war generates approximately $14.4 trillion in costs including $98.3 billion in losses in the supply chain. during conflicts, the fighters attack business facilities and workers, thwarting supply networks and daily operations. hence, fair policymaking is extremely pivotal for global supply chain assurance and mitigating war’s crippling effects. according to our study, information is also a pivotal indicator for the selection of viable suppliers. this is in line with the findings by bäckstrand and fredriksson (2020) who identified how supplier information can affect delivery patterns in construction businesses. it was deduced that a lack of supplier information and coordination resulted in a surplus/shortage of goods, data entry errors (wrong address or wrong transport inputs), extra administration costs, and delayed deliveries. stojanovic et al./oper. res. eng. sci. theor. appl. first online based on this study, digital communication methods, weekly meetings, and b core scm software allow the free flow of information. consequently, these methods would aid businesses to avoid hindrances in projects due to a lack of information flow. our study indicated the very strong importance of digital twins that enables computerized supply chain models of real state network or virtual supply chain replica that consists of hundreds of assets, warehouses, logistics, and inventory positions used for prediction. this sub-criterion is ranked in fifth place. considering the period of lockdowns in specific counties during the covid 19 pandemic, it is crucial to see some alternative possibilities for supply while simultaneously keeping the focus on minimizing the costs. thus, digital twins can play a very important role, and a suggestion for software developers is to find these findings as an opportunity for business collaboration with project organizations around the world. the organization is among lowers ranked criteria, but still important for the selection of viable suppliers. thus, we should agree with hou & sun (2016) who suggested adjusting sourcing decisions to cope with long-term disruption. this scholar proposed several strategies that can work. the first strategy is to have a single-source supplier along with a contingent supplier. under this strategy, the contingent supplier restores inventory during unexpected events when the main supplier faces disruption. however, firms may suffer due to contingent suppliers’ lack of adequate capacity or technical uncertainty. this is because of variability in the production coefficient. the results showed that companies would benefit from stocking more under long disruptions rather than using contingent suppliers. a larger disruption probability increases the firm’s optimal base stock level and expected cost. the second sourcing strategy is the dual sourcing strategy. the firm uses a second supplier as a regular source when the supply chain of the first supplier is disrupted. according to the literature, bifurcating orders among different suppliers can mitigate the disruption caused by the pandemic. the strategy is beneficial, as the second supplier can increase its output with extra capacity. the study observed that buyers prefer to stock more during a large disruption to avoid large purchasing costs. process-functional criterion was ranked in last place for the importance of the selection of viable suppliers. we cannot say it is not an important criterion, but compared with other criteria, it has not the same value when selecting a viable supplier. zamani et al. (2020) pointed out that construction projects had to follow “standard operating procedures”, causing a slow and lengthy project timeline. authority offices were closed during covid 19 pandemic hence, getting approval for processes became time-consuming leading to delays in project completion. secondly, foreign workers were sent back to their respective countries during the pandemic as their work permits expired. logistics was another factor that caused delays in the projects. for instance, most project materials were imported from foreign countries. as the supplier operations were suspended due to the pandemic, the deliveries of materials ceased. even when government regulations were relaxed, the delivery of supplies became slow due to new procedures that needed to be followed. thus, although ranked last place, the process-functional criterion should also take a place in deciding on supplier selection. selection of viable suppliers for project organizations during the long-term disruption of supply chains using imf swara some measures proposed by perez-batres & treviño (2020) can work for this situation. he suggested a physical hedging supply chain option that enables global suppliers to continue operations during pandemics. it’s essential to create physical capacity to power supply chains when lockdown measures are put into effect. hence, businesses and governments should build regional sourcing by creating miscellaneous webs of indispensable supply chain nodes in low-density locations that are less likely to be affected by pandemics, avoiding global supply chain systemic disruptions. additionally, other benefits include increased job creation, enhancement of human resources, regional development, and, global supply chain survival. however, economists would argue against this strategy, as this would threaten global connectedness. secondly, the globalization of the supply chain is responsible for huge productivity and monetary gains during normal economic conditions. this strategy is more likely to focus on adverse and abnormal economic conditions. to better understand which criteria are more important while selecting viable suppliers, it is not only important to look at findings in general. it is also important to the importance of main criteria and sub-criteria for different types of companies. it is not the same if a company has suppliers only within national borders, or outside of the national borders. usually, during covid 19 pandemic the lockdowns disabled communication outside of national borders preventing people and goods from entering the national market. thus, the same criteria for supplier selection are not always the same for companies that have different supplier profiles. our study provides adequate insight taking into consideration also this perspective. determining sub-criteria weights is significant because if there is a difference between them, it means that the importance of the sub-criteria is different for companies that operate within the national border compared to those that operate on the global market. having in mind the specificity of long-term disruptions of supply chains that are sometimes affected by closing national borders for a transition of people and goods, and covid 19 pandemic is an example, this is very important to understand. 6. conclusion the evolution of the literature regarding the choice of suppliers is evident. various challenges have led to a change in the framework for supplier selection, starting with a focus on price-based supplier selection, agile suppliers, and a reorientation of sustainable suppliers. the covid 19 pandemic unexpectedly impacted project organizations that had contracted business ventures. the first visible effect was a delay in the implementation of projects that lasted several months. another obvious effect was the increase in costs caused by the delay, which increased prices. this was a challenge for some project companies that had fixed contracts and it was very difficult to adjust the price to the newly created circumstances of increased costs. precisely this situation demanded a reorientation towards the selection of viable suppliers that enable survival in the period of longterm disruption of supply chains. stojanovic et al./oper. res. eng. sci. theor. appl. first online this paper aimed to assess the importance of certain criteria in the selection of viable suppliers. in this research, 5 basic and 20 sub-criteria were evaluated. the results show that the financial criterion was evaluated as the most important. this indicates that in the period of long-term disruption of supply chains, the greatest danger lies in the financing of business when there is a long-term disruption in project operations. this fact is also indicated by the most important evaluated subcriterion: liquidity reserves showing the importance of available cash and cash equivalents during long-term disruption. due to the interruption of business operations, but also due to unavoidable running operating costs, many companies found themselves in a liquidity problem, so their survival was threatened. thus, the financial criterion take the most important place in the selection of viable suppliers. after the financial criterion, the results show the order of importance of the other main criteria, namely information, followed by the technology criterion, then followed the organization criterion, while the process-functional criterion is ranked in the last place. this distribution of importance of the criteria indicates that having timely information about possible disruption, but also information about alternative solutions, becomes very crucial in the period of supply chain disruption. the research results made it possible to understand the importance of certain criteria for selecting viable suppliers that were proposed within the viable supplier framework. they provide a good basis for enacting public policies that would help project companies survive the conditions of long-term supply chain disruption. the results of the research provide a good basis for companies when choosing suppliers in the period of long-term disruption of supply chains. the recommendation to companies is to consider the importance of certain criteria and to apply this model when choosing suppliers. the results of the research can help in the development of stimulation policies by government bodies to avoid the negative consequences of long-term disruption of supply chains. the limitation of the research is the inclusion in the survey of companies of different profiles from different sectors. companies from different sectors have their specificities regarding the supply chain, and it is necessary to take that fact into account. this study included companies from different sectors, so the results can be viewed as general without taking into account the specifics of individual business sectors. one of the limitations is the number of companies that responded to this questionnaire. having in mind the limitation of this study, the recommendation for future research is to provide structured research that will determine the possible difference in ranking criteria for selecting viable suppliers in different sectors and industries. our assumption after conducting research is that companies operating in different sectors have different priorities when choosing viable suppliers. therefore, it would be interesting to conduct similar analyzes in individual sectors, especially those that were most affected by supply chain disruptions over a long period. this research provides a good basis for future similar research that will introduce additional specifics about the selection of viable suppliers. selection of viable suppliers for project organizations during the long-term disruption of supply chains using imf swara references aday, s., & aday, m. s. 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(2007). methodology for supply chain disruption analysis. international journal of production research, 45(7), 1665-1682. https://doi.org/10.1080/00207540500362138 zamani, s. h., rahman, r. a., fauzi, m. a., & yusof, l. m. (2021). effect of covid-19 on building construction projects: impact and response mechanisms. iop conference series: earth and environmental science, 682, 012049. https://doi.org/10.1088/1755-1315/682/1/012049 © 2022 by the authors. submitted for possible open access publication under the terms and conditions of the creative commons attribution (cc by) license (http://creativecommons.org/licenses/by/4.0/). operational research in engineering sciences: theory and applications first online issn: 2620-1607 eissn: 2620-1747 doi: https://doi.org/10.31181/oresta111022106t * corresponding author. dineshkumartripathi1980@gmail.com (d.k. tripathi), nigamsantosh01@gmail.com (s.k. nigam), arunodaya87@outlook.com (a.r. mishra), raoofstat15@gmail.com (a.r. shah) a novel intuitionistic fuzzy distance measureswara-copras method for multi-criteria food waste treatment technology selection dinesh kumar tripathi1, santosh k. nigam1, arunodaya raj mishra2*, abdul raoof shah3 1 department of mathematics, government college satna, india 2 department of mathematics, government college raigaon, satna, india 3 department of statistics, government degree college, pulwama, india received: 07 july 2022 accepted: 04 september first online: 11 october original scientific paper abstract: as an extension of fuzzy set, intuitionistic fuzzy set (ifs) considers the degrees of non-membership and hesitancy along with the degree of membership, therefore, the knowledge and semantic representation of ifs become more significant, resourceful and appropriate. however, with the presence of multiple sustainability indicators and uncertain information, the selection of appropriate food waste treatment technology (fwtt) can be considered as a multi-criteria decision-making (mcdm) problem. thus, this study aims to introduce a decision support system for assessing the fwtt alternative under uncertain environment. for this purpose, a new intuitionistic fuzzy information-based mcdm methodology is proposed by combining intuitionistic fuzzy distance measure, stepwise weight assessment ratio analysis (swara) and the complex proportional assessment (copras) methods. the combination of distance measure-based procedure and swara method is used to take the benefits of both the objective and subjective weights of criteria during fwtts evaluation. next, the hybridized copras methodology is presented to assess and rank the considered fwtts from sustainability perspective under intuitionistic fuzzy environment. further, the present method is implemented on a case study of fwtt selection problem within the context of ifs, which shows its feasibility and effectiveness. this method not only reflects the subjective perspective of decision expert but also captures the objective evaluation of the actual performance measures of each fwtt candidate. sensitivity and comparative analyses show a high degree of robustness and uniformity in the obtained results. obtained outcomes point out that the present copras model can effectively choose the suitable fwtt candidate and have the potential to offer practical reference for the policymakers. key words: intuitionistic fuzzy sets, food waste, distance measure, swara, copras, multi-criteria decision-analysis. mailto:dineshkumartripathi1980@gmail.com mailto:nigamsantosh01@gmail.com mailto:arunodaya87@outlook.com mailto:raoofstat15@gmail.com tripathi et al./oper. res. eng. sci. theor. appl. first online 1. introduction “food waste (fw)” is a primary component of “municipal solid waste (msw)”. the proper management of fws is a global challenge for the environmentalists, scientists, consumers and activists (morelli et al., 2020). poorly managed fw causes severe unfavorable consequences like as contamination of natural resources, greenhouse gas emission, environmental pollution, global warming etc (slorach et al., 2019). “food waste treatment (fwt)” can produce several positive outcomes including renewable energy production, reduced methane and other greenhouse gas emissions, air quality improvement, reduced reliance on landfills and fossil fuels, job creation, economic growth and sustainable infrastructure investments. in a study, elmashad & zhang (2010) added the fw into daily manure to extensively increase the biogas yield. lal & mohapatra (2020) employed kitchen waste as the source for biogas creation, followed by its consumption in dual-fuel compression ignition engine. due to increased amount of food wastes, many different “food waste treatment technologies (fwtts)” have been emerged in the market (pham et al., 2015; giwa et al., 2019). as an important part of sustainable waste management system, the fwtt provides a number of benefits such as maximizing energy recovery, fertilizer production and improved soil health, resulting in economic and environmental benefits (shewa et al., 2020; ren & toniolo, 2020). with the variable composition, high moisture content and low calorific value in fw, a suitable technology is required for the treatment of fws (rani et al., 2021, 2022a). the management and treatment of fw are affected by various indicators such as treatment cost, electricity consumption, water consumption, energy production yield, social acceptability, job creation, air/water pollution etc (garcia-garcia et al., 2017). in the assessment and selection of suitable fwtts, several aspects of sustainability including economic, environmental, social and technological are involved (sakcharoen et al., 2021), therefore, it can be considered as “multi-criteria decision-making” problem (chadderton et al., 2017; omar et al., 2021). during the process of mcdm, the data available for an alternative by means of several attributes may be qualitative linguistic values or imprecise or incomplete in nature. to handle the imprecise and unclear data, zadeh (1965) gave the notion of “fuzzy set (fs)” and applied to several decision-making applications by considering various perspectives. in fs, the element has only degree of membership but it may not always be sure that the non-membership grade of an element in a fs is just equal to 1 minus the membership grade. in addition, hesitation may have great impact on the final decision and should be considered in decision-making processes but fs ignores the hesitancy. to handle these situations, atanassov (1986) gave the theory of “intuitionistic fuzzy set (ifs)” to get over certain limitations of fs. it is portrayed by the “membership function (mf)”, “non-membership function (nf)” and “hesitancy function (hf)”, wherein the values of mf, nf and hf are real numbers between zero and one. in fs, only the mf of an element is considered, whereas in ifs, the mf, the nf and the hf are considered with the sum of mf and nf is less than or equal to 1. the flexibility of ifss in handling uncertain information is the main motive that we propose ifs-based mcdm approach in this work. to the best of authors’ information, there is no study regarding the assessment and prioritization of multi-criteria sustainable fwtt alternatives from intuitionistic a novel intuitionistic fuzzy distance measure-swara-copras method for multi-criteria food waste treatment technology selection fuzzy information perspective. as a consequence, this work proposes an innovative mcdm technique for assessing the sustainable fwtts under uncertain environment. the developed framework uses ifs theory to consider the uncertainty of information offered by the “decision experts (des)” in the evaluation process. in the process of mcdm, the criteria weights determination and ranking of alternatives are two important aspects for des. for this purpose, in this study, an integrated criteria weight-determining model is presented based on the combination of distance measure-based process for objective weights and the “step-wise weight assessment ratio analysis (swara)” (kersuliene et al., 2010) method for subjecting weights of criteria under ifs context. the swara is one of the significant weighting models being used to rank the considered criteria by means of des’ opinions. in addition, the classical “complex proportional assessment (copras)” (zavadskas et al., 1994) approach is presented to rank the options within “intuitionistic fuzzy (if)” context. the proposed copras approach utilizes a stepwise ordering and assessing process of the options concerning the utility degree based on intuitionistic fuzzy information. inspired by the advantages of swara and copras methods, we propose a hybridized method based on distance measure, swara and copras method with “intuitionistic fuzzy numbers (ifns)”, and to apply for evaluating fwtts with uncertainty. till now, no one has developed a hybrid approach which combines the distance measure, the swara and the copras methods with ifss to evaluate the fwtts from different aspects of sustainability. the key contributions of the developed work are given by • a new extension of copras model is proposed for solving intuitionistic fuzzy mcdm problems with completely anonymous experts and criteria weights. • a new weighting formula is presented to determine the des’ weights from intuitionistic fuzzy perspective. • to compute the criteria weights, a combined weighting process is suggested based on the combination of objective weighting model by distance measure-based formula and subjective weighting model by swara model under intuitionistic fuzzy environment. for this purpose, new distance measures are developed for ifss. • to exemplify the expediency of the present method, a case study of fwtts selection is discussed under if environment. the rest part of this study is prepared as: section 2 discusses the existing literatures. section 3 firstly presents the basic definitions and then proposes new intuitionistic fuzzy distance measures. section 3 introduces a hybrid copras method for solving mcdm problems within ifs context. section 5 executes the copras methodology on a case study of fwtts evaluation problem. this section further discusses the comparative study and sensitivity analysis over diverse parameter values. section 6 concludes the work and confers the further research scopes. tripathi et al./oper. res. eng. sci. theor. appl. first online 2. literature review in this part of the study, we present the comprehensive literature related to the current work. 2.1. intuitionistic fuzzy sets (ifss) due to the subjectivity of human mind and increasing complications of realistic applications, the “decision experts (des)” are unable to provide the exact numerical values for assessment information. fs theory (zadeh, 1965) has widely been used to address the vagueness in decision preferences. the notion of fss has presented its own measures of qualitative information, which finds relevance in diverse areas including pattern recognition (shahmoradi & shouraki, 2022; zhou et al., 2022), image processing (chen et al., 2022; maneckshaw & mahapatra, 2022), disease diagnosis (arzi et al., 2019; bahani et al., 2021), decision-making (cakar and çavuş, 2021; narang et al., 2022), science (szalai et al., 2022a,b) and engineering (tyagi et al., 2021; pamucar et al., 2022). to manage the uncertainty and vagueness of realistic applications, atanassov (1986) created the doctrine of ifs, which is an advance version of fs. in practical application, the use of ifs can depict the fuzziness and nonspecificity of problems by considering both the mf and nf. therefore, ifss are considered to be one of the most permissible theories than classical fs theory to handle the uncertainties and impreciseness in the data. past studies have witnessed the usefulness of ifs in pattern recognition (ashraf et al., 2019; gohain et al., 2022), image segmentation (arora and tushir, 2020; oskouei et al., 2021), clustering (feng et al., 2018; wei et al., 2021) etc. apart of these studies, zhang et al. (2020) presented an innovative infrared and visible image fusion technique through ifs. duan and li (2021) proposed some degrees of similarity for ifss by means of implication operator and the corresponding metric spaces. further, hao et al. (2021) put forward the contextfree intuitionistic fuzzy distance and similarity measures with their relevance in marine energy shipping route decision-making. du (2021) presented the division and subtraction operational laws for ifss based on the optimization method. in accordance with these operations, they studied the derivative and continuity operations of intuitionistic fuzzy functions. further, alkan and kahraman (2022) introduced a hybrid decision support system by combining if-critic and ifdevada approaches with application in waste disposal location selection. using pseudo probability transformation, xie et al. (2022) measures the information quality of intuitionistic fuzzy values, and derived its induced order for ranking the intuitionistic fuzzy alternatives. 2.2. swara method as the criteria weights are very important in making a decision, therefore, several weighting models have been developed in the literature (saaty, 1980; saaty, 2005; kersuliene et al., 2010; rezaei, 2015; haseli et al., 2020; keshavarz-ghorabaee et al., 2021; aytekin, 2022; đukić, 2022). the swara model introduced by kersuliene et al. (2010) is an expert opinion-oriented criteria weight-determining method. as the des’ preferences have a vital role in the process of mcdm, consequently, the swara tool is often preferred in applications that need subjective evaluations. its key benefit is to derive the criteria weights suitably according to the criteria that each de has a novel intuitionistic fuzzy distance measure-swara-copras method for multi-criteria food waste treatment technology selection created independently or mutually. as compared to “analytic hierarchy process (ahp)” (saaty, 1980), this method does not require a large number of pair wise comparisons, has lower computational intricacy and high reliability. the use of ahp will develop the models by means of the criteria and priorities; on the other hand, the swara acquire the models in accordance with the situation, priorities, and weights. as compared to “best worst method (bwm)” (haseli et al., 2021), the swara method does not require to compute linear objective functions, has minor computational intricacy and easy to understand (kersuliene et al., 2010). in comparison with “method based on the removal effects of criteria (merec)” method (keshavarz-ghorabaee et al., 2021; ulutaş et al., 2022), the swara model considers the subjective evaluations based on experts’ opinions. as compared to “base-criterion method (bcm)” (haseli et al., 2020; haseli & sheikh, 2022), the swara model does not require to choose a criterion as base criterion directly. in this method, the des rank the criteria in order of importance, from the most significant to the least significant, and then derive the final weights of the criteria. since its appearance, several ranking methods are combined with swara model for diverse purposes. for instance, mardani et al. (2020) investigated the digital health interventions by using a hybrid model incorporating the hesitant fuzzy swara and “weighted aggregated sum product assessment (waspas)” method. rani et al. (2020) incorporated the swara model with “vlsekriterijumska optimizacija kompromisno resenje (vikor)” technique for assessing the solar panels from pythagorean fuzzy information perspectives. he et al. (2021) incorporated the pythagorean fuzzy swara and “multi-objective optimization by ratio analysis plus the full multiplicative form (multimoora)” methods and applied to community based tourism. ayyildiz (2022) prioritized the indicators of sustainable development goal-7 by means of a collective fermatean fuzzy swarabased decision support system. in the literature, several combinations of swara method have been discussed (yücenur & şenol, 2021; alipour et al., 2021; rahmati et al., 2022; vojinović et al., 2022). 2.3. copras method mcdm process is an important part of decision science in which the de can choose an optimal candidate among a set of options by means of multiple criteria. literature consists of various mcdm methods developed to solve complex decisionmaking problems that may occur daily. in 1994, zavadskas et al. (1994) originated the notion of copras approach, which is a compensatory approach. it is used to estimate the maximizing and minimizing indexes of criteria individually (narang et al., 2021).this method describes the ratio to ideal solution and ratio to worst solution simultaneously. recently, alipour et al. (2021) ranked the fuel cell and hydrogen components suppliers based on integrated swara-copras method. rani et al. (2022b) gave a hybrid copras technique with the integration of critic and score function under interval-valued fermatean fuzzy environment. masoomi et al. (2022) evaluated a set of strategic suppliers by using an incorporated fuzzy bwmwaspas-copras method from sustainability perspective. kusakci et al. (2022) established a hybridized interval type-2 fuzzy ahp-copras methodology and tripathi et al./oper. res. eng. sci. theor. appl. first online applied for assessing the metropolitan cities from sustainable viewpoints. several extensions of copras approach have been reported in the literature (narang et al., 2021; lu et al., 2021; saraji & streimikiene, 2022). 2.4. methods for fwtts assessment because of the uncertain nature of the fwtt decision process concerning several sustainability indicators and their irregularity, the notion of fs and its extensions have widely been used in practice. for instance, büyük & temur (2022) introduced a new “spherical fuzzy analytic hierarchy process (sf-ahp)” for evaluating the fwtts candidates with multiple sustainability indicators. further, rani et al. (2021) assessed and prioritized the multiple criteria fwtts options based on single-valued neutrosophic-critic-multimoora technique. fan et al. (2022) accomplished the cost analysis and ecological impacts of fwtts by considering life cycle assessment and life cycle cost techniques. rani et al. (2022a) designed a hybrid fermatean fuzzy information-based mcdm approach based on the “method based on the removal effects of criteria (merec)” and the “additive ratio assessment (aras)” approaches, and utilized it to a fwtt selection problem. recently, few more authors have concentrated their focus on food waste treatment and management (garcia-garcia et al., 2017; omar et al., 2021; genc & ekici, 2022). nonetheless, there is no work in the existing body of the literature about the introduced mcdm approach for fwtts evaluation. so, for the first time, the current study captures the mutual benefits of the swara and the copras methods with ifss, and develops a novel intuitionistic fuzzy information-based mcdm methodology for evaluating and ranking the fwtt candidates from sustainability perspective. the reason of using of swara method is that it is easy-to-use and has not been utilized to determine the criteria weights in the process of fwtts assessment. on the other hand, the motive of using intuitionistic fuzzy copras approach is that it offers a consensual common solution to des in order to select the most suitable fwtt from various aspects of sustainability. in other words, we can say that this is first study which incorporates the swara and copras methods with ifss for assessing and prioritizing the fwtt alternatives. 3. distance measures for ifss here, a distance measure is introduced to quantify the distance between ifss. in this respect, we firstly present the fundamental ideas related to ifs. 3.1. preliminaries to conquer the drawbacks of fs theory, atanassov (1986) developed the concept of ifs for the better depiction on uncertainty. in ifs, an element is characterized by the mf and nf with their sum is less than 1. definition 3.1 (atanassov, 1986). an ifs f on a finite discourse  1 2, ,..., te e e = is mathematically presented as  , ( ), ( ) : ,i f i f i if e e e e =  (1) a novel intuitionistic fuzzy distance measure-swara-copras method for multi-criteria food waste treatment technology selection where : [0, 1]f  → and : [0, 1]f  → represent the mf and nf, respectively, of ie to f in , with the conditions ( ) ( ) ( ) ( ) 0 1, 0 1, 0 1, . f i f i f i f i i e e e e e          +    (2) the degree of hesitancy/indeterminacy of an element ie  to f is defined by ( ) ( ) ( ) ( )1 , 0 1, .f i f i f i f i ie e e e e   = − −     (3) for simplicity, xu (2007) defined the term ( )( ), ( )f i f ie e  as an “intuitionistic fuzzy number (ifn)” and indicated by ( ), ,   = where  , 0,1    and 0 1.     +  definition 3.2 (xu et al., 2015). suppose ( ),i i i  = be an ifn. then, the score and accuracy functions are defined as ( ) ( )( ) ( )  * * 1 1 ; 0,1 , 2 i i i   = +  (4) ( ) ( ) ( )   1 ; 0, 1 . 2 i i i i       = +  (5) definition 3.3 (xu, 2007). let ( ), ,i i i  = ( )1 1i t= be the ifns. the “intuitionistic fuzzy weighted averaging (ifwa)” and “intuitionistic fuzzy weighted geometric (ifwg)” operators are presented as ( ) ( )1 2 1 1 1 , ,..., 1 1 , , i i t tt w w w t i i i i i i i ifwa w      = = =   =  = − −      (6) ( ) ( )1 2 1 1 1 , ,..., , 1 1 , ii t tt ww w t i i i i i i i ifwg w      = = =   =  = − −      (7) wherein ( )1 2, ,..., t t w w w w= is a weight vector of ( ), 1 1 ,i i t = with 1 1 t j i w = = and  0, 1 .iw  definition 3.4 (xu and chen, 2008). an intuitionistic fuzzy distance measure : ( ) ( ) [0, 1]d ifss ifss   → is a real-valued function which fulfils (c1). ( )0 , 1,d f g  tripathi et al./oper. res. eng. sci. theor. appl. first online (c2). ( ), 0 ,d f g f g=  = (c3). ( ) ,, 1 cd f g f f=  = (c4). ( ) ( ),, ,d f g d g f= (c5). if ,f g h  then ( ) ( ), ,d df h f g and ( ) ( ), , ,d df h g h for all , , ( ).f g h ifss  3.2. new intuitionistic fuzzy distance measures the main goal of this section is to propose new distance measures for ifss and then, employ to derive the criteria weights in next section. for ( ) ( ) ( ), , , ,f f g gf g ifss   = =   we develop a new distance measure for computing the difference between two ifss, given as ( ) ( ) ( )( ) 1 1 1 1 1 1 exp ( ) ( ) ( ) ( ) ( ) ( ) 2 1 exp , t f i g i f i g i f i g i i e e e e e e t d f g            =     − − − + − + −      − − =  (8) where 0, 1.   lemma 3.1. if ( ) ( ) ( )( )1 1 exp 1 , 1 exp t h    − − − = − − then ( ) ( )min 0 0 [0, ] h h t   = =  and ( ) ( )max 1. [0, ] th h t   = =  proof. since exp( )'( ) 0, [0, ], 1 exp( 1) h t    − =    − − therefore, ( )h  is increasing in  0, .t theorem 3.1. the function ( )1 , ,d f g defined by eq. (8), is a suitable distance measure for ifss. proof. in this regard, ( )1 ,d f g must satisfy the requirements (c1)-(c5) of definition 3.4. (c1). let , ( )f g ifss  and ( ) 1 1 1 ( ) ( ) ( ) ( ) ( ) ( ) . 2 t f i g i f i g i f i g i i e e e e e e            =   = − + − + −       a novel intuitionistic fuzzy distance measure-swara-copras method for multi-criteria food waste treatment technology selection since  0, ,t therefore, ( ) ( )1 , .d f g h = hence, using lemma 3.1, we have ( )10 , 1.d f g  (c2). suppose ,f g= then ( ) ( ),f i g ie e = ( ) ( ), .f i f i ie e e =   then, it is evident from eq. (8) that ( )1 , 0.d f g = let ( )1 , 0.d f g = from eq. (8), we obtain ( ) ( )( ) 1 1 1 1 1 exp ( ) ( ) ( ) ( ) ( ) ( ) 2 0, 1 exp t f i g i f i g i f i g i i e e e e e e t            =     − − − + − + −      = − −  it implies that ( ) 1 ( ) ( ) ( ) ( ) ( ) ( ) 0, . t f i g i f i g i f i g i i i e e e e e e e          = − + − + − =   hence .f g= (c3). it is clear from the definition that ( )1 , .1 c d f g f f=  = (c4). clearly, ( ) ( )1 1, , .d f g d g f= (c5). given that ,f g h  then ( ) ( ) ( )f i g i h ie e e    and ( ) ( ) ( ), .f i g i h i ie e e e      now, ( ) 1 1 1 1 ( ) ( ) ( ) ( ) ( ) ( ) 2 t f i g i f i g i f i g i i e e e e e e           =   − + − + −    =  ( ) 1 2 1 1 ( ) ( ) ( ) ( ) ( ) ( ) . 2 t f i h i f i h i f i h i i e e e e e e           =   − + − + −     =  according to lemma 3.1, we obtain ( ) ( ) ( ) ( )1 1 2 1, , .d f g h h d f h =  = in the same way, we can show that ( ) ( )1 1, , .d g h d f h hence, measure ( )1 ,d f g is a suitable if-distance measure. next, a new distance measure between two matrices is introduced within ifs context. tripathi et al./oper. res. eng. sci. theor. appl. first online let ( )ijf f= and ( ), 1(1) , 1(1)ijg g i s j t= = = be two matrices, where , f f ij ij ij f  = and ,g g ij ij ij g  = are ifns. thus, the distance measure between f and g is proposed as ( ) ( ) ( ) 2 1 1 1 1 exp ( ) ( ) ( ) ( ) ( ) ( ) 2 , 1 exp 1 , s f g f g f g ij i ij i ij i ij i ij i ij i i e e e e e e s t d f g           =     − − − + − + −      − − =  (9) where 0, 1.   theorem 3.2. the measure ( )2 , ,d f g given in eq. (9), is a suitable distance measure for ifss. proof: proof is same as theorem 3.1. therefore, we have omitted the proof. 4. proposed if-distance measure-swara-copras method in this portion, we propose a hybrid decision support system, named as ifdistance measure-swara-copras. in this system, the distance measure-based formula is employed to obtain the objective weight of criteria and the swara tool is utilized to estimate the subjective weight of criteria. thus, an integrated weighting process is presented by combining objective and subjective weights of the criteria with ifns. in addition, the copras model is extended with ifns to rank the alternatives over considered criteria, and thus, the final ranking result has high reliability. the procedure of if-distance measure-swara-copras methodology is presented as follows (figure 1): a novel intuitionistic fuzzy distance measure-swara-copras method for multi-criteria food waste treatment technology selection figure 1. graphical representation of proposed method step 1: build an “intuitionistic fuzzy-decision matrix (if-dm)”. in mcdm process, we have to select an optimal candidate among a set of options  1 2, ,..., mv v v v= over a criterion set  1 2, ,..., .nq q q q= for this purpose, a team of des  1 2, ,..., lc c c c= is formed to make a suitable decision. based on des’ opinions for each alternative concerning a set of criteria, we create a “linguistic decisionmatrix (ldm)” ( )( ) ,kij m n t   = wherein ( )k ij  indicates the linguistic performance rating of an option vi over a criterion qj provided by kth de and further, transformed into if-dm by using linguistic rating table. step 2: acquire the weights of des. to compute the des’ weights, the formula is as follows: tripathi et al./oper. res. eng. sci. theor. appl. first online ( ) ( ) ( ) 1 1 2 11 , 2 2 1 k k k k k l l k k k kk k l r l r        = =  − − − +  = +   − − − +    (10) where 0k  and 1 1. l k k  = = step 3: construct the “aggregated intuitionistic fuzzy decision matrix (aif-dm)”. to combine the individual decision opinion of each de, we use ifwa (or ifwg) operator and then the “aggregated intuitionistic fuzzy decision matrix (aif-dm)” is ( ) ( ), ,ij ij ij m n z z    = = where ( ) ( ) ( ) ( )( )1 2, , ,..., k l ij ij ij ij ij ij z ifwa      = = (11a) ( ) ( ) ( ) ( )( )1 2or , , ,..., . k l ij ij ij ij ij ij ifwgz      = = (11b) step 4: determine the criteria weights by an incorporated weighting model. in the following, we compute the criteria weights by combining two weighting procedures: case i: intuitionistic fuzzy distance measure-based objective weighting formula. this method unites the degree of discrimination among the different criteria. the expression of distance measure-based criteria weight-determining procedure is given as ( ) ( ) ( ) 1 1 1 1 1 1 1 1 , 1 , 1 1 . 1 , 1 m m ij kj o i k j n m m ij kj j i k d z z m w j n d z z m = = = = = − = =     −     (12) case ii: subjective weights by “intuitionistic fuzzy swara (if-swara)”model. to find the subjective weights, we utilize the if-swara model based on intuitionistic fuzzy information. the procedural steps are given as step 4a: estimate the score degrees ( )* kjz by eq. (4). step 4b: prioritize the criteria as per the des’ preferences from the most to the least important criteria. step 4c: establish the relative importance levels. from the second criterion, the relative importance levels are assessed as: the relative importance of criterion (j) in relation to the preceding criterion (j − 1). this ratio is called as “comparative significance of the mean value” and denoted by j . step 4d: evaluate the “comparative coefficient (cc)” with the use of eq. (13). a novel intuitionistic fuzzy distance measure-swara-copras method for multi-criteria food waste treatment technology selection 1, 1, 1, 1. j j j j   = =  +  (13) step 4e: estimate the initial weight of each criterion. 1 1, 1 , 1. jj j j j   − =  =     (14) step 4f: determine the final weight of each criterion. 1 . js j n j j w   = =  (15) case iii: integrated weights using if-distance measure and if-swara method here, the des want to utilize the advantages of both the subjective and objective weights of criteria. thus, the combined weight of the jth criterion is given as ( )1 ,o sj j jw w w = + − (16) wherein  0,1 is the precision objective factor of decision strategy. step 5: add the criteria values with benefit and cost types of criteria. here, each option is expressed with its sum of maximizing criterion i  and minimizing criterion . i  to get the numerical values of i  and , i  eq. (17) and eq. (18) are presented. 1 , . l i j ij j w z i = =   (17) 1 , . n i j ij j l w z i = + =   (18) here, l and n refer to the beneficial and total number of criteria, respectively. step 6: determine the “relative degree (rd)”. based on eq. (17), the rd of each alternative is assessed. tripathi et al./oper. res. eng. sci. theor. appl. first online ( ) ( ) ( ) ( ) ( ) ( ) ( ) * * * 1 * * * 1 min 1 , . min m i i i i i i m i i i i i i          = = = + −    (19) here, ( )* i and ( )* i are the score values of i and ,i respectively, and  0,1 denotes the strategy value of de. step 7: derive the “utility degree (ud)”. to evaluate the ud of each option, eq. (20) is applied. 100 %, . i i i e    =   (20) here, max , 1, 2,..., i i e i m  = = . 5. case study: fwtts assessment fw needs different treatment methods from common “municipal solid waste (msw)” because it has the feature of high moisture, salinity, organic and oil substance. copious researchers (giwa et al., 2019; ren and toniolo, 2020; shewa et al., 2020; rani et al., 2021, 2022a) have focused their attention on fw management and treatment from ecological perspective. in general, the selection of appropriate fwtt option is a complicated mcdm process due to existence of diverse quantitative and qualitative criteria, and uncertainty (rani et al., 2021, 2022a). thus, there is a need to develop a suitable model to treat the fwtts assessment under uncertain environment. in order to assess the fwtt candidates according to several criteria, a team of four des is formed who have 15+ years of experience in the area of sustainable development. out of 04 des, 01 is from municipality, who is master’s degree holder, 02 are environmentalists, who are doctorate degree holder and 01 is from engineering department, who is master’s degree holder. after establishing the decision-making team, we have prepared an online survey with the purpose of determining the sustainability indicators’ importance in the process of fwtts evaluation. the indicators that have an effect on the fwtts assessment were assembled and then discussed with the panel of four des. based on the literatures and conversations with specialists, 13 sustainability indicators/factors/criteria are preferred for the given case study of fwtts selection, which aims to promise the sustainability perspective (see table 1). in the meantime, open interviews assisted to decide four fwtts as the most appropriate where the study was conducted. in this study, considered alternatives are as follows: anaerobic digestion (v1), composting (v2), landfill (v3) and incineration (v4). a novel intuitionistic fuzzy distance measure-swara-copras method for multi-criteria food waste treatment technology selection table 1. details of chosen indicators for fwtts evaluation dimension criteria description type economic (l1) investment cost (q1) considers the set up cost of treatment technologies & their rescue assessment cost operation cost (q2) considers the operation costs of assessed treatment technologies cost collection and transportation cost (q3) considers each cost made for fw collection and their transportation cost energy production yield (q4) considers the energy production from methane and co2 rich biogas benefit social (l2) social acceptability (q5) the quality of fwtt should be accepted socially benefit benefit to society (q6) provides benefits to the local residents benefit compatibility (q7) capability of fwtt to use in small scale benefit health and safety (q8) determines the health and safety of employees and local residents benefit environmental (l3) energy consumption(q9) shows the amount of energy consumed by each fwtt option cost environmental risks(q10) considers the pollution, spread of diseases through the execution of fwtt option cost soil and water pollution (q11) pollution and contamination of groundwater resources produced by landfilling cost technological (l4) technology maturity (q12) tends to how suitable the current technology is chosen treatment alternative benefit capacity (q13) considers the capability and infrastructural capacity of fwtt option benefit in the present part of the study, we implement the hybrid copras methodology on the selection of suitable fwtt candidate from a set of options, which establishes the applicability and usefulness of the proposed methodology. now, the procedural steps of introduced copras method on the present case study are discussed as follows: tripathi et al./oper. res. eng. sci. theor. appl. first online steps 1-3: tables 2-3 (mishra et al.2019) present the linguistic ratings and their corresponding ifns to express the significance values of des and the considered criteria for fwtts assessment. by utilizing table 2 and eq. (10), the significance values of des are derived and shown in table 4. table 5 shows the “linguistic decision matrix (ldm)” provided by four des for each alternative vi concerning the considered sustainability indicators. according to eq. (11) and table 5, the aif-dm is constructed in table 6. table 2. des’ ratings for fwtts assessment lvs ifns absolutely important (ai) (0.90, 0.10) very important (vi) (0.80, 0.15) important (f) (0.70, 0.25) fair (f) (0.60, 0.35) unimportant (u) (0.50, 0.45) very unimportant (vu) (0.40, 0.55) absolutely unimportant (au) (0.20, 0.70) table 3. linguistic performances of given fwtts and criteria lvs ifns absolutely significant (as) (0.95, 0.05) very very significant (vvs) (0.85, 0.10) very significant (vs) (0.80, 0.15) significant (s) (0.70, 0.20) moderately significant (ms) (0.60, 0.30) moderate (a) (0.50, 0.40) moderately insignificant (mi) (0.40, 0.50) insignificant (i) (0.30,0.60) very insignificant (vi) (0.20, 0.70) very very insignificant (vvi) (0.10, 0.80) extremely insignificant (ei) (0.05, 0.95) table 4. des’ weights des c1 c2 c3 c4 ratings vi i i ai rk 2 3.5 3.5 1 weight 0.2808 0.1895 0.1895 0.3402 a novel intuitionistic fuzzy distance measure-swara-copras method for multi-criteria food waste treatment technology selection table 5. linguistic decision matrix for fwtts assessment criteria v1 v2 v3 v4 q1 (mi,i,vi,mi) (i,mi,vi,i) (m,mi,m,i) (mi,mi,m,i) q2 (i,i,m,i) (i,mi,vi,mi) (mi,m,mi,m) (i,mi,mi,i) q3 (mi,i,i,vi) (i,m,vi,i) (m,mi,m,mi) (mi,vi,m,m) q4 (m,s,ms,as) (s,ms,s,ms) (s,ms,m,s) (s,mi,vs,vs) q5 (ms,s,m,ms) (vvs,s,vs,m) (mi,ms,m,ms) (vs,mi,m,ms) q6 (m,mi,vs,m) (mi,mi,m,s) (as,vs,m,ms) (m,ms,m,s) q7 (ms,i,m,vvs) (m,i,mi,ms) (ms,m,vs,s) (vs,s,m,ms) q8 (vvs,s,m,ms) (ms,s,vs,s) (mi,ms,m,vs) (s,ms,m,s) q9 (m,i,mi,ms) (s,i,mi,m) (mi,i,m,ms) (mi,l,m,mi) q10 (vi,i,m,mi) (m,vi,i,mi) (m,ms,vi,i) (vi,mi,vi,mi) q11 (mi, m,vi,mi) (m,mi,ms,s) (s,m,s,vvs) (ms,mi,m,vs) q12 (s,mi,m,ms) (v,as,m,ms) (vvs,m,ms,mi) (mi,ms,vs,s) q13 (vs,s,vs,m) (s,as,vs,ms) (ms,mi,m,ms) (ms,vs,ms,s) table 6. aggregated decision matrix for fwtts assessment criteria v1 v2 v3 v4 q1 (0.348, 0.552, 0.101) (0.303, 0.597, 0.100) (0.420, 0.479, 0.101) (0.389, 0.510, 0.101) q2 (0.343, 0.556, 0.101) (0.338, 0.561, 0.101) (0.455, 0.444, 0.101) (0.340, 0.560, 0.100) q3 (0.298, 0.601, 0.101) (0.326, 0.572, 0.101) (0.449, 0.450, 0.101) (0.425, 0.474, 0.102) q4 (0.801, 0.164, 0.035) (0.651, 0.248, 0.101) (0.651, 0.246, 0.103) (0.724, 0.204, 0.072) q5 (0.605, 0.293, 0.102) (0.728, 0.197, 0.075) (0.532, 0.366, 0.102) (0.629, 0.287, 0.084) q6 (0.565, 0.347, 0.089) (0.542, 0.351, 0.107) (0.796, 0.168, 0.036) (0.597, 0.299, 0.104) q7 (0.668, 0.249, 0.084) (0.489, 0.409, 0.103) (0.668, 0.242, 0.090) (0.675, 0.241, 0.084) q8 (0.700, 0.216, 0.085) (0.699, 0.212, 0.089) (0.618, 0.301, 0.081) (0.651, 0.246, 0.103) q9 (0.489, 0.409, 0.103) (0.522, 0.371, 0.107) (0.480, 0.417, 0.103) (0.403, 0.496, 0.101) q10 (0.353, 0.545, 0.102) (0.380, 0.518, 0.102) (0.413, 0.483, 0.104) (0.313, 0.586, 0.101) q11 (0.388, 0.511, 0.101) (0.583, 0.312, 0.105) (0.739, 0.180, 0.081) (0.644, 0.276, 0.080) q12 (0.584, 0.311, 0.104) (0.768, 0.186, 0.046) (0.636, 0.277, 0.087) (0.644, 0.265, 0.092) q13 (0.705, 0.221, 0.074) (0.782, 0.167, 0.051) (0.549, 0.349, 0.102) (0.682, 0.229, 0.089) tripathi et al./oper. res. eng. sci. theor. appl. first online step 4: with the use of eq. (12), we have calculated the objective weight of each criteria by utilizing the proposed distance measure (8) (or (9)). the resultant values are given as follows (see figure 2): o jw = (0.0024, 0.0023, 0.0039, 0.1980, 0.0855, 0.1934, 0.0542, 0.0597, 0.0166, 0.0074, 0.0807, 0.1534, 0.1426). based on the if-swara model given by steps 4a-4f, we have derived the subjective weights of criteria in table 8. the resultant values are presented as follows (see figure 2): s jw = (0.0857, 0.0746, 0.0775, 0.0784, 0.0681, 0.0856, 0.0741, 0.0793, 0.0738, 0.0806, 0.0695, 0.0717, 0.0811). table 7. score values of criteria for fwtts given by des criteria c1 c2 c3 c4 aggregated ifns score values q1 s ms m ms (0.615, 0.283, 0.102) 0.6662 q2 ms m m i (0.473, 0.424, 0.103) 0.5249 q3 ms m mi m (0.514, 0.385, 0.101) 0.5645 q4 s i mi m (0.522, 0.371, 0.107) 0.5756 q5 mi mi i mi (0.382, 0.518, 0.100) 0.4323 q6 ms s s m (0.613, 0.284, 0.103) 0.6647 q7 mi m s i (0.464, 0.429, 0.107) 0.5178 q8 ms m i ms (0.536, 0.361, 0.103) 0.5874 q9 mi m ms mi (0.463, 0.435, 0.102) 0.5141 q10 s m mi ms (0.552, 0.343, 0.105) 0.6041 q11 i i ms mi (0.403, 0.495, 0.103) 0.4540 q12 mi m ms i (0.434, 0.463, 0.103) 0.4857 q13 s mi i ms (0.557, 0.336, 0.107) 0.6103 table 8. criteria weights using swara model indicators score values comparative significance of criteria cc initial weight final weight q1 0.6662 1.000 1.0000 0.0857 q6 0.6647 0.0015 1.0015 0.9985 0.0856 q13 0.6103 0.0544 1.0544 0.9470 0.0811 q10 0.6041 0.0062 1.0062 0.9412 0.0806 q8 0.5874 0.0167 1.0167 0.9257 0.0793 q4 0.5756 0.0118 1.0118 0.9149 0.0784 q3 0.5645 0.0111 1.0111 0.9049 0.0775 q2 0.5249 0.0396 1.0396 0.8704 0.0746 q7 0.5178 0.0071 1.0071 0.8643 0.0741 q9 0.5141 0.0037 1.0037 0.8611 0.0738 q12 0.4857 0.0284 1.0284 0.8373 0.0717 q11 0.4540 0.0317 1.0317 0.8116 0.0695 q5 0.4323 0.0217 1.0217 0.7944 0.0681 a novel intuitionistic fuzzy distance measure-swara-copras method for multi-criteria food waste treatment technology selection next, we have combined the if-distance measure-based weighting procedure for objective weights and if-swara for subjective weights by using eq. (16). thus, the integrated weight is depicted in figure 2 and presented as wj= (0.0440, 0.0439, 0.0425, 0.1393, 0.0824, 0.1359, 0.0658, 0.0672, 0.0454, 0.0406, 0.0762, 0.1115, 0.1053). figure 2. criteria weights for fwtts assessment using proposed weight-determining model steps 5-7: through eqs (17)-(20), the values of ( ) ( )* *, , , ,i i i i i     and i are derived and shown in table 9. on the basis of obtained results, the ranking of the fwtts is 1 4 2 3 v v v v and thus, fwtts (v1) is the most desirable alternative. table 9. outcomes of if-distance measure-swara-copras method fwtts i ( ) * i  i  ( )* i i i v1 (0.548, 0.375, 0.077) 0.587 (0.129, 0.827, 0.044) 0.151 0.4084 100.00 v2 (0.554, 0.364, 0.081) 0.595 (0.157, 0.793, 0.051) 0.182 0.3930 96.21 v3 (0.532, 0.387, 0.081) 0.572 (0.205, 0.739, 0.055) 0.233 0.3608 88.33 v4 (0.585, 0.376, 0.039) 0.605 (0.165, 0.788, 0.047) 0.189 0.3944 96.56 tripathi et al./oper. res. eng. sci. theor. appl. first online 5.1. sensitivity analysis in this part, we have analyzed the significance of subjective and objective weights for considered criteria in the proposed weight finding technique. in addition, we have changed the values of parameter to show the performance of uds. for this purpose, we have following cases: case i: different values of [0,1] are taken for analysis. this investigation is presented to examine the variation of if-distance measure-swara-copras method. based on the table 10 and figure 3, the preference ranking is 1 2 4 3 v v v v when  = 0.0 to 0.4, while ranking order is 1 4 2 3 v v v v when  = 0.5 to 0.7, ranking order is 4 1 2 3 v v v v when  = 0.8 to 0.9 and ranking order is 4 2 1 3 v v v v when  = 1.0. as a consequence, the evaluation of fwtts is depend on and sensitive to the parameter  . table 10. the ud of option with diverse parameter values  v1 v2 v3 v4 ranking order  = 0.0 0.2303 0.1910 0.1493 0.1840 1 2 4 3v v v v  = 0.1 0.2659 0.2314 0.1916 0.2261 1 2 4 3v v v v  = 0.2 0.3015 0.2718 0.2339 0.2682 1 2 4 3v v v v  = 0.3 0.3372 0.3122 0.2762 0.3103 1 2 4 3v v v v  = 0.4 0.3728 0.3526 0.3185 0.3523 1 2 4 3v v v v  = 0.5 0.4084 0.3930 0.3608 0.3944 1 2 4 3v v v v  = 0.6 0.4441 0.4333 0.4031 0.4365 1 4 2 3v v v v  = 0.7 0.4797 0.4737 0.4454 0.4785 1 4 2 3v v v v  = 0.8 0.5153 0.5141 0.4877 0.5206 4 1 2 3v v v v  = 0.9 0.5510 0.5545 0.5300 0.5627 4 1 2 3v v v v  = 1.0 0.5866 0.5949 0.5723 0.6047 4 2 1 3v v v v figure 3.the uds over diverse values of ( ) a novel intuitionistic fuzzy distance measure-swara-copras method for multi-criteria food waste treatment technology selection case ii: in this case, the ranking results have been made by changing the objective weights instead of if-distance measure-based weighting procedureswara and given in table 11 and figure 4. using if-distance measure-based weighting procedure, the performance values of fwtts are given as follows: v1 = 0.4088, v2 = 0.3884, v3 = 0.3654 and v4 = 0.3908 and the ranking order of fwtts is 1 4 2 3 .v v v v applying the if-swara method, the performance values of fwtts are given as follows: v1 = 0.3947, v2 = 0.3805, v3 =0.3412 and v4 = 0.3807 and the ranking order of fwtts is given as 1 4 2 3 .v v v v thus, it is found that by using the several parameter values has improved the stability of the if-distance measureswara-copras method. table 11. subordinate ud of fwtts over diverse weighting models weightdetermining procedure subordinate uds of fwtt candidates ordering v1 v2 v3 v4 if-distance measure-based weighting procedure 0.4088 0.3884 0.3654 0.3908 1 4 2 3v v v v if-swara method 0.3947 0.3805 0.3412 0.3807 1 4 2 3v v v v integrated method 0.4084 0.3930 0.3608 0.3944 1 4 2 3v v v v figure 4. results of sensitivity analysis by different weighting models for fwtts assessment tripathi et al./oper. res. eng. sci. theor. appl. first online 5.2. comparative study this section presents the comparison between the if-distance measure-swaracopras method and some other previous methods. for this purpose, we have taken the if-waspas (mishra et al., 2019) and if-topsis method (mishra, 2016), and executed to handle the given case study. 5.2.1. if-topsis (mishra, 2016) from table 6, “intuitionistic fuzzy ideal solution (if-is)” and “intuitionistic fuzzy anti-ideal solution (if-ais)” are computed, where 1, 2,...,13j = . now, the whole computational results of if-topsis (mishra, 2016) are presented in table 12. j  + = {(0.303, 0.597, 0.100), (0.338, 0.561, 0.101), (0.298, 0.601, 0.101), (0.801, 0.164, 0.035), (0.728, 0.197, 0.075), (0.796, 0.168, 0.036), (0.675, 0.241, 0.084), (0.699, 0.212, 0.089), (0.403, 0.496, 0.101), (0.313, 0.586, 0.101), (0.388, 0.511, 0.101), (0.768, 0.186, 0.046), (0.782, 0.167, 0.051)} j  − = {(0.420, 0.479, 0.101), (0.455, 0.444, 0.101), (0.449, 0.450, 0.101), (0.651, 0.248, 0.101), (0.532, 0.366, 0.102), (0.542, 0.351, 0.107), (0.489, 0.409, 0.103), (0.618, 0.301, 0.081), (0.522, 0.371, 0.107), (0.413, 0.483, 0.104), (0.739, 0.180, 0.081), (0.584, 0.311, 0.104), (0.549, 0.349, 0.102)}. thus, from table 12, v1 is the best fwtt alternative and ranking order of fwtt options is 1 2 4 3 .v v v v table 12. ranking orders of iftopsis method for fwtts fwtts degree of similarity between fwtt options and if-is degree of similarity between fwtt options and if-ais relative closeness coefficient ranking v1 0.132 0.182 0.5799 1 v2 0.146 0.162 0.5249 2 v3 0.221 0.090 0.2883 4 v4 0.171 0.151 0.4680 3 5.2.2. if-waspas (mishra et al., 2019) using if-waspas, we determine the measures of “weighted sum model (wsm)”, “weighted product model (wpm)” and “weighted aggregated sum product assessment (waspas)” in the context of ifns. table 13 presents the whole computational outcomes of the if-waspas model. therefore, the ranking of fwtt choice is 1 4 2 3v v v v and the alternative v1 is best fwtt alternative for given case study. a novel intuitionistic fuzzy distance measure-swara-copras method for multi-criteria food waste treatment technology selection table 13. computational outcomes of the if-waspas method options measure of “weighted sum model (wsm)” measure of “weighted product model (wpm)” score function of wsm score function of wpm measure of waspas ranking order v1 (0.638, 0.280, 0.082) (0.614, 0.297, 0.089) 0.679 0.659 0.6687 1 v2 (0.632, 0.282, 0.086) (0.590, 0.316, 0.094) 0.675 0.637 0.6560 3 v3 (0.596, 0.285, 0.119) (0.601, 0.366, 0.033) 0.655 0.618 0.6365 4 v4 (0.614, 0.275, 0.111) (0.624, 0.321, 0.054) 0.669 0.651 0.6604 2 figure 5. ranking order of fwtts option with different methods based on the comparisons between the present and existing methodologies, the advantages of the present copras model are listed in the following points: ▪ this study computes the des’ weights under if environment, while the previous methods consider the assumed des’ weights. this means that the proposed methodology can offer more exact results for mcdm problems from uncertainty perspective. ▪ the present copras method derives the objective and subjective weights of criteria using if-distance measure and if-swara model, respectively. therefore, it provides the more accurate outcomes under intuitionistic fuzzy environment. while the if-waspas uses only objective weights of criteria by utilizing degree of similarity and ifcopras considers the direct weight of each criterion. tripathi et al./oper. res. eng. sci. theor. appl. first online ▪ in the developed method, benefit and cost types of criteria are utilized. in copras, both types of criteria with complex proportion contains more precise information as compared to only dealing with the cost or benefit criteria. thus, the present approach increases the readability of initial data and the accurateness of obtained outcomes. ▪ the developed framework has higher operability than the if-topsis method in case of large numbers of criteria or alternatives. for the proposed framework, the if-is and if-ais are not required as if-topsis. in copras, the results are computed with managing the real data, which reveals that the proposed copras model can tackle more complicated and practical decision-making applications. 6. conclusions in this part of the study, we present the comprehensive literature related to the current work. fwtt offers a promising solution for handling the speedily generated food waste. to meet the sustainable food waste management goals, it is required to select the suitable fwtt alternative. here, we presented a hybrid decision support system for evaluating and prioritizing the fwtts from uncertainty perspective. in this regard, we have incorporated the copras approach with distance measure and the swara model within the environment of ifss. to calculate the criteria’s weights, we have integrated the objective weights of criteria by intuitionistic fuzzy distance measurebased procedure and the subjective weights of criteria by if-swara model. for objective weights, new distance measures have been proposed for ifss. next, a case study for fwtts assessment has been presented to show the practicability of the hybrid copras methodology. the evaluation index framework for fwtt selection is developed, which contains four aspects of sustainability, namely economic, social, environmental and technological. these four dimensions respectively consist of four, four, three and two sub-criteria and the weights of all sub-criteria are computed by an integrated weighting model. the calculation result shows that the alternative ‘anaerobic digestion (v1)’ should be chosen as the most suitable alternative for given case study. further, sensitivity and comparative analyses have been discussed to confirm the results acquired by proposed hybrid model. the key benefits of the presented framework are the ease of calculation in intuitionistic fuzzy background and utilizing a model for deriving more reasonable weights of indicators. the method proposed in this paper has some limitations, which are ▪ this method ignores the objective weights of criteria. ▪ the present mcdm approach does not consider the interrelationships among the criteria. ▪ this study has given equal importance to each of the dimension but in fact, this is not true for a real case study. ▪ in this method, we consider only benefit and cost type s of criteria and a novel intuitionistic fuzzy distance measure-swara-copras method for multi-criteria food waste treatment technology selection ignore the target-based criteria. in future, it would be exciting to improve the limitations of the present study by proposing some new methods such as “weighted sum-product (wisp)”, “double normalization-based multiple aggregation (dnma)”, “gained lost dominance score (glds)” etc. in addition, this study can be extended to “q-rung orthopair fuzzy rough sets (q-rofrss)”, “pythagorean fuzzy soft sets (pfsss)”, “interval-valued q-rung orthopair fuzzy rough sets (ivq-rofrss)”, and can be executed for kitchen waste treatment technologies assessment, 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(2022). agricultural drought vulnerability assessment and diagnosis based on entropy fuzzy pattern recognition and subtraction set pair potential. alexandria engineering journal, 61(1), 51-63. © 2022 by the authors. submitted for possible open access publication under the terms and conditions of the creative commons attribution (cc by) license (http://creativecommons.org/licenses/by/4.0/). https://doi.org/10.31181/oresta2040123t https://doi.org/10.1016/j.engappai.2021.104209 https://doi.org/10.1016/j.engappai.2021.104568 https://doi.org/10.1016/j.jobe.2021.103196 a novel intuitionistic fuzzy distance measure-swara-copras method for multi-criteria food waste treatment technology selection dinesh kumar tripathi1, santosh k. nigam1, arunodaya raj mishra2*, abdul raoof shah3 1. introduction 2. literature review 2.1. intuitionistic fuzzy sets (ifss) 2.2. swara method 2.3. copras method 2.4. methods for fwtts assessment 3. distance measures for ifss 3.1. preliminaries 3.2. new intuitionistic fuzzy distance measures 4. proposed if-distance measure-swara-copras method 5. case study: fwtts assessment 5.1. sensitivity analysis 5.2. comparative study 5.2.1. if-topsis (mishra, 2016) 5.2.2. if-waspas (mishra et al., 2019) 6. conclusions references operational research in engineering sciences: theory and applications vol. 5, issue 3, 2022, pp. 68-91 issn: 2620-1607 eissn: 2620-1747 doi: https://doi.org/10.31181/oresta031022031b * corresponding author broumisaid78@gmail.com, s.broumi@flbenmsik.ma (s.b) dajaypravin@gmail.com (a. pravin), joshmani238@gmail.com (p. chellamani), lathamax@gmail.com (l. karthik), taleamohamed@yahoo.fr (m. talea), assiabakali@yahoo.fr (a. bakali), flippe2@gmail.com (p. schweizer), jafaripersia@gmail.com (s. jafari) interval valued pentapartitioned neutrosophic graphs with an application to mcdm said broumi 1,2*, d. ajay 3, p. chellamani 3, lathamaheswari malayalan 4, mohamed talea 1, assia bakali 5, philippe schweizer 6, saeid jafari 7 1 laboratory of information processing, faculty of science ben m’sik, university of hassan ii, casablanca, morocco 2 regional center for the professions of education and training (c.r.m.e.f), casablanca-settat, morocco. 3 department of mathematics, sacred heart college (autonomous), tamilnadu, india 4 department of mathematics, hindustan institute of technology & science, chennai, india 5 ecole royale navale-boulevard sour jdid, morocco 6 independent researcher, switzerland 7 college of vestsjaelland south herrestarede 11, denmark received: 20 june 2022 accepted: 27 august 2022 first online: 03 october 2022 original scientific paper abstract: the concept of interval valued pentapartitioned neutrosophic set is the extension of interval-valued neutrosophic set, quadripartitioned neutrosophic set, interval valued quadripartitioned neutrosophic set and pentapartitioned neutrosophic set. the powerful mathematical tool known as the interval valued pentapartitioned neutrosophic set divides indeterminacy into three separate components: unknown, contradiction, and ignorance. there are several applications for graph theory in everyday life, and it is a rapidly growing topic. the concept of an interval valued pentapartitioned neutrosophic set is used in graph theory. a decision-making method multicriteria (mcdm) is proposed by using the developed interval valued pentapartitioned neutrosophic set with a numerical illustration. in this paper, as an extension of interval valued neutrosophic graph theory, we introduce the notions of interval-valued pentapartitioned neutrosophic graph (ivppn-graph) with degree, size, and order of an ivppn-graph. key words: neutrosophic set, interval valued pentapartitioned neutrosophic sets, neutrosophic graph, ivppn-graph. mailto:author.%20broumisaid78@gmail.com mailto:author.%20broumisaid78@gmail.com interval valued pentapartitioned neutrosophic graphs with an application to mcdm 69 1. introduction linguistic variables with uncertainties such as vagueness, imprecision and ambiguity are handled with a special type of mathematical tool known as fuzzy set theory (zadeh, 1965). the contribution of research articles in the field of fuzzy sets in mathematics and wide range of applications are growing exponentially. the advantage of introducing zadeh’s fuzzy sets in the place of classical sets has been its accuracy and precision in theory and compatibility and efficiency in case of applications. fuzzy set has been extended to intuitionistic fuzzy set (atanasov, 1986). in which the membership and non-membership degree of the element of that set ranges between 0 and 1. intuitionistic set was further extended to interval valued fuzzy sets, neutrosophic sets, pythagorean sets and so on. (smarandache,1999 &2020) presented a new type of set as an extension of intuitionistic fuzzy set which is called neutrosophic set. a neutrosophic set is characterized by a truth membership degree (t), an indeterminacy membership degree (i) and a falsity membership degree (f) independently, which are within the real unit interval ]0-,1+[ satisfying the condition that the total of the membership grades is within the range of 0 to 3. in (wang, 2010) single valued neutrosophic set (svns) with set-theoretic operators was investigated by wang et al. svnss have been developed into many new concepts and are applied in different disciplines (broumi et al., 2016 & 2016a & 2016b &2016c; chatterjee et al., 2016&2016b). pythagorean set (yager, 2013). is an extension of the intutionistic set in which the condition differs from the intutionistic set that the sum of the squares the membership is less than 1. by combining the idea of fuzzy graphs and pythagorean neutrosophic set ajay and chellamani et al. presented pythagorean neutrosophic graphs (ajay & chellamani, 2020) is a combination of the pythagorean and neutrosophic set in which the the sum of the squares of the membership, non-membership and indeterminacy membership lies in [0,2] and further theoretical concepts were developed in (ajay & chellamani, , 2021 ; chellamani & ajay, 2021; ajay et al., 2021 , 2022 ,2020a) ; chellamani et al.,2021). the partition of indeterminacy function of the neutrosophic set into contradiction part and ignorance part is defined as the quadripartitioned singlevalued neutrosophic set (chatterjee et al., 2016, 2020) (quek et al, 2022) introduced the notion of pentapartitionned neutrosophic graphs (ppngs), as an extended version of single valued neutrosophic graphs. (mallick & pramanik, 2020) proposed the concept of interval-valued pentapartitionned neutrosophic sets (ivppnss) as a generalization of pentapartitionned neutrosophic sets in the spirit of interval-valued neutrosophic sets (broumi, 2016) the concept of interval valued pentapartitioned neutrosophic sets (ivppnss) allows a decisionmaking expert to represented the membership degree contradiction membership function 𝐶𝐴(𝑥), an unknown membership function 𝑈𝐴(𝑥) and a falsity membership degree of a set of options in terms of the interval; hence, the range of uncertain information they can describe is widened. interval-valued pentapartitioned neutrosophic numbers (ivppnns) are the generalized version of pentapartitioned neutrosophic numbers, quadripartitioned neutrosophic numbers, interval-valued quadripartitioned neutrosophic numbers. ivppnns will help model problems with incomplete, uncertain and indeterminate information. and further theoretical concepts were developed in (das et al, 2022& 2022a; pramanik, 2022). (hussain et al, 2022) introduced the notion of quadripartitioned single-valued neutrosophic graphs s. broumi et al./oper. res. eng. sci. theor. appl. 5(3)2022 68-91 70 and developed some operations on it. the cartesian product, cross product, lexicographic product, strong product and composition of quadripartitioned singlevalued neutrosophic graph have been investigated. the proposed concepts are illustrated with an application in the climatic analysis of apple cultivation. (kaufmann, 1973), based on fuzzy relation (zadeh, 2020). developed the idea of fuzzy graphs (fgs). later, (rosenfeld, 1975) defined the basic properties of fuzzy relations which are generalized with fuzzy set as a base set and fuzzy analogues of graphic theoretical concepts like bridges and trees were established with their properties and further fuzzy graph concepts were developed and applied in the real life situations in (mohamed et al., 2020; mordeson & chang-shyh, 1994; naz et al, 2017 &2018; quek, et al., 2018 ; smarandache, 2013 ; tan et al., 2021 ; das et al., 2021 ; majumder et al, 2021; saha et al., 2022). recent developments of the fuzzy extensions are developed as in (kumar et al., 2019 ; radha et al.,2021 ; vellapandi & gunasekaran, 2020 ;das & edalatpanah, 2020 ; polymenis, 2021; mao et al, 2020 ; voskoglou & broumi, 2022 ; zhang et al., 2022 ; al-hamido, 2022). to the best of authors knowledge, a very less work is being done on the interval-valued pentapartitioned neutrosophic set (ivppns), so the present study define the operations on the ivppns and later on extend it to graphs environment. the major contributions in this work are explained as follows: 1. the notions of interval valued pentapartitioned neutrosophic graphs (ivppngs) are introduced. this manuscript makes the first attempt in the literature about the concept in neutrosophic graphs. 2. in addition, the complete and strong ivppng are defined. the operations like a cartesian product, cross product, lexicographic product, strong product and the composition of ivppngs with their properties are discussed. 3. in addition, the complete, strong and complement of ivppngs are defined. 4. we extend some of the basic properties for this pnfg along with few examples. we have developed a decision-making model using the introduced interval valued pentapartitioned neutrosophic graphs and applied it for a numerical illustration. a list of contribution (table 1) of authors is presented below. table 1. contribution of authors to extension of neutrosophic graphs authors year contributions akram and siddique 2017 introduced neutrosophic competition graph broumi et al. 2018 introduced generalized neutrosophic graph das et al 2020 introduced generalized neutrosophic competition graph ajay and chellamani 2020 pythagorean neutrosophic fuzzy graphs s. satham hussain 2022 quadripartitioned neutrosophic soft graphs s. satham hussain 2022 quadripartitioned bipolar single valued neutrosophic graph s. satham hussain 2022 quadripartitioned single-valued neutrosophic graph quek et al. 2022 pentapartitioned single-valued neutrosophic graph our approch 2022 interval valued pentapartitioned single-valued neutrosophic graph interval valued pentapartitioned neutrosophic graphs with an application to mcdm 71 2. preliminaries this section summarizes some basic concepts from the theory of ivnss and the concept of ivppnss, which is the foundation for the concept of ivppngs. further details on the ns, svns and ivns theories can be found in [3-6] smarandache (1999) and (wang et al. 2010), respectively. definition 2.1: [5] let a and b be two svnss over a universe y. (i) a is contained in b, if 𝑇𝐴(𝑦) ≤ 𝑇𝐵 (𝑦), 𝐼𝐴(𝑦) ≥ 𝐼𝐵 (𝑦), and 𝐹𝐴(𝑦) ≥ 𝐹𝐵 (𝑦), for all 𝑦 ∈ y . this relationship is denoted as a ⊆ b (1) (ii) a and b are said to be equal if a ⊆ b and b ⊆ a (2) (iii) 𝐴𝑐 = (𝑦, (𝐹𝐴(𝑦) , 1 − 𝐼𝐴(𝑦), 𝑇𝐴(𝑦))), for all 𝑦 ∈ y (3) (iv) a ∪ b = (𝑦, (max (𝑇𝐴, 𝑇𝐵 ), min (𝐼𝐴 , 𝐼𝐵 ), min (𝐹𝐴, 𝐹𝐵 ))), for all 𝑦 ∈ y. (4) (v) a ∩ b = (𝑦, (min (𝑇𝐴, 𝑇𝐵 ), max (𝐼𝐴 , 𝐼𝐵 ), max (𝐹𝐴, 𝐹𝐵 ))), for all 𝑦 ∈ y. (5) definition 2.2: (wang et al, 2010) an interval valued neutrosophic sets (ivns) a in x is denoted by an interval truth-membership function 𝑇𝐴(𝑥), an interval indterminacy-membership function 𝐼𝐴(𝑥),and an interval falsity membership function 𝐹𝐴(𝑥) for each point x in x, there are �̃�𝐴(𝑥) = [𝑇𝐴 𝐿 (𝑥), 𝑇𝐴 𝑈 (𝑥)] ⊆ [0,1], (6) 𝐼𝐴(𝑥) = [𝐼𝐴 𝐿 (𝑥), 𝐼𝐴 𝑈 (𝑥)] ⊆ [0,1], (7) �̃�𝐴(𝑥) = [𝐹𝐴 𝐿 (𝑥), 𝐹𝐴 𝑈 (𝑥)] ⊆ [0,1]. (8) therefore an ivns a can be denoted as, a= {〈𝑥, �̃�𝐴(𝑥), 𝐼𝐴 (𝑥), , �̃�𝐴(𝑥)〉| 𝑥 ∈ 𝑋} then the sum of �̃�𝐴(𝑥), 𝐼𝐴(𝑥), �̃�𝐴(𝑥) satisfies the condition 0 ≤ 𝑇𝐴 𝑈 (𝑥) + 𝐼𝐴 𝑈 (𝑥) + 𝐹𝐴 𝑈 (𝑥) ≤ 3 (9) if the upper and lower ends of the interval values of 𝑇𝐴(𝑥), 𝐼𝐴 (𝑥) 𝑎𝑛𝑑 𝐹𝐴(𝑥) in an ivns are equal then ivns reduces to the svns. definition 2.3: (wang et al, 2010) let a and b be two ivnss over a universe y . (i) a is contained in b, if 𝑇𝐴 𝐿 (𝑦) ≤ 𝑇𝐵 𝐿 (𝑦), 𝑇𝐴 𝑈 (𝑦) ≤ 𝑇𝐵 𝑈 (𝑦) , 𝐼𝐴 𝐿 (𝑦) ≥ 𝐼𝐵 𝐿 (𝑦), 𝐼𝐴 𝑈 (𝑦) ≥ 𝐼𝐵 𝑈 (𝑦), and 𝐹𝐴 𝐿 (𝑦) ≥ 𝐹𝐵 𝐿 (𝑦), 𝐹𝐴 𝑈 (𝑦) ≥ 𝐹𝐵 𝑈 (𝑦), for all 𝑦 ∈ y. this relationship is denoted as a ⊆ b. (10) (ii) a and b are said to be equal if a ⊆ b and b ⊆ a. (11) (iii) 𝐴𝑐 = (𝑦, (𝐹𝐴(𝑦) , 1 − 𝐼𝐴(𝑦), 𝑇𝐴(𝑦))), for all 𝑦 ∈ y. (12) (iv) a ∪ b = (𝑦, (max(𝑇𝐴, 𝑇𝐵 ), min(𝐼𝐴, 𝐼𝐵 ), min(𝐹𝐴, 𝐹𝐵 ))), for all 𝑦 ∈ y. (13) (v) a ∩ b = (𝑦, (min(𝑇𝐴, 𝑇𝐵 ), max(𝐼𝐴, 𝐼𝐵 ), max(𝐹𝐴, 𝐹𝐵 ))), for all 𝑦 ∈ y (14) definition 2.4: (chatterjee eta al., 2016) quadripartitioned neutrosophic sets let x be a universe. a quadripartitioned neutrosophic set a with independent neutrosophic components on x is an object of the form 𝐴 = {< 𝑥, 𝑇𝐴(𝑥), 𝐶𝐴(𝑥), 𝑈𝐴(𝑥), 𝐹𝐴(𝑥) >: 𝑥 ∈ x} (15) s. broumi et al./oper. res. eng. sci. theor. appl. 5(3)2022 68-91 72 𝑎𝑛𝑑 0 ≤ 𝑇𝐴 (𝑥) + 𝐶𝐴(𝑥) + 𝑈𝐴(𝑥) + 𝐹𝐴 (𝑥) ≤ 4 (16) here, 𝑇𝐴(𝑥) is the truth membership, 𝐶𝐴(𝑥) is contradiction membership, 𝑈𝐴 (𝑥) is ignorance membership and 𝐹𝐴(𝑥) is the false membership. definition 2.5: (pramanik, 2022). interval quadripartionned neutrosophic sets an interval quadripartionned neutrosophic sets (iqns) a in x is denoted by truthmembership function 𝑇𝐴(𝑥), a contradiction membership function 𝐶𝐴(𝑥), an unknown membership function 𝑈𝐴(𝑥) and a falsity membership function 𝐹𝐴(𝑥), for each point x in x, there are 𝑇𝐴 (𝑥) = [𝑇𝐴 𝐿 (𝑥), 𝑇𝐴 𝑈 (𝑥)] ⊆ [0,1], 𝐶𝐴(𝑥) = [𝐶𝐴 𝐿 (𝑥), 𝑇𝐴 𝑈 (𝑥)] ⊆ [0,1], 𝑈𝐴(𝑥) = [𝑈𝐴 𝐿 (𝑥), 𝑈𝐴 𝑈 (𝑥)] ⊆ [0,1], 𝐹𝐴(𝑥) = [𝐹𝐴 𝐿 (𝑥), 𝐹𝐴 𝑈 (𝑥)] ⊆ [0,1], therefore an iqns a can be denoted as, a= {〈𝑥, 𝑇𝐴 (𝑥), 𝐶𝐴(𝑥), 𝑈𝐴(𝑥), 𝐹𝐴(𝑥)〉| 𝑥 ∈ 𝑋} (17) a={〈 𝑥,[𝑇𝐴 𝐿(𝑥),𝑇𝐴 𝑈 (𝑥)],[𝐶𝐴 𝐿(𝑥),𝑇𝐴 𝑈 (𝑥)] [𝑈𝐴 𝐿 (𝑥),𝑈𝐴 𝑈(𝑥)],[𝐹𝐴 𝐿(𝑥),𝐹𝐴 𝑈(𝑥)] 〉 | 𝑥 ∈ 𝑋} (18) then the sum of 𝑇𝐴(𝑥), 𝐶𝐴(𝑥), 𝑈𝐴(𝑥), 𝐹𝐴(𝑥) satisfies the condition 0 ≤ 𝑇𝐴 𝑈 (𝑥) + 𝐶𝐴 𝑈 (𝑥) + 𝑈𝐴 𝑈 (𝑥) + 𝐹𝐴 𝑈 (𝑥) ≤ 4 (19) if the upper and lower bounds of the interval values of 𝑇𝐴(𝑥), 𝐶𝐴(𝑥), 𝑈𝐴(𝑥) 𝑎𝑛𝑑 𝐹𝐴(𝑥) in an iqns are equal then iqns reduces to the qsvns. definition 2.6: (mallick & pramanik, 2020). pentapartitioned neutrosophic sets let x be a universe. a pentapartitioned neutrosophic set a with independent neutrosophic components on x is an object of the form 𝐴 = {< 𝑥, 𝑇𝐴(𝑥), 𝐶𝐴(𝑥), 𝑈𝐴(𝑥), 𝐺𝐴(𝑥), 𝐹𝐴(𝑥) >: 𝑥 ∈ x} (20) 𝑎𝑛𝑑 0 ≤ 𝑇𝐴 (𝑥) + 𝐶𝐴(𝑥) + 𝑈𝐴(𝑥) + 𝐺𝐴 (𝑥) + 𝐹𝐴 (𝑥) ≤ 5 (21) here, 𝑇𝐴(𝑥) is the truth membership, 𝐶𝐴(𝑥) is contradiction membership, 𝑈𝐴 (𝑥) is ignorance membership, 𝐺𝐴(𝑥) 𝑖𝑠 ignorance membership, and 𝐹𝐴(𝑥) is the false membership. definition 2.7: (das et al., 2022) interval pentapartionned neutrosophic sets an interval pentapartionned neutrosophic sets (ipns) a in x is denoted by truthmembership function 𝑇𝐴(𝑥), a contradiction membership function 𝐶𝐴(𝑥), an unknown membership function 𝑈𝐴(𝑥), 𝐺𝐴(𝑥)𝑖𝑠 ignorance membership and a falsity membership function 𝐹𝐴(𝑥) for each point x in x, there are 𝑇𝐴 (𝑥) = [𝑇𝐴 𝐿 (𝑥), 𝑇𝐴 𝑈 (𝑥)] ⊆ [0,1], 𝐶𝐴(𝑥) = [𝐶𝐴 𝐿 (𝑥), 𝑇𝐴 𝑈 (𝑥)] ⊆ [0,1], 𝑈𝐴(𝑥) = [𝑈𝐴 𝐿 (𝑥), 𝑈𝐴 𝑈 (𝑥)] ⊆ [0,1], 𝐺𝐴(𝑥) = [𝐺𝐴 𝐿 (𝑥), 𝐺𝐴 𝑈 (𝑥)] ⊆ [0,1], 𝐹𝐴(𝑥) = [𝐹𝐴 𝐿 (𝑥), 𝐹𝐴 𝑈 (𝑥)] ⊆ [0,1], therefore an ipns a can be denoted as, a= {〈𝑥, 𝑇𝐴 (𝑥), 𝐶𝐴(𝑥), 𝑈𝐴(𝑥), 𝐺𝐴(𝑥), 𝐹𝐴(𝑥)〉| 𝑥 ∈ 𝑋} (22) interval valued pentapartitioned neutrosophic graphs with an application to mcdm 73 a={〈 𝑥,[𝑇𝐴 𝐿(𝑥),𝑇𝐴 𝑈 (𝑥)],[𝐶𝐴 𝐿(𝑥),𝑇𝐴 𝑈 (𝑥)] [𝑈𝐴 𝐿 (𝑥),𝑈𝐴 𝑈(𝑥)],[𝐺𝐴 𝐿(𝑥),𝐺𝐴 𝑈(𝑥)],[𝐹𝐴 𝐿(𝑥),𝐹𝐴 𝑈(𝑥)] 〉 | 𝑥 ∈ 𝑋} then the sum of 𝑇𝐴(𝑥), 𝐶𝐴(𝑥), 𝑈𝐴(𝑥), 𝐺𝐴(𝑥), 𝐹𝐴(𝑥) satisfies the condition 0 ≤ 𝑇𝐴 𝑈 (𝑥) + 𝐶𝐴 𝑈 (𝑥) + 𝑈𝐴 𝑈 (𝑥) + 𝐺𝐴 𝑈 (𝑥) + 𝐹𝐴 𝑈 (𝑥) ≤ 5 (23) if the upper and lower bounds of the interval values of 𝑇𝐴(𝑥), 𝐶𝐴(𝑥), 𝑈𝐴(𝑥), 𝐺𝐴(𝑥) 𝑎𝑛𝑑 𝐹𝐴(𝑥) in an ipns are equal then ipns reduces to the psvns. definition 2.8: (broumi et al., 2016) let v be a set. let e ⊆ {{𝜇, 𝑣}: 𝜇, 𝑣 ∈ 𝑉 𝑤𝑖𝑡ℎ 𝜇 ≠ 𝑣}. let a be an ivns on v and b be an ivns on e with 𝑇𝐵 𝑙 (𝜇, 𝑣) ≤ min{𝑇𝐴 𝑙 (𝜇), 𝑇𝐴 𝑙 (𝑣)}, 𝑇𝐵 𝑢(𝜇, 𝑣) ≤ min{𝑇𝐴 𝑢 (𝜇), 𝑇𝐴 𝑢 (𝑣)} (24) 𝐼𝐵 𝑙 (𝜇, 𝑣) ≥ max{𝐼𝐴 𝑙 (𝜇), 𝐼𝐴 𝑙 (𝑣)}, 𝐼𝐵 𝑢(𝜇, 𝑣) ≥ max{𝐼𝐴 𝑢(𝜇), 𝐼𝐴 𝑢(𝑣)} (25) 𝐹𝐵 𝑙 (𝜇, 𝑣) ≥ min{𝐹𝐴 𝑙 (𝜇), 𝐹𝐴 𝑙 (𝑣)}, 𝐹𝐵 𝑢(𝜇, 𝑣) ≥ min{𝐹𝐴 𝑢(𝜇), 𝐹𝐴 𝑢(𝑣)}for all {𝜇, 𝑣}∈ e. then g=(a, b, v, e) is said to be an interval-valued neutrosophic graph. (26) definition 2.9: [22] let v be a set. let 𝐸⊆ {{𝑣, 𝜔}: 𝑣, 𝜔 ∈ 𝑉 ′ 𝑤𝑖𝑡ℎ 𝜇 ≠ 𝑣}. let a be a ppns on v, and b be a ppns on e, with 𝑡𝐵 (𝜇, 𝑣) ≤ min{𝑡𝐴(𝜇), 𝑡𝐴(𝑣)}, 𝑐𝐵 (𝜇, 𝑣) ≥ max{𝑐𝐴(𝜇), 𝑐𝐴(𝑣)}, 𝑔𝐵 (𝜇, 𝑣) ≥ max{𝑔𝐴(𝜇), 𝑔𝐴(𝑣)}, 𝑢𝐵 (𝜇, 𝑣) ≥ max{𝑢𝐴(𝜇), 𝑢𝐴(𝑣)}and 𝑓𝐵 (𝜇, 𝑣) ≥ max{𝑓𝐴(𝜇), 𝑓𝐴(𝑣)}for all { 𝜇, 𝑣 }∈ e. then we have the following: (i) g=(a, b, v, e) is said to be a pentapartitioned neutrosophic graph (ppng). (ii) each 𝑣 ∈ v is said to be a vertex of g. (iii) each{𝜇, 𝑣}∈ e is said to be an edge of g. 3. interval pentapartitioned neutrosophic graphs in this section, first the concept of interval pentapartitioned neutrosophic graphs (ivppngs) is introduced. then based on the definitions of ivns, interval-valued neutrosophic graphs [24] and ivppns given in definition 2.6 and definition 2.7, respectively will be used to put forward the novel concept of ivppngs. the related properties pertaining to this concept will be subsequently investigated. definition 3.1. let v be a set. let 𝐸⊆ {{𝜇, 𝑣}: 𝑣, 𝜇 ∈ 𝑉 𝑤𝑖𝑡ℎ 𝜇 ≠ 𝑣}. let a be an ivppns on v, and b be an ivppns on e, with 𝑡𝐵 𝑙 (𝜇, 𝑣) ≤ min{𝑡𝐴 𝑙 (𝜇), 𝑡𝐴 𝑙 (𝑣)}, 𝑡𝐵 𝑢(𝜇, 𝑣) ≤ min{𝑡𝐴 𝑢(𝜇), 𝑡𝐴 𝑢(𝑣)}, (27) 𝑐𝐵 𝑙 (𝜇, 𝑣) ≥ max{𝑐𝐴 𝑙 (𝜇), 𝑐𝐴 𝑙 (𝑣)},𝑐𝐵 𝑢 (𝜇, 𝑣) ≥ max{𝑐𝐴 𝑢 (𝜇), 𝑐𝐴 𝑢 (𝑣)}, (28) 𝑔𝐵 𝑙 (𝜇, 𝑣) ≥ max{𝑔𝐴 𝑙 (𝜇), 𝑔𝐴 𝑙 (𝑣)},𝑔𝐵 𝑢(𝜇, 𝑣) ≥ max{𝑔𝐴 𝑢 (𝜇), 𝑔𝐴 𝑢 (𝑣)}, (29) 𝑢𝐵 𝑙 (𝜇, 𝑣) ≥ max{𝑢𝐴 𝑙 (𝜇), 𝑢𝐴 𝑙 (𝑣)},𝑢𝐵 𝑢(𝜇, 𝑣) ≥ max{𝑢𝐴 𝑢(𝜇), 𝑢𝐴 𝑢(𝑣)}, (30) and 𝑓𝐵 𝑙 (𝜇, 𝑣) ≥ max{𝑓𝐴 𝑙 (𝜇), 𝑓𝐴 𝑙 (𝑣)},𝑓𝐵 𝑢 (𝜇, 𝑣) ≥ max{𝑓𝐴 𝑢(𝜇), 𝑓𝐴 𝑢(𝑣)}, (31) for all { 𝜇, 𝑣 }∈ e. then we have the following: s. broumi et al./oper. res. eng. sci. theor. appl. 5(3)2022 68-91 74 (i) g=(a, b, v, e) is said to be an interval pentapartitioned neutrosophic graph (ivppng). (32) (ii) each 𝑣 ∈ v is said to be a vertex of g. (33) (iii) each{ 𝜇, 𝑣 }∈ e is said to be an edge of g. (34) fig. 1 a graphical representation of the ppng g. notation 3.1.1 let g = (a, b, v, e) be a ivppng. denote 𝑚𝐴 : v → [0, 1] 5, where 𝑚𝐴(𝑣)=(�̃�𝐴(𝑣), �̃�𝐴(𝑣), �̃�𝐴(𝑣), �̃�𝐴(𝑣), 𝑓𝐴(𝑣)) for all 𝑣 ∈ v. denote 𝑚𝐵 : e →int( [0, 1] 5), where 𝑚𝐵 (𝜇, 𝑣 ) =(�̃�𝐵 (𝜇, 𝑣), �̃�𝐵 (𝜇, 𝑣), �̃�𝐵 (𝜇, 𝑣), �̃�𝐵 (𝜇, 𝑣), 𝑓𝐵 (𝜇, 𝑣)) for all { 𝜇, 𝑣 } ∈ e. example 3.2 let g = (a, b, v, e) be an ivppng with v = {𝑣1, 𝑣2, 𝑣3, 𝑣4, 𝑣5} and e = {{𝑣1, 𝑣2}, {𝑣1, 𝑣3}, {v1,v4}, {𝑣2, 𝑣5}, {𝑣4, 𝑣5}}. then we have the following (fig. 1): figure 1. interval valued pentapartitioned neutrosophic graph 𝑚𝐴(𝑣1) = ([. 7, .9], [. 6, .7], [. 5, .7], [. 4, .6], [. 3, .5]), 𝑚𝐴(𝑣2) = ([. 6, .7], [. 5, .8], [. 3, .6], [. 4, .9], [. 1, .5]), 𝑚𝐴(𝑣3) = ([. 4, .8], [. 5, .7], [. 6, .9], [. 7, .9], [. 2, .5]), 𝑚𝐴(𝑣4) = ([. 3, .6], [. 4, .7], [. 5, .9], [. 7, .9], [. 2, .5]), 𝑚𝐵 (𝑣5) = ([. 7, .9], [. 6, .8], [. 5, .7], [. 3, .6], [. 2, .5]). 𝑚𝐵 (𝑣1𝑣2) = ([. 6, .7], [. 7, .9], [. 5, .7], [. 5, .9], [. 4, .6]), 𝑚𝐵 (𝑣1𝑣3) = ([. 4, .8], [. 6, .8], [. 6, .9], [. 4, .6], [. 3, .6]), 𝑚𝐵 (𝑣1𝑣4) = ([. 3, .6], [. 6, .8], [. 5, .9], [. 7, .9], [. 3, .5]), 𝑚𝐵 (𝑣2𝑣5) = ([. 6, .7], [. 6, .8], [. 5, .7], [. 4, .9], [. 2, .6]), 𝑚𝐵 (𝑣4𝑣5) = ([. 3, .6], [. 6, .8], [. 5, .9], [. 7, .9], [. 3, .7]). definition 3.3. let g = (a, b, v, e) and h = (𝐴′, 𝐵′, 𝑉 ′, 𝐸′) be two ivppngs that satisfies the following conditions: (i) 𝑉 ′⊆ v (35) interval valued pentapartitioned neutrosophic graphs with an application to mcdm 75 (ii) 𝐸′⊆ {{𝑣, 𝜇}: 𝑣, 𝜇 ∈ 𝑉 ′ 𝑤𝑖𝑡ℎ 𝜇 ≠ 𝑣} (36) (iii) 𝑚𝐴′ (𝑣)= 𝑚𝐴(𝑣), for all 𝑣 ∈ 𝑉 ′⊆ v (37) (iv) 𝑚𝐵′ (𝑣, 𝜇)=𝑚𝐵 (𝑣, 𝜇), for all {𝑣, 𝜇} ∈ 𝐸 ′ ⊆ e. (38) then, h is said to be a partial interval valued pentapartitioned neutrosophic graph (partial-ivppng) of g. definition 3.4. let g = (a, b, v, e) and h = (𝐴′, 𝐵′, 𝑉 ′, 𝐸′) be two ivppngs that satisfies the following conditions: (i) 𝑉 ′⊆ v (39) (ii) 𝐸′⊆ {{𝑣, 𝜔}: 𝑣, 𝜔 ∈ 𝑉 ′ 𝑤𝑖𝑡ℎ 𝜔 ≠ 𝑣} (40) (iii) 𝑡 𝐴′ 𝑙 (𝑣) ≤ 𝑡𝐴 𝑙 (𝑣), 𝑡 𝐴′ 𝑢 (𝑣) ≤ 𝑡𝐴 𝑢(𝑣), 𝑐 𝐴′ 𝑙 (𝑣) ≥ 𝑐𝐴 𝑙 (𝑣), 𝑐 𝐴′ 𝑢 (𝑣) ≥ 𝑐𝐴 𝑢 (𝑣), 𝑔 𝐴′ 𝑙 (𝑣) ≥ 𝑔𝐴 𝑙 (𝑣), 𝑔 𝐴′ 𝑢 (𝑣) ≥ 𝑔𝐴 𝑢 (𝑣), 𝑢 𝐴′ 𝑙 (𝑣) ≥ 𝑢𝐴 𝑙 (𝑣), 𝑢 𝐴′ 𝑢 (𝑣) ≥ 𝑢𝐴 𝑢(𝑣), 𝑓 𝐴′ 𝑙 (𝑣) ≥ 𝑓𝐴 𝑙(𝑣), 𝑓 𝐴′ 𝑢 (𝑣) ≥ 𝑓𝐴 𝑢(𝑣) for all 𝑣 ∈ 𝑉 ′⊆v (41) (iv) 𝑡 𝐵′ 𝑙 (𝑣, 𝜔) ≤ 𝑡𝐵 𝑙 (𝑣, 𝜔), 𝑡 𝐵′ 𝑢 (𝑣, 𝜔) ≤ 𝑡𝐵 𝑢(𝑣, 𝜔), 𝑐 𝐵′ 𝑙 (𝑣, 𝜔) ≥ 𝑐𝐵 𝑙 (𝑣, 𝜔), 𝑐 𝐵′ 𝑢 (𝑣, 𝜔) ≥ 𝑐𝐵 𝑢 (𝑣, 𝜔), 𝑔 𝐵′ 𝑙 (𝑣, 𝜔) ≥ 𝑔𝐵 𝑙 (𝑣), 𝑔 𝐵′ 𝑢 (𝑣, 𝜔) ≥ 𝑔𝐵 𝑢(𝑣, 𝜔), 𝑢 𝐵′ 𝑙 (𝑣, 𝜔) ≥ 𝑢𝐵 𝑙 (𝑣, 𝜔), 𝑢 𝐵′ 𝑢 (𝑣, 𝜔) ≥ 𝑢𝐵 𝑢 (𝑣, 𝜔), 𝑓 𝐵′ 𝑙 (𝑣, 𝜔) ≥ 𝑓𝐵 𝑙 (𝑣, 𝜔), 𝑓 𝐵′ 𝑢 (𝑣, 𝜔) ≥ 𝑓𝐵 𝑢(𝑣, 𝜔), for all { 𝑣, 𝜔 } ∈ 𝐸′ ⊆ e. (42) then, h is said to be an interval valued pentapartitioned neutrosophic subgraph (ivppnsg) of g. example 3.5. let 𝐺1be an ivppng and 𝐻1, 𝐻2 be the partial-ivppng and ivppnsg of 𝐺1, respectively. the graphical representation of 𝐺1, 𝐻1 and 𝐻2 are shown in figs. 2, 3 and 4, respectively. here 𝐻2 is a ivppnsg of 𝐺1 but not a partial-ivppng of 𝐺1. 𝑚𝐴(𝑣1) = ([. 7, .9], [. 6, .7], [. 5, .7], [. 4, .6], [. 3, .5]), 𝑚𝐴(𝑣2) = ([. 6, .7], [. 5, .8], [. 3, .6], [. 4, .9], [. 1, .5]), 𝑚𝐴(𝑣3) = ([. 4, .8], [. 5, .7], [. 6, .9], [. 7, .9], [. 2, .5]), 𝑚𝐴(𝑣4) = ([. 3, .6], [. 4, .7], [. 5, .9], [. 7, .9], [. 2, .5]), 𝑚𝐵 (𝑣5) = ([. 7, .9], [. 6, .8], [. 5, .7], [. 3, .6], [. 2, .5]). figure 2. interval valued pentapartitioned neutrosophic graph s. broumi et al./oper. res. eng. sci. theor. appl. 5(3)2022 68-91 76 figure 3. partial interval valued pentapartitioned neutrosophic graph figure 4. interval valued pentapartitioned neutrosophic subgraph definition 3.6. let g = (a, b, v, e) be an ivppng. let 𝑣0 , 𝑣1,..., 𝑣𝑛 ∈ v , with {𝑣𝑖 , 𝑣𝑖+1} ∈ e for all 0 < i ≤ n-1, and with 𝑣𝑖 ≠ 𝑣𝑗 for all 0 ≤ i < j ≤ n-1. then we have the following: p =(𝑣0, 𝑣1,..., 𝑣𝑛) is said to be a an interval valued pentapartitioned neutrosophic path (ivppnp) in g. for each i, {𝑣𝑖 , 𝑣𝑖+1} is said to be an edge of p. n is said to be the length of p. interval valued pentapartitioned neutrosophic graphs with an application to mcdm 77 definition 3.7. let g = (a, b, v, e) be an ivppng. then g is said to be connected if there exists at least one { 𝑣, 𝜔 } ∈ e for all 𝑣 ∈ v. definition 3.8. let g =(a, b, v, e) be an ivppng. then 𝑣 ∈ v is said to be isolated if { 𝑣, 𝜔 } ∉ / e for all 𝜔 ∈ v \ { 𝑣 }. the ivppng has 𝑣1 as the isolated vertex. definition 3.9. let g = (a, b, v, e) be an ivppng and let 𝑣 ∈ v. the degree of v, written as d(v), is defined as d(v) =∑ 𝑚𝐵𝜇∈𝑉 𝑤𝑖𝑡ℎ{𝑣,𝜔}∈𝐸 (𝑣, 𝜔). remark 3.9.1. it follows that d(𝑣) ∈ [0, 1]5. example 3.10. in fig. 3 under eg. 3.5, the degree of the vertices are as follows. d(𝑣1) = (0.5, 1.7, 1.5, 1.1, 1.2), d(𝑣3) =(0.6, 1.7, 1.7, 1.2, 1.2), d(𝑣4)= (0.5, 1.8, 1.6, 1.3, 1.6). definition 3.11. let g =(a, b, v, e) be an ivppng and let p =(𝑣0, 𝑣1,..., 𝑣𝑛) be an ivppnp in g. the strength of p, denoted as s(p), is defined as : s(p)= ([𝑠 𝑡𝐴 𝑙 (𝑃), 𝑠𝑡𝐴 𝑢 (𝑃)] , [𝑠 𝑐𝐴 𝑙 (𝑃), 𝑠𝑐𝐴 𝑢 (𝑃)] , [𝑠 𝑔𝐴 𝑙 (𝑃), 𝑠𝑔𝐴 𝑢 (𝑃)] , [𝑠 𝑢𝐴 𝑙 (𝑃), 𝑠𝑢𝐴 𝑢 (𝑃)] , [𝑠 𝑓𝐴 𝑙 (𝑃), 𝑠𝑓𝐴 𝑢 (𝑃)]) = (𝑠𝑡 (𝑃), 𝑠𝑐̃ (𝑃), 𝑠�̃� (𝑃), 𝑠𝑢 (𝑃), 𝑠�̃� (𝑃)) (43) where 𝑠 𝑡𝐴 𝑙 (𝑃)= 𝑚𝑖𝑛{𝑡𝐵 𝑙 (𝑣𝑖 , 𝑣𝑖+1): 0 ≤ 𝑖 ≤ 𝑛 − 1}, 𝑠𝑡𝐴 𝑢 (𝑃)= 𝑚𝑖𝑛{𝑡𝐵 𝑢(𝑣𝑖 , 𝑣𝑖+1) ∶ 0 ≤ 𝑖 ≤ 𝑛 − 1}, 𝑠 𝑐𝐴 𝑙 (𝑃)= 𝑚𝑎𝑥{𝑐𝐵 𝑙 (𝑣𝑖 , 𝑣𝑖+1) ∶ 0 ≤ 𝑖 ≤ 𝑛 − 1}, 𝑠𝑐𝐴 𝑢 (𝑃)= 𝑚𝑎𝑥{𝑐𝐵 𝑢(𝑣𝑖 , 𝑣𝑖+1) ∶ 0 ≤ 𝑖 ≤ 𝑛 − 1}, 𝑠 𝑔𝐴 𝑙 (𝑃)= 𝑚𝑎𝑥{𝑔𝐵 𝑙 (𝑣𝑖 , 𝑣𝑖+1) ∶ 0 ≤ 𝑖 ≤ 𝑛 − 1}, 𝑠𝑔𝐴 𝑢 (𝑃)= 𝑚𝑎𝑥{𝑔𝐵 𝑢 (𝑣𝑖 , 𝑣𝑖+1) ∶ 0 ≤ 𝑖 ≤ 𝑛 − 1}, 𝑠 𝑢𝐴 𝑙 (𝑃)= 𝑚𝑎𝑥{𝑢𝐵 𝑙 (𝑣𝑖 , 𝑣𝑖+1) ∶ 0 ≤ 𝑖 ≤ 𝑛 − 1}, 𝑠𝑢𝐴 𝑢 (𝑃)= 𝑚𝑎𝑥{𝑢𝐵 𝑢(𝑣𝑖 , 𝑣𝑖+1) ∶ 0 ≤ 𝑖 ≤ 𝑛 − 1}, and 𝑠 𝑓𝐴 𝑙 (𝑃)= 𝑚𝑎𝑥{𝑓𝐵 𝑙 (𝑣𝑖 , 𝑣𝑖+1) ∶ 0 ≤ 𝑖 ≤ 𝑛 − 1}, 𝑠𝑓𝐴 𝑢 (𝑃)= 𝑚𝑎𝑥{𝑓𝐵 𝑢(𝑣𝑖 , 𝑣𝑖+1) ∶ 0 ≤ 𝑖 ≤ 𝑛 − 1}, moreover, the strength of connectedness among the vertices a, b ∈ v in g, denoted as 𝑟𝐺 (a, b), is defined as: 𝑟𝐺 (a, b)=(𝑟𝑡,𝐺 (a, b), 𝑟𝑐̃,𝐺 (a, b), 𝑟�̃�,𝐺 (a, b), 𝑟𝑢,𝐺 (a, b), 𝑟�̃�,𝐺 (a, b)) with (44) 𝑟𝑡,𝐺 (a, b) = [𝑟𝑡𝐴 𝑙 ,𝐺 (a, b), 𝑟𝑡𝐴 𝑢 ,𝐺 (a, b)], 𝑟𝑐̃,𝐺 (a, b) = [𝑟𝑐𝐴 𝑙 ,𝐺 (a, b), 𝑟𝑐𝐴 𝑢 ,𝐺 (a, b)] 𝑟�̃�,𝐺 (a, b) = [𝑟𝑔𝐴 𝑙 ,𝐺 (a, b), 𝑟𝑔𝐴 𝑢 ,𝐺 (a, b)], 𝑟𝑢,𝐺 (a, b) = [𝑟𝑢𝐴 𝑙 ,𝐺 (a, b), 𝑟𝑢𝐴 𝑢 ,𝐺 (a, b)] and 𝑟�̃�,𝐺 (a, b) = [𝑟𝑓𝐴 𝑙 ,𝐺 (a, b), 𝑟𝑓𝐴 𝑢 ,𝐺 (a, b)] where 𝑟 𝑡𝐴 𝑙 ,𝐺 (a, b) = 𝑚𝑎𝑥 {𝑠 𝑡𝐴 𝑙 (𝑃): p = (𝑣0, 𝑣1, . . . , 𝑣𝑛𝑃) in g 𝑤𝑖𝑡ℎ 𝑣0 = 𝑎 𝑎𝑛𝑑 𝑣𝑛𝑃 = 𝑏}, 𝑟𝑡𝐴 𝑢 ,𝐺 (a, b) = 𝑚𝑎𝑥{𝑠𝑡𝐴 𝑢 (𝑃): p = (𝑣0, 𝑣1, . . . , 𝑣𝑛𝑃 ) in g 𝑤𝑖𝑡ℎ 𝑣0 = 𝑎 𝑎𝑛𝑑 𝑣𝑛𝑃 = 𝑏}, 𝑟 𝑐𝐴 𝑙 ,𝐺 (a, b) = 𝑚𝑖𝑛 {𝑠 𝑐𝐴 𝑙 (𝑃): p = (𝑣0, 𝑣1, . . . , 𝑣𝑛𝑃) in g 𝑤𝑖𝑡ℎ 𝑣0 = 𝑎 𝑎𝑛𝑑 𝑣𝑛𝑃 = 𝑏}, s. broumi et al./oper. res. eng. sci. theor. appl. 5(3)2022 68-91 78 𝑟𝑐𝐴 𝑢 ,𝐺 (a, b) = 𝑚𝑖𝑛{𝑠𝑐𝐴 𝑢 (𝑃): p = (𝑣0, 𝑣1, . . . , 𝑣𝑛𝑃) in g 𝑤𝑖𝑡ℎ 𝑣0 = 𝑎 𝑎𝑛𝑑 𝑣𝑛𝑃 = 𝑏}, 𝑟 𝑔𝐴 𝑙 ,𝐺 (a, b) = 𝑚𝑖𝑛 {𝑠 𝑔𝐴 𝑙 (𝑃): p = (𝑣0, 𝑣1, . . . , 𝑣𝑛𝑃 ) in g 𝑤𝑖𝑡ℎ 𝑣0 = 𝑎 𝑎𝑛𝑑 𝑣𝑛𝑃 = 𝑏}, 𝑟𝑔𝐴 𝑢 ,𝐺 (a, b) = 𝑚𝑖𝑛{𝑠𝑔𝐴 𝑢 (𝑃) : p = (𝑣0, 𝑣1, . . . , 𝑣𝑛𝑃 ) in g 𝑤𝑖𝑡ℎ 𝑣0 = 𝑎 𝑎𝑛𝑑 𝑣𝑛𝑃 = 𝑏}, 𝑟 𝑢𝐴 𝑙 ,𝐺 (a, b) = 𝑚𝑖𝑛 {𝑠 𝑢𝐴 𝑙 (𝑃): p = (𝑣0, 𝑣1, . . . , 𝑣𝑛𝑃 ) in g 𝑤𝑖𝑡ℎ 𝑣0 = 𝑎 𝑎𝑛𝑑 𝑣𝑛𝑃 = 𝑏}, 𝑟𝑢𝐴 𝑢 ,𝐺 (a, b) = 𝑚𝑖𝑛{𝑠𝑢𝐴 𝑢 (𝑃): p = (𝑣0, 𝑣1, . . . , 𝑣𝑛𝑃 ) in g 𝑤𝑖𝑡ℎ 𝑣0 = 𝑎 𝑎𝑛𝑑 𝑣𝑛𝑃 = 𝑏}, 𝑟 𝑓𝐴 𝑙 ,𝐺 (a, b) = 𝑚𝑖𝑛 {𝑠 𝑓𝐴 𝑙 (𝑃): p = (𝑣0, 𝑣1, . . . , 𝑣𝑛𝑃 ) in g 𝑤𝑖𝑡ℎ 𝑣0 = 𝑎 𝑎𝑛𝑑 𝑣𝑛𝑃 = 𝑏}, 𝑟𝑓𝐴 𝑢 ,𝐺 (a, b) = 𝑚𝑖𝑛{𝑠𝑓𝐴 𝑢 (𝑃): p = (𝑣0, 𝑣1, . . . , 𝑣𝑛𝑃) in g 𝑤𝑖𝑡ℎ 𝑣0 = 𝑎 𝑎𝑛𝑑 𝑣𝑛𝑃 = 𝑏}. definition 3.12. let g = (a, b, v, e) be an ivppng and and let {𝑣, 𝜔} be an edge in g. denote 𝐺{𝑣,𝜔} ′ as the partial-ivppng of g, in which 𝐺{𝑣,𝜔} ′ =(𝐴′, 𝐵′, 𝑉 ′, 𝐸′) with 𝑉 = 𝑉 ′and 𝐸′={{𝑣, 𝜔}}. then, {𝑣, 𝜔} is said to be an interval valued pentapartitioned neutrosophic bridge (ivppnb) in g if at least one of the following conditions holds for some a,b ∈ v. (i) 𝑟𝑡,𝐺{𝑣,𝜔} ′ (a, b) < 𝑟𝑡,𝐺 (a, b) (45) (ii) 𝑟𝑐̃,𝐺{𝑣,𝜔} ′ (a, b) > 𝑟𝑐̃,𝐺 (a, b) (46) (iii) 𝑟�̃�,𝐺{𝑣,𝜔} ′ (a, b) > 𝑟�̃�,𝐺 (a, b) (47) (iv) 𝑟𝑢,𝐺{𝑣,𝜔} ′ (a, b) > 𝑟𝑢,𝐺 (a, b) (48) (v) 𝑟�̃�,𝐺{𝑣,𝜔} ′ (a, b) > 𝑟�̃�,𝐺 (a, b) (49) with 𝑟 𝑡𝐴 𝑙 ,𝐺{𝑣,𝜔} ′ (a, b) < 𝑟𝑡𝐴 𝑙 ,𝐺 (a, b), 𝑟𝑡𝐴 𝑢 ,𝐺{𝑣,𝜔} ′ (a, b) < 𝑟𝑡𝐴 𝑢 ,𝐺 (a, b), 𝑟 𝑐𝐴 𝑙 ,𝐺{𝑣,𝜔} ′ (a, b) > 𝑟𝑐𝐴 𝑙 ,𝐺 (a, b), 𝑟𝑐𝐴 𝑢 ,𝐺{𝑣,𝜔} ′ (a, b) > 𝑟𝑐𝐴 𝑢 ,𝐺 (a, b), 𝑟 𝑔𝐴 𝑙 ,𝐺{𝑣,𝜔} ′ (a, b) > 𝑟𝑔𝐴 𝑙 ,𝐺 (a, b), 𝑟𝑔𝐴 𝑢 ,𝐺{𝑣,𝜔} ′ (a, b) > 𝑟𝑔𝐴 𝑢 ,𝐺 (a, b), 𝑟 𝑢𝐴 𝑙 ,𝐺{𝑣,𝜔} ′ (a, b) > 𝑟𝑢𝐴 𝑙 ,𝐺 (a, b), 𝑟𝑢𝐴 𝑢 ,𝐺{𝑣,𝜔} ′ (a, b) > 𝑟𝑢𝐴 𝑢 ,𝐺 (a, b) and 𝑟 𝑓𝐴 𝑙 ,𝐺{𝑣,𝜔} ′ (a, b) > 𝑟𝑓𝐴 𝑙 ,𝐺 (a, b), 𝑟𝑓𝐴 𝑢 ,𝐺{𝑣,𝜔} ′ (a, b) > 𝑟𝑓𝐴 𝑢 ,𝐺 (a, b). in particular, if all of the conditions (i)–(v) are true for some a,b ∈ v , then {𝑣, 𝜔} is said to be a strong interval valued pentapartitioned neutrosophic bridge (strongivppnb) in g. definition 3.13. let g =(a, b, v, e) be an ivppng and and let 𝑣 be a vertex in g. denote 𝐺𝑣 ′ as the partial-ivppng of g, in which 𝐺𝑣 ′ =(𝐴′, 𝐵′, 𝑉 ′, 𝐸′) with 𝑉 ′ = 𝑉 − { 𝑣} and 𝐸′= e-{{𝑎, 𝑣} : a∈ 𝑉 − { 𝑣} }. then, 𝑣is said to be an interval valued pentapartitioned neutrosophic cut vertex (ivppncv) in g if at least one of the following conditions holds for some a,b ∈ v (i) 𝑟𝑡,𝐺𝑣 ′ (a, b) < 𝑟𝑡,𝐺 (a, b) (50) (ii) 𝑟𝑐̃,𝐺𝑣 ′ (a, b) > 𝑟𝑐̃,𝐺 (a, b) (51) (iii) 𝑟�̃�,𝐺𝑣 ′ (a, b) > 𝑟�̃�,𝐺 (a, b) (52) interval valued pentapartitioned neutrosophic graphs with an application to mcdm 79 (iv) 𝑟𝑢,𝐺𝑣 ′ (a, b) > 𝑟𝑢,𝐺 (a, b) (53) (v) 𝑟�̃�,𝐺𝑣 ′ (a, b) > 𝑟�̃�,𝐺 (a, b) (54) with 𝑟 𝑡𝐴 𝑙 ,𝐺𝑣 ′ (a, b) < 𝑟𝑡𝐴 𝑙 ,𝐺 (a, b), 𝑟𝑡𝐴 𝑢 ,𝐺𝑣 ′ (a, b) < 𝑟𝑡𝐴 𝑢 ,𝐺 (a, b), 𝑟 𝑐𝐴 𝑙 ,𝐺𝑣 ′ (a, b) > 𝑟𝑐𝐴 𝑙 ,𝐺 (a, b), 𝑟𝑐𝐴 𝑢 ,𝐺𝑣 ′ (a, b) > 𝑟𝑐𝐴 𝑢 ,𝐺 (a, b), 𝑟 𝑔𝐴 𝑙 ,𝐺𝑣 ′ (a, b) > 𝑟𝑔𝐴 𝑙 ,𝐺 (a, b), 𝑟𝑔𝐴 𝑢 ,𝐺𝑣 ′ (a, b) > 𝑟𝑔𝐴 𝑢 ,𝐺 (a, b), 𝑟 𝑢𝐴 𝑙 ,𝐺𝑣 ′ (a, b) > 𝑟𝑢𝐴 𝑙 ,𝐺 (a, b), 𝑟𝑢𝐴 𝑢 ,𝐺𝑣 ′ (a, b) > 𝑟𝑢𝐴 𝑢 ,𝐺 (a, b) and 𝑟 𝑓𝐴 𝑙 ,𝐺𝑣 ′ (a, b) > 𝑟𝑓𝐴 𝑙 ,𝐺 (a, b), 𝑟𝑓𝐴 𝑢 ,𝐺𝑣 ′ (a, b) > 𝑟𝑓𝐴 𝑢 ,𝐺 (a, b). in particular, if all of the conditions (i)–(v) are true for some a, b ∈ v, then 𝑣 is said to be a strong interval valued pentapartitioned neutrosophic cut vertex (strongivppncv) in g. definition 3.15. suppose that ĝ= (p, q) is an svpn-graph. then, the size of ĝ= (p, q), denoted by s(ĝ) is defined by s(ĝ)= (st(ĝ), sc(ĝ), sr(ĝ), su(ĝ), sf(ĝ)), where st(ĝ)=∑ u≠k tq(u, k) denotes the t-size of ĝ= (p, q); (55) sc(ĝ)=∑ u≠k cq(u, k) denotes the c-size of ĝ= (p, q); (56) sr(ĝ)=∑ u≠k rq(u, k) denotes the r-size of ĝ= (p, q); (57) su(ĝ)=∑ u≠k uq(u, k) denotes the u-size of ĝ= (p, q); (58) sf(ĝ)= ∑ u≠k fq(u, k) denotes the f-size of ĝ= (p, q). (59) 4. application in decision making problem rapid development of the application of the fuzzy decision making in the real-life application is remarkable. there are many applications of the implementation of the fuzzy graph model in decision making is evident in the recent research articles. multi attribute decision-making is one of the decision-making methods in which we analyze the attributes according to the criteria for the problems chosen and using an algorithm the attributes are evaluated and the best attributes will be selected. more models are proposed according to each further developments and extensions of the fuzzy theory, we have proposed the decision-making method according to the developed concept of interval valued pentapartioned neutrosohic graphs. the proposed algorithm using the interval valued pentapartionied neutrosophic graphs is as follows: 4.1. algorithm: step 1: input the attributes 𝐴 = {𝐴1, 𝐴2, … 𝐴𝑚 } and set of criteria 𝐶 = {𝐶1, 𝐶2, … 𝐶𝑛}. step 2: construct the interval valued pentapartitioned relation 𝐾 𝑖 = (𝑘𝑙𝑝 (𝑖) ) 𝑚𝑥𝑚 where 𝑖 = 1,2, … 𝑛 & 𝑘𝑙𝑝 𝑖 = ([𝑇𝑙𝑝 (𝑖)𝐿 , 𝑇𝑙𝑝 (𝑖)𝑈 ], [𝐶𝑙𝑝 (𝑖)𝐿 , 𝐶𝑙𝑝 (𝑖)𝑈 ], [𝑈𝑙𝑝 (𝑖)𝐿 , 𝑈𝑙𝑝 (𝑖)𝑈 ], [𝐺𝑙𝑝 (𝑖)𝐿 , 𝐺𝑙𝑝 (𝑖)𝑈 ], [𝐹𝑙𝑝 (𝑖)𝐿 , 𝐹𝑙𝑝 (𝑖)𝑈 ]), 𝑙, 𝑝 = 1,2, … 𝑛. step 3: compute the resultant adjacency matrix (k) for the attributes under the criteria using the intersection of all the interval valued pentapartitioned relation (𝐾 𝑖) as given, 𝐾 = ⋂ 𝐾 𝑖𝑖 s. broumi et al./oper. res. eng. sci. theor. appl. 5(3)2022 68-91 80 step 4: calculate the score value of resultant adjacency matrix 𝐾 by using score function 𝑆𝑖𝑗 . 𝑆𝑙𝑝 = 𝑇𝑙𝑝 𝐿 +𝑇𝑙𝑝 𝑈 +(1−𝐶𝑙𝑝 𝐿 )+(1−𝐶𝑙𝑝 𝑈 )+(1−𝑈𝑙𝑝 𝐿 )+(1−𝑈𝑙𝑝 𝑈 )+ (1−𝐺𝑙𝑝 𝐿 )+(1−𝐺𝑙𝑝 𝑈 )+(1−𝐹𝑙𝑝 𝐿 )(1−𝐹𝑙𝑝 𝑈 ) 5 (60) step 5: calculate the choice values 𝐴ℎ = ∑ 𝑆ℎ𝑗𝑗 h, j=1,2,…m of each alternative. step 6: the final decision is the 𝐴𝑗 with maximum choice value. step 7: if the 𝑗 has more than one maximum value, then any one may be chosen. 4.2. an illustrative example: in the fuzzy set and its extensions, the membership and the other membership degree function is sufficient but does not satisfy the needed vague categories. thus, the introduction of the pentapartitioned neutrosophic set have paved the way for that advancement in the application area. it has five membership degree which mostly consider the vagueness of the real-life situations. the introduction of interval valued pentapartitioned neutrosophic set is like a cream on top of the cake which adds more fuzziness in the conditions and criteria. now we consider the decision-making problems to choose the best international airline to take up the journey. the proposed decision-making method based on the interval valued pentapartitioned neutrosophic set and graph is used to solve this decision-making problem. the proposed method is more effective than the other proposed models due its membership degrees. let the attributes be 𝐴 = {𝐴1, 𝐴2, … 𝐴6} where 𝐴𝑖 ’s are the airlines which we consider in our list. the selection of the best airline is based the criteria’s 𝐶 = {𝐶1, 𝐶2, … 𝐶5}. where the criteria’s are 𝐶1 = safe air travel for passengers during covid-19 airline safety rating. 𝐶2 = high standards of airport. 𝐶3 = onboard product with excellent standards of staff service delivery 𝐶4 = specialist intelligence and save time & resources 𝐶5 = trusted experience and efficient workflows using the proposed method, we input the attributes and the criteria’s. according to each criteria interval valued pentapartitioned neutrosophic relation is developed (𝐾𝑖 ) as directed graphs. then the intersection of all the criteria’s are calculated and the resultant matrix is given in a graph. then the score values are calculated for each alternative and framed into a graph structure. the choice values are found for each attribute and arranged according to find the optimal alternative. the method of solving the selected problem is as follows.: step 1: the attributes 𝐴 = {𝐴1, 𝐴2, … 𝐴6} and criteria are 𝐶 = {𝐶1, 𝐶2, … 𝐶6}. step 2: the interval valued pentapartitioned relation 𝐾 𝑖 (𝑖 = 1, 2, 3, 4, 5) is developed for each criteria as in the tables 2 to 6. interval valued pentapartitioned neutrosophic graphs with an application to mcdm 81 table 2. interval valued pentapartitioned neutrosophic relation (k1) for criteria 1 k1 a1 a2 a3 a4 a5 a6 a1 ([0.3,0.7], [0.2,0.6], [0.4,0.5], [0.1,0.4], [0.2,0.6]) ([0.1,0.5], [0.2,0.7], [0.3,0.8], [0.5,0.9], [0.1,0.4]) ([0.1,0.5], [0.2,0.8], [0.3,0.6], [0.4,0.7], [0.5,0.8]) ([0.2,0.4], [0.3,0.5], [0.2,0.8], [0.1,0.7], [0.3,0.6]) ([0.4,0.8], [0.3,0.6], [0.3,0.7], [0.2,0.6], [0.1,0.6]) ([0.2,0.7], [0.1,0.4], [0.3,0.7], [0.6,0.9], [0.4,0.6]) a2 ([0.1,0.5], [0.2,0.4], [0.2,0.6], [0.3,0.7], [0.4,0.8]) ([0.3,0.7], [0.2,0.6], [0.4,0.5], [0.1,0.4], [0.2,0.6]) ([0.2,0.6], [0.3,0.7], [0.4,0.8], [0.2,0.7], [0.1,0.6]) ([0.1,0.6], [0.2,0.5], [0.3,0.7], [0.4,0.9], [0.5,0.8]) ([0.2,0.6], [0.4,0.8], [0.1,0.6], [0.3,0.7], [0.5,0.9]) ([0.4,0.8], [0.1,0.7], [0.5,0.8], [0.3,0.6], [0.2,0.6]) a3 ([0.3,0.6], [0.4,0.7], [0.1,0.5], [0.2,0.8], [0.1,0.6]) ([0.1,0.5], [0.2,0.8], [0.3,0.6], [0.4,0.7], [0.1,0.7]) ([0.3,0.7], [0.2,0.6], [0.4,0.5], [0.1,0.4], [0.2,0.6]) ([0.5,0.9], [0.3,0.8], [0.2,0.6], [0.1,0.5], [0.3,0.7]) ([0.3,0.8], [0.2,0.7], [0.5,0.9], [0.4,0.8], [0.1,0.5]) ([0.1,0.5], [0.2,0.6], [0.3,0.7], [0.4,0.8], [0.5,0.8]) a4 ([0.2,0.5], [0.3,0.7], [0.4,0.9], [0.5,0.9], [0.1,0.7]) ([0.1,0.6], [0.2,0.7], [0.3,0.8], [0.5,0.9], [0.2,0.8]) ([0.2,0.8], [0.3,0.9], [0.5,0.7], [0.3,0.6], [0.1,0.4]) ([0.3,0.7], [0.2,0.6], [0.4,0.5], [0.1,0.4], [0.2,0.6]) ([0.3,0.9], [0.1,0.4], [0.4,0.6], [0.6,0.9], [0.2,0.8]) ([0.3,0.6], [0.4,0.7], [0.2,0.5], [0.2,0.8], [0.1,0.4]) a5 ([0.2,0.6], [0.1,0.5], [0.3,0.7], [0.4,0.7], [0.1,0.4]) ([0.1,0.4], [0.3,0.7], [0.2,0.6], [0.4,0.9], [0.1,0.7]) ([0.5,0.9], [0.4,0.7], [0.3,0.6], [0.1,0.7], [0.2,0.8]) ([0.3,0.9], [0.5,0.8], [0.1,0.6], [0.2,0.7], [0.4,0.8]) ([0.3,0.7], [0.2,0.6], [0.4,0.5], [0.1,0.4], [0.2,0.6]) ([0.2,0.6], [0.4,0.7], [0.2,0.5], [0.2,0.8], [0.1,0.4]) a6 ([0.2,0.6], [0.3,0.5], [0.3,0.8], [0.4,0.9], [0.3,0.7]) ([0.2,0.8], [0.3,0.6], [0.4,0.8], [0.5,0.7], [0.2,0.9]) ([0.6,0.8], [0.5,0.7], [0.3,0.6], [0.2,0.7], [0.1,0.4]) ([0.3,0.6], [0.2,0.8], [0.5,0.7], [0.4,0.9], [0.3,0.8]) ([0.1,0.6], [0.3,0.8], [0.4,0.7], [0.1,0.8], [0.2,0.9]) ([0.3,0.7], [0.2,0.6], [0.4,0.5], [0.1,0.4], [0.2,0.6]) table 3. interval valued pentapartitioned neutrosophic relation (k2) for criteria 2 k2 a1 a2 a3 a4 a5 a6 a1 ([0.2,0.5], [0.3,0.7], [0.4,0.9], [0.5,0.9], [0.1,0.7]) ([0.1,0.5], [0.2,0.7], [0.3,0.8], [0.5,0.9], [0.1,0.4]) ([0.1,0.5], [0.2,0.8], [0.3,0.6], [0.4,0.7], [0.1,0.7]) ([0.1,0.6], [0.2,0.7], [0.3,0.8], [0.5,0.9], [0.2,0.8]) ([0.1,0.4], [0.3,0.7], [0.2,0.6], [0.4,0.9], [0.1,0.7]) ([0.2,0.8], [0.3,0.6], [0.4,0.8], [0.5,0.7], [0.2,0.9]) a2 ([0.1,0.6], [0.2,0.7], [0.3,0.8], [0.5,0.9], [0.2,0.8]) ([0.2,0.5], [0.3,0.7], [0.4,0.9], [0.5,0.9], [0.1,0.7]) ([0.2,0.6], [0.3,0.7], [0.4,0.8], [0.2,0.7], [0.1,0.5]) ([0.2,0.7], [0.3,0.5], [0.4,0.8], [0.5,0.9], [0.4,0.6]) ([0.2,0.6], [0.4,0.8], [0.1,0.6], [0.3,0.7], [0.5,0.9]) ([0.4,0.8], [0.1,0.7], [0.5,0.8], [0.3,0.6], [0.2,0.6]) a3 ([0.2,0.8], [0.3,0.9], [0.5,0.7], [0.2,0.6], ([0.3,0.6], [0.4,0.7], [0.1,0.5], [0.2,0.8], ([0.2,0.5], [0.3,0.7], [0.4,0.9], [0.5,0.9], ([0.5,0.9], [0.3,0.8], [0.3,0.7], [0.2,0.8], ([0.4,0.7], [0.5,0.8], [0.3,0.6], [0.1,0.4], ([0.4,0.9], [0.5,0.8], [0.6,0.9], [0.3,0.7], s. broumi et al./oper. res. eng. sci. theor. appl. 5(3)2022 68-91 82 [0.1,0.4]) [0.1,0.6]) [0.1,0.7]) [0.4,0.9]) [0.2,0.5]) [0.2,0.5]) a4 ([0.3,0.7], [0.2,0.6], [0.4,0.5], [0.1,0.4], [0.2,0.6]) ([0.1,0.5], [0.2,0.8], [0.3,0.6], [0.4,0.7], [0.1,0.7]) ([0.5,0.9], [0.3,0.8], [0.2,0.6], [0.1,0.5], [0.3,0.7]) ([0.2,0.5], [0.3,0.7], [0.4,0.9], [0.5,0.9], [0.1,0.7]) ([0.3,0.8], [0.2,0.7], [0.5,0.9], [0.4,0.8], [0.2,0.5]) ([0.2,0.6], [0.1,0.5], [0.3,0.7], [0.5,0.8], [0.6,0.9]) a5 ([0.3,0.9], [0.1,0.4], [0.4,0.6], [0.6,0.9], [0.2,0.8]) ([0.4,0.7], [0.2,0.6], [0.1,0.4], [0.3,0.8], [0.5,0.8]) ([0.6,0.8], [0.6,0.9], [0.5,0.7], [0.4,0.6], [0.1,0.3]) ([0.7,0.9], [0.5,0.8], [0.4,0.6], [0.3,0.5], [0.2,0.7]) ([0.2,0.5], [0.3,0.7], [0.4,0.9], [0.5,0.9], [0.1,0.7]) ([0.5,0.7], [0.4,0.6], [0.3,0.6], [0.2,0.5], [0.1,0.6]) a6 ([0.3,0.6], [0.4,0.7], [0.2,0.5], [0.2,0.8], [0.1,0.4]) ([0.4,0.7], [0.3,0.5], [0.2,0.6], [0.3,0.8], [0.5,0.9]) ([0.5,0.8], [0.3,0.4], [0.4,0.7], [0.3,0.6], [0.2,0.6]) ([0.3,0.5], [0.2,0.6], [0.5,0.8], [0.4,0.9], [0.6,0.9]) ([0.4,0.6], [0.3,0.5], [0.2,0.8], [0.1,0.5], [0.6,0.9]) ([0.2,0.5], [0.3,0.7], [0.4,0.9], [0.5,0.9], [0.1,0.7]) table 4. interval valued pentapartitioned neutrosophic relation (k3) for criteria 3 k3 a1 a2 a3 a4 a5 a6 a1 ([0.3,0.6], [0.2,0.8], [0.5,0.7], [0.4,0.9], [0.3,0.8]) ([0.5,0.9], [0.3,0.8], [0.2,0.6], [0.1,0.5], [0.3,0.7]) ([0.1,0.5], [0.2,0.8], [0.3,0.6], [0.4,0.7], [0.1,0.7]) ([0.3,0.7], [0.2,0.6], [0.4,0.5], [0.1,0.4], [0.2,0.8]) ([0.4,0.6], [0.3,0.5], [0.2,0.8], [0.1,0.5], [0.6,0.9]) ([0.5,0.7], [0.4,0.6], [0.3,0.6], [0.2,0.5], [0.1,0.6]) a2 ([0.5,0.9], [0.3,0.8], [0.3,0.7], [0.2,0.8], [0.4,0.9]) ([0.3,0.6], [0.2,0.8], [0.5,0.7], [0.4,0.9], [0.3,0.8]) ([0.6,0.8], [0.6,0.9], [0.5,0.7], [0.4,0.6], [0.1,0.3]) ([0.1,0.6], [0.2,0.7], [0.3,0.8], [0.5,0.9], [0.2,0.5]) ([0.3,0.9], [0.1,0.4], [0.4,0.6], [0.6,0.9], [0.2,0.8]) ([0.4,0.8], [0.1,0.7], [0.5,0.8], [0.3,0.6], [0.2,0.6]) a3 ([0.3,0.9], [0.1,0.4], [0.4,0.6], [0.6,0.9], [0.2,0.8]) ([0.4,0.7], [0.5,0.8], [0.3,0.6], [0.1,0.4], [0.2,0.5]) ([0.3,0.6], [0.2,0.8], [0.5,0.7], [0.4,0.9], [0.3,0.8]) ([0.5,0.8], [0.3,0.4], [0.4,0.7], [0.3,0.6], [0.2,0.5]) ([0.1,0.4], [0.3,0.7], [0.2,0.6], [0.4,0.9], [0.1,0.7]) ([0.3,0.6], [0.4,0.7], [0.2,0.5], [0.2,0.8], [0.1,0.4]) a4 ([0.4,0.7], [0.2,0.6], [0.1,0.4], [0.3,0.8], [0.5,0.8]) ([0.3,0.6], [0.4,0.7], [0.1,0.5], [0.2,0.8], [0.1,0.6]) ([0.4,0.9], [0.5,0.8], [0.6,0.9], [0.5,0.7], [0.2,0.5]) ([0.3,0.6], [0.2,0.8], [0.5,0.7], [0.4,0.9], [0.3,0.8]) ([0.5,0.9], [0.3,0.8], [0.3,0.7], [0.2,0.8], [0.4,0.9]) ([0.2,0.8], [0.3,0.6], [0.4,0.8], [0.5,0.7], [0.2,0.9]) a5 ([0.6,0.8], [0.6,0.9], [0.5,0.7], [0.4,0.6], [0.1,0.3]) ([0.3,0.7], [0.2,0.6], [0.4,0.5], [0.1,0.4], [0.2,0.8]) ([0.1,0.5], [0.2,0.8], [0.3,0.6], [0.4,0.7], [0.1,0.7]) ([0.2,0.5], [0.3,0.7], [0.4,0.9], [0.5,0.8], [0.1,0.7]) ([0.3,0.6], [0.2,0.8], [0.5,0.7], [0.4,0.9], [0.3,0.8]) ([0.7,0.9], [0.5,0.8], [0.4,0.6], [0.3,0.5], [0.2,0.7]) a6 ([0.7,0.9], [0.5,0.8], [0.4,0.6], [0.3,0.5], [0.2,0.7]) ([0.3,0.9], [0.1,0.4], [0.4,0.6], [0.6,0.9], [0.2,0.8]) ([0.3,0.6], [0.4,0.7], [0.2,0.5], [0.2,0.8], [0.1,0.4]) ([0.4,0.7], [0.2,0.6], [0.1,0.4], [0.3,0.8], [0.5,0.8]) ([0.1,0.5], [0.2,0.7], [0.3,0.8], [0.5,0.9], [0.1,0.4]) ([0.3,0.6], [0.2,0.8], [0.5,0.7], [0.4,0.9], [0.3,0.8]) interval valued pentapartitioned neutrosophic graphs with an application to mcdm 83 table 5. interval valued pentapartitioned neutrosophic relation (k4) for criteria 4 k4 a1 a2 a3 a4 a5 a6 a1 ([0.3,0.5], [0.2,0.7], [0.5,0.9], [0.4,0.8], [0.3,0.8]) ([0.5,0.9], [0.3,0.8], [0.3,0.7], [0.2,0.8], [0.4,0.9]) ([0.3,0.9], [0.1,0.4], [0.4,0.6], [0.6,0.9], [0.2,0.8]) ([0.4,0.7], [0.2,0.6], [0.1,0.4], [0.3,0.8], [0.5,0.8]) ([0.6,0.8], [0.6,0.9], [0.5,0.7], [0.4,0.6], [0.1,0.3]) ([0.7,0.9], [0.5,0.8], [0.4,0.6], [0.3,0.5], [0.2,0.7]) a2 ([0.5,0.9], [0.3,0.8], [0.2,0.6], [0.1,0.5], [0.3,0.7]) ([0.3,0.5], [0.2,0.7], [0.5,0.9], [0.4,0.8], [0.3,0.8]) ([0.4,0.7], [0.5,0.8], [0.3,0.6], [0.1,0.4], [0.2,0.5]) ([0.3,0.6], [0.4,0.7], [0.1,0.5], [0.2,0.8], [0.1,0.6]) ([0.3,0.7], [0.2,0.6], [0.4,0.5], [0.1,0.4], [0.2,0.8]) ([0.3,0.9], [0.1,0.4], [0.4,0.6], [0.6,0.9], [0.2,0.8]) a3 ([0.1,0.5], [0.2,0.8], [0.3,0.6], [0.4,0.7], [0.1,0.7]) ([0.6,0.8], [0.6,0.9], [0.5,0.7], [0.4,0.6], [0.1,0.3]) ([0.3,0.5], [0.2,0.7], [0.5,0.9], [0.4,0.8], [0.3,0.8]) ([0.4,0.9], [0.5,0.8], [0.6,0.9], [0.5,0.7], [0.2,0.5]) ([0.1,0.3], [0.2,0.8], [0.3,0.7], [0.4,0.7], [0.1,0.5]) ([0.3,0.6], [0.4,0.7], [0.2,0.5], [0.2,0.8], [0.1,0.4]) a4 ([0.3,0.7], [0.2,0.6], [0.4,0.5], [0.1,0.4], [0.2,0.8]) ([0.1,0.6], [0.2,0.7], [0.3,0.8], [0.5,0.9], [0.2,0.5]) ([0.5,0.8], [0.3,0.4], [0.4,0.7], [0.3,0.6], [0.2,0.5]) ([0.3,0.5], [0.2,0.7], [0.5,0.9], [0.4,0.8], [0.3,0.8]) ([0.2,0.5], [0.3,0.7], [0.4,0.9], [0.5,0.8], [0.1,0.6]) ([0.4,0.7], [0.2,0.6], [0.1,0.4], [0.3,0.8], [0.5,0.8]) a5 ([0.4,0.6], [0.3,0.5], [0.2,0.8], [0.1,0.4], [0.6,0.9]) ([0.3,0.9], [0.1,0.4], [0.4,0.6], [0.6,0.9], [0.2,0.8]) ([0.1,0.4], [0.3,0.7], [0.2,0.6], [0.4,0.9], [0.1,0.7]) ([0.5,0.9], [0.3,0.8], [0.3,0.7], [0.2,0.8], [0.4,0.6]) ([0.3,0.5], [0.2,0.7], [0.5,0.9], [0.4,0.8], [0.3,0.8]) ([0.2,0.7], [0.1,0.5], [0.3,0.8], [0.5,0.9], [0.1,0.4]) a6 ([0.5,0.7], [0.4,0.6], [0.3,0.6], [0.2,0.5], [0.1,0.6]) ([0.4,0.8], [0.1,0.7], [0.5,0.8], [0.3,0.6], [0.2,0.5]) ([0.3,0.6], [0.4,0.7], [0.2,0.5], [0.2,0.8], [0.1,0.4]) ([0.2,0.8], [0.3,0.6], [0.4,0.8], [0.5,0.7], [0.2,0.9]) ([0.7,0.9], [0.5,0.8], [0.4,0.6], [0.3,0.5], [0.2,0.7]) ([0.3,0.5], [0.2,0.7], [0.5,0.9], [0.4,0.8], [0.3,0.8]) table 6. interval valued pentapartitioned neutrosophic relation (k5) for criteria 5 k5 a1 a2 a3 a4 a5 a6 a1 ([0.5,0.9], [0.3,0.8], [0.4,0.7], [0.2,0.6], [0.3,0.5]) ([0.3,0.7], [0.2,0.5], [0.1,0.4], [0.4,0.8], [0.3,0.6]) ([0.1,0.5], [0.2,0.8], [0.3,0.6], [0.4,0.7], [0.2,0.6]) ([0.3,0.7], [0.2,0.6], [0.4,0.5], [0.1,0.4], [0.2,0.8]) ([0.4,0.6], [0.3,0.5], [0.2,0.8], [0.1,0.4], [0.6,0.9]) ([0.5,0.7], [0.4,0.6], [0.3,0.6], [0.2,0.5], [0.1,0.6]) a2 ([0.4,0.8], [0.3,0.5], [0.4,0.6], [0.2,0.5], [0.3,0.9]) ([0.5,0.9], [0.3,0.8], [0.4,0.7], [0.2,0.6], [0.3,0.5]) ([0.6,0.8], [0.6,0.9], [0.5,0.7], [0.4,0.6], [0.2,0.4]) ([0.1,0.6], [0.2,0.7], [0.3,0.8], [0.5,0.9], [0.2,0.5]) ([0.3,0.9], [0.1,0.4], [0.4,0.6], [0.6,0.9], [0.1,0.5]) ([0.4,0.8], [0.1,0.7], [0.5,0.8], [0.3,0.6], [0.2,0.5]) a3 ([0.3,0.9], [0.1,0.4], [0.4,0.6], [0.6,0.9], ([0.4,0.7], [0.5,0.8], [0.3,0.6], [0.1,0.4], ([0.5,0.9], [0.3,0.8], [0.4,0.7], [0.2,0.6], ([0.5,0.8], [0.3,0.4], [0.4,0.7], [0.3,0.6], ([0.1,0.4], [0.3,0.7], [0.2,0.6], [0.4,0.9], ([0.3,0.6], [0.4,0.7], [0.2,0.5], [0.2,0.8], s. broumi et al./oper. res. eng. sci. theor. appl. 5(3)2022 68-91 84 [0.2,0.8]) [0.2,0.5]) [0.3,0.5]) [0.2,0.5]) [0.1,0.5]) [0.1,0.4]) a4 ([0.4,0.7], [0.2,0.6], [0.1,0.4], [0.3,0.8], [0.5,0.8]) ([0.3,0.6], [0.4,0.7], [0.1,0.5], [0.2,0.8], [0.1,0.6]) ([0.4,0.9], [0.5,0.8], [0.6,0.9], [0.5,0.7], [0.2,0.5]) ([0.5,0.9], [0.3,0.8], [0.4,0.7], [0.2,0.6], [0.3,0.5]) ([0.5,0.9], [0.3,0.8], [0.3,0.7], [0.2,0.8], [0.4,0.6]) ([0.2,0.8], [0.3,0.6], [0.4,0.8], [0.5,0.7], [0.2,0.9]) a5 ([0.6,0.8], [0.6,0.9], [0.5,0.7], [0.4,0.6], [0.1,0.3]) ([0.3,0.7], [0.2,0.6], [0.4,0.5], [0.1,0.4], [0.2,0.8]) ([0.1,0.3], [0.2,0.8], [0.3,0.7], [0.4,0.7], [0.6,0.9]) ([0.2,0.5], [0.3,0.7], [0.4,0.9], [0.5,0.8], [0.1,0.6]) ([0.5,0.9], [0.3,0.8], [0.4,0.7], [0.2,0.6], [0.3,0.5]) ([0.7,0.9], [0.5,0.8], [0.4,0.6], [0.3,0.5], [0.2,0.7]) a6 ([0.7,0.9], [0.5,0.8], [0.4,0.6], [0.6,0.9], [0.2,0.8]) ([0.3,0.9], [0.1,0.4], [0.4,0.6], [0.6,0.9], [0.2,0.8]) ([0.3,0.6], [0.4,0.7], [0.2,0.5], [0.2,0.8], [0.1,0.4]) ([0.4,0.7], [0.2,0.6], [0.1,0.4], [0.3,0.8], [0.5,0.9]) ([0.2,0.7], [0.1,0.5], [0.3,0.8], [0.5,0.9], [0.1,0.4]) ([0.5,0.9], [0.3,0.8], [0.4,0.7], [0.2,0.6], [0.3,0.5]) figure 5: interval valued pentapartitioned neutrosophic directed graph structure for 𝐶𝑖 (𝑖 = 1, 2, 3, 4, 5) step 3: from the interval valued pentapartitioned relation 𝐾 𝑖 (𝑖 = 1, 2, 3, 4, 5), computing the intersection and find the resultant matrix as in table 7. interval valued pentapartitioned neutrosophic graphs with an application to mcdm 85 table 7. the resultant matrix k a1 a2 a3 a4 a5 a6 a1 ([0.2,0.5], [0.3,0.8], [0.5,0.9], [0.5,0.9], [0.3,0.8]) ([0.1,0.5], [0.3,0.8], [0.3,0.8], [0.5,0.9], [0.4,0.9]) ([0.1,0.5], [0.2,0.8], [0.4,0.6], [0.6,0.9], [0.5,0.8]) ([0.1,0.4], [0.3,0.7], [0.4,0.8], [0.5,0.9], [0.5,0.8]) ([0.1,0.4], [0.6,0.9], [0.5,0.8], [0.4,0.9], [0.6,0.9]) ([0.2,0.7], [0.5,0.8], [0.4,0.8], [0.6,0.9], [0.4,0.9]) a2 ([0.1,0.5], [0.3,0.8], [0.4,0.8], [0.5,0.9], [0.4,0.9]) ([0.2,0.5], [0.3,0.8], [0.5,0.9], [0.5,0.9], [0.3,0.8]) ([0.2,0.6], [0.6,0.9], [0.5,0.8], [0.4,0.7], [0.2,0.6]) ([0.1,0.6], [0.3,0.8], [0.4,0.8], [0.5,0.9], [0.5,0.8]) ([0.2,0.6], [0.4,0.8], [0.4,0.6], [0.6,0.9], [0.5,0.9]) ([0.3,0.8], [0.1,0.7], [0.5,0.8], [0.6,0.9], [0.2,0.8]) a3 ([0.1,0.5], [0.4,0.9], [0.5,0.7], [0.6,0.9], [0.2,0.8]) ([0.1,0.5], [0.6,0.9], [0.5,0.7], [0.4,0.8], [0.2,0.7]) ([0.2,0.5], [0.3,0.8], [0.5,0.9], [0.5,0.9], [0.3,0.8]) ([0.4,0.8], [0.5,0.8], [0.6,0.9], [0.5,0.8], [0.4,0.9]) ([0.1,0.3], [0.5,0.8], [0.5,0.9], [0.4,0.9], [0.2,0.7]) ([0.1,0.5], [0.5,0.8], [0.6,0.9], [0.5,0.7], [0.5,0.8]) a4 ([0.2,0.5], [0.3,0.7], [0.4,0.9], [0.5,0.9], [0.5,0.8]) ([0.1,0.5], [0.4,0.8], [0.3,0.8], [0.5,0.9], [0.2,0.8]) ([0.2,0.8], [0.5,0.9], [0.6,0.9], [0.5,0.7], [0.3,0.7]) ([0.2,0.5], [0.3,0.8], [0.5,0.9], [0.5,0.9], [0.3,0.8]) ([0.2,0.5], [0.3,0.8], [0.5,0.9], [0.6,0.9], [0.4,0.9]) ([0.2,0.6], [0.4,0.7], [0.4,0.8], [0.5,0.8], [0.6,0.9]) a5 ([0.2,0.6], [0.6,0.9], [0.5,0.8], [0.6,0.9], [0.6,0.9]) ([0.1,0.4], [0.3,0.7], [0.4,0.6], [0.6,0.9], [0.5,0.8]) ([0.1,0.3], [0.6,0.9], [0.5,0.7], [0.4,0.9], [0.6,0.9]) ([0.2,0.5], [0.5,0.8], [0.4,0.9], [0.5,0.8], [0.4,0.8]) ([0.2,0.5], [0.3,0.8], [0.5,0.9], [0.5,0.9], [0.3,0.8]) ([0.2,0.6], [0.5,0.8], [0.4,0.8], [0.5,0.9], [0.2,0.7]) a6 ([0.2,0.6], [0.5,0.8], [0.4,0.8], [0.6,0.9], [0.3,0.8]) ([0.2,0.7], [0.3,0.7], [0.5,0.8], [0.6,0.9], [0.5,0.9]) ([0.3,0.6], [0.5,0.7], [0.4,0.7], [0.3,0.8], [0.2,0.6]) ([0.2,0.5], [0.3,0.8], [0.5,0.8], [0.5,0.9], [0.6,0.9]) ([0.1,0.5], [0.5,0.8], [0.4,0.8], [0.5,0.9], [0.6,0.9]) ([0.2,0.5], [0.3,0.8], [0.5,0.9], [0.5,0.9], [0.3,0.8]) step 4: by using the score function 𝑆𝑖𝑗 , in the resultant matrix of table 7, find the score matrix as in table 8. table 8. the score matrix of k and the choice values of the attributes 𝐴𝑗 k a1 a2 a3 a4 a5 a6 choice value a1 0.74 0.74 0.76 0.72 0.58 0.72 4.24 a2 0.72 0.74 0.82 0.74 0.74 0.9 4.66 a3 0.72 0.76 0.74 0.68 0.7 0.66 4.26 a4 0.74 0.78 0.78 0.86 0.68 0.74 4.58 a5 0.6 0.74 0.58 0.72 0.74 0.76 4.14 a6 0.74 0.78 0.94 0.68 0.64 0.74 4.52 s. broumi et al./oper. res. eng. sci. theor. appl. 5(3)2022 68-91 86 figure 6. interval valued pentapartitioned neutrosophic directed graph with score values step 5: from the score matrix of table 8, calculate the choice values for each attribute 𝐴𝑖 (𝑖 = 1 𝑡𝑜 6). step 6: arrange the attributes according to their choice values in descending order, the final decision is 𝐴2. 4.66 > 4.58 > 5.52 > 4.26 > 4.24 > 4.14 𝐴2 > 𝐴4 > 𝐴6 > 𝐴3 > 𝐴1 > 𝐴5 by using the proposed decision-making method, the optimal decision is decided. by using the method, the alternatives are arranged in descending order and the second airline is chosen as the best airline with the condition which satisfies all the criteria. 5. discussion interval valued pentapartitioned neutrosophic sets provide a powerful tool to represent the information with imprecise and indeterminate data and have fruitful applications. pentapartitioned neutrosophic sets is an extension of the neutrosophic sets with the membership function classified into five categories. the interval valued pentapartitioned neutrosophic sets which is introduced is an advancement of the pentapartitioned set like each membership representation comes in an interval. in this interval valued pentapartitioned neutrosophic graphs with an application to mcdm 87 paper, the interval valued pentapartitioned neutrosophic sets have been implemented on the graph theoretical concepts and interval valued pentapartitioned neutrosophic graph have been developed. the significant operations of interval-valued pentapartitioned neutrosophic sets and its graphs are investigated. this helps the decision makers more sufficient for taking their input best suit to their domain of reference. the properties of interval valued pentapartitioned neutrosophic graph as cut vertex, bridge, degree are studied and examined with suitable examples. hence, the proposed graphs and their basic properties have enough capabilities to address the related dependability on the indterminate information. a decision-making method have been developed using the interval valued pentapartitioned neutrosophic graph with a numerical illustration. 6. conclusion interval valued pentapartitioned nutrosophic graphs are generalization of pentapartitioned nutrosophic graphs and provide a sufficient space for complex decision-making situations. in this research paper some properties of interval valued pentapartitioned neutrosophic graph as cut vertex, bridge, degree are studied and examined with suitable examples. using the proposed interval valued pentapartitioned nutrosophic graphs, a decision-making method has been developed and applied in a real-life situation with numerical illustrations. in future, concepts can be developed in the interval valued pentapartitioned neutrosophic soft graphs, interval valued quadripartitioned neutrosophic graphs, strong interval valued pentapartitioned neutrosophic graphs, etc. also, one can extend the developed concepts into isomorphic properties and regularity properties in the proposed graph structures. the interval valued pentapartitioned neutrosophic graph can be extended to regular and irregular interval valued pentapartitioned neutrosophic graph, interval-valued pentapartitioned neutrosophic intersection graphs, interval-valued pentapartitioned neutrosophic hypergraphs, and so on. the interval-valued pentapartitioned neutrosophic graph can be used in modeling the network, telecommunication, image processing, computer networks, expert systems…etc. references: ajay, d., & chellamani, p. 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(2020). similarity relations and fuzzy orderings. inf. sci., vol. 3, 177 – 200. https://doi.org/10.1016/s0020-0255(71)80005-1 © 2022 by the authors. submitted for possible open access publication under the terms and conditions of the creative commons attribution (cc by) license (http://creativecommons.org/licenses/by/4.0/). https://doi.org/10.1109/ifsanafips.2013.6608375 https://doi.org/10.1108/md-01-2022-0120 https://doi.org/10.2307/2272014 interval valued pentapartitioned neutrosophic graphs with an application to mcdm said broumi 1,2*, d. ajay 3, p. chellamani 3, lathamaheswari malayalan 4, mohamed talea 1, assia bakali 5, philippe schweizer 6, saeid jafari 7 1. introduction 2. preliminaries 3. interval pentapartitioned neutrosophic graphs 4. application in decision making problem 4.1. algorithm: 4.2. an illustrative example: 5. discussion 6. conclusion references: operational research in engineering sciences: theory and applications vol. 3, issue 3, 2020, pp. 13-28 issn: 2620-1607 eissn: 2620-1747 doi: https://doi.org/10.31181/oresta20303013s * corresponding author. aleksandar.stankovic@masfak.ni.ac.rs (a. stanković), goran.petrovic@masfak.ni.ac.rs (g. petrović), zcojba@ni.ac.rs (ž. ćojbašić), danijel.markovic@masfak.ni.ac.rs (d. marković) an application of metaheuristic optimization algorithms for solving the flexible job-shop scheduling problem aleksandar stanković*, goran petrović, žarko ćojbašić, danijel marković faculty of mechanical engineering, university of niš, serbia received: 11 june 2020 accepted: 10 august 2020 first online: 24 september 2020 original scientific paper abstract. the flexible job shop planning (fjsp) problem is another planning and scheduling problem. it is a continuation of the classic problem of scheduling jobs, where each operation can be performed on different machines, while the processing time depends on the machine being used. fjsp is a difficult np problem that consists of two sub-problems, scheduling problems and scheduling operations. the paper presents a model for solving fjsp based on meta-heuristic algorithms: genetic algorithm (ga), tabu search (ts) and ant colony optimization (aco). the efficiency of the approach in solving the aforementioned problem is reflected in the flexible search of space and the choice of dominant solutions. the results of the computation are graphically represented on the gantt chart. keywords: scheduling, flexible job-shop, genetic algorithm, tabu search, ant colony optimization, local search. 1. introduction the planning of production and production processes has a very important role in the successful functioning of production. planning and scheduling problems occur in almost every field of economics, engineering, up to industrial production. one of the most important production issues is the planning and scheduling of operations. a key reason for scheduling and planning operations is to increase production productivity. scheduling and planning operations can be very easy, but it can also be one of the most difficult scheduling problems, depending on the type of problems and planning conditions. a problem where there is more than one machine available for each operation, where there is flexibility in selecting a machine from a set of alternative machines is called the flexible job shop problem (fjsp). according to the stanković, et al., /oper. res. eng. sci. theor. appl. 3 (3) (2020) 13-28 14 jsp action routine, each job is processed on a machine with a defined processing time, and each machine can only process one operation. in practice, a machine may have the flexible ability to perform more than one type of operation, leading to the modification of the jsp in the fjsp. as pinedo (2008) stated his book, the definition of fjsp can be expressed as a generalization of the workplace and the parallel environment of machines. instead of m machines in a row, there are c centers for working with each work center in parallel with the same number of identical machines. each job has its own route to follow throughout the shop; job j requires processing in each work center on only one machine and each machine can run. if a business on its way through the store can visit the work center more than once, then the b-field contains the rcrc entry for recirculation. the aim of this paper is to test and compare tree meta-heuristic optimization methods in order to minimize the amount of time spent planning and scheduling operations on the available set of machines. the results obtained using different approaches should help managers to identify an appropriate method for this class of problem. there are different approaches to solving fjsp available in the literature, and that will be reviewed in the next section. in the earlier years of research into planning and scheduling problems, exact methods were used in the allocation of resources. today, methods such as constraint programming and simulation methods are being used more and more in the planning world. the objective of this paper is reflected in the application of several meta-heuristic methods, namely tabu search (ts) algorithm, ant colony optimization (aco) and genetic algorithm (ga) and their comparison in the speed of the convergence and accuracy of the solutions. the basic idea is to assess which of the applied algorithms is most applicable for solving fjsp. 2. literature review resource planning and scheduling, as well as the methods used to solve scheduling problems, are gaining ground in many areas of logistics, planning, search, and routing, where this methodology is very significant and applicable. speaking of scheduling (brucker & schile, 1990), they are one of the first scientists to develop a graphical algorithm for planning and scheduling. the algorithms most commonly used today to solve scheduling problems within the fjsp are meta-heuristic algorithms: genetic algorithm (fraser, 1957; bremermann, 1958; holland, 1975), ant colony optimization (dorigo et al., 2006), simulated annealing (kirkpatrick et al., 1983), tabu search (glover & laguna, 1997), particle swarm optimization (kennedy & eberhart, 1995) and others. in the continuation of the work in figure 1, methods are presented on the basis of which it is possible to solve the problems of planning and scheduling resources. figure 1. methods for solving scheduling problems an application of metaheuristic optimization algorithms for solving the flexible job-shop scheduling problem 15 exact methods: the basic feature of exact methods is the accuracy in defining mathematical model as well as finding optimal solutions depending on the size of the data tested. one of the major drawbacks of exacting methods is solving robust models. this group of methods includes some of the basic techniques used to solve scheduling and planning problems: nonlinear, linear, dynamic, integer, and disjointed programming techniques. there are many exact algorithms in the research literature that are used to solve such research problems, such as branch and bound methods (lomnicki, 1965), and they can be defined through various techniques for determining the lower and upper bounds. klein & scholl (1996), as well as blazewicz, et al., (1996) present, in their works, the branch and baund method in the example of resource planning, and the main aim of their work is to assign tasks to a certain number of machines in order to achieve maximum productivity. liu, et al. (1996) and thomalla (2001) present, in their papers, the problem of scheduling by the lagrangian relaxation method, where they prove that the scheduling and planning problem can be successfully solved by this method. robson (1986) worked to refine an algorithm he had already developed to improve temporal complexity. ostergard (2002) proposed a branch and baund algorithm that defines each node with a different color to distinguish the nodes from each other, which at that point is a new tagging methodology. vandaele (2000), hasan & arefin (2017), and aslan et al. (2017) show, in their papers, the problem of planning and scheduling and the success in solving these problems by an integrated method of planning. heuristic methods: alan turing is probably the first to use heuristic algorithms when he broke the german enigma code during world war ii. the next significant step in the evolution of evolutionary algorithms was (holland, 1975) and his associates at the university of michigan in the 1960s and 1970s. such search methods do not guarantee finding the optimal solution, but effectively finding a good enough solution. heuristics are divided into: heuristics that give only one solution within the search and heuristics that give results during the search through a series of iterative solutions. in the works, (sentlelro, 1993), (lagodimos & leopoulos, 2000), (spyropoulos, 2000), (xing & zhang, 2000), we can see a heuristic approach to solving planning and scheduling problems, and also based on the obtained results, it can be seen that this approach gives optimal results. kung & chern (2009) show another way to solve planning problems. in this paper, we can see a scheduling heuristic approach that focuses on solving factory planning and scheduling operations for different job (product) structures. for this planning problem, a heuristic algorithm is proposed, and is referred to in the paper as the factory planning heuristic algorithm, abbreviated as hfpa. xing & zhang (2000) use a method of heuristic approach to solve the problem of planning and scheduling on the problem of m parallel machines with minimal total cost. sobeyko & mönch (2016) present a heuristic approach to solving scheduling problems in large-scale flexible operations. based on the results obtained in this paper, we can conclude that the proposed heuristics arrive at satisfactory solutions quickly. programming constraints: this problem-solving approach belongs to the group of np-hard problems, and the basic feature is the programming of constraints on problem solving in industrial planning and scheduling systems. there are a number stanković, et al., /oper. res. eng. sci. theor. appl. 3 (3) (2020) 13-28 16 of different software applications used in this troubleshooting category that can be used to program scheduling constraints. this approach originated in the field of artificial intelligence. the programming languages most commonly used today to solve artificial intelligence planning and scheduling problems are: matlab, python, c ++, c #, java, and more. when it comes to programming time, constraints planning, and scheduling problems are meta-heuristic methods largely presented. one example of solving scheduling problems can be seen in (stanković, et al., 2019). it should be noted that two approaches are presented in the literature: the deterministic approach and the stochastic approach (pinedo, 2008). the time of completion of the scheduling of operations (products) in the scientific literature is indicated by cmax which represents the total criterion value of the function. examples of solving problems of planning and scheduling can be seen in (jamili, 2018); (fan, et al., 2019). solving fjsps based on meta-heuristic algorithms with programming constraints in the form of time constraints, periods of unavailability can be seen in the papers (zhang, et al., 2011); (stanković, et al., 2019). tamssaouet, et al. (2018) compares several meta-heuristic algorithms with their associates with periods of machine unavailability in the form of preventive and corrective machine maintenance. liaw, (2000) presents the application of a hybrid algorithm with a basic genetic algorithm. further research includes a local tab-based search enhancement process. the results obtained show optimality compared to other search algorithms. simulation methods: simulation modeling has a great ability to present complex systems in a multitude of details, which is its main advantage over other methods. simulation-based planning is used for many operations and system controls, and as a final output, a detailed work plan is obtained. simulation-based planning models need to be more detailed than other typical simulation models. many models in practice with this type of problem can only be solved by the simulation-based optimization method, an approach in which the simulation model is integrated with meta-heuristic search methods such as ga and ts (laguna, et al., 2003). the kanban method is used to increase the productivity of product flow through a single production system and eliminate potential errors at the end of a cycle. kanban is a system that controls the flow of material (resources) through a number of multiple optimization processes. kanban system was developed by toyota engineers taiichi ohno (industrial engineer and businessman) to optimize their manufacturing process. the implementation and success of solving the problems of planning and scheduling operations in small and medium-sized enterprises can be seen in many professional papers. schaefers et al., (2000) is one example of solving product planning and flow problems as well as cost optimization. problems were identified, analyzed and optimized based on the kanban method. japanese industry management technique has been applied in many western countries. graver & price (1987) present the kanban method in their work and use it to solve jsp planning and scheduling problems in the form of simulation, and the final results of the simulation show a significant improvement of the system over previous planning practice. kumar & panneerselvam (2007) present the kanban system and 100 state-of-the-art research papers as well as suggestions for further research. an application of metaheuristic optimization algorithms for solving the flexible job-shop scheduling problem 17 the work load control (wlc) method involves three models: planning, control, and scheduling. the basic task of this method is to solve the problem of production load. in many cases, when planning and selecting a job, the rules of job priority are used, depending on the delivery time of a certain type of product, which is one of the most important factors during the planning process in small and medium-sized enterprises. such methods are of great use in the form of simulations and in solving planning and scheduling problems, which can be seen in papers (thürer et al., 2012); (thürer et al., 2017). 3. methodology accurate and heuristic methods are used to solve planning and scheduling problems. the application of exact methods is limited to simple problems, while more complex meta-heuristic methods are used for complex real systems. the term meta-heuristics was first proposed by fred glover in 1986, while the same author defined meta-heuristics many years later as a high-level problem-independent algorithmic framework that provides a set of guidelines or strategies to develop heuristic optimization algorithms (sörensen & glover, 2013). meta-heuristics are designed to solve complex optimization problems when other optimization methods fail to effectively solve the optimization problem. these methods are nowadays recognized as one of the most important practical approaches to solving many complex problems, and this is especially important for solving many real combinatorial optimization problems, hence the application for the fjsp problem. in general, meta-heuristics can be said to be higher level heuristics. below, we present three meta-heuristic methods that have been applied in solving the problems of allocation and scheduling of fjsp operations. 3.1. tabu search the tabu search (ts) algorithm was first mentioned by a famous scientist glover, (1986). the ts algorithm is a meta-heuristic search method that uses local search methods. search implementation uses structural models that describe average places, that is, possible solutions, or use sets that the user defines as the initial parameters of the problem under consideration. this means that if a potential solution was previously visited at some point in the search or if the set search rules were exceeded, then it will be marked in the tab list. so, the ts algorithm does not take the same solution multiple times as possible solutions during search. tabu searches during previous research have proven to be the optimal search method in a wide range of classic and practical planning problems, and even in the field of neural networks, as can be seen in papers (nowicki & smutnicki, 2005); (zhang et al. 2007). to avoid problems during the search, the size of the taboo list during the search needs to be modified (talbi, 2009). tabu list size is crucial during this type of search. for a taboo list that is too small, a search will tend to cycle through the same possible solutions multiple times, whereas if the taboo list is too stanković, et al., /oper. res. eng. sci. theor. appl. 3 (3) (2020) 13-28 18 large, the lack of available moves can lead to possible errors during the search. the ts algorithm is represented by a pseudocode in table 1 (glover, 1989). table 1. pseudocode of tabu search pseudocode of tabu search sbest ← s0 bestcandidate ← s0 tabulist ← [] tabulist.push(s0) while (not stoppingcondition()) sneighborhood ← getneighbors(bestcandidate) for (scandidate in sneighborhood) if ((not tabulist.contains(scandidate)) and (fitness(scandidate) > fitness(bestcandidate))) bestcandidate ← scandidate end for end if if (fitness(bestcandidate) > fitness(sbest)) sbest ← bestcandidate end if tabulist.push(bestcandidate) if (tabulist.size > maxtabusize) tabulist.removefirst() end if end while 3.2. ant colony optimization the ant colony optimization (aco) method was first proposed by dorigo (1992). ant colony optimization is a population-based meta-heuristic that can be used to find approximate optimal solutions for different test cases. the algorithm is inspired by the behavior of ants in nature. the basic characteristic of the collective behavior of ants is that all members of the colony exchange information about their environment indirectly or directly, i.e. the phenomenon of collective intelligence. it has been discovered in nature that each ant leaves a trail behind, releasing a certain amount of a chemical called a pheromone. the more ants go in one path, the more pheromones, and that is, for each subsequent ant, positive information about the correctness of that path. in this way, the ants indirectly communicate with each other via pheromones. all ants start with a value of 0, which means that no operations are scheduled before the search begins. all nodes have an initial pheromone 1. the pheromone will decrease after each round of search. local search depends on the number of pheromones and the search time, and the total time is calculated based on the extra time required to activate the next oij operation on the available mn machine. a random value is generated for comparison with r0. if the rand value is less than r0, the local search will select the planning route with the maximum amount of pheromone. only the best ants can deposit the pheromone on the path from point a to point b. the total amount of pheromone deposited is calculated based on the an application of metaheuristic optimization algorithms for solving the flexible job-shop scheduling problem 19 expression δτ = 1 / (𝑏𝑒𝑠𝑡 𝑐𝑜𝑠𝑡). the pseudocode of the aco algorithm is presented in table 2 (yang, 2010). table 2. pseudocode of ant colony optimization pseudocode of ant colony optimization objective function f (x), x = (x1,…xn)t [or f (xij) for routing problem where (i, j) € {1, 2, ….. n}] define pheromone evaporation rate ᵞ while (criterion) for loop over all n dimensions (or nodes) generate new solutions evaluate the new solutions mark better locations/routes with pheromone ᵟᵠij update pheromone: ᵠij – (1-ᵞ) ᵠij + ᵟᵠij end for daemon actions such as finding the current best end while output the best results and pheromone distributions 3.3. genetic algorithm genetic algorithm (ga) is an optimization technique used to solve nonlinear or non-differential optimization. the ga was developed by holland in the 1970s of the last century (holland, 1975). the genetic algorithm is characterized by several stages in solving a defined problem, in this case of planning and scheduling. the algorithm mimics the natural selection process, while changes in the genetic structure are possible by mutation of genetic material, the essence of which is to expand the search area and overcome local extremes. crossing in solving ga is a process of combining several units to get a new unit selected, and this type is compared to a natural process like parents and their offspring. new individuals inherit their parents' genes. when it comes to solving planning and scheduling problems, the most common examples are based on a genetic algorithm. one of the most common solutions is based on a coded job scheduling matrix used for scheduling problems on more than one machine, an example of such a matrix can be seen in figure 2. m1: o11; o13; o12 m1: j1; j3; j2 m2: o22; o23; o21 m2: j2; j3; j1 m3: o31; o32; o33 m3: j1; j2; j3 figure 2. job scheduling matrix the mutation involves a random change in the genes of the individuals. mutation achieves uncontrolled alteration of genetic material. by changing the genetic structure, completely new solutions are achieved. the basic goal is to get an individual that cannot be obtained in other stages. stanković, et al., /oper. res. eng. sci. theor. appl. 3 (3) (2020) 13-28 20 this random value initiates a search across the entire allowed domain. the mutation rate should be small from about 0.001% to 0.01% in order to avoid a random, stochastic and uncontrolled procedure. the pseudocode of ga is presented in table 3 (yang, 2010). figure 3. mutation in the case of scheduling machine table 3. pseudocode of ga pseudocode of ga objective function f(x), x= (x1,….,xn)t encode the solution into chromosomes (binary strings) define fitness f (eg, f ∞ f(x) for maximization) generate the initial population initial probabilities of crossover (pc) and mutation (pm) while (t < max number of generations) generate new solution by crossover and mutation if pc > rand, crossover; end if if pm > rand, mutate; end if accept the new solutions if their fitness increase select the current best for new generation end while decode the results and visualization 4. case study this section presents a method for solving fjsps based on three proposed metaheuristic algorithms. the first part of the case studies presents a model for testing algorithms on a classic data set. the efficiency of the algorithms is reflected in the speed of the convergence solution through a series of iterations. the input parameters consist of 25 jobs and 10 machines with a defined processing time of each operation on an individual machine. the mathematical model of solution optimization with objective function and time constraint is represented by the following notation: • j – number of jobs, • m – number of identical machines, • pi,j,k – the processing time of each operation. constraints: j > m > 1, j, m ϵ z+ (1) ∀ p ϵ t, p ϵ z+&1 ≤ p ≤m (2) an application of metaheuristic optimization algorithms for solving the flexible job-shop scheduling problem 21 cost function: f (x)=maxi f(i), i=1,2,…, m (3) the input parameters as well as the results of the optimization problem for all three meta-heuristic algorithms are presented in table 4. table 4. input parameters and results: ts, aco and ga ts parameters maxiter j m 1000 25 10 time for ts algorithm for which an optimal solution is found [s] local best found for 1000 iterations 187 aco algorithm parameters maxiter j m 1000 25 10 time for aco algorithm for which an optimal solution is found [s] local best found for 1000 iterations 182 ga parameters maxiter j m 1000 25 10 time for ga for which an optimal solution is found [s] local best found for 1000 iterations 176 based on the results presented in table 4, it can be concluded that ts, aco and ga give satisfactory results, but that ga gives the most favorable results. on the basis of the obtained results, ga was used in the fjsp case study of planning and scheduling operations in an industrial environment. the case study covers the planning and scheduling of production cycles related to the fjsp solution. the basic structure of the problem being solved relates to a set of jobs that need to be done on the machines, and each job is allocated to a list of activities that are processed in the order. the essence of the problem and the defined activity is to keep the total completion time as low as possible in accordance with the planned operations with defined time of each operation individually. the set of operations performed to make one job complete and therefore a finished product. the mathematical model of fjsp can be represented as follows (özgüven et al., 2010). it is necessary to schedule n products j = {j1, j2, ..., jn}, with each job jj (j = 1,2, ... n) having a predetermined order of operations nj (o1, j, o2, j ,. ... they, j), should be realized in the order given in m machines m = {m1, m2,…, mm}. for a completely flexible problem, each machine can perform only one operation at a time, and the processing time of each operation depends on the machines available and is represented by p, i, j, k (processing time of the operation oi, j on the machine mk). the goal of the problem observed is to assign each operation to a corresponding machine and then determine the arrangement of all the machines assigned to the operations stanković, et al., /oper. res. eng. sci. theor. appl. 3 (3) (2020) 13-28 22 to reduce the target function, in this case minimizing the manufacturing process based on ga. an example of the problem examined is presented in table 5. table 5. input matrix of partial fjsp jobs operations m1 m2 m3 m4 m5 m6 j1 o11 o21 o31 o41 o51 o61 7 3 7 7 6 5 1 5 5 5 7 7 6 6 8 10 3 3 j2 o12 o22 o32 o42 o52 o62 5 10 8 10 8 7 5 11 7 15 8 10 4 10 9 4 10 12 j3 o13 o23 o33 o43 o53 o63 8 9 4 3 5 5 8 6 4 5 7 6 7 7 8 3 j4 o14 o24 o34 o44 o54 o64 5 9 5 15 5 11 10 4 5 9 6 3 11 8 8 9 10 9 j5 o15 o25 o35 o45 o55 o65 9 3 3 6 6 8 9 6 7 4 5 6 9 8 5 4 4 9 j6 o16 o26 o36 o46 o56 o66 8 7 10 7 3 9 8 8 6 5 3 9 10 6 4 8 4 9 it should be noted that not all machines need to be able to perform all the operations as can be seen in the attached table 5. this troubleshooting approach is called partial troubleshooting or partial flexibility where some operations can only be performed on specific machines. such examples are much more common in realworld cases during optimization of production processes. table 5 of the problem described can show 6 jobs and 6 machines, job 1 has 6 operations, the first operation can only be processed by one machine and that machine is m3 with a processing time of 1. we can see the graphical results of the first investigated case of partial research flexibility in figure 4 in the gantt chart. an application of metaheuristic optimization algorithms for solving the flexible job-shop scheduling problem 23 one of the most common means of presenting a result in the case of production planning is gantt charts and as they are called in the research literature, gantt charts. gantt chart is a diagram in a coordinate system in which the horizontal axis is time, and the vertical axis shows the planning tasks on which to determine: the beginning, total duration and end of the cycle, which is the main problem in determining the planning and scheduling in this case of machine and work. another examined case of planning and scheduling is called total fjsp, with each operation being deployable on any of the available m machines, as all machines are capable of performing each operation at a specified time during a specified processing time of each operation. an example of the problem examined is presented in table 6. table 6. input matrix of total fjsp jobs operations m1 m2 m3 m4 m5 m6 j1 o11 o21 o31 o41 o51 o61 7 3 5 5 9 10 11 6 6 5 5 3 9 12 6 7 10 11 7 10 11 7 9 8 8 5 7 8 6 6 9 7 10 7 3 7 j2 o12 o22 o32 o42 o52 o62 7 4 5 3 10 3 8 7 7 5 7 9 7 5 9 11 9 5 5 10 10 10 9 4 7 9 10 9 6 11 7 8 9 10 6 10 j3 o13 o23 o33 o43 o53 o63 5 2 8 9 7 7 6 5 5 5 9 5 9 9 9 7 9 7 4 10 10 10 10 8 8 10 11 7 7 9 9 8 8 9 11 j4 o14 o24 o34 o44 o54 o64 7 5 5 6 2 7 5 5 9 7 5 9 7 7 5 8 9 9 8 9 10 3 9 10 9 9 6 9 8 11 10 9 10 3 10 9 j5 o15 o25 o35 o45 o55 o65 9 6 9 5 3 9 5 5 5 9 5 8 9 5 9 10 5 9 8 8 10 11 6 8 10 10 5 12 9 10 11 6 9 4 11 7 j6 o16 o26 o36 o46 o56 o66 2 2 2 10 9 10 3 5 5 9 5 5 9 9 9 10 10 9 8 3 9 9 6 4 10 9 10 9 4 9 7 7 9 10 9 8 stanković, et al., /oper. res. eng. sci. theor. appl. 3 (3) (2020) 13-28 24 table 6 shows the input parameters of the test problem where we have 6 jobs (products) where each of these 6 jobs has 6 operations, each of which defined operations with machine processing time in minutes can be performed on each machine. as we can see in the previous part of the paper, we call this case complete flexibility. graphical results of the survey can be seen in figure 5. as for the implementation of ga, the experimental results were tested in python and the numerical values were derived on standard ms windows based pc platform. figure 4. graphical representation of the results for the first case in table 5 figure 5. graphical representation of the results for the second case in table 6 5. results and discussion after introductory discussions and clarification of the fjsp, as well as a review of the research literature on the topic of planning, a specific set-up of the problems and an application of metaheuristic optimization algorithms for solving the flexible job-shop scheduling problem 25 results of the planning was made. it is important to note that the tested test data is randomly given. as can be seen in the previous part of the paper, two cases of planning and scheduling were tested, which was at the same time the aim of this problem. table 5 shows that not every machine can perform every operation during the planning and scheduling of operations. partial flexibility is one of the most common causes that can be encountered in manufacturing, it is often the case that not every machine can perform every operation to get the job (product) done. the results of the input data in table 5 are graphically presented in the chart in figure 4 for the first case of partial flexibility. in figure 4, we can see the layout of operations on individual machines depending on the initial constraints. j defines each job in a different color to differentiate jobs (products). on the horizontal axis, time is presented with the criterion function value cmax = 218 units in minutes. regarding testing, it was noted that the search was performed by genetic algorithm with maxiter = 500. ga based search in a python programming language, that is, total planning and scheduling time is 41.63 seconds for the first case tested. on the vertical axis, we can see all 6 machines that are linearly aligned. with regard to the second case examined, it is presented in table 6 and is clearly different from the first case examined. in table 6, based on the input data presented, it is possible to see complete flexibility where each machine can perform each operation with defined time. also, in this case, we have j = 6 jobs (products) and each of the jobs has oij = 6 operations that can be performed on each machine depending on the schedule of operations with a defined processing time of each operation individually. on the horizontal axis, we can see the total time represented by the value of the criterion function cmax = 652 units in minutes. the value of the criterion function representing the total time of completion of all operations and the completion of the planning process is represented by the cmax mark, which could be seen in the previous part of the paper and is presented in minutes. the gantt chart presents a detailed schedule of operations that will be performed on machines. the machines are represented linearly on the vertical axis. the total simulation time based on ga in a python programming language is 90.89 in seconds. the objective of the examined problem of planning and scheduling operations was successfully realized, as can be seen from the attached results. 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(2007). a tabu search algorithm with a new neighborhood structure for the job shop scheduling problem. computers & operations research, 34(11):3229-3242 zhang, g., gao, l., & shi, y. (2011). an effective genetic algorithm for the flexible jobshop scheduling problem, expert systems with applications, 38(4):3563–3573. © 2020 by the authors. submitted for possible open access publication under the terms and conditions of the creative commons attribution (cc by) license (http://creativecommons.org/licenses/by/4.0/). an application of metaheuristic optimization algorithms for solving the flexible job-shop scheduling problem aleksandar stanković*, goran petrović, žarko ćojbašić, danijel marković 1. introduction 2. literature review 3. methodology 3.1. tabu search 3.2. ant colony optimization 3.3. genetic algorithm 4. case study 5. results and discussion references plane thermoelastic waves in infinite half-space caused operational research in engineering sciences: theory and applications vol. 1, issue 1, 2018, pp. 40-61 issn: 2620-1607 eissn: 2620-1747 doi: https://doi.org/10.31181/oresta19012010140s e-mail address: mirko.stojcic@sf.ues.rs.ba, mirkostojcic1@hotmail.com application of the anfis model in road traffic and transportation: a literature review from 1993 to 2018 mirko stojčić faculty of transport and traffic engineering doboj, university of east sarajevo, vojvode mišića 52 doboj, bosnia and herzegovina received: 19 september 2018 accepted: 02 november 2018 published: 19 december 2018 review paper abstract: the paper’s focus is on researching the application of the anfis (adaptive neuro fuzzy inference system) model in traffic and transport through a review of relevant papers. the anfis, as an element of artificial intelligence, is widely used in intelligent transport systems. all collected papers are divided into 7 sub-areas, namely: 1) vehicle routing, 2) traffic control at intersections with light signaling, 3) vehicle steering and control, 4) safety, 5) modeling of fuel consumption, engine performance and exhaust emissions, 6) traffic congestion prediction, and 7) other applications. for each sub-area, the analysis of the proposed models is performed with a tabular overview of respective input and output variables, while in the third section the discussion of the results is given. it is found that the steering and control of vehicles represent a sub-area with the highest percentage in the total number of examined papers, while the security applications take second place. key words: anfis, intelligent transportation systems, light signaling, vehicle routing, prediction, modeling 1 introduction the development of science and technology has affected a wider study as well as application of the solutions based on artificial intelligence in various areas. intelligent transportation systems represent a scientific and engineering discipline that implies integration of modern information and communication technologies into transport infrastructure and vehicles. therefore, it is evident that smart solutions find their application in this field as well. some of the most commonly used elements of artificial intelligence are fuzzy logic, artificial neural networks, and genetic algorithms. in addition, there are popular combinations of techniques such as: neurofuzzy systems, genetic fuzzy systems, and genetic programming neural networks (kar et al., 2014). application of anfis model in road traffic and transportation: a literature review from 1993 to 2018 41 often, though, a realistic system cannot be modeled precisely due to either insufficient or unclear information. when that happens, the solutions based on traditional computer methods do not yield satisfactory results. therefore, an emphasis is placed on the neuro-fuzzy systems, which represent integration of fuzzy logic and artificial neural networks. fuzzy logic is an extension of the classical logic so that the variables can have a certain degree of belonging to either true or false. the basic elements for the processing of ambiguities and uncertainty in the fuzzy logic are the fuzzy sets which are mathematically represented by the membership functions. the fuzzy technologies are human-oriented, which means they simulate the human way of thinking and conclusion-making based on the linguistic variables, which are represented by fuzzy sets that linguistic expressions are associated with. in addition to the advantages, some of which are already mentioned, the disadvantage of the fuzzy logic is the impossibility of its adaptation. this problem is solved by artificial neural networks representing models of the human brain with interconnected basic process elements artificial neurons. the main features that distinguish them are the ability to learn from examples and adaptability, which is characteristic of man, as well as in the case of the fuzzy logic (arora & saini, 2014). each neural network is defined with three properties: the type of artificial neurons, i.e. the type of their transfer function, the connection between the nodes and their structure, and the training algorithm. it can be said that the fuzzy logic and the artificial neural networks complement each other. one of the most commonly used neuro-fuzzy systems is an adaptive neuro-fuzzy inference system (anfis), first introduced by jang 1993 (jang, 1993). the problems that have led to the development of the anfis are the lack of a unique methodology that would transform human knowledge into the base of fuzzy rules, as well as the need for a method that will provide, for certain inputs, the minimum deviation of outputs from the expected values. the anfis model is trained by the input-output pairs (vectors), which adjusts the parameters of the membership functions of the input and output variables (jang, 1996). the training algorithm is hybrid and combines the gradient descend method and the last square estimation (lse). the fuzzy inference is based on the takagi-sugeno system whose typical rule has the form: if a then b, where a and b fuzzy sets are described by the membership functions. the anfis has a five-layer structure, and the network is a feed-forward type where neurons transmit their outputs to neuron inputs in the next layer and so on, without a cycle. the most important applications of the observed neuro-fuzzy model are the modeling of non-linear systems, chaotic time series prediction, and clustering. the main objective of the survey is to review the anfis application in the field of road traffic and transportation, as components of the intelligent transportation systems. by searching the web and the google scholar bibliographic database, the papers that deal with this topic since 1993 have been collected. all papers are divided into 7 sub-areas, namely: 1) vehicle routing, 2) traffic control at intersections with light signaling, 3) vehicle steering and control, 4) safety, 5) modeling of fuel consumption, engine performance and exhaust emissions, 6) traffic congestion, and 7) other applications. following the introduction, the paper is structured in three sections. the literature review deals with the analysis of papers in individual sub-areas with tabular representations of the variables of the proposed anfis models. the stojčić/oper. res. eng. sci. theor. appl. 1 (1) (2018) 40-61 42 discussion is in the third section where the statistical review of the papers by the year of publication is given. on the basis of everything stated in the paper, the last section gives a conclusion. 2 literature review 2.1 vehicle routing an increasing number of vehicles on roads, especially in cities, are causing great traffic jams as existing roads do not have the required capacity. in order to avoid or mitigate this problem, the choice of the optimal route of the vehicle is a very big challenge. apart from avoiding traffic jams, the optimal route is selected on the basis of several criteria, some of which may be: travel time, distance, fuel consumption, road works, etc. it is evident that it is very difficult to find a route that meets all the requirements. abbas et al. (2011) propose a model that represents integration of artificial neural networks, a neuro-fuzzy model, and an ant colony optimization algorithm to select the optimal route. all necessary input data are provided by the traffic control center. the proposed model is capable of dynamically adjusting the route change. the choice of route for transport of dangerous goods in the city is a very complex task. in (pamucar et al., 2016), a modified anfis model with the dijskstra algorithm for determining the optimal route is proposed, i.e. anfis-d model. after training with the artificial bee colony algorithm, for the new input data, the model gives the value of the cost-risk ratio for each branch of the network individually. the role of the dijkstra algorithm is to find a route in the network that minimizes the total value of the given ratio. the described model was tested in (pamucar et al., 2016a) in the selection of optimal routes for the transport of oil and oil derivatives in belgrade, serbia. similarly to the described model, pamučar & ćirović (2018) represent the anfigs (adaptive neuro fuzzy inference guidance system) model for choosing the route of vehicle movement under the conditions of uncertainty. in the neuro-fuzzy system the knowledge of the dispatcher is accumulated and seven criteria are defined that influence the selection of the route. the clustering technique is applied in the paper. one of the main advantages of this model is its ability to dynamically adapt to unpredictable events on the route. in the conditions of natural disasters, it is very important to respond quickly and provide assistance to the affected areas as soon as possible. under such conditions, the roads are often damaged but other factors that adversely affect the rapid route planning appear as well. gharib et al. (2018) use the anfis in the first step of selecting a route for classification of critical areas into two clusters: 1) areas that can be assisted by road and 2) areas with an access only from the air. table 1 shows the input and output variables for the listed anfis models. application of anfis model in road traffic and transportation: a literature review from 1993 to 2018 43 table 1 input and output variables of the anfis models for vehicle routing author/year input variables output variables abbas et al. (2011) distance; traffic flow; environment monitoring; width; road condition; traffic lights pheromone level (ant colony) pamučar et al. (2016), pamučar et al. (2016a) carrier’s operating costs; emergency response; risk associated with the environment; risk of an accident; consequences of an accident; risk associated with infrastructure; risks of terror attack/hijack cost/risk value pamučar & ćirović (2018) type of road surface; travel distance; travel time; route capacity; traffic capacity; road capacity; the existence of alternative roads along the length of the route preference of the dispatcher to select a particular route gharib et al. (2018) road slope; weather conditions; intensity of disaster; population density; road risk; distance of vehicle; distance from airport; road width cluster (1 or 2) 2.2 traffic control at intersections with light signaling the application of light signalization to control traffic at intersections is one of the most common and most effective methods. however, a great lack of this kind of regulation is that the intervals are fixed, which can often cause unnecessary delays and congestions. an intelligent solution consists in forming an adaptive model that adjusts intervals to the real state of traffic at the intersection. such a model is presented in (udofia et al., 2014). its basis is the anfis model with two inputs. for training data, the urgency degree as an output variable is calculated analytically based on the input variables for each phase of the crossroads individually. the model uses real data collected by the sensor and gives a certain output based on them. the next green interval is assigned to the phase with the highest urgency degree. the model was tested at a real intersection and the results confirm its effectiveness. the described anfis model is also used in (george et al., 2015) within a system that receives incoming traffic data from the processing of video data. lai et al. (2015) also use the same inputs, while the output variable is an extension time of the duration of the green light interval. the testing has found that the performance of the proposed model is better than that of the traditional and fuzzy controllers. the anfis traffic control model can also be tested using the graphical user interface in the matlab software package, which was done in (abiodun et al., 2014). the model proposed in (wannige & sonnadara, 2008) has two inputs representing the number of vehicles entering the intersection in both directions. the model training was performed for the given input values and for calculating an optimal time of the green light interval based on them. according to seesara & gadit (2015), two input variables were selected based on the advice of competent institutions and traffic experts. in this paper, comparison of performance is performed between the anfis and the fuzzy controller with the anfis giving better results. arraghi et al. (2014) observe four stojčić/oper. res. eng. sci. theor. appl. 1 (1) (2018) 40-61 44 input variables for traffic control at the four-way intersection. in this case, the anfis justifies the application because it shows better testing results than fuzzy controllers and fixed-time models. korkmaz & akgüngör (2016) use the anfis to model vehicle delays at vehicle intersection, and, according to gokdag et al. (2007), a model of the same purpose has a different set of input variables. comparison of the prediction results with those of the usual methods, such as webster, hcm, ddf and ssm, indicates that the anfis represents a very promising modeling method. testing was carried out in the case of an intersection in erzurum, turkey. similar research is also presented in (hasiloglu et al., 2014), where comparison was done, instead of the ddf, with the multiple regression analyzes method. the observed variables are the same for the two above mentioned models. table 2 provides an overview of the input and output variables of the anfis models by authors. table 2 input and output variables of the anfis model for traffic control at intersections with light signaling author/year input variables output variables udofia et al. (2014) waiting time; queue length urgency degree george et al. (2015) waiting time; queue length urgency degree lai et al. (2015) waiting time; queue length extension time of the next phase abiodun et al. (2014) number of vehicles on the arrival side; number of vehicles on the queuing side extension time of green light wannige & sonnadara (2008) vehicle inflow in two roads green light time of one lane seesara & gadit (2015) arrival rate of the particular phase; last time vehicles that have not passed during last green phase green time extension arraghi et al. (2014) queue length of vehicles at each approaching link (for 4 links) green time for the current phase gokdag et al. (2007) time; number of approaching vehicles in the green duration; number of queuing vehicles in the red duration vehicle delay korkmaz & akgüngör (2016) cycle time of signalization; green time; degree of saturation vehicle delay hasiloglu et al. (2014) time; number of approaching vehicles in the green duration; number of queuing vehicles in the red duration vehicle delay application of anfis model in road traffic and transportation: a literature review from 1993 to 2018 45 2.3 vehicle steering and control a large number of controllers for control and stability in vehicles are based on neuro-fuzzy systems. selma & chouraqui (2012) propose anfis models to control vehicle paths based on previous training. two models for positioning the x and y axis have been developed. the model was tested by the simulation method and the results show its efficiency. according to saifizul et al. (2006), the anfis model for steering has the task of keeping the lateral error and the yaw error at an acceptable level while driving. in this case, the input data are collected by means of camera on-board, which is a much simpler solution than the existing ones, which implies the installation of a magnet or wiring on the road. the esc (electronic stability control) is an unavoidable system in newer cars that significantly improves passenger safety. the ecs systems mainly use measured yaw velocity of the chassis and the sideslip angle (the angle between the directions of the vehicle's velocity and its chassis). the problem is the determination of the given angle because it is difficult to measure with the sensor. a sideslip angle modeling involves the use of various methods, and boada et al. (2015), propose anfis for this purpose. in (boada et al., 2016), the same author uses the kalman filter to evaluate the sideslip angle, in combination with the anfis model. however, hou et al. (2008) uses the sideslip angle as one of the input variables in the integrated chassis control model. model training and testing are carried out using the simulation method. automatic transmission control in modern vehicles is done with the computer that selects the optimal shift based on the input signals received by the sensors. however, in some driving conditions such a system is not efficient (low speed, vehicle load, etc.). a potential solution is presented in (li et al., 2007) and is based on the anfis model. perez et al. (2010) present an anfis model for controlling the braking and acceleration of autonomous vehicles that tend to expand in the future. the tests confirm the efficiency of the anfis model in determining the value of the output variables. autonomous vehicles and the anfis model are also studied in (al mayyahi et al., 2014), where four such models are developed to avoid obstacles and reach the desired position. when it comes to electric vehicles, using the observed neuro-fuzzy model in the regenerative braking system, it is possible to provide greater autonomy (sindhuja et al., 2014). the system involves the use of an electric motor as a generator in braking, thus recycling the spent energy into a rechargeable battery. the anfis model is also applicable in the case of hybrid drives where it minimizes engine fuel consumption with internal combustion and maximizes torque (mohebbi et al., 2005). eski & yıldırım (2017) describe the use of anfis model for the electronic regulation of throttle of heavy vehicles. car parking is a demanding action, sometimes for experienced drivers, and if it is a truck with a trailer, the problem becomes very complex. due to the non-linearity of the movement of such a vehicle, the observed neuro-fuzzy system was applied by azadi et al. (2013). in the first stage of the proposed model, the vehicle in advance takes an adequate position in order to then position it back to the parking place. the use of sensors that provide environmental information is unavoidable in this case. several authors dealt with the use of an anfis suspension model to improve safety and travel comfort (shuliakov et al., 2015; nugroho et al., 2014; stojčić/oper. res. eng. sci. theor. appl. 1 (1) (2018) 40-61 46 kothandaraman & ponnusamy, 2012). depending on the input data, the model is capable of adapting the characteristics of the shock absorbers and other elements that make up the mentioned system. an overview of the input and output variables of some anfis models with application in vehicle steering and control systems is shown in table 3. table 3 input and output variables of the anfis model in vehicle steering and vehicle control systems author/year input variables output variables selma & chouraqui (2012) x position, y position x position, y position saifizul et al. (2006) lateral error; angle between longitudinal direction and local road tangent at look-ahead distance; yaw rate steering angle boada et al. (2015); boada et al. (2016) lateral acceleration; yaw rate; steering angle; longitudinal velocity; yaw rate/longitudinal velocity sideslip angle hou et al. (2008) yaw velocity discrepancy; sideslip angle discrepancy brake/throttle li et al. (2007) vehicle velocity; air damper angle shift point perez et al. (2010) speed error; acceleration brake/throttle sindhuja et al. (2014) distribution of braking force; (front)battery’s state of charge (soc); speed of the motor braking force ratio al mayyahi et al. (2014) angle difference (for the first and second controller); front, right and left distance (for for the third and fourth controller) right/left angular velocity mohebbi et al. (2005) desired torque; battery’s state of charge (soc) throttle angle of the internal combustion engine eski & yıldırım, (2017) two different random inputs of the heavy duty vehicle speed servo motor speed azadi et al. (2013) tractor yaw angle; trailer yaw angle; horizontal distance from the wall steering angle shuliakov et al. (2015) turn rate; angular transducer output deviation angle of a stabilization object nugroho et al. (2014) velocity of sprung mass (car body); relative velocity between sprung mass and unsprung mass/velocity of unsprung mass (wheel); relative velocity between the sprung mass and unsprung mass fuzzy-skyhook force/fuzzy-ground force kothandaraman & ponnusamy, (2012) suspension deflection; sprung mass velocity actuator force application of anfis model in road traffic and transportation: a literature review from 1993 to 2018 47 2.4 safety security has always been the highest priority in traffic, and today a large number of technologies (video surveillance, speed control, etc.) are present within intelligent transport systems, which have the task of raising safety to an even higher level (rahimi, 2017). every day, an increasing number of vehicles are in the streets and so are drivers who do not share the same experience and abilities. statistics say that the driver's behavior is the main cause of traffic accidents. bearing this in mind, a number of authors have paid attention to the development of various driver behavior prediction models, some of which are listed in (kumar & prasad, 2015). the anfis application for the car following model is presented in (poor et al., 2016; khodayari et al., 2010). similarly, ghaffari et al. (2015) represent a new approach to modeling the car following when changing the lane of the leading vehicle. such a maneuver can be viewed as a transient condition because the vehicle deviates from the conventional modeling for a certain time. the same author deals with the modeling of the overtaking path in (ghaffari et al., 2011, 2011a), as one of the most demanding traffic operations. modern collision avoidance systems involve the use of various sensors in order to collect the data necessary for determining the parameters. all this raises the price and complexity of such systems. bearing this in mind, saadeddin et al. (2013) develop a low-cost system based on a combination of the ins (inertial navigation system) data and a gps (global positioning system) in their research. this integration is realized through the idanfis (input-delayed anfis). the data provided by satellite systems have been used as inputs in (sun et al., 2017) in combination with a neuro-fuzzy model to develop a rear-end impact prevention system. dadula & dadios (2016) represent an anfis which has the function of detecting critical events in public passenger transport based on characteristic sounds. the system can differentiate the normal circumstances from alarming (e.g. shooting) with a high percentage of accuracy. pedestrians are a very vulnerable group of participants in the traffic. for the sake of their protection, various mechanisms can be implemented in intelligent transport systems. one of them is modeling the pedestrian decision to cross the street with the help of artificial neural networks and the fuzzy logic, as presented in (ottomanelli et al., 2010). determining critical points along the road can be of great use in preventing traffic accidents. in the case that statistical methods cannot provide reliable results, e.g. because of the lack of data, the authors use the observed neuro-fuzzy system that, based on the physical characteristics of the path and environmental factors, predicts the risk spots. such studies are presented in (hosseinlou & sohrabi, 2009; effati et al., 2014). prediction of traffic accidents in real time using anfis is presented in (liu & chen, 2017). the authors analyze the traffic flow factors just before an accident occurs. by comparing the results with other models, it can be concluded that the anfis in this case also shows better performance.mtraffic sign detection is an important part of the driver assistance system because it allows automatic adjustment to the conditions prescribed for them. billah et al. (2015) propose an anfis model for the recognition of circular signs based on the data obtained by image stojčić/oper. res. eng. sci. theor. appl. 1 (1) (2018) 40-61 48 processing and video processing. the recognition accuracy is more than 98%, which sufficiently highlights the model’s capabilities. in order to improve the vehicle stability as well as its handling, it is important to adjust the speed to the road geometry. the model that performs this function is presented in (wankhede et al., 2011). its output represents a certain degree of acceleration or deceleration of the vehicle, depending on the current acceleration and winding of the road. table 4 provides an overview of the security applications of the anfis model with input and output variables. table 4 input and output variables of the anfis model in security applications author/year input variables output variables poor et al. (2016) distance difference (between cars); velocity difference; speed of the front car; driver reaction time acceleration of following vehicle khodayari et al. (2010) relative speed; relative distance; acceleration of leading vehicle acceleration of following vehicle ghaffari et al. (2015) distance between follower and front vehicle; relative acceleration of these two vehicles; velocity of follower; acceleration of follower acceleration of following vehicle ghaffari et al. (2011) lateral coordinate; longitudinal coordinate; velocity; acceleration; movement angle; lateral coordinate; longitudinal coordinate ghaffari et al. (2011a) velocity; acceleration; jerk; heading angle; heading angle race acceleration; heading angle saadeddin et al. (2013) position and velocity components (x, y, and z axis) from ins error in ins position and velocity sun et al. (2017) relative distance; relative velocity; relative heading warning status dadula & dadios (2016) 12 mel frequency cepstral coefficients (mfccs) for each audio frame crisis condition or normal condition ottomanelli et al. (2010) vehicle’s speed; vehicle’s distance; interval between vehicle arrival and pedestrian arrival at the crossing (or gap) decision (wait or cross) hosseinlou & topographical and geometrical accident frequency of the application of anfis model in road traffic and transportation: a literature review from 1993 to 2018 49 sohrabi (2009) drawings of the road; amount of traffic volume per day; amount of hourly traffic volume in the day road effati et al. (2014) roadway geometry; environmental factors danger value liu & chen (2017) average speed; volume; occupancy in 30-second aggregation intervals (9 traffic flow variables) crash risk value billah et al. (2015) total black pixel; entropy; contrast; correlation; energy; homogeneity label which means a specific sign wankhede et al. (2011) angle curvature; acceleration acceleration 2.5 modeling of fuel consumption, engine performance and exhaust emissions fuel consumption in the world is growing rapidly every day, while, at the same time, the world reserves are decreasing. in addition to the problem of energy shortages, the problem of increasing pollution is present, that is, the problem of harmful substances emissions into the atmosphere. traffic and transport activities constitute a very large share of the total fuel consumption, and therefore, studies have focused on optimization. to do this, it is necessary to develop models for the consumption prediction. the model presented in (massoud et al., 2014) takes into account the interaction of transport and land use in urban areas so that the planners can efficiently analyze and plan fuel consumption. when it comes to passenger cars, the anfis prediction model is proposed in (syahputra, 2016; atmaca et al., 2001). according to abdallat et al. (2011), using the given model, it is possible to estimate the need for the amount of fuel for the transportation of the whole country. in the concrete case, the research was carried out for jordan. diesel fuel is mostly used for trucks, and in order to reduce co2 emissions, the use of alternative fuels, such as biodiesel, is increasingly considered. many studies deal with analyzing the effects of the addition of diesel fuel. the authors propose anfis models that have the task of predicting engine performance and concentration of harmful substances of exhaust gases when using such mixtures (hosoz et al., 2013; özkan et al., 2015; ghanbari et al., 2015; rai et al., 2015). table 5 provides an overview of the anfis model with application in modeling fuel consumption, engine performance and exhaust emissions. stojčić/oper. res. eng. sci. theor. appl. 1 (1) (2018) 40-61 50 table 5 input and output anfis variables for modeling fuel consumption, engine performance and exhaust emissions author/year input variables output variables massoud et al. (2014) land use; transportation energy consumption syahputra (2016) car weight; year miles per gallon atmaca et al. (2001) car weight; year miles per gallon hosoz et al. (2013) biodiesel content in the fuel; engine speed; engine load brake power; brake specific fuel consumption; brake thermal efficiency; emissions of hc, co, no; exhaust gas temperature özkan et al. (2015) types of engine fuels; injection pressure; speed torque; specific fuel consumption; air consumption; efficiency; lambda values ghanbari et al. (2015) diesel–biodiesel and nano particles blends; speed engine power; torque; brake specific fuel consumption; emission components rai et al. (2015) percentage load; percentage liquefied petroleum gas; injection timing brake specific energy consumption; brake thermal efficiency; exhaust gas temperature; smoke abdallat et al. (2011) annual number of vehicles; vehicle owner level; income level; fuel prices energy consumption (in tons of oil) 2.6 traffic congestion prediction traffic congestion is a part of everyday life in big cities, which has a negative impact on life quality because of considerable time spent. in addition to time application of anfis model in road traffic and transportation: a literature review from 1993 to 2018 51 expenditure, it is necessary to consider higher fuel consumption, which means more air pollution. due to a number of problems caused by traffic jams, intelligent transportation systems should provide mechanisms to anticipate and avoid them (joshi & hadi, 2015). zaki et al. (2016) present a framework for short-term prediction, where, apart from the anfis, a model based on the hidden markov models is being developed. the same variables are taken into account by shancar et al. (2012) in their model. kukadapwar & parbat (2015) represent an anfis model that uses real-time traffic data for the prediction of jams in nagpur city, india. an overview of these models is given in table 6. table 6 input and output variables of the anfis model for predicting traffic congestion author/year input variables output variables zaki et al. (2016) speed; density level of congestion kukadapwar & parbat (2015) speed reduction rate; proportion of time traveling at very low speed (below 5 kmph) compared with total travel time; traffic volume to roadway capacity ratio congestion index shankar et al. (2012) speed; density level of congestion 2.7 other applications for the purpose of surveillance, future planning and efficient management of the transportation system of a country, it is necessary to have accurate data on the classes and number of vehicles. intelligent transportation systems include various technologies, and the observed neuro-fuzzy vehicle classification system is proposed in (maurya & patel, 2015). the authors take into account the physical dimensions of the vehicle, such as the wheelbase and the average distance of the wheels on the same track. vehicle activated signs to warn drivers of over speeds are a very useful mechanism for intelligent transportation systems. however, if the threshold of speed is adapted to the conditions and dynamics of traffic, the benefits become even greater (jomaa et al., 2015). the prediction of travel time can be realized mostly on the basis of statistics or artificial neural networks. statistical solutions often do not yield satisfactory results due to the non-linear nature of the dependencies of the observed variables. therefore, the application of neural networks, more precisely the anfis model is more appropriate in this case (maghsoudi & moshiri, 2017). thipparat & thaseepetch (2012) propose an anfis model for predicting the possibility of sustainability of the highway construction. at the design and planning stage, expert knowledge is collected in order to evaluate some of the influential factors and, based on this, deduce the conclusion on sustainability. stojčić/oper. res. eng. sci. theor. appl. 1 (1) (2018) 40-61 52 the selection of an optimal vehicle for transportation in the serbian army based on a given neuro-fuzzy model was presented in (pamučar et al., 2013). the model is capable of simulating the decision-making process, as do logistics officers. in (ghaffari et al., 2012), the subject of research is a prediction of the future status of the vehicle with the stop&go system. the developed model can reduce the likelihood of impact on the rear of the vehicle, and in addition, improve the comfort experience during city driving. since traffic is an important source of noise, sharma et al. (2014) present an anfis model for predicting the value of the mentioned variable. vehicle speeds, traffic flows and the use of siren can be listed as the main influencing factors. table 7 provides an overview of the anfis model with applications in intelligent transportation systems. table 7. input and output variables of the anfis model for various applications in intelligent transportation systems author/year input variables output variables maurya & patel (2015) wheelbase; average track light commercial vehicle/ car-jeepvan/two axle trucksbus/three axle truck/ multi axle trucks jomaa et al. (2015) time of day; traffic flow; standard deviation of mean vehicle speeds 85th percentile speed for each hour on the day maghsoudi & moshiri (2017) vehicle speed; road occupation coefficient; traffic flow travel time thipparat & thaseepetch (2012) geometrics and alignments; earthworks; pavement; drainage; retaining walls; slope protection; landscape and ecology… (14 groups, 60 variables) sustainability level of highway design pamučar et al. (2013) reliability of the means of transport; mobility of the means of transport in field conditions; exploitation of the cubage of transport; cost of tonal kilometer preferential dispatcher ghaffari et al. (2012) relative speed; relative distance; acceleration of follower vehicle; velocity of follower vehicle acceleration of follower vehicle in next steps sharma et al. (2014) road traffic flow; vehicle speed; honking traffic noise application of anfis model in road traffic and transportation: a literature review from 1993 to 2018 53 3 discussion the adaptive neuro-fuzzy inference system provides wide application in road traffic and transportation. in this review, 62 papers were collected for a period of 25 years of its study. fig. 1 shows the number of papers published per year. it can be concluded that the application of the anfis in the observed area was not the subject of research until 2001, followed by a break until 2005. since then, the number of papers per year has grown exponentially in order to record the highest value in 2015. nevertheless, in the last few years, there has been a clear decrease in interest in studying the given topic. fig. 1 number of papers per years the collected papers are divided into 7 sub-areas, as already discussed in section 2. fig. 2 shows percentage share of the papers from each sub-area in the total number. it is obvious that the vehicle steering and control make up the largest percentage, 24%, and the safety is immediately behind with 23%. ultimately, the anfis application in the area of vehicle steering and control, in addition to driving comfort, aims at increasing passenger safety. the smallest number of authors dealt with predicting traffic congestion with the help of the observed neuro-fuzzy model. stojčić/oper. res. eng. sci. theor. appl. 1 (1) (2018) 40-61 54 fig. 2 participation of individual sub-areas in the total number of collected papers table 8 gives an overview of the number of papers by individual areas and by year of publication, with the years with no posts left in table. if observed in 2015, the greatest number of papers is published from the sub-area of traffic control at intersections with light signaling and modeling of fuel consumption, engine performance and exhaust emissions. the second year in terms of the number of published papers is 2014 where the largest number of papers is from the sub-area of traffic control at intersections with light signaling. table 8 number of papers by sub-areas and year of publication year vr tc sc s mf cp oa 2001 1 2005 1 2006 1 2007 1 1 2008 1 1 2009 1 2010 1 2 2011 1 3 1 2012 2 1 2 2013 1 1 1 1 2014 4 3 1 1 1 2015 3 2 2 3 1 2 2016 2 1 1 2 1 1 2017 1 2 1 2018 2 * vr – vehicle routing; tc – traffic control at intersections with light signaling; sc – vehicle steering and control; s – safety; mf – modeling of fuel consumption, engine performance and exhaust emissions; cp – traffic congestion prediction; oa – other applications application of anfis model in road traffic and transportation: a literature review from 1993 to 2018 55 the total number of the sources dealing with the topic 60, comprising 41 journals and 19 conferences. when it comes to the number of papers published by a single source, only two magazines have two published papers, namely,  mechanical systems and signal processing, and  international journal of scientific and engineering research. depending on the purpose of the anfis model itself, authors use different input and output variables, but in a single sub-area, there are many cases in which they have opted for the same. the sets of values of the observed variables are obtained mainly in two ways, which are measurements and simulation methods in one of the softwares. also, model testing and validation are in many cases performed in a simulation environment. for the functioning of anfis in real systems, such as road vehicles and generally intelligent transportation systems, sensors play a key role in providing input data. model outputs are forwarded as information to the user or used as an input of an actuator or a separate system that needs to perform a particular action. the basic limitation of this paper is the possibility of not including or failing to find all the referential papers from the observed area. in addition, papers in nonenglish languages are not taken into consideration. conclusions the paper analyzes the application of the anfis model in the field of road traffic and transportation. it presents an overview of the papers, while the proposed models for specific purposes are theoretically analyzed with the results tabulated and graphically presented. it can be concluded that the use of anfis in traffic is largely due to its ability to model non-linear systems ans well as its ability of adaptability (learning from examples). a key step in developing the anfis model is the correct choice of input variables depending on the desired output. in addition, in order for the model to be trained, it is necessary to collect adequate data. the results of the testing of the observed model show its superiority in comparison to the classical, previously used models. some authors combine the anfis with other techniques; hence, such modified models as anfis-d and anfigs. given that the field of intelligent transport systems develops every day, new opportunities for potential applications of anfis are being created. sensors for data acquisition have a very important role as the goal is to provide accurate inputs to the model. future research could aim at analyzing the anfis model application to other modes of transport. references abbas, s., khan, m. s., ahmed, k., abdullah, m., & farooq, u. 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(2011). intelligent speed adaptation system with hybrid algorithm. international journal of computer science and network security, 11(1), 97. application of anfis model in road traffic and transportation: a literature review from 1993 to 2018 61 zaki, j. f., ali-eldin, a. m. t., hussein, s. e., saraya, s. f., & areed, f. f. (2016). framework for traffic congestion prediction. international journal of scientific & engineering research, 7(5), 1205-1210. özkan, i̇. a., ciniviz, m., & candan, f. (2015). estimating engine performance and emission values using anfis/anfis kullanılarak motor performans ve emisyon değerleri tahmini. international journal of automotive engineering and technologies, 4(1), 63-67. http://dx.doi.org/10.18245/ijaet.95440 operational research in engineering sciences: theory and applications vol. 3, issue 2, 2020, pp. 87-110 issn: 2620-1607 eissn: 2620-1747 doi: https://doi.org/10.31181/oresta2003087b * corresponding author. dbozanic@yahoo.com (d. božanić), bicbl@yahoo.com (d. jurišić), drazan.erkic@hotmail.com (d. erkić) lbwa – z-mairca model supporting decision making in the army darko božanić 1*, dragiša jurišić 2, dražan erkić 3 1 university of defence in belgrade, military academy, belgrade, serbia 2 security research centre, banja luka, bosnia and herzegovina 3 police department zvornik, ministry of internal affairs republic of srpska, bosnia and herzegovina received: 19 june 2020 accepted: 24 july 2020 first online: 25 july 2020 original scientific paper abstract: the paper presents a hybrid model lbwa – z-mairca used to support decision making in the selection of a location of a camp (camp space), which has a role of providing individuals and army units with regular life and operation conditions in the field, i.e. in the conditions outside the barracks. the paper defines and explains the criteria affecting the selection of a camp (camp space), and the lbwa method is used to define the weight coefficients of the criteria. using the mairca method, which is modified with z-numbers, it is selected the best alternative. in the final phase of the model development, the sensitivity analysis is performed and the results obtained by the developed model are compared with the results obtained by applying other methods and their various modifications. keywords: lbwa, mairca, z-number, fuzzy number, mcdm 1. introduction the army performs numerous different activities. a part of these activities is realized outside the locations of permanent residence (outside the barracks), i.e. in the field. when organizing longer stays in the field, it is necessary to provide basic conditions for life and operation. these conditions are provided by adequate organization of a camp space (camp). the camp, i.e. the camp space, means organized land space with camp facilities for accommodation and resting of units outside the populated area (military lexicon, 1981). it consists of tents, barracks, huts, casemates, sometimes a building or a combination. it is organized in all situations when the need arises (in peace, state of emergency and war) for the realization of trainings, works, combat operations, etc. božanić et al./oper. res. eng. sci. theor. appl. 3 (2) (2020) 87-110 88 in the camps, it is necessary to provide space for various activities: accommodation, economic, medical, recreational, technical, storage, sanitary facilities and quarters. (hristov, 1978). considering a series of conditions that a camp space should meet, the selection of the location for the organization of a camp space is an issue ideal for solving by multi-criteria decision-making methods. the literature dealing with this issue usually provides general conditions on which the selection should depend, which further indicates that experience plays a significant role in making such decisions. in order to group experiences and help less experienced decision makers, a model is developed and presented in this paper. the model is based on the experiences of the engineering leaders of the serbian army, but it is also applicable to other branches. the experiences of engineering officers are used because the engineering units of the serbian army have constant engagements outside the barracks due to the performance of a wide range of operations and are very often in a situation to organize camp spaces for the life and operation of their units for longer periods. the camp space selection issue by multi-criteria decision-making methods has not been particularly considered in the literature available to the authors. this issue belongs to the group of the location issues, which have been considered in different ways in the literature. božanić and pamučar (2010) perform the selection of the bridge crossing location by applying fuzzy logic system. tavakkoli-moghaddam et al. (2011) perform plant location selection using the ahp and vikor method. żak and węglińsk (2014) perform the selection of the logistics center location base applying electre method. bagocius et al. (2014) use several methods (saw, topsis, copras) for selecting a location for a liquefied natural gas terminal in the eastern baltic sea. tomic et al. (2014) used ahp as a support in making logistic center location decisions. tuzkaya et al. (2015), by using the anp-dematel model, select the location for emergency logistics centers. božanić et al. (2016a) apply a hybrid model, fuzzy ahp – mabac, for the selection of the location for preparing laying-up positions. pamučar et al. (2016a) use a fuzzy ahp-topsis model for the selection of a brigade artillery group firing position in a defensive operation. di matteo et al. (2016) propose a methodology for the optimization of the location on the territory of emergency operation centers using the ahp-electre model. gigović et al. (2017), by applying gis and the dematel, anp and mabac methods, perform the selection of the location for wind farms in serbia. milosavljević et al. (2018) determine the potential macro location of the container terminal in serbia, by applying the topsis, electre and mabac methods. sennaroglu and celebi (2018) present a location selection problem for a military airport using the ahp, promethee and vikor methods. božanić et al. (2019b) use the fucom-fuzzy mabac model for the selection of the location for construction of single-span bailey bridge. as can be obtained from the analyzed literature, the authors use different methods of multi-criteria decision making in their research. in this paper, a hybrid model based on the lbwa (level based weight assessment) method and the mairca (multi-attributive ideal-real comparative analysis method) modified by znumbers (z-mairca) is applied. lbwa – z-mairca model supporting decision making in the army 89 2. lbwa – z-mairca model the lbwa – z-mairca model consists of four phases. in figure 1, it is presented the scheme of the model. phase 1 – identification of the criteria influencing the selection phase 2 – calculation of weight coefficients phase 4 – sensitivity analysis phase 3 – best alternative selection expert evaluation expert evaluation, lbwa method z-mairca change of weight coefficients of criteria lbwa – z-mairca model phases methods figure 1. graphic scheme of the lbwa – z-mairca model in the first phase of the model, the criteria on the basis of which the selection is made by expert evaluation are defined. through the second phase, it is performed the calculation of weight coefficients of the criteria using expert evaluation and the lbwa method. in the third phase, the best alternative is selected using z-numbers and the fuzzy mairca method. the last phase includes the sensitivity analysis of the developed model. 2.1. the lbwa method the lbwa method was presented for the first time in the paper by žižović and pamučar (2020). the method has a relatively simple mathematical apparatus, and can be used in both individual and group decision making. in the paper by pamučar et al. (2020), it is presented a fuzzified lbwa method. at the beginning of the application of the lbwa method, it is defined the set of criteria  1 2, , , ns c c c= , where n represents the number of criteria influencing the selection. after the set of criteria was defined (s), the method is to be applied. the steps of the lbwa method are presented in the following section (žižović and pamučar, 2020). step 1. determining the most significant criterion from the set of defined criteria(s), i.e. the criterion with the highest influence on the decision. božanić et al./oper. res. eng. sci. theor. appl. 3 (2) (2020) 87-110 90 step 2. grouping the criteria by significance level. the significance levels are defined as follows: − level 1 s : at the level 1 s , the criteria from the set s whose significance is equal to or up to twice as lower from the significance of the criterion defined as the most significant are grouped; − level 2 s : at the level 2 s , the criteria from the set s whose significance is exactly twice or up to three times as lower from the significance of the criterion defined as the most significant are grouped; − … − level k s : at the level k s , the criteria from the set s whose significance is exactly k times as lower from the significance of the criterion defined as the most significant, i.e. up to 1k + times as lower from the significance of the most significant criterion, are grouped. applying previously presented rules, a decision maker establishes rough classification of the observed criteria. if the significance of the criterion j c is denoted by ( ) j s c , where  1, 2, ,j n , then 1 2 ks s s s=    , where for every level  1, 2, ,i k , it is true that     1 2 , , , : ( ) 1 si i i i j j s c c c c s i s c i= =    + (1) also, for each  , 1, 2, ,p q k such that p q holds p qs s =  . thus, in this way, the partition of the set of criteria s is well defined. step 3. within the formed subsets (levels) of the influence of the criteria, it is performed the comparison of the criteria by their significance. every criterion pi i c s in the subset   1 2 , , , si i i i s c c c= is assigned an integer  0,1, , pi i r such that the most important criterion ic is assigned 0ii = , and if pi c is more significant than qi c , then p q i i , and if pi c is equivalent to qi c , then p q i i= . the maximum value of the scale for the criteria comparison is defined by applying the expression (2)  1 2max , , , kr s s s= (2) step 4. based on the defined maximum value of the scale for the comparison of criteria (r), it is defined the elasticity coefficient 0r n (where n represents the set of real numbers) which should meet the criteria where 0r r ,  1 2max , , , kr s s s= . the creators of the method recommend to define initial values of the weight coefficients based on the elasticity coefficient 0 1r r= + . considering that the parameter 0r causes smaller changes of the value of the weight coefficients, taking the other value of the elasticity coefficient is recommended for lbwa – z-mairca model supporting decision making in the army 91 additional settings of the weight coefficients in accordance with the decision makers’ own preferences. step 5. the calculation of the influence function of the criteria. the influence function :f s r→ is defined in the following way. for every criterion pi i c s , the influence function is defined: 0 0 ( ) p p i i r f c i r i =  + (3) where i represents the number of the level/subset into which the criterion is classified, 0 r represents the elasticity coefficient, while  0,1, , pi i r represents the value which is assigned to the criterion pi c within the observed level. step 6. the calculation of the optimum values of the weigh coefficients. by applying the expression (4), it is calculated the weight coefficient of the most influential criterion: 1 2 1 1 ( ) ( ) n w f c f c = + + + (4) the values of the weight coefficients of other criteria are obtained by applying the expression (5): 1 ( ) j j w f c w=  (5) where 2,3, ,j n= , and n represents a total number of criteria. 2.2. z-mairca a wide range of uncertainties following decision-making processes influences a number of researchers when they select a model of multi-criteria decision-making and opt for various modifications of classic methods (e.g. using fuzzy logic, rough numbers, etc.). the selection of a location for a camp space is accompanied by uncertainties and inaccuracies, which is why the mairca method, fuzzified with znumbers, is selected. the mairca method was first published in the papers written by pamučar et al. (2014) and gigović et al. (2016). since then, it has been applied in its original form (pamučar et al., 2018; tešić and božanić, 2018; adar and delice, 2019, 2020; ayçin and orçun, 2019; ayçin, 2020), but also through various modifications in fuzzy and rough environment (pamučar et al., 2017b; chatterjee et al., 2018; badi and ballem, 2018; stević, 2018; božanić et al., 2019a; arsić et al., 2019; hashemkhani et al., 2020; boral et al., 2020). given that the z-numbers are used for the modification, their most basic description is provided below. z-numbers represent a type of fuzzy numbers, i.e. two fuzzy numbers, which are in a specific relationship. triangular fuzzy numbers are used in this paper, as in figure 2. triangular fuzzy numbers have the form 1 2 3 ( , , )t t t t= ; t1 the left distribution of the confidence interval of fuzzy number t, t2 fuzzy number membership function božanić et al./oper. res. eng. sci. theor. appl. 3 (2) (2020) 87-110 92 has the maximum value equal to 1, and t3 the right distribution of the confidence interval of fuzzy number t (pamučar et al., 2012). a z-number represents an extension of classic fuzzy number and provides wider opportunities for considering additional uncertainties following decision making. the concept of z-number was proposed by zadeh (2011). in 2012, kang et al. (2012a, 2012b) have already shown in detail the application of z-numbers in uncertain environment. later, authors consider the application of z-numbers with different methods of multi-criteria decision making. sahrom and dom (2015) present the use of z-numbers in the hybrid ahp-z-number-dea method. azadeh and kokabi (2016) use z-numbers with the dea method, azadeh et al. (2013) with the ahp, yaakob and gegov (2015) with the topsis method, aboutorab et al. (2018) with the best worst method, bobar et al. (2020) and božanić et al. (2020) with the mabac method. salari et al. (2014) elaborate a novel earned value management model using a z-number. t1 t2 t3 1 ( )t x  ( ) 2 1, t x x t = = ( ) 1 1 2 2 1 , t x x t t x t t t  − =   − ( ) 3 2 3 3 2 , t x t x t x t t t  − =   − ( ) 1 0, t x x t =  ( ) 3 0, t x x t =   0 αt1 αt2 figure 2. triangular fuzzy number (pamučar et al., 2016b) a z-number represents an ordered pair of fuzzy numbers that appear as z = ( a , b ) (zadeh, 2011). the first component, fuzzy number a , represents the fuzzy limit of a particular variable x, while the second component, fuzzy number b , represents the reliability of the first component ( a ). the appearance of the znumber with triangular fuzzy numbers is shown in figure 3 (zadeh, 2011). a1 a3a2 ã(x) 1 x ã b1 b3b2  (x) 1 x bb( ),=z a b figure 3. a-simple z-number (kang et al., 2012a) lbwa – z-mairca model supporting decision making in the army 93 a general record of triangular z-numbers can be displayed as ( ) 1 2 3 1 2 3, , ; , ( , , ; )baz a a a w b b b w= (6) where the values a w and b w represent weight factors of fuzzy number a referring to b , which for the initial z-number, the majority of authors define as 1 ba w w= = ,  , 0,1 ba w w  ( a w is the height of generalized fuzzy number and 0 1 a w  ) (chutia et al., 2013). the transformation of the z-number into a classic fuzzy number, with the presented evidence, is shown in kang et al. (2012b). this transformation consists of three steps: convert the second part ( b ) into a crisp number using the centered method (kang et al., 2012b): 1 2 3 3 a a a  + + = (7) add the weight of the second part ( b ) to the first part ( a ). the weighted znumber can be presented as in kang et al. (2012b):  , ( ) ( ) ( )aa az x x x x     =   = (8) which can be presented by figure 4a. this can be written as (azadeh et al., 2013): 1 2 3 ( , , ; )z a a a  = (9) a1 a3a2 ã(x) 1 x ã  a a1 a3a2 ã(x) 1 x ã  a ã(x) 1 x `z 1  a 2  a 3  a a) b) figure 4. z-number after multiplying the reliability (a) and the regular fuzzy number transformed from a z-number (b) convert the weighted z-number into a regular fuzzy number. the regular fuzzy set can be presented as in kang et al. (2012b) ‚ ‚ ‚ , ( ) ( ) ( ) az z x z x x x      =   =    (10) ‚ 1 2 3 * ( * , * , * )z a a a a   = = (11) božanić et al./oper. res. eng. sci. theor. appl. 3 (2) (2020) 87-110 94 and it can be presented as in figure 4b (kang et al., 2012b). the steps of the mairca method modified by z-numbers are provided as follows: step 1. forming an initial z decision-making matrix ( z ) with m alternatives and n criteria. in this step, decision makers define the value of every alternative by all criteria ( ij a ) and the degree of certainty of the defined value ( ij b ). the arranged pair [ ij a , ij b ] represents a z-number, where i represents the number of alternatives,  1, 2,...i m , and j the number of criteria,  1, 2,...j n . 1 2 1 111 11 12 12 1 2 221 21 22 222 1 1 2 2 . . . . . . . . . . . .. . . . . . . . . . . . n n n n n m m m m m mn mn cc c a ba b a b a a ba b a ba z a a b a b a b           =            (12) the value ij a is defined in accordance with the characteristics of the criteria, while the value ij b is defined by the expressions presented on fuzzy linguistic scale, as in figure 5. 1 0.8 0.6 0.4 0.2 0 0.2 0.4 0.6 0.8 1 very small small medium high very high 0 figure 5. fuzzy linguistic descriptors for evaluating the degree of conviction of experts (bobar et al. 2020) step 2. forming an initial decision-making matrix ( x ). the elements of the initial decision-making matrix ( x ) are obtained by converting the elements of the initial z matrix ( z ) into the regular fuzzy numbers, by applying the expressions (7)-(11). lbwa – z-mairca model supporting decision making in the army 95 1 2 11 11 12 22 21 22 1 2 . . . . . . . . . . . . . . . . . . . . . n n n m m m mn cc c xa x x xa x x x a x x x         =            (13) step 3. normalization of the initial decision-making matrix. the calculation of the elements of normalized matrix depends on the type of criteria. for “benefit” type criteria (bigger criterion value is preferable), this calculation is executed according to the expression: ij i ij i i x x n x x − + − − = − (14) for “cost” type criteria (lower criterion value is preferable), the calculation is executed according to the expression: ij i ij i i x x n x x + − + − = − (15) the values ij x , i x + , i x − represent the elements of the initial decision-making matrix ( x ). the values i x + , i x − are defined as explained bellow: − 1 2 max( , ,..., ) i r r mr x x x x + = – represents maximal values of the right distribution of fuzzy numbers of the observed criteria alternatives; − 1 2 min( , ,..., ) i l l ml x x x x − = – represents minimal values of the left distribution of fuzzy numbers of the observed criteria alternatives. the normalized initial decision-making matrix has the following form: 1 2 11 11 12 22 21 22 1 2 . . . . . . . . . . . . . . . . . . . . . n n n m m m mn cc c na n n na n n n a n n n         =            (16) step 4. determination of the probability of selection of certain alternatives ( ia p ). decision makers may prefer certain alternatives by assigning different probabilities to the alternatives. in most cases, decision makers are neutral towards the selection božanić et al./oper. res. eng. sci. theor. appl. 3 (2) (2020) 87-110 96 of the alternatives. in such case, the preference towards the selection is equal for all the alternatives and it is expressed as follows: 1 1 ; 1, 1, 2,..., i i m a a i p p i m m = = = = (17) where m represents a total number of alternatives being selected. step 5. forming a theoretical assessment matrix ( p t ). in case the condition from step 4 is met, where the decision maker is neutral in terms of the initial selection of alternatives, so the initial probability ( ia p ) of the selection of certain alternatives is the same for all the alternatives, then the theoretical assessment matrix in the form n x 1 is created. 1 2 ... a ni p p p pn p xw t t t t =   (18) and the matrix elements are calculated as follows: 1 2 ... i i i a ni p a a a n p w t p w p w p w =   (19) where n w represents the weight coefficient of the criteria. step 6. calculation of real assessment matrix ( r t ). the calculation of real assessment matrix elements ( r t ) is performed by applying the expression: rij pj ij t t n=  (20) where pj t represents the elements of the theoretical assessment matrix, and ij n represents the elements of the normalized initial decision-making matrix ( n ). after the calculation, the theoretical assessment matrix is obtained: 1 2 1 11 12 1 2 21 22 2 1 2 ... ... ... ... ... ... ... ... ... n r r r n r r r n r m rm rm rmn c c c a t t t a t t t t a t t t      =       (21) where n represents a total number of criteria, and m represents a total number of alternatives. step 7. calculation of the gap matrix between theoretical and real weights ( g ): ij pj rij g t t= − (22) after the calculation, it is obtained the total gap matrix ( g ): lbwa – z-mairca model supporting decision making in the army 97 11 12 1 21 22 2 1 2 ... ... ... ... ... ... ... n n m m mn g g g g g g g g g g      =       (23) where n represents a total number of criteria, m represents a total number of alternatives being selected, and ij g represents the obtained gap of the alternative i by the criterion j. step 8. initial ranking of alternatives. for the purpose of ranking alternatives, it is first calculated the values of the criteria functions ( i q ) by alternatives. the values of the criteria functions are obtained by summing the gap the element of the matrix ( g ) by columns: 1 , 1, 2,..., n i ij j q g i m = = = (24) where n represents a total number of criteria, m represents a total number of alternatives being selected. before defining the initial rank, it is performed defuzzification of the values of the criteria functions ( i q ), by applying the expression (seiford, 1996; liou and wang, 1992): 3 1 2 1 1 (( ) ( )) / 3 ij ij ij ij ij ij q t t t t t= − + − + (25) ( )3 2 11 / 2ij ij ij ijq t t t  = + + −  (26) where  represents an index of optimism, which can be described as a belief/decision maker's relationship to decision-making risk (milićević, 2014). the most common optimism index is 0, 0.5 or 1, which corresponds to the pessimistic, average or optimistic view of the decision maker (milićević, 2014). step 9. final ranking of alternatives. final rank of alternatives is defined by the application of a dominance index of the first-ranked alternative ( ,1d j a − ). it represents the element which defines the value of the first-ranked alternative compared to the remaining alternatives. the dominance index shows the difference between the first-ranked and the other alternatives, and it is defined by the expression: 1 ,1 , 2, 3,.., j d j n q q a j m q − − = = (27) where 1q represents the criterion function of the first-ranked alternative, nq represents the criterion function of the last-ranked alternative, j q represents the criterion function of the alternative being compared with the first-ranked alternative, m represents a total number of alternatives. božanić et al./oper. res. eng. sci. theor. appl. 3 (2) (2020) 87-110 98 for final definition of the first-ranked alternative, it is also necessary to determine a dominance threshold d i according to the following expression: 2 1 d m i m − = (28) where m represents a total number of alternatives. if the condition is met where the dominance index ,1d j a − is higher or equal to the dominance threshold d i ( ,1d j d a i −  ), then the obtained rank is kept. in case the dominance index ,1d j a − is lower than the dominance threshold d i ( ,1d j d a i −  ), it cannot be certainly concluded that the first-ranked alternative has sufficient advantage compared to the observed alternative. 3. description of criteria and calculation of weight coefficients of criteria the selection of a camp space is influenced by a number of criteria. after the analysis of the literature and the survey of experts, seven criteria are defined on which the selection depends. criterion 1 (c1) general soil and environmental conditions. this criterion means the quality of the location where the camp space is planned. the place for the camp space should be clean, dry, drained, slightly sloping, separated from the settlement and away from ponds and swamps at least 2-3 kilometers, in the lee (if the land is exposed to strong winds), out of torrents and floodplains areas (hristov, 1978). in addition to the above, the camp space should be spacious in order to, under certain conditions, place facilities necessary for the life and operation of the units outside the barracks: residential, economic, medical, recreational, technical, storage, sanitary facilities, etc. the criterion is of a linguistic nature. criterion 2 (c2) distance from the road. in order to ensure uninterrupted life and operation in the field, it is necessary to connect the camp space with local and regional roads (hristov, 1978). the best variant is that the roads are located right next to the camp space, but very often it will be necessary to build a temporary military road to connect the camp space with the road. the criterion is of a numerical character, where the distance of the camp space from the nearest road is presented in kilometers. criterion 3 (c3) water supply options. water supply is a very important component of a camp space. in field conditions, it is necessary to provide sufficient amount of water for normal life and operation of every individual, and thus units, including drinking water, water for cooking food, water for maintaining personal hygiene and cleaning the camp space. the criterion is of a linguistic nature. criterion 4 (c4) scope of works on the arrangement of the camp space. regardless of the conditions of the soil on which the organization of the camp space is planned, it is necessary to perform certain works (construction/installation of facilities, construction of temporary roads that connect parts of camp space, etc.). the works are carried out in order to arrange the existing land for temporary life and lbwa – z-mairca model supporting decision making in the army 99 operation of the units. the scope of works depends on a number of factors, such as the type of facilities to be constructed, time planned to be spent by the units in the camp space, the season, and the like (hristov, 1978). the criterion is of a linguistic nature. criterion 5 (c5) distance from the site where the works are performed. the main goal of the field conditions is to perform certain works. the site where the unit performs the assigned works should be as close as possible to the camp space. the proximity of the site and the camp space ensures that the people engaged do not waste time traveling to the site and vice versa, that the funds are kept in one place, easier organization of food provision of the unit and the like. the criterion is of a numerical character, where the distance of the camp space from the site is presented in kilometers. in certain cases (e.g. construction of a road section), this distance may vary as the work progresses. criterion 6 (c6) direct security of camp space. both in peace and during the state of war, the units in the field are obliged to set up direct security of the camp space. the number of persons necessary for the organization of direct security varies and most often depends on the conditions of the land and the layout of the facilities in the camp area. the criterion is of a numerical character, where the minimum number of persons engaged in direct security during one day is defined. criterion 7 (c7) masking conditions. this criterion exerts its influence on the final decision in situations when the camp space is organized during the implementation of combat operations. the conditions for camouflage include the possibility of hiding or concealing the camp space from enemy reconnaissance (božanić et al., 2020). under this criterion, many factors are considered that affect masking, such as the distance from the objects that can be the subject of enemy reconnaissance or action (hristov, 1978), the possibility of setting up a camp space in the forest, etc. the criterion is of a linguistic nature. all the criteria presented can be divided in two subsets: − benefit-type criteria  1 3 7, ,c c c c +  , − cost-type criteria  2 4 5 6, , ,c c c c c −  . the evaluation of the linguistic criteria is performed by applying fuzzy linguistic descriptors, as in figure 6. 1 0.8 0.6 0.4 0.2 1 32 54 0 a b c d e figure 6. graphic display of fuzzy linguistic descriptors (božanić et al. 2016b) božanić et al./oper. res. eng. sci. theor. appl. 3 (2) (2020) 87-110 100 the description of the linguistic criteria is performed by the scale including five fuzzy linguistic descriptors. the marks presented in figure 6 have the following meanings, depending on the criterion: − for the criteria c1, c3 and c7: a=very bad (vb), b=bad (b), c=medium (m), d= good (g), e=very good (vg) − for the criterion c4: a=very small (vs), b=small (s), c=medium (m), d=large (l), e=very large (vl). in the second phase of the research, it is performed the calculation of the weight coefficients of the criteria by applying the lbwa method, described in the previous section, on the basis of the input parameters: − as the most significant criterion it is determined the criterion 1 c ; − the criteria are roughly arranged by levels as follows:  1 1 7 5, , ;s c c c=  2 3 2, ;s c c=  3 6 ;s c=  4 4 ;s c= − comparing the criteria by levels, the following values are obtained: 1 s : 1 0i = , 7 0.8i = , 5 1.1i = ; 2 s : 3 0i = , 2 2i = ; 3 s : 6 0.2i = ; 4 s : 4 0.4i = . applying the expressions (3)-(5), the following weight coefficients of the criteria are obtained: ( )0.244, 0.098, 0.122, 0.06, 0.192, 0.08, 0.204jw = . based on the calculation presented, the conditions for the following phase of the model application, i.e. the selection of the best alternative by the application of the zmairca method are created. 4. testing of the model – selection of the best alternative in the third phase of the paper, it is performed the testing of the model. testing is performed with ten alternatives, i.e. potential locations for the organization of a camp space. at the very beginning, it is defined the initial z decision-making matrix, as in table 1. table 1. initial z decision-making matrix crit. c1 c2 c3 c4 c5 c6 c7 alter. a b a b a b a b a b a b a b a1 vb vs (3,3.5,4.2) s vb m vl m (3,7,13) h (3,5,6) m m m a2 b m (2,2.9,3.9) vh m m m vs (4.2,9,15) m (2,5,7) vs m h a3 g s (3,3.3,3.6) vs b vs l m (1.5,6,11) s (6,8,11) s vb vh a4 m h (0.5,0.5,0.7) m vb s vl s (1.9,7,12) vs (4,4,6) h b vs a5 vg vh (1.3,1.8,2.2) s b vs vs h (6,12,17) vh (12,13,13) vh vb h a6 g m (4.5,5,5) h vg h s vh (5,11,16) m (4,5,5) vs g m a7 vb vs (2.2,2.7,2.9) vs g vh l vs (2,7,13) h (3,5,8) m b s a8 m s (0.4,0.6,1) h g h m h (1,3,7) vs (4,9,14) s m vs a9 b h (0.9,1.5,1.7) vh m s s s (1.5,3,8.5) s (3,7,8) h vg vh a10 vg vh (1.8,2.5,2.8) m vg vh vs vh (6,13,21) vh (5,11,14) vh g s lbwa – z-mairca model supporting decision making in the army 101 after the definition of the initial z decision-making matrix, it is performed its quantification, as in table 2. table 2. quantified initial z decision-making matrix crit. c1 c2 c7 alter. a b a b ... a b a1 (1,1,2) (0,0,0.2) (3,3.5,4.2) (0.1,0.25,0.4) ... (2,3,4) (0.3,0.5,0.7) a2 (1,2,3) (0.3,0.5,0.7) (2,2.9,3.9) (0.8,1,1) ... (2,3,4) (0.55,0.75,0.95) a3 (3,4,5) (0.1,0.25,0.4) (3,3.3,3.6) (0,0,0.2) ... (1,1,2) (0.8,1,1) a4 (2,3,4) (0.55,0.75,0.95) (0.5,0.5,0.7) (0.3,0.5,0.7) ... (1,2,3) (0,0,0.2) a5 (4,5,5) (0.8,1,1) (1.3,1.8,2.2) (0.1,0.25,0.4) ... (1,1,2) (0.55,0.75,0.95) a6 (3,4,5) (0.3,0.5,0.7) (4.5,5,5) (0.55,0.75,0.95) ... (3,4,5) (0.3,0.5,0.7) a7 (1,1,2) (0,0,0.2) (2.2,2.7,2.9) (0,0,0.2) ... (1,2,3) (0.1,0.25,0.4) a8 (2,3,4) (0.1,0.25,0.4) (0.4,0.6,1) (0.55,0.75,0.95) ... (2,3,4) (0,0,0.2) a9 (1,2,3) (0.55,0.75,0.95) (0.9,1.5,1.7) (0.8,1,1) ... (4,5,5) (0.8,1,1) a10 (4,5,5) (0.8,1,1) (1.8,2.5,2.8) (0.3,0.5,0.7) ... (3,4,5) (0.1,0.25,0.4) by converting z-numbers presented in table 2, it is formed the initial decisionmaking matrix ( x ), as in table 3. table 3. initial decision-making matrix alter. c1 c2 c7 a1 (0.258,0.258,0.516) (1.5,1.75,2.1) ... (1.414,2.121,2.828) a2 (0.707,1.414,2.121) (1.932,2.802,3.768) ... (1.732,2.598,3.464) a3 (1.5,2,2.5) (0.775,0.852,0.93) ... (0.966,0.966,1.932) a4 (1.732,2.598,3.464) (0.354,0.354,0.495) ... (0.258,0.516,0.775) a5 (3.864,4.83,4.83) (0.65,0.9,1.1) ... (0.866,0.866,1.732) a6 (2.121,2.828,3.536) (3.897,4.33,4.33) ... (2.121,2.828,3.536) a7 (0.258,0.258,0.516) (0.568,0.697,0.749) ... (0.5,1,1.5) a8 (1,1.5,2) (0.346,0.52,0.866) ... (0.516,0.775,1.033) a9 (0.866,1.732,2.598) (0.869,1.449,1.642) ... (3.864,4.83,4.83) a10 (3.864,4.83,4.83) (1.273,1.768,1.98) ... (1.5,2,2.5) further, it is performed the normalization of the initial decision-making matrix, as in table 4. table 4. normalized initial decision-making matrix alter. c1 c2 c7 a1 (0,0,0.056) (0.56,0.648,0.71) ... (0.253,0.407,0.562) a2 (0.098,0.253,0.407) (0.141,0.384,0.602) ... (0.322,0.512,0.701) a3 (0.272,0.381,0.49) (0.854,0.873,0.893) ... (0.155,0.155,0.366) a4 (0.322,0.512,0.701) (0.963,0.998,0.998) ... (0,0.056,0.113) a5 (0.789,1,1) (0.811,0.861,0.924) ... (0.133,0.133,0.322) a6 (0.407,0.562,0.717) (0,0,0.109) ... (0.407,0.562,0.717) a7 (0,0,0.056) (0.899,0.912,0.944) ... (0.053,0.162,0.272) a8 (0.162,0.272,0.381) (0.87,0.957,1) ... (0.056,0.113,0.169) a9 (0.133,0.322,0.512) (0.675,0.723,0.869) ... (0.789,1,1) a10 (0.789,1,1) (0.59,0.643,0.767) ... (0.272,0.381,0.49) božanić et al./oper. res. eng. sci. theor. appl. 3 (2) (2020) 87-110 102 considering that the decision makers did not have different preferences towards the selection of the alternatives, it is calculated that 1/ 10 0.1 ia p = = . based on that, it is performed the calculation of the elements of the theoretical assessment matrix provided in table 5. table 5. theoretical assessment matrix alter. c1 c2 c7 a1-10 (0.024,0.024,0.024) (0.01,0.01,0.01) ... (0.02,0.02,0.02) the elements of the real assessment matrix are presented in table 6. table 6. real assessment matrix alter. c1 c2 c7 a1 (0,0,0.001) (0.005,0.006,0.007) ... (0.005,0.008,0.011) a2 (0.002,0.006,0.01) (0.001,0.004,0.006) ... (0.007,0.01,0.014) a3 (0.007,0.009,0.012) (0.008,0.009,0.009) ... (0.003,0.003,0.007) a4 (0.008,0.012,0.017) (0.009,0.01,0.01) ... (0,0.001,0.002) a5 (0.019,0.024,0.024) (0.008,0.008,0.009) ... (0.003,0.003,0.007) a6 (0.01,0.014,0.017) (0,0,0.001) ... (0.008,0.011,0.015) a7 (0,0,0.001) (0.009,0.009,0.009) ... (0.001,0.003,0.006) a8 (0.004,0.007,0.009) (0.009,0.009,0.01) ... (0.001,0.002,0.003) a9 (0.003,0.008,0.012) (0.007,0.007,0.009) ... (0.016,0.02,0.02) a10 (0.019,0.024,0.024) (0.006,0.006,0.008) ... (0.006,0.008,0.01) further, it is performed the calculation of the total gap matrix, as in table 7. table 7. total gap matrix alter. c1 c2 c7 a1 (0.023,0.024,0.024) (0.003,0.003,0.004) ... (0.009,0.012,0.015) a2 (0.014,0.018,0.022) (0.004,0.006,0.008) ... (0.006,0.01,0.014) a3 (0.012,0.015,0.018) (0.001,0.001,0.001) ... (0.013,0.017,0.017) a4 (0.007,0.012,0.017) (0,0,0) ... (0.018,0.019,0.02) a5 (0,0,0.005) (0.001,0.001,0.002) ... (0.014,0.018,0.018) a6 (0.007,0.011,0.014) (0.009,0.01,0.01) ... (0.006,0.009,0.012) a7 (0.023,0.024,0.024) (0.001,0.001,0.001) ... (0.015,0.017,0.019) a8 (0.015,0.018,0.02) (0,0,0.001) ... (0.017,0.018,0.019) a9 (0.012,0.017,0.021) (0.001,0.003,0.003) ... (0,0,0.004) a10 (0,0,0.005) (0.002,0.003,0.004) ... (0.01,0.013,0.015) in the further process of application of the z-mairca model, the gap of alternatives is calculated, and the obtained values are defuzzified, on the basis of which the initial rank of the alternatives is defined. then, the calculation of the dominance index and the definition of the final rank are performed, as in table 8. lbwa – z-mairca model supporting decision making in the army 103 table 8. ranking alternatives alter. alternative gap i q alternative gap qi initial rank ad,1-j final rank a1 (0.052,0.064,0.074) 0.0559 10 0.534 10 a3 (0.042,0.054,0.063) 0.0465 9 0.365 9 a4 (0.041,0.05,0.058) 0.0437 7 0.316 7 a5 (0.038,0.05,0.062) 0.042 6 0.285 6 a6 (0.027,0.041,0.056) 0.0318 3 0.103 3 a7 (0.041,0.053,0.065) 0.0454 8 0.345 8 a8 (0.037,0.047,0.058) 0.0402 5 0.252 5 a9 (0.023,0.034,0.049) 0.0262 2 0.003 1* a10 (0.022,0.035,0.057) 0.0261 1 0.000 1 in accordance with the obtained dominance threshold ( 0.09 d i = ), it can be noted that the advantage of the initially first-ranked alternative (a10) is not significant enough, compared to the second-ranked alternative (a9). accordingly, a decision maker can select any of the two mentioned alternatives as the first-ranked. 5. sensitivity analysis an inevitable section of any model is a sensitivity analysis. there are different approaches to sensitivity analysis (pamučar et al., 2017a). in this paper, a sensitivity analysis is performed by favoring the significance (weight coefficient) of one criterion in every scenario. for the needs of the analysis, seven scenarios are defined, as in table 9. table 9. sensitivity analysis scenarios criteri a s-0 s-1 s-2 s-3 s-4 s5 s6 s7 c1 0.244 0.4 0.1 0.1 0.1 0.1 0.1 0.1 c2 0.098 0.1 0.4 0.1 0.1 0.1 0.1 0.1 c3 0.122 0.1 0.1 0.4 0.1 0.1 0.1 0.1 c4 0.06 0.1 0.1 0.1 0.4 0.1 0.1 0.1 c5 0.192 0.1 0.1 0.1 0.1 0.4 0.1 0.1 c6 0.08 0.1 0.1 0.1 0.1 0.1 0.4 0.1 c7 0.204 0.1 0.1 0.1 0.1 0.1 0.1 0.4 by applying the z-mairca model and the defined weight coefficients by scenarios, the ranks of alternatives shown in table 10 are obtained. the ranks shown indicate the initial rank, and an asterisk next to certain ranks indicates that in the final ranking, the alternatives marked with an asterisk would be ranked as the first ones. božanić et al./oper. res. eng. sci. theor. appl. 3 (2) (2020) 87-110 104 table 10. ranks of alternatives by different scenarios altern atives s-0 s-1 s-2 s-3 s-4 s5 s6 s7 a1 10 10 9 10 10 10 9 7 a2 4 6 8 5 3* 4 1 3 a3 9 8 7 9 9 8 8 8 a4 7 5 5 7 8 7 7 10 a5 6 2 6 8 6 9 10 9 a6 3 3 10 3 5 5 2* 2 a7 8 9 3* 2 4 3 4* 5 a8 5 7 2* 4 7 2 5 6 a9 2* 4 1* 6 1 1 3* 1 a10 1 1 4* 1 2* 6 6 4 the obtained ranks, shown in table 10, indicate that the favoring of certain criteria affects the differences in ranks, which indicates that the developed model is sensitive to changes in the weight coefficients of the criteria. the rank correlation control is performed using the spearman’s coefficient: 2 1 2 6 1 ( 1) n i i d s n n == − −  (29) where: s the value of the spearman’s coefficient; di the difference in the rank of the given element in the vector w and the rank of the correspondent element in the reference vector; n number of ranked elements. the values of the spearman’s coefficient range between -1 and 1, i.e. from the ideal negative to the ideal positive rank correlation. table 11 provides the values of the spearman’s coefficient by comparing all the scenarios mutually, based on the initial rank of alternatives. table 11. the value of the spearman’s coefficient based on the initial ranks of alternatives scenario s s-0 s-1 s-2 s-3 s-4 s5 s6 s7 s-0 1 0.794 0.285 0.594 0.830 0.606 0.727 0.727 s-1 1 0.091 0.370 0.552 0.055 0.091 0.224 s-2 1 0.000 0.158 0.606 0.048 -0.048 s-3 1 0.685 0.624 0.624 0.564 s-4 1 0.673 0.661 0.770 s-5 1 0.794 0.685 s-6 1 0.830 s-7 1 from table 11, it can be observed that the rank correlation in most of the cases is very high. however, the most important correlation of ranks is between the scenario s-0 and the others, where a significant deviation from the scenario s-2 is observed. the s-2 scenario has a low correlation with other scenarios as well. this result presents a combination of two factors: the values of the evaluated alternatives by the lbwa – z-mairca model supporting decision making in the army 105 criterion c2 and a significant increase in the weight coefficient of the criterion c2 in the scenario s-2 (by four times). the deviation is also observed in the correlation of the s-1 strategy with almost all other strategies. the analysis of the ranks shows that the most significant part of the non-correlation is the popping up of the alternative a5 in the second scenario as the second-ranked. finally, it is pointed out that in all scenarios, the alternatives a9 or a10 are ranked as the first or one of the first-ranked. according to all the above, it can be concluded that the developed model is sufficiently sensitive. also, the model can tolerate minor errors in defining the weight coefficients of the criteria, i.e. in the evaluation of the alternatives by criteria. given the existence of certain minor deviations in the sensitivity analysis, the results obtained by the z-mairca model are compared with the results obtained by the mabac and vikor methods (classic and modified with z-numbers z-mabac and z-vikor and fuzzy numbers fmabac and f-vikor) and the mairca (classic and modified with fuzzy numbers f-mairca). in table 12, the ranks obtained by the above methods are presented. table 12. ranks of alternatives obtained by applying different methods alte rnat ives z-mairca z-vikor z-mabac f-mairca f-vikor f-mabac mairca vikor mabac a1 10 10 10 10 10 10 10 10 10 a2 4 8 5 5 9 7 6 8 6 a3 9 7 8 8 6 8 7 6 7 a4 7 5 6 6 7 6 5 7 5 a5 6 3 7 7 4 5 8 5 8 a6 3 6 3 2 3 2 4 4 4 a7 8 9 9 9 8 9 9 9 9 a8 5 4 4 3 5 4 2 3 2 a9 2 2 1 4 2 3 1 2 1 a10 1 1 2 1 1 1 3 1 3 figure 7 shows the rank of alternatives using different methods from which the correlation of ranks is more clearly observed. figure 7. graphic presentation of the rank of alternatives obtained by applying different methods božanić et al./oper. res. eng. sci. theor. appl. 3 (2) (2020) 87-110 106 from figure 7 and table 12, it can be observed a clear dominance of the alternatives a9 and a10, as well as the rank of the alternatives a7 and a1, which are most often ranked as the last ones. despite the obvious correlation of ranks, in table 13, the values of the spearman's correlation coefficient of ranks for different methods and their modifications are provided. table 13. value of the spearman's coefficient for different methods method z-mairca z-vikor z-mabac f-mairca f-vikor f-mabac mairca vikor mabac z-mairca 1 0.733 0.952 0.909 0.770 0.903 0.806 0.806 0.806 z-vikor 1 0.770 0.709 0.891 0.855 0.745 0.915 0.745 z-mabac 1 0.442 0.309 0.430 0.648 0.867 0.648 f-mairca 1 0.758 0.939 0.867 0.842 0.867 f-vikor 1 0.915 0.721 0.952 0.721 f-mabac 1 0.830 0.927 0.830 mairca 1 0.855 1 vikor 1 0.855 mabac 1 from table 13, it is clear that there is a high correlation of ranks obtained by different methods and their modifications. it is especially important to point out the high correlation of the ranks of the z-mairca model with the f-mairca and the classic mairca method. accordingly, it can be concluded that the developed model provides usable results in conditions of uncertainty. it is also observed that there is an impact of uncertainty treatment on the final ranking of alternatives, and that it can significantly influence the selection, but not to such an extent where the ranks of alternatives are not correlated. 6. conclusion the paper explains the phases of development of multi-criteria decision-making model based on the lbwa method and the mairca method modified with znumbers. the presented model is successfully applied in the selection of camp space locations. in addition to the description of the model, the paper describes the problem that was being solved, i.e. the selection of a location for a camp space. the highlighted problem belongs to the group of location issues. the analysis of the literature indicates that multi-criteria decision-making methods have a great application in solving this type of problems. the paper describes in detail the steps of the lbwa method and the mairca method modified with z-numbers, as well as their previous application in the literature. the paper also presents the basics related to the application of z-numbers, as a very important way to deal with uncertainty. the model application process itself has followed the definition of the criteria for the selection of the best alternative and the calculation of their weight coefficients using the lbwa method. seven criteria of different character (benefit and cost-type criteria) are defined, on which the selection of a camp space depends. a part of the criteria, which is of a linguistic nature, clearly indicated the need to apply methods that deal with uncertainty. lbwa – z-mairca 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(2019). new model for determining criteria weights: level based weight assessment (lbwa) model. decision making: applications in management and engineering, 2(2), 126-137. *(1981). military lexicon (only in serbian: vojni leksikon). belgrade: military publishing institute/vojnoizdavački zavod. © 2020 by the authors. submitted for possible open access publication under the terms and conditions of the creative commons attribution (cc by) license (http://creativecommons.org/licenses/by/4.0/). lbwa – z-mairca model supporting decision making in the army darko božanić 1*, dragiša jurišić 2, dražan erkić 3 1. introduction 2. lbwa – z-mairca model 2.1. the lbwa method 2.2. z-mairca 3. description of criteria and calculation of weight coefficients of criteria 4. testing of the model – selection of the best alternative 5. sensitivity analysis 6. conclusion references operational research in engineering sciences: theory and applications vol. 3, issue 3, 2020, pp. 29-47 issn: 2620-1607 eissn: 2620-1747 doi: https://doi.org/10.31181/oresta20303029a * corresponding author farjashis@gmail.com (i. nur ariyanto), humiras.hardi@mercubuana.ac.id (h. hardi purba), purbaynu@gmail.com (a. purba) a systematic review and analysis of risk assessment in highway construction projects ismail nur ariyanto 1, humiras hardi purba 2, aleksander purba 3 1 civil engineering department, mercu buana university, jakarta, indonesia 2 industrial engineering department, mercu buana university, jakarta, indonesia 3 civil engineering department, lampung university, lampung, indonesia received: 20 june 2020 accepted: 10 august 2020 first online: 24 september 2020 review paper abstract: before planning and managing risks to reduce the causes of severe risks associated with road construction, it is very important to conduct an evaluation first. aspects related to risk are convoluted in several steps from design to planning to project fulfillment. this research aims to implement a complete risk management process for highway construction projects. through this process, there will be a list of risks in the highway construction project (risk identification) and the definition of the most significant risk through the application of the evaluation process (applying risk analysis and valuation). to successfully improve the performance of road projects, it is necessary to identify and assess various risk factors in a project for efficient project fulfillment. the research method begins by reviewing at least 50 articles to find a list of the main risk factors that might be encountered during highway construction. this analysis involves the identification, classification, and assessment of various risks involved in the construction of a highway project. keywords: risk, highway project, road, construction, pavement. 1. introduction progress in development in various fields continues to develop at any time, especially infrastructure development. in general, various types of construction are carried out by a contract involving various service providers in the construction sector. with a contract system, the implementation of development projects can be carried out effectively and can be accounted for, both in terms of quality and administration. in the implementation of construction, projects will not be separated from big risks and small risks. project accuracy in implementing risk management is mailto:purbaynu@gmail.com ariyanto et al./oper. res. eng. sci. theor. appl. 3 (3) (2020) 29-47 30 needed for the smoothness and success of a project. a smaller potential risk will benefit the project in terms of time, cost, and quality of construction. the larger the scale of the project, the greater the risk that will be faced and will affect the performance of project implementation if not handled properly. like other construction projects, this highway construction project is an infrastructure project that is not free from various risks that may occur. therefore, to reduce the risk of impacts that occur, we need a risk management system that includes identification, analysis, response, and monitoring of various risks that may occur during the development period. from the risk analysis, it can predict what risks will occur in the future based on the probability of the risk that has occurred and also other factors that will be very helpful for future projects. research related to project risks in road construction is necessary and important to do, especially those related to road structure work. this article aims to determine and analyze important factors that pose risks in the implementation of construction projects and to find out how they affect the implementation of project risks. with risk assessments, these tasks can be prioritized for the smooth completion of road construction projects. in completing research, there are various data and source collection methods commonly used. on this occasion, the research will be discussed further about data collection strategies through the literature review. this paper is based on a literature review from a trusted source that discusses the identification of risks and risk management in road construction, then obtained 50 articles selected and reviewed. risks are identified through a literature review, identified risks are then assessed in terms of the impact and priority risks that are dominant so that a rating is obtained based on risk factors. 2. research method the writing of this article is based on a literature review conducted online including various scientific articles relating to risk analysis on road construction projects, which are then reviewed and synthesized to provide comprehensive information. the research framework of this research of articles is shown in figure 1 bellow: figure 1. research framework the list of articles selected and analyzed from the aspect of risk assessment in the highway construction project is shown in table 1. a systematic review and analysis of risk assessment in highway construction project 31 table 1. summary literature review of risk assessment in highway construction projects no article risk category result internal project external tech nontech tech nontech tech nontech 1 (nasir et al., 2003) x x x ✓ x x evaluating risks in the construction model is carried out to develop a schedule risk model that discusses pessimistic and optimistic estimates of the duration of activities based on project characteristics. 2 (wang & chou, 2003) x ✓ x x x x when deciding on risk management strategies, a contractor must consider many aspects, including risk responsibilities, risk patterns, risk management capabilities, etc. 3 (molenaar, 2005) x x x ✓ x x provide estimates for road project cost estimates, which provide more transparent estimation, estimates and the significant and direct benefits of this process are the ability to increase high-risk items and potential mitigation measures that can be taken to improve safety. 4 (shiraki et al., 2007) x x ✓ x x x combines earthquake and transportation engineering techniques to better characterize the system risk curve for the highway system. 5 (damnjanovic & zhang, 2008) x x x ✓ x x a general and flexible framework for measuring risk-based performance with numerical examples where premium costs are estimated for various preventive maintenance and rehabilitation strategies and contract specifications. 6 (gharaibeh & shirazi, 2009) x x x ✓ x x the risk-based model presented here to fill the price gap of warranty offers is often estimated subjectively due to the lack of a systematic methodology for measuring warranty service costs for road infrastructure assets with wcem, estimated warranty costs, taking into account the pf of guaranteed goods as defined in the warranty clauses and costs which is projected to correct the failure. 7 (li & bai, 2009) x x ✓ x x x the facts show that there is room to increase the effectiveness of traffic control currently used in high-risk work zones and help engineers to understand these risk factors and how they can increase the likelihood of death when severe accidents occur in work zones. 8 (li & madanu, 2009) x x x ✓ x x using the project-level life cycle benefits estimated by the uncertainty-based analysis approach results in a higher percentage of the level of conformity with actual programming practices compared to the level of conformity using the project benefits calculated by the risk-based analysis approach. ariyanto et al./oper. res. eng. sci. theor. appl. 3 (3) (2020) 29-47 32 9 (le et al., 2009) x x ✓ x x x the development and testing of the apra method is an innovative tool that can help the project team to improve the road development process through the definition of proactive scope and risk management. 10 (zhao et al., 2009) x x ✓ x x x the results show that the risk of fatigue cracking is not possible at the surface layer for properly designed asphalt pavement with a semi-rigid base if all layer interfaces are fully bound. 11 (creedy et al., 2010) x x x ✓ x x that the arbitrary application of a base contingency percentage figure, such as 10%, to accommodate project risk can lead to those projects reporting a substantial budget overrun. 12 (sarkar & dutta, 2010) x x ✓ x x x efforts have been made to design and implement new cumulative addition procedures for the ready-mix concrete industry, which address the risks involved and related to concrete production. 13 (hall et al., 2011) x x ✓ x x x can be drawn: (1) risk analysis is illustrated to help pavement engineers; (2) the ahp method makes it possible to compare the importance of parameters not only in each category, but also between categories. 14 (honjo et al., 2011) x x ✓ x x x the results are (1) the probability of the relative failure risk of each slope successfully estimated; (2) the absolute failure probability of each slope is estimated by calibrating the relative failure probability. 15 (hu & huang, 2011) x x x ✓ x x some conclusions: (1) risks may be serious when the shielding machine advances under the cement concrete pavement; (2) loss of risk and pavement condition index associated with maximum settlement due to tunneling; (3) there are about 10 accidents that will occur in the construction of several subways. 16 (pantelidis., 2011) x x ✓ x x x the risk value for each embankment examined derives from the failure hazard and consequence value following the well-known definition of risk. 17 (heravi & hajihosseini, 2012) x x x ✓ x x the identification of the most important risks and their allocation and funding can be used by other parties who seek to attract private investment for large infrastructure projects in developing countries. 18 (mukhopadhyay et al., 2012) x x ✓ x x x reducing the risk of injury, death, and property damage in the highway work zone for employees who carry out operations/maintenance and the community of road users. 19 (tran & molenaar, 2012) x x x ✓ x x conduct a risk analysis at the beginning of the project development process, but also serves as an input to the risk-based framework for selecting the appropriate project delivery method. 20 (yasamis-speroni et al., 2012) ✓ x x x x x an evaluation of the contractor's quality performance, combined with an evaluation of the technical and financial performance of the contractor, can result in a better understanding of the contractor's overall capabilities. a systematic review and analysis of risk assessment in highway construction project 33 21 (cruz & marques, 2013) x x x x x ✓ this investigation revealed evidence that showed that although contracts became increasingly complex over time, the public sector assumed more production and commercial risks in the road development process. 22 (lu et al., 2013) x x ✓ x x x theory and method support in terms of sensible traffic organization to improve traffic safety as well as prevent traffic jams on-road working zones on urban freeways. 23 (azambuja & chen, 2014) x x ✓ x x x mode failure methodology and criticality analysis (fmeca) is an alternative scenario recommended for ready-mix concrete plants to achieve the desired balance between having more than enough resources and avoiding risks and disruptions in the supply chain on time. 24 (ghorbani et al., 2014) x x x x x ✓ time and costs are subject to adverse deviations that lead to the highest priority risk from time delays and cost overruns. 25 (kaleem et al., 2014) x x x ✓ x x the risk of overtime resulting from various factors is the most cardinal problem which ultimately leads to cost overruns and hence triggers turbulence in the estimated cost and initial time. 26 (pineda & arboleda, 2014) x ✓ x x x x the aggregate effect of increasing cost of emergency response, uninsured calamities, third party, and user influence on indicator results, shows a particular risk arising from the indicator-based model and the interaction with road safety policies. 27 (tran & molenaar, 2014) x x x ✓ x x the results indicate that seven delivery selection risk factors have the most influence on db delivery selection: (1) scope risk; (2) third-party and complexity risk; (3) construction risk; (4) utility and right-of-way (row) risk; (5) level of design and contract risk; (6) management risk; and (7) regulation and railroad risk. 28 (wang et al., 2014) x x ✓ x x x pavement engineers need to establish corrective measures such as building superior grooving textures, installing traffic signs at the right speed, etc. to avoid traffic accidents due to hydroplaning. 29 (yan et al., 2014) x x ✓ x x x the lowest evaluative criteria of the road operating environment are given to improve the design of road facilities and intensify the environmental safety risks of the operation of basic road facilities. 30 (el-sayegh & mansour, 2015) x x x ✓ x x inefficient planning is the most significant risk in the highway construction with a probability of moderate to high, inefficient planning weighed the highest among other risks, highway projects require efficient and accurate planning. 31 (hanna et al., 2015) x x x ✓ x x designed to identify the top misallocated risks in the highway construction industry and to provide recommendations to more appropriately allocate these risks on highway construction projects. ariyanto et al./oper. res. eng. sci. theor. appl. 3 (3) (2020) 29-47 34 32 (tran & molenaar, 2015) x ✓ x x x x based on the probabilistic risk analysis process, a risk-based project delivery model selection workshop utilizes probabilistic risk-cost estimation concurrently with the project delivery decision process. 33 (xiao et al., 2015) x x ✓ x x x the traffic risk on the rural highway in general, all of the risk factors can be classified as the four factors and natural environmental factors. 34 (chu & fwa, 2016) x x ✓ x x x the risk analysis procedure aims to overcome the inadequacy of the current asphalt pavement design methods, specifically the asphalt mix design, concerning the functional safety requirements of road operations. 35 (fontán-pagán et al., 2016) x x x ✓ x x the use of a hybrid contract method produces a significant reduction in costs when compared with the unit price contracting method for this particular construction project. 36 (louhghalam & ulm, 2016) x x ✓ x x x the model presented here is only a first-order approach towards a paradigm shift from current strength-based designs to fracture-based designs that are consistent to increase pavement resistance to various risks of distress mechanism, which ultimately aims to reduce maintenance costs and to improve environmental footprint from the aging infrastructure. 37 (tran & bypaneni, 2016) x x x ✓ x x the findings from this paper provide some guidelines for highway agencies to better perform a more accurate risk cost estimate. 38 (diab et al., 2017) x x x ✓ x x inadequate constructional reviews have a significant influence in determining owner contingencies, while changes in owner demand affect the number of owner and contractor contingencies, and also have a significant impact on project schedules. 39 (liu et al., 2017) x x ✓ x x x a comprehensive evaluation model of construction site risk based on the fuzzy mathematical method by establishing a construction risk index rating system derived from ahp, using risk management methodologies, and considering the risk probability and the severity of the consequences. 40 (tokiwa & queiroz, 2017) x x x ✓ x x in ppp projects on the road, it is important to identify risks and allocate responsibilities for risks identified between the public and private sectors specifically, allocating risks related to income is very important because it involves uncertainty for future demand. 41 (nguyen et al., 2018) x x x ✓ x x provide practitioners implementing or considering the implementation of public-private partnerships with a comprehensive overview of risk allocation practices and contractual language across a variety of public-private partnership project characteristics. 42 (nguyen et al., 2018) x x x ✓ x x inadequate constructional reviews have a significant influence in determining owner contingencies, while changes in owner demand affect the number of a systematic review and analysis of risk assessment in highway construction project 35 owner and contractor contingencies, and also have a significant impact on project schedules. 43 (yuan & li, 2018) x ✓ x x x x empirical evidence and simulation results have shown that p3 pavement assets significantly outperform psc pavement assets in terms of service life, probability and duration of maintenance delays, and remaining life after the concession period. 44 (bypaneni & tran, 2018) ✓ x x x x x decision-makers must have a clear understanding of how risks impact each delivery method to select the most suitable delivery method for their projects. 45 (castro-nova et al., 2018) x x ✓ x x x statistically significant differences in perception of the importance of geotechnical risk factors between public institutions and the design built industry. 46 (andrić et al., 2019) x x x ✓ x x risk considerations for bri projects are complex tasks requiring efficient tools that provide complex information about financial issues, to bridge this coverage, new methods developed and applied to complex, scattered and large-scale infrastructure project financial reports. 47 (firouzi & vahdatmanesh, 2019) x ✓ x x x x by using the bermudan collar option, the company will be able to make a more accurate estimate of the total operational costs at the pre-construction stage of the project thereby reducing the risk of failure. 48 (guo et al., 2019) x x ✓ x x x use risk assessments to provide risk specifications for operating rural mountain roads and decide on priority safety precautions. 49 (zheng et al., 2019) x x x x ✓ x the relationship between the risk of the likelihood of a collision and related factors is nonlinear and indicates that the independent variables are not completely independent of each other. 50 (nicholson, 2020) x x x ✓ x x risk communication and consultation will need to take account of variations between risk management specialists and the public, as well as variations between members of the public, in the understanding and interpretation of qualitative and quantitative probability terms. remarks: ✓=discussed x=not discussed ariyanto et al./oper. res. eng. sci. theor. appl. 3 (3) (2020) 29-47 36 based on the analysis of 50 articles in the above table, that in figure 2 shows the distribution of literature reviews from the aspect of risk assessment in highway construction projects. figure 2. distribution of literature reviews 3. risk identification 3.1. internal technical risk this article introduces a contractor quality performance evaluation model (cqp) which measures the quality performance of a pavement contractor that the dot that is in the process of selecting a pavement contractor for a project will benefit from the cqp evaluation model because this system allows clients to quickly assess the quality performance of potential pavement contractors in the list of their offers (yasamissperoni et al., 2012). cronbach's alpha test and correlation analysis were carried out to verify internal consistency, interdependence, and the reliability of delivery risk factors. the ranking of risk factors and their impact on each method of project delivery can help the road agency to increase appropriate risk allocation and risk-taking wisely, which can result in more efficient project delivery (bypaneni & tran, 2018). 3.2. internal non-technical risk the contractor's ability in risk management is a key factor for project performance when deciding on a risk management strategy, the contractor must consider many aspects, including risk responsibilities, risk patterns, risk management capabilities, etc. (wang & chou, 2003). performance analysis finds risks in the relationship between the owner and the concessionaire, revealing weaknesses in the indicator mechanism and dispute resolution. this analysis also reports that force majeure events are not easily distinguishable between insured and non-insured events. this shows a failure in guarantee management with separate incentives in premium costs, 0 5 10 15 20 25 eksternal nontechnical risk eksternal technical risk project nontechnical risk projecct technical risk internal nontechnical risk internal technical risk article 2 5 20 20 1 2 a systematic review and analysis of risk assessment in highway construction project 37 risk coverage, and the effect of moral hazard (pineda & arboleda, 2014). this article shows that this same team member can assist in the selection of project submissions. based on the probabilistic risk analysis process, a risk-based project delivery model selection workshop utilizes probabilistic risk-cost estimation concurrent with the project delivery decision process (tran & molenaar, 2015). empirical evidence and simulation results have shown that p3 pavement assets significantly outperform psc pavement assets in terms of service life, probability and duration of maintenance delays, and remaining life after the concession period. while the average lifetime of a psc residual is only 6.3 years, the average residual life of a p3 partner is 13.5 years (yuan & li, 2018). from numerical results, this article found that, by using the bermudan collar option traded in otc, the company would be able to make a more accurate estimate of the total operational costs at the pre-construction stage. it was also found that limiting future purchase prices could reduce the likelihood of unexpected cost overruns during the project construction phase. it can be concluded that using the bermudan otc collar option can reduce the risk of construction material prices (firouzi & vahdatmanesh, 2019). 3.3. project technical risk this article combines earthquake and transportation engineering techniques to better characterize the risk curve system for the los angeles and orange county, california highway systems. knowledge of seismic hazards must be combined with a means to adequately model system performance (shiraki et al., 2007). comprehensive knowledge about risk factors found from damage data, therefore, becomes important to reduce the level of risk and prevent severe accidents in the work zone (li & bai, 2009). it presents the development and testing of the apra method, which is an innovative tool that can help the project team to improve the highway development process through proactive scope definition and risk management (le et al., 2009). asphalt pavement fatigue behavior with semi-rigid bases: crack fatigue cracking is not possible in the ac layer for well-designed asphalt pavement with semi-rigid bases if the semi-base is rigid in good condition and all interface layers are fully bound (zhao et al., 2009). racusum and cusum can detect that a change has occurred in the process, but cannot predict the cause of the change. this research can be extended by applying the racusum technique to monitor quality in other sectors of the construction industry such as precast and modular manufacturing units including modular formwork and scaffolding, the highway industry including hot mix asphalt plants, units for manufacturing fly ash bricks, block pavers, and other related products (sarkar & dutta, 2010). the risk analysis method is applied to analyze the flexible pavement design using a mechanistic-empirical method. based on this research, the following conclusions can be drawn: (1) risk analysis is illustrated to help pavement engineers. the steps of risk analysis include risk identification using holographic hierarchical modeling (hhm), risk ranking using analytical hierarchy process (ahp), risk assessment, and risk management. (2) the ahp method makes it possible to compare the importance of parameters not only in each category, but also between categories (hall et al., 2011). the conclusions that can be drawn from the analysis are as follows: (1) the probability of the relative failure of each slope is successfully estimated based on the sat data; (2) the absolute failure probability of each slope is estimated by calibrating the relative failure probability based on rfar data (honjo et al., 2011). some conclusions are ariyanto et al./oper. res. eng. sci. theor. appl. 3 (3) (2020) 29-47 38 drawn from the analysis and case studies in this paper as follows: (1) risks may be serious when the shielding machine advances under a cement concrete pavement. this results in a lot of damage such as cracks, breakages, crashing, potholes and explosions, etc., which affect the pavement operation performance and traffic capacity; (2) loss of risk and pavement condition index associated with maximum settlement due to tunneling; (3) there are around 10 accidents that will occur in the construction of several subways in china. also, the risk of tunneling has received high attention in recent years (hu & huang, 2011). this system consists of three main stages, (1) quantification of the danger of failure of the road embankment, (2) calculation of the geometric characteristics of the possibility of failure, and (3) quantification of the consequences. the risk value for each embankment inspected originates from the hazards and the consequence values follow a known risk definition (risk = hazard x consequences) (pantelidis., 2011). intuitively, any process that reduces risk must improve worker safety, reduce agency costs, improve services to the public who are traveling, and lead to more efficient procedures in the long run (mukhopadhyay et al., 2012). with the application of remrue into the risk evaluation of sample road work zones on the beijing toll road, the difference in operating speed between neighboring parts of the road work zone is analyzed to check whether there is a risk of traffic safety and the value of the traffic performance subdivision in the road work zone related to the average operating speed calculated to evaluate the operational risk of traffic (lu et al., 2013). presenting an effective failure mode methodology and criticality analysis (fmeca) combined with a simulation modeling approach for just-in-time supply chain risk management. fmeca and discrete event simulation can be used to model the dynamic nature of justin-time supply chain networks. several alternative scenarios are recommended for ready-made concrete plants to achieve the desired balance between having more than enough resources and avoiding risks and disruptions in their timely supply chain (azambuja & chen, 2014). mtd, transverse, longitudinal slope, tire pattern, and rainfall intensity are important factors for hydroplaning prediction. this paper uses a volumetric measurement method based on 3d laser imaging technology to estimate mtd and to measure the texture depth of all paths. besides, directly using the imu to measure cross slope cannot guarantee good accuracy due to the dynamic movement of the data collection vehicle (wang et al., 2014). by assessing four aspects of the road operating environment including climate, roads, transportation, and administration, it provides road facilities with functions such as early warning before an accident, feedback in emergencies and quick repairs after a disaster, so that the safety of road operations is greatly enhanced (yan et al., 2014). ism is an effective method used to analyze and uncover complex structures, which transform complex and scattered relationships between various elements into a clear multilevel hierarchical structure model (xiao et al., 2015). frameworks and procedures have been presented to include consideration of road slip resistance and hydroplaning in the asphalt mixture design. the proposed framework and analysis procedures aim to address the inadequacy of the current asphalt pavement design methods, specifically asphalt mix designs, concerning the functional safety requirements of road operations (chu & fwa, 2016). the proposed mechanics-based model links the risk of concrete pavement fractures that experience different pressure mechanisms on the material and its structural properties. in addition to classic design recipes such as increasing pavement thickness and reducing a systematic review and analysis of risk assessment in highway construction project 39 joint spacing, both of which reduce the rate of release of energy, the results allow the following conclusions: (1) for fixed pavement structures, increasing fracture toughness and reducing material stiffness reduce the risk of fractures; (2) increasing the horizontal stiffness of the subgrade will improve the performance of concrete pavement that experiences autogenous shrinkage at an early age by reducing the rate of structural energy release; (3) for cases of pavement undergoing a thermal cycle, special attention must be paid to the ratio of the rate of release of dimensionless energy due to bending and axial contributions to ensure that fractures will not occur during transient conditions immediately after the application of sudden temperature changes (louhghalam & ulm, 2016). this paper proposes a comprehensive evaluation model of construction site risk based on the fuzzy mathematical method by building a construction risk rating system derived from ahp, using risk management methodologies, and considering risk probabilities and severity of consequences. the accuracy of the evaluation model is validated through calculation examples, so that it can provide theoretical and practical guidance to reduce the risk of road project construction (liu et al., 2017). the results prove that there is an optimism bias in the db highway project and that there are statistically significant differences in geotechnical risk perception (castro-nova et al., 2018). introducing the application procedure and ghslpe risk assessment model, then, with data on traffic accidents, road conditions, and traffic volume from typical rural mountain roads, the risk of traffic accidents (tar), and the risk of traffic operations (toa) are calculated; the difference between toa and post-tar predictions is compared based on actual conditions (guo et al., 2019). 3.4. project non-technical risk the resulting model is referred to as eric-s. this is the first risk-schedule construction model known by the author to measure the relationship between variables. this model is tested on large projects where target completion dates are monitored. the results are almost identical to those of project participants except that the data from experts took 6 weeks while incorporating project characteristics into the eric-s model only took 2 hours, indicating that the model was effective and efficient (nasir et al., 2003). the model described in this paper is a first-order model in which uncertainty is represented by using averages of each uncertain variable, and risk events are modeled as independent events uncorrelated events because they are actually possible. one possible improvement for the risk modeling process is to build a second-order model in which uncertainty is modeled by the mean and standard deviation of the uncertain variable, including the delay variable. such a model will produce more accurate results in the outermost range of the distribution of costs and time (molenaar, 2005). the premium pricing model developed can be used to assist transport agents and contractors in estimating the "fair" value for psmc. this paper presents a conditional reliability function which can be developed by entering information about in-service pavement conditions using indirect methods. besides, the formulation of boundary-state functions and the application of the moment method allow for direct consideration of different design approaches, as well as the different effects of preventive maintenance and rehabilitation measures. finally, this paper illustrates a framework with numerical examples in which premium costs are estimated for various pm&r strategies and contract specifications (damnjanovic & zhang, 2008). ariyanto et al./oper. res. eng. sci. theor. appl. 3 (3) (2020) 29-47 40 the case article results revealed that using project-level life cycle benefits estimated by the uncertainty-based analysis approach resulted in a higher percentage of conformity with actual indiana dot programming practices compared to the level of compliance using project benefits calculated by risk-based analysis approaches (li & madanu, 2009). the risk-based model presented here to fill the price gap of warranty offers is often estimated subjectively because of the lack of a systematic methodology for measuring warranty service costs for road infrastructure assets. under wcem, the cost of guarantee is estimated, taking into account the pf of the guaranteed item as defined in the warranty clause and the projected costs to correct the failure (gharaibeh & shirazi, 2009). regression analysis shows a weak correlation between the size of the highway project, as measured in indexed programmed costs and measures of excess costs. correlations develop after data transformation is carried out to improve the model. it can also be concluded from research that the arbitrary application of a basic contingency percentage rate, such as 10%, to accommodate project risks can cause projects that report substantial budget overruns (creedy et al., 2010). some conclusions: (1) risks may be serious when the shielding machine advances under the cement concrete pavement; (2) loss of risk and pavement condition index associated with maximum settlement due to tunneling; (3) there are about 10 accidents that will occur in the construction of several subways (hu & huang, 2011). lessons from two ppp case studies are used to improve the contract organization of the tehran-chalus toll road project. the findings from this case article on the identification of the most important risks and their allocation and funding can be used by others who are trying to attract private investment for large infrastructure projects in developing countries (heravi & hajihosseini, 2012). the findings from this article not only encourage decision-makers to carry out risk analysis at the beginning of the project development process, but also function as an input for a risk-based framework for selecting appropriate project delivery methods in high industries (tran & molenaar, 2012). the mathematical relationship between the duration of the highway project, the planned costs, and the type of project are shown in this paper by using various time correlation models flooded with potential risk factors investigated including attributes such as project type, costs, and geographic location. this paper identifies several significant risk variables and their severity that contribute to extensive delays and the consequences exceeding the planned time estimate (kaleem et al., 2014). the results of this test indicate that the risk preferences between public owners and designers and contractors towards the choice of db delivery method do not differ significantly in the scope of risk, third party risk, and complexity risk, utility risk and, row, level of design risk and contract risk, management risk, or regulatory and railroad risk, but statistically different in construction risk (tran & molenaar, 2014). external risks have little effect on the uae highway construction industry. research shows clearly that internal risks threaten projects more than external risks (el-sayegh & mansour, 2015). this flowchart acts as a guideline to assist contractors and owners in designing contracts that are transparent and that efficiently allocate risk to the parties best suited to bear it. by designing contracts with appropriate risk allocation strategies, the project will perform better from a cost and schedule perspective by eliminating activities that do not add value. contract disputes and litigation are examples of activities that did not add value to the project participants who were forced to do when the risk of misallocation. this research has revealed the a systematic review and analysis of risk assessment in highway construction project 41 pitfalls of improper risk allocation in the highway construction industry and offers practical considerations that, if combined from the beginning of the project, will result in higher performance projects (hanna et al., 2015). the use of the hybrid contract method results in a significant cost reduction when compared to the unit price contract method for this particular construction project. this article concludes the effectiveness of assigning contractors to risks associated with variations in the amount. implementation of items for unexpected possibilities shows benefits for both parties, the owner, and the contractor. contracting contingency estimates can be reduced by showing a higher chance of becoming the lowest bidder (fontán-pagán et al., 2016). simulation results show the importance of viewing data from a practical point of view. however, in this case, the difference is small and will not affect funding decisions. users are warned not to neglect the correlation between related inputs because that would result in underestimation of the total cost variance with the effect of cancellation during the simulation between uncorrelated variables (tran & bypaneni, 2016). the models developed and discussed in this paper can help deal with risks in road construction projects by looking at ri, ci, and si ratings of risk drivers and allocating appropriate contingency percentages for use (diab et al., 2017). potential ppp road projects in developing countries may want to take advantage of one or more financial instruments, such as the world bank partial risk guarantee and political risk insurance, even more, developed countries, such as france and spain, have subsidized projects, changing them into successful ppp projects, such as the perpignan-figueras rail concession (tokiwa & queiroz, 2017). this article has introduced practical guidelines for conducting detailed assessments of the impact of risks on the financial viability of ppp projects in developing countries. finally, this paper focuses on risk and the preferred allocation mechanism for ppp toll road projects in vietnam, recognizing that the risk allocation mechanism in ppp projects is dynamic and depends on several contextual variables at the country level (nguyen et al., 2018). the allocation results show that some risks are managed by the public sector such as changes by public authorities, but most of the 31 risks are transferred to the private sector or shared, practitioners who apply or consider implementing ppp, a comprehensive review of risk allocation practices and contract language in various project characteristics ppp in the us (nguyen et al., 2018). bri's project risk assessment demonstrates the application of the fuzzy logic method proposed for large-scale, complex, and geographic infrastructure projects. fuzzy logic-based methods are proven to be a systematic, efficient, and practical tool for infrastructure project risk assessment (andrić et al., 2019). transportation risk management will be improved if greater attention is given to so-called human factors, including risk perception, risk acceptance (including the factors that influence it and the relative importance of those factors), and the nature of the changes in driver behavior with perceived risk changes. (nicholson, 2020). 3.5. external technical risk the results prove that the nn model is a powerful tool for predicting and explaining hrgc crashes with the ability to reveal a continuous function relationship between the likelihood of an accident and contributors. the results showed that the relationship between the likelihood of a collision and related factors was nonlinear, ariyanto et al./oper. res. eng. sci. theor. appl. 3 (3) (2020) 29-47 42 and showed that the independent variables were not completely independent of each other (zheng et al., 2019). 3.6. external non-technical risk concessions were developed using completely different contract models, although certain features are common among these models, especially the duration of the contract and the conditions that must be met to trigger a mechanism to restore financial balance through renegotiation, the uncertainties and negative results of renegotiation lead to changes in risk allocation which have generally transferred commercial risk from the concession from the concessionaire to the grantor. renegotiated contract clauses generally guarantee that their returns will not change, even though their risks are significantly reduced (cruz & marques, 2013). the ppp toll road project in iran observes that the basic performance indicators of these projects due to time and cost may be subject to adverse deviations that lead to the highest priority risk of time delays and excessive costs, the risk of high inflation also results in excessive cost overruns (ghorbani et al., 2014). 4. result the results of the research article analysis based on risk factors are shown in table 2. table 2. mapping research articles analysis based on risk factor factor research article internal risk finance contractor experience client service (32) (47) (2) (20) (26) (43) (44) project risk material duration finance construction method structure construction project management contract field condition k3 (12) (23) (1) (25) (3) (6) (8) (9) (11) (37) (38) (40) (42) (13) (22) (33) (34) (39) (45) (4) (10) (14) (15) (16) (28) (36) (17) (29) (30) (31) (35) (46) (5) (19) (27) (41) (7) (18) (48) (50) external risk socio-economic conditions government (49) (21) (24) based on the analysis of risk sources above, it is found that the risk aspect in the construction of highways that has the highest percentage is financial factors, as shown in figure 3 below: a systematic review and analysis of risk assessment in highway construction project 43 figure 3. barchart analysis of research articles based on risk factors 5. conclusion this article concludes that there is one source of risk that is very influential, namely the risks originating from the project itself, both technically and non-technically. the potential risk weights of a project are based on the frequency parameters of the occurrence of risks and negative consequences due to the occurrence of these risks for project objectives. the results obtained show that from 50 identified risks, there are 11 risks originating from financial factors consisting of 2 internal risks and 9 project risks. finance is the highest risk percentage of the article analyzed. this shows that finance is an important factor in the implementation of construction projects, project financing must be managed properly to avoid problems during project implementation. contractors who do not have adequate finance and poor financial planning will have an impact on project implementation starting from delays in the realization of work, and poor quality of work. by knowing the main risks in a road project, this article is expected to assist the contractor in recognizing and investigating the effect of risk allocation on contractors' risk management decisions, so that prevention can be carried out earlier. this research is expected to assist future research in investigating rigorous analytical methods to verify project financial estimates and also must examine how to consider the effects of correlations on other risk analysis frameworks in the construction industry. 0 5 10 15 government socio-economic k3 field conditions contact project management structure construction construction method finance duration material client service contractor experience article 2 2 11 7 6 4 6 3 1 2 3 2 1 ariyanto et al./oper. res. eng. sci. theor. appl. 3 (3) (2020) 29-47 44 references andrić, j. m., wang, j., zou, p. x. w., zhang, j., & zhong, r. 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(2019). predicting highway-rail grade crossing collision risk by neural network systems. journal of transportation engineering part a: systems, 145(8), 1–8. © 2020 by the authors. submitted for possible open access publication under the terms and conditions of the creative commons attribution (cc by) license (http://creativecommons.org/licenses/by/4.0/). operational research in engineering sciences: theory and applications vol. 3, issue 2, 2020, pp. 54-73 issn: 2620-1607 eissn: 2620-1747 doi: https://doi.org/10.31181/oresta2003049p * corresponding author. dpamucar@gmail.com (d. pamucar), aleksandar.jankovic@gmail.com (a. janković) the application of the hybrid interval rough weighted power heronian operator in multicriteria decision-making dragan pamučar 1*, aleksandar janković 2 1 department of logistics, military academy, university of defence in belgrade, belgrade, serbia 2 ministry of transport and maritime affairs, directorate for transport, montenegro received: 28 may 2020 accepted: 03 july 2020 first online: 03 july 2020 original scientific paper abstract: in this paper, a new multi-criteria model which enables the processing of uncertainty and inaccuracy data through the application of interval rough numbers (irn) is presented. the multi-criteria model represents the integration of the power aggregator (pa) and the weighted heronian mean (whm) operators. the goal of the forming of a hybrid weighted power heronian mean (wphm) is to integrate the advantages of both operators into a single multi-criteria model, which has the following advantages: 1) it eliminates the influence of unreasonable arguments; 2) it takes into account the degree of support between input arguments and 3) it takes into account the interconnectedness of input arguments. based on the mathematical concept of the irn, the hybrid wphm operator was extended and the irnwphm multi-criteria model was created. the irnwpha multi-criteria model enables objective decision-making in the case of imprecise input parameters in the initial decision matrix. also, the irnwpha model allows flexible decision-making and the verification of the robustness of results through a variation of the p and q parameters. the irnwphm model was tested on a real-world multi-criteria example. the results showed that the irnwphm operator enabled a successful transformation of the uncertainties and inaccuracies that exist in group decision-making. key words: interval rough numbers; heronian mean; multi-criteria decisionmaking; power operator. 1. introduction the information that appears in real-world problems is often very difficult to quantify, since many facts, such as the complexity of phenomena and the ambiguity of human reasoning, represent significant limitations. in the multi-criteria modeling of decisions, different decision-makers are likely to use the linguistic expressions of a the application of the hybrid interval rough weighted power heronian operator in multicriteria decision-making 55 different precision to express their preferences (herrera and martínez, 2000). in such situations, uncertainty theories, such as fuzzy sets (zadeh, 1965), rough sets (pawlak, 1982) and the other generalizations of the mentioned theories, are a good tool for presenting uncertainty. in order to reach the best solution in group multi-criteria models, operators for the aggregation of group preferences and the calculation of the criterion functions of alternatives have been developed. in general, aggregation operators are important tools for the fusion of information into multi-criteria problems, which can also be used to evaluate alternatives. to date, many information fusion operators that can be used in decision-making models have been developed (beliakov et al., 2007; xu et al., 2012; liu et al., 2015), including: the bonferroni mean (bonferroni, 1950), the hamy mean (hara et al., 1998), the dombi operators (dombi, 1982), the maclaurin mean (maclaurin, 1729), the heronian mean (beliakov, 2007), the muirhead mean (muirhead, 1902), power aggregation (yager , 2001) and numerous hybrid forms of aggregation operators (pamučar et al., 2020; sinani et al., 2020). a better understanding of correlations between attributes can be very important for making objective decisions, so it is necessary to take into account the fact that relationships between attributes can be a significant determinant of an aggregated outcome. therefore, the operators that have this feature have attracted significant attention in multi-criteria decision-making. based on the analysis presented by liu et al. (2016), it can be concluded that some aggregation operators only take into account the significance of the information presented in a decision matrix, while the interrelationships between data are neglected. although there are aggregation operators which respect interrelationships between data, there are still significant shortcomings of some aggregation operators that need to be highlighted. for example, when aggregating data, power aggregation (yager, 2001) only takes into account the influence of a change in the vector of the weight coefficients of criteria on aggregated values. at the same time, power aggregation (pa) does not take into account the relationships between aggregated arguments. on the other hand, bonferroni mean (bm) operators respect the correlation between the attributes ic and jc ( i j ,  1 2, ,..., nc c c c= ), but ignore the relationship between the attributes ic and itself. considering the correlations between the attributes using the bm may also lead to redundancy (liu et al., 2016). bm operators consider the correlation between ic and j c ( i j ) and the simultaneous correlation between jc and ic ( i j ), which may result in potential redundancy (dutta et al., 2015). some of the requirements for decision-making in real-world systems include flexible decision-making, respect for the mutual influence between decision attributes and the elimination of the influence of awkward data. to achieve this goal, the integration of the pa and the weighted heronian mean (whm) operators into a hybrid wpha operator is presented in this paper. the hm operator is a very useful tool, which takes into consideration the relationships between the attributes being aggregated. the wpha operator combines the advantages of the pa and hm operators, and is a powerful tool with the following features: 1) it eliminates the influence of unreasonable arguments; 2) it takes into account the degree of support between input arguments, and 3) it takes into account the interconnectedness of input arguments. in recent years, the advantages of aggregation operators have been implemented pamučar and janković/oper. res. eng. sci. theor. appl. 3 (2) (2020) 54-73 56 through multi-criteria models in a number of uncertainty theories: fuzzy sets (pamucar et al., 2020; ecer and pamucar, 2020), intuitionistic fuzzy sets (xu and yager, 2011; he and he, 2016), intervalvalued intuitionistic fuzzy sets (liu and li, 2017), hesitant fuzzy sets (he et al., 2015), rough sets (sremac et al., 2018; pamucar et al., 2018; yazdani et al., 2020) and so on. to the authors’ knowledge, no study considering the fusion of the pa and whm aggregators in an interval rough environment has been carried out to date. therefore, the logical goal and motivation for this study imply the presentation of a hybrid irnwphm operator. in this paper, interval rough numbers were used to exploit uncertainties and inaccuracies, as they have certain advantages over traditional fuzzy sets (yazdani et al., 2020). these advantages are especially evident when irns are applied in group decision-making. the rest of the paper is organized into the next six sections. after the introduction, the preliminaries of irns are presented in the second section of the paper. in the third section, the mathematical integration of the whm and pa operators in an irn environment is presented. in the fourth section of the paper, the structure of the multicriteria irn wphm model is presented. in the fifth section, the model was tested on a real-world example, and the results were validated through the variation of the p and q parameters. finally, the concluding remarks are given in the sixth section of the paper. 2. interval rough numbers assume that u is the universe containing all the objects registered in an information table. assume that there is a set of the k classes representing the dm’s preferences 1 2 ( , ,..., ) k r j j j= provided that they belong to the row that satisfies the condition 1 2 ... k j j j   and another set of the k classes that also represent the dm’s preferences * 1 2 ( , ,..., ) k r i i i= . assuming that all the objects are defined in the universe and related to the dm’s preferences. in * r , every class of objects is represented by the interval  ,i li uii i i= , provided that li uii i (1 i m  ), and , li ui i i r are satisfied. then, lii denotes the lower interval limit, while uii denotes the upper interval limit of the i class. if both class limits (the lower and the upper limits) presented so as * * * * * * 1 2 1 2 ,..., , ,..., l l lj u u uk i i i i i i      ( 1 ,j k m  ) are satisfied, respectively, then the two new sets containing the lower class * * * * 1 2 ( , ,..., ) l l l lj r i i i= and the upper class * * * * 1 2 ( , ,..., ) u u u uk r i i i= can be defined, respectively. if that is the case, then for any class * li i r ( 1 i j  ) and * ui i r ( 1 i k  ), the lower approximation of * li i and * ui i can be defined as follows (pamucar et al., 2018):  * * *( ) / ( )li l liapr i y u r y i=   (1)  * * *( ) / ( )ui u uiapr i y u r y i=   (2) the above-mentioned approximations of * li i and * ui i are defined by applying the following equation:  * * *( ) / ( )li l liapr i y u r y i=   (3) the application of the hybrid interval rough weighted power heronian operator in multicriteria decision-making 57  * * *( ) / ( )ui u uiapr i y u r y i=   (4) both object classes (the upper and the lower classes ( * li i and * ui i , respectively)) are defined by their lower limits * ( ) li lim i and * ( ) ui lim i , and by their upper limits *( ) li lim i and *( ) ui lim i , respectively: * * *1 ( ) ( ) ( ) li l li l lim i r y y apr i m =  (5) * * * * 1 ( ) ( ) ( ) ui u ui l lim i r y y apr i m =  (6) where l m and * l m denote the number of the objects contained in the lower approximations * li i and * ui i , respectively. the upper limits *( ) li lim i and *( ) ui lim i are defined by the equations (7) and (8), as follows: * * *1 ( ) ( ) ( ) li l li u lim i r y y apr i m =  (7) * * * * 1 ( ) ( ) ( ) ui u ui u lim i r y y apr i m =  (8) where um and * u m denote the number of the objects contained in the upper approximations * li i and * ui i , respectively. for the lower class of objects, the rough boundary interval from * li i is represented as * ( ) li rb i and denotes the interval between the lower and the upper limits: * * * ( ) ( ) ( ) li li li rb i lim i lim i= − , (9) while for the upper object class, the rough boundary interval * ui i is obtained based on the following equation: * * * ( ) ( ) ( ) ui ui ui rb i lim i lim i= − (10) then, the uncertain class of the objects * li i and * ui i can be expressed by using their lower and upper limits, as follows: * * * ( ) ( ), ( ) li li li rn i lim i lim i =   (11) * * * ( ) ( ), ( ) ui ui ui rn i lim i lim i =   (12) it can be seen that every class of objects is defined by its lower and upper limits that create the interval rough number that can be defined as: * * * ( ) ( ), ( ) i li ui irn i rn i rn i =   (13) interval rough numbers are characterized by specific arithmetic operations, which differ from those dealing with typical rough numbers. arithmetic operations between pamučar and janković/oper. res. eng. sci. theor. appl. 3 (2) (2020) 54-73 58 two interval rough numbers    ( )1 2 3 4( ) , , ,irn a a a a a= and    ( )1 2 3 4( ) , , ,irn b b b b b= are done by applying the following expressions (14), (15), (16), (17) and (18) (pamučar et al., 2019): (1) the addition of interval rough numbers “+”    ( )    ( )    ( ) 1 2 3 4 1 2 3 4 1 1 2 2 3 3 4 4 ( ) ( ) , , , , , , , , , irn a irn b a a a a b b b b a b a b a b a b + = + = + + + + (14) (2) the subtraction of interval rough numbers “-”    ( )    ( )    ( ) 1 2 3 4 1 2 3 4 1 4 2 3 3 2 4 1 ( ) ( ) , , , , , , , , , irn a irn b a a a a b b b b a b a b a b a b − = − = − − − − (15) (3) the multiplication of interval rough numbers “×”    ( )    ( )    ( ) 1 2 3 4 1 2 3 4 1 1 2 2 3 3 4 4 ( ) ( ) , , , , , , , , , irn a irn b a a a a b b b b a b a b a b a b  =  =     (16) (4) the division of interval rough numbers “/”    ( )    ( )    ( ) 1 2 3 4 1 2 3 4 1 4 2 3 3 2 4 1 ( ) / ( ) , , , / , , , / , / , / , / irn a irn b a a a a b b b b a b a b a b a b = = and (17) (5) the scalar multiplication of interval rough numbers, where 0k     ( )    ( )1 2 3 4 1 2 3 4( ) , , , , , ,k irn a k a a a a k a k a k a k a =  =     (18) 3. interval rough weight power heronian operator the power aggregation (pa) operator proposed by yager (2001) is a very significant aggregation operator, which eliminates the impact of unreasonable arguments. the traditional pa operator can be defined as follows: definition 1 (yager, 2001): let ( 1 2 , ,..., n    ) be a set of non-negative numbers and p,q ≥ 0. if ( ) ( ) 1 1 2 1 1 ( ) ( , ,..., ) 1 ( ) n i i i n n i i t pa t       = = + = +   (19) where 1, ( ) ( , ) n i i j j j i t sup   =  =  and ( , )i jsup   denote the degree of the support that i received from j , where ( , )i jsup   satisfies the following axioms: 1) ( , ) ( , )i j j isup sup   = ; 2)  ( , ) 0,1i jsup   = ; 3) ( , ) ( , ), i j i k i j i k sup sup if        −  − . the application of the hybrid interval rough weighted power heronian operator in multicriteria decision-making 59 the heronian mean (hm) operator was proposed by beliakov (2007). the hm takes into account the interconnectedness between input arguments (liu and pei, 2012). the hm operator can be defined as follows: definition 2 (yu, 2013): let p,q ≥ 0, ( 1 2 , ,..., n    ) be a set of non-negative numbers. if 1 , 1 2 1 2 ( , ,..., ) ( 1) n n p q p q p q n i j i j i hm n n      + = =   =   +   (20) then hmp,q is called the heronian mean (hm) operator. definition 3 (zhao, 2019): let , 0p q  and ( 1 2, ,..., n   ) represent a set of nonnegative numbers. then, the weight heronian mean (whm) operator for averaging can be defined as follows: ( ) ( )( ) 1 , 1 2 1, 2 ( , ,..., ) ( 1) n p qqpp q n i i j j i j i whm nw nw n n      + = =   =   +   (21) where whmp,q is called the weighted heronian mean (whm) operator. based on the defined settings of the pa and whm operators, eqs. (19) and (21), in the following part a hybrid interval rough weighted power heronian aggregation (irwpha) operator was developed. definition 4: set ( )' ', , ,l u l ui i i i i       =     (i = 1,2,..,n) as a collection of irns in  ; then the irwpha can be defined as follows: 1 , 1 2 1, 1 1 2 ( , ,..., ) ( 1) p q p q n ii jp q i n i jn n i j i t tt tt t nw wnw w irnwpha n n n n w w w w      + = = = =            =       +            (22) where ( ) ( ) 1 1 ( ) 1 ( ) i t n i i t w t   = + = + , ( ) 1, ( , ) n i i j j j i t sup   =  =  and 1 1 n i i w = = , where ( , )i jsup   denote the degree of the support that i received from j , where ( , ) i j sup   satisfies the following axioms (đorđević et al., 2019): 1) ( ( ), ( )) ( ( ), ( ))i j j isup f f sup f f   = ; 2)  ( ( ), ( )) 0,1i jsup f f  = ; 3) ( ( ), ( )) ( ( ), ( )), ( , ) ( , )i j i k i j i ksup f f sup f f if d d         , where ( , ) i j d   represents the distance between the numbers i and j . then ,p qirnwpha represents the irn weight power heronian aggregation operator. theorem 1: set ( )' ', , ,l u l ui i i i i       =     as a collection of irns in  ; then, according to eq. (22), aggregation results are obtained for irns, and the following aggregation formula can be developed: pamučar and janković/oper. res. eng. sci. theor. appl. 3 (2) (2020) 54-73 60 1 , 1 2 1, 1 1 1, 1 1 2 ( , ,..., ) ( 1) 2 ( 1) p q p q n ii jp q i n i jn n i j i t tt tt t p q n ii jl li i jn n i j i t tt tt t nw wnw w irnwpha n n n n w w w w nw wnw w n n n n w w w w        + = = = = = = = =            =       +                       +       =       1 1 1, 1 1 ' ' 1 1 , , 2 ( 1) 2 ( 1) p q p q p q n ii ju ui i jn n i j i t tt tt t p q ii jl li i jn n t tt tt t nw wnw w n n n n w w w w nw wnw w n n n n w w w w     + + = = = = = =                                     +                      +          1 1, 1 ' ' 1, 1 1 , 2 ( 1) p q n i j i p q p q n ii ju ui i jn n i j i t tt tt t nw wnw w n n n n w w w w   + = = + = = = =                                                                     +                 (23) proof: the proof for theorem 1 is presented in the following section. based on the equations (19) and (22), the following is obtained: a) 1 i i i i in t tt nw w nw n w w   = =  and 1 i j j j jn t tt nw w nw n w w   = =  ; b) 1 1 1 ' ' 1 1 , , , p i il ui i p i in n t tt ti t ti in t t i it l ui i i in n t tt tt t nw w nw w n n w w w wnw w n w w nw w nw w n n w w w w      = = = = =               =                      ; c) 1 1 1 ' ' 1 1 , , , q i ij jl u q j jn n t tt ti t tj jn t t i it j jl u j jn n t tt tt t nw w nw w n n w w w wnw w n w w nw w nw w n n w w w w      = = = = =               =                      ; the application of the hybrid interval rough weighted power heronian operator in multicriteria decision-making 61 d) 1 1 1 1 1 1 ' 1 , , p q ii jl li i jn n t tt tt t p q ii ju ui i jp q n n t tt ti t ti ji i jn n t tt tt t i i in t tt nw wnw w n n w w w w nw wnw w n n w w w wnw wnw w n n w w w w nw w n w w        = = = = = = =                                                  =                ' 1 ' ' 1 1 , p q i jl l jn t tt p q ii ju ui i jn n t tt tt t nw w n w w nw wnw w n n w w w w    = = =                                                                        finally, the equation for irn is obtained by means of the weight power heronian operator ( ,p qirnwpha ) for aggregation, as follows: 1 , 1 2 1, 1 1 2 ( , ,..., ) ( 1) p q p q n ii jp q i n i jn n i j i t tt tt t nw wnw w irnwpha n n n n w w w w      + = = = =            =       +            1 1, 1 1 1 1, 1 1 2 , ( 1) 2 ( 1) p q p q n ii jl li i jn n i j i t tt tt t p q p q n ii ju ui i jn n i j i t tt tt t nw wnw w n n n n w w w w nw wnw w n n n n w w w w     + = = = = + = = = =                     +                           +         =       1 ' ' 1, 1 1 ' ' 1, 1 1 , 2 , ( 1) 2 ( 1) p q p q n ii jl li i jn n i j i t tt tt t p q n ii ju ui i jn n i j i t tt tt t nw wnw w n n n n w w w w nw wnw w n n n n w w w w     + = = = = = = = =                                +                          +             1 p q+                                                         so, theorem 1 is true. theorem 2 (idempotency): set ( )' ', , ,l u l ui i i i i       =     as a collection of irns in  ; if i = , then , , 1 2 ( , ,.., ) ( , ,.., ) p q p q n irnwpha irnwpha     = . proof: since i = , i.e. l l i  = , u u i  = , ' 'l l i  = , ' 'u u i  = , then pamučar and janković/oper. res. eng. sci. theor. appl. 3 (2) (2020) 54-73 62 ( )( ) ( )( ) ( )( ) ( )( ) ( )( ) ( )( ) ( )( ) ( )( ) , , 1 2 1 1 1 1 1 1 ( , ,.., ) ( , ,.., ) 1 12 , ( 1) 1 1 1 12 ( 1) 1 1 p q p q n p q p q l l n n i j l l i jn nl l i j i t tt t p u u i j u u i jn nu u t tt t irnwpha irnwpha n t n t n n t t n t n t n n t t                   + = = = = = = =     + +         + + +         + +      + + +    =      ( )( ) ( )( ) ( )( ) ( )( ) ( )( ) ( )( ) ( )( ) 1 1 1 ' ' ' ' ' ' 1 1 1 ' ' ' ' 1 , 1 12 , ( 1) 1 1 1 12 ( 1) 1 1 q p q n n i j i p q p q l l n n i j l l i jn nl l i j i t tt t p u u i j u in u tt n t n t n n t t n t n t n n t t           + = = + = = = = =                               + +         + + +       + +    + + +        ( )( ) 1 ' ' 1 1 q p q n n u jn u i j i tt   + = = =                                                                          ( )( ) ( )( ) ( )( ) ( )( ) ( )( ) ( )( ) ( )( ) ( )( ) 1 1 1 1 1 1 1 1 1 12 , ( 1) 1 1 , 1 12 ( 1) 1 1 2 p q p q l l n n l l n nl l i j i t tt t p q p q u u n n u u n nu u i j i t tt t n t n t n n t t n t n t n n t t             + = = = = + = = = =        + +           + + +              + +           + + +        =       ( )( ) ( )( ) ( )( ) ( )( ) ( )( ) ( )( ) ( )( ) ( )( ) 1 ' ' ' ' ' ' 1 1 1 1 ' ' ' ' ' ' 1 1 1 1 1 , ( 1) 1 1 1 12 ( 1) 1 1 p q p q l l n n l l n nl l i j i t tt t p q p q u u n n u u n nu u i j i t tt t n t n t n n t t n t n t n n t t             + = = = = + = = = =        + +          + + +           + +         + + +                                                                  1 1 1 1 1 '' '' 1 2 1 1 2 1 1 , , ( 1) ( 1) 2 1 1 2 1 1 , ( 1) ( 1) p q p qp q p qn n n n l l u u i j i i j i p q pp qn n l l u i j i n n n n n n n n n n n n n n n n n n n n n n n n         + + = = = = + = =                             + +              =               + +          1 1 q p qn n u i j i + = =                                 the application of the hybrid interval rough weighted power heronian operator in multicriteria decision-making 63 ( ) ( ) ( ) ( ) 1 1 1 1 1 1 ' ' 1 1 2 2 , , ( 1) ( 1) 2 2 , ( 1) ( 1) n n n np q p qp q p q l u i j i i j i n n n np q p qp q p q l u i j i i j i n n n n n n n n      + ++ + = = = = + ++ + = = = =               + +       = =                + +            the theorem 2 proof is completed. theorem 3 (boundedness): set ( )' ', , ,l u l ui i i i i       =     as a collection of rns in  ; let ( )' 'min( ), min( ) , min( ), min( )l u l ui i i i    −    =     and ( )' 'max( ), max( ) , max( ), max( )l u l ui i i i    +    =     , then , 1 2 ( , ,..., ) . p q n irnwpha     − +   proof: let ( )' '1 2min( , ,..., ) min( ), min( ) , min( ), min( )l u l un i i i i       −    = =     and ( )' '1 2max( , ,..., ) max( ), max( ) , max( ), max( )l u l un i i i i       +    = =     ; then, it can be said that min( )l l i i i   − = , min( )u u i i i   − = , ' 'min( )l l i i i   − = , ' 'min( )u u i i i   − = , max( ) l l i i i   + = , max( )u u i i i   + = , ' 'max( )l l i i i   + = , ' 'max( )u u i i i   + = . based on that, the following inequalities can be formulated: ' ' ' ' ' ' ; min( ) max( ); min( ) max( ); min( ) max( ); min( ) max( ). i l l l j j j i i u u u j j j i i l l l j j j i i u u u j j j i i                − +           according to the above-shown inequalities, it can be concluded that , 1 2 ( , ,.., ) p q n irnwpha     − +   holds. theorem 4 (commutativity): let the interval rough set ' ' ' 1 2 ( , ,..., ) n    be any permutation of 1 2( , ,.., ).n   then, , , ' ' ' 1 2 1 2 ( , ,.., ) ( , ,.., ) p q p q n n irnwpha irnwpha     = . proof: this property is obvious. 4. the irnwpha model for multi-criteria decision-making based on the irnwpha operator, a model for the group multi-criteria evaluation of alternatives that includes the following steps can be defined: pamučar and janković/oper. res. eng. sci. theor. appl. 3 (2) (2020) 54-73 64 step 1. the formation of the initial decision matrix. defining a set of the experts e e ( 1 e t  , t represents the number of the experts) who evaluate alternatives and form expert correspondent matrices ; e e e ij ij m n x x x   =   ( 1 e t  ). the aggregation of the expert matrices ij m n x x   =   into the initial decision matrix was performed by using the irn power heronian aggregator (đorđević et al., 2019). step 2. the initial decision matrix normalization. the normalization of the initial decision matrix is performed by applying the equation (24). thus, the normalized matrix ( ) ij m n n irn n   =   is formed. 1 1 / 1 / n ij ij i ij n ij ij i x x if j b n x x if j c = =   =  −    (24) step 3. the determination of the criterion function alternatives. by using irnwpha (23), the score function values ( )1 2 , , ( ) ( ), ( ),..., ( ) p q r i m h n irnwpha irn n irn n irn n= are obtained, representing the final values of the preferences by the alternatives. step 4. ranking alternatives. the ranking of the alternatives  1 1, ,..., ma a a is done based upon the value of the criterion function ( ) i h n , where the alternative that has a higher value ( ) i h n is preferable. 5. case study in the following section, the application of the irnwpha multi-criteria model for solving real-world problems is discussed. the irnwpha model was applied to evaluate the work of the advisors in dangerous goods transport. the criteria accounted for in table 1 were taken from a study by pamucar et al. (2019), in which the application of a linguistic neutrosophic methodology in order to evaluate advisors’ work was considered. table 1. the criteria for the evaluation of advisors’ work (pamucar et al. 2019) number criteria type 1. the knowledge of regulations and professional development benefit 2. the analytical processing of the established requirements benefit 3. the quality of the proposed measures benefit 4. the level of implementation of the proposed measures benefit 5. the quality of the professional training of the employees benefit 6. a response to situations of emergency benefit 7. the preparation of documents benefit 8. the method for solving professional questions benefit 9. activity in professional bodies benefit the application of the hybrid interval rough weighted power heronian operator in multicriteria decision-making 65 a total of eight experts participated in the research ( , 1, 2,..., 8 i e i = ). the experts used the following nine-point scale to evaluate the work of the ten advisors ( , 1, 2,...,10 i a i = ): 1 – very low (vl); 2 – medium low (ml); 3 – low (l); ... ; 8 – high (h); 9 – very high (vh). the weighting coefficients of the criteria were taken from the pamucar et al. (2019) study: ( )0.1178, 0.0875, 0.1020, 0.1087, 0.1302, 0.0904, 0.0838, 0.1163, 0.1632 t j w = . in the following section, the application of the irnwpha is presented through the steps defined in the previous section of the paper: step 1 the formation of the initial decision matrix: eight experts evaluated the advisors using a nine-point scale. expert correspondent matrices with evaluation of advisors are shown in table 2. table 2. the expert correspondent matrices expert 1 alt. c1 c2 c3 c4 c5 c6 c7 c8 a1 (3;3) (5;6) (7;8) (1;2) (5;6) (3;4) (3;4) (5;6) a2 (8;9) (7;8) (5;6) (9;9) (5;6) (5;6) (7;8) (5;6) a3 (6;5) (3;4) (1;2) (3;4) (3;3) (5;6) (9;9) (5;6) a4 (4;5) (3;3) (3;4) (7;8) (5;5) (5;6) (9;9) (5;6) a5 (7;7) (7;8) (9;9) (5;6) (7;7) (5;6) (5;6) (5;6) a6 (5;5) (3;4) (5;6) (1;2) (3;3) (3;4) (3;4) (5;6) a7 (5;5) (5;5) (3;4) (1;1) (7;7) (5;6) (1;1) (3;4) a8 (6;7) (9;9) (5;6) (1;1) (7;8) (5;6) (5;6) (5;5) a9 (5;5) (3;4) (3;4) (1;2) (3;4) (5;6) (3;4) (5;6) a10 (4;5) (5;5) (5;6) (3;3) (5;5) (3;4) (5;6) (7;7) … expert 8 alt. c1 c2 c3 c4 c5 c6 c7 c8 a1 (5;6) (9;9) (7;8) (7;8) (1;2) (3;3) (8;9) (7;8) a2 (9;9) (9;9) (9;9) (8;9) (9;9) (9;9) (9;9) (7;7) a3 (7;8) (3;4) (5;6) (7;8) (8;9) (8;9) (7;8) (7;8) a4 (9;9) (8;9) (8;9) (9;9) (8;9) (8;9) (9;9) (5;6) a5 (7;8) (7;8) (5;6) (7;8) (8;9) (5;6) (7;8) (5;6) a6 (7;8) (3;4) (5;5) (7;8) (8;9) (5;5) (8;9) (8;9) a7 (7;8) (5;6) (5;5) (1;1) (8;9) (8;9) (8;9) (8;9) a8 (7;8) (7;8) (5;6) (1;2) (9;9) (9;9) (7;8) (9;9) a9 (5;6) (1;2) (1;1) (7;8) (3;4) (5;6) (7;7) (8;9) a10 (5;5) (5;6) (5;6) (7;8) (1;2) (7;8) (7;8) (5;6) the dilemmas and uncertainties that exist during the expert evaluation of the advisors are shown by using the values given in table 2. thus, for example, for the expert e8 in the position a1-c1, the value is (5;6). this means that, during the evaluation of the advisor a1 (for the criterion c1), the e8 expert had a dilemma between the two values from the nine-point scale, i.e. there was a dilemma between the values 5 and 6 from the scale. also, with the expert e8 in the position a1-c2, it is pamučar and janković/oper. res. eng. sci. theor. appl. 3 (2) (2020) 54-73 66 possible to notice that there was no dilemma about the choice of the values from the composition, so the value (9;9) was assigned. in the next part, the transformation of uncertainty into an irn was performed by using the equations (1) – (13). after the aggregation of the irn expert correspondence matrices, an aggregated irn initial decision matrix was obtained, as in table 3. the aggregation was performed by using the equation (21). t a b le 3 . t h e a g g re g a te i n it ia l d e ci si o n m a tr ix a lt . c 1 c 2 c 3 … c 9 a 1 ([ 4 .0 0 ,6 .0 0 ], [4 .6 3 ,6 .7 0 ]) ([ 5 .6 3 ,7 .4 1 ], [6 .5 8 ,8 .0 6 ]) ([ 3 .8 7 ,6 .6 0 ], [4 .8 6 ,7 .3 3 ]) ([ 5 .8 5 ,7 .5 0 ], [6 .5 8 ,8 .2 8 ]) a 2 ([ 8 .3 5 ,8 .9 5 ], [8 .3 5 ,8 .9 5 ]) ([ 7 .5 8 ,8 .6 3 ], [8 .4 4 ,8 .8 9 ]) ([ 5 .0 9 ,7 .7 5 ], [5 .8 5 ,8 .2 8 ]) ([ 5 .1 6 ,7 .6 1 ], [5 .9 1 ,8 .5 9 ]) a 3 ([ 6 .2 0 ,7 .7 7 ], [7 .1 9 ,8 .3 3 ]) ([ 4 .3 6 ,7 .3 8 ], [5 .3 1 ,7 .9 1 ]) ([ 3 .7 0 ,4 .9 0 ], [4 .7 0 ,5 .9 0 ]) ([ 6 .2 6 ,7 .9 0 ], [7 .2 9 ,8 .6 3 ]) a 4 ([ 6 .4 9 ,8 .3 7 ], [6 .5 5 ,8 .6 1 ]) ([ 5 .8 1 ,8 .3 8 ], [6 .5 4 ,8 .7 7 ]) ([ 5 .7 7 ,8 .2 2 ], [6 .6 5 ,8 .7 1 ]) ([ 5 .8 5 ,7 .5 0 ], [6 .5 8 ,8 .2 5 ]) a 5 ([ 6 .6 2 ,7 .8 2 ], [7 .3 5 ,8 .3 8 ]) ([ 5 .8 6 ,7 .6 7 ], [6 .8 9 ,8 .3 9 ]) ([ 5 .2 1 ,6 .6 3 ], [5 .7 5 ,7 .4 2 ]) ([ 6 .6 2 ,7 .8 2 ], [7 .3 9 ,8 .5 5 ]) a 6 ([ 4 .4 9 ,6 .3 7 ], [4 .8 4 ,7 .2 8 ]) ([ 3 .8 6 ,6 .3 3 ], [4 .7 9 ,7 .2 6 ]) ([ 4 .6 8 ,7 .4 0 ], [5 .2 9 ,7 .9 8 ]) ([ 5 .1 5 ,7 .6 5 ], [6 .2 0 ,8 .3 8 ]) a 7 ([ 6 .6 4 ,7 .8 0 ], [6 .7 0 ,8 .1 6 ]) ([ 5 .9 0 ,7 .6 7 ], [6 .0 8 ,8 .1 0 ]) ([ 3 .9 7 ,6 .5 6 ], [4 .6 3 ,6 .8 4 ]) ([ 4 .2 4 ,6 .3 0 ], [5 .0 1 ,7 .0 4 ]) a 8 ([ 5 .8 5 ,7 .5 0 ], [6 .1 1 ,7 .8 8 ]) ([ 5 .7 8 ,8 .1 0 ], [6 .2 2 ,8 .4 1 ]) ([ 4 .7 1 ,6 .4 0 ], [5 .4 7 ,7 .4 3 ]) ([ 4 .3 3 ,6 .1 0 ], [5 .0 0 ,7 .0 6 ]) a 9 ([ 4 .2 0 ,5 .3 6 ], [4 .8 4 ,6 .3 0 ]) ([ 2 .3 8 ,5 .0 4 ], [3 .3 4 ,5 .9 2 ]) ([ 3 .3 3 ,5 .9 7 ], [3 .8 5 ,6 .9 6 ]) ([ 5 .0 6 ,6 .8 8 ], [6 .0 6 ,7 .8 8 ]) a 1 0 ([ 6 .1 7 ,8 .2 6 ], [5 .8 1 ,8 .2 9 ]) ([ 5 .8 7 ,7 .2 6 ], [5 .9 7 ,7 .5 9 ]) ([ 4 .5 8 ,6 .4 0 ], [5 .4 7 ,7 .4 3 ]) ([ 6 .1 8 ,7 .6 0 ], [6 .8 4 ,8 .2 6 ]) the application of the hybrid interval rough weighted power heronian operator in multicriteria decision-making 67 step 2 – the initial decision matrix normalization: the normalization of the elements of the initial decision matrix is a logical step in the multi-criteria models in which criteria are represented by the different units of measurement and/or in which there are two types of criteria (benefit and cost). in this paper, the normalization of the value of the initial decision matrix is omitted because: 1) a nine-point scale was used to evaluate all the alternatives, i.e., all the criteria are presented by the same units, and 2) all the criteria belong to the group of the benefit criteria, i.e. there are no two types of the criteria. steps 3 and 4 the determination of the criterion function ( ) i h n of alternatives and the ranking of alternatives by using the irnwpha, equation (23), the alternatives of the criterion functions are obtained as in table 4. table 4. the ranking of the alternatives alt. irn ( )ih n crisp ( )ih n rank a1 ([4.12,6.18],[4.96,7.05]) 5.58 9 a2 ([6.52,8.04],[7.13,8.54]) 7.57 1 a3 ([5.46,7.34],[6.38,8.03]) 6.83 4 a4 ([6.38,8.12],[7.04,8.59]) 7.55 2 a5 ([6.16,7.52],[6.93,8.22]) 7.22 3 a6 ([4.43,6.7],[5.19,7.54]) 5.96 8 a7 ([4.97,6.93],[5.55,7.6]) 6.26 7 a8 ([5.15,7.2],[5.8,7.84]) 6.50 6 a9 ([3.91,6.1],[4.67,6.93]) 5.40 10 a10 ([5.21,7.39],[5.73,7.97]) 6.57 5 the calculation of the irn value from table 4 is shown in the next section. table 5 shows the values of the alternative a1 according to the criteria c1-c9. table 5. the values of the alternative a1 criterion irn value c1 ([4.00,6.00],[4.63,6.70]) c2 ([5.63,7.41],[6.58,8.06]) c3 ([3.87,6.60],[4.86,7.33]) c4 ([2.04,4.96],[3.04,5.96]) c5 ([3.07,5.13],[4.07,6.13]) c6 ([2.87,4.93],[3.50,5.90]) c7 ([5.32,7.03],[6.32,8.03]) c8 ([3.63,5.51],[4.36,6.57]) c9 ([5.85,7.50],[6.58,8.28]) since ( )' '1 1 1 1 1 ( ) , , ,l u l uirn h n n n n n   =     consists of the four segments, 1 ( )irn h n aggregation will be performed separately for each of the segments, i.e. ( )1,1 1 1 1( 1); ( 2),..., ( 9) l l l n c nirnwp nh ca c , ( )1,1 1 1 1( 1); ( 2),..., ( 9) u u u n c nirnwp nh ca c , ( )1,1 ' ' '1 1 1( 1); ( 2),..., ( 9) l l l i n c n cnwpha cr n and pamučar and janković/oper. res. eng. sci. theor. appl. 3 (2) (2020) 54-73 68 ( )1,1 ' ' '1 1 1( 1); ( 2),..., ( 9) u u u i n c n cnwpha cr n . the segment calculation ( )1,1 1 1 1( 1); ( 2),..., ( 9) l l l n c nirnwp nh ca c is shown in detail in the next section: step 1: normalized number functions are calculated: ( )1 4 ( 1) 0.11 4 5.63 ... 5.85 l f n c = = + + + ; ( )1 5.63 ( 2) 0.16 4 5.63 ... 5.85 l f n c = = + + + , …, ( )1 5.85 ( 9) 0.16 4 5.63 ... 5.85 l f n c = = + + + . step 2: the calculation of the degree of support for numbers: 1 1 ( ( ( 1)), ( ( 1))) 0.045 l l sup f n c f n c = , 1 1 ( ( ( 1)), ( ( 3))) 0.003 l l sup f n c f n c = , 1 1 ( ( ( 1)), ( ( 4))) 0.054 l l sup f n c f n c = , …, 1 1 ( ( ( 8)), ( ( 9))) 0.061 l l sup f n c f n c = step 3: by applying equation (23), ( )1, 1 1 1 1( 1); ( 2),..., ( 9) p q l l l irnwpha n c n c n c = = is calculated as follows: ( ) ( ) ( ) 1, 1 1 0.118 1 0.257 9 4.00 0.118(1 0.257) 0.088 (1 0.409) 0.102 (1 0.254) 0.109 (1 0.495) ... 0.163 (1 0.450) 0.118 1 0.257 9 0. 4.00; 5.63; 3.87; 2.04; 3.07; 2.87; 5 2 .32; 3.63; 8 9(9 5. 5 1) p q irnwpha = = =      +     + +  + +  + +    + + +  +   +  = + ( ) 1 4.00 118(1 0.257) 0.088 (1 0.409) 0.102 (1 0.254) 0.109 (1 0.495) ... 0.163 (1 0.450) 0.088 1 0.409 9 5.6 0.118(1 0.257) 0.088 (1 0.409) 0.102 (1 0.254) 0.109 (1 0.495) ... 0.163 (1 0.450)       +  + +  + +  + +    + + +  +   +   + +  + +  + +  + + +  + ( ) ( ) 1 1 3 0.088 1 0.409 9 5.63 0.118(1 0.257) 0.088 (1 0.409) 0.102 (1 0.254) 0.109 (1 0.495) ... 0.163 (1 0.450) ... 0.163 1 0.450 9 0.118(1 0.257) 0.088 (1 0.409) 0.102 (1 0.254) 0.1                   +    + +  + +  + +    + + +  +  + +  +  + +  + +  + + ( ) 1 1 5.85 09 (1 0.495) ... 0.163 (1 0.450) 0.163 1 0.450 9 5.85 0.118(1 0.257) 0.088 (1 0.409) 0.102 (1 0.254) 0.109 (1 0.495) ... 0.163 (1 0.450)                                           + + +  +       +    + +  + +  + +    + + +  +   1 1 1 4.124 +                                                            = the remaining segments are calculated in the same manner: ( )1,1 1 1 1( 1); ( 2),..., ( 9) u u u n c nirnwp nh ca c , ( )1,1 ' ' '1 1 1( 1); ( 2),..., ( 9) l l l i n c n cnwpha cr n the application of the hybrid interval rough weighted power heronian operator in multicriteria decision-making 69 and ( )1,1 ' ' '1 1 1( 1); ( 2),..., ( 9) u u u i n c n cnwpha cr n , so    ( )1 4.12, 6.18 , 4.96, 7.05 ( )irn h n = is obtained. thus, the remaining values ( ) i irn h n from table 4 are obtained. for an easier ranking of the alternatives, the irn values ( ) i irn h n were transformed into crisp ( ) i h n values, and the following rank of the advisors was defined: a2> a4> a5> a3> a10> a8> a7> a6> a1> a9. the previous research (pamucar et al., 2018) showed that changes in the p and q parameters had led to changes in the structure of the heronian function, which further led to changes in the values of the decision model. since it is inevitable that there is an influence of the parameters p and q on the results of the functions, it is necessary to check their influence on the results of the model. the initial rank shown in table 4 was obtained based upon the values of the parameters p=q=1. in the next part, two scenarios were formed. in the first scenario, the influence of changing the parameter p in the interval [1, 100]p  was considered, while the value of the parameter q did not change (q=1), see figure 1. 0 10 20 30 40 50 60 70 80 90 100 5 5 8 12 a1 a2 a3 a4 a5 a6 a7 a8 a9 a10 s c o re f u n c ti o n v a lu e q=1, 1 ≤ p ≤ 100 figure 1. the influence of the parameter p on the ranking results in the second scenario, the influence of changing the parameter q in the interval [1, 100]q  was considered, while the value of the parameter p did not change (p=1), see figure 2. pamučar and janković/oper. res. eng. sci. theor. appl. 3 (2) (2020) 54-73 70 0 10 20 30 40 50 60 70 80 90 100 5 6 8 10 a1 a2 a3 a4 a5 a6 a7 a8 a9 a10 s c o re f u n c ti o n v a lu e 1 ≤ q ≤ 100, p=1 figure 2. the influence of the parameter q on the ranking results both scenarios confirmed the expectations that a change in the values of the parameters p and q leads to a change in the values of criterion functions. also, with a change in parameter values, the calculation of criterion functions becomes more complicated, since a larger number of mutual connections between criteria are simultaneously considered. both scenarios showed that, when the values of the parameters p and q changed, there were minor changes in the ranks of the considered alternatives. according to figures 1 and 2, it is also clear that there are no changes in the ranks of the first four ranked alternatives (a2, a4, a5 and a3). from this, it can be concluded that there is a satisfactory advantage between the considered alternatives, and that the alternatives a2 and a4 stand out as dominant from the considered set. based on all the above-said, it is possible to conclude that the obtained rank a2> a4> a5> a3> a10> a8> a7> a6> a1> a9 is both confirmed and credible. 6. conclusions the application of the original irnwpha multi-criteria model for the evaluation of advisors in dangerous goods transport is presented. the model modified the weighted heronian aggregator by using a power aggregator in an interval rough environment. the irnwpha multi-criteria model enables objective decision-making in the case of uncertain and imprecise input parameters in the initial decision matrix. also, the irnwpha model allows flexible decision-making and the verification of the robustness of the results through the variation of p and q parameters. the irnwpha combines the advantages of the pa and whm operators, and is a powerful decisionmaking tool characterized by the following features: 1) it eliminates the impact of unreasonable arguments; 2) it takes into account the degree of support between input arguments. and 3) it takes into account the interconnectedness of input arguments. since this is a new multi-criteria model, whose application has successfully been demonstrated in real research, it can be concluded that there is justification for the development of the presented methodology. future 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(2019). some single-valued neutrosophic power heronian aggregation operators and their application to multiple-attribute group decision-making. symmetry, 11, 653. © 2020 by the authors. submitted for possible open access publication under the terms and conditions of the creative commons attribution (cc by) license (http://creativecommons.org/licenses/by/4.0/). the application of the hybrid interval rough weighted power heronian operator in multi-criteria decision-making dragan pamučar 1*, aleksandar janković 2 1. introduction 2. interval rough numbers 3. interval rough weight power heronian operator 4. the irnwpha model for multi-criteria decision-making 5. case study 6. conclusions references operational research in engineering sciences: theory and applications vol. 3, issue 2, 2020, pp. 1-23 issn: 2620-1607 eissn: 2620-1747 doi: https://doi.org/10.31181/oresta2003001b *corresponding author. e-mail addresses: aleksandar.blagojevic23@gmail.com (blagojević a.), veskos@sf.bg.ac.rs (vesković s.), sandra.kasalica@gmail.com (kasalica s.), gojic.aleksandra@gmail.com (gojić a.), ahmet.allamani@dih.gov.al (allamani a.) the application of the fuzzy ahp and dea for measuring the efficiency of freight transport railway undertakings aleksandar blagojević 1*, slavko vesković 2, sandra kasalica 1, aleksandra gojić 3, ahmet allamani 4 1 academy of technical and artistic professional studies belgrade, section: college of railway engineering, belgrade, serbia 2 university of belgrade, faculty of transport and traffic engineering, vojvode stepe 305, 11000, belgrade, serbia 3 railways of republic of srpska, svetog save 71, 74000 doboj, b&h 4 railway inspection directorate, albania received: 25 april 2020 accepted: 02 june 2020 first online: 08 june 2020 original scientific paper abstract: measuring the performance of railway undertakings is inevitably becoming a prerequisite for their survival on the market in today's dynamic and highly turbulent environment. railway undertakings must find optimal solutions in order to efficiently and effectively operate, survive on the transport market, and develop and maintain their competitive advantages as well. the objective of this research is to define and evaluate the criteria that affect the efficiency of railway undertakings, increase their competitiveness and propose a dea-based approach (i.e. a data-envelopment-analysisbased approach) to the assessment of the efficiency of railway undertakings in increasing competitiveness. in order to solve the criteria selection problem, the fuzzy analytical hierarchical processes (fahp) method was experimented with, which showed the priority of the assessment of the efficiency of railway undertakings, on the basis of the five groups of criteria. the criteria in a group that outperformed the other criteria in that group for their freight transport railway undertakings within a composite normalized range were used as the input and output indicators for the dea. the evaluation of the efficiency of the railway undertakings was considered by using the dea approach. the results show that the proposed approach successfully enables the consolidation of a set of criteria (resource, operational, financial, quality and safety) into a single assessment of the efficiency of the railway undertakings, while providing information on the corrective actions that can improve the efficiency of the railway undertakings. key words: railway undertaking, efficiency, dea, fuzzy ahp blagojević et al./oper. res. eng. sci. theor. appl. 3 (2) (2020) 1-23 2 1. introduction the twenty-first century can also be called a century of change, and the conditions under which organizations operate can be seen as very complex. the rapid changes in the business world and the increasing competition in the transport services market have imposed on all organizations, including transport companies, the need to harmonize their business with the requirements of the modern business environment. the market has become an arena in which product and service providers are ruthlessly battling for every promile of the market. survival on the market can be ensured only by the fittest who are able to outperform competitors. new business conditions dictate new market demands and establish new competitive relationships on the market. the struggle for survival in the marketplace is becoming inevitable. in order to persist in this struggle, companies need to accept and adapt to new business conditions. the ever more intensive development of the transport market and the ever more complex demands of the users of transport services, with the growing pressure of competition, requires that the organization of the company should become the central determinant of business and the activities carried out should completely be harmonized and financially viable for both the provider and the user of services. in order to survive on the market, companies seek to find the optimal relationship between the resources invested and the goals achieved. the application of the new european transport policy at the end of the last century caused major changes in europe's transport system. there is a major transformation of transport companies into the efficient companies that will be operating in a liberalized european transport market in the future. in a large number of european countries, as well as in the other countries of the world, standards have been adopted regarding the restructuring of the railway system. appropriate legal acts were adopted for the transformation of railways. the previous restructuring stages had not allowed the complete liberalization of the railway transport market, the expected positive operation of the railway sector, the fulfilment of the requirements of the transport market, raising the quality of railway services to the required level, the interests of the community at the national, regional and local levels and others. the restructuring of the railway system only partially brought positive business results in the main railways or pan-european corridors, mainly in transit traffic (stojić et al., 2012). although the quality of the services of the railway system has slightly increased, it is still far from the quality required by the transport market. in providing an adequate quality of railway services, railway undertakings have a very important role, in addition to the railway infrastructure, in terms of: reliability, frequency, the timetable, traffic speed, safety, the organization of work in railway stations, competitive prices in the transport market, and so on. in a large number of countries in the present conditions, transport is mainly performed by the national operators that have emerged from the transformation, i.e. division of railway companies. mostly, these companies are managed by the state. the liberalization of the railway transport market implies, above all, free and non-discriminatory access to the railway infrastructure, bearing in mind the fact that the transport function is performed by a larger number of operators on the appropriate national railway network. the efficiency of transport activities significantly affects the profitability of the business of all the entities involved in the process, but they cannot be provided without much effort in the process of quality management and transport activities. given the fact that, in modern companies, it is necessary to constantly measure the causes of the achieved effect, it is quite clear that the system for performance/efficiency measurement of the railway operator must the application of the fuzzy ahp and dea for measuring the efficiency of freight transport railway undertakings 3 include all the criteria that affect it. in order for railway companies to successfully operate, it is very important for them to form a performance/efficiency measurement system appropriate to modern business conditions. railway operators’ operations in today's dynamic and competitive intensive environment require the precise and constant measurement of non-financial criteria, which are identified as the causes of the financial result, so that potential negative trends can be corrected before their effect negatively affects the final result of such operations, which, as a rule, is evaluated from a financial perspective. the subject matter of this research paper stems from the needs of the european countries, regardless of whether they are eu member states or the states applying for the membership, and its aim is to establish the market principles of business in the railway sector. bearing in mind the fact that the efficiency of railway transport depends on the number of the services offered and the content of the services that have been implemented, it is necessary to determine the criteria that can define efficiency. based on a detailed analysis of the situation in the research field, a fact was established that the methodological procedure for selecting the key criteria for the evaluation of the efficiency of railway undertakings is not sufficiently researched. for this reason, the objective of this research was to define and evaluate the criteria that affect the efficiency of railway undertakings and propose an approach based on the dea method for the assessment of the efficiency of railway undertakings in order to increase competitiveness. the contribution of this paper reflects in the criteria selection approach and the evaluation of the efficiency of railway undertakings through the proposed dea approach. increasing the revenue, quality and scope of services and reducing the operating costs of the railway undertakings themselves can be improved by applying the proposed efficiency assessment approach. 2. research methodology in addition to general scientific research methods (analysis, synthesis, induction, deduction and analogy), various methods and techniques were used to assess the efficiency of freight transport railway undertakings, such as the fuzzy analytical hierarchical process (fahp) and data envelopment analysis (dea). the research itself was conducted in several phases (figure 1). the first phase of the research was carried out through several mutually conditioned steps. the initial step in this paper was to identify the problem. once the problem was identified and the importance of the efficiency of freight transport railway undertakings was determined, the subject matter of the research was defined, together with its objective. the second phase of the research covered an analysis of the literature, scientific and professional information on the railway system for the railway undertakings from the western balkans, slovenia and croatia, together with the aspects of efficiency measurement, as well as the criteria used. based on the research done in the most frequently used criteria for the efficiency of railway undertakings from the available literature, the authors defined five groups of criteria. the additional difficulties in the implementation of these tasks imply the mutual influences and conditionality of the mentioned criteria. thus, for example, the criteria selection problem, which is the initial problem, in a situation of conflicting goals, gives the level of measuring efficiency an additional importance. to select the priority criteria, the fuzzy analytical hierarchical process (fahp) was used, which is supported by the literature fact that this method generates the results that are more precise than those obtained by the blagojević et al./oper. res. eng. sci. theor. appl. 3 (2) (2020) 1-23 4 ahp method. the third phase was the “core of the research study”. in this phase, the previously defined problems related to the evaluation of the efficiency of railway undertakings were solved. a new dea approach was proposed so as to assess the efficiency of a group of freight transport railway undertakings, which can greatly help in the function of increasing the competitiveness of the railway undertakings. in the fourth phase, the testing of the proposed dea approach was performed on the selected/proposed (examples of) railway undertakings, with an analysis of the obtained results. this paper provides concluding remarks, as well as directions for future research. problem identification research subject research goal phase i review of relevant literature analysis of railway undertakings of slovenia and croatia defining and evaluating criteria phase ii analysis of railway undertakings in the western balkans selection of performance evaluation criteria by the fuzzy ahp method dea approach to the evaluation of efficiency of a group of railway undertakings testing on real examples of railway undertakings for freight transport phase iii analysis of the obtained results phase iv phase v concluding remarks directions for further research figure 1 the research methodology 3. the situation in the research area in the conditions of the global market and increasingly intense competition, the european union seeks to restructure railways and develop their competitiveness. the european union is embarking on a comprehensive process for the restructuring and commercialization of rail transport, enabling the reaffirmation and improvement of rail quality and rail efficiency. the starting documents for the achievement of the objective are the railway plan, the freight charter, directive 2004/51/ec, the european technical strategy for railway undertakings (white paper 1996 and 2011). the main objective of the eu documents is to enable railways to be competitive in the transport market. according to the european railway technical strategy, european rail infrastructure management managers (2008), the efficiency of rail passenger and freight traffic would increase even more than necessary if the overall costs of the company were reduced. the challenging scenario for railways is to facilitate major economic development in the future, which would generate greater demand for passenger and freight transport while maintaining a high level of the public awareness the application of the fuzzy ahp and dea for measuring the efficiency of freight transport railway undertakings 5 of the environment and reducing carbon dioxide emissions (increased energy efficiency). the scenario of large-scale economic development is the basis of the aforementioned strategy, as well as the need for the rail sector to be cost-effective and offer an attractive transport mode that will meet environmental standards, while introducing sustainable solutions. in order to be eligible, in line with the scenario presented above, the railway must be multi-functional and should reduce the total cost through: a high capacity (passenger and freight kilometers per kilometer of railway); the high reliability of services (an increased percentage of timely deliveries and fewer delays); the low levels of carbon dioxide emissions (tonnes per passenger and freight kilometers); noise reduction; increased comfort and adequate passenger space (the train station); the increased availability of the rolling stock; better information (before and during the trip); better safety (from the moment of entering the station to the moment of leaving it); a stable confidence level (the total equivalent of the lives lost as a result of the system operation). garcia-cebrian and jorge-moreno (1999) present the results of a study in which, on an example of 21 railway companies, they observed the impact of organizational change on business efficiency (increased revenue, reduced costs, increased productivity). ehrma nn (2001) points out the fact that the deficit of state-owned railways is enormous and that the issue of the efficiency of companies has become an issue in economic and political debates. permanent rail deficits also indicate the fact that an excess capacity throughout the industry, with a lack of state-run rail efficiency, could be a major reason for an insufficient or negative return on invested capital. in times when there is a large public debt throughout the world, the state has a natural interest in adjusting railway undertakings and making the capital allocated to them profitable. in the paper (borenstein et al., 2004), a methodology is proposed to evaluate the performance of service providers. the goals of this paper were to identify the factors that could be used to evaluate the effectiveness of these decision-making units and identify the groups of similar units that develop the same functions and only differ in resource intensity. the analysis included the comparisons of the relative efficiency of several different units, including postal operators in brazil, using the dea. the authors indicated the fact that the proposed methodology could provide the useful information that might be helpful for managers in the decision-making process. ming-miin yu and erwin t.j. lin (2008) evaluated the passenger and freight technical efficiency, service efficiency and technical efficiency of the 20 selected railways of other countries for 2002. the study found that those measures differed significantly. because the data envelopment analysis of the multi-active network models the reality of rail operations, a further insight can be obtained and strategies for the improvement of operational performance can be proposed. in his study entitled "an efficiency analysis of european countries' railways", pavlyuk dmitry (2008) uses stochastic boundary analysis to evaluate the efficiency of the rail system in european countries. he views the rail as a system using its length of operating lines, a number of cars and wagons, employees and a market scale such as the population and tourists to carry passengers and freight. the result of the study showed that the rail systems show huge differences in technical efficiency between different countries, as well as between freight and passenger transport within the same country. friebel, ivaldi and vibes (2010) attempted to measure the impact of reforms in european railways on the technical efficiency of the railways. to do this, they used input and output data analysis, applying the cobb-douglas function that implicitly assumes a separation between the blagojević et al./oper. res. eng. sci. theor. appl. 3 (2) (2020) 1-23 6 input and the output. for the input data, they used the length of the lines on the network and the number of the employees, whereas as the output data, they used passenger km and tonne-kilometers, especially for passenger and freight transport. they worked on a sample of 11 european countries for the period 1980-2003. the three types of the reforms that have taken place in europe (namely, separation, entry of other companies (competition) and the existence of an independent regulatory body) were added to the prior physical data. their results indicate the fact that the rail reforms have increased rail transport efficiency, and that the reforms have been more successful when applied sequentially rather than all at once. lan-bing li and jin-li hu (2011) model rail transport in their paper into the three processes: the production process (the input and the output), the consumption process (consumption/the output) and the earnings process (earnings/consumption), thus creating a unique multi-phase framework for measuring the chinese railway performance from 1999 to 2008. first, they used the dea model to evaluate productivity efficiency, consumption efficiency, and earnings efficiency from a statistical point of view. then, they used the malmquist tfp index to evaluate production productivity, consumption productivity, and earnings productivity from a dynamic point of view. they also used the average cumulative malmquist tfp index to evaluate the impact of the management system reform of the chinese rail system on rail transport in 2005. jianjun (2012) analyzes the inefficiencies in production and points out the fact that rail transport has the need for the introduction of economical production by changing the way transport is organized by improving internal contractual relations and optimizing the business organizational structure, the rational use of resources, and an economically significant improvement of efficiency and effectiveness by creating a new way of economically organizing rail transport. azadeh and salehi (2014) define a methodology based on the dea analysis in order to examine the efficiencies of infrastructure managers and railway undertakings and define deficiencies. the authors state that the level of the durability of the system depends on the amount of deficiencies. the smaller the operating deficiencies between the railway undertaking and the infrastructure manager (the smaller the gap between them), the more efficient the company will be in terms of challenges and difficulties in actual operations. marchetti, d, & wanke, p. (2017) use the dea analysis to assess the efficiency of the brazilian railway concessionaires between 2010 and 2014, when new competition regulations were introduced. the public policies designed so as to increase cluster efficiency are presented, and the options such as increasing, decreasing and magnitude inputs, restructuring, the best management practices, and infrastructure improvements are addressed. kapetanovic, m. et al. (2017) use the dea method to evaluate the efficiency of the railway undertakings of the majority of the european countries over the most recent period of time, analyzing the different input-output configurations of the model. 4. the definition and assessment of the criteria for the evaluation of the efficiency of freight transport railway undertakings deciding on the selection of the criteria for the assessment of the efficiency of railway undertakings is a very complex process and belongs to the domain of strategic decisions. the adoption of this decision is in the function of managing a railway undertaking and, as such, this activity is complex, creative and permanent. in order to decide on the selection of the criteria for the assessment of the efficiency of railway undertakings, it is necessary to evaluate the proposed variant solutions of different the application of the fuzzy ahp and dea for measuring the efficiency of freight transport railway undertakings 7 criteria. how to evaluate them is the key issue in determining the method. there is a wide range of the criteria that can be studied when speaking about the efficiency of freight transport railway undertakings. in most cases, there are several criteria that are very often conflicting with one another. to select the best evaluation method or make the best decision when selecting criteria, previous experience and the literature in this field indicate the fact that the problem should be addressed by using multi-criteria decision-making methods. in this paper, one of today’s most popular decision-making methods – fuzzy analytic hierarchy process (fahp), is experimented with. 4.1. fuzzy analytic hierarchy process (fahp) the analytic hierarchy process (ahp) method, developed by tomas saaty, is widely spread and has been in use for over 25 years, with a number of pieces of software developed to support its application. this method is a tool in decisionmaking, designed to enable decision-makers solve complex decision-making issues, involving a larger number of decision-makers, a greater number of criteria, and multiple time periods. the detailed explanations of this method are provided in many references dealing with decision theory. in this regard, the paper presents a new approach to the ahp method by using interval fuzzy numbers and the application of the modified fuzzy ahp method in defining and evaluating the criteria that influence the evaluation of the efficiency and effectiveness of railway undertakings. different methods for transferring the previously mentioned ahp method into its fuzzy form are presented in the literature (bottani, 2005). in addition, the paper (van laarhoven and pedrcyz, 1983) proposes the first study that introduces the principles of fuzzy logic in the ahp method, using triangular fuzzy numbers. at the same time, a study by buckley (1985) initiates the fact that trapezoidal fuzzy numbers express decision-makers’ assessments, while the authors of the study (boender et al., 1989) present a modification to the fuzzy multicriteria method proposed in chang's paper (1996). in the study (chang, 1996), the severity of the criteria is calculated as the minimization of the logarithmic regression function. in this manner, weight alternatives are calculated by each criterion separately, while the aggregation of calculated weights can determine the fuzzy final result of the alternative. the study (cebi and bayraktar, 2003) presents a new approach to solving the ahp phase (fahp) by using triangular fuzzy numbers. this approach is called an extended analytical method, which can be summarized as follows: define the association function for each attribute and sub-attribute, then calculate their degree of association, and ultimately apply the ahp phase for weight aggregation. also, vesković s., et al. (2015) apply the fahp to evaluate the criteria for public transport obligations. fuzzy sets generally use triangular, trapezoidal and gaus fuzzy numbers, which convert uncertain numbers into fuzzy numbers. using more complicated fuzzy numbers, such as trapezoidal or gaus, allows a more precise description of the decision-making problem. to solve the problem of defining and evaluating the criteria for the assessment of the efficiency and effectiveness of railway undertakings, triangular fuzzy numbers (chang, 1996) are used in this paper. 4.2. criteria for the assessment of the efficiency of freight transport railway undertakings in the process of defining the dea approach to efficiency evaluation, it is necessary to consider and define the criteria that affect the efficiency of a railway blagojević et al./oper. res. eng. sci. theor. appl. 3 (2) (2020) 1-23 8 undertaking. the criteria are chosen so as to allow for the evaluation of the efficiency of railway undertakings. for the purpose of defining and evaluating the criteria, research in the most frequently used literature criteria regarding the efficiency and effectiveness of railway companies was carried out. based on the conducted research, it was concluded that the used criteria could be categorized into the following criteria groups: the resource criteria (capacity), the operational criteria, the financial criteria, the service quality criteria and the safety criteria. the management of railway undertakings can monitor partial activities and processes with the help of these criteria, but they cannot acquire a complete picture of how the whole system works. it is necessary to define an integrated measure that will somehow integrate all of these criteria. such a measure would provide a much quicker and more comprehensive picture of how the system works and define appropriate corrective actions as well. the first phase involves the defining and grouping of the criteria. it is desirable at this stage that the information on how the analyzed system works should be used. it is also necessary to group the criteria by the type, by the subsystem they belong to, and by the decision level. accordingly, a broader set of criteria need to be defined. there are different ways to group criteria in the railway system. in terms of the measurement level, it is possible to define criteria at the strategic, tactical and operational levels. railway systems are complex systems with numerous interconnected subsystems, processes and activities. each subsystem, process or activity is characterized by certain criteria. based on the literature and knowledge, the following criteria of the freight transport operator are defined and shown in table 1. table 1. the criteria for the assessment of the efficiency of freight transport railways undertakings group criteria resource criteria (capacity) the network length the number of staff per km of the railway network the number of employees operational criteria commercial speed for freight trains the quantity of transported goods/freight net tonne km gross tonne km train km financial criteria total income profit per employee electricity costs fuel costs railway infrastructure charges service quality criteria the suitability of the available services the stability of services the reliability of services (the overdue delivery time) available rolling stock safety criteria the number of serious accidents per train km the number of accidents per train km the number of incidents per train km the essence, meaning and reasons of each criteria group are explained further in the paper. the application of the fuzzy ahp and dea for measuring the efficiency of freight transport railway undertakings 9 1) the resource (capacity) group criteria. the first group of the criteria was considered based on the network length, the number of staff per km of the railway network, and the total number of employees and the available number of the rolling stock of railway undertakings. the efficiency achieved by freight transport railway undertakings by carrying out their activities depends on the results of the work accomplished using resources (the capacity). there is a need to understand the state of the resources and the extent to which the resources have been used. the network length criterion relates to the characteristics of the network and greatly affects the efficiency of railway undertakings; namely, it is important for railway undertakings that railway networks should be branched and well connected. in addition, it is important that it should be well connected with international lines. our railway networks are small and dense, with highly aligned timetables. the density of the network is significantly reflected through the accessibility of the rail service. the number of employees is one of the most sensitive segments of the railway sector restructuring process. the economic transition of the central and eastern european countries has resulted in very large differences between the individual systems of railway undertakings. it is actually easy to find the causes in some country-specific or group-of-counties-specific processes, for example: the successfulness of the restructuring of the extractive and heavy industries, the privatization and growth of road transport, the collapse of economic blocks (e.g. yugoslavia), and the impact of military conflicts. in such circumstances, there is a simultaneous redundancy and shortage of labor. railway companies' systems are burdened with a substantial excess of staff, which is increasingly evident due to the negative trend of rail transport, while on the other hand, there is a deficit of the labor force that has the knowledge and experience needed to meet new market demands. the number of employees is an important component of the efficient operation of railway undertakings, because low costs are the basis for the achievement of competitive advantages today. fixed and operating costs of business are under increasing pressure and generally record growth trends. railway undertakings are, by their very nature, a labor-intensive industry, which means that one of the main cost drivers is the cost of employees. this statement assumes an even greater weight given the fact that almost all transition countries, or their railway systems, have insufficient productivity in relation to the number of employees. 2) operational group criteria. the second group of criteria was considered on the basis of the commercial speed of cargo transport trains, the quantity of the goods transported, net tonne and gross tonne kilometers, as well as driving kilometers. commercial speed can be viewed as operational and as a quality service criterion. the efficiency of freight transport railway undertakings is indirectly dependent on commercial speed and the retention time in railway stations. taking into consideration the fact that organizational measures cannot significantly affect the speed and time of travel during the circulation of the car, it can be concluded that, according to this criterion, the development of railway traffic depends on the retention time, i.e. on the criteria that can be influenced by organizational measures. in other words, lower retention times mean fewer circuits and more efficient transport. in the conditions of the further development of railway transport and the growing demands the economy and the population pose in terms of the speed of travel or the transport of goods, the speed of transportation means will play an increasingly important role in transport users’ decision-making when selecting a type of transport. therefore, blagojević et al./oper. res. eng. sci. theor. appl. 3 (2) (2020) 1-23 10 transport speed will certainly be one of the most important factors, which must be taken into consideration when conducting comparative analyzes of the efficiency of railway undertakings. the criteria of the production task, the transport of goods, as the main activities of railway undertakings, are expressed through the quantity of the goods transported. railway undertakings generate certain revenues through the criteria that give the opportunity to see the amount of the work done. in the transport of goods, these are net tonne kilometers (the product of the mass of the goods transported in tonnes and transport distances). railway undertakings do certain work in net tonne kilometers, which is considered to be a transport service for which the price for the net tonne kilometer is charged. 3) financial group criteria. the third group of criteria was considered on the basis of the total revenue, earnings per employee, electricity costs, fuel costs and charges for the use of the railway infrastructure. railway undertakings achieve income through the sale of products and services. the main activity carried out by railway undertakings is the transport of goods, and revenues from this activity are defined as transport revenues. in this sense, income is a reliable criterion of efficiency, as well as a precondition for the survival of the company. if a company generates no revenue, then it cannot survive on the market. hence the obligation of railway undertakings to fully understand the function of demand for their services, because in this way they can assess the level of income they strive to achieve or they do achieve. a company’s total income is realized as the product of the transport service and the price of the service. for the transport service as a specific product, the ratio of the consumed production factors (production costs, services) and the realized revenues is all the more significant, since production also simultaneously produces its final consumption, realizes the effects of investment in the transport process and achieves production goals (the financial result of the operations of railway undertakings). transport costs are defined as the value of the factors consumed in the transport service production process or in the goods transport process. in this sense, according to the economic essence of the transport service production process, the basic structure of transport costs includes the costs of labor, which are a very heterogeneous group of investments in the transport process, which consist of the costs of electricity and the costs of fuel. the amount of these costs for a certain volume of production and the technological labor process is conditioned by objectively standardized consumption according to the quantity, the structure and values in a certain real time, and affects the evaluation of the efficiency of railway undertakings to a great extent. the costs of charges for the use of the railway infrastructure directly affect the situation on the transport market. newly-introduced charges affect the position and role of domestic railway undertakings on the market. the survival of domestic railway undertakings depends on their conditions (the state of technical means, technology, organization, the commercial sector, etc.). when a domestic undertaking is/domestic undertakings are able to provide an appropriate level of the quality of the transport service, high charges will discourage competition on the railway market. if charges are high, the private sector will have no interest in introducing new railway undertakings. no foreign railway undertakings will come to the countries and railways where these charges are high, either. on the other hand, low charges increase the number of railway undertakings and win better-equipped, more capable, more competitive carriers on the free market. this is particularly true for countries in transition and countries where charges have just been introduced. in the countries and rail markets that are underdeveloped and where domestic railway undertakings cannot provide an the application of the fuzzy ahp and dea for measuring the efficiency of freight transport railway undertakings 11 appropriate level of the service quality, the situation is just the opposite. there, high charges can only bear the bargain, which is usually a foreign railway undertaking, so it "chokes" domestic railway undertakings. low charges stimulate competition, and in equal conditions, again, it will be difficult to "defend" domestic railway undertakings. to conclude, fees directly affect the evaluation of the efficiency of railway undertakings. 4) service quality group criteria. the fourth group of criteria was considered based on the suitability-ability of the offered services, the stability of services, the reliability of the service – exceeding the delivery deadline and the available number of the rolling stock of railway undertakings. the service quality is what constitutes the mirror of railway undertakings, what the customer sees as their image. the customer sees no business premises, no equipment, no technology, no management system and no organizational structure. everything the customer sees is the quality of the transport service. the quality of the services rendered by railway undertakings lies in the key competences, i.e. sustainable competitive advantages, in relation to other railway undertakings, and significantly influences the assessment of the efficiency of railway undertakings. the convenience ability of the offered services is the criterion whose goal is to adapt railway undertakings to the requirements of service users in terms of the required capacity, mobility and elasticity in order to satisfy the requested service. reliability is the core of the quality of a railway undertaking’s service, bearing in mind the fact that reliability appears as the most significant qualitative feature from the user's perspective. research shows that there is a significantly higher reliability effect, as a measure of quality, on the satisfaction of service users than product users. this is particularly due to the specific nature of the transport service: the user's insolvency in the production process and the synchronization of the production and consumption processes, which makes it difficult at the same time to measure and maintain the default level of the service reliability. thus, the level of the railway service reliability is very important for railway undertakings. the available number of the rolling stock is one of the key criteria for the competitiveness of railway undertakings in the open transport market. it can be seen as the service quality criterion and the operational criterion. the rolling stock is the fixed assets of railway undertakings that have the function of the means of work in the transport service manufacturing process. the rolling stock includes traction vehicles, i.e. locomotives, and hauled vehicles, i.e. all types of freight cars. it is of particular importance for a railway undertaking to achieve the optimal capacity, which implies such a use of the rolling stock which will establish the relatively most favorable relationship between the wearing of their useful properties, on the one hand, and their productivity, on the other. the rolling stock should be fast, energy-efficient and environmentally friendly and, above all, secure in order to achieve a higher quality of the service. with the liberalization of the market, there is growing competition between railway undertakings, both in terms of the scope and in terms of the quality of transport services, so it is very important to dispose of modern means of transport. 5) safety group criteria. the fifth group of criteria was considered based on the number of serious accidents, accidents and incidents per driving kilometer. safety is an important factor in determining the transport user for certain transport sectors, and therefore a significant factor in the size of transport and the volume of income. in addition to the impact on the transport size and the volume of income, traffic safety blagojević et al./oper. res. eng. sci. theor. appl. 3 (2) (2020) 1-23 12 affects the efficiency of railway undertakings as a result of railway accidents, damaging and destroying assets of high value, thus causing great material damage and traffic disruptions, which are also a cost for railway undertakings. serious accidents mean any collision or slipping/derailing of trains resulting in the death of at least one person, or a serious injury to five or a larger number of persons, or a significant damage to the rolling stock (it implies the damage that may immediately be estimated by the railway investigating authority, the total value being at least eur 2 million), the infrastructure or the living environment, as well as any other similar accident with an obvious impact on rail safety regulation or safety management. an accident means an unwanted or unintentional event or a special chain of events having severe consequences. accidents are divided into the following categories: crashes, slipping from a rail track (derailing), accidents at a crossing, and accidents to persons caused by the rolling stock, fires and so forth. an incident means any event which is not an accident or a serious accident, which is related to the traffic of trains and which affects the safety of operation. in order to maintain high-level safety, the european union has laid down the limit of common safety objectives in its documents. the assessment of the criteria was based on the fuzzy ahp (fahp) method. experts from the railway sector participated in the process of the evaluation of the relative importance of particular criteria for each group. experts from the ministry of transport (e1), the railway directorate (e2), the railway safety agency (e3), the railway infrastructure manager (e4) and the railway undertaking (e5) were interviewed. they filled out a survey, in which they evaluated the importance of each criterion against the linguistic preference scale for each group. table 2 shows the conversion of the linguistic variables into triangular fuzzy numbers (chang, 1996.). table 2. the linguistic variables and their corresponding fuzzy numbers linguistic variable triangular fuzzy scales fuzzy reciprocal scale just equal (1, 1, 1) (1, 1, 1) equally important (1/2, 1, 3/2) (2/3, 1, 2) weakly important (1, 3/2, 2) (1/2, 2/3, 1) strongly more important (3/2, 2, 5/2) (2/5, 1/2, 2/3) very strongly more important (2, 5/2, 3) (1/3, 2/5, 1/2) absolutely more important (5/2, 3, 7/2) (2/7, 1/3, 2/5) solving the highest-importance criteria selection problem for the purpose of assessing the efficiency of railway undertakings between the aforementioned groups was initiated by the application of the fahp approach. for the illustrated example of the highest-importance criteria selection, an example of the selection of the criteria for the operational group is presented in this paper. in table 3, a fuzzy matrix of the benchmarking criteria from the operational criteria group (commercial speed for freight trains – b1, the quantity of transported goods/freight – b2, net tonne km – b3, gross tonne km – b4, train km – b5), is given. the application of the fuzzy ahp and dea for measuring the efficiency of freight transport railway undertakings 13 table 3. the comparative matrix for the operational group criteria of freight railway undertakings b1 b2 b3 b4 b5 b1 e1 (1,1,1) (2/7,1/3,2/5) (2/3,1,2) (2/3,1,2) (2/5,1/2,2/3) e2 (1,1,1) (2/5,1/2,2/3) (1/2,1,3/2) (2/5,1/2,2/3) (2/3,1,2) e3 (1,1,1) (2/5,1/2,2/3) (2/5,1/2,2/3) (2/5,1/2,2/3) (2/3,1,2) e4 (1,1,1) (2/3,1,2) (2/3,1,2) (2/5,1/2,2/3) (2/3,1,2) e5 (1,1,1) (2/7,1/3,2/5) (1/2,1,3/2) (2/3,1,2) (1/2,1,3/2) b2 e1 (5/2,3,7/2) (1,1,1) (1/2,1,3/2) (1/2,1,3/2) (3/2,2,5/2) e2 (3/2,2,5/2) (1,1,1) (1,1,1) (1,1,1) (1/2,1,3/2) e3 (3/2,2,5/2) (1,1,1) (1/2,1,3/2) (1,1,1) (1/2,1,3/2) e4 (1/2,1,3/2) (1,1,1) (1/2,1,3/2) (1/2,1,3/2) (1/2,1,3/2) e5 (5/2,3,7/2) (1,1,1) (1/2,1,3/2) (1,1,1) (3/2,2,5/2) b3 e1 (1/2,1,3/2) (2/3,1,2) (1,1,1) (1,1,1) (1/2,1,3/2) e2 (2/3,1,2) (1,1,1) (1,1,1) (1,1,1) (2/3,1,2) e3 (3/2,2,5/2) (2/3,1,2) (1,1,1) (2/3,1,2) (1,1,1) e4 (1/2,1,3/2) (2/3,1,2) (1,1,1) (1,1,1) (1,1,1) e5 (2/3,1,2) (2/3,1,2) (1,1,1) (2/3,1,2) (1/2,1,3/2) b4 e1 (1/2,1,3/2) (2/3,1,2) (1,1,1) (1,1,1) (1/2,1,3/2) e2 (3/2,2,5/2) (1,1,1) (1,1,1) (1,1,1) (1/2,1,3/2) e3 (3/2,2,5/2) (1,1,1) (1/2,1,3/2) (1,1,1) (1/2,1,3/2) e4 3/2,2,5/2) (2/3,1,2) (1,1,1) (1,1,1) (1/2,1,3/2) e5 (1/2,1,3/2) (1,1,1) (1/2,1,3/2) (1,1,1) (1/2,1,3/2) b5 e1 (3/2,2,5/2) (2/5,1/2,2/3) (2/3,1,2) (2/3,1,2) (1,1,1) e2 (1/2,1,3/2) (2/3,1,2) (1/2,1,3/2) (2/3,1,2) (1,1,1) e3 (1/2,1,3/2) (2/3,1,2) (1,1,1) (2/3,1,2) (1,1,1) e4 (1/2,1,3/2) (2/3,1,2) (1,1,1) (2/3,1,2) (1,1,1) e5 (2/3,1,2) (2/5,1/2,2/3) (2/3,1,2) (2/3,1,2) (1,1,1) the fuzzy weight of the criteria is calculated by taking the geometric average of the expert’s response (lee, 2009). an example of the geometric mean calculation is only provided for b12, while the other values shown in table 4 are calculated analogously. an example of the calculation of the geometric mean for b12 reads as follows: n− = (2/7x2/5x2/5x2/3x2/7)1/5 = 0.387 n− = (1/3x1/2x1/2x1x1/3)1/5 = 0.488 n+ = (2/5x2/3x2/3x2x2/5)1/5 = 0.677 table 4. the fuzzy comparative matrix for the operational criteria group b1 b2 b3 b4 b5 b1 (1,1,1) (0.387, 0.488, 0.677) (0.536, 0.870, 1.431) (0.491, 0.660, 1.035) (0.568, 0.871, 1.516) b2 (1.477, 2.047, 2.252) (1,1,1) (0.574, 1, 1.383) (0.758, 1, 1.176) (0.776, 1.319, 1.840) b3 (0.698, 1.149, 1.864) (0.723, 1, 1.741) (1,1,1) (0.850, 1, 1.319) (0.699, 1, 1.351) b4 (0.967, 1.516, 2.038) (0.850, 1, 1.319) (0.758, 1, 1.176) (1,1,1) (0.500, 1, 1.500) b5 (0.659, 1.149, 1.759) (0.543, 0.758, 1.289) (0.740, 1, 1.431) (0.667, 1, 2) (1,1,1) blagojević et al./oper. res. eng. sci. theor. appl. 3 (2) (2020) 1-23 14 in addition, the standard steps of the fahp method are used in this paper (stević, ž. et al. 2015). the relative ranking of the importance of particular criteria based upon a criteria-pairwise comparison, for all the groups in freight transport is presented in table 5. table 5. the relative ranking of the importance of particular criteria based upon the criteria-pairwise comparison of all the groups in freight transport group criteria w' (fuzzy weight vector) w (normalized weight vector) resource criteria (capacity) the network length 0.101 0.065 the number of staff per km of the railway network 1 0.654 the number of employees 0.430 0.281 operational criteria commercial speed for freight trains 0.632 0.151 the quantity of transported goods/freight 1 0.240 net tonne km 0.841 0.202 gross tonne km 0.878 0.210 train km 0.821 0.197 financial criteria the total income 0.916 0.213 profit per employee 0.919 0.214 electricity costs 0.816 0.190 fuel costs 0.639 0.149 railway infrastructure charges 1 0.233 service quality criteria the suitability of the available services 0.738 0.256 the stability of services 0.512 0.177 the reliability of services (the overdue delivery time) 0.638 0.221 the available rolling stock 1 0.346 safety criteria the number of serious accidents per train km 1 0.558 the number of accidents per train km 0.473 0.264 the number of incidents per train km 0.318 0.178 the comparative analysis carried out by using the fahp method showed that, for each group, the priority criteria affected the assessment of the efficiency of the railway undertakings. based on the results shown in the above table 5, a conclusion can be drawn that, for the group of the resource criteria, the greatest relative weight is that of the number of staff per km of the railway network (0.654), only to be followed by the operational criteria group, the quantity of goods transported (0.240), the financial criteria group, the cost of charges for the use of the railway infrastructure (0.233), the service quality criteria, the available rolling stock (0.346) and the safety criteria group, the highest relative weight being that of the number of serious accidents criterion (0.558), based on the railway experts’ survey. the criteria that took precedence over the other criteria in their respective group(s) were used as the inputs and outputs for the application of the fuzzy ahp and dea for measuring the efficiency of freight transport railway undertakings 15 the evaluation of the efficiency of freight transport railway undertakings by applying the dea method. 5. the application of the dea method in order to assess the efficiency of freight transport railway undertakings regardless of the system type, there is a need to monitor and quantify the effects of business. one of the basic criteria implies defining the relationship between the resources invested and the goals achieved. in the literature, that ratio is known as efficiency. common to most approaches in the literature is the fact that the term “efficiency” pertains to the best utilization of resources while providing as many services as possible. in the literature, the problem of measuring the efficiency of railway undertakings has been emphasized as the problem of measuring the efficiency of multiphase (multistage) processes. the most commonly used method for the evaluation of the efficiency of multiphase processes is the data envelopment analysis (dea) method. there is a full range of models in the literature intended for the evaluation of the efficiency based on the dea models. the dea method makes it possible to compare the efficiency of comparable units, in this case a group of undertakings with a greater number of input and output variables. in this paper, a new approach to the assessment of the efficiency of freight transport railway undertakings is proposed. the proposed approach is based on the evaluation of efficiency by using the dea method. the implementation/application of the proposed approach envisages several stages. first, it is necessary to define the inputs and outputs for the decision-making unit (dmu), which requires an evaluation of efficiency and effectiveness (in this case, these are railway undertakings). furthermore, the dea approach is executed through two parallel processes. the first process implies the classifications of dmus as either effective or ineffective, depending on the ccr grade (a model named after the initial letters of the surnames of the authors, charnes, cooper, rhodes), and the bcc grade (a model named after initial letters of the surnames of the authors, banker, charnes, cooper, 1984). the second process requires an rts classification. this enables the identification of the dmus that need rationalization. finally, the optimal values for the inputs and outputs are derived by using the slack-based crs (constant returns to scale) model. the proposed dea approach is shown in figure 2. figure 2. the application of the dea method for the assessment of the efficiency of freight transport railway undertakings blagojević et al./oper. res. eng. sci. theor. appl. 3 (2) (2020) 1-23 16 the proposed dea approach was tested and verified through a survey conducted on a sample of the national goods transportation railway undertakings in the western balkans, slovenia and croatia, which is accounted for in table 6. table 6. the freight transport railways undertakings country railway undertakings abbreviation albania hekurudha shqiptarë sh hsh bosnia and herzegovina railways of the republic of srpska žrs railways of the federation of bosnia and herzegovina žfbh montenegro montecargo montecargo croatia croatian railways cargo d.o.o. hž-cargo north macedonia railways of the republic of north macedonia transportation department j.s.c. skopje mžt slovenia slovenian railways-freight transport sž-freight transport serbia serbia cargo sk the freight transport railway undertakings as dmus were designated with four inputs and one output, as previously determined by the fuzzy ahp and as shown in figure 3 below. the first input stands for the number of employees per kilometer of the railway network; the second input stands for the cost of the fees paid by the railway undertaking to the payment infrastructure manager; the third input stands for the available number of the vehicles of the rolling stock, and the fourth input stands for the number of serious accidents. the output of the model is the quantity of the goods transported. number of staff per km of railway network railway infrastructura charges available rolling stock number of serious accidents per train km railway undertakings quantity of transported goods/freight figure 3. the railway undertaking as the dmu for efficiency assessment the values for the input and output parameters for all the eight national railway undertakings are shown in table 7. the data for the railway undertakings were obtained from the uic statistics and the railway undertakings' annual reports for the year 2018 (https://www.uic.org/). the application of the fuzzy ahp and dea for measuring the efficiency of freight transport railway undertakings 17 table 7. the input and output parameters for the dea model railway undertakings number of staff per km of the railway network railway infrastructure charges (euro) available number of rolling stock number of serious accidents per train km quantity of the transported goods/freight (tons) hsh 2.3 2.2 592 6 930000 žrs 4 2.1 2134 6 4568698 žfbh 2 2.1 2271 10 9120000 montecargo 6 3.0 577 5 1000000 hž-cargo 1.1 3.3 5513 7 6870000 mžt 4 2.0 1353 3 1680000 sž freight transport 1 2.23 3142 13 20436000 sk 0.7 1.1 6901 6 10160000 the ccr is an original dea model for the determination of relative efficiency for a dmu group. the one formulation of the ccr model aims to minimize inputs, while maintaining a given output level, i.e. the ccr input-oriented model (model a1). the second formulation of the ccr model aims to maximize the outputs without increasing the value of any of the observed inputs, i.e. the ccr output-oriented model (model a1'). the ccr models assume a constant crs (constant returns to scale), and ccr ratings measure overall efficiency. model a1 (primal) model a1' (dual) 𝜃 ∗ = 𝑚𝑖𝑛 𝜃 with conditions: ∑ 𝜆𝑗 𝑥𝑖𝑗 𝑗∈{1,2,3,...,𝑛} ≤ 𝜃𝑥𝑖𝑜 , 𝑖 = 1,2,3, . . , 𝑚; ∑ 𝜆𝑗 𝑦𝑟𝑗 𝑗∈{1,2,3,...,𝑛} ≥ 𝑦𝑟𝑜 , 𝑟 = 1,2,3, . . , 𝑠; 𝜆𝑗 ≥ 0, 𝑗 = 1,2,3, . . . , 𝑛. 𝜙 ∗ = 𝑚𝑎𝑥𝜙 with conditions: ∑ 𝜆𝑗 𝑥𝑖𝑗 𝑗∈{1,2,3,...,𝑛} ≤ 𝑥𝑖𝑜 , 𝑖 = 1,2,3, . . . , 𝑚; ∑ 𝜆𝑗 𝑦𝑟𝑗 𝑗∈{1,2,3,...,𝑛} ≥ 𝜙𝑦𝑟𝑜 , 𝑟 = 1,2,3, . , 𝑠; 𝜆𝑗 ≥ 0, 𝑗 = 1,2,3, . . . , 𝑛. (1) if in the models a1 and a1' ∑ 𝜆𝑗 = 1 is added, then the bcc input-oriented and the bcc output-oriented models are obtained, respectively. the bcc models assume the variable vrs (variable returns to scale), and the bcc ratings measure pure technical efficiency. in the paper (seiford and thrall, 1990), a connection was established between the solutions obtained by using the a1 and a1' models. 𝜆𝑗 ∗, 𝑗 = 1,2,3, . . . , 𝑛 and 𝜃 ∗ are the optimal solutions obtained with the model a1; then, there are the corresponding optimal solutions, 𝜆𝑗 ∗∗, 𝑗 = 1,2,3, . . . , 𝑛 i 𝜙∗ obtained with the model a1’, whereby 𝜆𝑗 ∗ = 𝜆𝑗 ∗∗ 𝜙∗ i 𝜃 ∗ = 1 𝜙∗ . in this paper, the ccr and bcc models are used to investigate the sources of the inefficiency of the railway undertakings. in general, the sources of the inefficiency of railway undertakings may be caused by their inefficient operation or the noncompetitive conditions within which they operate. for this purpose, the scale efficiency score 𝑆𝑆 = 𝑄𝐶𝐶𝑅 𝑄𝐵𝐶𝐶 is used. this approach describes the sources of inefficiency, blagojević et al./oper. res. eng. sci. theor. appl. 3 (2) (2020) 1-23 18 i.e. whether it is caused by inefficient work practices (bcc efficiency) or the noncompetitive conditions shown by a proportional efficiency assessment (ss) or both. there are several approaches in the literature dedicated to the dea that may be used to evaluate the rts (return to scale) classification. the paper (seiford and zhu, 1999a) shows that there are at least three equivalent rts methods. the first ccr rts method is that introduced by banker (banker, 1984). the second bcc rts method was developed by banker et al. (1984), “some models for estimating technical and scale inefficiencies in data envelopment analysis”, management science, vol. 30, no. 1-9, pp. 1078-1092), as an alternative approach to using free variables in the bcc dual model. the third rts method is based on the scale efficiency index, and the same is proposed in the paper (fare et al., 1994a). the ccr rts method is based on the sum of the values of the dual variables λ_j in the ccr model, and the same was used for the rts classification of the observed railway undertakings. the methods for the estimation of the rts classification in the dea provide important information about possible input and output data perturbations in a dmu analysis. this information may have a positive effect on the result achieved by the dmu. they allow ineffective dmus to determine guidance in order to improve efficiency. the problem of the determination of the optimum values for the inputs and outputs of those dmus that demonstrate inefficiency can be solved by using additive dea models. these models can simultaneously set effective goals to be pursued. this allows those dmus that demonstrate inefficiency to achieve the optimum input/output ratio (ralevic, 2014). the optimum values for each input and output separately can be calculated by determining input and output slots. the results and the analysis of the real-example model test results are presented further in this paper. 6. analysis of the research results using the model a1, relative efficiency was developed for the observed group of the 8 freight transport railway undertakings. the ccr and bcc characteristics for each railway undertaking are given in table 8. table 8. the evaluation of the efficiency of the freight transport railway undertakings railway undertakings efficiency evaluation by the ccr model benchmarks efficiency evaluation by the bcc model rts classification scale score (ss) hsh 0.242 sžfreight transport 1 increasing 0.242 žrs 0.480 sžfreight transport, sk 0.933 increasing 0.514 žfbh 0.617 sžfreight transport 0.988 increasing 0.624 montecargo 0.266 sžfreight transport 1 increasing 0.266 the application of the fuzzy ahp and dea for measuring the efficiency of freight transport railway undertakings 19 hž-cargo 0.597 sžfreight transport, sk 0.955 increasing 0.625 mžt 0.350 sžfreight transport, sk 1 increasing 0.350 sžfreight transport 1 1 constant 1 sk 1 1 constant 1 average 0.569 0.984 0.578 the results presented in the table show that there are two railway undertakings with the ccr ratings equal to 1. this rating measures the overall efficiency when a constant rts is assumed. these are the railway undertakings of the slovenian railways – freight transport and serbia cargo. these railway undertakings can be seen as realistic and useful benchmarks for the other inefficient railway undertakings. slovenian railways – freight transport is one of the two undertakings with the best result. in addition, it is the undertaking that is apparently considered to be a benchmark. the railway undertakings rated below the average (0.569) are considered to be inefficient. each railway undertaking is distinguished by its specific characteristics in rail transport; nonetheless, the railway undertakings should be open to improving performance and there should be one or more railway undertakings as an example for them to follow. the selection of the relevant benchmarks was derived from the calculation of the ccr dea model by using the values obtained for the dual variables. the results shown in the fourth column of table 9 show, for each inefficient railway undertaking, another railway undertaking suitable for comparison out of the set of the efficient ones. the bcc rating measures efficiency by assuming the variable rts. in this empirical study, there are five railway undertakings awarded the bcc effective status, in addition to the two already retaining their previous effective status. for example, it can be concluded that the railway undertakings hekurudha shqiptarë sh., montecargo and the railways of the republic of north macedonia transportation department j.s.c. skopje are efficiently operated, i.e. (𝜃𝐵𝐶𝐶 ∗ = 1). in addition, it can be considered that the railways of the federation of bosnia and herzegovina have a bcc rating above the average, which means that they have good operating efficiency. based on the results of the proportional efficiency evaluations, these are the railway undertakings with a good ratio of the achieved work result and the engaged resources (work in competitive conditions): sž-tovorni promet, srbija cargo, railways of the federation of b&h and hž cargo. their relative efficiency scores are higher than the average value (0.578). 7. conclusion measuring and improving the efficiency of the operations of railway undertaking are a precondition for their successful business and survival on the market. measuring the efficiency of a company is one of the key managerial activities in modern companies that provides us with an insight into the current status of the company, the goals to be achieved in the future, as well as its current position on its way towards blagojević et al./oper. res. eng. sci. theor. appl. 3 (2) (2020) 1-23 20 the achievement the set goals. such a system is undoubtedly of strategic importance for every company that wants to survive and develop in today's conditions. therefore, such a system must adequately be integrated into the strategic management system. efficiency has a positive impact on a number of other important criteria pertaining to the work of railway undertakings, such as a better use of resources, a more rational use of energy, increased safety, an increased quality of service and so on. in order to evaluate the proper performance of operations in goods rail transport, i.e. the efficiency of railway operations, it was necessary to define and determine appropriate criteria. in this paper, group criteria are defined and evaluated, and priority criteria are selected for the purpose of evaluating the efficiency of freight transport railway undertakings based upon multi-criteria decision making and the fuzzy ahp method. from each group, the used fahp method revealed the priority criteria for the assessment of the efficiency of railway undertakings. the criteria that achieved an advantage within the composite normalized range over the other criteria from their respective group for the freight railway undertakings are as follows: • from the resource criteria group, the number of employees per kilometer of the railway network has the highest relative weight; • from the operational criteria group, it is the quantity of the transported goods; • from the financial criteria group, it is the costs of the fees for the use of the railway infrastructure, • from the service quality group, it is the available number of vehicles, and • from the safety criteria group, it is the number of serious accidents that has the highest relative weight. the dea method was chosen so as to evaluate the efficiency of the railway undertakings, because it enables an analysis of mutually comparable units despite heterogeneous data, expressed by different units of measurement and affecting business efficiency in different ways. an approach to the assessment of the efficiency of freight transport railway undertakings by using the dea method is proposed, which enables the aggregation of all the groups of criteria into a single efficiency assessment, thus also providing information on the corrective actions that can improve the efficiency of railway undertakings. the paper evaluates the efficiency of the freight transport railway undertakings performed on the basis of the selected priority criteria and by using dea excel solvers, using the ccr output-oriented model (the model assumes constant return in relation to the investment volume) and the bcc output-oriented model (the model assumes a variable return relative to the volume of investment/input). the output criterion on the basis of which the efficiency of railway undertakings was evaluated was the quantity of the transported goods. the output used in the analysis is a realistic one. the proposed approach based on the dea method was tested and verified through a survey conducted on a sample of eight freight transport railway undertakings. the application of the fuzzy ahp and dea for measuring the efficiency of freight transport railway undertakings 21 the model testing results show that there are two railway undertakings with the ccr ratings equal to 1, which is to say that this rating measures the overall efficiency when a constant rts is assumed. these are the railway undertakings slovenian railways – freight transport and serbia cargo. these railway undertakings can be seen as realistic and useful benchmarks for the other inefficient railway undertakings. thus, the railway undertakings demonstrating good efficiency appear as benchmarks for those inefficient railway undertakings. the slovenian railways freight transport has the best result. also, it is the railway undertaking that appears most as a benchmark. the selection of relevant benchmarks was derived from the calculation of the ccr dea model by using the values obtained for the dual variables. based upon the results of the bcc evaluation that measures efficiency under the assumption of the variable rts in this research, it can be concluded that five railway undertakings out of the observed eight are efficiently operated. these are the railway undertakings slovenian railways – freight, serbia cargo, hekurudha shqiptarë sh., montecargo and the railways of the republic of north macedonia transportation department j.s.c. skopje. the results show, for each inefficient railway undertaking, which railway undertaking is suitable for comparison with it from the set of the efficient ones. each railway undertaking is characterized by its specific characteristics in rail transport; 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for performance evaluation and benchmarking: data envelopment analysis with spreadsheets and dea excel solver, kluwer academic publishers, boston. © 2020 by the authors. submitted for possible open access publication under the terms and conditions of the creative commons attribution (cc by) license (http://creativecommons.org/licenses/by/4.0/). the application of the fuzzy ahp and dea for measuring the efficiency of freight transport railway undertakings aleksandar blagojević 1*, slavko vesković 2, sandra kasalica 1, aleksandra gojić 3, ahmet allamani 4 1. introduction 2. research methodology 3. the situation in the research area 4. the definition and assessment of the criteria for the evaluation of the efficiency of freight transport railway undertakings 4.1. fuzzy analytic hierarchy process (fahp) 4.2. criteria for the assessment of the efficiency of freight transport railway undertakings 5. the application of the dea method in order to assess the efficiency of freight transport railway undertakings 6. analysis of the research results 7. conclusion references operational research in engineering sciences: theory and applications vol. 3, issue 3, 2020, pp. 48-64 issn: 2620-1607 eissn: 2620-1747 doi: https://doi.org/10.31181/oresta20303048k * corresponding author. kravande58@gmail.com (r. kishore), salimousavi.d32@gmail.com (a. mousavi dehmourdi), mgnaikc@gmail.com (m. gopal naik), / (m. hassanpour). designing a framework for subcontractor’s selection in construction projects using an mcdm model ravande kishore 1, seyed ali mousavi dehmourdi 1*, m. gopal naik 1, malek hassanpour 2 1 department of civil engineering, uce, osmania university, telangana state 2 department of environmental science, ucs, osmania university, telangana state received: 20 june 2020 accepted: 10 august 2020 first online: 24 september 2020 research paper abstract: the difficulties discovered in selecting subcontractors via a simple method of bid price as the main factor along with an initial screening of subcontractor properties impressed us to look at a little beyond the existing trend and offer a coherent procedure for this purpose. despite this, we know that the main factor in outsourcing a project is a bid price and this is in full agreement with the existing circumstances of subcontractor selection in iran, but the objective of this research was integrating all criteria with the same importance for selecting a subcontractor. the questionnaire was used for collecting initial data of research to pass through the analytic hierarchy process (ahp) and multi-criteria decision-making (mcdm) model of simple additive weighting (saw). the findings showed the priority in subcontractors' selection as hejrat manesh izeh (1), khesht sazan karoun (2), yeganeh saze omid (3), sakht karan moongasht (4), darya sanat khavarmianeh (5), omran mehragane yosef (6) respectively. the present study offered a coherent procedure to select the subcontractor regardless of the bid price importance and integrating all interfering criteria in the same importance. keywords: subcontractor, construction projects, mcdm, model 1. introduction the construction industry is a well-developing and thriving industry in the world. the industry encompasses a huge budget of nations to implement road and building projects. the maintenance, lack of rework, use of innovative techniques comprised main aspects of advances in the construction industry. the aspects ensure the durability of construction projects with regard to the fact that this industry surrounds complex endeavors with a huge outlay and costs. that is why this industry mailto:salimousavi.d32@gmail.com mailto:mgnaikc@gmail.com https://link.springer.com/article/10.1007/s11269-008-9288-y#auth-1 mailto:malek.hassanpour@yahoo.com https://link.springer.com/article/10.1007/s11269-008-9288-y#auth-1 designing a framework for subcontractor’s selection in construction projects using an mcdm model 49 expanded and included excellent opportunities for business and commerce. the government construction budget was around two billion two hundred and sixty-one million dollars for khuzestan province in 2019. the ahwaz municipality construction budget allocated around 91,058,000 usd. it has been spent a huge budget for other provinces too. we are reporting the budget associated with khuzestan province because of project location in iran. nowadays, iran is under the pressure of heavy sanctions that resulted in a recession of construction projects, but it will move towards progress levels by providing budget. to construct the projects, lots of private and semi-private companies participate in iran. the procedure of contractor and subcontractor selection has been based on the bid price, and technical and professional experiences of companies (jafari and hassanpour, 2014). outsourcing construction projects to contractors and subcontractors is a common rule in lots of nations. the successful implementation of construction projects depends on solutions defined by in-charge organizations. the responsibility of the contractor is very weighting in comparison to the subcontractor. actually, the subcontractor plays the second role in the implementation of a project, as suppliers of materials, manpower, equipment, tools, or assigns lots of specialists in this regard (kumaraswamy and matthews, 2000). the use of mcdm models in lots of projects containing various scales and vague dimensions to make a clear decision has been widely expanded. the influencing parameters make the designer, constructor and engineers to select the best choice among a series of items. to solve and hold back this kind of difficulty, a large number of models that are called mcdm models have been introduced. the circumstances of application and use of models are explained by kahraman (2008), zavadskas, and turskis (2011), as the famous scientists in this regard, in a variety of studies. the selection of the best subcontractor, quality control, risk assessment, crisis management, reasons for delays in the project schedule, identification of causes of delay, value engineering also underwent mcdm systems and sensitivity analysis in terms of comparison of different models to make a decision by lots of studies. by the present study, we used an mcdm model to select the subcontractor for the project. the subcontractors hold a prominent role with regard to the first contractor or firsthand contractor in such a way to be its effect around 70-90% of the total value of the project (hinze and tracey, 1994). its role is ensuring the project wellimplementation in parallel with a contractor role. the firsthand contractor takes the highest responsibility in the project development stage as a supervisor who involves upper hand supervisors from ruling organizations. the subcontractor is introduced to the project when the contractor has got financial support difficulties or encountered a peak in project construction, etc. so, hiring the subcontractor performs an especial task and influences the project performance and its completion. the selection of subcontractor came through some complex pathways such as the relationship with the firsthand contractor, relationship with the main supervisor of project or employer, selection based on financial ability, equipment and facilities ability, and selection by bids and beneficiary purposes and lots of other options and definitions (clough et al., 2015). nowadays, company managers forced to comply with existing rules and take enough responsibility in better performing duties. on the other hand, the competition between stockholders and employers caused the definition of strict rules to improve their efficiency in the constructive processes. following a certain kishore et al./oper. res. eng. sci. theor. appl. 3 (3) (2020) 48-64 50 strategy is an important task to promote efficiency and performance (lingard et al., 2017). therefore, selecting the subcontractor is a good strategy to confer part of work to third parties with new breath in proceeding the task. however, the very important task is associated with circumstances of subcontractor selection in the defeat of successful proceeding the project. the subcontractor selection can experience lots of difficulties in terms of incomplete and biased, and lacking consideration to time, cost, and quality and safety standards from subcontractor and contractor sides. improper selection of subcontractors leads to delay, defeat, losing time, rework, and other kinds of project crises. therefore, lots of cases and factors interfere with the right selection of subcontractors. the current research study attempting to select the subcontractor depends on the main criteria in a practical project that is being constructed in iran now. the experts in completing the project were the consultants and executive managers, project engineers, and supervisors. the ranking and weighing systems were chosen to prioritize the options and alternatives and finally, the right decision was made for selecting the relevant subcontractor. many studies show the procedure to select subcontractors in construction projects, and some of them have defined conceptual frameworks, but in iran, khuzestan province, additional research is needed to be approached to choose subcontractors in the construction industry through the mcdm model. since uncertainty always exists, one is always somewhere in the middle, somewhere between the extremes, etc. mcdm is concerned with structuring and solving decision and planning problems involving multiple criteria. the purpose is to support decision-makers who are facing such problems and decision-maker preference facilitates project development. the specific objectives of current research are stated below. • investigating the general subcontractor selection methods from existing literature. • conducting the questionnaire-based survey with iranian construction experts to identify the significance of essential criteria in subcontractor selection. • evaluating the subcontractor competence and performance, based on the questionnaire to obtain the capacity of each subcontractor. • applying the mcdm model to select the best subcontractors in the construction industry by keeping the existing situations. generally, the present research objectives encompassed (1) important criteria selection, (2) subcontractor selection, (3) weighing and ranking alternatives, (4) subcontractor competence evaluation. in iran, due to the lack of a defined framework to select a subcontractor according to the existing situation in terms of the subcontractor's financial capacity, ownership of equipment for the project, compliance with administrative instructions and the subcontractor’s managerial capacity, this study considering the same importance of factors for tendering the construction projects has formulated important criteria in this regard. on the other hand, lots of companies participate in attracting the project, and in iran, the project is assigned at the lowest bid price, regardless of other important factors involved in an apparent situation. therefore, designing a framework for subcontractor’s selection in construction projects using an mcdm model 51 questionnaires were designed with the cooperation of experts involved in the tendering of the project to solve the existing problem. first, the authors tried to do a relevant literature review for the research and collect appropriate studies, then the criteria were chosen regarding the location of project and workplace conditions. then, questionnaires were designed and distributed among experts to determine the main criteria of subcontractor selection and prequalification assay, and the results were presented in tables. in the subcontractor competence assay, a questionnaire was distributed among the subcontractors to know the inventory list of each company, which included various parameters, such as 18 factors related to the equipment and devices required for the construction of the project. the other items consisted of various factors, most of which were associated to managerial aspects such as company's professional work experience records in implementing previous projects, professional experience of prominent staff, project purpose achievements, planning and managing ability, experience in similar contracts, hse guidelines observation, expert workforces along with the bid price offered by each company to obtain the project. the questionnaires were analyzed according to different criteria and the results were further analyzed in tables and excel sheets according to the methodology. in the end, the weight and ranking systems used led to the selection of the best option. 2. literature review to conduct present research, we first tried to come through the literature review to understand and identify the criteria and most difficulties recognized in selecting the subcontractors. also, it was taken into consideration the reasons for the defeat and success of conducted construction projects and a glance view based on weighing and ranking models employed in prioritizing the criteria and alternatives. a study reported the emergence of satisfaction from the employer for the implemented project regardless of the presence of main performance criteria in contractor selection. it was recommended by clients in south africa and the universal construction industry (bowen et al., 1997). russell et al. (1992) applied the effects of 20 decision criteria via spearman rank correlation analysis to find the major influencing criteria on contractor selection. so, it was found a series of major criteria including financial stability, experience, and past performance. a study came through a strong literature review pointing out the inclusion of the contractor’s prequalification method as one of the main criteria in the tendering process (holt et al., 1995). the competence screening step has carried out via interview, questionnaire, and various strategic methods with taking account of the global benchmarks in this field, contractors and subcontractors experiences, professionally completed projects, etc. the most important criteria have been detected to be economical soundness, technical ability, management capability, and the health and safety performance of contractors (hatush and skitmore, 1997a, b). the study of doloi (2009) aimed to understand the quality of criteria selected (43 cases) to evaluate the performance of the project via multiple linear regression models. sacks and harel (2006) deployed a predictive model for assessing the subcontractor resources via game theory. the successful move of the project joined the relationship between managers and having strong commitments in going ahead. by research, 29 experts participated to demystify the scores of criteria in selecting the suitable sub-contractor via a kishore et al./oper. res. eng. sci. theor. appl. 3 (3) (2020) 48-64 52 questionnaire survey supported by spss software analysis (marzouk et al., 2013). the most important criteria have been realized to be the project price among criteria of quality, cooperation, and technical know-how in subcontractor selection by the multi-nominal model in singapore (hartmann, and tan, 2009). the performance of the sub-contractor has been recognized to be an important point in conducting the objective of the project. the study revealed that 80-90% of australian building projects outsourced to the subcontractor with regard to the affordability of contractors and consultants to move the project in terms of time, quality, and costs (hinze and tracy, 1994). the subcontractors play some prominent roles in project risks and take responsibilities against redeployment, hiring and firing of workers, and financial difficulties. however, reliable subcontractor selection will recede the difficulties experienced by the way. sari and el-sayegh (2007) suggested considering a collection of factors through the literature review for distinguishing the right criteria for a certain company among general factors, construction management factors, and general contracting factors. so, they will enable you to figure out the proper matrix of criteria for the construction management at-risk contractor. akintan and morledge (2013) assessed the relations between the main contractor and subcontractor based on qualitative and quantitative factors and connections between them via integrated project delivery and the last planner system. in the united kingdom, the questionnaire was applied to assess a contractor view in terms of particular criteria of construction projects. the data were analyzed using spss software and taking into account the lowest-price wins principle (wong and et al., 2000). in singapore, industry-based contractors’ selection was performed using questionnaires and criteria and alternative choices. findings manifested to offer the most important criteria for the criterion of contractor professional experience (singh and tiong, 2006). in australia, the questionnaire method was used to assay the relationship among 20 contractors in a selection program. the questionnaire included three main success reasons for the project such as time, quality, and outlay. findings comprised a set of contributed criteria with identifying the most and least interfering criteria (hatush and skitmore, 1998). kumaraswamy and matthews (2000) used the questionnaire procedure to select the subcontractor regarding 20step interviews. so, it showed the subcontractor’s thrift by 10% of outlays in tender price and promoting the time and quality performances in the project. maturana et al. (2007) took the questionnaire procedure to select subcontractors from among 29 cases. the performance was reported by the contractor’s experience mostly. it has been used as an algorithm for the selection of sub-contractor pertaining to fuzzy preference relation, from a mathematical point of view containing an example regarding the criteria of reputation, technical capabilities, financial situation, and organizational skills (ibadov, 2015). ahp was taken into consideration to select the subcontractor via a questionnaire participated by 29 persons with allocating some criteria and alternatives extracted from the literature review in putrajaya, malaysia (manoharan, 2005). li et al. (2007) accepted the prequalification screening step as a standard procedure in sub-contractor selection. they passed through the step in a tunnel construction project based on a fuzzy approach to prioritize the criteria and alternatives in china. juan et al. (2009) applied a hybrid approach combining fuzzy set theory and quality function deployment to set up a housing refurbishment contractor selection model with lots of criteria and alternatives. the developed model passed through the sensitivity analysis via another mcdm model such as preference ranking organization method for enrichment evaluation (promethee) designing a framework for subcontractor’s selection in construction projects using an mcdm model 53 successfully. araujo, et al. (2015) approached to objectives of his research for contractor selection by paying attention to a set of contractors, resources, and limitations by assigning mcdm models such as group decision and integer programming, delphi, and prometheegdss models. in the united kingdom, utility theory was exploited to contractor selection via mcdm models along with bid price assessment (hatush and skitmore, 1998). in india, a questionnaire passed out among project managers to evaluate the contractor based on theoretical methods. in the following step, mcdm models of topsis and grey-saw determined the best option considering bids and financial affordability (puri and tiwari, 2014). in hong kong, a study underpins the framework of a matrix of data for best contractor selection via ahp joined to mcdm models in a variety of scenarios along with a minimum bid (fong and choi, 2000). ng and luu (2008) proposed a case-based intellectual model for selecting subcontractors. the technical aspect of performing the contract was pointed out to be a point for the decision-making process and developing standards and frameworks of subcontractor selection. borujeni and gitinavard (2017) studied the mining contractor selection problem via a hesitation phase compromise model. the weighing and ranking of alternatives were followed with a sensitivity analysis to promote the accuracy and precision of results. chiang and et al. (2017) used the ahp to find important aspects in selecting contractors during the bidding phase via identifying the appropriate criteria and embarking the criteria in a hierarchical structure collecting opinions of experts for making a decision matrix. cheaitou et al. (2019) have done a case study to select the efficient contractor in a public organization via mcdm models and fuzzy logic theory following with data envelopment analysis. so, in terms of the efficient contractors identified in the united arab emirates, mirmousa, and dehnavi (2016) used mcdm models for the supplier selection purpose in yazd, iran. by the way, 43 important criteria were chosen and then around 14 criteria were confirmed for further processing in the questionnaire designed. further processing was completed by 11 experts and data passed through the decision making systems to rank and weight alternatives. by morkunaite et al. (2019), contractor selection passed through the quantitative and qualitative criteria, weighing system of ahp and evaluation in the promethee model. stević et al. (2020) used measurement alternatives and ranking according to the compromise solution (marcos) model to select the sustainable supplier for the healthcare industry in bosnia and herzegovina. to classify and rank the matrix of 8×21 alternative × criteria, the marcos model was assigned along with a sensitivity analysis including rank reversal and findings of other mcdm model. 3. methodology 3.1. research design the survey questionnaire procedure was used to collect the data and literature review and the authors’ experiences were taken into account for the right selection of criteria and alternatives. the literature review was also used to select criteria. the present project is a building construction and is currently being developed in khuzestan, iran. the present project has included the area of a school to be built and is located in ahvaz, khuzestan province, iran. the main contractor of the project was shahin niloofar jangi company and all consultants had been recruited based on the kishore et al./oper. res. eng. sci. theor. appl. 3 (3) (2020) 48-64 54 lowest bid price and competitive tender, and coincidentally. the supervision of the project was undertaken by the first contractor and government office of the school innovation and equipment department in khuzestan, iran. the khuzestan province is located in the southwest of iran, as a neighbor with iraq and the persian gulf, covering an area of 63, 238 km2. the total built-up area of the building was 2800 m2. the main structure of the building was structural steelwork and this paper tried to select a subcontractor through a mcdm model. the main contractor, shahin niloofar jangi company, had been invited to undertake the project with described conditions. the figure 1 displays the steps undergone by conducted research. figure 1. flowchart of the conducted research 3.2. ahp method ahp, introduced by saaty in the 1980s, is a popular mcdm instrument. it consists of a defined mathematical structure built over consistent matrices and associated with eigenvectors to derive the true weights of compared criteria. although the ahp technique is more than three-decade-old, its flexibility and robustness keep it in use as a reliable method. the ahp method used in this study is the result of a multiplication of the criteria (αij i) with an inverse exponent of criteria numbers (1/k) according to equation 1. then, the values in columns (xij) have been divided by the sum of them according to equation 2. designing a framework for subcontractor’s selection in construction projects using an mcdm model 55 (1) one of the reasons for using the ahp method, which also states the advantages of this weighting method, is the fact that it has the ability to determine the weight of both quantitative and qualitative criteria. it has been introduced as one of the methods with a high degree of reliability because it has a strong theory and is formulated based on obvious principles (stankovic et al., 2019). 3.3. saw model it is a long time that the saw model has been used to solve various uncertainties in global world challenges. the model of saw is one of the simplest methods of mcdm techniques, which can be easily used in ranking the alternatives. to use this method, the decision matrix is normalized by the linear conversion method and then the weighted and normalized values are added together to determine the ranking values of alternatives (subcontractors). its framework is composed of two simple equations. by equations 2 and 3, xij, r and wj are the values, ranked, and weighted values respectively. the normalization of the decision matrix was done based on equation (2) (hassanpour and pamucar, 2019). it is needed to explain that xij is the values for the saw model. (2) (3) 4. result and discussion lots of criteria are interfered with in selecting the best-qualified subcontractors. the criteria were listed in two separate questionnaires and the opinions of decision makers (dm) who were holding enough experience and knowledge in this regard were used. the numerical values of 1, 2, 3, 4, 5, 6, and 7 for the criteria encompassed linguistic words as very low, low, slightly low, medium, slightly high, high, and very high in questionnaires respectively. the main criteria used in a separate questionnaire encompass the following according to table 1. the dm reached to priority and importance of main subcontractor selection factors as tender price > executive human resource = good performance in previous projects > equipment, tools and machinery ability > management and planning ability = experience in similar projects = hse instructions. according to table 1, we figured out that the main criterion in outsourcing a project is a bid price and this is in full agreement with the existing circumstances of subcontractor selection in iran. however, the objective of this research was integrating all criteria with the same importance. it means the bid price is held back and lots of criteria are interfering in subcontractor selection. that is why this research attempted to offer a coherent procedure to be taken into consideration. the criteria taken into account kishore et al./oper. res. eng. sci. theor. appl. 3 (3) (2020) 48-64 56 for conducting this study comprised the below cases in full detail. in table 2, the full names of criteria are as 400 amp diesel welding motor (c1), cnc drill (c2), rectifier (c3), h-instrument (c4), 7-function punch scissors (c5), round drill (c6), drill magnet (magnet) (c7), 8 ton tower crane (c8), powder under welding machine (c9), wind compressor 8 times (c10), fire saw (c11), diesel generator (c12), 5, 10, 15 ton crane (c13), truck for cargo transportation (c14), air capsules (c15), 10 ton jack (c16), handheld electrode heater (c17), grinding stone wall machine (c18), other aspects (c19). also, the remaining symbols are company (co), number of devices and facilities (n), ownership (o), score (s), professional experience (pe), professional experience of prominent staff (peps), project purpose achievements (ppa), planning and managing ability (pma), experience in similar contracts (esc), hse guidelines consideration (hsegc), expert workforces (ewf), bid price (bp). in table 2, lots of various criteria are actually composed of two parts (qualitative and quantitative aspects). the c1-c18 that are the same among companies in three rows of n, o, and s representing the inventory list of each company, which has included various parameters, belong to the equipment and devices required for the construction of the project. the second part included the other items (c19) consisted of various criteria, most of which were associated to the company's professional work experience records in implementing previous projects and the bid price offered by each company to obtain the project, such as pe, peps, ppa, pma, esc, hsegc, ewf, and bp. table 2 was arranged to include all criteria together as the research design of the current study. the data were gone through the normalization step and then the values of the weights were assigned to determine the final weights. the ahp method was used as the weighing system of this study. its procedure accounts for the values of tables to be multiplied with each other and then reaches to the exponential reverse of numbers. finally, each number was divided into the sum of amounts released via the exponential reverse of numbers. table 3 denotes the values of weights obtained by the ahp and saw models. according to table 3, the highest weight was devoted to the criterion of n in both systems of ahp and saw models because of variations in the number of devices, tools, and equipment applied. reasonable results appeared by the current research with looking at the values of bp that were as $ 8055.55, $ 10000, $ 9166.66, $ 6666.66, $ 8333.33, and $ 7500 for the companies of hejrat manesh izeh (1), khesht sazan karoun (2), yeganeh saze omid (3), sakht karan moongasht (4), darya sanat khavarmianeh (5), omran mehragane yosef (6) respectively. designing a framework for subcontractor’s selection in construction projects using an mcdm model 57 table 1. the main criteria of subcontractor selection by dm opinion main criteria equipment, tools and machinery ability good performance in previous projects management and planning ability experience in similar projects hse instructions executive human resources tender price dm 5 6 3 3 3 6 7 table 2. the criteria for subcontractor selection co/criteria c1 c2 c3 c4 c5 c6 c7 c8 c9 c10 c11 c12 c13 c14 c15 c16 c17 c18 c19 (1) n 3 2 1 1 2 1 1 1 1 1 1 1 1 3 2 2 o 1 1 0. 5 0. 5 1 0.5 0. 5 1 0.5 1 1 0.5 0.5 1 1 1 s 1 0. 5 0. 5 1 0.5 0. 5 1 0.5 1 1 0.5 1 1 pe 5 peps 7 ppa 6 pma 1* esc 3* hsegc 1* ewf 4* bp 1 (2) n 3 1 4 1 1 2 1 1 1 2 1 1 1 1 1 o 1 1 1 0. 5 1 1 0. 5 0.5 1 0.5 0.5 0.5 1 1 0.5 s 1 1 1 0. 5 0. 5 0.5 1 0.5 0.5 1 1 0.5 pe 5 peps 6 ppa 6 pma 1* esc 1* hsegc 1* kishore et al./oper. res. eng. sci. theor. appl. 3 (3) (2020) 48-64 58 ewf 4.5* bp 3 (3) n 2 1 2 1 3 4 2 2 1 2 2 1 2 4 2 2 o 1 1 0. 5 0. 5 1 1 0. 5 1 0.5 1 0.5 0.5 0.5 1 0.5 1 s 1 1 0. 5 0. 5 1 1 0. 5 1 1 0.5 0.5 0.5 1 0.5 1 pe 6 peps 5 ppa 5 pma 1* esc 1* hsegc 1* ewf 5* bp 4 (4) n 1 2 1 1 2 2 2 2 2 2 1 1 3 1 2 o 1 0. 5 1 0. 5 0. 5 0.5 1 1 0.5 1 1 0.5 1 0.5 0.5 s 1 0. 5 1 0. 5 0.5 1 0.5 1 1 0.5 0.5 0.5 pe 6 peps 5 ppa 5 pma 1* esc 2.5* hsegc ewf 5.5* bp 2 (5) n 1 2 1 3 1 2 2 2 2 1 1 1 2 o 1 0. 5 1 1 0. 5 1 1 0.5 1 1 0.5 1 0.5 s 1 0. 1 0. 0.5 1 0.5 0.5 1 0.5 designing a framework for subcontractor’s selection in construction projects using an mcdm model 59 5 5 pe 6 peps 4 ppa 5 pma 1* esc 2* hsegc 1* ewf 6* bp 5 (6) n 2 2 2 1 2 1 1 2 1 1 2 1 1 2 o 1 1 1 0. 5 1 0. 5 0. 5 1 0.5 0.5 1 0.5 0.5 1 s 1 1 0. 5 0. 5 0. 5 1 0.5 0.5 1 0.5 0.5 pe 6 peps 5 ppa 6 pma 2* esc 1* hsegc 0.5* ewf 6* bp 6 ownership=1, rented=0.5, full score=1, no score=0, medium score=0.5 *sum of scores depends on the number of managers and professional experience khesht sazan karoun (1), darya sanat khavarmianeh (2), hejrat manesh izeh (3), yeganeh saze omid (4), omran mehragane yosef (5), sakht karan moongasht (6) kishore et al./oper. res. eng. sci. theor. appl. 3 (3) (2020) 48-64 60 table 3.: the values of weights in ahp method and ranks for alternatives co/criteria ahp saw rank (1) n 0.48226106 3.954540667 2 o 0.26102609 1.148514787 s 0.25671286 0.872823707 pe 0.17857143 0.031887755 peps 0.25 0.0625 ppa 0.21428571 0.045918367 pma 0.03571429 0.00127551 esc 0.10714286 0.107142857 hsegc 0.03571429 0.00127551 ewf 0.14285714 0.020408163 bp 0.03571429 0.00127551 6.247 (2) n 0.47499271 3.609944573 5 o 0.26553607 1.137379511 s 0.25947122 0.808685304 pe 0.18181818 0.033057851 peps 0.21818182 0.047603306 ppa 0.21818182 0.047603306 pma 0.03636364 0.001322314 esc 0.03636364 0.001322314 hsegc 0.03636364 0.001322314 ewf 0.16363636 0.02677686 bp 0.10909091 0.011900826 5.727 (3) n 0.56798939 5.263368325 1 o 0.21351003 0.754402092 s 0.21850059 0.699201876 pe 0.21428571 0.045918367 peps 0.17857143 0.031887755 ppa 0.17857143 0.031887755 pma 0.03571429 0.00127551 esc 0.03571429 0.00127551 hsegc 0.03571429 0.00127551 ewf 0.17857143 0.031887755 bp 0.14285714 0.020408163 6.882 (4) n 0.53410426 4.495377498 3 o 0.23698415 0.888690549 s 0.2289116 0.648582857 pe 0.22222222 0.049382716 peps 0.18518519 0.034293553 ppa 0.18518519 0.034293553 pma 0.03703704 0.001371742 esc 0.09259259 0.008573388 hsegc 0 0 ewf 0.2037037 0.041495199 bp 0.07407407 0.005486968 6.2 (5) n 0.51243088 3.751726 6 o 0.26194853 0.991662 s 0.22562059 0.539878 designing a framework for subcontractor’s selection in construction projects using an mcdm model 61 pe 0.2 0.04 peps 0.13333333 0.017777778 ppa 0.16666667 0.027777778 pma 0.03333333 0.001111111 esc 0.06666667 0.004444444 hsegc 0.03333333 0.001111111 ewf 0.2 0.04 bp 0.16666667 0.027777778 5.44 (6) n 0.51153388 3.83650408 4 o 0.25576694 0.95912602 s 0.23269918 0.83174796 pe 0.18461539 0.03408284 peps 0.15384615 0.023668639 ppa 0.18461539 0.03408284 pma 0.06153846 0.003786982 esc 0.03076923 0.000946746 hsegc 0.01538462 0.000236686 ewf 0.18461539 0.03408284 bp 0.18461539 0.03408284 5.8 5. conclusion the challenges posed in subcontractor selection based on the lowest bid price seem to be forgotten by considering and taking into account the same importance for all criteria. by the way, it conducts an easy way for in-charge staff to recede the difficulties, challenges, and argues in subcontractor selection. the saw model used had a relevant connection for all partitions and released the ranks in a reasonable and discernible way. the findings and procedures of the current study can be taken into consideration across iran and other nations. it can be concluded that the lowest bid price cannot be a strong decision in holding back the construction crises unless there are lots of interfering criteria in this regard. the sensitivity analysis ignored to verify the implemented method because of variation raised in contents of table 3 and difficulties in research design based on existing conditions and circumstances in tendering. that is why future research orientation may include lots of criteria and factors despite we took important matters in iranian projects. the bid price also converted to crisp numbers to rise the precision and accuracy applied in the objective followed. we hopefully declare the civil engineers will extend the procedure and questionnaire designed in the workplace to choose the right subcontractors in future plans. 6. acknowledgment this research was conducted as part of the corresponding author's ph.d. any opinions, findings, and conclusions expressed in this publication are those of the author and necessarily reflect the current views and policies. the authors would 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(2000). lowest price or value? investigation of uk construction clients' tender selection process. construction management and economics, 18(7), 767-774. zavadskas, e.k., turskis, z. 2011. multiple criteria decision making (mcdm) methods in economics: an overview. technol. econ. dev. eco. 17 (2), 397–427. © 2020 by the authors. submitted for possible open access publication under the terms and conditions of the creative commons attribution (cc by) license (http://creativecommons.org/licenses/by/4.0/). designing a framework for subcontractor’s selection in construction projects using an mcdm model references operational research in engineering sciences: theory and applications first online issn: 2620-1607 eissn: 2620-1747 doi: https://doi.org/10.31181/oresta2811221961b * corresponding author. a.biglar@yahoo.com (a. biglar), n.hamta@arakut.ac.ir (n. hamta)thor. @arakut.ac.ir (n. hama), a.biglar@yahoo.com (a. biglar) an optimal design of combined supply chain networks considering financial ratios abbas biglar1, nima hamta2* 1 department of industrial engineering, north tehran branch, islamic azad university, tehran, iran 2 department of mechanical engineering, arak university of technology, arak, iran received: 04 august 2022 accepted: 17 november 2022 first online: 28 november 2022 research paper abstract: the more common approaches used in supply chain management consider only the physical logistic operations and ignore the financial aspects of the chain. this study presents a supply chain network design model focusing on the interactions between logistic and financial considerations. the model tries to integrate both areas of operations and financial aspects to maximize the value created for shareholders. from the logistic point of view, the main contribution of this paper is to provide the possibility of opening or closing facilities in order to deal with market fluctuations during the planning horizon. it specifies the location of each facility and determines the quantities of the products to be produced and stored to satisfy customers’ demands. from the financial point of view, unlike previous models, it considers the amount of loan, bank repayment and new capital from shareholders as decision variables, therefore, it provides managers with an accounts payable policy. the model also imposes lower limit and/or upper limit values for financial ratios in order to support the financial health of the corporation. moreover, instead of traditional approaches such as maximizing profits or minimizing costs, shareholder value analysis (sva) is used as a new objective function. to show the advantages of the presented approach, the model was solved by branchand-reduce optimization navigator (baron) solver in gams software with data provided from the literature and sensitivity analyses on financial parameters were performed to evaluate the results. the results show that with appropriate financial decisions, creating more value for the company and its shareholders is achievable. the developed model with a new financial approach is able to improve the total created shareholder value by as much as 0.7% larger than the sva obtained without financial aspects and 0.93% larger than the value created by the basic model. key words: supply chain network design (scnd), financial decisions, financial ratios, shareholder value analysis (sva) biglar and hamta/oper. res. eng. sci. theor. appl. first online 1. introduction supply chain network design (scnd) aims at optimizing strategic decisions such as "where" and "when" to locate facilities. it also determines the capacity of facilities and product flows in logistics networks. the primary goal in classical scnd models is to maximize profit or minimize logistics costs. the overall financial performance of a company can be affected by its strategic decisions and operational actions and also financial decisions in supply chain management can affect the future tactical and operational decisions (max shen, 2007). therefore, they should be simultaneously considered for optimizing the supply chain network. the importance of incorporating financial considerations into supply chain management decisions has been reported many times in the literaturesuch as studies by hammami et al. (2008), klibi et al. (2010), longinidis and georgiadis (2014), ramezani et al. (2014), mohammadi et al. (2017), yousefi and pishvaee (2018), borges et al. (2018), asadi et al. (2020), goli et al. (2020), ghasemiaslet al. (2021), shahsavari et al. (2021), ranjbari et al. (2021), tsao et al. (2021), rahman et al. (2021), mcnultyet al. (2021), badakhshan and ball (2022), musha et al. (2022), varnosfaderani et al. (2022) and molana et al. (2022). however, a limited number ofthese studies have an optimization model that merges supply chain planning with financial decisions such as investment, financing and dividend decisions. based on the previous studies, there are two different approaches in this field of research. in the first approach, financial considerations are considered as endogenous variables and optimized with other variables. in the second approach, financial aspectsare applied in objective functions and constraints as known parameters. financial considerations are very often considered in the literature as side constraints rather than the core of the decision model (rezaei et al., 2020). the goal of this paper is to fill this gap by proposing a mathematical model for the joint optimization of the supply chain network design and of the firm’s value. this study addresses a deterministic multi-echelon, multi-product and multi-period problem that considers operations and financial decisions simultaneously. in order to integrate financial aspects in supply chain network design, a mixed-integer nonlinear programming (minlp) model was developed that considers operational and financial decisions simultaneously for designing a deterministic multi-echelon, multi-product, and multi-period supply chain network. to show the model applicability, the data of a case study in literature was employed and solved by using branch-and-reduce optimization navigator (baron) solver in gams software. the major contributions of this study can be summarized as follows:  this study presents a mathematical model to solve a supply chain network design problem that considers tactical, strategic and financial decisions at the same time.  maximizing the creation of economic value for shareholders measured by shareholder value analysis (sva) as a new objective function instead of traditional approaches such as maximizing profits or minimizing costs. it has not been still used in the general model in supply chain network design problems.  providing the possibility of opening or closing facilities in order to deal with market fluctuations at any time period of the planning horizon.  the proposed model considers the amount of loan, bank repayment and new capital from shareholders as decision variables, therefore, it provides an accounts payable an optimal design of supply chain network considering financial ratios policy for the company managers instead of considering that all payments should be paid in cash. this is a contribution to the literature because previous studies consider them as parameters.  at the strategic level, the model specifies the number and location of each facility. at the tactical level, it determines the products quantities to be produced and stored to satisfy customers demand. regarding to financial decisions, the model specifies the amount of investment and their sources such as cash, bank debt or shareholders’ capital as decision variables and it provides managers with a repayment policy.  regarding the constraints, in addition to common operational constraints, we also consider lower limit and/or upper limit values for financial ratios (performance, efficiency, liquidity and leverage), in order to support the financial health of the corporation. in order to retain a better financial performance, the proposed model provides a balance among new capital entries, loans and repayment. with consideration of large cost of new capital entries, the model imposes upper bound on it and to avoid an ever-increasing debt, it considers lower bound for bank repayments. besides, these benefits our model provides for manager an accounts payable guideline.  in contrast with basic models in previous studies which have too many assumptions, the presented model uses accounting principles with lessassumptions that made it more realistic. for example, we use the net liabilities in the analysis of financial statements that balances bank loans and payments, determines the exact value of deprecation by knowing the lifetime of each asset in each time period, and applies real cash value instead of pre-determined proportion of profit. the main steps of this study can be outlined as follows:  addressing a scnd problem that simultaneously considers operations and financial decisions and considerations.  developing anminlp (mixed-integer nonlinear programming)model to solve the problem.  integrating new financial considerations in the developed model to ensure financial health and growth of the company.  testing the applicability and efficiency of the proposed model with data as reported in the literature.  comparing the results obtained by the proposed model with the basic model through different criteria to show its applicability and advantages. the remaining sections of this paper are as follows: in section 2, the relevant studies are reviewed. section 3 describes the problem and presents a mathematical model for designing a supply chain with financial considerations. section 4 explains a numerical example and discusses the results. finally, in section 5 the conclusions and some suggestions for future studies are given. biglar and hamta/oper. res. eng. sci. theor. appl. first online 2. literature review as mentioned before, the available published studies on supply chain network design which simultaneously take operations and financial dimensions into account are still rare. table 1 presented an overview of studies which integrate financial aspect in the supply change management. table 1. overview of financial studies in supply chain paper p e rio d f in ish e d p ro d u c t p a ra m e te rs o b je cti v e fu n ctio n f in a n ci a l fu tu re s s in g le m u ltip l e s in g le m u ltip l e d e te r m in isti c s to ch a stic p ro fit/ co st c h a n g e in e q u ity e v a s v a f in a n ci a l ra tio s f in a n ci n g (l o a n , ca sh , . . .) t a x r e ce iv e p a y m e n t p la n n i n g longinidis et al.(2014)       ramezani et al.(2014)       mohammadi et al. (2017)          alavi and jabbarzadeh (2018)      yousefi and pishvaee (2018)        polo et al. (2019)      zhang and wang (2019)      brahmi et al. (2020)      goli et al. (2020)     mohammadi et al. (2020)     escobar et al. (2020)      yousefi et al. (2021)        biglar and hamta (2021)        tsao et al. (2021)     badakhshan and ball (2022)     this study          in these studies, moussawi-haidar and jaber (2013) formulated a nonlinear program to find the optimal order amounts and the payment time of the supplier by using cash management integration. in their model, maximizing cash level and loan amount are financial decisions that need to be made to minimize inventory and financial costs. longinidis et al. (2014) introduced an minlp scn design model that considers the sale and leaseback (slb) technique model to find the optimal configuration of an scn, under uncertainty in product demand. their model's financial objectives are maximizing net operating profits after taxes (nopat) and unearned profit on slb (upslb). ramezani et al. (2014) presented a financial approach that considers financial and physical flows to model a supply chain network design for long-term and mid-term decisions. they applied the change in a company equity as the objective function instead of traditional approaches such as minimizing cost or maximizing profit. mohammadi et al. (2017) developed a milp model to consider financial and physical flows in mid-term and long-term decisions. the objective functions of their study are maximizing the economic value added (eva), shareholders' equity, and corporate value. brahmi et al. (2020) addressed the planning problem of which considers physical and financial flows at the same time. in their research, supply chain an optimal design of supply chain network considering financial ratios contracts were combined and supply chain tactical planning was also considered within an uncertain condition; budgetary, environmental, and contractual constraints were also incorporated. they also developed and implemented a planning model on a rolling horizon basis to minimize the impact of uncertainties. goli et al. (2020) addressed a supply chain network design with uncertain parameters. they presented a model to incorporate the financial flow, constraints of debts, and employment under fuzzy uncertainty with three objective functions: maximize the cash flow, maximize the reliability of raw materials, and maximize the total jobs created. biswas (2020) carried out a comparative analysis of the supply chain performances of leading healthcare organizations in india. the study presented an integrated multi-criteria decision-making (mcdm) framework wherein the weights of the criteria were based on experts’ opinions using pivot pairwise relative criteria importance assessment (piprecia) method. then three distinct frameworks such as multi-attributive border approximation area comparison (mabac), combined compromise solution (cocoso) and measurement of alternatives and ranking according to compromise solution (marcos) for ranking purposes. the results showed that large-cap firms do not necessarily perform well. further, the results of the three mcdm frameworks demonstrated consistency. goli and kianfar (2022) developed a bi-objective mathematical model and fuzzy ɛ-constraint method for a closed-loop mask supply chain design with the objectives of increasing the total profit and reducing the total environmental impact is presented. in their problem, there are some potential locations for collection, recycling and disposal centers and the model should decide about location of the established centers as well as the amount of produced masks and raw materials. babaee tirkolaee and serhan aydin (2022) designed a bi-level dss to configure supply chain and transportation networks and address the sustainable development of the problem by developing two milp models. they applied a fuzzy weighted goal programming approach to deal with multiobjectiveness. babaeinesami et al. (2022) addressed a closed-loop supply chain (clsc) network design considering suppliers, assembly centers, retailers, customers, collection centers, refurbishing centers, disassembly centers and disposal centers to design a distribution network based on customers’ needs and simultaneously minimize the total cost and total co2 emission. to tackle the complexity of the problem, a self-adaptive, non-dominated sorting genetic algorithm ii (nsga-ii) algorithm is designed, which is then evaluated against the ε-constraint method. sadeghi darvazeh et al. (2022) proposed a hybrid methodology to expose the process of this problem which helps managers learn how they can determine the optimal number of suppliers. they addressed this gap by developing an integrated approach based on multi-criteria decision-making (mcdm) comprising best-worst method (bwm), simple additive weighting (saw), and a technique for order preference by similarity to ideal solution (topsis), and simulation to determine the optimal number of suppliers. babaee tirkolaee et al. (2022) developed a novel mixed-integer linear programming (milp) model for msw management. the objectives were to simultaneously minimize the total cost and total environmental emission, maximize citizenship satisfaction and minimize the workload deviation. to treat the problem efficiently, a hybrid multi-objective optimization algorithm, namely, mosa-moiwoa is designed based on the multi-objective simulated annealing algorithm (mosa) and multi-objective invasive weed optimization algorithm (moiwoa). biglar and hamta/oper. res. eng. sci. theor. appl. first online mondal et al. (2022) developed an integrated model and three manufacturer-led decentralized models depending on different collection options of used products under selling price and corporate social responsibility efforts. the aim of their study was to explore how the corporate social responsibility effort of a retailer can influence the optimal decisions of the supply chain members. alinezhad et. al (2022) developed a multi-product, multi-period problem which is formulated by a bi-objective mixedinteger linear programming model with fuzzy demand and return rate . the objectives of their model are to maximize the supply chain profit and customer satisfaction at the same time. moreover, the carbon footprint is included in the first objective function in terms of cost (tax) to affect the total profit and treat the environmental aspect. they applied the fuzzy linear programming and lp-metric method to deal with the uncertainty and bi-objectiveness of the model, respectively. babaee tirkolaee et al. (2022) developed a novel mixed-integer linear programming (milp) model for msw management. the objectives were to simultaneously minimize the total cost and total environmental emission, maximize citizenship satisfaction and minimize the workload deviation. to treat the problem efficiently, a hybrid multi-objective optimization algorithm, namely, mosa-moiwoa is designed based on the multiobjective simulated annealing algorithm (mosa) and multi-objective invasive weed optimization algorithm (moiwoa). based on the above-mentioned works, this study suggests a mathematical model that simultaneously considers physical and financial aspects in a supply chain planning problem. a deterministic mixed integer nonlinear programming (minlp) model is developed to specify the number and location of facilities and the links between them. the model also determines the quantities to be produced, stored and transported in order to meet customers' demands as well as maximize shareholder value analysis (sva). as financial decisions, we consider the amount to invest, the source of the money needed (cash, bank loan, or new capital from shareholders), and repayments to the bank. 3. problem definition and assumptions in this study, a multi-echelon, multi-period, and multi-product supply chain was discussed.the supply chain consists of plants, warehouses, distribution centers and customer zones. the problem incorporates operational and financial decisions simultaneously, therefore, the mathematical formulation needs proper variables and parameters.the facilities' parameters also are independent of each other.the objective function and financial constraints are calculated based on the study by blyth et al. (1986), brealey et al. (2011) and borges at al. (2018). the goals of the proposed model are to determine:  strategic decisions about the facilities to be established (opening or closing) in given locations and the supply routes among them for each time period.  tactical operation decisions regarding the quantity produced for each product at each factory, the materials flow between facilities and the levels of inventory that consist of maximum inventory at plants, products safety stock and max and min inventory of products at warehouses and distribution centers. an optimal design of supply chain network considering financial ratios  financial decisions for determining the amount of bank loans, new capital entries and total investments to establish the network and the quantity of repayments to the bank for each time period. these three kinds of decisions were made for maximizing the value of company at the end of planning horizon that was measured by shareholder value analysis(sva) as an indicator of the corporation profitability (biglar et al., 2021). as presented in the previous sections, supply chain strategic decisions and its operation impact corporate finances and consequently financial value created for shareholders. sva is a method that values the whole equity in a company. this method assumes that the value of a business is the net present value of its future cash flows, discounted at the appropriate cost of capital. once the value of a business is calculated, the next step is to calculate the shareholder value by the equation: 𝑠ℎ𝑎𝑟𝑒ℎ𝑜𝑙𝑑𝑒𝑟 𝑣𝑎𝑙𝑢𝑒 = 𝑣𝑎𝑙𝑢𝑒 𝑜𝑓 𝑏𝑢𝑠𝑖𝑛𝑒𝑠𝑠– 𝑑𝑒𝑏𝑡 this method was first presented by alfred rappaport in the 1980s.that shows how well the company utilizes its properties in order to create value. this method is one of the most accepted lines of thought on how the corporate performance relates to the shareholder value (brealey et al., 2011). moreover, the assumptions of the proposed model can be summarized as follows:  in each duration, the demand of each customer zone is clear.  to satisfy customers' demands, the company can decide what kind of facilities to be involved at a particular time.  products can be kept at the company as inventory or distributed among warehouses.  there is not any back-order.  transportation of products among different facilities has capacity limitation.  cost and revenue are derived from the operation of firm.  fixed and variable expenses are related to transportation and production.  the establishment of facilities has fixed costs.  financial considerations are defined regarding capital cost, financial ratios, tax and depreciation rates and long-term borrowing. 3.1 mathematical formulation the decision variables, parameters, and indices applied in the mathematical model of this study have been presented in the appendix. 3.2 objective function as presented in the previous sections, strategic and operational decisions in supply chain management impact company financial performance and, consequently, the financial value created for shareholders. shareholder value is the value delivered to the equity owners of a corporation; it is created when earnings exceed the total costs of invested capital (brealey et al., 2011). therefore, in this study shareholder value biglar and hamta/oper. res. eng. sci. theor. appl. first online analysis (sva) was applied as an objective function in order to maximize shareholder value created with the supply chain network configuration. sva calculates the shareholder value (or equity value) by deducting the long-term liabilities value at the end of the project lifetime (𝐿𝑇𝐷𝑇) from the firm value for the time period under analysis. equation (1) shows the objective function. 𝑚𝑎𝑥 𝑆𝑉𝐴 = 𝐷𝐹𝐶𝐹 − 𝐿𝑇𝐷𝑇 (1) now, we explain 𝐷𝐹𝐶𝐹 , 𝐿𝑇𝐷𝑇 and other components involved to calculate them. as given by equation (2), the discounted free cash flow (𝐷𝐹𝐶𝐹) is obtained by adding the summation of the discounted free cash flows (𝐹𝐶𝐹𝐹𝑡) to the terminal value of a firm (𝑉𝑇) over the planning period. 𝐷𝐹𝐶𝐹 = ∑ 𝐹𝐶𝐹𝐹𝑡 (1+𝑟𝑡) 𝑡 + 𝑉𝑇 (1+𝑟𝑇) 𝑇𝑡∈𝒯 (2) note that 𝑇 shows the number of time periods of the planning horizon. (𝑟𝑇 ) is a parameter to show the discount rate and cost of capital and represents the time value of money and investment risk. also, 𝑉𝑇 shows the final value of the firm, that is, the value of total future cash flows, beyond the planning horizon. in this study, 𝑉𝑇 is calculated by the growing perpetuity model, which presumes that free cash flows grow at a fixed rate (𝑔) constantly. equation (3) shows how the terminal value of the firm is calculated. 𝑉𝑇 = 𝐹𝐶𝐹𝐹𝑇+1 𝑟𝑇−𝑔 ∀𝑡 ∈ 𝑇 (3) because we estimate 𝐹𝐶𝐹𝐹𝑇+1 based on an adjustment to fcff from the last period of the planning horizon, making it grow at fixed rate 𝑔 (see equation (4)), therefore modification in the fcff is needed since we have assumed stability beyond the planning horizon. this means that non-operating income is considered zero and new investments will be offset by depreciation. 𝐹𝐶𝐹𝐹𝑇+1 = [(𝑅𝐸𝑉𝑇 − 𝐶𝑆𝑇 − 𝐷𝑃𝑉𝑇 )(1 − 𝑇𝑅𝑇 ) − ∆𝑊𝐶𝑇 ](1 − 𝑔) (4) 3.2.1. free cash flow to the firm (fcff) fcff represents the quantity of cash flow from operations after accounting for depreciation expenses, taxes, working capital, and investments. it is calculated by equation (5) which deducts the net fixed asset investment (𝐹𝐴𝐼𝑡 − 𝐷𝑃𝑉𝑡) and the changes in working capital (∆𝑊𝐶𝑡) from the operating income after taxes. in this quation, (𝑅𝐸𝑉𝑡) is the revenue, the non-operating income (noi), the icost of sales (𝐶𝑆𝑡), and depreciation (𝐷𝑃𝑉𝑡). note that operating earnings are a taxable revenue; it means that in order to get net income, taxes must be subtracted from incomes. the tax rate (𝑇𝑅𝑡) is according to current tax laws. as shown in equation (5), depreciation is considered a cost because it decreases taxable income, and it is not related to a real payment (cash outflow). this means that in order to calculate the (𝐹𝐶𝐹𝐹𝑡 ), depreciation has to be added again. 𝐹𝐶𝐹𝐹𝑡 = (𝑅𝐸𝑉𝑡 + 𝑁𝑂𝐼𝑡 − 𝐶𝑆𝑡 − 𝐷𝑃𝑉𝑡 )(1 − 𝑇𝑅𝑡 ) − (𝐹𝐴𝐼𝑡 − 𝐷𝑃𝑉𝑡 ) − ∆𝑊𝐶𝑡 . ∀𝑡 ∈ 𝑇 (5) next, the free cash flow components will be explained in more detail. an optimal design of supply chain network considering financial ratios 3.2.2. revenues the revenues (𝑅𝐸𝑉t) coming from selling products/providing services are calculated as shown in equation (6): 𝑅𝐸𝑉t = ∑ priltoilti∈i.l∈l ∀t ∈ t (6) 3.2.3. non-operating income (𝑁𝑂𝐼𝑡 ) 𝑁𝑂𝐼t is the portion of a firm's income that is derived from activities not related to its core business operations including gains/losses from property or property sales. therefore, in a period that physical assets are not sold, the non-operating income will be zero. in this model, we have assumed that if there is a decision to close a facility, it will be sold. as shown in equation (7), the 𝑁𝑂𝐼t consists of three income components derived from the sale of plants, warehouses, or distribution centers. the profit or loss from selling a plant is the difference between the cash inflow resulting from alienation and calculated by the market price of the plant for the period (ajt p ) minus the cost of closing it (cjt p−) and the plant net value. 𝑁𝑂𝐼t = ∑(ajt p − cjt p−)yjt p− − ∑ cjs p+(1 − acdprst)wjst p− t s=1j∈j + ∑ (amt w − cmt w−)ymt w− − ∑ cms w+(1 − acdprst)wmst w− t s=1𝑚∈𝑀 + ∑ (akt d − ckt d−)ykt d− − ∑ cks d+(1 − acdprst)wkst d−. ∀t ∈ t ts=1𝑘∈𝐾 (7) 3.2.4. cost of sales as expressed in equation (8), cost of sales (𝐶𝑆𝑡) represents all the expenditures that are needed for producing and delivering products to customers. it consists of four parts: costs of production (𝑃𝐶𝑡), costs of transportation (𝑇𝐶𝑡), costs of inventory holding (𝐼𝐶𝑡), and changes in inventory value (𝐼𝑉𝑡 − 𝐼𝑉𝑡−1). 𝐶𝑆𝑡 = 𝑃𝐶𝑡 + 𝑇𝐶𝑡 + 𝐼𝐶𝑡 − (𝐼𝑉𝑡 − 𝐼𝑉𝑡−1) ∀t ∈ t (8) production costs have a fixed and variable part, as follows: pct = ∑ ∑ (𝐶𝑖𝑗𝑡 𝑉𝑃𝑃 𝑝𝑖𝑗𝑡 + 𝐶𝑖𝑗𝑡 𝐹𝑃𝑃 𝑢𝑖𝑗𝑡 ) ∀t ∈ t 𝑗∈𝐽𝑖∈𝐼 (9) in equation (9), 𝐶𝑖𝑗𝑡 𝑉𝑃𝑃 and 𝐶𝑖𝑗𝑡 𝐹𝑃𝑃represent the variable and fixed cost of production, respectively, at plant j, in time period t. also, 𝑝𝑖𝑗𝑡 is the quantity of product i produced in plant j at time period t and 𝑢𝑖𝑗𝑡 is a binary value which has the value 1 if product i is produced in plant j at the time period t and zero otherwise. equation (10) shows the transportation costs which include three parts with fixed and variable costs; these costs are incurred during transporting products from plants to warehouses, distribution centers, and customer zones. 𝑇𝐶𝑡 = ∑ ∑ ∑ (𝐶𝑖𝑗𝑚𝑡 𝑉𝑇𝑃𝑊𝑥𝑖𝑗𝑚𝑡 𝑃𝑊 + 𝐶𝑖𝑗𝑚𝑡 𝐹𝑇𝑃𝑊𝑧𝑗𝑚𝑡 𝑃𝑊 ) 𝑚∈𝑀𝑗∈𝐽𝑖∈𝐼 biglar and hamta/oper. res. eng. sci. theor. appl. first online + ∑ ∑ ∑(𝐶𝑖𝑚𝑘𝑡 𝑉𝑇𝑊𝐷 𝑥𝑖𝑚𝑘𝑡 𝑊𝐷 + 𝐶𝑖𝑚𝑘𝑡 𝐹𝑇𝑊𝐷 𝑧𝑚𝑘𝑡 𝑊𝐷 ) 𝑘∈𝐾𝑚∈𝑀𝑖∈𝐼 + ∑ ∑ ∑ (𝐶𝑖𝑘𝑙𝑡 𝑉𝑇𝐷𝐶 𝑥𝑖𝑘𝑙𝑡 𝐷𝐶 + 𝐶𝑖𝑘𝑙𝑡 𝑉𝑇𝐷𝐶 𝑧𝑖𝑘𝑡 𝐷𝐶 ) ∀t ∈ t𝑙 𝑘 𝐿𝑘∈𝐾𝑖∈𝐼 (10) equation (11) shows the total inventory holding costs and it has three parts related to the average quantity held at each facility (plants, warehouses, and distribution centers) during the time period. 𝐼𝐶t = ∑ ∑ (𝐶𝑖𝑗𝑡 𝐼𝑃 𝑞𝑖𝑗𝑡 𝑃 +𝑞𝑖𝑗𝑡−1 𝑃 2 ) + ∑ ∑ (𝐶𝑖𝑚𝑡 𝐼𝑊 𝑞𝑖𝑚𝑡 𝑊 +𝑞𝑖𝑚𝑡−1 𝑊 2 )𝑚∈𝑀𝑖∈𝐼𝑗∈𝐽𝑖∈𝐼 + ∑ ∑ (𝐶𝑖𝑘𝑡 𝐼𝐷 𝑞𝑖𝑘𝑡 𝐷 +𝑞𝑖𝑘𝑡−1 𝐷 2 ) ∀t ∈ t𝑘∈𝐾𝑖∈𝐼 (11) based on accounting principles, the value of inventory is calculated by historical cost; in this case, equation (12) shows the production price for each product at each time period. 𝐼𝑉𝑡 = ∑ ∑ ∑ ∑ 𝐶𝑖𝑗𝑡 𝑉𝑃𝑃 (𝑞𝑖𝑗𝑡 𝑃 + 𝑞𝑖𝑚𝑡 𝑊 +𝑞𝑖𝑘𝑡 𝐷 ) ∀t ∈ t 𝑘∈𝐾𝑚∈𝑀𝑗∈𝐽𝑖∈𝐼 (12) 3.2.5. depreciation the value of fixed assets such as plants, warehouses, and distribution centers should be modified for devaluation. based on this accounting rule, the total depreciation value at the time period t (𝐷𝑃𝑉𝑡 ) is calculated by the summation of the depreciated value of plants, warehouses, and distribution centers which are operating during the time period t. in this model, we assume that fixed assets existing before the planning horizon have been completely depreciated. 𝐷𝑃𝑉𝑡 = ∑ ∑ 𝐷𝑃𝑅𝑠𝑡 𝐶𝑗𝑠 𝑃+𝑊𝑗𝑠𝑡 𝑃+ 𝑡 𝑠=1 + 𝑗∈𝐽 ∑ ∑ 𝐷𝑃𝑅𝑠𝑡 𝐶𝑚𝑠 𝑊+𝑊𝑚𝑠𝑡 𝑊+ 𝑡 𝑠=1 𝑚∈𝑀 + ∑ ∑ 𝐷𝑃𝑅𝑠𝑡 𝐶𝑘𝑠 𝐷+𝑊𝑘𝑠𝑡 𝑊+ ∀t ∈ t 𝑡𝑠=1𝑘∈𝐾 (13) in equation (13), 𝑊𝑗𝑠𝑡 𝑃+, 𝑊𝑚𝑠𝑡 𝑊+ , and 𝑊𝑘𝑠𝑡 𝑊+ are binary variables set to 1 if a facility opened at the time period s is still open at the time period t. 3.2.6. fixed assets investment fixed assets are long-term tangible properties which a firm owns and utilizes in its operations to generate income. in our model, (𝐹𝐴𝐼𝑡) represents fixed assets investment at the time period t which is the needed finance to establish facilities (plants, warehouses, and distribution centers) in the time period t: 𝐹𝐴𝐼t = ∑ 𝐶jt p+𝑦jt p+ +𝑗∈𝐽 ∑ 𝐶mt w+𝑦mt w+ +𝑚∈𝑀 ∑ 𝐶kt d+𝑦kt d+ 𝑘∈𝐾 ∀t ∈ t (14) 3.2.7. changes in working capital the changes in working capital (∆𝑊𝐶𝑡) are obtained by the difference between the working capital in two successive periods. the working capital is calculated by adding receivable accounts to the value of inventory and deducting payable accounts. it is assumed that the accounts receivable and the accounts payable are a portion of the revenues and of the operational costs, respectively, at the end of time period t. therefore, ∆𝑊𝐶t can be obtained as follows: an optimal design of supply chain network considering financial ratios ∆𝑊𝐶t = (αtrevt − αt−1revt−1) + (ivt − ivt−1) − [μt(pct + tct + ict) − μt−1(pct−1 + tct−1 + ict−1)] ∀t ∈ t (15) note that αt and μt represent the amount of revenues and payments (in percentage), respectively, which are outstanding in the current time period and defined by the company policy on payables and receivables. 3.2.8. long-term liabilities calculation long term liabilities are represented by long-term debt (𝐿𝑇𝐷𝑡 ), that is incurred to finance fixed assets investments, and calculated by equation (16). this is a function of the previous period debt value and current period loans (𝐵𝑡 ) and bank repayments (𝑅𝑃𝑡 ). 𝐿𝑇𝐷𝑡 = 𝐿𝑇𝐷𝑡−1 + 𝐵𝑡 − 𝑅𝑃𝑡 ∀t ∈ t (16) 3.3. the model constraints the model constraints can be categorized into two groups that should be satisfied as financial constraints and operational constraints. 3.3.1. financial constraints financial ratios are one of the beneficial parts of financial statements which prepare standard tools to evaluate the overall financial condition of a company's performance, efficiency, liquidity, and leverage. the financial constrains enforce financial ratios in order to support the financial health of the corporation. this study used the ratio categories defined by blyth et al. (1986) and breally et al. (2011) and sets upper/lower limits value for them. 3.3.2. performance ratios performance ratios measure the financial performance of the company. in this study we considered two common measures, that is, return on equity (roe) and return on assets (roa). equations (20) and (21) present the least values of 𝑅𝑂𝐸𝑡 and 𝑅𝑂𝐴𝑡 that have to be satisfied in each time duration. (i)return on equity (roe) roe illustrates the marginal investment income of shareholders and is calculated by dividing the net income by shareholders’ equity. the net income (𝑁𝐼𝑡 ) is what the business has left over after all expenses. also, (𝐸𝐵𝐼𝑇𝑡 ) is named earnings before interests and taxes. they are calculated by equations (17) and (18): 𝐸𝐵𝐼𝑇𝑡 = 𝑅𝐸𝑉𝑡 + 𝑁𝑂𝐼𝑡 − 𝐶𝑆𝑡 − 𝐷𝑃𝑉𝑡 ∀t ∈ t (17) 𝑁𝐼𝑡 = (𝐸𝐵𝐼𝑇𝑡 − 𝐼𝑅𝑡 ∗ 𝐿𝑇𝐷𝑡 )(1 − 𝑇𝑅𝑡 ) ∀t ∈ t (18) 𝐸𝑡 = 𝐸𝑡−1 + (𝐸𝐵𝐼𝑇𝑡 − 𝐼𝑅𝑡 ∗ 𝐿𝑇𝐷𝑡 )(1 − 𝑇𝑅𝑡 ) + 𝑁𝐶𝑃𝑡 ∀t ∈ t (19) according to the previous descriptions, the 𝑅𝑂𝐸 equation can be written as: (𝐸𝐵𝐼𝑇𝑡−𝐼𝑅𝑡∗𝐿𝑇𝐷𝑡)(1−𝑇𝑅𝑡) 𝐸𝑡 ≥ 𝑅𝑂𝐸𝑡 ∀t ∈ t (20) (ii) return on assets (roa) biglar and hamta/oper. res. eng. sci. theor. appl. first online roa is a measure of financial performance and represents the percentage of how profitable a company's assets are for generating revenue. it is calculated by equation (21). note that in this equation, (𝑁𝑂𝑃𝐴𝑇),(𝑁𝐹𝐴𝑡) and (𝐶𝐴𝑡) are the net operating profit after taxes, net fixed assets, and the current assets, respectively. 𝐸𝐵𝐼𝑇𝑡(1−𝑇𝑅𝑡) +𝐶𝐴𝑡 ≥ 𝑅𝑂𝐴𝑡 ∀t ∈ t (21) equation (22) shows how the current net fixed assets (𝑁𝐹𝐴𝑡) are calculated from those of the previous period, which are increased/decreased in an amount equal to the value of the investment (𝐹𝐴𝐼𝑡 ) /divestment (𝐹𝐴𝐷𝑡 ) in fixed assets of depreciation in time period t, as follows: 𝑁𝐹𝐴𝑡 = 𝑁𝐹𝐴𝑡−1 + 𝐹𝐴𝐼𝑡 − 𝐹𝐴𝐷𝑡 − 𝐷𝑃𝑉𝑡 ∀t ∈ t (22) investment expresses the ownership of fixed assets, while divestment represents sales fixed assets. in this study, we have assumed that before the planning horizon, existing assets were completely depreciated, also ( 𝐹𝐴𝐷𝑡 ) shows the net value (accounting value of the asset after depreciation) of the assets which bought during the planning horizon and until-time period t: 𝐹𝐴𝐷𝑡 = ∑ [∑ 𝐶𝑗𝑠 𝑃+(1 − 𝐴𝐶𝐷𝑃𝑅𝑠𝑡 )𝑊𝑗𝑠𝑡 𝑃− + ∑ 𝐶𝑚𝑠 𝑊+(1 − 𝐴𝐶𝐷𝑃𝑅𝑠𝑡 )𝑊𝑚𝑠𝑡 𝑊− 𝑚∈𝑀𝑗∈𝐽 𝑡 𝑠=1 + ∑ 𝐶𝑘𝑠 𝐷+(1 − 𝐴𝐶𝐷𝑃𝑅𝑠𝑡 )𝑊𝑘𝑠𝑡 𝐷− 𝑘∈𝐾 ] ∀t ∈ t (23) 𝐷𝑃𝑉𝑡 and 𝐹𝐴𝐼𝑡 reffer to equations (13) and (14) . current assets are any assets that can be expected to be sold, consumed, or exhausted by the operations of a business. in this study, current assets (𝐶𝐴t) consist of: cash and banks (ct); accounts receivable, here represented as a percent of the revenues (𝛼𝑡 𝑅𝐸𝑉𝑡 ), and inventory value (𝐼𝑉𝑡 ): 𝐶𝐴t = ct + αtrevt + ivt ∀t ∈ t (24) equation (25) represents the cash function during the time duration (ct). the cash at time period t is the available cash in the previous period, cash inflows, and cash outflows. cash inflows come from different sources:  customer and receivables (αt−1revt−1) and product sales( (1 − αt)revt),  fixed assets sales,  new capital entries (𝑁𝐶𝑃𝑡 ),  loans of the period to finance investments (𝐵𝑡 ). also, cash outflows come from different sources:  repayments of debt to the bank (𝑅𝑃𝑡 ),  costs of interest; they are calculated by multiplying an interest rate by the debt of the period (𝐼𝑅𝑡 𝐿𝑇𝐷𝑡 ),  accounts payable(μt−1(pct−1 + tct−1 + ict−1) and payments to suppliers ((1 − μt)(pct + tct + ict)),  payment of income taxes of the previous period, an optimal design of supply chain network considering financial ratios  the amount invested in new assets. ct = ct−1 + αt−1revt−1 + (1 − αt)revt + [∑(𝐴𝑗𝑡 𝑃 − 𝐶𝑗𝑡 𝑃−)𝑦𝑗𝑡 𝑃− + 𝑗∈𝐽 ∑ (𝐴𝑚𝑡 𝑊 − 𝐶𝑚𝑡 𝑊−)𝑦𝑚𝑡 𝑊− + 𝑚∈𝑀 ∑(𝐴𝑘𝑡 𝐷 − 𝐶𝑘𝑡 𝐷−)𝑦𝑗𝑡 𝐷− 𝑘∈𝐾 ] +𝑁𝐶𝑃𝑡 + 𝐵𝑡 − 𝑅𝑃𝑡 − 𝐼𝑅𝑡 𝐿𝑇𝐷𝑡 − 𝜇𝑡−1(𝑃𝐶𝑡−1 + 𝑇𝐶𝑡−1 + 𝐼𝐶𝑡−1) − (1 − 𝜇𝑡 )(𝑃𝐶𝑡 + 𝑇𝐶𝑡 + 𝐼𝐶𝑡 ) − 𝑇𝑅𝑡−1(𝐸𝐵𝐼𝑇𝑡−1 − 𝐼𝑅𝑡−1𝐿𝑇𝐷𝑡−1) − 𝐹𝐴𝐼𝑡 ∀𝑡 ∈ 𝒯 (25) note that (revt) is defined in equation (6) and income taxes are due only if there is a taxable income. 3.3.3. efficiency ratios efficiency ratios measure how well the company utilizes its different assets. these ratios allow the company to evaluate its efficiency. in this study, we considered profit margin (pmr) and asset turnover (atr) as efficiency ratios. (i) profit margin (pmr) profit margin is defined as the ratio of net income to sales and must attain a minimum value at each time duration (𝑃𝑀𝑅𝑡 ); its ratios are given by equation (26): (𝐸𝐵𝐼𝑇𝑡−irtltdt)(1−𝑇𝑅𝑡) 𝑅𝐸𝑉𝑡 ≥ 𝑃𝑀𝑅𝑡 ∀t ∈ t (26) (ii) asset turnover (atr) atr the incomes generated per monetary unit of total assets, measuring how hard the firm’s assets are working. it is given by the ratio of sales revenue to total assets in time period t. equation (27) shows asset turnover ratios. 𝑅𝐸𝑉𝑡 𝑁𝐹𝐴𝑡+𝐶𝐴𝑡 ≥ 𝐴𝑇𝑅𝑡 ∀t ∈ t (27) 3.3.4. liquidity ratios liquidity ratios determine how quickly assets can be converted into cash. the liquidity ratios analysis helps the company to evaluate its ability to keep more liquid assets. (i) current ratio (cur) current ratio is the ratio of current assets to its current liabilities and must attain a minimum value (𝐶𝑈𝑅𝑡 ). equation (28) shows current ratio constraint: 𝐶𝐴𝑡 𝑆𝑇𝐷𝑡 ≥ 𝐶𝑈𝑅𝑡 ∀t ∈ t (28) as in our model, short-term loans are negligible, thus short-term debt (𝑆𝑇𝐷𝑡 ) is due to accounts payable and taxes, as follows: 𝑆𝑇𝐷𝑡 = μt(pct + tct + ict) + (ebitt − irtltdt)𝑇𝑅𝑡 ∀t ∈ t (29) (ii) quick ratio (qr) qr is the ratio of current assets (except inventory) to its current liabilities which must satisfy a threshold value (𝑄𝑅𝑡 ) as follows: biglar and hamta/oper. res. eng. sci. theor. appl. first online 𝐶𝑡+αt𝑅𝐸𝑉𝑡 𝑆𝑇𝐷𝑡 ≥ 𝑄𝑅𝑡 ∀t ∈ t (30) (iii) cash ratio (cr) cr is the ratio of its current liabilities which must satisfy a threshold value (𝐶𝑅𝑡) as follows: 𝐶𝑡 𝑆𝑇𝐷𝑡 ≥ 𝐶𝑅𝑡 ∀t ∈ t (31) 3.3.5. leverage ratios leverage ratios assess the firm’s ability to meet the financial obligations. (i) long term debt to equity ratio (ltdr) ltdr provides an index of how much debt is used to finance its assets in a company. this ratio must be below a given limit: 𝐿𝑇𝐷𝑡 𝐸𝑡 ≥ 𝐿𝑇𝐷𝑅𝑡 ∀t ∈ t (32) (ii) total debt ratio (tdr) rdr provides an indication on the total amount of debt relative to assets; it is obtained by dividing total debt by total assets, and must be lower a given limit: 𝑆𝑇𝐷𝑡+𝐿𝑇𝐷𝑡 𝑁𝐹𝐴𝑡+𝐶𝐴𝑡 ≥ 𝐿𝑇𝐷𝑡 ∀t ∈ t (33) (iii) cash coverage ratio (ccr) ccr measures the firm’s capacity to meet interest payments in cash, thus it must satisfy a given lower limit: ebitt+𝐷𝑃𝑅𝑡 irt𝐿𝑇𝐷𝑡 ≥ 𝐶𝐶𝑅𝑡 ∀t ∈ t (34) 3.3.6 other financial constraints equation (35) shows that new capital entries are limited to the quantity that company partners desire to invest in the company ncpt ≤ 𝐶𝑃𝑡 ∀t ∈ t (35) commonly, banks constrain the repayment (rpt) to be at least the interest costs to barricade a growing debt: rpt ≥ irt𝐿𝑇𝐷𝑡 ∀t ∈ t (36) furthermore, because repayments (rpt) are part of the debt, in each period they must satisfy the constraint (37): rpt ≥ 𝐿𝑇𝐷𝑡 ∀t ∈ t (37) for each time period, the company may limit the amount borrowed to the percentage of the value of investments, as follows: bt ≤ γt𝐹𝐴𝐼𝑡 ∀t ∈ t (38) an optimal design of supply chain network considering financial ratios 3.6.2. operational constraints 3.6.2.1. at the plant level equations (39) and (40) show that production constraints enforce the production quantities in each time period, each plant, and for each product to be in a specified range. 𝑝ijt ≤ pij max ∑ wjst p+ ∀i ∈ i j ∈ j and t ∈ t ts=0 (39) 𝑝ijt ≤ pij min ∑ wjst p+ ∀i ∈ i j ∈ j and t ∈ t ts=0 (40) production quantities are also collectively limited by the available quantity of each time period, each resource, and each plant (constraint (41). note that the availability of the resources is fixed over time. ∑ ρije pijt ≤ rje ∀j ∈ j and e ∈ e and t ∈ t t i∈i (41) because production has a fixed cost, in equation (42), a binary variable (𝑢𝑖𝑗𝑡) is used to show the existence of production that assumes the value 1 whenever some non-zero quantity is produced. pijt ≤ 𝑀𝑢ijt ∀i ∈ i and j ∈ j and t ∈ t (42) plants might send all or part of the products to the warehouses that have been established. this is stated by equations (43) and (44): ∑ ∑ xijmt pw m∈m𝑖∈𝐼 ≤ m ∑ wjst p+t s=0 ∀j ∈ j and t ∈ t. (43) ∑ ∑ xijmt pw j∈j𝑖∈𝐼 ≤ m ∑ wmst w+t s=0 ∀m ∈ m and t ∈ t. (44) the total production quantity sent by each plant to each warehouse must satisfy the transport capacity, which is shown by equation (45) (note that m is enough large number). ∑ xijmt pw 𝑖∈𝐼 ≤ 𝑄jm pw 𝑍jmt pw ∀j ∈ j and m ∈ m and t ∈ t (45) equation (46) is for inventory balance at each plant and each product in each time period. the available inventory is calculated by the available inventory in the previous period, plus the produced quantity in the current period minus the quantity sent to warehouses. 𝑞ijt p = qijt−1 p + pijt − ∑ xijmt pw ∀i ∈ i and j ∈ j and t ∈ t m∈m (46) equation (47) shows that at each plant and in each time period, inventory for each product is limited. 𝑞ijt p ≤ 𝐼ijt max ∀i ∈ i j ∈ j and t ∈ t (47) finally, the proper auxiliary variables associated with the closing/remaining open status of the facilities should be set to confirm the accuracy of the opening and closing decisions in the model. during the whole planning period, if a plant was not initially open, it can only be opened at most once (equation (48)). ∑ 𝑦jt p+ ≤ 1 ∀j ∈ j t∈𝒯 (48) biglar and hamta/oper. res. eng. sci. theor. appl. first online throughout the planning period, a plant can be closed at most once if it was opened before (equations (49) and (50)). ∑ 𝑦jt p− ≤ 1 ∀j ∈ j t∈𝒯 (49) 𝑦jt p− ≤ ∑ 𝑦j𝑠 p+ ∀j ∈ j and t ∈ t t−1s=0 (50) it is impossible for a plant to be opened and closed in the same time period (equation (51)). 𝑦jt p+ + 𝑦jt p− ≤ 1 ∀j ∈ j and t ∈ t (51) equation (52) illustrates that if a plant was opened in the time period s and then closed in the time period t, therefore all decision variables: opening (𝑦js p+), closing (𝑦jt p−), and closing status (wjst p−) should be set to 1. 𝑦js p+ + 𝑦jt p− ≤ wjst p− + 1 ∀j ∈ j and s = 0. … t − 1 and t = s + 1. … t (52) if only a closing decision was made, the closing status variable would be set to 1: wjst p− ≤ 𝑦jt p− ∀j ∈ j and s = 0. … 𝒯 − 1 and t = s + 1. … t (53) also, the opening status variable (wjst p+) would be set to 1 if an opening decision was made: wjst p+ ≤ 𝑦j𝑠 p+ ∀j ∈ j and s ∈ 𝒯 and t = s. … t (54) if a plant was opened in the time period s and is yet open in the time period t, in any of the periods in the internal s+1 and t, a closing decision would be impossible: wjst p+ − 𝑦j𝑠 p+ + ∑ 𝑦jv p−t v=s+1 ≤ 0 ∀j ∈ j and s = 0. … t − 1 and t = s + 1. … t (55) 3.6.2.2 at the warehouse level equations (56) and (57) show that the stored quantities in each warehouse for each product and time period to be within a pre-specified range. ∑ qimt w i∈i ≤ wm max ∑ wmst w+t s=0 ∀m ∈ m and t ∈ t (56) ∑ qimt w i ≥ wm min ∑ wmst w+t s=0 ∀m ∈ m and t ∈ t (57) active warehouses might send all or part of their products to distribution centers in operation as stated by equations (58) and (59). ∑ ∑ ximkt wd k∈ki∈i ≤ m ∑ wmst d+ .ts=0 ∀ m ∈ m and t ∈ t. (58) ∑ ∑ ximkt wd 𝓂∈mi∈i ≤ m ∑ wkst d+t s=0 ∀ k ∈ k and t ∈ t. (59) equation (60) shows that the total quantity sent by warehouses to distribution centers in each time period, if any, must satisfy the transport capacity. ∑ ximkt wd i∈i ≤ qmk wdzmkt wd ∀ m ∈ m. k ∈ k and t ∈ t (60) equation (61) is for inventory balance at warehouses and shows that for each warehouse and each product in each time period, the available inventory is calculated by the available inventory in the previous period plus the quantity received from the plants in the current period minus the quantity sent to distribution centers. an optimal design of supply chain network considering financial ratios qimt w = qimt−1 w + ∑ xijmt pw j∈j − ∑ ximkt wd ∀i ∈ i. m ∈ m. k ∈ k and t ∈ t k∈k (61) also, for each product, safety stock is defined in each time period at each warehouse (see equation (62)). qimt w ≥ ssimt w ∑ wmst w+ ∀i ∈ i. m ∈ m. k ∈ k and t ∈ t ts=0 (62) now the proper auxiliary variables associated with the closing / remaining open status of the facilities should be set to confirm the accuracy of the opening and closing decisions in the model. equations (63) to (66) show that during the whole planning period, firstly, if a warehouse was not initially open, it could only be opened at most once. secondly, it also could be closed at most once if it was opened before. finally, a warehouse cannot be opened and closed in the same time period. ∑ ymt w+ t∈𝒯 ≤ 1 ∀m ∈ m (63) ∑ ymt w− t∈𝒯 ≤ 1 ∀m ∈ m (64) ymt w− ≤ ∑ ymt w+t−1 s=0 ∀m ∈ m and t ∈ t (65) ymt w+ + ymt w− ≤ 1 ∀m ∈ m and t ∈ t (66) equation (67) illustrates that if a plant was opened in the time period s then closed in the time period t, therefore all decision variables: opening (yms w+), closing (ymt w−), and closing status (wmst w−) should be set to 1. yms w+ + ymt w− ≤ wmst w− + 1 ∀ m ∈ m. s = 0. … t − 1. and t = s + 1. … t (67) if only a closing decision was made, a closing status variable would be set to 1: wmst w− ≤ ymt w− ∀m ∈ m. s = 0. … t − 1. and t = s + 1. … t (68) also, an opening status variable (wmst w+) would be set to 1 if an opening decision was made: wmst w+ ≤ yms w+ ∀m ∈ m. s ∈ 𝒯. and t = s + 1. … t (69) if a warehouse was opened in the time period s and is yet open in the time period t, in any of the periods in the internal s+1 and t, a closing decision is impossible: wmst w+ − yms w+ + ∑ ymv w−t v=s+1 ≤ 0 ∀m ∈ m. s = 0. … 𝒯 − 1. and t = s + 1. … t (70) 3.6.2.3. at the distribution center level equations (71) and (72) show that the stored quantities in each distribution center for each product and time period must be within a pre-specified range. ∑ qikt d i∈i ≤ dk max ∑ wkst d+t s=0 ∀k ∈ kand t ∈ t (71) ∑ qikt d i∈i ≥ dk min ∑ wkst d+t s=0 ∀k ∈ kand t ∈ t (72) active distribution centers might send all or part of their products to customer zones as stated by equation (73). ∑ ∑ xiklt dc l∈li∈i ≤ m ∑ wkst d+t s=0 ∀k ∈ k and t ∈ t (73) equation (74) shows that the total quantity sent by distribution centers to customer zones in each time period, if any, must satisfy the transport capacity. biglar and hamta/oper. res. eng. sci. theor. appl. first online ∑ xiklt dc ≤ qkl dc zklt dc i∈i ∀k ∈ k. l ∈ l. and t ∈ t (74) note that customer zones do not hold inventory, so the total product received by each customer zone from the distribution centers has to be the same as the market demand (see equations (75)). ∑ xiklt dc = oilt.k∈k ∀i ∈ i. l ∈ l. and t ∈ t (75) equation (76) is for inventory balance at distribution centers. it shows that for each distribution center and each product in each time period, the available inventory is calculated by the inventory available in the previous period, plus the quantity received from the warehouses minus the quantity sent to the customer zones. qikt d = qikt−1 d + ∑ ximkt wd 𝓂∈m − ∑ xiklt dc ∀i ∈ i. m ∈ m. and t ∈ t k∈k (76) also, at each warehouse, safety stock is defined for each product and time period (see equation (77)). qikt d ≥ ssikt d ∀i ∈ i. m ∈ m. k ∈ k. and t ∈ t (77) now the proper auxiliary variables associated with the closing / remaining open status of the facilities should be set to confirm the accuracy of the opening and closing decisions in the model. equations (78) to (81) show that during the whole planning period, firstly, if a distribution center was not initially open, it could only be opened at most once. secondly, it could also be closed at most once if it was opened before. finally, a distribution center cannot be opened and closed in the same time period. ∑ ykt d+ ≤ 1 ∀k ∈ k t∈𝒯 (78) ∑ ykt d− ≤ 1 ∀k ∈ k t∈𝒯 (79) ykt d− ≤ ∑ yks d+t−1 s=0 ∀k ∈ k. and t ∈ t (80) ykt d+ + ykt d− ≤ 1 ∀k ∈ k. and t ∈ t (81) equation (82) illustrates that if a plant was opened in the time period s then closed in the time period t, therefore, all decision variables: opening (yks d+), closing (ykt d−), and closing status (wkst d−) should be set to 1. yks d+ + ykt d− ≤ wkst d− + 1 ∀k ∈ k. s = 0. … 𝒯 − 1. and t = s + 1. … . t (82) if only a closing decision was made, a closing status variable would be set to 1: wkst d− ≤ ykt d− ∀k ∈ k. s = 0. … 𝒯 − 1. and t = s + 1. … . t (83) also, an opening status variable (wkst d+) would be set to 1 if an opening decision was made: wkst d+ ≤ yks d+ ∀k ∈ k. s = 1. … 𝒯. and t = s. … . t (84) if a distribution center was opened in the time period s and is yet open in the time period t, in any of the periods in the internal s+1 and t, a closing decision would be impossible: wkst d+ ≤ yks d+ + ∑ ykv d−t v=s+1 ≤ 0 ∀k ∈ k. s = 0. … 𝒯 − 1. and t = s + 1. … . t (85) an optimal design of supply chain network considering financial ratios 4. case study implementation and evaluation 4.1. input parameters of the model in order to evaluate the applicability and efficiency of the developed model presented in the previous section, we applied the data of a real company which is located in the uk as is shown in figure 1 and studied by longinidis and georgiadis (2014) and borges et al. (2018). note that, because of some data incongruity and missing data, their case study could not be directly applied and we have considered the following assumptions regarding the missing information:  this company has three plants in three different locations and four possible locations for warehouses and six potential locations for distribution centers.  the facilities parameters are independent from each other  each plant is able to produce six of seven products within its limitations of production capacity. each plant also holds about two times of the average annual demand as initial inventories.  in each time duration, each warehouse and also distribution centers have an upper and lower bound handling capacity and need safety stock.  initial inventories are considered about two times of the average annual demand.  safety stock for each product at each facility is equal to the total quantity transferred from the facility during a period of 15 days.  product flows among plants, warehouses, distribution centers and customer zones have upper bounds.  prices and demands of products in each customer zone are known.  the company has a 4-year planning horizon.  before the planning horizon, balance sheet data areintegrated into the optimization process.  all tangible assets have been deprecated. short-term liabilities (accounts payables and taxes of previous profits) should be paid in one year. the real value of cash has been calculated, instead of considering it as a percent of net income. figure 1. the case study supply chain network (longinidis and georgiadis, 2014) biglar and hamta/oper. res. eng. sci. theor. appl. first online 4.2 comparison between basic model and developed models now, to show the improvements in the proposed model, we compared the results of the basic model presented by longinidis and georgiadis (2014) with our developed models which have a new objective function, accurate calculations, and additional financial considerations. all the problems were solved by baron solver in gams software on a personal computer with core i5 cpu 2.50 ghz and 8 gb of ram on windows 8. 4.2.1. basic model the basic model was considered with the same decision-making assumptions and objective function presented by longinidis and georgiadis (2014). its objective is to maximize the company’s net created value which is measured by economic value added (eva) index.the model was solved and the total value created was 85,855,590 monetary units. the optimal results of the basic model will be used to compare them with results obtained from other developed models. in this way, it is possible to show the advantages of the proposed approach clearly. 4.2.2. the first developed model with new objective function according to what explained in section 2, sva is one of the most accepted methods to measure the value of a company. sva by looking at the returns provided for its stockholders determines the financial value of a company. this measure is based on the view that the objective of company managers is to maximize the wealth of company stockholders. sva calculates the shareholder value by deducting the value of long-term liabilities at the end of planning horizon from the value of the firm for the time period. in this study, the final value of the company is obtained by discounted free cash flow (dfcf) method with a fixed growth rate (0.5%). now, in the first stage of developing the model, shareholder value analysis (sva) is applied as an objective function in basic model. the model was solved and the total value created amountsis 86,855,590 monetary units.the optimal network configuration is shown in figure 2. the total production quantities for the whole planning horizon is only 1407 units: plant 1 and plant 3 produce 809 and 598, respectively; plant 2 does not produce at all.therefore, reducing inventory was clearly shown and had these results: i) decreasing production quantities to reduce the product quantities in stock. ii) more flow leads to opening a new distribution center to meet demands.in order to reduce the needs for working capital, sva tends to reduce the inventory. therefore, the produced quantity by sva model is smaller than the eva model.this feature of sva model also makes a large number of flows between some facilities (warehouses, distribution centers, and customer zones). the total quantities transported from plants to warehouses for both models are compared in table 2. an optimal design of supply chain network considering financial ratios figure 2. network structure and produced products for the developed model table 2. total products transported from plants to warehouses w1 w2 w3 w4 w1 w2 w3 w4 plant 1 7901 plant 1 7471 plant 2 6210 plant 2 1498 plant 3 3502 plant 3 3201 developed model basic model according to table 3, by sva model, warehouse 1 receives more products supplying distribution centers 1 and 6. similarly, warehouse 2 receives more quantity, therefore it supplies distribution centers 1,2, 5, and 6. but by eva model, warehouse 2 just supplied distribution center 2. table 3. total products transported from warehouses to distribution centers dc1 dc2 dc3 dc4 dc5 dc6 w1 5298 2543 w2 105 2303 508 3321 w3 161 3298 w4 developed model dc1 dc2 dc3 dc4 dc5 dc6 w1 7471 w2 1498 w3 3201 w4 basic model cz4 p = 598 dc3 cz3 w3 pl3 cz5 dc4 p = 809 w1 dc1 cz1 pl1 dc2 cz2 w2 p = 0 pl2 w4 c6 dc5 dc6 cz7 cz8 biglar and hamta/oper. res. eng. sci. theor. appl. first online as shown in tables 3 and 4, by applying the model with sva as the objective function, inventory was stored in five distribution centers (all distribution centers except 4), therefore, total flows between distribution centers and customer zones are much larger than total flows transported when eva was the objective function. note that since distribution center 6 has the lowest inventory cost among others, it received most of the inventory transferred from warehouses to distribution centers. it receives 5864 units but it only supplies the customer zone 6 with 531 units and 5333 units are kept as inventory.also, the model with sva as the objective function tends to reduce the inventory quantities to decrease the need for working capital. only 878 units stay at the plants as inventory. table 4. total products transported from distribution centers to customer zones (sva base model) cz1 cz2 cz3 cz4 cz5 cz6 cz7 cz8 dc1 1349 114 1672 123 904 1443 dc2 1515 728 dc3 1498 346 620 816 dc4 dc5 508 dc6 531 developed model cz1 cz2 cz3 cz4 cz5 cz6 cz7 cz8 dc1 1349 2018 1241 1413 1458 dc2 1498 dc3 1498 1559 dc4 dc5 dc6 basic model 4.2.3. the second developed model with new financial aspects now, in the second phase of model development, we add new financial aspects to the previous version of the model to make it similar to real conditions. these new features include the possibility of closing and opening facilities at any time period of the planning horizon, repayments obligation to the bank, adding the possibility of new capital entries from shareholders, and adoption of an accounts payable policy. to better understand the effect of these aspects, we explained them separately. first, to test the possibility of closing and opening facilities at any time period, we considered two times of the establishment price of each facility as selling prices. the value created for shareholders is 87,397,697 monetary units which is 0.88% larger than the value created by the basic model that is the gains resulting from selling the plants. then the new model with the obligation of bank repayments created 89,407,636 monetary units, which is 3.02% larger than the value created by the model with sva asobjective function.the network structure remains the same. by repaying to the bank every year, long term debt is reduced and a lower amount is deducted from the free cash flow that was generated over the planning horizon, creating more value for shareholders. an optimal design of supply chain network considering financial ratios next, in order to consider an account payable policy, it is assumed that 60% of payments to suppliers are made in cash and 40% are made in credit.in this situation, the value created for shareholders is 88,549,322 monetary units, that is, 0.96% smaller. because more amount of money (working capital) is needed to support operating expenses and pay suppliers, the free cash flow decreases and the value created is 858,314 monetary units lower. finally, we add the possibility of raising new capital from shareholders and also set a peryear limit of 60,000 monetary units for the new capital entries. this limit shows the maximum that shareholders are willing to invest in the company to receive dividends in the future. the new developed model was solved optimally and the value for shareholders increased to 92,460,308 monetary units, that is 3.18% larger than the value without these financial considerations created and 6.3% larger the value created by the basic model. figures 3to 6 display the network structure during the planning horizon. as it can be seen, the flows between facilities and the quantities transported change during the time. figure 3. network structure for the complete model in year 1 and for the developed model with new financial aspects figure 4. network structure in year 2 and for the developed model with new financial aspects biglar and hamta/oper. res. eng. sci. theor. appl. first online figure 5. network structure in year 3 and for the developed model with new financial aspects figure 6. network structure in year 4 and for the developed model with new financial aspects according to figures 3 to 6, plants only produce during the first two years and their total quantity is 1394 units.the total quantity produced by the sva model is much lower than the quantity production when eva was the objective function. therefore, the need for working capital and payments to suppliers is smaller. these changes lead to an increase in the value created for shareholders.also, by using eva as the objective an optimal design of supply chain network considering financial ratios function, the value of the company improves by creating higher inventories (which are a part of current assets). plant 2 closes at the start of second year with a final inventory of 3341 units, reducing its initial inventory by 76%. plant 1 and plant 3 are closed at the beginning of third year, with the final inventory of 1971 and 881 units. this means an inventory reduction of 245% and 285%, respectively.note that products 2, 4, and 7 at plant 1 which were not sold within the planning horizon are considered as the final inventory. also, products like 3 and 6 at plant 1 that were produced in the years 1 and 2, have no final inventory. as explained before, in accordance with the evolution of the number of flows among facilities, the product quantities transported from plants to warehouses increase from year 1 to year 2. table 5 presented the operating costs (production, transportation, and inventory holding costs) that resulted from the decisions described above.as we can see, the largest portion of the operating costs is transportation costs (50.58%), then inventory holding costs (40.27%), and production costs (9.15%). there are production costs in the first and second years. also, due to high inventory at the beginning of the planning horizon, there is no production in the years three and four.in these two years, from plants to warehouses and from warehouses to distribution centers, there are no transportation costs because plants are closed and the warehouses are not operating.as shown in table 5, inventory costs decrease over time. the inventory costs at plants in years' tree and four refer to products that were already in inventory at the beginning of the planning horizon and the ones customers didn't request.it is important to note that although the final inventory at the distribution centers is equal to zero, there is an inventory cost since inventory is calculated based on its average during a year. table 5. production, transportation, and inventory costs for year for the developed model with new financial aspects year (1) year (2) year (3) year (4) total production cost 1013 90,102 0 0 91,115 transportation cost 162,717 209,856 60,417 71,303 504,293 inventory cost 141,402 109,542 89,502 60,991 401,437 according to financial decisions made by the final model, managers are provided with an accounts payable policy in table 6. it shows that the company has enough cash (based on the initial balance sheet) and does not need bank loans. therefore, all capital entries are captured from shareholders.as we can see, production costs by the developed model are low, since high levels of inventory and money are available fo r investment. therefore, the company is in a good condition for repayments to the bank, decreasing debt and maximizing the value of the corporate which is measured by sva. table 6. financial decisions for each year for the developed model with new financial aspects financial decisions year (1) year (2) year (3) year (4) total loans 0 0 0 0 0 new capital entries 60,000 60,000 60,000 60,000 240,000 investment 300,000 0 0 0 300,000 repayments 540,000 270,000 135,000 67,500 1,012,500 biglar and hamta/oper. res. eng. sci. theor. appl. first online 4.3. financial sensitivity analysis in this section, the performance of proposed model was tested by changing some important financial parameters. these parameters are important because they are suggestive of the economic environment and in many cases are accepted conditions that the company has no impact on them. the cost of capital rate at time period t (rt) is an important parameter.also, one of the important financial parameters affecting the company’s wealth is the tax rate (𝑇𝑅𝑡 ).moreover, we selected the depreciation (𝐷𝑃𝑅𝑠𝑡 ) rate as a financial parameter for the sensitivity test. table 7 presents the effects on the proposed model by changing these parameters from −15% to +15%. the results illustrate that the model with new financial considerations is resistant to the changes of these financial parameters. table 7. sensitivity analysis of the objective function by changing in financial parameters parameter change (%) -15 -10 -5 -2 +2 +5 +10 +15 cost of capital rate at time period t (rt) 105,947,496 101,350,940 96,869,752 94,204,964 90,717,780 88,114,172 83,796,384 79,838,788 tax rate (trt ) 99,756,840 97,326,664 94,896,184 93,435,236 91,484,468 90,020,784 87,580,196 85,139,760 depreciation rate (dprst) 93,832,792 93,377,628 92,919,880 92,644,304 92,275,780 91,998,608 91,534,324 91,070,724 4.4. results and discussions in the previous section, the optimal results of a basic model were used to compare them with the results obtained from other developed models to show the advantages of the developed models. we carried out two phases of development in order to improve the basic model: i) applying a new objective function, which maximizes the value of the company measured by the sva method, ii) adding new financial aspects to the previous version of the model to make it more realistic. in the first step, sva was applied as a new objective function instead of eva. the model with the new objective was solved and the total value created for shareholders was increased by 86,635,307 monetary units. in the second step, the new financial aspects were integrated into the previous version of the model. the total value created by the complete version of the model was 92,460,308 monetary units which is 0.7% larger than the sva obtained without financial aspects and 0.93% larger than the value created in the basic model. the main reasons for an increase in value creation for shareholders are due to new operational and financial aspects, which mainly show the possibility of closing facilities and bankdebt repayments. bank repayments which reduce debt and new capital enables the company to choose better operational options. the value created by each model is reported in table 8. an optimal design of supply chain network considering financial ratios table 8. values obtained by each model model value created (monetary units) the basic model 85,855,590 the first developed model with new objective function 86,635,307 the second developed model with new financial aspects 92,460,308 the main reasons for an increase in the value created of company are due to both operational and financial aspects such as the possibility of closing facilities and bank repayments. in this study instead of eva index, which is based on conventional accounting principles, sva is applied as an objective function that is one of the most accepted methods of measuring how corporate performance relates to shareholder value. as mentioned before, the sva for a company is calculated by adding the present value of cash flows to their terminal value, which represents the value of the company discounted at the proper cost of capital. the eva for measuring a company's financial performance deducts its cost of capital from its net operating profit after taxes. as explained in the previous sections, since eva is based on accounting principles, making unreasonable decisions is possible. for example, increasing current assets by higher inventories in order to make more eva. 4.5. managerial insight as a result of decreasing profit margins and the competitive landscape, supply chain managers are forced to design and optimize the operation of their supply chain networks by considering operational and financial performance indexes at the same time. therefore, they need comprehensive decision support models that track and measure the financial impact of their production and distribution decision by integrating various financial performances (hamta et al., 2022). moreover, this integration makes a “common language” between supply chain managers and financial managers and improves cooperation between them. this study suggests a mathematical programming decision model that considers the physical and financial aspects of a supply chain planning problem simultaneously. a deterministic mixedinteger nonlinear programming (minlp) model has been developed to specify the number and location of facilities and the links between them. the model also determines the quantities to be produced, stored, and transported in order to meet customers' demands. according to financial decisions made by the model, managers are provided with an accounts payable policy since we consider the amount to invest, the source of the money needed (cash, bank loan, or new capital from shareholders), and repayments. it enables supply chain managers to take holistic decisions without underestimating the basic objective of a profit company which is the creation of value for shareholders measured by the sva index. this objective indicates a satisfactory financial status in order to guarantee new funds from shareholders and financial institutions. biglar and hamta/oper. res. eng. sci. theor. appl. first online 5. conclusions and future research classically, supply chain networks are designed according to economic criteria such as cost minimization or profit maximization. performance-based criteria such as service level or responsiveness maximization are also among the traditional objective functions adopted in the scnd models. nowadays, other criteria including sustainability, energy, and financial factors, are employed in network design. the importance of incorporating financial considerations into scm has been reported many times in the literature. many of the previous studies emphasize that strategic decisions such as supply chain decisions have a significant impact on shareholder value creation. investment decisions also should be considered as critical inputs to financial planning. since these kinds of decisions for supply chain networks play a key role in financial health of companies, therefore, financial considerations should also be regarded when modeling supply chains.however, studies on supply chain models integrating financial aspects are limited. in these studies, financial aspects have been considered as endogenous variables or known parameters in objective functions and constraints. regarding the significant importance of financial decisions, the primary goal of this study is to integrate financial decisions into the process of scnd, this study suggests a mathematical model that considers the physical and financial aspects of a supply chain planning problem, simultaneously. a deterministic mixed-integer nonlinear programming (minlp) model was developed to specify the number and location of facilities and the links between them. the model also determines the quantities to be produced, stored, and transported in order to meet customers’ demands as well as maximize the shareholder value measured by sva method. in financial decisions, the amount of investment, the source of the money needed (cash, bank loan, or new capital from shareholders) and repayments to the bank were considered. to show the applicability and efficiency of the developed model, data of longinidis and georgiadis (2014) were used. the results show that with appropriate financial decisions, creating more value for the company and its shareholders is achievable. the model could be used by supply chain managers as an effective decision tool, supporting their decisions with figures and indexes convenient for financial managers. the major contributions of this study can be summarized as follow: this study presents a mathematical model to solve a scnd problem that considers tactical, strategic and financial decisions simultaneously.maximizing the creation of economic value for shareholders measured by shareholder value analysis (sva) as a new objective function instead of traditional approaches such as maximizing profits or minimizing costs. the proposed model considers the amount of loan, bank repayment and new capital from shareholders as decision variables, therefore, it providesmanagers an accounts payable policy, instead of considering that all payments should be paid in cash. previous studies of the literature consider them as parameters. at the strategic level, the model specifies the location of each facility. at the tactical level, it determines the products quantities to be produced and stored to satisfy customers’ demand. regarding financial decisions, the model specifies the amount of investment and their sources such as cash, bank debt or shareholders’ capital as decision variables and it provides a repayment policy for managers. regarding the constraints, in addition to common operational constraints, lower limit and/or upper limit values for financial ratios in order to support the financial an optimal design of supply chain network considering financial ratios health of the corporation. to retain a better financial performance, the proposed model provides a balance among new capital entries, loans and repayment. with consideration of large cost of new capital entries, the model imposes upper bound on it and avoid an ever-increasing debt; it considers lower bound for bank repayments. besides, these benefits of our model provide managers with an accounts payable guideline.providing the possibility of opening or closing facilities in order to deal with market fluctuations during the planning horizon. in contrast with basic models in previous studies which have too many assumptions, the presented model uses accounting principles with less assumptions that made it more realistic. for example, we use the net liabilities in the analysis of financial statements that balances bank loans and payments, determines the exact value of deprecation by knowing the lifetime of each asset in each time period, and applies real cash value instead of pre-determined proportion of profit. however, this study is limited in several ways; firstly, the most limitation is that the model hasonly been tested on a case study. it would be better to demonstrate the efficiency of the proposed model, with more numerical experiments.secondly, it is assumed that when a facility is opened it is immediately operational, which is hardly possible in a real-world situation.finally, it is assumed a facility can only be supplied by the facilities in the previous echelon of the supply chain; however, real situations often consider the possibility of direct sales for instance sales from manufacturers to final customers. in summary, it should be pointed out that our model can be expanded in the following directions: in order to make the model similar to real conditions, future studies can consider uncertainty in some parameters such as product prices and demand. applying financial ratios as objective functions in the proposed model in order to find a way to increase and improve the firm soundness. the green supply chain with a closed-loop structure can be the other research trend for the model considering environmental, social, technological and economic facets; such facets can be included in the supply chain network design. the problem would get more complicated with such developments. therefore, other solutions, such as metaheuristics, can be considered as other suggestions for futures research. acknowledgement: the paper is a part of the research done within project 23036. the authors would like to thank markazi industrial estates corporation (miec). appendix table 9. notations sets and indices e resources of production indexed by e i products indexed by i j locations of plant, indexed by j k locations of distribution center, indexed by k l locations of customer zone, indexed by l m locations of warehouse, indexed by m t planning periods indexed by s and t parameters biglar and hamta/oper. res. eng. sci. theor. appl. first online ajt p plant market price j during the time period t, with j ∈ j and t ∈ t amt w warehouse market price m during the time periodt, with m ∈ m and t ∈ t akt d distribution center market price k at time periodt, with k ∈ k and t ∈ t cjt p+ cost for establishing a plant at location j during the time periodt, with j ∈ j and t ∈ t cmt w+ cost for establishing a warehouse at location m during the time period t, with m ∈ m and t ∈ t ckt d+ cost for establishing a distribution center at location k at time periodt, with k ∈ k and t ∈ t cjt p− cost for closing a plant at location j during the time period t, with j ∈ j and t ∈ t cmt w− cost for closing a warehouse at location m during the time periodt, with m ∈ m and t ∈ t ckt d− cost for closing a distribution center at location k during the time period t, with k ∈ k and t ∈ t cijt fp fixed production cost for product i at plant j at time periodt, with i ∈ i, j ∈ j, and t ∈ t cijt vpp unit production cost for product i at plant j at time periodt, with i ∈ i, j ∈ j, and t ∈ 𝒯 cijmt ftpw fixed transportation cost of product i from plant j to warehousem at time periodt, with i ∈ i, j ∈ j, m ∈ m, and t ∈ t cijmt vtpw unit transportation cost of product i from plant j to warehousem at time periodt, with i ∈ i, j ∈ j, m ∈ m, and t ∈ t cimkt ftwd fixed transportation cost of product i from warehousem to distribution center k at time periodt, with i ∈ i, m ∈ m, k ∈ k and t ∈ t cimkt vtwd unit transportation cost of product i from warehouse m to distribution center k at time periodt, with i ∈ i, m ∈ m, k ∈ k and t ∈ t ciklt ftdc fixed transportation cost of product i from distribution centerk to customer zonel at time periodt, with i ∈ i, k ∈ k, l ∈ l and t ∈ t ciklt vtdc unit transportation cost of product i from distribution center k to customer zonel at time periodt, with i ∈ i, k ∈ k, l ∈ l and t ∈ t cijt ip unit inventory cost of product i at plant j at time periodt, with i ∈ i. j ∈ j and t ∈ t cimt iw unit inventory cost of product i at warehousem at time periodt, with i ∈ i. m ∈ m. and t ∈ t cikt id unit inventory cost of product i at distribution centerk at time periodt, with i ∈ i. k ∈ k. and t ∈ t dk max maximum capacity of distribution centerk, with k ∈ k dk min minimum capacity of distribution centerk, with k ∈ k iijt max maximum inventory level of product i being held at plant j at the end of time periodt, with i ∈ i. j ∈ j. and t ∈ t oilt demand of product i from customer zone l at time periodt, with i ∈ i, l ∈ l, and t ∈ t pij max maximum production capacity of product i at plant j with i ∈ i end j ∈ j pij min minimum production capacity of product i at plant j with i ∈ i end j ∈ j prilt unit selling price of product i at customer zonel at time periodt, with i ∈ i, l ∈ l, and t ∈ t an optimal design of supply chain network considering financial ratios qim pw maximum limit of products that can be transferred from plant j to warehousem, with j ∈ j end m ∈ m qmk wd maximum limit of products that can be transferred from warehousem to distribution center k, with m ∈ m end k ∈ k qkl dc maximum limit of products that can be transferred from distribution centerk to customer zone l, with k ∈ k end l ∈ l rje available quantity of resource e at plant j,with e ∈ e and j ∈ j wm max maximum capacity of warehousem, with m ∈ m wm min minimum capacity of warehousem, with m ∈ m ssikt d safety stock of product i at distribution centerk, during the time period t with j ∈ j, k ∈ k, and t ∈ t ssimt w safety stock of product i at warehousem, during the time periodt with i ∈ i. m ∈ m, and t ∈ t crt lower bound for cash ratio during the time period t, with t ∈ t curt lower bound for current ratio during the time period t, with t ∈ t ccrt lower bound for cash coverage ratio during the time periodt, with t ∈ t atrt lower bound for assets turnover ratio during the time period t, with t ∈ t cpt upper bound for new capital entries during the time periodt, with t ∈ t ltdrt upper bound for long-term debt ratio during the time period t, with t ∈ t tdrt upper bound for total debt ratio during the time periodt, with t ∈ t roet lower bound for return on equity ratio during the time period t, with t ∈ t pmrt lower bound for profit margin ratio during the time periodt, with t ∈ t roat lower bound for return on assets ratio during the time periodt, with t ∈ t qrt lower bound for quick ratio during the time periodt, with t ∈ t acdprst rate of accumulated depreciation of a facility opened at time periods and closed during the time period t, with s and t ∈ t irt rate of long-term interest during the time periodt, with t ∈ t trt rate of tax at the time periodt, with t ∈ t rt rate of capital cost during time periodt, with t ∈ t dprst rate of depreciation of a facility at the end of time periodt, with s and t ∈ t ϱeij coefficient relating resource utilization rate of e to produce product i in plant j, with e ∈ e, i ∈ i, and j ∈ j γt coefficient relating loans during the time periodt, with t ∈ t μt coefficient relating payables outstanding at time periodt, with t ∈ t αt coefficient relating revenues outstanding at time periodt, with t ∈ t decisions and auxiliary variables qijt p inventory level of product i being held at plant j at time periodt, with i ∈ i, j ∈ j. and t ∈ t qimt w inventory level of product i being held at warehousem at time periodt, with i ∈ i. m ∈ m. and t ∈ t qikt d inventory level of product i being held at distribution centerk at time periodt, with i ∈ i. k ∈ k. and t ∈ t pijt product quantity i produced at plant j at time periodt, with i ∈ i, j ∈ j, and t ∈ t xijmt pw product quantity i transferred from plant j to warehousem in time periodt, with i ∈ i, j ∈ j, m ∈ m, and t ∈ t biglar and hamta/oper. res. eng. sci. theor. appl. first online ximkt wd product quantity i transferred from warehousem to distribution centerk in time periodt, with i ∈ i, m ∈ m, k ∈ k and t ∈ t xiklt dc quantity of product i transferred from distribution centerk to customer zonel during time periodt, with i ∈ i. k ∈ k. l ∈ l and t ∈ t yjt p+ { 1 if a plant at location 𝑗 is opened at time period𝑡; 0 otherwise. with j ∈ j and t ∈ t yjt p− { 1 if a plant at location 𝑗 is closed at time period𝑡; 0 otherwise. with j ∈ j and t ∈ t ymt w+ { 1 if a warehouse at location m is opened at time period𝑡; 0 otherwise. with 𝓂 ∈ m and t ∈ t ymt w− { 1 if a warehouse at location m is closed at time period𝑡; 0 otherwise. with 𝓂 ∈ m and t ∈ t ykt d+ { 1 if a distribution center at location k is opened at time period𝑡; 0 otherwise. with 𝒦 ∈ k and t ∈ t ykt d− { 1 if a distribution center at location k is closed at time period𝑡; 0 otherwise. with k ∈ k and t ∈ t uijt { 1 if product 𝑖 is produced at plant 𝑗 at time period𝑡 ; 0 otherwise. with i ∈ i. j ∈ j. and t ∈ t zjmt pw { 1 if plant 𝑗 supplies warehouse m at time period𝑡; 0 otherwise. with j ∈ j. m ∈ m and t ∈ t zmkt wd { 1 if warehouse m supplies distribution center k at time period𝑡; 0 otherwise. with 𝓂 ∈ m. k ∈ k and t ∈ t zklt dc { 1 if distribution center k supplies customer zone 𝑙 at time period𝑡; 0 otherwise. with k ∈ k. l ∈ l and t ∈ t wjst p− { 1 if plant j was opened at time period s and closed at time period t 0 otherwise. with j ∈ j and s and t ∈ t wjst p+ { 1 if plant j was opened at time period s and is still open at time period t 0 otherwise. with k j ∈ j and s and t ∈ t wmst w− { 1 if warehouse m was opened at time period s and closed at time period t; 0 otherwise. with m ∈ m and s and t ∈ t wmst w+ { 1 if m was opened at time period s and is still open at time period t; 0 otherwise. with m ∈ m and s and t ∈ t wkst d+ { 1 if distribution center k was opened at time period s and is still open at time period t; 0 otherwise. with k ∈ k and s and t ∈ t an optimal design of supply chain network considering financial ratios wkst d− { 1 if customer zone k was opened at time period𝑠 and closed at time period𝑡; 0 otherwise. with k ∈ 𝐾 and 𝑠 and 𝑡 ∈ t ncpt new capital entries from shareholders during the time period t, with t ∈ t rpt repaid amount to the bank during the time periodt, with t ∈ t cat current assets during the time periodt, with t ∈ t bt bank debts during the time periodt, with t ∈ t dpvt depreciation value at time periodt, with t ∈ t cst cost of sales at time period t, with t ∈ t ct cash during the time period t, with t ∈ t fait investment of fixed assets during the time period t, with t ∈ t fadt divestment of fixed assets during the time periodt, with t ∈ t ipt interest paid(interest expense) during the time periodt, with t ∈ t ict cost of holding inventory during the time periodt, with t ∈ t ltdt long-term debt during the time periodt, with t ∈ t ivt value of inventory at time periodt, with t ∈ t noit non-operating income during the time periodt, with t ∈ t pct cost of production during the time period t, with t ∈ t nfat net fixed assets during the time period t, with t ∈ t revt revenues from sales during the time period t, with t ∈ t tct cost of transportation during the time period t, with t ∈ t references alavi, seyyed hossein, and 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"a multi-echelon global supply chain network design based on transfer-pricing strategy.", journal of industrial integration and management 4(1), 1850020. https://doi.org/10.1142/s2424862218500203 © 2022 by the authors. submitted for possible open access publication under the terms and conditions of the creative commons attribution (cc by) license (http://creativecommons.org/licenses/by/4.0/). https://doi.org/10.24018/compute.2022.2.4.71 https://doi.org/10.1016/j.omega.2018.11.016 https://doi.org/10.22111/ijfs.2021.5877 https://doi.org/10.1007/s40815-018-0511-6 https://doi.org/10.1142/s2424862218500203 an optimal design of combined supply chain networks considering financial ratios abbas biglar1, nima hamta2* 1. introduction 2. literature review 3. problem definition and assumptions 3.1 mathematical formulation 3.2 objective function 3.2.1. free cash flow to the firm (fcff) 3.2.2. revenues 3.2.3. non-operating income (,𝑁𝑂𝐼-𝑡.) 3.2.4. cost of sales 3.2.5. depreciation 3.2.6. fixed assets investment 3.2.7. changes in working capital 3.2.8. long-term liabilities calculation 3.3. the model constraints 3.3.1. financial constraints 3.3.2. performance ratios 3.3.3. efficiency ratios 3.3.4. liquidity ratios 3.3.5. leverage ratios 3.3.6 other financial constraints 3.6.2. operational constraints 3.6.2.1. at the plant level 3.6.2.2 at the warehouse level 3.6.2.3. at the distribution center level 4. case study implementation and evaluation 4.1. input parameters of the model 4.2 comparison between basic model and developed models 4.2.1. basic model 4.2.2. the first developed model with new objective function 4.2.3. the second developed model with new financial aspects 4.3. financial sensitivity analysis 4.4. results and discussions 4.5. managerial insight 5. conclusions and future research references operational research in engineering sciences: theory and applications vol. 5, issue 3, 2022, pp. 153-193 issn: 2620-1607 eissn: 2620-1747 doi: https://doi.org/10.31181/oresta161122121b * corresponding author. sb.16ms1302@phd.nitdgp.ac.in (s. biswas), gautam.bandyopadhyay@dms.nitdgp.ac.in (g. bandyopadhyay), dpamucar@gmail.com (d. pamucar), nehajoshi.1608@gmail.com (n. joshi) a multi-criteria based stock selection framework in emerging market sanjib biswas 1, gautam bandyopadhyay 1, dragan pamucar 2*, neha joshi 3 1 department of management studies, national institute of technology, west bengal, india 2 university of belgrade, faculty of organizational sciences, department of operations research and statistics, belgrade, serbia 3 calcutta business school, bishnupur, west bengal, india received: 19 august 2022 accepted: 18 october 2022 first online: 11 november 2022 original scientific paper abstract: the present study aims to compare the stock performances of the fast moving consumer goods (fmcg) and consumer durables (cd) firms at the bombay stock exchange (bse), india. it is evident from the extant literature that investment in the stock market depends on two broad objectives such as maximization of return while minimization of risk. besides, investment decisions are also influenced by the behavioral nature of the investors. to this end, the current work considers the earning prospect (average market return, return on net worth, earning per share, and yield), marketcentric risk (beta), market perception (price to book value, shares traded), momentum (turnover) and benchmarked performance (alpha) to set the criteria for comparison. the study period considers seven consecutive financial years to discern the performance. for the comparative analysis, a combined multi-criteria decision-making (mcdm) framework of logarithmic percentage change-driven objective weighting (lopcow) (used to determine criteria weights) and evaluation based on distance from average solution (edas) (for ranking) methods has been utilized. borda count method (bc), copeland method, and simple additive weighting (saw) have been used to aggregate the year-wise rankings. the calculated weights show consistency to the modern portfolio theory as average return, beta, and return on net worth obtain higher weightage than others. it is observed that there are variations in the year-wise comparative ranking, while on aggregation, fmcg firms dominate the top positions. the analysis reveals that avanti feeds ltd., hindustan unilever ltd., procter & gamble hygiene & health care ltd., britannia industries ltd., and nestle india ltd. are the top five performers, while godfrey phillips india ltd., e i d-parry (india) ltd., united biswas et al./oper. res. eng. sci. theor. appl. 5(3)2022 153-193 154 breweries ltd., rajesh exports ltd., and radico khaitan ltd. hold the bottom five positions during the same period. the results also indicate that, more or less, the firms having higher market capitalizations have performed well. the results obtained using the edas method and other popular mcdm models, such as multi-attributive border approximation area comparison (mabac) and the complex proportional assessment (copras), show a significant correlation. further, the outcome of the sensitivity analysis confirms the stability of the performance-based ranking results. key words: stock performance, portfolio selection, logarithmic percentage changedriven objective weighting (lopcow), evaluation based on distance from average solution (edas), borda count 1. introduction investment decision-making is a multi-factors-based complex activity. the investors consider several aspects such as financial goals, present condition prior to investment, objectives of investment, and selection of financial instruments vis-à-vis intended outcome (asad et al., 2018). essentially, financial investment intends to generate wealth to achieve financial security and independence and fulfill the desired financial goals (goyal et al., 2021; gupta et al., 2019a). the underlying objective is to formulate a portfolio of financial instruments to optimize the overall return at an affordable risk (ren et al., 2017). among all financial instruments, the equity stock market has been an attractive option for investment over the last several decades (gupta et al., 2019b). the portfolio selection is a complex issue that gets influenced by many aspects encompassing investors’ characteristics, backgrounds and their decisions, performance, and characteristics of the stocks, entry and exit timing, market behavior, and macro-economic influences (biswas et al., 2019; bhattacharya et al., 2022). the vastly expanded strand of literature on security analysis and portfolio selection has the genesis in two celebrated contributions, such as security analysis for value investing (graham et al., 1934) and the mean-variance framework (modern portfolio theory) of markowitz (1952). according to their work, investment decisions entail maximization of the mean (return) while minimizing the variance (risk). in subsequent years, the stated school of thoughts has been enriched and expanded with many notable contributions, for instances capital asset price model (capm), market efficiency and conditions for capital market equilibrium (sharpe, 1964; lintner, 1965; mossin, 1966; fama, 1970; black, 1993), effect of organizational characteristics on stock returns (stattman, 1980; banz, 1981; reinganum, 1981; basu, 1983; rosenberg et al., 1985; bhandari, 1988; chan et al., 1991), three factor model for asset pricing and stock selection (fama and french, 1992, 1993), momentum and contranian effect on stock performance (jegadeesh and titman, 1993, grinblatt et al., 1995, cooper et al., 2004), four factor model for asset pricing (carhart, 1997), estimation of volatility and its effect on stock performance (chong and phillips, 2012; hsu and li, 2013), integration of fundamental and technical indicators for assessment of stock performance for portfolio selection (peachavanish, 2016), multi-factor based portfolio selection (fama and french, 2017, 2018) among others. the modern portfolio theory (mpt) and capm depend on the theoretical foundations of the expected utility theory (morgenstern and von neumann, 1953), which state that investors make rational decisions using the available information a multi-criteria based stock selection framework in emerging market 155 fully and also on the notions of bounded rationality (barnard and simon, 1947). further, the market is also treated as an efficient one wherein the market price determines the intrinsic values of the firms. however, in real-life scenarios, investment decisions are not always grounded on rationality or bounded rationality, and the investment market is not necessarily efficient. the mpt and capm do not consider the behavioral manifestations, such as emotions, social orientations, and cognitive dissonance of the investors, which notably affect the final decisions (ogunlusi and obademi, 2021; huang et al., 2011). keeping into consideration the impact of behavioral factors on investment decision-making, a new school of thought (“behavioral finance theory or bft”) has emerged and evolved with the proposal of the prospect theory (pt) by tversky and kahneman (1979). in the subsequent years, the extant literature has been contributed by the cumulative prospect theory, aka cpt (tversky and kahneman, 1992), modified cpt with uncertain information (schmidt et al., 2008; schmidt and zank, 2009). all these theories entail the impact of abnormal phenomena on investment decisions. the pt and cpt are based on the value function that explains the investment decisions regarding potential gains and losses with respect to the reference point. the other strand of the bft points out that the investors safeguard the risk or potential loss over the gain (disposition effect) while contradicting the fundamental propositions of the expected utility theory (shefrin and statman, 1985; levy, 1992). from a linked perspective, the researchers (loomes and sugden, 1982; bell, 1985) also highlighted the disappointment of the investors if the outcome is below par with expectations. investors prefer to have better gains at an affordable risk (gul, 1991), leading to their choices for a low risk-free rate with a higher equity gain (li et al., 2021). from the theories of the investment decision making it is understood that investors do select the portfolio from multiple perspectives such as market performance indicators like return, risk, price to book value and earnings, and volatility along with fundamental performance and technical analysis (patil and bagodi, 2021). hence, the investment decisions stand on multiple criteria or features which are conflicting to each other and complex in nature (aouni et al., 2019). in this paper we aim to carry out a comparative analysis of selected fmcg and cd stocks listed in bse, india over a period of seven consecutive financial years (fy 2013-14 to fy 2019-20). fmcg products are the consumer packaged goods that are regularly consumed by the common households in their daily life. the fmcg sector is characterized by a number of interesting features such as a higher level of consumption, wider range for products and prices available to a large consumer base (both urban and rural segments), lower entry and exit conditions for the firms leading to stiff intra-industry competitions among several domestic and multinational firms and presence of substantial number of unorganized players (dhingra et al., 2018). on the other side, cd products (white, brown and consumer electronics items) are also used in the kitchens for utility purpose, as electronic gadgets for daily entertainment purpose, for home furnishing and as leisure items. the sector is featured by rapid developments of technology, presence of organized and/or unorganized domestic players and multinationals and intense competitions on brands. with the rise in the disposable income and increasing urbanizations, the sector has been witnessing a notable growth over the last few decades and there has been an increasing familiarity among common households belonging to rural area also (sarangi, 2019). hence, fmcg and cd sectors have been drawing growing attentions from the indian investors and fetching a substantial inflow from abroad biswas et al./oper. res. eng. sci. theor. appl. 5(3)2022 153-193 156 too (ibef, 2022a, 2022b). the present paper attempts to answer the following research questions: rq1. how can a multi-criteria based model be formulated to compare the market performance of a set of selected fmcg and cd stocks? rq2. to what extent do the stocks differ from each other in terms of their market performance? we construct the rest of the paper in the following manner. in section 2, a brief summary of the recently published research work is presented. section 3 sketches out the data and methodology used in this paper while in section 4, the major findings are highlighted. section 5 exhibits the discussions on the result and includes the implications of the work. at the end, section 6 makes the concluding remarks while mentioning some of the future research scope. 2. related work the extant literature is vastly contributed with the research work on stock selection approaches and frameworks. in this section, we shall present a summary of some related work published recently. for this purpose, we organize the literature review section in two parts. the first part summarizes the work applying statistical analysis and predictive and machine learning (ml) algorithms are discussed. the second part highlights some of the work that used mcdm models for stock selection. 2.1. stock selection using statistical analysis and predictive and ml algorithms the extant literature shows ubiquitous applications of statistical models and ml algorithms for predicting stock performances and portfolio selection. for instance, dai and zhou (2019) considered equal-weight linear models and machine learning frameworks to identify the criteria for stock selection and put forth an efficient portfolio. wu et al. (2019) presented a cross-sectional forecasting model for the stocks listed in the shanghai composite index. they advocated selling lower decile stocks while buying upper decile stocks to formulate the portfolio. tan et al. (2019) proposed a nonlinear predictive analytics framework such as random forest and examined its efficacy in stock selection. two types of features such as technical/fundamental and momentum were considered to compare the chinese stocks and observed lesser efficiency of the market in the stock market. yang et al. (2019) suggested a hybrid stock selection method incorporating stock prediction and effectively capturing the future features of complex stock markets. the result implies that the proposed model can be an efficient tool for profit generation portfolios by outperforming a series of benchmark models by incorporating stock prediction into stock selection. asadi and mohammadi (2020) proposed a semi-variance model for analyzing information development with cross-sectional return for selecting portfolios in a fuzzy environment. the study used 14 financial parameters collected from financial statements of 40 companies listed on the tehran stock exchange. the analysis concluded that the proposed method was more suitable than other methods as it provided better results for performance analysis, efficiency, and company selection which helps in selecting a portfolio in a fuzzy multipurpose model. chen et. al (2020) a multi-criteria based stock selection framework in emerging market 157 proposed a solution to the portfolio selection problem with high order moments. the study aimed to extend the mean-variance model to the mean-variance skewness kurtosis model. daily trading data of the 50 shanghai stock exchange index was taken from the period of january 04, 2010 to february 20, 2017 to verify the effectiveness and robustness of the proposed model. the out-of-the-sample performance of the suggested model showed significantly better results than the classic mean-variance model. the proposed hybrid approach also included three machine learning algorithms for constructing a portfolio to invest in. alfonso and ramirez (2020) suggested a combinational approach with a neural network to guarantee better results in stock forecasting. the study used 6 different chinese stock indexes and 36 technical indicators as inputs in a non-linear model. the results showed that the suggested model can be a feasible one for stock forecasting. wu (2020) suggested an investment strategy based on the k-clustering model using machine learning. the monthly data of 5175 stocks from the us stock market from the period of august 2009 to august 2016 along with their technical indicators likema, kdj & macd was used for the study. these stocks were divided into several clusters and the stock closest to the center of the best cluster was chosen for the construction of the portfolio. the results showed that the investment in the portfolio created using the model had the highest excess return during the bull market and the same showed a decline in synch with s&p 500 index during the bear market. arif and sohail (2020) attempted to incorporate additional dimensions to risk in the markowitz mean-variance framework. they suggested incorporating skewness, kurtosis, and coherent risk measure (cvar) for obtaining an optimal portfolio with the pgp approach. the model used stock selected from the kse-100 index during the period of 2009-to 2018 and analyzed their mean-variance, mean-variance skewness, mean-variance skewness kurtosis, and mean cvar skewness kurtosis. the analysis concluded that the return of the portfolio constructed using higher-order comoments and a more sophisticated risk measuring tool gave a higher return over the benchmark portfolio. somathilake (2020) explored the factors that influence the investment decisions of individual investors. the data used for the study were collected from 150 individual investors who were actively participating in columbia stock exchange during the year 2020 using a standard questionnaire created using the likert scale. the factors likeaccounting information, neutral information, and recommendations were considered independent variables for the study. the data collected were analyzed using correlation and regression. the results showed neutral information and advocated recommendations influences individual investment decision more than accounting information available which concludes that investors are not so rational while making investment decisions. ogbebor and alalade (2020) examined the factors considered by the individual investors while selecting stock and how they affect the stock prices. the study was made taking into consideration individual investors including stock brokers, investment bankers, and equity investors, and the stock prices of the companies listed on the nigerian stock exchange. the responses of 250 investors collected through a questionnaire were analyzed using regression (correlation & anova). the study showed that the independent variables such as investment, earnings, dividends, bills (three months treasury bill rates), inflation rate, board characteristics, public (public image), product and history, product line, and long history of existence jointly along with the biswas et al./oper. res. eng. sci. theor. appl. 5(3)2022 153-193 158 personal preference of individual investors significantly affect the stock price behavior of the companies listed in nigerian stock exchange. zhou and yin (2020) proposed a multi-factor stock selection model based on kernel principal component analysis. the study adopted a tree-like method that took factors like fundamental, technical, macro, investor sentiment, and analyst prediction, and these factors are further sub-classified to create a new method of processing a large amount of high dimensional nonlinear factors quickly and accurately. the paper takes all stocks of the shanghai and shenzhen 300 index in 2016 as the benchmark for the stock pool and analyses data from 2010 to 2016 in multi-dimensional space. the data was arranged, processed, identified, and extracted by the characteristic of factors by kernel regression. the robustness of the model was verified using the bootstrap method. the result concluded that a combination of kernel principal component analysis and multifactor stocks selection model could beat the market with high profitability and also can effectively overcome the problem of random stock selection. huang et al. (2021) applied three machine learning models such as feed-forward neural network (fnn), random forest (rf) and adaptive neural fuzzy inference system (anfis) to predict stock performance based on fundamental performance. bernal et al. (2021) aimed to present a multiple criterion hierarchical process (mchp) approach for the first stage of portfolio selection, the evaluation of stock. 21 financial indicators (financial ratios, volatility, and beta of shares) from 121 companies listed on the mexican stock exchange were used to propose a structure hierarchical analysis of three levels. the multi-criteria ranking of stocks based on selected financial indicators was done using the multiple criteria hierarchical process which evaluated each macro criterion by directly interacting with immediate descending sub-criteria forming the hierarchical structure. lastly, a preferential model is generated to understand how a company performs against another company at the given time and how that impacts the problem of portfolio selection. the study concluded that subgroups of indicators for market influence were ranked highly as they are considered the most important decision criteria in stock evaluation compared to other indicators. it also observed that some companies showed a better ranking when the company’s performance values were considered in the stock evaluation. de nard et al. (2021) blends the traditional factor model of covariance matrix estimation with modern large -dimensional asymptotic theory. the study proposes a new afm1-dcc-nl model and allowing time-varying conditional heteroscedasticity on historical data. further, they also suggested a new forecasting covariance matrix where the dynamic estimator is used and the holding period of portfolio exceeds the frequency of the observed returns. the suggested techniques aimed at helping portfolio manager develop better-performing investment strategies along with contributing to academics to develop more powerful predictive tests. nazneena et al. (2021) studied comparative analysis of methods of constructing an optimal portfolio and thereby creating an optimum portfolio for the investment of the funds based on cnx nifty and the indices of the relative sub-group. daily data for the period of november 09, 2020 to february 05, 2021 of 5 sectors were considered for the study. sharpe single index model is used to construct the portfolio. the study compares the risk and return of an individual sector with the risk and return associated with the market and creates an optimal portfolio. a multi-criteria based stock selection framework in emerging market 159 cheng et al. (2021) have applied data mining techniques and decision tree analysis to explore the relationship between financial ratios, corporate governance, and stock return to form a basis for making stock selection decisions. the study also employs another algorithm, the apriori in association rules to supplement the explanation of mutual influence between various variables. 10 years of complete data of sports and leisure companies listed in taiwan from 2005 to 2014 were used to construct the investment decision model. the annual rate of return as the dependent variable and 19 independent variables likestock price, years on market, ds&f holding, eps, r&d expense, roe, roa, etc of the sample companies were studied as the case study formulating the proposed model. the study established an effective investment decision model and also provides a reference basis for stock-picking. dou et al. (2021) used support vector model (svm) for multi-factor stock selection. the study uses quarterly financial information such as profitability, income quality, debt-paying ability, etc of all the constituent stocks of the csi 300 index from 2013 to 2017 along with the risk indicators and investor sentiment indicators to make the model more comprehensive and effective. further, principal component analysis (pca) is used for reducing the dimension and establishing the model before testing it empirically. the stock selection is done according to the sample values generated by the prediction of the model and it was concluded that its reliability was higher when compared to other research. bermejo et al. (2021) proposed a factorbased long-term investing approach that evaluates the performance of the combined portfolios using the factors such as value, profitability, and momentum. the factor investment methodologies were applied to a balanced panel of 17,400 observations of 1830 different european companies distributed among 29 countries and 19 economic sectors from 1991 to 2019. the results showed that risk-adjusted returns can be improved by combining the factors into a single portfolio and the topperforming mixed portfolios are made from the combination of two different factors (profitability and momentum). the study also shows how the investor can combine value, profitability, and momentum factors in top quintile value portfolios to increasingly improve the risk-adjusted returns of those portfolios. mortazian (2021) investigated the changes in stocks’ liquidity and return volatility after their movement from the main market to alternative investment market (aim). the study is made on the companies that moved from the main market to aim between january 1996 to december 2013 on london stock exchange. the results showed that the stock that moved to aim had a lower level of treading activity, higher transaction cost, and less stock return volatility in comparison to the stock that stayed. further, it was also observed that the increase in illiquidity and decrease in volatility are sustained for four years after the movement. jin et al. (2021) created an investment portfolio using the markowitz model and index model. the study used the historical daily returns on 10 stocks from different sectors for 20 years (2001-2021) to design the best portfolio for different risk preferences with the best possible rate of return. the daily data were aggregated into the monthly observation to reduce the non-gaussian effects. the results of the markowitz model & index model were presented in tabular and graphical form which concluded, that the index model, compared to the markowitz model, is more practical in the real situation of the market. as the index model involves a simpler calculation of covariance which decreases the demand for the number of estimators. hence, investors may largely use the index model to help themselves find optimal portfolios. biswas et al./oper. res. eng. sci. theor. appl. 5(3)2022 153-193 160 chaya et al. (2021) validated the fama french factor model by studying the effect of systematic risk, size, and valuation of stock return. the study is made on the daily stock prices on the lebanese stock market from the period of 2011 to 2018. it was concluded that market risk and valuation are significant in explaining the average stock market variation whereas the size factor appears to be very insignificantly small. it was also seen that the stock market exhibited a negative market risk premium due to us t-bills and a high level of other factors inter-correlated during the period of study. nugroho and tjong (2021) aimed to determine the optimal stock as a basis for decisions in investment in company shares using single index model. 19 stocks were selected from the purposive sampling from the idx30 index listed on the indonesia stock exchange from 2015 to 2019. zhang et al. (2021) forecasts the closing of 10 stocks for the next 100 days through the time series, considering multiple constraints such as maximum return and minimum risk and thereby selecting an optimal portfolio strategy. the study uses the long-term and shortterm memory (lstm) is used with a good prediction effect along with the mape index to judge the error between the predicted result and the real value. finally, the effectiveness of the model is verified by analyzing the new portfolio which shows that the expected income along with other investment benefits is positive. shahidin et al. (2021) proposed a mathematical method of variance covariance to determine the stocks for the creation of portfolios by following the risk preference of the investors and evaluating the value at risk (var) of multiple stock portfolios. geometric brownian motion was also used to forecast share prices for future investment. the study was conducted on five different sectors from october 2017 to april 2018. the study of the var of each stock portfolio concludes that industrial products and trading are more suitable for risk-averse and service sectors for risk premium investors. gubu et al. (2021) suggest a robust way of portfolio selection by grouping the stocks into clusters based on the different sectors. sharpe ratio is used to select representatives from each cluster and a portfolio is constructed that optimized the use of fcmd and sestimation. the proposed method was employed in the stock listed on the indonesia stock exchange for the period starting from august 2017 to july 2018. the study showed that the portfolio created using clustering based on the business sector of stocks combined with fmcd estimation, outperformed the other possible combinations. mustafa et al. (2022) proposed a new generalized auto regression conditional heteroscedasticity (garch) econometric model with fuzzy numbers to forecast stock prices and observed significant accuracy in the results. vo-van et al. (2022) suggested a new approach for short-term stock trend prediction using the bayesian classifier. the proposed stock selection method aimed at maximizing the probability of correct identification of peaks and troughs, thereby limiting risk and ensuring relatively higher profit. the study uses a new approach to computing the stock variation from the closing value of the last two days of the stock listed on the vietnamese stock exchange. the time series data is transformed into tabular data and then the prediction is done using a bayesian classifier. the results showed that the proposed two-step ahead prediction model is feasible and is better suited for short-term profits. in a recent work, solares et al. (2022) demonstrated a combined forecasting, selection and optimization framework related to investment in equity market. the authors applied artificial neural network, fundamental analysis, differential evolution and evolutionary algorithms like genetic algorithm for the stocks listed at the s&p’s 500 index. further, the authors compared the performances (in terms of the features a multi-criteria based stock selection framework in emerging market 161 like risk adjusted returns, actual return etc.) with respect to the benchmark market indices and observed that the proposed portfolio outperforms the benchmark. on a different note, devine and siddiqui (2022) formulated an equilibrium constraint based model (grounded on the concept of oligopoly) to explain the stock performance in the context of electricity market. the authors considered two categories of firms such as market leaders and followers. 2.2. stock selection using mcdm algorithms mcdm algorithms have also been extensively used for comparing stock performances for portfolio selection problems. for example, tey et al. (2019) used single valued neutrosophic fuzzy based ahp model to compare the financial performance of a sample of five public companies listed in kuala lumpur stock exchange (klse). the authors considered 15 fundamental financial ratios as criteria. in the same direction, witayakiattilerd (2019) considered price to earnings and book value, and return ratios to compare the stock performance of the property & construction industry in thailand. sang et al. (2019) designed an mcdm stock selection model which deals simultaneously with possibilities and probabilities under an interval type-2 fuzzy environment. the model is applied to financial data and its corresponding probabilities on 7 selected real estate companies in china from 2000 to2017. the study considered the subjective uncertainty of the investors and objective uncertainty of information insufficiency in decision making. entropy weight was also computed based on the theory of information entropy, through which investors were able to assess potential stocks more scientifically and objectively. the interval type-2 fuzzy positive-ideal and the negative-ideal solution are used as the points of reference and the relative closeness is used to select an ideal alternative by ranking. rahiminezhad et al. (2020) aimed to identify the main criteria for selecting and assessing portfolios and to develop a fuzzy analytic network process to improve the process of stock selection in a portfolio. the study is made on stocks listed on tehran stock exchange and 23 portfolio selection criteria were identified from previous literature. a likert-type questionnaire was developed using the identified criteria and was analyzed after it was filled by experts. the findings suggested that the classical model of portfolio selection developed by markowitz is not adequate as it takes only yield and risk into consideration whereas the present study showed that stock selection for portfolio creation involves multiple factors so mcdm techniques should be used. fanp was used and helped in ranking 10 different tse portfolios which helped investors in selecting the best portfolio. nguyen et al. (2020) proposed an integrated method based on analytical hierarchy process (ahp), grey relational analysis (gra), technique for order performance by similarity to ideal situation (topsis), and multi-objective optimization ratio analysis (moora) to evaluate the financial performance of the agriculture companies listed on vietnamese stock exchange. the 20 financial ratios of 13 agricultural companies were analyzed from 2013-to 2019. ahp was used to determine the weights of the financial ratios and the stocks of the selected companies were ranked using gra, topsis, and moora. the results showed that the stock hsl was the top stock with the highest ranking and gra, topsis, and moora rankings are highly correlated. the study also suggested that the proposed model along with biswas et al./oper. res. eng. sci. theor. appl. 5(3)2022 153-193 162 copras, kemira & edas could be implemented to evaluate the financial performance of other industries likeoil & gas, textile, etc. tang et al. (2020) established a novel q-rung orthopair fuzzy (qrof) based mcdm model. a practical case about risk evaluation of stock investment was analyzed to check the practicality and viability of the proposed methods. the results were contrasted with liang and liu’s method which concluded that the proposed method can handle a wide range of fuzzy information. vuković et al. (2020) applied five mcdm models on the ground of the modern portfolio theory for a period of three years while considering stock return and beta, average traded volume, price to book value and equity and sales ratios and turnover ratios. peng et al. (2021) introduced an innovative solution of z-numbers and electre i to deal with the issues of information reliability and criterion non-compensation of the stock selection process. the study uses z-number as a tool for describing the information and identifying its reliability, next it defines the outranking degree of znumbers based on fuzzy and probability. lastly, outranking aggregation and exploitation procedures are presented based on electre i to handle the noncompensation among stock evaluation criteria. the study concluded that the developed znumber and electre i can qualitatively and flexibly deal with uncertain and unreliable information dealing with stock investment and can also effectively manage non-compensation among criteria. tatlari et al. (2021) proposed a solution combining the data envelopment analysis (dea) and multi-criteria decision making (mcdm) approach to retrieve the financial information for solving the problem of stock selection. the solution of designing an optimal portfolio using the suggested model is worked out in two stages. in the first stage, the dea approach was used to calculate the cost-effectiveness and profit, while in the second stage companies were classified using the mcdm approach. the study was made using financial information of the petrochemical companies listed on the tehran stock exchange for the period from 2015 to 2019. suroso et al. (2021) applied the preference ranking organisation method of enrichment evaluation (promethee) model to select the optimal stock of sustainable certification and risk criteria. the model is applied to the annual data from 2016 to 2018 of 11 palm oil companies listed on the indonesia stock exchange. the study is made by integrating aspects of the rspo sustainability certificate and risk criteria proxied by beta. the results of the study show the three best stock alternatives from the sample studied and conclude that the above said criteria can be used by the investors as a preference along with the company’s internal criteria. jankova et al. (2021) proposed to apply a higher degree of fuzzy logic (typeii) as a tool for investment decision making in exchange traded funds (etfs) in the us stock market. the model uses the return, risk, dividend, and a total expense ratio of 10 etfs of the real state sector. the study showed that the type-2 fuzzy logic is preferable to use than typei, as it gives more realistic and accurate results as it uses a 3dimensional set of functions and includes the footprint of uncertainty. jain et al. (2021) investigated the major behavioral stock selection criteria of individual equity investors in india by focusing on the factors influencing the decisions of the retail investors’ stock selection. the study is conducted on the primary data collected from a questionnaire and the response of 168 traders at the national stock exchange was selected as the sample for study during the last quarter a multi-criteria based stock selection framework in emerging market 163 of 2019. the sample was analyzed using the fuzzy analytic hierarchy process (ahp) approach. the results highlighted that behavioral factors, trading opportunities, and accounting information are the three most influential criteria for stock selection. factors likeaffordable price, recent price movement, the sensitivity of the company, trend of major indices, and evaluation by well-known experts are the five most important sub-criteria. arasu et al. (2021) aimed to identify and compare the appropriate variables for stock selection by testing three different sets of input and output variables using data envelopment analysis (dea). the first set consists of fundamental variables, the second set comprises technical variables and the third set includes both fundamental and technical variables. 69 companies were selected from national stock exchange and their financial ratios, momentum variables were classified as input & output for the study. the results show that the average returns of the effective stocks, identified using the three sets of variables gives higher return than the market return. further, it can also be concluded that a portfolio created using just the momentum variables gives a higher return than the other two. narang et al. (2021) proposed a hybrid multi-criteria decision-making method consisting of group fuzzy copras and fuzzy bcm. fuzzy bcm is used for the relative weights of the criteria derived from the group decision-making process and then to rank the alternatives, these criteria weights are integrated with the fuzzy copras method. the study aims at increasing the practicability of soft computing in the selection of stocks for creating a portfolio with a better return. both the methods are applied in a real case study where 5 stocks were selected based on the criteria long term beta, revenue, and roe for the period of january 2009 to december 2019. an exponential moving average was used to convert the multi-dimensional data into a single numerical value. the portfolio constructed based on the proposed ranking gave a better return. narang et al. (2022) proposed a new integrated f-cocoso-h model based on the two-stage framework aiming to solve the problem of investment decision-making. the study also suggests some modifications to the main structure like – the heronian mean operator is combined with the traditional combined compromise solution method to calculate the relative optimal weights of specific decision criteria, which is calculated using the base-criterion method. the proposed model eliminates the efficacy of anomalous data and also makes complex decisions more flexible. the model is validated with the help of 15 stocks selected based on revenue and roe as beneficial criteria and der & p/e as non-beneficial criteria. the study was made taking 11 years of historical data and different portfolios were constructed using particle swarm optimization. the study validates the prominence and stability of the proposed model. thakur et al. (2022) applied a mixed approach of artificial intelligence models and dempster-shafer (ds) theory for generating stock returns based on fuzzy rules and optimization of the portfolio by the ant colony optimization (aco) algorithm under a mean-variance framework. gong et al. (2022) presented a dynamic fuzzy portfolio for the investors of different risk tolerance levels and observed a superior performance of the portfolio in the long-run. ecer et al. (2022) focused on the cryptocurrency market to figure out a comparative evaluation. the authors compared a set of 15 popular cryptocurrencies (based on market capitalization) subject to the influence of 16 features. the analysis was carried out using a combination of evaluation based on distance from average solution (edas), multi-attributive ideal real comparative analysis (mairca) and measurement of alternatives and ranking according to compromise solution (marcos) framework biswas et al./oper. res. eng. sci. theor. appl. 5(3)2022 153-193 164 in a group decision-making set up with user opinions expressed in terms of intuitionistic fuzzy information. the authors noted that reliability, ease of use and stability are the dominant features to declare ethereum, tether, and bitcoin as the most preferred options. 2.3. findings from the literature review and research gap we have noticed that a sizeable amount of research carried out in past regarding the selection of the portfolio of equity stocks. table 1 provides a summary of the review of the past work as described in section 2.1 and 2.2. it is evident that the past research has extended the fundamental work on mean-variance framework while considering the other higher order moments, technical indicators, fundamental performance indicators and momentum variables. the extant literature shows umpteen evidences of using predictive models, machine learning algorithms, classical and extended optimization methods and mcdm frameworks. from the theoretical perspectives, past work have used mpt, capm framework, expected utility theory, pt and mpt. there has been a numerous work that considered bft and its propositions to explore the behaviors of the investors and their impact on the stock selection process. still, the interesting fact is that the volume of work in the stated field has been increasing over the years which is an indication of an ever increasing importance of research on stock selection. further, the extant literature shows a scantiness of comprehensive evaluation (considering the earning prospect, market centric risk, market perception, momentum and benchmarked performance to set the criteria for comparison) of the market performance of the stocks using mcdm models. we also observe that there is a scantiness of work that considered performance evaluation of stocks over a longitudinal period using mcdm models and subsequently aggregating the results to arrive at the conclusion. table 1. summary of literature review theme theoretical framework methods used references classification and prediction of stock performance for portfolio selection modern portfolio theory is followed. fundamental and/or technical indicators are considered. the analysis have been carried out using objective information. linear statistical models; nonlinear predictive models; ml algorithms dai and zhou (2019); wu et al. (2019); tan et al. (2019); yang et al. (2019); asadi and mohammadi (2020); chen et. al (2020); alfonso and ramirez (2020); wu (2020); arif and sohail (2020); zhou and yin (2020); huang et al. (2021); bernal et al. (2021); de nard et al. (2021); nazneena et al. (2021); cheng et al. (2021); dou et al. (2021); bermejo et al. (2021); mortazian (2021); jin et al. (2021); chaya et al. (2021); nugroho and tjong (2021); zhang et al. (2021); shahidin et al. (2021); gubu et al. (2021); vo-van et al. (2022); solares et al. (2022); a multi-criteria based stock selection framework in emerging market 165 theme theoretical framework methods used references mustafa et al. (2022) investment decisionmaking for stock selection behavioural aspects of the investors and performance indicators are considered. the analysis was carried out using subjective information. qualitative and statistical analysis ogbebor and alalade (2020); somathilake (2020) evaluation of stock performance for portfolio selection fundamental and market based multiple indicators are used. mostly, objective information has been used. in some cases, subjective information has also been used. mcdm models like analytic hierarchy process, analytic network process, grey relational analysis (gra), technique for order performance by similarity to ideal situation (topsis), multi-objective optimization ratio analysis (moora), copras, kemira, edas, electre i, data envelopment analysis, preference ranking organisation method of enrichment evaluation (promethee) and cocoso with crisp, fuzzy, interval type2 fuzzy, neutrosophic fuzzy, qrung orthopair fuzzy, znumbers tey et al. (2019); witayakiattilerd (2019); sang et al. (2019); rahiminezhad et al. (2020); nguyen et al. (2020); tang et al. (2020); vuković et al. (2020); peng et al. (2021); tatlari et al. (2021); suroso et al. (2021); jankova et al. (2021); jankova et al. (2021); jain et al. (2021); arasu et al. (2021); narang et al. (2021); narang et al. (2022); thakur et al. (2022); gong et al. (2022); ecer et al. (2022) 2.4. main contributions of the work the present paper fills the gap in the literature and contributes to the growing volume of literature on stock selection as follows a) the present paper presents a comprehensive mix of market performance indicators in tune with the mpt, expected utility theory, pt, intrinsic value of the firms and fundamental performance of the stocks for the comparative analysis using mcdm model. b) it is seen that assessment of stock performance related to fmcg and cd sectors in indian context vis-à-vis investment decision making is quite rare in the extant literature. hence, the present paper sheds a new direction in this regard. in this context, the present work provides a year to year comparative analysis over seven consecutive financial years to arrive at the overall performance based ranking of the stocks. biswas et al./oper. res. eng. sci. theor. appl. 5(3)2022 153-193 166 c) the current work provides a new hybrid mcdm framework combining the most recently developed algorithm for calculating the criteria weights with objective information such as lopcow (ecer and pamucar, 2022) and a widely used ranking model such as edas (keshavarz ghorabaee et al., 2015) for portfolio selection problems. d) finally, the present research utilizes three types of ranking aggregation methods such as borda method, copeland method and simple additive weighting (saw) in connection with the year wise ranking of the stocks using lopcow-edas framework to arrive at the final selection of stocks. 3. materials and methods in this paper, we aim to compare the market performances of the stocks of the selected fmcg and cd firms listed in bse, india. in what follows are the brief description of the methodology including the sample selection, criteria description and procedural steps of the methods used. the flow of the steps is depicted in figure 1. 3.1. sample the present paper considers the study period from april 01, 2013 to march 31, 2020 (i.e., from fy 2013-14 to fy 2019-20). at the first stage, we consider the fmcg and cd stocks which have been listed in bse, india during this period and discard the others. further, we find out the average market capitalization values using geometric mean (gm) for all the stocks (screened at the first stage) over the study period. gm is preferred here to reduce the effect of the outliers (if any) and is applicable as there are no missing and/or zero values for the market capitalization. finally, we select top 25 fmcg and 05 cd stocks (based on the average market capitalization value) to form our sample for comparative analysis. the size of our sample (i.e., 30) satisfies the minimum requirement for a standard sample size as recommended by many researchers (for example, roscoe, 1975; luanglath and rewtrakunphaiboon, 2013; louangrath, 2014; luanglath, 2014; agresti and kateri, 2021) vis-à-vis the central limit theorem, n-hat and n-omega methods. in effect, the sample selected for the present study comprises of more than 30 percent of elements of fmcg and cd sectors (i.e., 25 out of total 72 stocks from fmcg and 5 out of total 10 stocks from cd sectors respectively). the constituent stocks of the sample used in the present study is listed in table 2. these 30 stocks are the alternatives or decision making units (dmu) under comparison subject to a set of criteria as described in the subsequent section. table 2. list of dmus (i.e., stocks) under comparison s/l dmu category a1 avanti feeds ltd. fmcg a2 bajaj consumer care ltd. fmcg a3 bombay burmah trdg. corpn. ltd. fmcg a4 britannia industries ltd. fmcg a5 c c l products (india) ltd. fmcg a6 colgate-palmolive (india) ltd. fmcg a7 dabur india ltd. fmcg a8 e i d-parry (india) ltd. fmcg a multi-criteria based stock selection framework in emerging market 167 s/l dmu category a9 emami ltd. fmcg a10 future consumer ltd. fmcg a11 gillette india ltd. fmcg a12 godfrey phillips india ltd. fmcg a13 godrej consumer products ltd. fmcg a14 hatsun agro products ltd. fmcg a15 hindustan unilever ltd. fmcg a16 i t c ltd. fmcg a17 jyothy labs ltd. fmcg a18 k r b l ltd. fmcg a19 marico ltd. fmcg a20 nestle india ltd. fmcg a21 procter & gamble hygiene & health care ltd. fmcg a22 radico khaitan ltd. fmcg a23 tata consumer products ltd. fmcg a24 united breweries ltd. fmcg a25 zydus wellness ltd. fmcg a26 rajesh exports ltd. cd a27 symphony ltd. cd a28 titan company ltd. cd a29 voltas ltd. cd a30 whirlpool of india ltd. cd 3.2. criteria description to compare the stock performance nine criteria are selected in this paper. the selection of the criteria is based on the literature review. in this section we briefly describe the criteria and their relevance to stock selection strategy. average rate of return (aror) (c1) in this paper, for a given financial year the monthly closing prices of the stocks are considered. the rate of return or simply return (ror) for the th i stock ( 1, 2,.....,30i  ) for the th t month is calculated as (gupta et al., 2022) 1 ln( )t it t p r p   (1) where, t p is the closing price of the th t month. to calculate the aror for for the th i stock for a given financial year we take the average of the monthly ror. the aror represents the average return generated by the stock in a particular financial year. from the perspectives of the mpt and expected utility theory, an investor wants to maximize the gain. hence, higher is value of aror more is the attractiveness for investment. return on net worth (ronw) (c2) the return of equity (roe) or ronw is defined as (2) biswas et al./oper. res. eng. sci. theor. appl. 5(3)2022 153-193 168 ronw indicates the utilization of the shareholders’ invested amount in generating the net return through business operations. hence, from an investor’s perspective a higher value of ronw indicates a better earning prospect through efficient fundamental performance of the company. therefore, an investor wants to see a higher value of ronw before selection of the stock. earnings per share (eps) (c3) literature review criteria selection total listed companies in bse (fmcg: 72; cd:10) 2 stage filtering: a) consider the companies listed in bse for the study period (fy 201314 to fy 2020-21) b) sort according to average market capitalization final sample: fmcg: top 25 and cd: top 05 companies based on average market capitalization sample selection formation of the decision matrix criteria weight lopcow normalization of the decision matrix calculation of the percentage value calculation of the criteria weights aggregation of year wise ranks validation concluding remarks normalization of the weighted sum of pda and nda find out average solution, pda and nda find out the appraisal scores and ranking of the dmus (in descending order) calculation of the weighted sum of pda and nda ranking: edas method figure 1. research framework eps is defined as the net profit divided by the number of outstanding common shares. it is an indication of the intrinsic value of the firm in terms of profit made per share. a higher value of eps allures the investors as they find the possibility of higher a multi-criteria based stock selection framework in emerging market 169 earnings given the share price (indrayono, 2019). hence, from mpt and expected utility theory perspective, the investors want maximum value of eps. price to book value (p/b) (c4) the p/b ratio is given as the stock price divided by the book value per share. a higher value of p/b ratio is the reflection of the efficient fundamental performance of the firms to maximizing the wealth of the shareholders in terms of higher stock price (indrayono, 2019). hence, from the investors’ perspective a higher value of p/b is recommended. turnover (c5) it is an indicator of the liquidity of the stocks and is measured as a ratio of number of shares traded and average number of common shares outstanding in a given period. a higher value of turnover is an indication of momentum and therefore, from the investors’ point of view more is the better. shares traded (c6) it signifies the total number of shares of a specific equity stock being traded during a given period. though this variable is not an absolute measures influencing the investment decision making, however, a higher value provides a positive signal to the investors about the continuation of the upward trend and future prospect. hence, a period with higher trading volume is marked as a period of investors’ trust and agreement and positive sentiment with belief of future earnings and cash flow (baker and wurgler, 2006; hong and stein, 2007; chiah and zhong, 2020). in other words, higher is the volume better is the prospect of the stock to the investors. yield (c7) yield is a measurement of the amount of cash flow to the investors given the investment in the stock. a higher value of yield signifies a higher growth potential of the company. stock market yield positive influences the investors’ sentiment (an et al., 2018). alpha (c8) the value of the alpha signifies the ability of the stock to beat the market (karmakar et al., 2018). in other words, alpha is the estimated risk-adjusted performance representing the average return of the portfolio in excess of that is predicted by the capm (abu-alkheil et al., 2020). therefore, a higher value is an indicator of better total performance. beta (c9) the systematic or undiversifiable risk is measured in terms of the beta values. the value is determined through the following equation it i mt it r r e   (3) where, mt r is the market return at time t and  and i  are the intercept and slope respectively. using the ordinary least square method, the beta value is calculated as biswas et al./oper. res. eng. sci. theor. appl. 5(3)2022 153-193 170 var( , ) ( ) it mt i mt co r r var r   (4) a lower value of beta is an indication of lower risk (gupta et al., 2022). from the perspectives of bft, an investor wants to minimize the risk to an affordable level given the optimal value of the return. hence, a lower value of beta is recommended. table 3 provides a summary of all criteria used in this paper for comparing the stocks. table 3. list of criteria s/l criteria effect direction uom c1 average stock return (aror) max value c2 return on net worth (ronw) max % c3 eps max rs. c4 p/b max times c5 turnover max rs. million c6 shares traded max nos. c7 yield max % c8 alpha max value c9 beta min value 3.3. data in the present paper we have a total of 30 dmus and 9 criteria for constructing the decision matrices for seven consecutive financial years (i.e., fy 2013-14 to fy 201920). the period fy 2020-21 and fy 2021-22 have not been considered as these periods are significantly affected by the recent covid-19. therefore, in our paper a comparatively less interrupted period has been considered. the data have been collected from the bse website and cmie prowess iq database (version 1.96). the decision matrices are given in appendix a. 3.4. criteria weight calculation: lopcow method the lopcow method is an objective measure to calculate the criteria weights that provides the following benefits (ecer and pamucar, 2022) a comparatively lesser unevenness in the distribution of the criteria weights capability to work properly with the negative performance values of the dmus under the criteria influence which is of particular use in this paper as most often returns are negative. can deal with a large number of criteria and alternatives let, ij m n x x      denotes the decision-matrix where, m is the number of dmus (i.e., stocks under comparison; 30m ) and n is the number of criteria ( 8n  ). the computational steps can be elaborated following ecer and pamucar (2022) step 1. construction of the normalized decision matrix a multi-criteria based stock selection framework in emerging market 171 we obtain the normalized decision matrix through application of linear max-min type scheme as follows. let, ij m n r r      is the normalized decision matrix whose elements are found as under min max min j ij ij j j x x r x x    (when j j   , desired direction: maximizing) (5) max max min j ij ij j j x x r x x    (when j j   , desired direction: minimizing) (6) step 2. find the percentage value (pv) for each criterion the pv for each criterion is given by 2 1 ln .100 m rij i m pj                   (7)  denotes the standard deviation. as the mean square value is expressed as a proportion of the standard deviation this step helps to reduce the narrow the gaps among the criteria weights. step 3. calculation of the criteria weights the weight for the th j criterion is given by 1 ij j n ij j p w p    (8) where, 1 1 n j j w   (i.e., sum of the weights of all criteria = 1) 3.5. edas method to compare the dmus, the edas method derives two distances such as pda (positive distance from the average) and nda (negative distance from the average) while satisfying the effects of the criteria (keshavarz ghorabaee et al., 2015). edas extends a number of advantages over the other mcdm models (pramanik et al., 2021) such as stability in the outcome reliability of the result even under the presence of a large number of dmus and criteria capability to withstand variations in the values in the decision matrix no presence of rank reversal phenomenon biswas et al./oper. res. eng. sci. theor. appl. 5(3)2022 153-193 172 as a result of its benefits, edas method has been extensively applied in various real-life complex problems and extended over the years. for instance, stanujkic et al. (2017) extended the classical edas model with the use of interval grey numbers for practical applications. ecer (2018) put forth an integrated fuzzy ahp and edas framework for providing logistics solution to select the best third party service provider in terms of cost, quality of service and efficiency. darko and liang (2020) defined new extensions of hamacher aggregation operators for q-rung orthopair fuzzy numbers and applied to modify the edas method for mobile payment selection problem. in the turkish market, demirdağ et al. (2021) applied edas based methodology for comparing innovative practices of the hotels and subsequently finding out the success factors. for a competitive bidding purpose naik et al. (2021) applied edas method in assessing prior qualifications of the contractors in the construction industry. jiang et al. (2022) utilized edas method in conjunction with the cpt for selection of appropriate site for construction of shopping mall. in the context of investment decision-making, in a very recent work biswas et al. (2022c) applied edas method for determining the dividend payment capabilities of indian fmcg and consumer durables organizations. the extant literature shows a noteworthy growth in the volume of work utilizing edas method. in this paper we consider the edas method for evaluation of the stock performance which is subject to significant variations in the performance values of the stocks vis-à-vis the criteria. further, we have considered 30 stocks (i.e., dmus) for comparison purpose with respect to nine criteria over seven financial years. hence, the dataset is considerably large. in addition, there may be variations in the performance based ranking leading to false aggregation if rank reversal happens. to this end, edas method provides a number of advantages. we deal with objective information for comparison purpose. therefore, we have not considered any fuzzy based analysis. however, that may be an extension of the present work. the computational steps are demonstrated below. step 1. formation of the decision matrix the decision matrix is expressed as 11 1 1 n ij m n m mn x x x x x x                 (9) where m and n are having usual meaning as given above step 2. find out the average solution the average solution is found as ; 1, 2, ... 1 j n m xij i x j m     (10) step 3. obtain the distances such as pda and nda the pda and nda are obtained as follows pda: a multi-criteria based stock selection framework in emerging market 173 (0,( )) ; (max ) (0,( )) ; (min ) max x xij j j j imizing x j ij max x xj ij j j imizing x j d                  (11) nda: (0,( )) ; (max ) (0,( )) ; (min ) max x xj ij j j imizing x j ij max x xij j j j imizing x j d                  (12) step 4. find out the weighted sum of pda (sp) and nda values (sn) for all the dmus the weighted sums are calculated as 1 n s w ji ij j d     (13) 1 n s w ji ij j d     (14) here, w j is the weight of the criterion. step 5. find out the normalized weighted sum of pda (nsp) and nda values (nsn) for weighted sum of pdas: ( ) si ns i max si i     (15) for weighted sum of ndas: 1 ( ) si ns i max si i      (16) step 6. calculate the appraisal scores (as) of the dmus the appraisal score of the dmu is computed as 1 ( ) 2 s ns ns ai i i     (17) here, 0 1s ai   step 7. ranking of the alternatives the dmus are ranked as per their appraisal scores in descending order. biswas et al./oper. res. eng. sci. theor. appl. 5(3)2022 153-193 174 3.6. aggregation of the mcdm results mcdm methods are useful in explaining the tradeoffs of the influences of the criteria to select the best course of actions and/or optimizing the benefits over the cost in various real-life scenarios (biswas, 2020a). however, achieving a consensus in a typical group decision making and/or in a situation wherein multiple decision making premises are considered is a critical factor to obtain reliable solutions (biswas et al., 2021a; biswas, 2020b). hence, selection of appropriate aggregation methods assumes mentionable importance. in what follows are the two popular approaches available in the literature. borda count (bc) bc is a widely used preference based aggregation method (borda, 1784). the procedural steps are given below (ecer, 2021) step 1. obtain the ranking of the dmus based on different opinion makers or method. step 2. assign a point to the dmu under focus which is equal to the number of options succeeding that dmu. therefore, the best option (dmu) shall receive (m-1) points, the second best shall get (m-2) points and so on. step 3. calculate the sum of the points obtained by each dmu step 4. rank the dmus based on the total points in descending order. copeland method (cm) the cm is the extended and modified version of the bc method. the cm starts after the bc. the procedural steps are given as (ecer, 2021) step 1. find out the win score for each dmu with respect to other options step 2. find out the loss score which is obtained by subtracting of the score obtained by the dmu in the first stage from majority wins’ score step 3. derive the final score as the difference between the win and loss scores. step 4. rank the dmus in terms of their corresponding overall scores in descending order. in addition, the present paper also utilizes the simple additive weighting (saw) method (simanaviciene and ustinovichius, 2010) to arrive at the aggregated final ranking. saw method works on determining the significance of the alternatives subject to the influence of the criteria based on a robust and simple method (karamaşa et al., 2021). hence, it is quite applicable for aggregation of rakings. for calculation and analysis purpose, ms office (2016) and spss (version 25) software tools on a computer with intel(r) core(tm) i3-1005g1 cpu @ 1.20ghz 1.19 ghz, 8gb ram have been used. 4. results this section exhibits the key findings of the present research. in what follows are the step by step results. first, we find out the criteria weights for all the fys using the a multi-criteria based stock selection framework in emerging market 175 procedural steps of lopcow method as described in section 3.4. the normalized decision matrices are given in the appendix b. using the normalized decision matrices, we apply the expressions (7) and (8) to calculate the criteria weights for the financial years. tables 4-10 provide the results of the criteria weights. table 11 provides a comparative preferential orders of the criteria based on their weights. table 4. criteria weights (fy 2013-14) c1 c2 c3 c4 c5 c6 c7 c8 c9 mean square 0.321 0.111 0.066 0.092 0.094 0.056 0.203 0.193 0.438 sd 0.171 0.215 0.219 0.227 0.264 0.209 0.246 0.190 0.279 pv 120.031 43.530 15.858 29.240 15.006 12.079 60.399 83.881 86.171 wj 0.258 0.093 0.034 0.063 0.032 0.026 0.130 0.180 0.185 table 5. criteria weights (fy 2014-15) c1 c2 c3 c4 c5 c6 c7 c8 c9 mean square 0.553 0.152 0.100 0.105 0.036 0.038 0.156 0.129 0.510 sd 0.189 0.201 0.257 0.226 0.183 0.189 0.234 0.196 0.283 pv 137.272 66.147 20.801 35.810 3.490 3.794 52.204 60.569 92.640 wj 0.290 0.140 0.044 0.076 0.007 0.008 0.110 0.128 0.196 table 6. criteria weights (fy 2015-16) c1 c2 c3 c4 c5 c6 c7 c8 c9 mean square 0.319 0.208 0.094 0.171 0.042 0.045 0.190 0.120 0.511 sd 0.185 0.208 0.223 0.254 0.187 0.195 0.255 0.196 0.281 pv 111.818 78.581 32.054 48.971 9.458 8.193 53.803 57.035 93.459 wj 0.227 0.159 0.065 0.099 0.019 0.017 0.109 0.116 0.189 table 7. criteria weights (fy 2016-17) c1 c2 c3 c4 c5 c6 c7 c8 c9 mean square 0.299 0.263 0.087 0.166 0.102 0.067 0.112 0.169 0.527 sd 0.203 0.217 0.225 0.242 0.262 0.232 0.236 0.233 0.245 pv 99.055 85.890 27.060 52.243 19.632 10.882 35.042 56.722 108.690 wj 0.200 0.173 0.055 0.106 0.040 0.022 0.071 0.115 0.220 table 8. criteria weights (fy 2017-18) c1 c2 c3 c4 c5 c6 c7 c8 c9 mean square 0.233 0.256 0.119 0.140 0.075 0.077 0.094 0.169 0.527 sd 0.213 0.191 0.262 0.250 0.229 0.250 0.225 0.233 0.245 pv 81.908 97.481 27.713 40.373 17.874 10.323 31.179 56.722 108.690 wj 0.173 0.206 0.059 0.086 0.038 0.022 0.066 0.120 0.230 table 9. criteria weights (fy 2018-19) c1 c2 c3 c4 c5 c6 c7 c8 c9 mean square 0.618 0.179 0.074 0.119 0.048 0.050 0.084 0.107 0.504 sd 0.211 0.186 0.208 0.252 0.208 0.206 0.201 0.206 0.236 pv 131.813 82.102 27.117 31.172 5.047 8.221 36.809 46.348 109.996 wj 0.275 0.172 0.057 0.065 0.011 0.017 0.077 0.097 0.230 table 10. criteria weights (fy 2019-20) c1 c2 c3 c4 c5 c6 c7 c8 c9 mean square 0.506 0.172 0.067 0.091 0.055 0.042 0.136 0.393 0.455 sd 0.198 0.206 0.202 0.249 0.213 0.197 0.265 0.235 0.263 pv 127.815 69.763 24.609 18.886 9.515 3.566 33.276 98.009 94.171 wj 0.267 0.146 0.051 0.039 0.020 0.007 0.069 0.204 0.196 biswas et al./oper. res. eng. sci. theor. appl. 5(3)2022 153-193 176 table 11. comparative preferential orders of the criteria (year wise) criteria 2013-14 2014-15 2015-16 2016-17 2017-18 2018-19 2019-20 c1 1 1 1 2 3 1 1 c2 5 3 3 3 2 3 4 c3 7 7 7 7 7 7 6 c4 6 6 6 5 5 6 7 c5 8 9 8 8 8 9 8 c6 9 8 9 9 9 8 9 c7 4 5 5 6 6 5 5 c8 3 4 4 4 4 4 2 c9 2 2 2 1 1 2 3 from the table 11, it is seen that the ranking orders are maintaining considerable consistency in their relative importance over the years. from figure 2 also it is concluded that there are no abrupt variations in the preferential order of the criteria based on their calculated weights. further, we apply the dominance theory (brauers and zavadskas, 2011) and find that 1 9 2 8 7 4 3 5 6 c c c c c c c c c figure 2. year wise preferential order of the criteria based on calculated weights it is observed that based on the calculated weights the average return, beta and ronw hold top 3 priorities. the result is justified as the primary motive behind any investment is to maximize the return while minimizing the risk. now we move to use the calculated criteria weights to rank the stocks by applying the procedural steps of the edas method as explained in section 3.5 (see the expressions (10) to (17)). tables 12 provides the appraisal scores and the ranking of the dmus for the fy 201314. in the similar way, the ranking is done for all other fys (i.e., fy 2014-15 to fy 2019-20) which are given in appendix c. table 12. ranking of the dmus (i.e., stocks) using edas method (fy 2013-14) dmu sp sn nsp nsn as rank a1 3.159 0.095 1.000 0.973 0.986 1 a2 0.216 0.450 0.069 0.870 0.469 21 a3 0.212 0.950 0.067 0.725 0.396 25 a4 0.756 0.109 0.239 0.968 0.604 7 a5 0.058 3.453 0.018 0.000 0.009 30 a multi-criteria based stock selection framework in emerging market 177 a6 0.561 0.165 0.178 0.952 0.565 8 a7 0.409 0.126 0.130 0.963 0.547 9 a8 0.000 1.002 0.000 0.710 0.355 27 a9 0.125 0.915 0.039 0.735 0.387 26 a10 0.112 2.229 0.036 0.355 0.195 29 a11 0.072 0.564 0.023 0.837 0.430 24 a12 0.254 0.152 0.080 0.956 0.518 14 a13 0.156 0.224 0.049 0.935 0.492 16 a14 1.937 0.091 0.613 0.974 0.793 2 a15 0.917 0.084 0.290 0.976 0.633 5 a16 0.352 0.071 0.111 0.979 0.545 10 a17 0.255 0.157 0.081 0.955 0.518 15 a18 1.318 0.303 0.417 0.912 0.665 4 a19 0.194 0.400 0.061 0.884 0.473 20 a20 0.405 0.217 0.128 0.937 0.533 12 a21 0.334 0.098 0.106 0.971 0.539 11 a22 0.074 0.384 0.023 0.889 0.456 22 a23 0.411 0.237 0.130 0.931 0.531 13 a24 0.138 0.295 0.044 0.914 0.479 19 a25 0.050 0.133 0.016 0.962 0.489 18 a26 0.013 1.169 0.004 0.662 0.333 28 a27 1.497 0.056 0.474 0.984 0.729 3 a28 0.215 0.294 0.068 0.915 0.492 17 a29 1.199 0.486 0.380 0.859 0.619 6 a30 0.045 0.533 0.014 0.846 0.430 23 we find that there has been a mentionable variation in the ranking order of the dmus over the different financial years. to obtain the final ranking of the dmus we proceed for aggregation of the results using the methods described in section 3.6. tables 13 provides the aggregated ranking obtained by using the bc method. table 13. aggregation of year wise ranks of the dmus (bc method) dmu borda count final rank_ borda dmu borda count final rank_ borda a1 198 1 a16 106 14 a2 135 8 a17 108 12 a3 72 23 a18 138 7 a4 148 4 a19 110 11 a5 85 19 a20 144 5 a6 138 6 a21 155 3 a7 93 16 a22 67 26 a8 38 29 a23 69 24 a9 104 15 a24 49 28 a10 90 18 a25 81 20 a11 106 13 a26 59 27 a12 37 30 a27 124 9 a13 73 22 a28 91 17 a14 121 10 a29 68 25 a15 160 2 a30 78 21 in the present study we use the aggregated ranks of the dmus (i.e., stocks) derived by using bc method. however, to validate the result of the bc method we find the aggregated ranks by using cm and saw methods also. tables 14-15 provide the aggregated ranking obtained by using the cm and saw models. biswas et al./oper. res. eng. sci. theor. appl. 5(3)2022 153-193 178 table 14. aggregation of year wise ranks of the dmus (cm method) dmu wins losses final score final rank dmu wins losses final score final rank a1 198 2847 -2649 1 a16 106 2939 -2833 14 a2 135 2910 -2775 8 a17 108 2937 -2829 12 a3 72 2973 -2901 23 a18 138 2907 -2769 7 a4 148 2897 -2749 4 a19 110 2935 -2825 11 a5 85 2960 -2875 19 a20 144 2901 -2757 5 a6 138 2907 -2769 6 a21 155 2890 -2735 3 a7 93 2952 -2859 16 a22 67 2978 -2911 26 a8 38 3007 -2969 29 a23 69 2976 -2907 24 a9 104 2941 -2837 15 a24 49 2996 -2947 28 a10 90 2955 -2865 18 a25 81 2964 -2883 20 a11 106 2939 -2833 13 a26 59 2986 -2927 27 a12 37 3008 -2971 30 a27 124 2921 -2797 9 a13 73 2972 -2899 22 a28 91 2954 -2863 17 a14 121 2924 -2803 10 a29 68 2977 -2909 25 a15 160 2885 -2725 2 a30 78 2967 -2889 21 table 15. aggregation of year wise ranks of the dmus (saw method) dmu final score rank dmu final score rank a1 0.9642 1 a16 0.4888 13 a2 0.5474 8 a17 0.4921 12 a3 0.3706 24 a18 0.5761 5 a4 0.5964 4 a19 0.4836 14 a5 0.3960 20 a20 0.5629 6 a6 0.5542 7 a21 0.6325 3 a7 0.4254 18 a22 0.3677 25 a8 0.2538 29 a23 0.2982 27 a9 0.4929 11 a24 0.2944 28 a10 0.4388 17 a25 0.3785 23 a11 0.4746 15 a26 0.3171 26 a12 0.1723 30 a27 0.4972 10 a13 0.3939 21 a28 0.4451 16 a14 0.5360 9 a29 0.3839 22 a15 0.6711 2 a30 0.4172 19 figure 3 shows a comparative analysis pictorially and table 16 exhibits the statistical test (spearman’s rank correlation) for examining the consistency among the aggregated ranking results as provided by bc, cm and saw methods. from figure 3 and table 15 it is evident that all there is a significant consistency among all these methods. the summary of year wise ranking including the final ranking of the stocks using the edas method is given in table 17. a multi-criteria based stock selection framework in emerging market 179 figure 3. comparison of results (bc, cm and saw methods) table 16. spearman’s rank correlation among the results of bc, cm and saw method final_rank_copeland final_rank_saw final_rank_ borda spearman's rho 1.000** 0.982** sig. (2-tailed) . 0.000 final_rank_ saw spearman's rho 0.982** 0.982** sig. (2-tailed) 0.000 0.000 ** correlation is significant at the 0.01 level (2-tailed). table 17. summary of the rankings of the dmus (i.e., stocks) company rank 2013-14 2014-15 2015-16 2016-17 2017-18 2018-19 2019-20 final a1 1 1 1 1 1 1 6 1 a2 21 6 6 8 9 4 21 8 a3 25 10 10 13 28 28 24 23 a4 7 4 23 6 6 5 11 4 a5 30 13 22 7 26 18 9 19 a6 8 5 2 10 10 19 18 6 a7 9 16 15 16 11 25 25 16 a8 27 27 25 25 29 11 28 29 a9 26 9 14 17 21 2 17 15 a10 29 19 28 18 12 13 1 18 a11 24 12 13 20 4 9 22 13 a12 14 30 29 30 30 30 10 30 a13 16 23 26 19 27 6 20 22 a14 2 21 24 5 8 15 14 10 a15 5 3 16 2 3 16 5 2 a16 10 15 18 15 19 23 4 14 a17 15 24 20 14 18 3 8 12 a18 4 11 27 4 17 7 2 7 a19 20 18 3 12 14 17 16 11 a20 12 7 5 11 7 21 3 5 a21 11 8 9 3 2 10 12 3 a22 22 29 21 24 13 27 7 26 a23 13 28 7 28 23 12 30 24 a24 19 25 8 29 25 29 26 28 a25 18 17 4 21 16 24 29 20 biswas et al./oper. res. eng. sci. theor. appl. 5(3)2022 153-193 180 company rank 2013-14 2014-15 2015-16 2016-17 2017-18 2018-19 2019-20 final a26 28 20 30 26 20 14 13 27 a27 3 2 12 27 15 8 19 9 a28 17 22 11 23 5 26 15 17 a29 6 26 19 22 24 22 23 25 a30 23 14 17 9 22 20 27 21 we observe that avanti feeds ltd. (a1), hindustan unilever ltd. (a15), procter & gamble hygiene & health care ltd. (a21), britannia industries ltd. (a4), and nestle india ltd. (a20) are the top five performers based on their stock performance during fy 2013-14 to fy 2019-20 while godfrey phillips india ltd. (a12), e i d-parry (india) ltd. (a8), united breweries ltd. (a24), rajesh exports ltd. (a26), and radico khaitan ltd. (a22) hold the bottom five positions during the same period. we also test the correlations among the year wise ranks and the final rank obtained by using the edas method (see table 18) and observe that the rankings are consistent. table 18. spearman’s rank correlation among year wise ranks and the final rank (edas method) fy 1314 fy 14-15 fy 1516 fy 1617 fy 1718 fy 1819 fy 1920 final spearman's rho .568** .815** .390* .788** .799** .504** .456* sig. (2-tailed) 0.001 0.000 0.033 0.000 0.000 0.005 0.011 * correlation is significant at the 0.05 level (2-tailed). ** correlation is significant at the 0.01 level (2-tailed). 4.1. validation the results of mcdm models are vulnerable to the changes in the fundamental considerations related to formulation of the decision matrix, variations in the criteria weights and entry and removal of the criteria and changes in the dimensions and features among others (pamucar et al., 2021; pamucar et al., 2022). therefore, it is essential to validate the result. in this paper we follow the approaches available in the extant literature (for instance, biswas et al., 2022a, 2022b, 2021b) and compare the result obtained by using the edas method with the outcomes of two other methods such as mabac (pamučar and ćirović, 2015) and copras method (zavadskas et al., 2007). we rank the stocks for all the years and derive the final aggregated rank for both these methods separately. then the ranking results of edas, mabac and copras are compared and statistical correlations are tested. table 19 provides the values of the rank correlation coefficients that reflect that the ranking results are consistent. hence, we contend that edas method provides reasonably valid result. table 19. spearman’s rank correlation among the final ranks (edas, mabac and copras) mabac_final copras final edas_final spearman's rho .849** 0.992** sig. (2-tailed) 0.000 0.000 ** correlation is significant at the 0.01 level (2-tailed). a multi-criteria based stock selection framework in emerging market 181 4.2. sensitivity analysis for any mcdm based analysis it is important to examine the changes in the overall ranking subject to variations in the given conditions such as changes in the alternatives, variations in the criteria weights and so on. the sensitivity analysis is carried out to the stability in the result (pamucar et al., 2021, 2022). to this end, in the present paper we follow the work of pamucar et al. (2021). the sensitivity analysis is carried out for all years. we have observed that the ranking results are stable in nature with respect to changes in the criteria weights. in what follows is the sample demonstration of the sensitivity analysis for fy 2019-20. for fy 2019-20, c1 is the criterion with highest weight. we reduce the weight of the criterion c1 by 5% at each experimental case and subsequently, proportionately increase the weights of all other criteria to make the sum of criteria weights equal to one. in this way, we generate 10 experimental cases (see table 20) table 20. criteria weights in different experimental cases (fy 2019-20) cases c1 c2 c3 c4 c5 c6 c7 c8 c9 original 0.2665 0.1455 0.0513 0.0394 0.0198 0.0074 0.0694 0.2044 0.1963 exp 1 0.2532 0.1471 0.0530 0.0410 0.0215 0.0091 0.0710 0.2060 0.1980 exp 2 0.2405 0.1487 0.0546 0.0426 0.0231 0.0107 0.0726 0.2076 0.1996 exp 3 0.2285 0.1502 0.0561 0.0441 0.0246 0.0122 0.0741 0.2091 0.2011 exp 4 0.2171 0.1516 0.0575 0.0456 0.0260 0.0136 0.0756 0.2105 0.2025 exp 5 0.2062 0.1530 0.0588 0.0469 0.0274 0.0150 0.0769 0.2119 0.2039 exp 6 0.1959 0.1543 0.0601 0.0482 0.0287 0.0163 0.0782 0.2132 0.2052 exp 7 0.1861 0.1555 0.0614 0.0494 0.0299 0.0175 0.0794 0.2144 0.2064 exp 8 0.1768 0.1567 0.0625 0.0506 0.0311 0.0186 0.0806 0.2156 0.2076 exp 9 0.1680 0.1578 0.0636 0.0517 0.0322 0.0198 0.0817 0.2167 0.2087 exp 10 0.1596 0.1588 0.0647 0.0527 0.0332 0.0208 0.0827 0.2177 0.2097 now, we use these criteria weights to rank the dmus. once we get the ranks, the distribution of the ranks of the dmus is plotted (see figure 4) which indicates that the ranking distributions do not change substantially with respect to the changes in the criteria weights. hence, it may be concluded that the sensitivity analysis supports the stability in the result for fy 2019-20. in the similar way, we conduct the sensitivity analysis for all other fys and observe the stability in the result. therefore, for our problem, edas provides a stable and reliable outcome. figure 4. result of the sensitivity analysis (fy 2019-20) biswas et al./oper. res. eng. sci. theor. appl. 5(3)2022 153-193 182 5. discussion we observe that based on the calculated weights the average return, beta and ronw hold top 3 priorities. further, turnover (c5) and shares traded (c6) are in the bottom bracket. the result is justified as the primary motive behind any investment is to maximize the return while minimizing the risk. the result is in line with findings of the past work (for example, chen et al., 2020; wu et al., 2020). the final aggregated ranking of the dmus (i.e., fmcg and cd stocks) reveals some interesting observations. it is a common notion that a company which is having higher market capitalization is expected to have a better stock performance at the market place. but, in our case we notice that not all top fmcg and cd stocks (as per average market capitalization) are found to be the top performers. this finding suggests that market capitalization does not necessarily contributed by the stock performance always. this finding is consistent with the observations of marito and sjarif (2020) wherein the authors found a negative influence of market capitalization on the stock return. in fact, the market capitalization is influenced by the fundamental financial performance, competitive strategy, product performance, sales and promotion etc. further, stock performance is subject to the influence of several factors like market sentiment and news, company performance, dividend payment, changes in macroeconomic factors (for instance, changes in the export-import policy, foreign exchange rate, raw material availability, oil price, climate conditions, social and geopolitical environmental conditions and many others) and their impact on business operations and expected earnings, behavioural bias of the investors among others. though, in our study we have not considered the behavioural aspects, but still the findings reflect against the common notion and is in sync with the previous work (for instance, indrayono, 2021; marito and sjarif, 2020). however, it may be noted that more or less the firms having higher market capitalizations have performed well. this is more visible for the bottom performers at the stock level. one interesting subject is itc limited, the top most company in terms of market capitalization but ranked 14 on aggregate based on the stock performance. itc has a multi-product portfolio with related and unrelated diversifications which helped them to capture the market but as far as the stock performance is concerned, it shows below par performance in most of the financial years under the study period. we also notice that fy 2014-15, fy 2016-17 and fy 2017-18 show higher correlation with the final ranking while the other fys are having low correlation with the aggregated ranking. from the technical point of view, the present study shows that a reasonably reliable solution is provided by the combined lopcow-edas method. in view of the above findings and observations, the present paper shall be of interest to readers, policy makers and investors. 6. conclusion the primary objective of the current work is to compare a selected group of stocks belonging to indian fmcg and cd sectors. the sample has been decided on the basis of the average market capitalization over the study period (fy 2013-14 to fy 201920). accordingly, 30 stocks (25 from fmcg and 5 from cd) have been compared with respect to their performance at bse during the study period. for comparative analysis 9 criteria such as aror, ronw, eps, p/b, turnover, shares traded, yield, a multi-criteria based stock selection framework in emerging market 183 alpha and beta have been considered. the selection of criteria has been done in line with the past research while taking into consideration the theoretical cornerstones of mpt, capm, expected utility theory and bft in addition to intrinsic value of the firms. for comparative analysis, we have utilized a combined lopcow-edas framework. for aggregation of the year wise ranks, widely used methods like bc, cm and saw have been used. we note that average return, beta and ronw obtain higher weights than others. the analysis reveals that avanti feeds ltd. (a1), hindustan unilever ltd. (a15), procter & gamble hygiene & health care ltd. (a21), britannia industries ltd. (a4), and nestle india ltd. (a20) are the top five performers based on their stock performance during fy 2013-14 to fy 2019-20 while godfrey phillips india ltd. (a12), e i d-parry (india) ltd. (a8), united breweries ltd. (a24), rajesh exports ltd. (a26), and radico khaitan ltd. (a22) hold the bottom five positions during the same period. based on the results we contend that market capitalization does not necessarily contributed by the stock performance always. moreover, the performance of the stocks over the fys show significant variations. the present paper presents a comprehensive mix of market performance indicators in tune with the mpt, expected utility theory, pt, intrinsic value of the firms and fundamental performance of the stocks for the comparative analysis using mcdm model. a year to year comparative analysis over seven consecutive financial years to arrive at the overall performance based ranking of the stocks is carried out. in this sense, the ongoing work is topical. in addition, the current work provides an unique combination of lopcow-edas and bc methods which may be used in solving various contextual real-life problems. however, the present study is too limited in some aspects and invokes the following future research. first, the major limitation of this paper is that we have not considered the opinions of the investors and carried out the comparison grounded on the fundamental assumptions of the bft. therefore, a future study may attempt to combine objective information based and subjective opinion based comparison of the stock performance. secondly, a deep down study may be carried out to discern the reasons of the year to year variations in the ranking. in this regard as a third scope, one future study may be carried out to explore the causal relationship of fundamental performance, financial stability, dividend payment, innovativeness, growth prospect and economic sustainability with the stock performance for a comprehensive portfolio selection. fourth, a granular analysis may be thought which shall consider the low beta and higher market capitalization organization and shall attempt to find out their performance. fifth, from the technical point of view, the lopcow model may be modified in future with imprecise information. nevertheless, we do hope that the current study shall be of interest to readers, policy makers and investors. supplementary materials: along with this paper appendices a to d are provided for dataset and supporting calculations. authors’ contributions conceptualization: sb, dp, gb, nj; data collection and formatting: nj; formal analysis: sb; validation: sb, gb, dp; writing original draft: sb, nj; review and editing the final draft: dp, gb; supervision: gb acknowledgement: the authors are sincerely grateful to all anonymous reviewers whose valuable comments have helped to improve the quality of the paper. biswas et al./oper. res. eng. sci. theor. appl. 5(3)2022 153-193 184 declaration: the authors state that this is an original and unpublished version which has not submitted elsewhere. further, the authors declare no conflict of interest to anyone. this work has not received any fund. references abu-alkheil, a., khan, w. a., & parikh, b. 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(2020). quantitative stock selection strategies based on kernel principal component analysis. journal of financial risk management, 9(1), 23-43. http://www.scirp.org/journal/paperabs.aspx?paperid=98781 © 2022 by the authors. submitted for possible open access publication under the terms and conditions of the creative commons attribution (cc by) license (http://creativecommons.org/licenses/by/4.0/). https://doi.org/10.1109/access.2019.2912913 https://doi.org/10.48550/arxiv.2204.13385 https://doi.org/10.2307/1914185 https://doi.org/10.1007/bf00122574 https://doi.org/10.2478/crebss-2020-0011 https://doi.org/10.2478/crebss-2020-0011 http://epg.science.cmu.ac.th/ejournal/ https://doi.org/10.1186/s40854-019-0137-1 https://doi.org/10.1016/j.asoc.2019.03.028 http://www.scirp.org/journal/paperabs.aspx?paperid=98781 a multi-criteria based stock selection framework in emerging market sanjib biswas 1, gautam bandyopadhyay 1, dragan pamucar 2*, neha joshi 3 1. introduction 2. related work 2.1. stock selection using statistical analysis and predictive and ml algorithms 2.2. stock selection using mcdm algorithms 2.3. findings from the literature review and research gap 2.4. main contributions of the work 3. materials and methods 3.1. sample 3.2. criteria description 3.3. data 3.4. criteria weight calculation: lopcow method 3.5. edas method 3.6. aggregation of the mcdm results 4. results 4.1. validation 4.2. sensitivity analysis 5. discussion 6. conclusion plane thermoelastic waves in infinite half-space caused operational research in engineering sciences: theory and applications vol. 1, issue 1, 2018, pp. 62-75 issn: 2620-1607 eissn: 2620-1747 doi: https://doi.org/10.31181/oresta19012010162s * corresponding author. e-mail address: gordan@uns.ac.rs (g. stojić), sremacs@uns.ac.rs (s. sremac) a fuzzy model for determining the justifiability of investing in a road freight vehicle fleet gordan stojić *, siniša sremac, igor vasiljković faculty of technical science, university of novi sad, novi sad, serbia received: 3 september 2018 accepted: 7 november 2018 published: 19 december 2018 original scientific paper abstract: a road freight vehicle fleet represents the basic means of work of a transport company which makes it the most important element of its business activities. namely, it has a direct influence on the transport company’s volume of income as well as costs of its business operations. the correct sizing and the management of the road freight vehicle fleet are both of essential significance for cost-effectiveness of the company and satisfaction of transporting demands. both the defining of the road freight vehicle fleet and the selection of the vehicles that it will comprise are a complex problem, which should be approached from several aspects. in the paper, a fuzzy model for determining the justifiability of investing in the renewal of a truck road freight vehicle fleet is presented and so is assessment of the time period needed for the return on such investment. the forecasts of the expected volume of transport, i.e. income from transport, have been made on the routes with constant flows of freight for realistic, pessimistic and optimistic variants for the recommended period of the vehicle’s exploitation. key words: fuzzy logic, road freight transport, vehicle fleet, fleet sizing, investments 1 introduction a successful transport company is recognized by constant monitoring, planning and management of its road freight vehicle fleet. the road freight vehicle fleet planning is a complex process, which directly influences efficiency and effectiveness of both freight transport, and, at the same time, its economy. on the one hand, an insufficient and inadequate road freight vehicle fleet may influence the choice of another form of traffic or, ultimately, inefficiency of the economy. on the other hand, an excessive and improperly structured road freight vehicle fleet has an influence on efficiency and effectiveness of the transport company (a loss of transport and income, costs of “tied up” capital, costs of maintenance, etc.). a fuzzy model for determining the justifiability of investing in a road freight vehicle fleet 63 in other words, the sizing of the road freight vehicle fleet and the selection of the vehicles that it will comprise are a complex problem that should be approached from several aspects. the road freight vehicle fleet of the road transport means consists of road and trailers, whose exploitation-technical characteristics are different and the technical conditions unequal. the exploitation-technical characteristics imply the overall dimensions of a vehicle – its length, width and height; the distance between the pivots (wheelbase), the distance between the wheels, the length of the front and rear overhangs, the semi-diameters of longitudinal and transverse maneuvering capability, the turning radius, the dynamic characteristics of a vehicle, the empty vehicle mass, the engine efficiency, a suitability for technical maintenance, the vehicle’s capacity – the useful cargo load capacity, the specific area and volume capacity in t/m2, and so on. if the road freight vehicle fleet consists of the vehicles of the same brand and type, then it is regarded as homogenous. yet, the structure of the road freight vehicle fleet is, as a rule, rarely homogenous, which causes the need for its homogenization to the greatest possible extent. this step facilitates, to a great extent, the purchase of spare parts, while, at the same time, lowering the vehicles’’ maintenance costs. the assets of the road freight vehicle fleet have a greater value and account for the biggest portion of the capital of a transport company. accordingly, when the vehicles are not used, or when they are used in an inappropriate manner, they may be implicative of an unrealized profit and high opportunity costs. in the case of investing in a road freight vehicle fleet, the purchase of newer vehicles, or brand new vehicles, which are going to replace the existing ones in the company, is what we primarily have in mind. the selection of the vehicles which are being invested in, as well as the type, or the price of new vehicles, directly dictate the amount of the investment, and pursuant to that – the repayment period, i.e. the period of return on investment. in the literature, there are a significant number of the papers dealing with fleet sizing. one of the first papers concerning the sizing of the fleet but in the maritime sector is published by dantzig & fulkerson (1954). they presented the problem of determining the minimum number of tankers to carry out the timetable, while kirby (1959) made one of the first attempts concerning optimization of the fleet of the railways. he dealt with the problem of increasing the degree of utilization of wagons owned by the small rail system and of reducing the level of rental cars by determining the relative cost of the system’s own and leased cars per day. etezadi & beasley (1983) studied the problem of determining the fleet’s optimal structure and size. assuming that the decisions made concerning the given task are long-term ones, they presented a model that is based on integer linear programming. in the same paper, the authors suggested that the problem may more accurately be solved by using simulation. bojovic (2002) addressed the problem of optimizing the size of the fleet through meeting demand and minimizing the total cost. lima et al. (2004) described a mathematical algorithm for problem-solving. this algorithm is a hybrid of genetic algorithm and local search based on genius algorithm. wu et al. (2005) addressed the problem of the dimensioning fleet in road traffic. operational and tactical decisions for heterogeneous fleet were explicitly stojić et al./oper. res. eng. sci. theor. appl. 1 (1) (2018) 62-75 64 designed by the model of linear programming in order to determine the optimal size and mix of the fleet. demand is assumed as known, while travel time is a stochastic parameter. choi & tcha (2007) presented an approach based on generating columns for problem resolution. the authors proposed an integer programming model whose lp relaxation is dealt with by the method of generating columns. models of optimization based on the behavior of swarms (colonies) "swarm intelligence" are partly inspired by the behavior of ants and bees in nature (teodorovic, 2008). they solve the problems of combinatorial organization. it is a problem that occurs in the dimensioning of capacity of railway transport. bojovic et al. (2010) worked out the problem of determining the optimal composition of the freight wagon fleet. the problem is divided into two parts, namely, into determination of an optimal mix and that of an optimal size of the freight wagon fleet. sayarshad et al. (2010) proposed formulation and procedure for solving optimization size of the freight wagon fleet and allocation of wagons for the case of stochastic demand. the authors proposed a two-phase procedure based on the algorithm of simulated problem solving. loxston et al. (2012) considered the problem of forming a heterogeneous fleet with the presence of stochastic demand. the problem is based on determining the number of vehicles to be purchased for each type of vehicle specifically so that the total expected cost of the fleet would be set to minimum. these authors developed an algorithm that combines the dynamic programming method and the golden section to resolve the problem. milenković and bojović (2013) proposed a fuzzy random model for the rail freight road freight vehicle fleet sizing problem. the problem is formulated as that of finding an optimal fuzzy regulator for a fuzzy linear system with a fuzzy quadratic performance index and fuzzy random initial conditions. for a fleet size with environmental aspects, sawik et al. (2017) used multicriteria optimization. costa-salas et al. (2017) presented the fleet size optimization in the discarded tire collection process. in their study, valmikia et al. (2018) presented a simulation model for the evaluation of an agv fleet size in a flexible manufacturing system. telleza et al. (2018) introduced the fleet size and the mix dial-a-ride problem with multiple passenger types and a heterogeneous fleet of reconfigurable vehicles. in the foregoing papers, different fleet-sizing aspects are observed. the basic goal of this paper is the development of the model that will give answers to the following questions: 1. when should vehicles be bought? 2. how many vehicles should be bought for the observed period? 3. what is the value of investment per single vehicle? and so on. a fuzzy model for determining the justifiability of investing in a road freight vehicle fleet 65 the model should be able to include more factors, commonly with different sizes and values. avoiding mixing of different sizes and values or linguistic variables as the most appropriate method that can measure and compare differences represents the method of artificial intelligence "fuzzy logics" (fuzzy logic). this method allows measuring, comparing and synthesizing different variables that are hard to be quantified to carry more qualitative features, as well as simplifying the uncertainty regarding the input data and parameters regarding uncertainty, subjectivity, inaccuracy and ambiguity. 2 the prognostic model of the volume of business operations in this paper, our observation focuses on the “m” company, which realizes its most significant transport services through five different activities with approximately constant cargo flows at the level of the whole of the fiscal year. in those activities, the three scenarios of business operations are forecast, namely pessimistic, optimistic and real scenarios. each combination is attributed a certain financial value for each of the next 10 fiscal years, which is the length of the exploitation period. the prognostic model provides input data for the development of the fuzzy model. the growth rate method is used for the prognostic model. in order to define the growth rate according to different forecast scenarios, eight experts did the surveying. by applying the delphi method, the sublimation of their answers regarding the expected growth rate is performed (table 1). table 1 the growth rates for different forecasts as per each year in the next 10 years of the exploitation period years of exploit. period growth rate prognosis pessimistic real optimistic relativ e cumulative relativ e cumulativ e relativ e cumulative 1 0% 0% 1% 1% 2% 2% 2 0% 0% 1% 2% 2% 4% 3 0% 0% 1% 3% 2% 6% 4 0% 0% 1% 4% 2% 8,2% 5 0% 0% 1% 5,1% 2% 10,4% 6 -1% -1% 3% 8.2% 5% 15,9% 7 -2% -3%3% 11,3% 6% 22.8% 8 -3% -6% 3% 14,6 7% 31,4% 9 -4% -10,3% 3% 18% 9% 43.2% 10 -5% -15,8% 3% 21,5% 10% 57,5% stojić et al./oper. res. eng. sci. theor. appl. 1 (1) (2018) 62-75 66 3 the development of a fuzzy model for determining the justifiability of investing in a road freight vehicle fleet 3.1 fuzzy sets and fuzzy logic fuzzy sets are sets whose elements have degrees of membership. in the classical set theory, the membership of elements in a set is assessed in binary terms according to a bivalent condition an element either belongs or does not belong to the set. by contrast, the fuzzy set theory permits the gradual assessment of the membership of elements in a set; this is described with the aid of a membership function valued in the real unit interval [0,1]. fuzzy logic is the base of fuzzy system. it enables making decisions based on incomplete information, while the models based on fuzzy logic consist of the so-called "if-then" rules. "if-then" rules are interconnected with "else" or "and". fuzzy logic is defined using algorithms for approximate reasoning. when we assume that x =[x1, x2, . . . , xn] is a vector of features describing any object or state and y = [y1, y2, . . . , ym] is the vector of output values of a system, the rules are represented in the form, see eq. (1). r mm rr r nn rrr bisybisybisythen aisxandandaisxandaisxifr ,,, : 2211 2211   (1) where mn yyyyyxxxxx   2121 , and ybbbbxaaaa r n rrrr n rrr   2121 , are the fuzzy sets. the special significance of fuzzy logic is in the possibility of its application for modeling complex systems in which it is very difficult to determine the correlation of certain variables that exist in the model. possible and logical rules are with weight 1, less possible 0.5. the fuzzy rules are a manner of processing the numerical or information data obtained from the input interface. in the fuzzy model scheme, the rules are contained in the “processing” segment. therefore, by means of the fuzzy rules, certain combinations of fuzzy numbers that will later be interpreted in the form of results, or fuzzy conclusions, are singled out. there are several different forms of the fuzzy model use, whereas the model using numeric results, besides generating numeric results in the form of fuzzy sets, is the most important for this research study. the characteristics of this type of the fuzzy model are as follows:  the model reflects a broad modeling spectrum,  numeric data are used and numeric results are generated, and,  after its development, the model is applied for purely numeric purposes, while simultaneously accepting numbers and using them to obtain numbers in the form of a nonlinear input/output mirroring. the scheme of this model is shown in fig. 1 and consists of: the input interface, the processing module, and the output interface. the input interface stands for a a fuzzy model for determining the justifiability of investing in a road freight vehicle fleet 67 fuzzy set, whereas the output interface is a set of outcomes, i.e. conclusions (pedrycz & gomide, 2007). fig. 1 general architecture of fuzzy model (pedrycz & gomide, 2007) fuzzy numbers, or the fuzzy sets consisting of such fuzzy numbers, represent the numeric data that create an input to the fuzzy model. so, the input interface uses fuzzy numbers or fuzzy sets, depending on how they are organized, and after processing data in the model, it comes to output data, i.e. conclusions. 3.2 the idealized fuzzy tree representing the basis of the fuzzy investment model the fuzzy model type used in this paper is based on the fuzzy tree rule (fig. 2). fig. 2 simple fuzzy tree (pedrycz & gomide, 2007) this fuzzy tree contains three fuzzy sets: a, b, and c, which are differently organized and generate results, i.e. conclusions, by performing a defined algorithm. it is clear that b and c elements cannot intersect, and that only two elements from fuzzy sets, i.e. a and b elements, as well as a and c elements, can intersect. 3.3 the input and output data of the model the input data in this model are financial parameters. they are presented in the form of the company’s income from business operations. stojić et al./oper. res. eng. sci. theor. appl. 1 (1) (2018) 62-75 68 table 2 accounts for the income as per activities obtained with cargo permanent flows. they represent the input data for the development of the model. in the observed example of the “m” company, as already mentioned, income with constant income is realized on five relations, i.e. five activities (business). table 2 the total forecast (discounted) income of the company according to the pessimistic, real and optimistic forecasts for the period of 10 years business forecast income p [103 €/10 god] pessimistic real optimistic business 1 1458.33 4416.67 5833.33 business 2 437.50 1271.67 1675.00 business 3 187.50 530.00 700.00 business 4 46.67 141.67 186.67 business 5 163.33 495.00 653.33 total 2293.33 6855.00 9048.33 the input data are divided into fuzzy elements and fuzzy sets. the fuzzy elements are grouped into fuzzy sets and are marked by colored circles, and represent the total financial income from one activity in a single year on the observed relation with constant income. it may have three forms, depending on the forecast: the red – pessimistic (a1, a2,…,a5), the yellow – real (b1, b2,…,b5), and the green – optimistic (c1, c2,…,c5). by combining these elements, of which five combinations with different indices are chosen, a model for the assessment of the company’s income is generated, while, at the same time, the model can be formed for each year, even on a quarterly basis, all depending on the needs of the company’s management (fig. 3). fig. 3 fuzzy tree used as the basis for model formation fig. 3 shows an idealized fuzzy tree generated based on the assumption that the maximum of eight vehicles are to be bought, according to the three possible prognostic scenarios for each activity with approximately constant commodity flows. a fuzzy model for determining the justifiability of investing in a road freight vehicle fleet 69 the output data are given in the d fuzzy set. the d fuzzy set will refer to the set of the conclusions, i.e. how many cargo vehicles, and of which type, to buy. in the model, eight groups are created: d1, d2,…,d8. for example, the set marked as d1 represents a decision to buy only one vehicle. this is important in the case the model is observed on a temporal basis, i.e. if we are interested in the number of the vehicles we will be able to pay off in a particular year. so, for example, at the end of the third year, it is necessary to determine the potentially available amount of income to be invested. each of these groups will receive one combination generated from the three conditions, which means that the number of the vehicles to be bought annually will depend on the future business operations. in this manner, we are enabled to gradually observe investments in the model, from one year to another, depending on income. depending on the desired degree of the model’s sophistication, every such tree can represent one business year, while the investment potential of each business year, i.e. the degree of return on investment, could simultaneously be determined. the “m” company’s current road freight vehicle fleet consists of the vehicles older than 10 years; hence, all the vehicles should be replaced with newer ones (second-hand or new vehicles). 4 the fuzzy model testing and the results analysis while testing the fuzzy model, the fuzzy sets are formed with the forecast income, from which conclusions are derived. the fuzzy sets, i.e. the pessimistic, real and optimistic assessments of business operations will be the conditions, and investment in certain vehicles will be the conclusions. in other words, the three sets of conditions will be formed with one of them derived as the set of conclusions. the basic assumption used in the paper is that the period of return on investment can be observed as the ratio between the costs and income of the annual forecast in any observed year or period. at the same time, taking into consideration the prescribed amortization rate for transport means in road traffic and the exploitation period, it is determined that 9.8% of income needs to be designated for the amortization of vehicles (pa=9.8%). for the sake of the unification of the “m” company’s road freight vehicle fleet, experience, need and ecological parameters, the man tgx vehicle model is selected. in order to purchase one new vehicle, an investment of and exceeding eur105000 needs to be earmarked, depending on the vehicle equipment. as the forecast volumes of the scope of transport of the “m” company required a larger number of vehicles in the road freight vehicle fleet, also taking into consideration the age of the existing vehicles, a possibility of purchasing second-hand vehicles of the man tgx brand, whose residual exploitation cycle can be fitted into the observed one, was the subject matter of consideration. the average purchase price of one such vehicle is eur18480. the potential investment groups are formed in table 4. stojić et al./oper. res. eng. sci. theor. appl. 1 (1) (2018) 62-75 70 table 4 investment groups of the man tgx vehicle, depending on the number of the vehicles to be bought investment group – number of the vehicles to be purchased (103 €) 1 2 3 4 5 6 7 8 value of investment (i) 39.1 78.2 108.3 144.3 180.3 218.3 254.0 292.0 there are several combinations related to the possible variants of business operations in the future, namely only for business operations on the five relations with constant flows. in the paper, only several such combinations are presented. based on the input parameters, the fuzzy model schematically shown in fig. 4 is formed. as can be seen in fig. 4, the fuzzy numbers are organized in the three fuzzy sets, whereas the fuzzy rules are organized within the processing segment. one of the rules reads as follows: “if the sum of any five fuzzy numbers is equal to or greater than 254 103 € , and less than 292 103 €, i.e. if the forecasts indicate that the enterprise’s income in the year to come will be within the alleged range, then the d7 option, namely the purchase of seven vehicles, will be opted for.” in this case, the income (pi) according to the realistic scenario can be generated from equation (2).           €10 .006.004.67530.00 .6714416.67bbbbbp then bisxandandbisxandbisxif 3 r 85595141 271 , 543211 552211  (2) where xi is the expected income according to the forecast bi for i=1, 2, 3, 4 and 5 for the observed case of the realistic scenario (table 2). fig. 4 illustration of the investment fuzzy model a fuzzy model for determining the justifiability of investing in a road freight vehicle fleet 71 the total expected income from all business activities according to the realistic forecast amounts to 6855.00103 €. according to the assumption about the proportionality of income and the costs of investment that was mentioned earlier, the investment repayment period (k) for the observed exploitation period (n) in the case of the seven vehicles (d1 variant) can be obtained by applying the following equation:  years pp in k a r r 6.0 098.000.6855 1.3910 1 1        (3) if all incomes of all businesses would be realized according to the real scenario, then the expected period for repayment of the investment for the d8 variant is:  years pp in k a r r 4.4 098.000.6855 29210 1 8        (4) analyzing all possible cases of realization of the relay scenario, it is possible to get periods of vehicle repayment for the cases of realization of variant di for i = 1, 2, 3, ..., 7. the test results are shown in fig. 5. fig. 5 investment repayment period according to the forecast realistic scenario as can be seen in fig. 5, the model shows that the company "m" can obtain and replace all (eight) second-hand vehicles of the existing fleet in the first year of observation because the ratio of revenues and expenses is favorable and allows the return of invested funds within a reasonable period. this indicates that in the observation period, the company can once again renew the fleet with second-hand vehicles. practical experience also points to such a conclusion. depending on the condition of the used vehicle and the planned volume of exploitation, the remaining period of exploitation is usually up to 5 years. the model can also be tested for different exploitation periods, different allocations from company income for investment repayment (e.g. by reducing the other costs of business operations in favor of greater amounts for repayment), as well as for the cases of the purchase of only new vehicles (the values in table 4 change). when it comes to purchasing of new vehicles, whose value is estimated at 120103 €, for the period of observation (fifteen years), only three new vehicles can be purchased, if the procurement is carried out in the first year, see eq. 5. stojić et al./oper. res. eng. sci. theor. appl. 1 (1) (2018) 62-75 72  years pp in k a r r new 8 098.000.6855 120315 1        (5) if the expected period of exploitation will decrease to 10 years then only two new vehicles can be repaid, under condition to be purchased in the first year of observation. 4 sensitivity analysis during the model’s testing, the questions to arise are always the following: what happens with the results if the expected revenues will not be realized in the observed period, if operating costs will be higher than expected, if the market conditions will change… therefore, the model is tested in the cases of realization of pessimistic and optimistic scenarios. according to the pessimistic scenario incomes (pi) of all businesses can be obtained from the formula (6).           €10 2293.33163.3346.67187.50 437.501458.33aaaaap then aisxandandaisxandaisxif 3 p 543211 552211 , (6) where xi is the expected income according to the forecast ai for i=1, 2, 3, 4 and 5 for the observed case of the pessimistic scenario (table 2). according to the optimistic scenario, incomes of all businesses can be obtained from the formula (7).           €10 .339.336.671700.00 .0015833.33cccccp then cisxandandcisxandcisxif 3 o 0485386 675 , 543211 552211  (7) should all income according to all business activities be only realized according to the pessimistic, or only according to the optimistic scenario, the expected investment repayment period (k) according to different variants is shown in fig. 6. fig. 6 investment repayment period according to the different scenarios forecast a fuzzy model for determining the justifiability of investing in a road freight vehicle fleet 73 the model can also be tested for a combined forecasting revenue scenarios. so, for example, if we consider the combined revenue realization: real for business 1, 3 and 5, pessimistic for business 2 and optimistic for business 4, we get the expected revenue from 6065.83103 €, see eq. 8.           €10 6065.83495186.67530437.50 4416.67bcbabp then bisxandcisxandbisxandaisxandbisxif 3 com i 54321 5544332211 , (8) in this case, for example, for the purchase of eight vehicles, the repayment period of the investment is:  years pp in k a com i com i 9.4 098.083.6065 29210        (9) for this variant of revenue realization, eight vehicles can be purchased in the first year of observation and after five years, if the state of the vehicle requires, it is possible to purchase another eight used vehicles. the sensitivity analysis of the model was also carried out for the cases of the purchase of new vehicles (fig. 6). fig. 6 period of the repayment of investment in new trucks according to the different scenarios forecast as can be seen from fig. 6, the observed company "m" in the case of a pessimistic business scenario can return investments for only one truck in the observed period (15 years), in the case of the real scenario five, and in the case of the optimistic scenario, seven trucks. further testing of the model shows that the model is extremely sensitive to the height of the investments (type and number of vehicles) and the amount of realized revenues, primarily business 1, 2 and 3. the model is least sensitive to the realization of revenues of business 4. stojić et al./oper. res. eng. sci. theor. appl. 1 (1) (2018) 62-75 74 5 conclusions in order for a transport company to successfully operate, it is extremely important that it should have an appropriate road freight vehicle fleet, with respect to both the quantity and the structure. besides, the road freight vehicle fleet ages during the exploitation period, so it is extremely important to plan investments in its renewal. investing in the renewal of the road freight vehicle fleet is a complex process, simultaneously taking different aspects into account. it is very important that vehicles should be chosen in accordance with future income. for that reason, it is very important to make a good forecast. in the paper, the pessimistic, real and optimistic forecasts are subjected to observation. the assessments of income, as well as the return-on-investment period, were performed for all of the three forecasts. in all of the three cases, the results were acceptable, and the conclusion is that the road freight vehicle fleet should be renewed irrespective of which forecast will come up to expectations, since it is very important that the emission standards should be followed due to the announcement of raising the minimum emission standard in the eu from euro 3 to euro 5 in the forthcoming period (3 years have been planned in that regard). that would mean that a large majority of transport means in serbia do not meet the conditions and have to be replaced; in order to avoid problems related to that, the road freight vehicle fleet should be adapted as soon as possible to the conditions existent on the european transportation market, especially in the eu region. although the economic business market, and simultaneously the market of transport companies as well, has its regularities, it also contains certain uncertainties, such as, for example, demand, competition development, the transport policy, the fuel price, etc. in the majority of cases, the known fleet management analytical models do not take into consideration that uncertainty. for that reason, this paper suggests the use of fuzzy logic for the development of the fleet management model that can provide answers to the following questions: should the road freight vehicle fleet be invested in? how many vehicles are cost-effective to buy? when to buy them? and how long is the return-on-investment period? apart from that, the model can also be used for the variant of investing in the road freight vehicle fleet by purchasing new or second-hand vehicles. the deficiency of this model is its sensitivity to more significant changes in the volume of business operations (a decrease or increase in income). in that case, the reconfiguration of certain segments of the fuzzy model is required. acknowledgements: the paper is a part of the research done within the project tr36030. the authors would like to thank to the ministry of education, science and technological development of the republic of serbia. references bojovic, n. 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(2018). a study on simulation methods for agv fleet size estimation in a flexible manufacturing system, 7th international conference on materials processing and characterization icmpc 2017, 17 19 march, 2017, hyderabad, india, proceedings 5, 3994–3999. wu, p., hartman, j. c. & wilson g. r. (2005). an integreated model and solution approach for fleet sizin with heterogeneous assets. transportation science, vol. 39, issue 1, 87 – 103. © 2018 by the authors. submitted for possible open access publication under the terms and conditions of the creative commons attribution (cc by) license (http://creativecommons.org/licenses/by/4.0/). operational research in engineering sciences: theory and applications vol. 4, issue 1, 2021, pp. 1-18 issn: 2620-1607 eissn: 2620-1747 doi: https:// doi.org/10.31181/oresta2040101w * corresponding author enditwardito@gmail.com (e. wardito), humiras.hardi@mercubuana.ac.id (h. hardi purba), aleksander.purba@eng.unila.ac.id (a. purba) system dynamic modeling of risk management in construction projects: a systematic literature review endit wardito1, humiras hardi purba1 , aleksander purba2* 1 industrial engineering department, mercu buana university, jakarta, indonesia 2 civil engineering department, lampung university, lampung, indonesia received: 26 june 2020 accepted: 09 october 2020 first online: 28 january 2021 review paper abstract. this literature review discusses risk management research with system dynamic modeling. literature is reviewed by summarizing the research that has been done and examining research findings, research relationships, and research problems that require further research. the risk management paper with system dynamic modeling (2000-2020) is reviewed by dividing risk into 3 groups, namely: internal risk, external risk, and project risk. each group is further divided into technical risks and nontechnical risks. the results of the study stated that risk management with system dynamic modeling has not been widely used as evidenced by research (2000-2020); there are only 25 papers that match the keywords and can be written reviews. ten internal risk papers include: project members, location risk, document risk & information. external risk papers are only found in 2 papers that discuss: weather risk and social risk, while the project risks are found in 13 papers discussing: cost risk, time risk, work quality risk, and construction risk. keywords: system dynamic, risk, construction. 1. introduction in research related to risk management, many approaches can be done, one of which is to use system dynamic, fuzzy logic, or other methods. the system dynamics approach is a simulation method in solving real problems to describe the relationship between variables in a complex system (maryani et al., 2015). the system dynamic (sd) can be used as a basis for simulating the effects of various risks on the project schedule to explore optimal measures to prevent prior risks (j. wang & yuan, 2016). system dynamic (sd) can use dynamics and feedback to understand the structure and characteristics of a complex system so that it can help decision making (yang & yeh, wardito et al/oper. res. eng. sci. theor. appl. 4 (1) (2021) 1-18 2 2014). system dynamic can also be combined with other analytical methods such as fuzzy; an integrated fuzzy-sd model can be applied to all bot projects to determine the concession period (khanzadi et al., 2012). the use of system dynamics in construction projects has a good track record and has been used for a long time. in (boateng et al., 2012), the sd method has been used extensively over the past 35 years on complex projects and has proven the track record of project management performance in the project life cycle. this review aims to examine risk management research using system dynamic modeling to determine what can be accomplished using system dynamic and to see research gap for further research. 2. methodology this review is based on a summary of the literature obtained online from trusted sources that discuss risk management using system dynamic modeling, which is then reviewed and synthesized to provide the latest information. in research (zavadskas et al., 2010), risk was divided into 3 parts, namely: internal risk, external risk, and project risk. risk allocation structure is shown in figure 1. figure 1. risk allocation structure (zavadskas et al. 2010) internal risks (intrinsic criteria): (1) resource risk; (2) project member risk; (3) stakeholders risks; (4) designer risk; (5) contractor risk; (6) subcontractor risk; (7) supplier risk; (8) team risk; (9) construction site risk; and (10) documents and information risk. external risks (environmental criteria): (1) political risk; (2) economic risk; (3) social risk; (4) weather risk. project risks (construction process criteria): (1) time risk; (2) cost risk; (3) work quality; (4) construction risk; and (5) technological risk. the study method is shown in figure 2. system dynamic modeling of risk management in construction projects: a systematic literature review 3 figure 2. study framework: a systematic literature review 3. results 3.1. summary of results the summary of the paper review related to risk management with system dynamics modeling is shown in table 1 (1.1-1.4). wardito et al/oper. res. eng. sci. theor. appl. 4 (1) (2021) 1-18 4 table 1.1. summary of results, risk groups & risk criteria based on (zavadskas et al. 2010) no. paper risk group criteria (risk) summary of results 1. (love et al., 2002) project work quality variation, rework, or both have a significant impact on the level of progress of the project, caused by: (1) purchaser changes; (2) design freezing; (3) information management; (4) building regulations; (5) consultant fees; (6) communication; (7) coordination and integration of the project team; and (8) training and skills development. 2. (nasirzadeh et al., 2008) project cost because of the more obvious negative side effects of the modified labor/equipment policy (mlep), the quality is better than the overtime workforce policy (otp) which experiences increased cost overruns. 3. (nasirzadeh et al., 2008) project cost a large negative impact on project objectives in terms of cost overruns and project delays can be caused by machine breakdowns. the following alternative response scenarios for that risk: (1) use of overtime policy; (2) modification in labor/equipment policy; (3) use of subcontractors; (4) schedule changes. 4. (yi & xiao, 2008) project cost project risks and costs by building a system dynamics model are influenced by the allocation of stimulating costs between elements and elements between departments. 5. (han et al., 2010) internal construction site the relationship between the main indicators, safety culture, and organizational safety conditions and sensitivity analysis based on observing behavior towards the safety climate does not have a significant effect on the safety climate. 6. (mohamed & chinda, 2011) internal construction site an organization with ad-hoc safety implementation (starting from the basic level of maturity of safety culture) must primarily focus on improving leadership attributes, in the context of safety, for rapid and successful progress to a higher level of maturity in the future. 7. (boateng et al., 2012) external weather four weather conditions that have an impact on the project: (1) snowfall; (2) high temperature; (3) rainfall; and (4) wind. 8. (khanzadi et al., 2012) project time the proposed integrated fuzzy-sd model can be applied to all built operate transfer (bot) projects to determine the concession period. 9. (shin et al., 2014) internal team examine three safety enhancement policies: (1) provide incentives to workers, offer as early as possible for their safe behavior to be most effective; (2) sharing accident information among workers; and (3) helping workers experience accidents when sharing accident information. system dynamic modeling of risk management in construction projects: a systematic literature review 5 table 1.2. summary of results, risk groups & risk criteria based on (zavadskas et al. 2010) no. paper risk group criteria (risk) summary of results 10. (y. xu et al., 2012) project cost finally, the price of public private partnership (ppp) highway project concessions can be determined by the following formula: finalprice = basicprice* (1+ λ1prs1 λ2− λ1 prs2−prs1 where: final price = basic price + adjustment price final price = (1 +λ) basic price prs𝑖 = 𝑊𝑖𝑗 × (𝑅𝑖𝑗 𝑅𝑜𝑗 ) ∑ 𝑊𝑖𝑗 𝑛 j=1 =1 where, prs𝑖 is the overall risk similarity between a reference case i and a target case; 𝑊𝑖𝑗 is the weighting of each risk factor; 𝑅𝑖𝑗 denotes the reference case i's risk factor j, 𝑅𝑜𝑗 denotes the target case n's risk factor j; ∑ 𝑊𝑖𝑗 𝑛 j=1 denotes the summation of weighting of all risk factors. 11. (nasirzadeh et al., 2014) project cost the optimal percentage of risk allocation is set at 46%. if the client accepts 46% of the risk consequences, the project costs will be minimized. 12. (yang & yeh, 2014) external political 7 steps to solve environmental risk management problems systematically and efficiently. (step 1) verification of stakeholders with related problems; (step 2) determine important issues between two stakeholders; (step 3) draw the important causal feedback loop diagram for reference the indicated problem to the system template; (step 4) building a stock flow system dynamics model referring to the causal feedback loop diagram; (step 5) building a framework including a system dynamics model for stakeholder negotiations on related issues; (step 6) repeat steps 2–5 until all stakeholders are involved; and (step 7) list of environmental risks. 13. (jiang et al., 2015) internal team a system dynamics model for the causation of unsafe behaviors (sd-cub) produce correct behavior patterns. that is: (1) safety and production can support each other; (2) management conditions on the supervisory level are effective on the improvement of workers’ safety awareness; (3) preventive actions are more effective than reactive actions on the enhancement of safety performance. wardito et al/oper. res. eng. sci. theor. appl. 4 (1) (2021) 1-18 6 table 1.3. summary of results, risk groups & risk criteria based on (zavadskas et al, 2010) no. paper risk group criteria (risk) summary of results 14. (cunbin et al., 2015) internal team the sd model of the transmission of risk elements that simulate the scope and depth of projects affected by human risk elements, we can illustrate as follows: (1) the theory of transmitting risk elements is introduced into the process that how human risk impacts construction and transfer projects, can carry out quantitative analysis at procedures and levels; (2) schedules will temporarily disrupt elements of human risk; (3) if risks occur late, the right expansion saves more costs, while increasing the number of personnel cannot be completed on schedule; (4) staff and general staff ratios will be considered. during the increase in technical staff, if it does not reduce construction speed, it will rework more, and form more waste; (5) when the proportion of key staff and general staff is more than standard, the workload of key staff is not saturated, while the risk of general staff increases. 15. (maryani et al., 2015) internal construc tion site the contractor must pay attention to the components that make up k3 costs, namely: (1) direct costs; (2) indirect costs; (3) training costs; (4) consumption and non-consumables; (5) osh equipment and inventory costs; (6) prize and penalty fees; (7) prevention costs; (8) insurance fee; and (9) costs outside of insurance coverage. 16. (boateng et al., 2016) project construc tion launched the analytical network process (anp) and system dynamic (sd), (integrated sd-anp), to model the ease of design and construction of megaproject projects, sd-anp model. the new framework is a superior solution for completing dynamics during design and construction megaprojects. 17. (nasir bedewi siraj, 2016) project construc tion this paper develops fsd (fuzzy system dynamic) work commitments that will address many issues related to financial management by using higher funds that focus on risk issues, complex interactions between various risk factors, and dynamic effects. 18. (wang & yuan, 2016) project time there are six main risks, which are very important in influencing infrastructure project schedules, which include: (1) change request by the client; (2) project payment delays; (3) pressure due to tight project schedules; (4) site investigation information is not accurate; (5) loss of skilled labor, and (6) bad contractor management. 19. (l. xu et al., 2017) project documen ts and informati on the public-private partnership (ppp). this is a form of collaboration between one or more public and private sectors, which is long-term in nature. based on the project's risk allocation mechanism, the risk factors system is summarized, divided into three sub-systems, including cooperation effectiveness sub-system, cooperation environment sub-system, and construction and operation sub-system. system dynamic modeling of risk management in construction projects: a systematic literature review 7 table 1.4. summary of results, risk groups & risk criteria based on (zavadskas et al. 2010) no. paper risk group criteria (risk) summary of results 20. (mohammadi et al., 2018) internal constructi on site four archetypes are developed to address the identified safety problems during the data collection process, including (1) delay in design; (2) number of subcontractors; (3) project cost and safety; and (4) supervisors and safety. 21. (ullah et al., 2018) project time this study proves 59 csf that affects cp. the results of a survey of 26 industry experts and 30 academics determined that net present value (npv), project income (pi), revenue stream (rs), severity involved risks (sir), market situation (ms), and investment size (is) were the most complicated aspects, with a minimum of 8% usage by ms and is, and a maximum of 29% generated by npv. 22. (x. xu et al., 2018) project time the hybrid dynamic model developed was applied in the bridge engineering project to analyze the impact of the four risks selected on schedule. the results are as follows: (1) the degree of influence of risk on performance schedules varies across the project timeline; (2) the effect of risk may have a different rating when the risk occurs at different stages; (3) the effect of multiple risks on a schedule may be more significant than the simple amount of each risk. 23. (mohammadi & tavakolan, 2019) internal constructi on site the simulation model presented in this paper can be used to: (1) identify changes in safety performance results during project time; (2) evaluate the effect of various factors on the results of safety performance; (3) make new policies or corrective actions to respond to changes in the project correctly. 24. (nasir & hadikusumo, 2019) project document s and informati on that owner & contractor relationships could be managed with integrated contract management activities both before and during the construction stage. the preconstruction stage has more potential to influence contractual relationships than the construction stage. the best result was found when all of the previously mentioned policies (preconstruction stage policies, and construction stage policies) were implemented together. 25. (mortazavi et al., 2020) project constructi on ten diagrams are selected and analyzed, the results are: (1) 10-fold increase in lack of budget coefficient; (2) 10-fold increase in the coefficient of delays in the project implementation; (3) 10-fold increase in claim coefficient; (4) 10-fold increase in the incomplete design coefficient; (5) 10-fold increase in the coefficient of employing poorquality second-class contractors; (6) 10-fold increase in the coefficient of low labor productivity; and (7) 10-fold increase in the coefficient of employing unskilled labor. 3.2. risk group based on table 1 (sections 1-3) of the resume review paper, it can be concluded that: papers discussing internal risk include 10 papers (40%), 2 papers (8%) discuss wardito et al/oper. res. eng. sci. theor. appl. 4 (1) (2021) 1-18 8 external risks, and 13 papers (52%) discuss project risks. the results of the grouping appear in figure 3. figure 3. risk group count 3.3. risk criteria based on table 1 (sections 1-4) in the discussion continue review paper, it can be concluded that the risk criteria discussed are as shown in table 2. the grouping results are then sorted by the number of papers discussing the most risk criteria, as well as in table 3. furthermore, the discussion of the papers according to risk criteria will be discussed in more detail. table 2. the most researched risk criteria risk group risk criteria count internal risk construction site risk 5 project risk cost risk 5 project risk time risk 4 internal risk team risk 3 project risk construction risk 3 internal risk documents and information risk 2 exsternal risk political risk 1 exsternal risk weather risk 1 project risk work quality 1 internal ri s k int 10 40% external ri s k ext 2 8% project ri s k pro 13 52% int 40% ext 8% pro 52% system dynamic modeling of risk management in construction projects: a systematic literature review 9 table 3. risk criteria count risk count percentage internal risk 10 40% resource risk 0 0% project member risk 0 0% stakeholder risk 0 0% designer risk 0 0% contractor risk 0 0% sub contractor risk 0 0% supplier risk 0 0% team risk 3 12% construction site risk 5 20% documents and information risk 2 8% exsternal risk 2 8% political risk 1 4% economical risk 0 0% social risk 0 0% weather risk 1 4% project risk 13 52% time risk 4 16% costruction risk 5 20% work quality 1 4% construction risk 3 12% technological risk 0 0% total 25 100% 4. discussion 4.1. internal risk, team risk team risk refers to problems associated with project team members, which can increase uncertainty about project outcomes, such as team member turnover, staff improvement, inadequate knowledge among team members, collaboration, motivation, and team communication problems (zavadskas et al., 2010). the results show that, during the specified period (2000-2020), there were 3 papers that discussed the internal risk for team risk criteria. construction accidents are caused by unsafe actions (e.g. behavior or activities of someone who deviates from the safe wardito et al/oper. res. eng. sci. theor. appl. 4 (1) (2021) 1-18 10 procedure that is normally accepted) and/or unsafe conditions (for example, hazard or unsafe physical environment). relatively little is known about eliminating unsafe construction workers' actions. three safety improvement policies are examined: (1) providing incentives to workers to make their safe behavior most effective if offered as early as possible, (2) sharing accident information among workers can help reduce accident incidents, and (3) helping workers feel an accident when sharing accident information because they assess the risk an accident is based on how likely it is to occur. difficulties experienced by people in changing their habits and interests related to safety and safety in construction companies. this will be effective for sharing audiovisual accident information (shin et al., 2014). unsafe construction workers getting the direct cause of construction accidents, but the causes are not well understood (jiang et al., 2015). this study discusses the modeling of system dynamics to understand the systematic construction of unsafe construction. the sd-cub model was developed to facilitate understanding of how the system optimizes. the sd-cub model produces correct behavior patterns. the test model also implies that: (1) safety and production can truly support each other; (2) management conditions at the supervisory level are effective in increasing employee safety awareness; (3) preventive measures are more effective than reactive measures to improve safety performance. the characteristics of human resources are complex and flexible, predicting and controlling risks resulting from human resources is more difficult than other risk factors (cunbin et al., 2015). in the research, the aim is to achieve effective construction objectives, then develop an sd model to transmit elements of human resources during the construction project. the sd model of the transmission of risk elements that simulate the scope and depth of projects affected by human risk elements, we can illustrate as follows: (1) the theory of transmission of risk elements is incorporated into the process that how human risk impacts on construction and transfer projects, can carry out quantitative analysis at procedures and levels, (2) schedules will disrupt while human elements of risk occur, (3) if risks occur late, the right expansion saves more costs, while increasing the number of personnel cannot be completed on schedule, (4) staff and general staff ratios will be considered. during the improvement of technical staff, if it does not reduce the speed of construction, it will process more, and form more waste, and (5) when general staff risks occur, the proportion of key staff and general staff is more than standard, the workload of the main staff is not saturated, while general staff increased. 4.2. internal risk, construction site risk it means that construction site risk is workplace accident exposure that is inherent like the work and is considered best by contractors and their insurance and safety advisors (zavadskas et al., 2010). the results show that, during the specified period (2000-2020), there were 5 papers that discussed the internal risk for site construction risk criteria. strong safety culture in companies and the influence of superior main indicators for safety culture: (1) worker's behavior; (2) employee perception; (3) schedule of delays; (4) participation of the safety committee management; (5) meetings; (6) toolbox talks; (7) safety education; (8) inspection of superiors; (9) worker involvement; (10) inspections at work; (11) danger; (12) competence; and (13) safety training. by integrating all concepts into the system dynamics model, it is activated to analyze the feasibility of using key indicators previously understood, factors related to safety culture, and improving them on organizational safety. the relationship between the main indicators, safety culture, system dynamic modeling of risk management in construction projects: a systematic literature review 11 and organizational safety conditions and sensitivity analysis based on observing behavior towards the safety climate does not have a significant effect on the safety climate (han et al., 2010). the construction of safety culture and the interaction between five key construction safety culture enablers, as well as the potential of each enabler on the organization's safety objectives during a certain period (mohamed & chinda, 2011). the following are 5 key enablers in a construction project: (1) leadership; (2) policies and strategies; (3) people; (4) partnerships and resources; (5) process. organizations with ad-hoc safety implementation (starting from the basic level of safety culture maturity) must primarily focus on improving leadership attributes, in the context of safety, for rapid and successful progress to a higher level of maturity in the future. work accidents can be caused by members of the supply chain, i.e. parties involved in development projects, from management to workers, work environment, and work pressure related to targets, costs, quality, and time. accidents will have an impact on costs, especially k3 costs (maryani et al., 2015). the components that makeup ohs costs that require contractor attention are: (1) direct costs; (2) indirect costs; (3) training costs; (4) consumption and non-consumables; (5) cost of osh equipment and supplies; (6) prize and penalty fees; (7) prevention costs; (8) insurance costs; (9) costs outside the insurance coverage. repeated behavioral patterns in work safety management continuously have four archetypes identified, namely: (1) design delays; (2) number of subcontractors; (3) project costs and security; and (4) supervisors and safety. each archetype is discussed at different stages of dynamic complexity, behavior over time, and the point of leverage to show how to deal with archetypes (mohammadi et al., 2018). in construction projects caused by system failures, not just because of a single factor such as an unsafe problem or condition (mohammadi & tavakolan, 2019). therefore, the construction of safety must be investigated using a systematic view that can think of the complex nature of reporting. construction projects are also often canceled from the schedule issued and decided from the pressure caused by contract or client deadlines. therefore, good project managers are needed for dynamic change. the simulation results in this paper can be used to: (1) identify changes in safety performance results during project time; (2) evaluate the effect of various factors on the results of safety performance; (3) make new policies or corrective actions to respond to changes in projects correctly. 4.3. internal risk, documentation & information risk document and information risk assumptions include: contradictions in documents; pretermission; law and communication. changing order negotiations and pending dispute resolution are significant risks during project construction. communication is very important throughout all construction periods and after completing construction work (zavadskas et al., 2010). the results showed that, during the specified period (2000-2020), there were 2 papers that discussed the internal risk for documentation & information risk criteria. the public-private partnership (ppp) is a form of collaboration between one or more public and private sectors, which is long-term in nature. based on the project's risk allocation mechanism, the risk factors system is summarized, divided into three sub-systems, including cooperation effectiveness subwardito et al/oper. res. eng. sci. theor. appl. 4 (1) (2021) 1-18 12 system, cooperation environment sub-system, and construction and operation subsystem. by setting the system dynamics model, it can be concluded that government efficiency and contract document conflicts are key elements. in conclusion, the conflict of contract documents and the efficiency of the project company must be strictly controlled in this project (l. xu et al., 2017). another paper has examined the contract documents between owners and contractors in a construction project as a facilitating and integrated way to facilitate owner-contractor (o/c) relations in construction projects. this paper focuses more on discussing policy in pre-construction phase policy, construction phase policy & combined policy. police simulation in preconstruction stage: (1) standard value; (2) procedure for selecting the right contractor; (3) proactive contracting process; (4) contractor involvement in design; (5) quality of the written clause; (6) abnormal low bids. police simulation in construction: (7) bureaucracy and politics deadline; (8) late payment progress; (9) efficient reporting; (10) adequate scheduling system; (11) adjustments to adequate and fair compensation. police simulation in combined police: (12) policy 2 + 3 + 4 + 5 + 6; (13) policies 7 + 8 + 9 + 10 + 11; and (14) 12 + 13 policy. the study results state: the hostile nature of the o/c relationship has been a matter of concern and can lead to poor relationships in the construction contract, which causes a bad relationship in the contract. this study reveals that the development of the o/c relationships can be better understood if it regulates management approval for a combination of several improvements and balances. o / relationship can be managed with good contract management activities before and during construction. the pre-construction stage has a greater potential to influence contractual relations than the construction stage. the best results are found when all the policies mentioned earlier (pre-construction stage policies, and construction phase policies) are implemented together (nasir & hadikusumo, 2019). 4.4. external risk, political risk political risk is a change in government laws regarding the legislative system, regulations, and policies as well as inappropriate administrative systems, etc. (zavadskas et al., 2010). the results show that, during the specified period (20002020), there was only 1 paper that discussed the external risk for political risk criteria environmental risks arise from external forces that can easily place a project outside management's control. to avoid the influence of external forces, it is necessary to understand the problems between the project and external stakeholders. seven processes are proposed using the sd model to solve environmental risk management problems in a systematic and efficient manner. in the case study, there are seven steps to solve the problem of environmental risk management systematically, and efficiently. step 1: kernel stakeholder verification with the relevant problem; step 2: determine meaningful issues between two stakeholders; step 3: draw the feedback loop diagram cause of cause for reference problems indicated for system archetypes; step 4: build a dynamics model of the stock-flow system by referring to the causal feedback loop diagram; step 5: build a frame including a system dynamics model for negotiations among stakeholders for the problem indicated; step 6: repeat steps 2–5 until all stakeholders are involved; step 7: make a list of environmental risks. this process allows project managers to reduce the negative impact of project threats (yang & yeh, 2014). system dynamic modeling of risk management in construction projects: a systematic literature review 13 4.5. external risk, weather risk in connection with a very abnormal problem, the contractor is risking because it affects the construction method that can be agreed by the contractor (zavadskas et al., 2010). the results show that, during the specified period (2000-2020), there was only 1 paper that discussed the external risk for weather risk criteria. the effect of critical weather conditions (cwc) and addressing their direct impact on construction activities is very important for contractors, clients, and affected communities (p boateng et al., 2012). the reason is that sd is used to model delays and cause cost overruns for the results of weather phenomena. four weather conditions that impact the project: (1) snow falling; (2) high temperature; (3) rainfall; (4) wind. 4.6. project risk, time risk time risk can be determined by assessing construction delays, technology, and for all jobs (zavadskas et al., 2010). the results show that, during the specified period (2000-2020), there were 4 papers that discussed the project risks for time risk criteria. the project bot financing using system dynamic modeling is integrated with fuzzy. it chooses the integrated fuzzy-sd model that can be applied to all bot projects to determine the concession period (khanzadi et al., 2012). effects of risk schedule delay are generated. there are six main risks (wang & yuan, 2016) which are very important in influencing infrastructure project schedules, which include: (1) changes in demand by clients; (2) project payment delays; (3) pressure from tight project schedules; (4) the information from the site investigation is inaccurate; (5) loss of skilled labor, (6) poor contractor management. another paper has examined the planning scheduling problems in infrastructure project management. this study is a research modeling, system dynamic (sd) and discrete event simulation (des). the results are as follows: (1) the degree of influence of risk on the performance schedule varies across the project schedule; (2) risk effects can have different ratings when risks occur at different stages; (3) the effect of various risks on a schedule may be more significant than the simple amount of each risk. sd-des modeling that can be used easily compares models for real reflection, performs various sensitivity and analysis analyzes and determines the results of more effective comparisons (x. xu et al., 2018). the system dynamic (sd) approach to provide deep understanding of the critical success factors (csf) that determine the project concession period (cp) and model it for local use. this study proves 59 csf that affects cp. the survey results from 26 industry experts and 30 academics determined that present value (npv), project income (pi), revenue stream (rs), severity involved risks (sir), market situation (ms), and investment size (is) is the most complicated aspect, with a minimum use of 8% by ms and is, and a maximum of 29% generated by npv (ullah et al., 2018). 4.7. project risk, cost risk cost risk is the opportunity cost of the product that goes up because it ignores management (zavadskas et al., 2010). the results show that, during the specified period (2000-2020), there were 5 papers that discussed project risks for cost risk criteria. overtime employment policies result in more significant swelling costs and poor quality compared to modification of labor/equipment policies (mlep) due to their more prominent negative side effects (nasirzadeh et al., 2008). this time, they discussed the risk of engine damage that can cause a large negative impact on project wardito et al/oper. res. eng. sci. theor. appl. 4 (1) (2021) 1-18 14 objectives in terms of cost overruns and project delays (nasirzadeh et al., 2008). the following alternative response scenarios for this risk: (1) use of overtime policy; (2) modification in labor/equipment policy; (3) use of subcontractors; and (4) schedule changes. another paper analyzed the optimal percentage of risk allocation determined at 46% (nasirzadeh et al., 2014). the output of the model shows that if the client receives 46% of the risk consequences, the project costs (client costs) will be minimized. the price of highway project concessions, as a result, the price of ppp highway project concessions can be determined by the following formula (y. xu et al., 2012): final price = basic price* (1+ λ1prs1 λ2− λ1 prs2−prs1 ) (1) where: final price = basic price + adjustment price final price = (1 +λ) basic price prs𝑖 = 𝑊𝑖𝑗 × (𝑅𝑖𝑗 𝑅𝑜𝑗 ) ∑ 𝑊𝑖𝑗 𝑛 j=1 =1 where, prs𝑖 is the overall risk similarity between reference case i and a target case; 𝑊𝑖𝑗 is the weighting of each risk factor; 𝑅𝑖𝑗 denotes the reference case i's risk factor j, 𝑅𝑜𝑗 denotes the target case n's risk factor j; ∑ 𝑊𝑖𝑗 𝑛 j=1 denotes the summation of weighting of all risk factors. the stimulation of cost allocation between elements and elements between departments influence project risk and costs by building a system dynamics model (yi & xiao, 2008). allocation ratio is shown in table 4. from the output results, when the allocation ratio is 0.6: 0.3: 0.1, cost savings reach the maximum of 2707 (2704) and the risk reaches the minimum of 0.28 (0.27). when the probability of the project risk occurrence is 0.27 or 0.28, it is in the supportability scope. table 4. allocation ratio (yi & xiao, 2008) allocation ratio bonus: environment cost: training cost 0.6: 0.3: 0.1 0.45: 0.35: 0.2 0.3: 0.4: 0.3 risk 0.28 (0.27) 0.30 (0.29) 0.32 (0.31) saved cost 2707 (2704) 2622 (2619) 2521 (2518) time (week) 10.5 (10.75) 10.5 (10.75) 10.5 (10.75) 4.8. project risk, work quality risk construction delays and additional costs for contractors are due to the quality of the work that is damaged and easily creates disputes regarding deflection obligations. (zavadskas et al., 2010). the results show that, during the specified period (20002020), there was only 1 paper that discussed the project risks for work quality risk criteria. matters that have a significant impact on the level of project progress that can cause variation, rework, or both (love et al., 2002), namely: (1) buyer changes; (2) system dynamic modeling of risk management in construction projects: a systematic literature review 15 freezing of design; (3) information management; (4) building regulations; (5) consultant fees; (6) communication; (7) coordination and integration of the project team; (8) training and skills development. 4.9. project risk, construction risk construction risk refers to the risks involved in construction delays, changes in work, and construction technology (zavadskas et al., 2010). the results show that, during the specified period (2000-2020), there were 3 papers that discussed the project risks for construction risk criteria. the 10 diagrams selected and analyzed to identify and assess risks, and to develop predictive models for feedback behavior and to illustrate the effects of risks to each other in bridge construction projects (mortazavi et al., 2020), the results are: (1) 10-fold increase in lack of budget coefficient; (2) 10-fold increase in the coefficient of delays in the project implementation; (3) 10-fold increase in claim coefficient; (4) 10-fold increase in the incomplete design coefficient; (5) 10-fold increase in the coefficient of employing poor-quality second-class contractors; (6) 10-fold increase in the coefficient of low labor productivity; and (7) 10-fold increase in the coefficient of employing unskilled labor. the analytical network process and system dynamic, (integrated sdanp) are used to model the ease of design and construction of megaproject (prince boateng et al., 2016). the new framework is a superior solution for completing dynamics during design and construction megaprojects. another paper develops fsd (fuzzy system dynamic) work commitments that will address many issues related to financial management using higher funds that focus on risk issues, complex interactions between various risk factors, and effects dynamic (nasir bedewi siraj, 2016). 5. system dynamic software out of 25 papers regarding risk management with system dynamic modeling, 12 papers used vensim software while the other 13 papers do not explain the use of system dynamic software. recent research (mortazavi et al., 2020) also uses vensim software for system dynamic modeling. 6. future research some of the papers reviewed mostly did not inform future research, only (boateng et al., 2016) that proposed future research would look at risks such as social, technology, economics, ecology, and politics (steep) in construction projects. this research was later published in 2016 by the same author. in table 3, there are many risks that have not been studied with system dynamic, and this can be used as a research gap for further research. the research gap for the internal risk group: resource risk; project member risk; stakeholder risk; designer risk; contractor risk; sub contractor risk; and supplier risk. the research gap for the external risk group: economical risk; and social risk. the research gap for the project risk group: technological risk. wardito et al/oper. res. eng. sci. theor. appl. 4 (1) (2021) 1-18 16 7. conclusion the results of the study stated that risk management with system dynamic modeling has not been widely used as evidenced by research (2000-2020); there are only 25 papers that match the keywords and can be written reviews. ten internal risk papers include: project members, location risk, document risk & information. external risk papers are only found in 2 papers that discuss: weather risk and social risk, while the project risks are found in 13 papers discussing: cost risk, time risk, work quality risk, and construction risk. the most widely used software is vensim. the internal risk group: system dynamic modeling helps systematically understand unsafe behavior structures that result in correct behavior patterns; dynamic modeling system is also able to simulate the scope and depth of projects affected by human risk elements; using the system dynamic on the main indicators of safety culture allows to analyze the appropriateness of the use of key indicators and factors related to safety culture, and improve organizational safety; work accidents can be caused by parties involved in a development project, from management to workers, work environment, and work pressure related to targets, costs, quality and time. accidents will have an impact on costs, especially k3 costs; in the ppp project, the use of system dynamics can conclude that government efficiency and contract document conflicts are key elements; in the contact relationship between owner and contractor (o/ c), dynamic systems are used for police simulation at pre-construction stage. the external risk group: the problem between the project and external stakeholders must be understood to avoid the influence of external forces. dynamic systems can be used for studies that allow project managers to systematically and efficiently reduce the negative impacts of project threats; meanwhile, to deal with weather risk, sd is used to model delay and cause cost overruns due to weather phenomena. the project risk group: time-related system dynamic modeling can be integrated with fuzzy which can be used in all bot financing projects to determine the concession period; dynamic systems can also be integrated with discrete event simulation (des) to be able to compare real reflection models, perform various models and sensitivity testing and determine the results of a more effective comparison; regarding costs, the dynamic systems project can support policies relating to overtime, additional employees or additional equipment; in job quality risk using a dynamic system capable of identifying project progress and rework or both; construction risk uses a dynamic system to identify and assess risk, and to develop predictive models for feedback behavior and to describe the effects of risk; dynamic systems can also be integrated with network process analytics (anp) to model the ease of megaproject design and construction; 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(2010). risk assessment of construction projects. journal of civil engineering and management, 16(1), 33–46. https://doi.org/10.3846/jcem.2010.03 © 2021 by the authors. submitted for possible open access publication under the terms and conditions of the creative commons attribution (cc by) license (http://creativecommons.org/licenses/by/4.0/). system dynamic modeling of risk management in construction projects: a systematic literature review endit wardito1, humiras hardi purba1 , aleksander purba2* 1. introduction 2. methodology 3. results 3.1. summary of results 3.2. risk group 3.3. risk criteria 4. discussion 4.1. internal risk, team risk 4.2. internal risk, construction site risk 4.3. internal risk, documentation & information risk 4.4. external risk, political risk 4.5. external risk, weather risk 4.6. project risk, time risk 4.7. project risk, cost risk 4.8. project risk, work quality risk 4.9. project risk, construction risk 5. system dynamic software 6. future research 7. conclusion reference operational research in engineering sciences: theory and applications first online issn: 2620-1607 eissn: 2620-1747 doi: https:// doi.org/10.31181/oresta2812222016b * corresponding author. prasad.bari@fcrit.ac.in (p. bari), pmkarande@me.vjti.ac.in (p. karande) cost factor focused scheduling and sequencing: a neoteric literature review prasad bari 1,2*, prasad karande 1 1 department of mechanical engineering, veermata jijabai technological institute, mumbai, india 2 department of mechanical engineering, fr. c. rodrigues institute of technology, vashi, navi-mumbai, india received: 13 july 2022 accepted: 31 october 2022 first online: 28 december 2022 review paper abstract: the hastily emergent concern from researchers in the application of scheduling and sequencing has urged the necessity for analysis of the latest research growth to construct a new outline. this paper focuses on the literature on cost minimization as a primary aim in scheduling problems represented with less significance as a whole in the past literature reviews. the purpose of this paper is to have an intensive study to clarify the development of cost-based scheduling and sequencing (css) by reviewing the work published over several parameters for improving the understanding in this field. various parameters, such as scheduling models, algorithms, industries, journals, publishers, publication year, authors, countries, constraints, objectives, uncertainties, computational time, and programming languages and optimization software packages are considered. in this research, the literature review of css is done for thirteen years (2010-2022). although css research originated in manufacturing, it has been observed that css research publications also addressed case studies based on health, transportation, railway, airport, steel, textile, education, ship, petrochemical, inspection, and construction projects. a detailed evaluation of the literature is followed by significant information found in the study, literature analysis, gaps identification, constraints of work done, and opportunities in future research for the researchers and experts from the industries in css. keywords: scheduling, sequencing, cost, literature review 1. introduction scheduling is a method that determines when a specific task can be feasibly accomplished. the boundary of the scheduling problem can be defined by specifying the resources, the time duration of the task, the initial time at which it may begin, and the time by when it is expected to finish. in fact, this is a decision-making procedure that optimizes one or more objectives (pinedo, 2004). the purpose of the scheduling mailto:prasad.bari@fcrit.ac.in mailto:pmkarande@me.vjti.ac.in bari and karande / oper. res. eng. sci. theor. appl. – first online process is thus to decrease the end time of the task and to curtail the cost associated with completing that task. therefore, for decades, the study of scheduling problems concentrated on reducing objectives like average flow-time, maximum tardiness, and makespan. for these objectives, delaying the completion of the tasks affects a greater cost. however, the present attention in the firm is on just-in-time (jit) thinking, which assists the view that not only tardiness but earliness also should be dejected. this has inspired the research of scheduling issues where tasks are favoured to be completed just at their individual due dates, and both early and tardy jobs are penalized. for instance, consider a job shop that manufactures parts for successive assembly into end products. the due dates for parts are reliant on the assembly scheme of the finished product. if orders of parts are stuck, then the assembly of the products may be hindered. the adverse influence could be that assembly effectiveness and client satisfaction will be hammered. if an order of parts is completed earlier than the due date, it must be retained in stock up to its delivery date. the adverse influence is the build-up of inventory. sidney (1977) introduced the concept of the earliness and tardiness (e/t) problem; later, many authors concentrated on the notion where the processing times and due dates are specified. broad reviews are seen in baker and scudder (1990), gordon et al. (2002), and lauff and werner (2004). thus, during this period, the study of penalties due to e/t scheduling problems was studied extensively in the form of mathematical models. boysen et al. (2009) reviewed a mixed-model sequencing approach for reducing workload and production costs. they also classified sequencing approaches considering different objectives like setup operations and due dates. they stated that constraint programming has been superseded as a suggested solution technique by combinatorial optimization. stanković et al. (2020) provided a model for resolving the flexible job shop scheduling problem (fjsp) that is based on metaheuristic algorithms, tabu search, genetic algorithm (ga), and ant colony optimization. later on, researchers felt a need to develop advanced computational algorithms for easy and quick solutions in cost minimization considering the e/t scheduling problems. this research was done exhaustively in the next decade; therefore, the review concentrates on the study published after the year 2010. imitation of research, points of argument and conclusions necessitate more perspicuous and logical techniques. to the authors' best knowledge, not many studies have been done previously which analyse the research articles extensively in terms of scheduling and sequencing and classified them on the various parameters. therefore, a more classified review is required that reveals the current situation, mentions the growth of css, and discusses the research over multiple parameters. this research work aims to elaborate on explaining emerging scenarios, developments, and the significance of scheduling and sequencing for minimizing cost by studying the published work over various parameters for superior comprehension of the research area for which the study is done in journal articles published between 2010 and 2022. 2. background of scheduling and sequencing the scheduling principle first appears in the middle of the 1950s. following that, the challenges linked to this were brought up to industrialised applications by considering shop layouts, shops with a number of identical machines, an operation requiring many resources at the same time, or multipurpose machines. as a result, the cost factor focused scheduling and sequencing: a neoteric literature review level of difficulty rises (t'kindt and billaut, 2005). the scheduling models can be classified by identifying the resource arrangement and the jobs' nature (baker and trietsch, 2009). to be more precise, a model may consist single machine or multiple machines. it may be static (a set of jobs that do not vary over time, ready for scheduling) or dynamic (new jobs appear continuously). dynamic models are essential from practical judgment, but still, static models are widely considered since they are useful to know the fundamentals. bari and karande (2021) ranked the sequencing rules in dynamic job shop applying the promethee-gaia method. investigation of static problems usually discovers useful understandings, and later heuristic methods are used in the dynamic approach. finally, the model may be deterministic (where certain assumptions are made with certainty) or stochastic (where uncertainty is recognized with explicit probability distributions). in recent years, a due-window assignment has obtained a stronger focus. the approach to the due window problem can be applied in several realistic situations. for instance, the contractor is specified about flexibility concerning the supply time and is unrestricted to an exact due date, that is, orders (or jobs) accomplishment can be taken without fine in a period; this is known as the due window (j. b. wang et al., 2020). usually, a client gives a common due date which is considered external or may be considered by the company itself as internal. common due date related to the system in which various jobs/tasks are to be accomplished altogether, for example, various jobs are given by the same client that forms one order, or the parts of a product should be prepared for assembly simultaneously. this common due date model is generally applicable in the chemical and food production industries. here usually more or less, the substances or components used for the whole mixture or the end product have a limited/short period of existence which forces a common due date concept (yin et al., 2012). in general, these due dates arise from negotiations with clients. particularly when the company does not know in advance, as the job handled by the company may be part of new work, in such a situation, the due date may be used as a decision factor surrounded by the limitations of the scheduling. apart from this, most of the time, the job's processing times are unknown with surety. this hypothesis is rational wherever a) the scheduler cannot find production processing times with exactness, b) if the methods of measuring these times consist of faults, and c) the machine or the operator is dependent on arbitrary variations or while the machine set up times vary haphazardly. this ambiguity may exemplify the in-built threat of the company's failure consisting of processing times of the tasks. this characteristic represents a stochastic concept. a usual methodology is to have the processing time of tasks as an arbitrary factor with a given distribution and find a schedule and due dates to optimize a specific criterion (lemos and ronconi, 2015). oyetunji (2009) discussed 29 performance parameters of scheduling as objective functions based on key parameters such as completion time, flow time, lateness, late or tardy jobs, tardiness, earliness, and early jobs. apart from these traditional parameters, the cost is considered due to the jit concept. this concept affects the overall cost of a product, which focuses not only on job delay but also on the job that completes before the due date. these parameters are summarized with their notation and mathematical representation, as shown in table 1. bari and karande / oper. res. eng. sci. theor. appl. – first online table 1. summary of objective functions used in scheduling and sequencing objective notations meaning objective function cj completion time of job j cj rj release time of job j rj wj weight of job j wj dj due-date of job j dj ∝𝑗 earliness cost of job j ∝𝑗 can be any numeric value 𝛽𝑗 tardiness cost of job j 𝛽𝑗 can be any numeric value n total jobs in the system n completion time ct total completion time of jobs ∑ 𝐶𝑗 𝑁 𝑗=1 ctw total weighted (tw)completion time of jobs ∑ (𝑤𝑗 ∗ 𝐶𝑗 ) 𝑁 𝑗=1 cμ average (μ) completion time of jobs 1 𝑁 ∑ 𝐶𝑗 𝑁 𝑗=1 cμw average weighted (μw) completion time of jobs 1 𝑁 ∑ (𝑤𝑗 ∗ 𝐶𝑗 ) 𝑁 𝑗=1 cmax maximum completion time of job which completes at last on the system 𝑚𝑎𝑥{𝐶1, 𝐶2, 𝐶3 … 𝐶𝑁 } flow time fj flow time of job j cj – rj ft total flow time of jobs ∑ 𝐹𝑗 𝑁 𝑗=1 ftw total weighted (tw) flow time of jobs ∑ (𝑤𝑗 ∗ 𝐹𝑗 𝑁 𝑗=1 ) fμ average (μ) flow time of jobs 1 𝑁 ∑ 𝐹𝑗 𝑁 𝑗=1 fμw average weighted (μw) flow time of jobs 1 𝑁 ∑ (𝑤𝑗 ∗ 𝐹𝑗 ) 𝑁 𝑗=1 fmax maximum flow time 𝑚𝑎𝑥{𝐹1, 𝐹2, 𝐹3 … 𝐹𝑁 } lateness lj lateness of job j 𝐶𝑗 − 𝑑𝑗 lt total lateness of jobs ∑ 𝐿𝑗 𝑁 𝑗=1 ltw total weighted (tw) lateness of jobs ∑( 𝑤𝑗 ∗ 𝐿𝑗 𝑁 𝑗=1 ) lμ average (μ) lateness of jobs 1 𝑁 ∑ 𝐿𝑗 𝑁 𝑗=1 cost factor focused scheduling and sequencing: a neoteric literature review lμw average weighted (μw) lateness of jobs 1 𝑁 ∑ (𝑤𝑗 ∗ 𝐿𝑗 ) 𝑁 𝑗=1 lmax maximum lateness 𝑚𝑎𝑥{𝐿1, 𝐿2, 𝐿3 … 𝐿𝑁 } tardy jobs ntj number of tardy jobs ∑ 𝛿(𝑇𝑗 ) 𝑁 𝑗=1 { 𝛿(𝑥) = 1 𝑖𝑓 𝑥 > 0 = 0 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒 μntj average number of tardy jobs 𝑁𝑡𝑗 𝑁 tardiness tj tardiness of job j tj = max {0, lj} tt total tardiness of jobs ∑ 𝑇𝑗 𝑁 𝑗=1 ttw total weighted (tw) tardiness of jobs ∑(𝑤𝑗 ∗ 𝑇𝑗 ) 𝑁 𝑗=1 tμ average (μ) tardiness of jobs 1 𝑁 ∑ 𝑇𝑗 𝑁 𝑗=1 tμw average weighted (μw) tardiness of jobs 1 𝑁 ∑(𝑤𝑗 ∗ 𝑇𝑗 𝑁 𝑗=1 ) tmax maximum tardiness 𝑚𝑎𝑥{𝑇1, 𝑇2, 𝑇3 … 𝑇𝑁 } earliness ej earliness of job j 𝑑𝑗 − 𝐶𝑗 et total earliness of jobs ∑ 𝐸𝑗 𝑁 𝑗=1 etw total weighted (tw) earliness of jobs ∑ 𝑤𝑗 ∗ 𝐸𝑗 𝑁 𝑗=1 eμ average (μ) earliness of jobs 1 𝑁 ∑ 𝐸𝑗 𝑁 𝑗=1 eμw average weighted (μw) earliness of jobs 1 𝑁 ∑(𝑤𝑗 ∗ 𝐸𝑗 ) 𝑁 𝑗=1 emax maximum earliness 𝑚𝑎𝑥{𝐸1, 𝐸2, 𝐸3 … 𝐸𝑁 } early jobs nej number of early jobs ∑ δ(𝐿𝑗 ) 𝑁 𝑗=1 { 𝛿(𝑥) = 1 𝑖𝑓 𝑥 > 0 = 0 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒 μnej average number of early jobs nej 𝑁 cost 𝑇𝑜𝑡𝑎𝑙𝑐𝑜𝑠𝑡 cost function for e/t of schedule for n jobs ∑(∝𝑗 𝐸𝑗 𝑁 𝑗=1 + 𝛽𝑗 𝑇𝑗 ) bari and karande / oper. res. eng. sci. theor. appl. – first online the literature on scheduling work mainly consists of the performance criteria like completion time, flow-time, tardiness, and earliness. çetinkaya and duman (2021) proposed a method for reducing the completion time of sub lots and job lots with a single task and many jobs. however, achieving due dates is also one of the important goals. in traditional scheduling methods, due dates are expected to be given externally. still, they are determined by seeing the system's capability to accomplish the given delivery dates. as a result, in several research works, it has been observed that duedate allocation is a portion of the scheduling process. generally, it is expected to finish the job as early as possible. however, the theory of jit production supports the idea that tardiness, as well as earliness, should be discouraged. costs related to e/t are some of the common criteria considered for finding the performance of the production. completing the jobs before time affects inventory carrying costs such as storing and insurance costs. on the other hand, jobs that get completed after their due dates affect fines like late dues, damage to a client concern, and harm to trades. in sequencing, taking into consideration the due dates, the key factor is normally to complete all the jobs on time. if due dates are unrestricted, apparently, this intent may be accomplished by allowing the loose due dates. still, in a condition wherein due dates can be carefully selected, it is intended to allot due dates to be tight as probable, which is a restricted one. tight due dates, bid more clients than due-dates which are loose in a marketplace full of competition and specify better client facility. tighter due dates also have an affinity to yield smaller inventory levels; hence they are essential for scheduling. 3. research approach reviewing the literature is a typical technique to explore various methods of the topic to be studied exhaustively. in this study, a simple research process is followed that includes a literature review with respect to the development of scheduling and sequencing with cost minimization as a primary aim. a classification scheme is developed and used to figure out the progress in cost minimization in scheduling and sequencing. this review uses a classification scheme to present existing work, identifies some gaps, and provides ideas for further investigation related to the topic. the research approach used for this study is shown in figure 1. the purpose of the review is to underline the variety of research existent in the area of scheduling and sequencing with cost minimization as the primary aim and by using advanced computational algorithms. these algorithms give easy, quick, and efficient solutions. secondary aims pursued by different scholars are also discussed in section 5.9. this work is studied extensively and explored in the last decade. therefore, the existing work published in peer-reviewed publications between 2010 and the present year is considered for review. the articles having the word "scheduling and sequencing" in the title, abstract and keywords are searched from the scopus database. on june 29, 2022, the last search for updating was conducted. a total of 2026 research papers were found. this comprised several objectives, with cost being the most important. as a result, the word "cost" was searched in the abstract. 430 research papers were found with cost as an objective. the work does not consider book cost factor focused scheduling and sequencing: a neoteric literature review chapters, conference papers, phd and master's degree theses, news reports, or textbooks. figure 1. framework for research study literature search on “scheduling and sequencing” from scopus database from year 2010-2022 including the research papers containing “scheduling and sequencing” in the title, abstract and keywords including the research papers containing “cost" word in abstract inclusion of only journal articles (excluding conference paper, short survey, book chapter, conference review) including only english language articles final review conducted of 281 shortlisted cost base scheduling and sequencing articles taxonomy for review of 281 shortlisted cost base scheduling and sequencing articles based on models, algorithms, industrial sectors, journalspublishers, year, active authors, contribution of countries worldwide, constraints, objectives, uncertainty, computational time, and programming languages and optimization software packages gaps identification and scope for further investigation based on the results obtained through analysis 2026 articles found 430 articles found 308 articles found 281 articles found bari and karande / oper. res. eng. sci. theor. appl. – first online considering the research on scheduling, it would be tough to take the literature under all the categories. thus databases of a peer-reviewed journals are selected and surveyed to present work done on scheduling under one umbrella. journals from wellknown publishers such as elsevier, springer, taylor and francis, ieee, informs, and others are considered. these databases permit to access full-text to many good research papers and journals, which include a variety of collections for social and applied science subjects comprising management and business areas, engineering, health, and computer science. in the above-stated databases, the search brings in 281 journal research papers from 153 journals. there were few research papers found with aforesaid mentioned search words, for example, the paper titled "a statistical approach to selecting and confirming validation targets in -omics experiments" but did not consider in the literature as it was not focused on the css topic. the review approach is built on the content analysis approach suggested by yadav and desai (2016). each research paper was thoroughly studied, and then the information was collected to represent the classification scheme from different viewpoints. this review assists as a complete base for explaining the research of cost minimization in scheduling and sequencing. an attempt has been made to gather information from all the related research papers. it is anticipated that the projected methodology, concepts, considerations of grouping, and interpretation of the study will be suitable means for research scholars and practitioners, who are connected in research of cost optimization in scheduling and will support to encourage advanced study in this field. 4. classification framework after going through the work on css according to the methodology mentioned in section 3, a method of classification framework is put forward. after study and analysis of existing work in css, the proposed classification is explained with twelve main dimensions as mentioned below: (1) scheduling models (2) algorithms used (3) industrial sectors (4) journals and publishers (5) publication year (6) authors in the study (concerning research papers published) (7) contribution of countries worldwide (8) constraints (9) objectives (10) uncertainties (11) computational time (12) programming languages and optimization software packages the classification framework expedites the css research in different ways for imminent researchers. the scheduling model will help to tackle real-world problems in industries. the classification of algorithms expresses how a near-optimal answer for the research aim in css can be attained. industrial sectors help in choosing case studies for scheduling and sequencing. journals and publishers' classification focuses on where more work related to css has been published. publication year states the trend in css study over the past thirteen years. the authors in the study support cost factor focused scheduling and sequencing: a neoteric literature review bringing up the work in related research. countrywide classification speaks geographical location where the research is carried out. constraints taxonomy helps researchers know what constraints are in scheduling and sequencing to achieve the goal related to specific industrial sectors. objectives arrangements state secondary aims in scheduling and sequencing other than cost discussed in different industrial sectors. the uncertainties section conveys how authors control the uncertainty in the css study. the programming languages and optimization software packages section gives an idea of which software can be used to perform computations and automate the optimization process. this study will guide the pursuit of comprehensive research by describing the historical growth, application areas, challenging concepts in the research, and the most important sources of css data. 5. study of the classification scheme 5.1. classification of research papers on scheduling models 5.1.1. single and multiple machines in practice, the industry may have more than one machine. so it is logical to study the concept of jobs being scheduled on multiple machines, which increases the difficulty of the problem. however, the concept of a single machine is still by large under study by the authors, which helps to understand the fundamental knowledge. it has been observed from the literature that almost 70% of the css work is carried out on a single machine, and on the other hand, approximately 30% of the work is performed on multiple machines. 5.1.2. static and dynamic in a static model, the number of jobs that are scheduled on a machine is fixed over a given period. static models are useful for understanding the fundamental theory of scheduling and sequencing. xian-ru (2012) developed a model for sequencing static aircraft arrival and solving scheduling problems of their landings to reduce overall costs in delay. in a dynamic model, the number of jobs that are scheduled on a machine is not fixed over a given period, and new jobs continuously appear over time. in real-world judgement, dynamic models are more vital. generally, heuristic methods are used in the dynamic approach. kobayashi (2021) applied a model on a printed circuit board that includes a multi-item single-machine dynamic lot size to achieve the optimal solution in scheduling. lakhan et al. (2021a) proposed an algorithm based on a neural network for partitioning and scheduling in the health sector that accepts dynamic changes concerning network content and resource setting to minimize energy consumption and overall cost. zhang et al. (2021) developed a collaborative approach to increase the efficiency of genetic programming in dynamic, flexible job shop scheduling and showed that the computational cost could be reduced. vandenberghe et al. (2020) solved the scheduling problem by considering the emergency entry of patients on a regular schedule. murça (2017) formulated a model and applied it to a case study of an airport in brazil for optimal departure sequencing and operations scheduling with dynamic nature. liang et al. (2015) developed a surgical treatment scheduling system that manages real-time modification in the operation room. nguyen et al. (2015) applied automatic programming via iterated local search algorithm to find out dispatching rules with the dynamic model environment in dynamic job shop bari and karande / oper. res. eng. sci. theor. appl. – first online scheduling. savino et al. (2010) presented a heuristic method in the painting industry where a novel product demand occurred during particular production sub-periods. they demonstrated the method's usefulness in a dynamic environment to lessen the setup number for the lot sequencing to increase throughput in the metal sheets painting industry. 5.1.3. deterministic and stochastic in a deterministic model, certain assumptions are made with certainty. though this model may have limited applications in practice, it is still useful to study basic concepts. choi and wilhelm (2020) studied an appointment method with deterministic entrance times and different exponential service times. the goal was to reduce the customer-waiting and server-idle times. the work is more related to situations in which two or three clients are scheduled in each time slot. glazer et al. (2018) considered a single-machine problem with a fine for deviance from the due date with the basics of job sizes being identical and deterministic. agnetis et al. (2015) applied the concept of game theory to a deterministic scheduling problem where two agents strive to utilize a machine. in the stochastic model, uncertainty is known with explicit probability distributions. the uncertainty, which includes the random processing time, makes it difficult for the due date assignment. it is observed that in the literature, the stochastic model is mainly targeted at jobs and patients. cheng (1991) is considered one of the pioneers who studied the due-date assignment problem and job sequencing using random processing times arranged on one machine. elyasi and salmasi (2013) proposed the due date assignment and stochastic processing time of jobs in a single machine to curtail determining due dates and to reduce the overall cost of fined early and tardy jobs. baker (2014) highlighted that problems with stochastic scheduling containing e/t have hardly been considered in the literature. he, therefore, studied the problem of how to reduce the overall e/t cost in a single-machine situation. a single machine using a stochastic situation with unequal e/t costs of jobs was reflected in the research paper of lemos and ronconi (2015). d. j. wang, et al. (2019) examined the capability of pre-emptive scheduling techniques using stochastic machine breakdown, processing time, and some other worsening conditions in the steel industry. in clinics or hospitals, patients visit doctors at random times, and hence, the stochastic model was studied by authors in this field. mancilla and storer (2012, 2013) proposed an algorithm for a stochastic nature of appointment sequencing/scheduling with waiting, idle, and overtime costs for a single-machine environment. they applied an algorithm for ordering surgical procedures for a doctor working in a parallel operating theatre with no certainty nature. tsai et al. (2021), sun et al. (2021), jafarnia-jahromi and jain (2020) described the concept of stochastic scheduling surgery to tackle patients’ arrival and patient appointment scheduling problem, respectively. zhou and yue (2021a) and zhou and yue (2021b) considered stochastic service times in multistage service systems to reduce the total costs of customers' waiting time. wu and zhou, (2022) considered the problem of scheduling and sequencing with stochastic service durations and client’s arrivals. they formulated a model with multiple stochastic linear programs to reduce the weighted sum of server staffing cost and the total expected cost of client waiting, server idleness and overtime. cost factor focused scheduling and sequencing: a neoteric literature review 5.2. classification of research papers on solution approaches used by authors to obtain an optimum solution for objective functions, there are different methods that one could implement. although many optimization algorithms could be used, there is not such a core one that is reflected to be the best for any case. the optimization approach which is appropriate for getting the solution to one problem may not be applicable to the other one, as it is subjected to various features. after review, some of the major solution approaches are identified and shown in figure 2. 5.2.1. optimization methods the authors used integer models to optimize the objective function in scheduling and sequencing. integer models are known by a variety of names, mixed integer linear/nonlinear programming (milp/minlp) and integer linear programming (ilp), according to the generality of the restrictions on their variables. 5.2.1.1. milp and minlp linear programming achieves the output of a linear objective function related to one or more constraints. in mixed integer programming, at least one variable should have an integer value. this approach is broadly used in the operations research area. the basic mixed integer programming (mip) problem can be represented as: 𝑍 = 𝐶𝑋 the above equation is a linear objective function that can either maximize or minimize given one or more constraints in the form of cx (example: 2x1+3x2 ≤ 12), where 𝑋 = (𝑥1, 𝑥2, … , 𝑥𝑛 ) are variables of objective function and 𝐶 = (𝑐1, 𝑐2, … , 𝑐𝑛 ) are constants. minlp is an optimization technique that handles nonlinear problems with continuous and integer variables. the algebraic representation of the minlp problem in its basic form is given below: 𝑍 = 𝑓(𝑥, 𝑦) where x and y are the variables. bueno et al. (2020), abdullah et al. (2019), haoran et al. (2018), mostafaei et al. (2015), and cafaro and cerdá (2010) applied milp. pautasso et al. (2019) and cerda et al. (2015) applied milp as well as minlp optimization techniques in their work for petroleum-based industries and demonstrated that the model yields an optimal schedule with low computational costs. milp was also used in automobiles, airports, and manufacturing industries for optimizing the cost of parts, aircraft, and tasks sequencing, respectively. dang et al. (2021) proposed milp and large neighbourhood search with a combined local search technique to determine a schedule to reduce the tardiness costs of demands and agvs transportable cost within an industrial unit. tsai et al. (2021) formulated milp with rapid screening and stochastic approximation algorithms to tackle planning and sequencing decisions in a surgical scheduling problem. their investigational results showed that their suggested algorithms are better. zhou and yue (2021b) articulated a stochastic program and utilized a sample average approximation approach to reframe this as a mixed-integer program as advanced. this approach is altered and improved as the benders decomposition algorithm to discover near-optimum results. bari and karande / oper. res. eng. sci. theor. appl. – first online figure 2. solution approaches used by authors 5.2.1.2. dynamic programming dynamic programming (dp) optimization is a type of exact algorithm which guarantees to discover the optimal result for the problem. in this, the results of subproblems are stored and reused so that re-computation is not required. the advantage of this optimization approach is to reduce time complexity from exponential to polynomial, but the larger the problem, the more complex the solution space and can make the algorithm slower. liu et al. (2018) developed an optimal pseudo-polynomial time dp algorithm for rescheduling and for saving the overall cost of jobs in manufacturing, mohan and kumar (2016) adopted dp for solving the waste load scheduling problem, lu et al. (2013) demonstrated dp algorithm to find the optimal price quotations and production scheduling in manufacturing, chou et al. (2013) analysed dp as a scheduling framework to determine the optimal development plan of a local water supply system. yeung et al. (2011) implemented the dp algorithm to get the optimal supply chain scheduling problem solution to reduce inventory holding costs. 0 10 20 30 40 50 60 70 minlp load balancing discrete differential evolution tabu search fuzzy approach dynamic programming particle swarm optimization ant colony optimization simulated annealing branch and bound search algorithm genetic algorithm milp no. of research papers cost factor focused scheduling and sequencing: a neoteric literature review 5.2.1.3. branch and bound branch and bound (bb) is another exact algorithm that helps to search for the optimal solution for combinatorial, discrete, and all-purpose algebraic optimization problems. in the bb algorithm, the procedure of dividing a large problem into more than one sub-problems is branching, and the procedure of computing a lower/upper bound for the optimum solution of a known sub-problem is bounding. the branch and cut method is a combinatorial optimization algorithm. this method uses both the bb approach and the cutting plane approach. in particular, this augments the formulation of the sub-problem with additional cuts in order to improve the bounds obtained from the linear programming relaxations. domínguez-martín et al. (2017), rudek (2016), chaieb memmi and hammani laaroussi (2013), lin and chu (2013), and eun et al. (2010) investigated the model using bb algorithm with constraints like production lines, labour, warehouse capacity, time period for production, order fulfilment rate, resource precedence and job sequence to curtail the overall cost in the manufacturing industry. baker (2014) studied this algorithm to find optimal solutions to minimize complete expected earliness and tardiness costs. martínez et al. (2019) used branch and check to find the best solutions to the production planning problem of the packaging industry. canca et al. (2019) applied a model with a branch and cut in the town of seville (spain) for constructing a metro network. 5.2.2. heuristic, metaheuristic, and hyper-heuristic heuristic defines a computational method that finds an optimal result through repetition to develop a candidate result with respect to a given measure of quality but doesn't assure optimality. it is noticed that many stand-alone and hybrid heuristics are present to address scheduling and sequencing problems to achieve objective function. some are deliberated for a particular application, and others are aimed at general applications and referred to as meta-heuristics. the integration of the machine learning approach, the practice of selecting, combining, generating, or adapting different simple heuristics to solve problems, is referred to as hyper-heuristics. cayo and onal (2020) applied a heuristic approach for sequencing production orders and aimed to reduce overall tardiness with setup time. ardakani et al. (2020) presented that a heuristic algorithm works better than the mathematical model for the truck to door sequencing. braat et al. (2019) applied an equilibrium heuristic to develop a framework for sequencing situations with selfish agents. zhou et al. (2019) used it in flexible job shop scheduling for the assignment of machines and sequencing rules of jobs. musavi and bozorgi-amiri (2017) studied the optimization of the vehicles at hubs by proposing a metaheuristic approach in css considering a case study of the food supply chain. lemos and ronconi (2015) determined the job sequence and the due dates, which reduce the probable e/t costs by applying a heuristic approach. li et al. (2015) used a hyper-heuristic approach in cellular manufacturing systems for scheduling inter-cell. 5.2.2.1. genetic algorithm genetic algorithm (ga) is built on the darwinian principle, of "survival of the fittest". ga is a random-based classical evolutionary algorithm. in ga, a list of promising solutions is generated at each phase, and reiteration generates an improved solution by searching a special neighbourhood. it merges two existing sequences, bari and karande / oper. res. eng. sci. theor. appl. – first online choosing some features from one and the remaining from the other. the new candidates are observed as descendants of the present, and thus the term is taken from evolution and genetics. the ga algorithm typically ends with a given number of reiterations, but other discontinuing rules can be forced. the best-performing sequence in the last reiteration is taken as the solution. shen et al. (2021) considered unrelated parallel machines in the pasta manufacturing industry’s flexible job shop scheduling problem and applied ga to handle the sequencing of the job with machine allocation. they illustrated that the proposed algorithm outperforms with the reduction in makespan, energy cost and labour cost. bayu et al. (2020) developed a model using ga including a discrete-time for sequencing the operations in gasoline blending. kurniawan et al. (2020a), kurniawan et al. (2020b), alaghebandha et al. (2019), biele and mönch (2019), weiss et al. (2019), zhou et al. (2019), yue et al. (2016) and su et al. (2015) executed ga approach in manufacturing company, and optimum scheduling was realized through it, considering the specific costs and value inputs from broad task cost modelling. toledo et al. (2014) showed that the ga programming approach performs better concerning production costs and run times when implemented considering the case study of a soft drink company. costa et al. (2013) tested to evaluate the impact of the workers' skills on both manpower cost and makespan. from research, it is noticed that ga outperforms not only in manufacturing but also in other industries like warehouse, railway, education, textile, and transport. 5.2.2.2. discrete differential evolution in the discrete differential evolution (dde) algorithm, initially, the target population gets altered to yield the new population. later the target population remerges with the new population to yield an experimental population. lastly, a selection operator is used to both target and experimental populations to decide who will be there for the succeeding generation depending on fitness evaluations. in the dde algorithm, the construction and destruction process is used as an operator to yield a new population. zhang et al. (2018), nonsiri et al. (2014), and mokhtari et al. (2011) optimized the sequencing of jobs, the engineering tasks with the use of the dde algorithm. 5.2.2.3. ant colony optimization ant colony optimization (aco) is used to find near-optimum results for challenging optimization problems. it is one of the metaheuristic approaches to optimization. here, artificial ants as agents find near-optimal results. the problem is altered to search for a better path on a weighted graph. the agents (ants) move on the graph gradually to yield better results. here, the finding of the near-optimal solution is a stochastic approach and depends on a model of pheromone. the pheromone model has a list of factors related to either edges or nodes of the graph for which values are altered at run-time by agents. shobaki et al. (2022) described an aco algorithm to schedule register pressure-aware instructions. nazif (2018), haoran et al. (2018), and li et al. (2015) provided an aco algorithm that helps in the sequencing of jobs and allotting resources at the same time. fernandez et al. (2014) implemented aco for interpreting the scheduling rules in a galvanizing line and showed that a good solution could be obtained in a bit of calculation time. xian-ru (2012) used aco to reduce the overall delay cost by finding the aircraft's sequencing and landing times schedule. udhayakumar and kumanan (2010) successfully accomplished the sequencing and cost factor focused scheduling and sequencing: a neoteric literature review scheduling of jobs and tools with the intent of reducing makespan in a flexible manufacturing system. 5.2.2.4. particle swarm optimization particle swarm optimization (pso) is a random search approach. in pso, the animal activities of the individuals in the swarm get copied as a searching technique. the pso notion was initiated from the behaviour of bees' swarm, birds flocking, or fish schooling. the pso result is denoted as a particle, while the group of results is known as a particle swarm. for every particle, there are two key features, velocity and position. the particle acquires logical understanding from its experiences and societal understanding from the swarm to help the particle for getting a better position; with the help of a new velocity, a particle shifts to a different location. the better position of every particle and also the position of the swarm of particles is altered if necessary. accordingly, the velocity of the particle is then modified depending on the particle's experiences (wisittipanich and hengmeechai, 2017). pso has been successfully applied by m. z. wang et al. (2020), wu et al. (2019), rohaninejad et al. (2016), fang and lin (2013) in different areas like manufacturing, logistics/transport, job shop, and health. the study described that pso could resolve the operating room scheduling efficiently and effectively, and optimize the jobs allocation and jobs sequencing to help in reducing overall completion time and reduction in cost incurred for raw materials. it was also applied to reduce the overall tardiness and power cost by finding the optimal sequence of jobs. sadhasivam et al. (2018) developed an improved pso algorithm which helped in overall cost reduction for revealing epigenetic irregularities of application for cancer diagnosis by getting appropriate resources and assignment of epigenomics tasks. 5.2.2.5. tabu search tabu search (ts) is a combinatorial approach of optimization and search techniques built on getting the better existing neighbourhood solution point. it finds the better point of search space concerning the objective function, although it may not be as good as the present solution point. if some tabu motions result in better solutions, these tabu statuses are acknowledged, according to an aim. the ts technique is a search methodology with a flexible memory arrangement, and various problems can be solved (mobaieen et al., 2012). ts, a metaheuristic algorithm, was studied by rezaeiahari and khasawneh (2020) to find a near-optimal solution for scheduling medical tourists’. wei et al. (2017) used ts for the sequencing of components, and mobaieen et al. (2012) used ts to locate optimal solutions in a robot project. mazdeh et al. (2010b) applied ts to obtain optimal solutions in the manufacturing industry. 5.2.2.6. simulated annealing simulated annealing (sa) is a mathematical meta-heuristic approach with a stochastic feature. the concept of sa is based on the simulation of thermal annealing of critically heated solids. in sa, initially, the search space examines original results and yields a new one through alteration. the cost of a new result which is acquired after alteration is calculated. if the objective function's value is improved than the current value of the objective function, then the altered solution is accepted, or else it is accepted according to the threshold probability. bari and karande / oper. res. eng. sci. theor. appl. – first online mendonça et al. (2022) used sa and discovered that it is an efficient strategy for solving silviculture optimization problems in a short amount of period. singh et al. (2021) used sa to optimize the schedule for pipe installation in the piping project to reduce the cost and length of project time. rezaeiahari and khasawneh (2020) used sa with ts for scheduling health visitors who travel to targeted health centres to reduce the flow time of visitors. sa with ga was used for the sequencing of several courses related to the classroom in education by czibula et al. (2016). areal et al. (2011) applied sa and ga in the automobile industry to get the optimum sequence for car assembly lines to utilize the workforce and resources efficiently. 5.2.2.7. crow search algorithm crow search algorithm (csa) is a metaheuristic algorithm dependent on the intelligent behaviour of a crow. even though csa is nature motivated, it has prime peculiarities from a few accepted algorithms such as pso, ga, or heuristic search. there are only two considerations in csa, flight length and awareness probability, which should modify. reddy et al. (2019) applied csa in the combined scheduling of machines, automated guided vehicles, and tools in flexible manufacturing systems to reduce the makespan. reddy et al. (2021) used the csa to resolve the problem of scheduling tasks and tools in a multi-machine flexible manufacturing environment, and they demonstrated that the csa delivers better solutions to reduce makespan. 5.2.2.8. search algorithms authors used different search algorithms for optimization such as variable neighbourhood search (yan et al., 2014, mokhtari et al., 2011), iterated reference greedy algorithm (pei et al., 2019), multi-start iterative search heuristic (czibula et al., 2017), greedy randomized adaptive search procedure (molina-sánchez and gonzález-neira 2016, heath et al., 2013), automatic programming via iterated local search-aprils (nguyen et al., 2015), stochastic mixed integer programming based local search (santos and almada-lobo, 2012), scatter search (gholipour-kanani et al., 2011), and backward search algorithm (supithak et al., 2010). 5.2.2.9. fuzzy approach if enough information is not present with respect to objective functions and there is not essential certainty about the significance of objectives, then the problem may be expressed as a fuzzy goal programming problem, for example, aircraft landing time. haoran et al. (2018) proposed a self-learning approach by merging fuzzy analysis and aco to acquire complete optimum scheduling of a multi-product pipeline. tavakkolimoghaddam et al. (2012) mentioned that if complete data is not present, then one can use a fuzzy approach. murugesan and chellappan (2012), mazdeh et al. (2010a) used the fuzzy approach due to uncertainty in real-world grid scheduling and deteriorating job scheduling problem, respectively. 5.3. classification of research papers based on industries to conduct any research, industrial applications perform an important role. due to extensive growth and competition in the industry, the research should have improved quality. the research papers that appeared in the literature search have applications of css in several industrial zones. figure 3 shows the industrial sectors relating to css research work. css application in the manufacturing zone appears in large amounts cost factor focused scheduling and sequencing: a neoteric literature review (45%) following this service (37%), and health (18%). the most important industries found in research that have concentrated on css are shown in figure 4. research papers on css are mainly found in the manufacturing sector with a large number (54) following this the health industry (35), information technology (it) industry (16), transport (13) and airport (10) sectors. the researchers and practitioners worked in several types of industries like automobiles, construction, construction machinery, cement, door lock manufacturing, education, electrical and electronics, energy manufacturing, food, logistics, mining, packaging, painting, petrochemical, plywood, process, pulp and paper mill, ship, soap, steel, supermarket, textile, water and waste management. out of the 281 papers studied, there were 82 research papers where no specific industrial sector information was mentioned. css work done in the manufacturing sector contributes the maximum amount of research papers, followed by service and health sectors. from the literature, it is found that generally, manufacturing industries focused on sequencing of jobs to schedule on machines (álvarez-gil et al., 2022; cayo and onal, 2020; j. b. wang et al. 2020; kurniawan et al., 2020a; pei et al., 2019). apart from general manufacturing industries, researchers worked in specific industries like steel, food, textile, pulp and paper, vehicle, electronics, education, airport, and ship port. health industries mainly stressed sequencing of patients or surgeries to schedule in operation rooms. service industries that include transportation or logistics concentrated on sequencing trucks, aircraft, ships, pipelines and packaging lines. in the computer or it branch, the css is mainly focused on sequencing tasks on servers with the allocation of resources. c. wang et al. (2020) investigated instruction scheduling to achieve increased instruction-level parallelism. they used a machine learning approach to discover inter-task dependency in an out-of-order scheduling strategy. in the project management area, the researchers mostly studied sequencing activities/elements to minimize the cost. classification of the surveyed literature by key industrial sector is summarized in table 2. the research papers studied in the literature highlighted case studies and also involved model development using algorithms, structures, and practices in industries. figure 3. article distribution using industrial sectors manufacturing 45% service 37% health 18% industrial sectors bari and karande / oper. res. eng. sci. theor. appl. – first online figure 4. research papers based on focused industries table 2. summary of literature by the industrial sector industrial sector industry paper manufacturing door lock lin and chu, 2013 plywood alfieri and cantamessa, 2010 soap bhosale and pawar, 2020 process subbiah et al., 2011 cement asad, 2011 construction machinery seif et al., 2018; faghihi et al., 2014 energy manufacturing kurniawan et al., 2020b; zhu et al. 2017 pulp and paper martínez et al., 2018; santos and almada-lobo, 2012 textile molina-sánchez and gonzález-neira, 2016; aitalla et al., 2014; mathur and süer, 2013 food carvalho and nascimento, 2022; shen et al., 2021; musavi and bozorgi-amiri, 2017; toledo et al., 2014; kopanos et al., 2011 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 3 3 5 5 5 7 7 8 9 10 13 16 35 54 0 10 20 30 40 50 60 d o o rl o c k m a n u fa c tu ri n g in sp e c ti o n p a in ti n g p ly w o o d l o g is ti c s s u p e rm a rk e t s o a p p ro c e ss c e m e n t e d u c a ti o n w a te r a n d w a st e m a n a g e m e n t c o n st ru c ti o n m a c h in e ry e n e rg y m a n u fa c tu ri n g p u lp a n d p a p e r m il l p a c k a g in g m in in g t e x ti le f o o d s te e l a u to m o b il e s s h ip e le c tr ic a l a n d e le c tr o n ic s c o n st ru c ti o n p e tr o c h e m ic a l a ir p o rt t ra n sp o rt in fo rm a ti o n t e c h n o lo g y h e a lt h m a n u fa c tu ri n g s e c to r n o . o f r e se a r c h p a p e r s industries * there is no specific industrial sector information mentioned in 82 research papers cost factor focused scheduling and sequencing: a neoteric literature review steel álvarez-gil et al., 2022; gao et al., 2021; d. j. wang et al., 2019; weiss et al., 2019; fernandez et al., 2014 automobiles wu et al., 2021; ferro et al., 2019; domínguezmartín et al., 2017; tang et al., 2012; areal et al., 2011 electrical and electronics kobayashi, 2021; cui et al., 2020; ferro et al., 2019; heath et al., 2013; eguia et al., 2011; paik et al., 2011; ho et al., 2010 general c. n. wang et al., 2022; guzman et al., 2022; laili et al., 2022; f. zhang 2021; farmand et al., 2021; grigoriev et al., 2021; liu et al., 2021; said et al., 2021; xu et al., 2021; yamada et al., 2021; cayo et al., 2020; dou et al., 2020; j. wang et al., 2020; kurniawan et al., 2020a; lopes et al., 2020; alaghebandha et al., 2019; djassemi and seifoddini, 2019; pei et al., 2019; reddy et al., 2019; x. zhang et al. 2019; g. zhang, et al. 2018; gao and qu, 2018; glazer et al., 2018; liu et al., 2018; lopes et al., 2018; purohit and lad, 2016; rohaninejad et al., 2016; gao et al., 2015; li et al., 2015; nguyen et al., 2015; suet al., 2015; chaieb and hammani, 2013; costa et al., 2013; fang and lin., 2013; fumero et al., 2013; huang and yao 2013; le and pang, 2013; lu et al., 2013; golmakani and namazi, 2012; ramezanian and saidi-mehrabad, 2012; gholipour-kanani et al., 2011; mokhtari et al., 2011; subbiah et al., 2011; transchel et al., 2011; yeung et al., 2011; barlatt et al., 2010; barman and lisboa, 2010; gürel et al., 2010; leyvand et al., 2010; mazdeh et al., 2010b; palaniappan and jawahar, 2010; paul and azeem, 2010; supithak et al., 2010; udhayakumar and kumanan, 2010 health health industry ballester et al., 2022; lakhan et al., 2022a; lakhan et al., 2022b; shehadeh and padman, 2022; lakhan et al., 2021a; pan et al., 2021; sun et al., 2021; tsai et al., 2021; j. wang et al., 2020; jafarnia-jahromi and jain, 2020; m. z. wang et al., 2020; mandelbaum et al., 2020; rezaeiahari and khasawneh, 2020; vandenberghe et al., 2020; wu et al., 2019; alrefaie et al., 2018a; al-refaie et al., 2018b; deceuninck et al., 2018; haddad et al., 2018; nazif, 2018; sadhasivam et al., 2018; roshanaei et al., 2017; samorani and ganguly, 2016; liang et al., 2015; saadouli et al., 2015; azari-rad et al., 2014; chen and robinson, 2014; mancilla and storer, 2013; choi and wilhelm, 2012; bari and karande / oper. res. eng. sci. theor. appl. – first online mancilla and storer, 2012; gul et al., 2011; zhao et al., 2011; ho et al., 2010 service inspection sinisterra and cavalcante, 2020 painting savino et al., 2010 logistics ardakani et al., 2020 supermarket rijal et al., 2021 education czibula et al., 2016 water and waste management mohan and kumar, 2016; chou et al., 2013 packaging martínez et al., 2019; burger et al., 2015 mining hosseini et al., 2020; campos et al., 2018; armstrong and galli, 2012 ship al-refaie and abedalqader, 2022; zheng et al., 2022; gao et al., 2021; wang and wang, 2021; corry and bierwirth, 2019; c. wang et al., 2016; sun et al., 2014 construction xu et al., 2022; abadi et al., 2021; singh et al., 2021; yuan et al., 2021; abotaleb et al., 2020; wah-peng et al., 2017; eguia et al., 2011; feng et al., 2010 petrochemical bayu et al., 2020; bueno et al., 2020; abdullah et al., 2019; pautasso, et al., 2019; quinteros, et al., 2019; cerdá et al., 2015; mostafaei et al., 2015; fumero et al., 2012; cafaro et al., 2010 airport h. zhao et al., 2022; rodríguez-sanz et al., 2021; biele and mönch, 2019; de maere et al., 2018; murça, 2017; farhadi et al., 2014; tan, 2012; tavakkoli-moghaddam et al., 2012; stiverson and rathinam, 2011; eun et al., 2010 transport dang et al., 2021; canca et al., 2019; corry and bierwirth, 2019; reddy et al., 2019; shahram and vahdani, 2019; y. zhang et al. 2019; durazo-cardenas et al., 2018; gifford et al., 2018; haoran et al., 2018; domínguez-martín et al., 2017; murça, 2017; wisittipanich and hengmeechai, 2017; mohtashami a., 2015 information technology ali and iqbal, 2022; hussain et al., 2022; s. wang et al., 2022; yang and shen, 2022; gu et al., 2021; hussain et al., 2021; lakhan et al., 2021b; c. wang et al., 2020; zhao and huang, 2020; hu et al., 2019; senturk et al., 2018; kong et al., 2016; nonsiri et al., 2014; kim et al., 2012; mobaieen et al., 2012; murugesan and chellappan, 2012 5.4. classification of research papers based on publishers and journals the journals from different areas such as production/industrial engineering, management, logistics, transportation, information systems/technology, cost factor focused scheduling and sequencing: a neoteric literature review optimization, applications, statistics, and healthcare disciplines published research work based on scheduling and sequencing with cost as the primary aim. among the leading journals, computers and industrial engineering (7.4%), computers and operations research (4.9%), and the international journal of production research (4.2%) have the most significant number of articles considerably. this may be due to the vast developments in the computer field in recent years and their involvement in industries and optimization techniques. these journals mainly focus on developing new computerized methods for resolving industrial engineering issues and their applications. european journal of operational research, which primarily focuses on innovative applications of operational research, and industrial and engineering chemistry research, which deals with research in applied chemistry and chemical and bimolecular/biochemical engineering, holds the fourth and fifth position respectively (3.5% and 2.4%). iie transactions (2.1%) have the sixth position. ieee access mainly focuses on research or development across all electrical and electronics engineering fields, including multidisciplinary applications, international journal of production economics, which covers the topics treating the interface between engineering and management, and the journal of scheduling which broadly covers the techniques and applications of scheduling, are in the seventh position (1.8%). applied mathematical modelling deals with the mathematical modelling of engineering and environmental processes, and industrial and manufacturing systems. computers and chemical engineering highlights the new growth in the application of computers and systems technology to engineering issues related to chemical industries. expert systems with applications deals with intelligent systems. production and operations management, and production engineering cover the latest research in industrial and production engineering. the journals mentioned above are in eighth place (1.4% each). other journals wherein 2 to 3 papers are published (around 1%) are listed in table 3. due to space limitations, journals with one research paper are not mentioned. considering the publishers, elsevier contributed the most number of research papers (31%) on scheduling and sequencing with cost as the main aim, followed by springer (12%), taylor and francis (11%), institute of electrical and electronics engineers inc. (ieee 6%), institute for operations research and the management sciences (informs 4%), american chemical industry (acs 2%), hindawi (2%), inderscience (2%), wiley (2%), growing science (1%), mdpi (2%), emerald (2%), american institute of mathematical sciences (aims 1%), maxwell (1%), sage (1%). other publishers contributed 20% altogether to the research. the literature study from the above-stated publishers shows diverse research in work. figure 5 presents the classification of research papers with publishers' details. table 3. journals classification source title publisher total articles* computers and industrial engineering elsevier 21 computers and operations research elsevier 14 international journal of production research taylor and francis 12 european journal of operational research elsevier 10 industrial and engineering chemistry research american chemical society 7 iie transactions (institute of industrial engineers) taylor and francis 6 bari and karande / oper. res. eng. sci. theor. appl. – first online ieee access ieee 5 international journal of production economics elsevier 5 journal of scheduling springer 5 applied mathematical modelling elsevier 4 computers and chemical engineering elsevier 4 expert systems with applications elsevier 4 production and operations management wiley 4 production engineering springer 4 ieee transactions on computer-aided design of integrated circuits and systems ieee 3 international journal of advanced manufacturing technology springer 3 international journal of industrial engineering computations growing science 3 journal of industrial engineering and management omniascience 3 journal of the operational research society taylor and francis 3 transportation science informs 3 aircraft engineering and aerospace technology emerald group holdings ltd. 2 automation in construction elsevier 2 engineering optimization taylor and francis 2 future generation computer systems elsevier b.v. 2 health care management science springer 2 ieee transactions on cybernetics ieee 2 ieee transactions on systems, man, and cybernetics: systems ieee 2 information sciences elsevier 2 interfaces informs 2 international journal of industrial engineering: theory applications and practice university of cincinnati 2 international journal of manufacturing technology and management inderscience 2 international journal of operations and quantitative management infoms 2 international journal of simulation modelling daaam international vienna 2 management science informs 2 mathematical problems in engineering hindawi 2 operational research springer 2 transportation research part e: logistics and transportation review elsevier 2 * journals with one research paper are excluded cost factor focused scheduling and sequencing: a neoteric literature review figure 5. research papers based on publishers 5.5. classification of research papers based on year of publication figure 6 shows the classification of css research papers published from 2010 to 2022. the researchers mostly applied mathematical computations till the initial years of the 21st century. still, later researchers felt to have easy and quick solutions due to the exponential growth of industries which can be achieved by applying the advanced computational algorithm in the css field, especially in the last few years. some of the commendable recent research papers which described applications of css optimization algorithms in different fields are manufacturing (zhang et al., 2018; liu et al.2018), health (deceuninck et al., 2018; roshanaei et al., 2017), education (czibula et al. 2016), service (haoran et al., 2018; durazo-cardenas et al., 2018), project management (zhao and huang, 2020; hu et al., 2019), computer cloud server (senturk et al., 2018). still, there are some areas where the growth in several css works is notable. figure 6. research papers based on year of publication elsevier 31% springer 12% taylor and francis 11% ieee 6% informs 4% acs 2% hindawi 2% inderscience 2% wiley 2% others 20% mdpi 2% growing science 1% emerald 2% omniascience 1% aims 1% maxwell 1% sage 1% 20 20 17 18 15 20 14 13 25 26 29 32 32 0 5 10 15 20 25 30 35 2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 2020 2021 2022 n u m b e r o f a rt ic le s publication year bari and karande / oper. res. eng. sci. theor. appl. – first online 5.6. dynamic authors in css research authors who are actively involved and participated in the recent publication of the research papers are identified in this study. overall, 832 authors contributed to 281 research papers on css work. all the authors, that is main author as well as coauthor/s, are considered from 281 research papers the top 12 authors with three or more research papers, each contributing to publishing and demonstrating related work, are listed in table 4. a. al-refaie with five articles, s. zhou with four articles and d. c. cafaro, y. dong, x. li, r. morabito, j. cerdá, z. gao, l. magatão, a. al-hawadi, m. elhoseny, and q. yue with three articles each, seems to be the most contributing authors in terms of publishing the research work. while the rest, 820 authors who published one or two research papers, are not mentioned in the table due to space constraints. fang and lin (2013) in manufacturing, gul et al. (2011) in health, and mak et al. (2013) in appointment scheduling are the authors whose work received more than 100 citations till now as shown by the publishers. table 4. top 12 authors with the most contribution in research on css name of authors articles a. al-refaie 5 s. zhou 4 d. c. cafaro 3 y. dong 3 x. li 3 r. morabito 3 j. cerdá 3 z. gao 3 l. magatão 3 a. al-hawadi 3 m. elhoseny 3 q. yue 3 5.7. classification of research papers based on countries table 5 shows that 41 major countries worldwide have done literature on the findings on scheduling and sequencing with cost as the primary aim. when the country of the first author is considered, out of 281 research papers, china and united states have done the most research in terms of research papers. apart from these two countries, other countries like iran, india, brazil, spain, germany, netherlands, canada, italy and taiwan, have also made a significant contribution to the number of publications. the countries like bangladesh, egypt, finland, indonesia, malaysia, poland, portugal, saudi arabia, singapore, slovakia, south africa, and the united arab emirates are the places where the number of publications is somewhat less in number. this shows that there are plenty of opportunities in these nations to research and further develop the area mentioned above. china and the usa collectively contributed around 36% of the total research in this area. most of the researchers from china (liu et al., 2021; dou et al., 2020; zhang et al., 2018) focused on the manufacturing industry. the study tells that from year 2010, consistent research is there in css. on the other hand, united states (sun et al., 2021, jafarnia-jahromi and jain, 2020; rezaeiahari and khasawneh, 2020; j. wang et al., 2020; mandelbaum et al., 2020) research appears mostly in health, and authors concentrated on sequencing and scheduling of patient’s appointments, and surgeries cost factor focused scheduling and sequencing: a neoteric literature review in operating rooms. the review reports that authors from the united states targeted this area recently more in numbers. table 5. classification of research papers based on countries country name number of articles china 64 united states 39 iran 21 india 19 brazil 13 spain 11 germany 9 netherlands 8 canada 7 italy 7 taiwan 7 argentina 6 belgium 6 israel 6 jordan 6 south korea 5 pakistan 4 united kingdom 4 australia 3 colombia 3 hong kong 3 japan 3 thailand 3 belgium 2 chile 2 france 2 new zealand 2 tunisia 2 turkey 2 bangladesh 1 egypt 1 finland 1 indonesia 1 malaysia 1 poland 1 portugal 1 saudi arabia 1 singapore 1 slovakia 1 south africa 1 united arab emirates 1 5.8. classification of research papers based on various constraints a scheduling constraint is a restriction placed on a schedule that affects the start or finish period of activity. scheduling problems have constraints exclusive to the particular industry. scheduling methods must be highly tailored to handle the constraints. these bari and karande / oper. res. eng. sci. theor. appl. – first online constraints can be in the form of cost, quality, customer satisfaction, time and resources. in finding the near-optimal solution in scheduling and sequencing, there can be hard constraints and soft constraints. a hard constraint is a constraint that must be fulfilled by some practical resolution to the model. instead, a soft constraint can be disrupted, but disrupting the constraint acquires a fine in the objective function. table 6 shows various possible constraints in different industrial sectors focused on by the authors. table 6. constraints in different industrial sectors industrial sector / industry constraints description airport capacity rodríguez-sanz et al. (2021) considered constraints on the number of arrival and departures at the airport, which results in delays with a significant effect on costs for air companies and travellers. time, ordering, safety, en route stiverson and rathinam (2011) elaborated on the management of aircraft on the runway concerning time ordering and safety constraints. situational and operational eun et al. (2010) suggested different sets of delay times, types of aircraft and approaching route constraints. runway separations de maere et al. (2018) discussed the different constraints like separations of the runway, hard time window and take-off /landing deadlines. in addition, the authors noted that the constraints assuming departures are complex as compared to arrival. automobiles resource, precedence areal et al. (2011) addressed that car sequencing is a resource-constrained scheduling problem and needs to preserve order while moving through the assembly line. cement manufacturing quality asad (2011) suggested that the raw material (limestone) must contain the required percentage of chemical elements. computer/ information technology deadline lakhan et al. (2021b) addressed that completing the internet of things application in a certain time period or earliest completion time helps achieve deadlines. data skew and deadline gu et al. (2021) proposed an algorithm for achieving an optimum solution for execution time and thus reducing rental costs. resource kim et al. (2012) discussed the limit to the assignment of computing elements to datasets. cost factor focused scheduling and sequencing: a neoteric literature review construction resource to achieve optimization, yuan et al. (2021) considered time-resource constraints and attempted to diminish the effect of the activity execution period on the total task. safety abadi et al. (2021) addressed the resident’s safety constraints in case of fire conditions at the renovation construction site. electronics time cui et al. (2020) addressed the timeliness constraints to find the optimum highest temperature and variant in temperature. flow shop block x. zhang et al. (2019) proposed a concept to find the best solution in the scheduling with a limited block or buffer in the flow shop of each factory in a scattered manufacturing situation. pre-ordering fumero et al. (2013) elaborated on batch allocation, the design of the plant, and production scheduling constraints in the flow shop. planned production ramezanian and saidi-mehrabad (2012) addressed constraints such as precedence, resource, the capability of the work centre, time and the relationship between inventory, production plan and customer demand. job sequence paul and azeem (2010) pointed out that the sequence of jobs on the machine should be the same for all the machines. general precedence constraint said et al. (2021) addressed that the lowerlevel task should be optimal, then only the upper level can achieve the near-optimal solution. precedence wisittipanich and hengmeechai (2017) suggested that precedence constraint is vital to achieve the goal in industries. warehouse space and transportation costs golmohammadi (2013) explained internal and external constraints like warehouse space and transportation costs in scheduling. precedence, resource, time werner et al. (2018) discussed batch production situation constraints, precedence constraints, resource constraints, and time for operation arrangement or costs. health security lakhan et al. (2022a) mentioned the security of data as a constraint and proposed blockchain-enabled internet of medical things to address it. bari and karande / oper. res. eng. sci. theor. appl. – first online resource nazif (2018) considered arrangements in the operating room, surgery time, and recovery time of patients as constraints. job shop capacity rohaninejad et al. (2015) addressed that capability of each machine is limited in flexible job shop scheduling. stock level álvarez-gil et al. (2022) mentioned the stock levels at the galvanizing line as constraints. manufacturing machine interference kobayashi (2021) considered that only one item could be set up or handled in a single period, and there should not be any machine interference. shelf-life m. z. wang et al. (2020) focused on optimizing the job allocation and sequencing to reduce overall completion time and cost considering the shelf life of raw materials. precedence su et al. (2015) mentioned operations should fulfil precedence constraints. the precedence constraint is represented by the precedence graph of operations. time huang and yao (2013) proposed that sufficient time to be allocated to an item to attain its demand quality. innate constraints of the production le and pang (2013) discussed constraints like the due date of part type, precedence constraints, resource allocation constraints, and non-pre-emption constraints. production line constraints lin and chu (2013) tackled the constraints like a production line, labour, warehouse capability and order fulfilment in a given time by articulating a model with integer programming. due dates, operation, resource barlatt et al. (2010) addressed the limit to the assignment of labours across the shift and the limit to the financial aspect of the industry. mining accessibility/ precedence armstrong and gallim (2012) discussed accessible blocks to be mined, limiting the amount to be mined, and limiting the duration of extraction as constraints. oil volume and flow rate constraints quinteros et al. (2019) studied the volume and flow rate constraints of products in the pipeline and used a computerised model for planning and scheduling operations. petrochemical carryover setup abdullah et al. (2019) described the supplier, warehouse, a customer with cost factor focused scheduling and sequencing: a neoteric literature review affiliate constraints associated with the product. process resource, recipes, additional timing subbiah et al. (2011) modelled the constraints independently as sets of timed automata methods. pulp synchronization martínez et al. (2018) addressed different constraints like the availability of a number of molds, the capacity of machines and the synchronization of steps in product manufacturing. railway movement of the train, route of the train, speed restriction and speed reduction after track maintenance y. zhang et al. (2019) highlighted that after the maintenance of the track, speed restriction constraint should be considered for the first two trains active on the way instead, a speed reduction of the operational train is modelled while the reverse route is under maintenance. robot project cost, time, quality nonsiri et al. (2014) mentioned that to overcome constraints related to cost, time and quality of product, the formation of a suitable schedule of tasks is prominent in the engineering process. ship time c. wang et al. (2016) mentioned blocks should be transported in planning time to avoid penalty of unfilled transporter travel and tardy time. channels corry and bierwirth (2019) presented shipping channels as a constraint due to less space to pass two opposite ships and depth constraints because of tide cycles in water. steel technical constraints fernandez et al. (2014) focused on technical constraints, including jobs’ release date, operations sequence in the job, waiting time, and volume of machines on which operation is performed. transportation flowrate lower limit haoran et al. (2018) modelled injection, delivery constraint, time and pipeline conditions constraints using milp. time window shahram and vahdani (2019) considered the time window for the arrival and departure of trucks by assigning the doors after arriving at cross-dock according to their arrival sequence. transport (chemical and fuel) product sequencing gifford et al. (2018) described the product sequencing constraints for the transportation of chemicals and fuels due to the supply characteristics. bari and karande / oper. res. eng. sci. theor. appl. – first online 5.9. classification based on objectives of research in different industrial sectors the paper's primary aim is to focus on the work related to the minimization of cost in all the papers considered. the authors depending on their application areas have classified the cost minimization as – • in manufacturing related industries production, operation, setup costs, investment, labour, inventory, hardware, maintenance, costs associated with machine idle time and overtime, and finished products inventory costs. • in health-related industries, cost comprises surgeon, patient-waiting cost, operating room idle cost, and staff overtime. • in service and project-related industries the overall cost for procuring energy from the external grid, electricity cost, energy consumption cost, the cost associated to the use of fossil fuels, cost of resources, labour distribution cost, warehouse capacity costs, transportation costs, component costs, equipment compliance cost, pump operating and maintenance costs, completion time cost, transition costs and tardiness costs. apart from these different cost minimizations as the primary aims, authors have also considered optimizing other parameters as the secondary aim in the various industries. these secondary aims are listed in detail in table 7 below. table 7. secondary aims in the different industries type of industry aims airport i. less computation time to generate the optimal sequence of runway ii. minimizing the time of landing the planes iii. optimal arrival flight sequencing iv. reducing runway delays and taxi-out times apparel i. more minor delays in production orders for apparel suppliers on stochastic demand automobiles i. increasing productivity of plant ii. reducing the completion time of production iii. reducing manpower at the car assembly line cellular manufacturing i. minimizing the makespan and costs of intra-cell movement ii. optimal sequence-dependent setup cloud server/ computer it i. reducing services delay ii. enhancing server utilization and minimizing makespan by sequencing resources and operations, minimizing data delay, optimizing throughput in average response time iii. minimizing power consumption construction i. minimizing work in construction projects ii. increasing productivity iii. scheduling processes to reduce time as well as the cost of the project container terminal i. increasing controlling effectiveness of the loading process education i. finding an optimal sequence of classes for courses and students to enhance the performance cost factor focused scheduling and sequencing: a neoteric literature review electric vehicles i. lessening the tardiness of services to the customer electronics i. minimizing the time required in pulse latch, condensed sequencing overhead of elements energy manufacturing i. minimizing energy intake and tardiness engineer–to-order (eto) i. minimizing lead time flow shop i. use of needed resources, minimizing maximum completion time ii. minimizing flow time and lateness measures by different sequencing rules of jobs iii. minimizing the aggregate work-in-process inventory iv. diminishing overall weighted tardiness v. increasing make-to-order system throughput food i. optimizing freshness and superiority of foods during distribution ii. curtailing overall arrangement costs in the production plant iii. optimizing the production capability of the plant freight i. increasing driver efficiency and lessening the time of transportation health i. minimizing operating room idle time and delay in service start-time ii. minimum deviation from the patient's chosen start day and the minimum average patient flow time iii. minimizing waiting plus overtime iv. optimizing over and under-utilisation of medical resources v. enhancing patients’ satisfaction by scheduling and sequencing appointments vi. minimizing appointment delay vii. reducing the makespan of operating rooms viii. minimizing execution time of schedule job shop i. reducing the total machines’ workload and makespan ii. minimizing the completion time and the cost of performing schedules iii. minimalizing makespan and setup time logistics i. minimizing makespan and the overall penalization costs manufacturing/ production i. minimizing total tardiness by sequencing the jobs and planning the maintenance activities ii. attaining greater production capability and shorter throughput times iii. increasing the overall net revenue iv. minimizing earliness tardiness penalties v. shapley value for the cost bari and karande / oper. res. eng. sci. theor. appl. – first online vi. reducing the weighted sum of key device shortages, exploiting the weighted sum of lots processed, reducing the amount of machines used vii. maximizing machine utilization viii. lessening the waiting time for queued jobs ix. reducing the completion time of products x. minimizing the total variation in parts consumption in the assembly line and minimizing the total makespan cost maritime ports i. minimizing overall efforts/time of the crane movement mining i. maximizing the net present value ii. minimizing completion time oil/ petroleum i. minimizing computational time in demand planning ii. reducing the overall time in sending petroleum refined products from oil refineries to distribution depot pulp and paper mill (p and p) i. maximizing customer demand railway transport i. profit in railway transportation project ii. minimizing travel time and delay in maintenance robot project i. reducing the overall processing time associated with tasks in robot arm movement ii. minimizing iterations and reducing lead-time development of robot ship i. minimizing penalty time, empty transporter travel time, and tardy time steel i. minimizing the number of coil transitions and thus improving productivity ii. optimizing the scheduling and sequencing with constraints like width, thickness, thermal cycle, and weldability of material to minimize calculation time textile i. minimizing the number of tardy jobs transport i. enhancing productivity and improvement in customer service ii. minimizing total operation time in scheduling vehicles in cross-docking systems warehouse i. minimizing the makespan of transporting the product from warehouse to customer ii. fulfilling customers’ orders in less time waste management i. minimizing overall inequity and minimizing total waste load released into the river cost factor focused scheduling and sequencing: a neoteric literature review 5.10. uncertainty studied in css uncertainty is an erratic event that interrupts the process of the completion of a task. it can be controlled by reducing the degree of uncertainty and its impact on the process by making a survey of tendencies related to the process used in various industrial sectors to predict demand and create explicit specifications of customers’ requirements. in uncertainty, researches primarily comprise stochastic scheduling, robust scheduling and fuzzy scheduling. the probability distributions approach is used in the representation of stochastic scheduling. robust scheduling is an amount of the flexible target of the scheduling considering uncertain parameters and unpredicted events. the fuzzy logic methodology is used to represent fuzzy scheduling to define the uncertainties with the satisfaction of constraints. the concept of uncertainty is applicable in all fields, however, researchers mainly highlighted its importance in the health sector. according to pang et al. (2022), scheduling mri jobs entails uncertainties such as patient arrival, scanning time, and preparation time. rezaeiahari and khasawneh (2020) considered the treatment duration of patients as uncertain and presented a simulation-optimization method for scheduling the patients who visited the medical centre over multiple days. mandelbaum et al. (2020) highlighted that patients’ punctuality and service durations are uncertain and bring out a data-driven, robust approach to handle the uncertainty. nazif (2018) observed that the time required for surgery is uncertain, the author represented the uncertainty of time with fuzzy numbers. saadouli et al. (2015) stated that optimizing the allocation of surgeries to operating rooms in orthopaedics medical centres is difficult due to uncertainty in the duration of surgery and recovery of patients. they applied lognormal probability distributions to generate time and handled the uncertainty to achieve the near-optimal solution. gul et al. (2011) addressed the complications in scheduling outpatient procedure center activities as it depends on uncertain parameters like surgery duration. in manufacturing, purohit and lad (2016) considered uncertainties regarding raw material quality, error in demand forecast, and machine production and handled these uncertainties parameters with a probability distribution approach. lu et al. (2013) focused on customer order placement which is uncertain as a client may order inquiries to several suppliers and give the order to only one of them. this uncertainty in order placement is represented by the probability function to reduce its impact. le and pang (2013) studied dynamic scheduling with power consumption uncertainties, formulated these uncertainties using the probability distribution function and found a way to reduce the effect of uncertainties. paul and azeem (2010) represented the uncertainties in the flow shop scheduling problem and handled them using fuzzy sets and logic. apart from health and manufacturing, uncertainty was also highlighted by authors in other areas. yuan et al. (2021) formulated the model with the representation of uncertain execution time of activity in terms of fuzzy sets which helped in reducing the effect of uncertainty on the execution period of the task in the project. rodríguezsanz et al. (2021) proposed a model which manages runway usage by sequencing aircraft operations by minimizing delays. they presented a robust model of scheduling optimization by considering uncertainties in tactical working steps of aircraft operations. durazo-cardenas et al. (2018) analysed track incidents, inspected data and developed a model to raise degradation alarms that initiate the automatic maintenance tasks scheduling that will help in reducing uncertainty in time. murça (2017) considered that taxi-out time is uncertain in nature, applied a robust approach bari and karande / oper. res. eng. sci. theor. appl. – first online for finding optimal solutions and showed optimistic results against uncertainty which helped in the reduction of delay in the taxi-out time of the airport. 5.11. computational time computational time is an important parameter in the industry for task scheduling and sequencing problems. the length of time necessary to complete a computation process is computational time. with cost parameters, computational time is also important. researchers can find the best solution for small instances in a fraction of the time, but finding the best solution for large-scale instances is more difficult. some articles emphasised reducing computational time, but just a handful expressed it in terms of figures. tsai et al., (2021) adapted a stochastic optimization model for a surgical scheduling problem. the experimental results demonstrated that the suggested algorithms obtain a nearly optimal schedule in reasonable computational time. martnez et al., (2019) used an exact optimization technique in the packaging sector and found that a solution to the problem may be found 10.9-97 times faster than usual computational times. abdullah et al., (2019) investigated a demand planning problem in the petrochemical sector and compared solutions in terms of computational time. they discovered a heuristic that can tackle large instance problems in less amount of time than traditional techniques providing high-quality solutions. haddad et al., (2018) employed micro/nanofluidic biochips to automate clinical diagnosis and dna sequencing, finding a 12.52 per cent reduction in computational time. the hybrid method, as presented by gao and qu (2018), solves instances very quickly and uses significantly less computing time than either milp or constraint programming alone. they stated that the computing time was lowered by 10.9 per cent. fernandez et al., (2014) used aco to schedule a galvanising line at a steel mill and discovered that it produces a solution in a short calculation time. using the ts algorithm, mobaieen et al., (2012) developed an optimum strategy for calculating the optimal robot arm movement for processing a large number of tasks. they compared task sequencing run time using the ts algorithm to pso, ga, and neighbourhood job search and found that ts can produce better solutions with more computational time. asad (2011) applied a blend of a heuristic sequencing algorithm and a milp-based blending formulation to ensure that raw materials for the cement manufacturing activity were always available. he compared the heuristic model to manual scheduling and discovered that the heuristic model contributed to substantial time savings in the solution generation process. eun et al., (2010) introduced a lagrangian dual decomposition approach, noting that the computation time can be greatly lowered, especially in congested airspace. 5.12. programming languages and optimization software packages the algorithm to produce an optimal solution for objective functions is formulated using a variety of programming languages and optimization software packages. after review, the programming languages and software packages used by the authors are identified and mentioned below. 5.12.1. cplex the package is based on the idea of a simplex algorithm and developed in c named cplex software. for issues involving linear programming, mip, quadratic cost factor focused scheduling and sequencing: a neoteric literature review programming, and quadratically restricted programming, the cplex optimizer offers adaptable, high-performance mathematical programming solvers. operations researchers were able to develop novel optimization algorithms, models, and applications because of their unmatched flexibility, dependability, and performance. wu et al. (2019), toledo et al. (2014), fang and lin (2013), lin and chu (2013), mancilla and storer (2012), santos and almada-lobo (2012), barlatt et al. (2010) and alfieri and cantamessa (2010) developed model in cplex programming solver to find the optimal solution for targeted objectives. 5.12.2. gams the general algebraic modeling system (gams) is an advanced modeling system for mathematical optimization. gams is made for modeling and handling mixedinteger, linear, and nonlinear optimization problems. the system can be used on a variety of computer platforms. the system is designed specifically for complicated, large-scale modeling applications and enables the user to create robust models that can be modified to fit different circumstances. zhao and huang (2020), pautasso et al. (2019), shahram and vahdani (2019), quinteros et al. (2019), musavi and bozorgiamiri (2017), fumero et al. (2012), tang et al. (2012), kopanos et al. (2011), subbiah et al. (2011) designed model of optimization using gams. hadidi et al. (2011) created an optimization system employing gams to input the model and the branch and reduce the optimization navigator (baron) solver to reach the best solution. the baron solver is a computational system intended for solving non-convex nonlinear programming optimization problems to achieve global optimality. 5.12.3. matlab engineers and scientists can utilise the programming environment matrix laboratory (matlab) to design the system and to analyse the product. a matrix based language that allows computational mathematics to be expressed in the most natural way. it comes with an editor for writing scripts that compile code, produces output, and format text into executable notebooks. reddy et al. (2019), roshanaei et al. (2017), rohaninejad et al. (2016), su et al. (2015), le and pang (2013), mathur and süer (2013), ramezanian and saidi-mehrabad (2012), mokhtari et al. (2011), and mazdeh et al. (2010a) used the matlab programming solver to develop and analyse a system to determine the best course of action for the intended goals. 5.12.4. lingo lingo is a straightforward tool for expressing huge problems succinctly, solving them, and analysing the answer. it makes use of the power of linear and nonlinear optimization. a robust language for describing optimization models, a fully featured environment for creating and editing problems, and a number of quick built-in solvers are all included in the lingo package. dou et al. (2020), alaghebandha et al. (2019), golmakani and namazi (2012), and mazdeh et al. (2010b) expressed and solved the problems by lingo. 5.12.5. programming languages a programming language is a method of notation for creating computer programmes. the majority of programming languages are formal text-based https://en.wikipedia.org/wiki/optimization_(mathematics) bari and karande / oper. res. eng. sci. theor. appl. – first online languages, while some are graphical. computer programming languages are frequently used to create software and websites and automate processes. the authors coded the algorithm in python, java, c++, visual basic (vb), and vb.net in order to produce the best result for objective functions. guzman et al. (2022), dang et al. (2021), lakhan et al. (2021a, 2021b), liu et al. (2021), sun et al. (2021), martínez et al. (2018), implemented experiments using python programming language. gu et al. (2021), yuan et al. (2021), bueno et al. (2020), kurniawan et al. (2020a, 2020b), m. z. wang et al. (2020), zhou et al. (2019), gifford et al. (2018), de maere et al. (2018), zhu et al. 2017, and sun et al. (2014) developed simulation programs by using java. algorithms were programmed in c++ by tsai et al. (2021), biele and mönch (2019), and paul and azeem (2010). grabenstetter and usher (2015), and chan et al. (2011) implemented a model using vb and vb.net programming languages respectively. it has been noted that python has become increasingly popular recently for the development of optimization systems. 6. the gist of cost reduction estimation in css by authors authors in the field of css showed that the optimization model helped in saving the cost and the computational time required to complete the activities in scheduling and sequencing. the notable papers are discussed in this section. laili et al. (2022) used the internet of things environment to minimize the cost of the order with many jobs, which they accomplished by applying local search algorithms and saved 5.6 to 11.8 per cent on rental costs. dang et al. (2021) illustrated the effectiveness of the combinatorial approach of local search with neighbourhood search to reduce the travel cost of automated guided vehicles within a plant by 20%-50%. shen et al. (2021) applied a ga to actual-world data of the pasta industry and achieved a reduction in makespan, energy cost and labour cost by 8.50%, 5.24% and 6.02%, respectively. singh et al. (2021) applied a 3d and 4d building information modelling approach in multiple pipe system installation projects for capturing important information. the time period required for planning, sequencing and scheduling in this project was reduced by 96%-97%. rijal et al. (2021) demonstrated a case-study of the supermarket chain in netherlands. they showed that the metaheuristics approach for allotting and sequencing orders to ordering pickers effectively reduces computation time by 80%. gao et al. (2021) applied milp to find an optimal solution for sequencing ship problems for the transportation of raw material at a steel plant which effectively helped in the reduction of 20 million chinese yuan renminbi (cny) per year. mandelbaum et al. (2020) applied a data-driven robust approach for optimization by considering appointment scheduling and sequencing on a dataset of the cancer centre. as a result, they could reduce overtime and waiting time costs by 15%-40% uniformly. quinteros et al. (2019) developed a computerized model by applying an integer programming approach for an oil company where oil product sequencing is required and showed that the operating cost could be saved by 10%. to solve the mixed-integer model in patient-surgeon allocation with surgeon schedule compacting, roshanaei et al. (2017) developed a new logic-based model that results in 45-63% cost savings per surgery. gao et al. (2015) suggested the assignment of tools to machine, optimal sequencing of lots to machine, and changeover of the machine, a three-stage technique for semiconductor devices. they were found to be effective in the cost factor focused scheduling and sequencing: a neoteric literature review reduction of costs by 62%. chaieb memmi and hammani laaroussi (2013) applied a branch and bound algorithm for deciding optimum products sequencing and estimated the start-up plus setup cost over a period and attained to curtail overall manufacturing cost by 30%. heath et al. (2013) presented a scheduling and sequencing model for the electronics industry by applying a heuristic approach that helped in cost savings and 17-18% improvement. 7. conclusions the review's goal is to bring attention to css ideas. the review consists of research papers from the years 2010-2022. the term "scheduling and sequencing" is searched in the research paper's title, abstract and keywords of the scopus database. the research mainly focuses on cost minimization as the primary aim, and hence the word "cost" is searched in the abstract of these papers. according to this, 281 research papers are found, and the data is collected considering different parameters; later, these papers are studied and organized. all papers are distributed to the important groups based on their applications. this literature review deliberated the report of css based on scheduling models, algorithms applied, and research sectors, objectives, constraints and uncertainties. the basic judgement of the review shows that more research is done using a simple integer model. most progressive algorithms are being used for the exploration of real-world problems. high-configuration computers can help reduce computational time, but in reality, the model normally runs on desktop computers with basic configuration in some industrial units. the solo optimization technique is observed to be insufficient to find optimal solutions; thus, the authors used a hybrid approach. the optimization model helped in saving cost and also the computational time required to complete the activities in scheduling and sequencing. the resource precedence, capacity, technical and time constraints in css can be prevented by analysing the past data of related plants. it is seen that the uncertainty in health, manufacturing, service and project management described by researchers can be handled by a probability distribution and fuzzy logic approach. this study is one of the precise analyses that systematically details the css and adds the general literature review. this study will help improve the understanding of the present state of work in the scheduling and sequencing field. even though a sufficient amount of research work is presented on css in journals considered in this review, the concept of css still has opportunities for future development. the significant findings, gaps, and future research directions in the field of css is discussed in detail as follows; 7.1. significant findings • single-machine models are studied more as compared to multi-machine models. static and deterministic models being the basic ones are still being studied, but considering the realistic nature, the shift can be seen more towards dynamic and stochastic models during recent years. • most of the work is done using an integer linear programming model, while few give the theoretical concepts of css. various algorithms based on heuristic and metaheuristic approaches are used for finding optimal solutions. some authors also used a combinatorial approach to find a nearoptimal solution. bari and karande / oper. res. eng. sci. theor. appl. – first online • in research papers, css application is found in almost all industrial sectors, the manufacturing domain has a maximum share (45%), followed by service (37%) and health (18%), • more css work can be seen in manufacturing as its original base, but at the same time, it is observed that the health and service zones have also contributed to the literature. authors presented their work on css using different case studies in computer/it, airport, project management, painting, textile, steel, medical industries, construction project, food, vehicle, education, pulp and paper, ship port, and soap. • the topic of scheduling and sequencing has been studied since the middle of the nineteenth century. still, css literature has made significant contributions since the year 2018 by applying different algorithms and models. • most of the research in css comes up in two countries china and the usa; together, they hold 36% of the study. • a. al-refaie with five articles, s. zhou with four articles and d.c. cafaro, y. dong, x. li, r. morabito, j. cerdá, z. gao, l. magatão, a. al-hawadi, m. elhoseny, and q. yue with three articles each, seems to be the most contributing authors in publishing the research work on css. 7.2. gaps identified • a large number of research papers explained the integer model, but methods such as simulation for the support have been used in a very small number of articles. • very few papers discussed the combinatorial approach of different optimization algorithms. • even though many research papers are presented on the css concept in the manufacturing background, these papers fail to show a systematized model for improving real-world situations in manufacturing. • mathematical and structural equation modelling is put forward in research papers, but automatic programming in an innovative way for the industry is required to get quick output. • research shows that the maximum work is done in a single-machine environment, but research on multiple machines is limited, and usually used in industries. 7.3. limitations • this study is limited in reviewing those articles which contain the term "scheduling and sequencing" in the title, abstract and keywords of the article and then the term "cost" in the abstract of these papers. chances are there that there may be studies, which might not have included the phrase "scheduling and sequencing" in the title, abstract and keywords as well as "cost" in the abstract, even though it concentrates on the css as the essential background. • a few articles from the 281 articles considered in this study which have the term ‘cost’ in their abstract may have other objective functions as the main goal instead of cost. • in order to keep the study's focus narrow, only journal articles are taken into account; conference papers, brief surveys, book chapters, and conference reviews are not included. cost factor focused scheduling and sequencing: a neoteric literature review • only articles written in english are taken into account; the analysis excludes 27 articles written in other languages. • this research covers publishers from the scopus database like elsevier, springer, taylor and francis, ieee, informs, acs, hindawi, inderscience, wiley, emerald, mdpi, and maxwell. it gathers a wide range of technical studies published in several reputed journals. all the determinations have been taken in, including the several parameters and bases for the judgement of articles. still, in the future extensive study can be done to deliver clearer insight into css. 7.4. future research directions • literature on css is examined, and it is revealed that the research started with the use of the integer model and moved towards developing the algorithm for optimizing scheduling and sequencing. future research in the css area requires the combinatorial approach of different computational models. with this computational, algorithmic model, and the automatic programming approach is also needed to optimize the scheduling and sequencing area. • the number of research papers provides a sense of the industries where the most work has been done and the regions where the same might be explored. as an alternative, researchers can focus on fields where no research has been done in this area. • there are many criteria such as completion time, flow time, lateness, late or tardy jobs, tardiness, earliness, early jobs, the cost of optimizing scheduling, and sequencing discipline but researchers focused on one or two criteria at a time. according to a real situation, there is a need to consider the criteria simultaneously, which may be complex but can be achieved with cutting-edge technology or a multidisciplinary approach. references abadi, s. t. s., tokmehdash, n. m., hosny, a., nik‐bakht, m. 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(2017). an effective heuristic for project scheduling with resource availability cost. european journal of operational research, 257(3), 746– 762. https://doi.org/10.1016/j.ejor.2016.08.049 © 2022 by the authors. submitted for possible open access publication under the terms and conditions of the creative commons attribution (cc by) license (http://creativecommons.org/licenses/by/4.0/). operational research in engineering sciences: theory and applications vol. 3, issue 3, 2020, pp. 84-100 issn: 2620-1607 eissn: 2620-1747 doi: https://doi.org/10.31181/oresta20303085k sandra.kasalica@gmail.com (s. kasalica)*, relzzup@gmail.com (m. obradović), aleksandar.blagojevic23@gmail.com (a.blagojević), jeremicd@gmail.com (d. jeremić), milivoje.vukovic1962@gmail.com (m.vuković), models for ranking railway crossings for safety improvement sandra kasalica 1*, marko obradović 2, aleksandar blagojević 1, dušan jeremić 1, milivoje vuković 3 1 academy of technical and art applied studies belgrade, department high railway school, belgrade, serbia 2 faculty of mathematics, university of belgrade, belgrade, serbia 3 infrastructure of serbian railways, belgrade, serbia received: 20 august 2020 accepted: 11 november 2020 first online: 15 november 2020 original scientific paper abstract: analysis of high-risk locations, accident frequency and severity for railway crossing is necessary in order to improve the safety and consequently diminish the number of accidents and their severity. in order to extract the necessary parameters that quantify the risk associated with railway crossings in serbia, we have carefully analyzed available statistical models commonly used in this kind of studies. a zeroinflated poisson model and a multinomial logistic model were used for the assessment of accident frequency and accident severity respectively. in order to quantitatively evaluate the risk, a well known measure – total risk was modified and a new measure for risk – empirical risk was introduced. the road sign warning device (𝑝 = 2.76 ∙ 10−9), exposure to traffic (𝑝 = 4.3 ∙ 10−7), and maximum train speed at a given crossing (𝑝 = 1.36 ∙ 10−5) were significantly associated with probability of accident frequency and significantly influenced the expected total number of fatalities or injuries caused by traffic accidents. keywords: railway crossings, high-risk locations, accidents, regression models 1. introduction the identification of the high-risk railway crossings in serbia is of great importance because, to our knowledge, no such study has been performed in the past. for example, from 2007 to 2011, 312 accidents occurred at 2,138 railway crossings in serbia. these accidents resulted in 59 fatalities and 130 injuries (statistics on accidents at serbian railways 2011). currently, more than 74% of the 2,138 railway crossings in serbia are of passive control type (st. andrew’s cross and stop sign). from 2004 to 2012, only 22 railway crossings were equipped with an mailto:sandra.kasalica@gmail.com mailto:relzzup@gmail.com mailto:aleksandar.blagojevic23@gmail.com mailto:jeremicd@gmail.com mailto:milivoje.vukovic1962@gmail.com models for ranking railway crossings for safety improvement 85 active control type (flashing lights with half gates). along with a control type, other railway crossing factors (e.g., train frequency, train speed, daily road traffic, sight triangle, crossing width and angle) might increase the likelihood of accident occurring at railway crossings. therefore, investigations of the risk factors that may be associated with accidents at railway crossings are vital in order to identify the crossings for future safety improvement. statistical regression models are formulated to express the expected accident count of an entity as a function of its traits. because of non-negative and count data nature of accident frequency for a time period, the poisson or negative binomial (nb) models and their variants are developed to model crash or accident frequency, or both, at spatial locations on highways (miaou, 1994; persaud et al., 1999; lord et al., 2005). the nb was verified by (austin & carson, 2002). saccomanno et al. (2004) used poisson and nb distribution in their risk based statistical models which were also used for identifying the high-risk railway crossings. extensions of these two models are a zero-inflated poisson (zip) regression model and a zero-inflated negative binomial (zinb) regression model which have also been utilized for modeling accident data on railway crossings (miranda-moreno & fu, 2006). three alternative models the nb model, the heterogeneous negative binomial (hnb) model, and the poisson lognormal model and two ranking criteria marginal and posterior mean of accident frequency are considered in a study by miranda-moreno et al. (2005) for identification of the high-risk railway crossings. similarly, mirandamoreno et al. (2009) proposed a bayesian multinomial model to estimate the severity levels of each individual involved in an accident. the generalized logit model was used to explore the key factors that may be responsible for different degrees of accident severity at railway crossings (huet et al., 2010). a zip model was used to describe the relationship between the extra zero count fatality or injury data and explanatory variables on railway crossings in taiwan (hu et al., 2011). rovšek et al. (2014) identified the key risk factors of traffic accident injury severity on slovenian roads using a non-parametric classification tree. recently, washington et al. (2014) applied a quintile regression model for identifying black spots. moreover, they proposed a more complex formula for modeling a number of crashes based on equivalent property damage crashes. this paper is the first attempt to analyze accident data using count data and multinomial regression in serbia and countries in our region. due to the fact that we have gathered the unique set of the data, we believe that the analyses will serve not only to identify unsafe railway crossings but also additionally verify the methodology used. four types of regression models are considered for accident frequency and empirical risk: poisson, nb, zip and zinb. the analysis of accident severity was performed using a multinomial logit model. the high-risk locations were determined using total risk analysis (saccomanno et al., 2003). finding out that variables of accident frequency and accident severity are slightly correlated, we also introduced a new risk measure empirical risk. the final high-risk location was created using both of these methods. kasalica et al./oper. res. eng. sci. theor. appl. 3 (3) (2020) 84-100 86 2. data source and description 2.1. inventory data set the data supporting this research came from two sources; (1) the serbian railway crossing inventory database (2007-2011) (srcid) and (2) accident database of serbian railway crossings (2007-2011) (adsrc). the second one is the first database of this kind in serbia, and we created it for the purpose of this very research. srcid contains the characteristics of each railway crossing and its traffic conditions. on the territory of the republic of serbia, the railway network has the total length of about 4,000 km, out of which 276 km are multiple tracks and 934 km are electrified. there are 2,138 railway crossings in total. all these crossings have various warning devices. certain numbers of crossings were found to be poorly specified. namely, some attributes associated with railway and highway features and traffic exposure with regard to the number of daily trains and average annual daily traffic (aadt) were missing. in the present study, we have excluded the crossings with incomplete data. in order to avoid possible selection bias, we have carefully analyzed distributions of the excluded crossings and found no significant statistical grouping (see appendix). the final set was compiled by merging srcid and adsrc databases and it consisted of 745 railway crossings. there were 17 independent variables considered in this study for modeling purpose and they were derived from the srcid (table 1). they can be classified as follows: • railway characteristics: railway category, maximal train speed at a given crossing and number of tracks. • traffic volume: exposure (expo) at a given crossing is defined as the geometric mean of number of trains per day and average annual daily traffic volume (aadt). • crossing characteristics: crossing surface type, crossing width, sight triangle and crossing angle. • road characteristics: road category mainline, road category regional, road category rural and local, road category farm and non-categorized and road category street. • warning devices: road signs, flashing lights, full gates and half gates. table 1. independent variables and their characteristics variable short name description coding / unit x1 katprm railway category mainlines =1; others =0 x2 expo b sqrt [aadt ∙ daily trains] vehicles/day x3 mbrz b maximal train speed at a given crossing km/h x4 brkolb number of tracks single track = 1; multiple tracks = 0 x5 vrkola crossing surface type asphalt, concrete panels and rubber panels = 1; cobblestone, wood planks and gravel = 0 x6 kpm road category mainline indicator models for ranking railway crossings for safety improvement 87 x7 kpr road category regional indicator x8 kpsl road category rural and local indicator x9 kppnp road category farm and non-categorized indicator x10 kpu road category street indicator x11 sirppb crossing width 6m or less = 1; more than 6m = 0 x12 trprp sight triangle exist = 1; does not exist = 0 x13 ugukr crossing angle from 60° to 90° = 1; less than 60° = 0 x14 vosig warning devices road signs indicator x15 vosv warning devices flashing lights indicator x16 vobr warning devices full gates indicator x17 vrosp warning devices half gates indicator note: all variables are categorical except expo and mbrz which are numerical; a the mainline includes reference and intermediate lines and others are supplementary lines. b in order to get more convenient coefficients for the models, the observed values for maximum train speed at a given crossing and daily traffic volume were divided by ten. 2.2. accident occurrence data the available historical accident data-set for modeling accidents at railway crossings were collected from 2007-2011 (5 years of accident information). the data-set provides the information about the time, location and conditions of accident for 2,138 railway crossings, but we observed 745 crossings. the accident database of serbian railway crossings (2007-2011), contains four types of information: • basic accident data: including the accident reference number, the date and the time of accident, location and cause of accident. • involved road vehicle driver, vehicle and train data: including information on road vehicle driver action at time of collision (e.g., ignored warning devices, drove through gates, failed to stop), gender and age, visibility, vehicle type and train type. it should be noted that our data lacked the information about the train operator. • accident type: a road vehicle was hit by a train or a train was hit by a road vehicle. • data on severity of consequences: including information on the number of fatalities, serious injuries and a property damage-level for each accident. in this paper, we considered three dependent variables: accident frequency, accident severity and empirical risk. the accident frequency is the number of accidents that took place at a given time period. it is a countable variable that, in our observations, takes values from 0 to 5. the frequency of these values is given in kasalica et al./oper. res. eng. sci. theor. appl. 3 (3) (2020) 84-100 88 table 2. it represents the number of accidents that took place at observed 745 crossings in the period from 2007 through 2011. in this period of time, at 514 (69%) crossings there were no accidents, and at the remaining 231 (31%) crossings there were 312 accidents in total. accident severity is defined as an average impact per accident. the average impact is a weighted average of deaths and injuries in each accident. in this paper, the accident severity is characterized as equivalent fatality. for example, saccomanno et al. (2004) equalized one fatality to 44 injuries to yield a crossing collision consequence score (cs) for the purpose of further crash severity modeling. in taiwan, one injury from a highway accident has been equalized to 0.37 fatalities, or conversely, a fatality has been treated as 2.72 injuries (hu et al., 2010). similarly, we equalized three injuries as an equivalent of one death. the factor 3 was chosen out of practical considerations and matches the regulations for personal compensation stated in the regulation on personal compensation (official gazette of the republic of serbia, no. 34/2010). therefore, the formula for accident severity becomes: accident severity = (3 × fatalities injuries) /accident frequency (1) this dependent variable is further categorized into three levels: 0 (0 accident severities), 1 (less than 3 accident severities), and 2 (3 or more accident severities). in other words, accident severity is 0 if there were no injuries or fatalities, it takes value 1 if there were less than 3 injuries (or 1 fatality) per accident, and it takes value 2 if there were 3 or more injuries (or 1 fatality) per accident. the frequency of these values is given in table 2. the empirical risk is defined as a weighted sum of number of fatalities and the number of injuries. once again, three injuries were considered an equivalent of one fatality. consequently, empirical risk is defined as follows: empirical risk = (3 × fatalities) + injuries (2) the observed empirical risk frequency is shown in table 2. in our sample, the empirical risk takes values from 0 to 14. table 2. observed accident frequency, accident severity frequency and empirical risk frequency of y=y accident frequency level observed frequency accident severity level observed frequency empirical risk level observed frequency y = 0 514 y = 0 633 y = 0 633 y = 1 180 y = 1 72 y = 1 45 y = 2 35 y = 2 40 y = 2 18 y = 3 6 y = 3 31 y = 4 6 y = 4 3 y ≥ 5 4 y ≥ 5 15 models for ranking railway crossings for safety improvement 89 3. developed models regarding crossing accidents 3.1. accident frequency model the review of the prior research for the accident frequency modeling helped us find the most suitable model. four types of regression models are considered: poisson, nb, zip and zinb. in our analysis, we included 17 independent variables shown in table 1. the outcome variable was accident frequency at railway crossings in the period from 2007 to 2011, (table 2). for the comparison of two non-nested models, the vuong test was used (washington et al., 2003; miranda-moreno & fu, 2006). results of three vuong’s tests are presented in table 3. table 3. the comparison of models with vuong’s statistic first model second model value of |𝑉| 𝑝 value better model poisson nb |𝑉| = 3.60 𝑝 = 1.70 ∙ 10−6 nb nb zip |𝑉| = 5.84 𝑝 = 2.56 ∙ 10−9 zip zip zinb |𝑉| = 2.15 𝑝 = 0.016 zip the zip model was chosen for modeling accident frequencies (p = 0.016). the particular zip model considered in this study has the following form (lambert, 1992): p(yi = yi) = pi + (1 − pi)e −λi if yi = 0 p(yi = yi) = (1 − pi) e−yiλyi y! if yi = 1,2,3,… (3) where pi is the probability of being in the zero state and y is the number of events per period. the coefficients for the final zip model are presented in table 4. the model was obtained using the function zero-infl from the r-package (zeileis et al., 2008). eight independent variables out of 17 were found to be of significance for the model. the variables regarding the warning device have been shown to be significant. the zip model chose two out of four dummy variables, namely road signs (vosig) p = 2.76 ∙ 10−9 and full gates (vobr) p = 1.23 ∙ 10−5. the half gates variable (vrosp) here acts as a reference variable and the flashing light signal (vosv) was excluded from the model probably because of lack of enough crossings with this type of device. this means that the probability number of accidents at crossings with road signs, which is the most common type of site protection, is higher than on reference (half gates) crossings. the full gates device has a negative coefficient, which shows us that they are superior to half gates regarding accident prevention. the prevalence of passive control devices may be attributed to a large number of sites with low traffic and train volumes for which the cost of upgrading to automated devices is not justifiable from a cost-benefit analysis in terms of the projected accident reductions at these sites (ehrlich, 1989). one would suspect that the presence of gates would predictably result in fewer accidents, and the model estimation process did in fact result in a positive effect for the presence of half gate. the gates provide a physical blockade that serves as a deterrent to crossing, but is also cost prohibitive for implementation at all sites. also, according to wigglesworth & uber (1991), kasalica et al./oper. res. eng. sci. theor. appl. 3 (3) (2020) 84-100 90 upgrading crossings with flashing light to boom barrier status reduce fatal accidents at crossings. however, many accidents are caused by vehicles running through a crossing to beat a train, occasionally around gates that are deployed (caird et al., 2002; cooper & ragland, 2012). and indeed, automated control devices are not faultless. for example, automated signal control devices are susceptible to false alarms and excessive warning times, which may lead driver to rely on their own hazard judgment and ignore the signal, as well resorting to risky behavior by circumventing the lowered gates (leibowitz, 1985; meeker & barr, 1989). table 4. zip accident prediction model result description independent variable estimated coefficients standard error 𝑧– statistic pr(> |z|) model count intercept constant -1.668 0.287 -5.823 5.78e-09 *** road signs vosig 0.984 0.166 5.945 2.76e-09 *** full gates vobr -1.394 0.319 -4.373 1.23e-05 *** crossing width sirppb -0.530 0.155 -3.416 0.001 *** sqrt[aadt ∙ daily trains] expo 0.020 0.005 4.320 1.56e-05 *** maximal train speed mbrz 0.122 0.028 4.350 1.36e-05 *** number of tracks brkolb -0.370 0.180 -2.053 0.040 * crossing surface type vrkola -0.228 0.137 -1.662 0.096 . farm and non-categorized road kppnp 0.188 0.147 1.285 0.199 log (theta) -1.322 0.167 -7.896 2.87e-15 *** model zero intercept constant -1.160 1.626 -0.713 0.476 road signs vosig 2.012 1.293 1.556 0.120 full gates vobr -0.580 2.786 -0.208 0.835 crossing width sirppb -22.424 1203.8 -0.019 0.985 sqrt[aadt ∙ daily trains] expo -0.058 0.060 -0.969 0.333 maximal train speed mbrz 0.078 0.142 0.546 0.585 number of tracks brkolb 0.462 1.069 0.432 0.665 crossing surface type vrkola -3.860 1.233 -3.132 0.002 ** farm and noncategorized road kppnp 3.771 1.135 3.321 0.001 *** log-likelihood: -509.4 on 18 df aic: 1054.79 level of significance: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 two different traffic characteristics proved to be significant in affecting the railway crossing accident frequency. the exposure (expo) coefficient is positive (p = 4.3 ∙ 10−7). the numbers of trains and road vehicles are often first variables that are considered in developing a model for accident prediction (austin & carson, 2002; saccomanno et al., 2004; miranda-moreno et al., 2005). the higher the traffic volume, the more vehicles are exposed to risky situations with incoming trains, which models for ranking railway crossings for safety improvement 91 enlarges the accident probability. according to austin & carson (2002), higher numbers of trains and the aadt were found to increase a railway crossing accident frequency. the maximum train speed at a given crossing (mbrz) is also associated with a higher predicted accident frequency (p = 1.36 ∙ 10−5). this is consistent with austin & carson (2002), the higher the defined maximum train speed, the higher the predicted accident frequency. as the train speed increases, the stopping distances of trains extend, and the time available for driver to spot the obstacle and stop the train decreases. on the other hand, difficulties that the drivers of vehicles have, concerning speed and distance of incoming train, are known (leibowitz, 1985; meeker et al., 1997; meeker & barr 1989; kasalica et al., 2012), and as the train speed increases, the time the driver has got to react in order to change the wrong decision to cross decreases. the crossing width, as well as the number of tracks, has been shown to have some significance. this finding is most likely related to the earlier; higher train and traffic volumes require a greater number of tracks and traffic lanes to operate. road surface also have some significance, but this factor seems inconsequential compared to other railway, road or crossing characteristics likely to affect railway crossing safety. it should be noted that some crossing characteristics (crossing angle or sight triangle), as well as road category do not have observable influence on the number of accidents. from this model, we can conclude that the best way in which safety can be improved and the number of accidents can be reduced is upgrading the warning device system. the other variables are either out of our control (maximum train speed and exposure) or do not have significant influence on the number of accidents (road category, road geometry, road surface, etc.). 3.2. accident severity model the analysis of accident severity is performed using a multinomial logit model. multinomial logit models have gained popularity for this type of data mainly because they can account for the dependent variable's ordinal nature. let πj(𝐱) = p(y = j;𝐱) be the probability of y = j, j = 0, 1, 2. the multinomial logit model is given as follows (hu et al., 2010): logit[πj(𝐱)] = log πj(𝐱) π0(𝐱) = αj + 𝐱 βj, j = 1,2. (4) here αj is the intercept parameter, and βj = (βjαj 1 , β j2 ,…, β j17 )t is 17dimensional vector of regression parameters for j − the value of dependent variable. from eq.(4), taking α0 = 0 and β0 = 0 , we obtain: πj(𝐱) = exp (αj + 𝐱𝛃j) ∑ exp (αk + 𝐱𝛃j) 2 k=0 , j = 0,1,2 (5) the analyses have been done using the r-function multinom (venables & ripley, 2002). here, we also used the akaike information criterion (aic) stepwise procedure. the parameters were estimated using the maximum likelihood estimate (mle) method. the results were presented using the function mlogic.display (chongsuvivatwong, 2012). the coefficients for the final model accident severity are presented in table 5. kasalica et al./oper. res. eng. sci. theor. appl. 3 (3) (2020) 84-100 92 table 5. multinomial logit model result for accident severity independent variable severity level (y = 1) confidence interval severity level (y = 2) confidence interval coefficients/se rrr (95% ci) coefficients/se rrr (95% ci) intercept -5.76 0.694*** -5.55 0.826*** vosig(x14) 1.33 0.385*** 3.78(1.78,8.04) 0.65 0.428 1.92(0.83,4.44) vobr(x16) -1.28 0.667 0.28(0.08,1.03) -1.93 1.051 0.15(0.02,1.14) sirppb(x11) 1.26 0.297*** 3.53(1.97,6.31) 1.20 0.378** 3.33(1.58,6.98) mbrz(x3) 0.22 0.068** 1.24(1.09,1.42) 0.12 0.083 1.12(0.95,1.32) expo(x2) 0.08 0.015*** 1.08(1.05,1.11) 0.05 0.017** 1.05(1.02,1.09) brkolb (x4) -0.87 0.427* 0.42(0.18,0.97) -0.36 0.463 0.70(0.28,1.73) katprm(x1) -0.39 0.311 0.67(0.37,1.24) 0.74 0.430 2.09(0.90,4.87) residual deviance: 668.53 aic = 700.53 level of significance: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 these estimated results of the effects of independent variables from this model by the use of the relative risk ratio (rrr) are described in the following section. the relative risk ratio is the ratio of probabilities of a chosen state and the reference state. in table 5, their rrr values and 95% confidence intervals (ci) are given. the ratios given are for y = 1 (e.g., accident severity of 1) and y = 2 (e.g., accident severity of 2), while y = 0 (e.g., accident severity of 0). the variables regarding the warning device have been shown to be significant. the multinomial logit model chose two out of four dummy variables, namely road signs (vosig) and full gates (vobr). the half gates variable (vrosp) here acts as a reference variable. the value for rrr of road signs (vosig) for accident severity of y = 1 is rrr = 3.78, 95% ci (1.78, 8.04), which means that upgrading road signs to reference half gates will result in a lower probability of accident severity of y = 1. the value for rrr of road signs (vosig) for accident severity of y = 2 is rrr = 1.92, 95% ci (0.83, 4.44), which means that upgrading road signs to reference half gates will also result in lower probability of accident severity of y = 1. however, since the rrr is smaller in the second case, we can see that the upgrading from road signs to half gates will better prevent less severe accidents than more severe ones. from the rrr values for full gates (vobr), we can see that upgrading from half gates to full gates will result in lowering probabilities for both accident severities of y = 1 and y = 2. however, this is much less significant change than the one when upgrading from road signs to half gates. this finding confirms the design-related issues of this investigation. this is in an agreement with austin & carson (2002): “... rather than focus on design-related improvements, one may want to consider improvements in the use of warning devices at railway crossings”. however, railway crossings in serbia are not adequately equipped with modern devices which are standardized, used and are part of the national railway level crossing safety strategy in the developed countries. in such circumstances, the safety at railway crossings in serbia depends mostly on human and physical factors according to reports of safety and functionality of serbian railways (2002-2012). according to cairney (2003), “the form of traffic control implemented at a railway crossing greatly affects the decision that has to be made by the driver of the road vehicle on the safety of the crossings”. regarding crossing width variable, the rrr values indicate that wider crossings have higher probabilities for accident severities for both states, rrr = models for ranking railway crossings for safety improvement 93 3.53, 95% ci (1.97, 6.31) for y = 1 and rrr = 3.33, 95% ci (1.58, 6.98) for y = 2. it can be noted that this variable has about the same influence on less severe and more severe accidents. the maximum train speed variable also has a significant influence on accident severity. the rrr value indicates that the ratio of probabilities for y = 1 and y = 0 will increase 1.24 times when the maximum train speed is increased by 10 km/h. the ratio of probabilities for y = 2 and y = 0 is increased 1.12 times when the maximum train speed is increased by 10 km/h. this means that increasing the speed of trains has not a direct impact on mortality. the exposure to traffic also has a significant influence. for one unit increase of expo, the ratio of probabilities is increased rrr = 1.08 times (y = 1) and rrr = 1.05 times (y = 2). the exposure to traffic has been shown to be an important factor for accident prediction (ogden, 2002; austin & carson, 2007; hu et al., 2010). a higher number of trains and road vehicles, which is often found in urban areas, are shown in this paper to have an impact on high accident severity. it could be said that crossings with a higher exposure to traffic can provide higher probability of accidents and irregular behavior (fitzpatrick et al., 1997). also, according to hu et al. (2010), one common characteristic found in the railway crossings with more severe accidents is that these railway crossings are usually located in urban areas where traffic exposure is relatively high, and compared to rural areas more traffic accidents are observed in these traffic busy areas. regarding number of tracks, the rrr indicates that the probabilities for accident severities are higher when there are multiple tracks as opposed to a single one. as for the last variable from the model, the railway category, it can be seen that the main railways have lower probabilities for accident severity of y = 1, and higher probabilities for accident severity of y = 2. it can be noted that crossing parameters, such as road and railway geometry (crossing angle and sight triangle), as well as the road type, as it was the case with the zip model of accident frequencies, were not accepted by this model. 4. high-risk location analysis one of the primary tasks in the development of the program for safety improvement in some parts of traffic infrastructure (e.g., road crossings or railway crossings), is to identify the locations that have a high accident risk. this process is also known as black spot identification (saccomanno et al., 2003; saccomanno & lai, 2005). identifying high-risk locations is the initial step of the process of improving safety (persaud, 2001). this would then lead to further engineering treatment such as crossing closure or grade separation, improving the crossing geometry or upgrading warning devices to make the crossing safer. one of the approaches to high-risk identification is based on regression models. this method uses some ranking criteria in order to sort the list of locations and identify the ones with the highest risk. miranda-moreno et al. (2009) proposed a bayesian multinomial model in order to estimate the accident severity for each person involved in an accident. the total risk is defined as the product of accident frequency and its severity (saccomanno et al., 2004; miranda-moreno et al., 2009). the deaths and injuries are our main concern, so the total risk is the goal we want to achieve. two criteria are considered for estimating the total risk. the first kasalica et al./oper. res. eng. sci. theor. appl. 3 (3) (2020) 84-100 94 criterion is the mean total risk for a crossing obtained as the product of mean accident frequency and mean accident severity, given as follows: mtri = mfreqi ∗ msevi (6) where: mtri is mean total risk for crossing i; mfreqi is mean accident frequency for crossing i obtained from the accident frequency model (table 4) and msevi is mean accident severity for crossing i obtained from the accident severity model (table 5). the second criterion presented here is based on the empirical risk model. the estimate for total risk for a crossing i would be the mean empirical risk (meri). the reason for introducing this additional criterion is that in our data the variables accident frequency and accident severity are slightly correlated (r = 0.36). similar to what was done for modeling accident frequency; we tried different count data regression models for empirical risk modeling. four types of models are considered: poisson, nb, zip and zinb. those models were obtained using the stepwise aic. obtained models were then compared using vuong's test (table 6). table 6. the comparison of models with vuong’s statistic first model second model value of |v| p value better model poisson nb |v| = 4.60 p = 1.70 ∙ 10−6 nb nb zinb |v| = 4.30 p = 8.3 4 ∙ 10−6 zinb zip zinb |v| = 1.98 p = 0.029 zinb the comparison with vuong's test showed significant difference (p = 0.029) between zero inflated poisson (zip) and zero inflated negative binomial (zinb), which means that overdispersion is not only caused by excess of zeros, but there is another source of overdispersion. suppose 𝑦 is a discrete random variable consisting of the counts on 𝑛 subjects, 𝑦1,𝑦2, …,𝑦𝑛. observations that go into structural zeros (𝑦𝑖 = 0) have a degenerate distribution at zero with a probability of occurring is p. while the observations included in the nb counts (yi = 0,1,2…) 2, follow a negative binomial distribution with probability of occurring is (1 − 𝑝). therefore, 𝑌 is zinb distributed, which is defined by: 𝑌 = { 𝑠𝑡𝑟𝑢𝑐𝑡𝑢𝑟𝑎𝑙 𝑧𝑒𝑟𝑜𝑠, with probability 𝑝 𝑐𝑜𝑢𝑛𝑡𝑖𝑛𝑔 𝑝𝑟𝑜𝑐𝑒𝑠𝑠,with probability 1 − 𝑝 (7) based on the probability function of the zero-modified distribution, then probability mass function (pmf) for zinb distribution is (garay et al., 2015): 𝑃𝑟(𝑌 = 𝑦) = { 𝑝 + (1 − 𝑝)( ø 𝜇 + ø )ø, 𝑦 = 0 (1 − 𝑝) γ(y + ø) γ(y + 1)γ(ø) ( ø 𝜇 + ø ) ø ( 𝜇 𝜇 + ø )𝑦, 𝑦 = 1,2,… (8) where (ø)−1, 𝜇 and γ(.) represent a dispersion parameter, mean, and gamma function, respectively. the estimated parameters of the zinb model for empirical risk are given in table 7. models for ranking railway crossings for safety improvement 95 table 7. zinb accident prediction model result for empirical risk description independent variable estimated coefficients standard error z statistic pr(> |z|) model count intercept constant -1.926 0.667 -2.886 0.004 ** road signs vosig 0.618 0.314 1.969 0.049 * full gates vobr -2.121 0.520 -4.080 4.50e-05 *** crossing width sirppb -0.535 0.324 -1.650 0.099 . maximal train speed mbrz 0.240 0.066 3.666 2.46e-04*** sqrt[aadt ∙ daily trains] expo 0.011 0.012 0.928 0.354 crossing surface type vrkola -0.665 0.275 -2.416 0.016 * log (theta) -1.322 0.167 -7.896 2.87e-15 *** model zero intercept constant 9.613 3.863 2.489 0.013 * road signs vosig -5.095 2.013 -2.531 0.011 * full gates vobr -5.181 3.118 -1.662 0.011 * crossing width sirppb -7.600 1.789 -4.248 2.15e-05 *** maximal train speed mbrz 0.829 0.489 1.695 0.090 . sqrt[aadt ∙ daily trains] expo -0.999 0.321 -3.115 0.002 ** crossing surface type vrkola 2.868 1.531 -1.873 0.061 . theta = 0.2666 log-likelihood: -509.4 on 18 df the variable that has the highest impact on empirical risk is maximum train speed (p = 0.000246). other variables of importance are road signs (p = 0.048910), exposure to traffic (p = 0.353520), crossing width (p = 0.098971) and road surface type (p = 0.06110). therefore, the probability of the railway crossing being at risk of a fatality varied with these risk factors. two lists of railway crossings are compared using two methods, namely percentage deviation and the spearman correlation coefficient. these two criteria were used in order to create a list of high-risk locations for crossings on the serbian railway network. based on each criterion, two lists were made. a simple way to compare the two lists is the percentage deviation. for this purpose, a certain number of top locations from both lists were selected. the percentage deviation is defined in the following way (miranda-moreno & fu, 2006): % deviation = 100 × (1 − b m⁄ ) (9) where b is the number of common locations on the two lists, and m is the number of selected top locations. the percentage deviation is calculated for various thresholds (no. of crossings). the value of deviation is between 40% and 60%. it can be noted that this deviation is greater when there are shorter lists of top locations, and gradually goes down when the length of lists is increased. the spearman correlation coefficient is a non-parametric technique to measure the linear correlation between two variables (miranda-moreno et al., 2005). here, the spearman coefficient is calculated to measure the correlation between these two risk models. in other words, it measures the degree of matching between the two lists. it is calculated in the following way (miranda-moreno et al., 2005): kasalica et al./oper. res. eng. sci. theor. appl. 3 (3) (2020) 84-100 96 r = 1 − 6 ∙ ∑ di 2n i=1 m ∙ (m2 − 1) (10) where: 𝑟 is the spearman coefficient, di is the difference in ranks between the two models for the same crossing i and, m is the number of selected top locations. the correlation is r = 0.50. in table 8, there is a list of 20 crossings that were identified as high-risk locations that were common for both estimation criteria. for each crossing it is shown how many top locations appear in both lists, as well as the value of mean total risk and mean empirical risk. in this list, we can notice that 60% of crossings are with road signs, and 40% are with half gates. the high-risk location list in table 8 shows that most crossings, 90%, are located on main railways in urban areas. one of the possible explanations is that urban areas experience greater volume of traffic, which can cause a higher accident rate. on the other hand, the mean maximum train speed at these 20 crossings is 100 km/h, which is significantly higher than the mean maximum speed for the whole sample (70 km/h). this confirms that the maximum train speed has a more pronounced effect on the number of injuries and deaths. table 8. list of high-risk locations based on two criteria first 20 high risk locations crossing no. km position competent railway station warning devices mean total risk mean empirical risk 10 87 20+993 batajnica pb 4.116 2.879 10 28 7+070 rakovica ds 2.220 2.495 10 94 34+694 stara pazova pb 1.123 2.502 20 22 253+700 belotince ds 1.053 2.108 20 121 74+241 pirot ds 1.032 1.990 20 276 252+523 niš ds 0.945 2.057 20 298 82+030 sr. mitrovica pb 0.668 4.238 30 27 335+818 suva morava ds 0.901 1.670 30 90 116+080 šid pb 0.831 1.573 30 164 57+306 odžaci ds 0.651 1.857 30 521 76+983 ruma ds 0.637 2.670 30 92 74+019 voganj pb 0.581 2.180 30 300 99+549 sr. mitrovica pb 0.581 2.180 30 36 94+920 velika plana ds 0.558 2.110 40 244 119+207 vrbas ds 0.854 1.354 40 72 31+037 kr. trnovče ds 0.733 1.310 40 257 78+247 palanka pb 0.615 1.294 40 96 97+785 sr. mitrovica ds 0.562 1.298 40 24 79+362 palanka pb 0.518 1.254 40 79 26+019 loz. saraoci ds 0.691 1.294 note: pb = half gates; ds = road signs; a value for a period of five years it should be noted that many of the predicted high-risk locations were not upgraded during the analysis period, suggesting that possible high-risk crossings as predicted by the model were not considered for safety intervention. models for ranking railway crossings for safety improvement 97 to assess the railway crossing for safety intervention, the serbian railways method is based on engineering judgment supplemented by simple statistical analysis of the historical accident data. we examined the original data (first 20 locations according to the highest accident frequency and accident severity). then, we compared the lists of predicted and historical highrisk locations. four crossings have been found common in both lists for accident frequency, and two crossings for accident severity. in this paper, it is asserted that high-risk locations cannot be established solely on the basis of historical accident experience. this is supported by (saccomanno et al., 2004), a longer view of accident risk is needed to reflect the expected risk over a given period of time. such estimates can be obtained only with accurate and reliable accident frequency and severity prediction models. 5. conclusion ideally, the final outcome of this work would be reducing the number or the severity of accidents at railway crossings in serbia. in order to achieve this goal, it was important to develop a model that can be applicable to the limited data set at our disposal and to estimate the influence of various parameters contained within the data. we have considered three risk models and two criteria for the identification of high-risk locations. data points used in this study, i.e. accident reports and railway crossings’ characteristics were extracted from two official data-bases containing actual events and site descriptions. prior to the modeling, we had analyzed available data in order to ensure that the data sample used was truly representative. the first considered risk model was the accident frequency model. in this model, we have found that the zip regression model produces the best fit for the data used. the second risk model we considered was also well-known in literature – the accident severity model and the multinomial logit regression analysis. both mentioned models provide useful information about the risks involved. however, our needs regarding the risk assessment required some additional quantitative parameters. a novel third model – empirical risk model was introduced in order to satisfy these requirements. two criteria for the identification and risk-ranking of the railway crossings in serbia were presented. one criterion was calculated as a product of mean accident frequency and mean accident severity. the other criterion was obtained using the empirical risk model and we suggest the name mean empirical risk for the name of this quantity. because crash frequency and severity jointly determine the casualty risk level at a railway crossing, one can alternatively predict the casualty risk level by using a bivariate count data model. to incorporate the accident severity and some of the key factors such as vehicle occupancy into a total risk model (miranda-moreno et al., 2009), the use of posterior distributions through the bayesian approach (mirandamoreno & fu, 2006; persaud et al., 1999) has been widely recommended for identification of high-risk locations. furthermore, an in-depth investigation on vehicle drivers’ behavior at individual railway crossings, which is currently being conducted by the authors, might answer the contradictory model estimation results found in this research. these are topics that are worthy of future research. kasalica et al./oper. res. eng. sci. theor. appl. 3 (3) (2020) 84-100 98 appendix analysis of the site selection criteria the sample of 745 railway crossings out of total 2,138 is located throughout the whole network of serbian railways. the railway line of major international importance through serbia (according to european agreement on main international railway lines agc) is reference line e70 (croatia)–šid–beograd–niš–dimitrovgrad– (bulgaria). on this reference line, 215 out of total of 329 railway crossings were considered. for other main lines, the numbers of included railway crossings are the following: on reference line e85 (hungary)–subotica–beograd–preševo– (macedonia) 39 out of 68; on intermediate line e79 beograd–vrbnica–(montenegro) 11 out of 30; on e66 intermediate line beograd–pančevo–vršac–(romania) 25 out of 75; on supplementary line lapovo–kraljevo–kosovo polje 42 out of 78. on other supplementary railway lines, 413 out of remaining 1,558 railway crossings were considered. therefore, railway crossings of national and local importance, which are located both in urban and rural areas, were included. the sample of 745 railway crossings is composed of 231 (31%) railway crossings on which accidents occurred in 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(2008). regression models for count data in r. journal of statistical software, 27(8), 1-25. © 2020 by the authors. submitted for possible open access publication under the terms and conditions of the creative commons attribution (cc by) license (http://creativecommons.org/licenses/by/4.0/). models for ranking railway crossings sandra kasalica 1*, marko obradović 2, aleksandar blagojević 1, dušan jeremić 1, milivoje vuković 3 1. introduction 2. data source and description 2.1. inventory data set 2.2. accident occurrence data 3. developed models regarding crossing accidents 3.1. accident frequency model 3.2. accident severity model 4. high-risk location analysis 5. conclusion appendix analysis of the site selection criteria references operational research in engineering sciences: theory and applications vol. 4, issue 1, 2021, pp. 67-81 issn: 2620-1607 eissn: 2620-1747 doi: https://doi.org/10.31181/oresta2040127s * corresponding author. nikolasimicva@hotmail.com (n. simić), miladin@kg.ac.rs (m.stefanović), pgoran@masfak.ni.ac.rs (g.petrović), aleksandar.stankovic@masfak.ni.ac.rs (a.stanković) use of the risk analysis approach in the serbian army integration process against covid-19 nikola simić*1, miladin stefanović2, goran petrović3, aleksandar stanković3 1 the serbian army, logistics training centre, kruševac, serbia 2 faculty of engineering, university of kragujevac, serbia 3 faculty of mechanical engineering, university of niš, serbia received: 29 september 2020 accepted: 03 january 2021 published: 23 february 2021 research paper abstract: current developments have contributed to organisations paying increasing attention to protecting resources, employee safety, and applying quality products and services. there is a need for increasing the application of standards that define the way of managing quality, safety at work, risk, and many others. one such organisation is the serbian army, a complex centralised system that requires integrating these standards, and often stricter, in all fields of its activities. the current situation in the world, and therefore in serbia, is sufficient motivation for the project provided by this paper. this project aims to show the integration of risk management systems and occupational safety systems, through the level of protection and exposure of members of the army to the virus infection covid-19 during the implementation of emergency tasks, by defining risks and proposing additional measures to reduce the level of risk and increase the protection of military personnel. keywords: virus infection, risk, safety management, emergencies, serbian army 1. introduction the development of the most critical events in the 21st century has confirmed that the survival of nations and citizens will increasingly depend on the security of the essential functions of society. the ability to protect the population, ensure the functioning of government and civil society institutions, maintain critical infrastructure, and the democratic principles of functioning of state institutions are under enormous pressure in the face of crises. as no crisis is an isolated event "per se," awareness and readiness to counter non-military threats are focused on analysing complex security policy fields based on different management systems, which imposes the need for so-called integrated management systems (ims). because of this complexity, the identification and analysis of threats usually mailto:nikolasimicva@hotmail.com mailto:miladin@kg.ac.rs mailto:pgoran@masfak.ni.ac.rs mailto:aleksandar.stankovic@masfak.ni.ac.rs simić, et al., /oper. res. eng. sci. theor. appl. 4 (1) (2021) 67-81 68 involve assessing multiple risks and studying scenarios of a limited number of situations identified as potentially risky or catastrophic (jørgensen et al., 2006). at present, risk assessments and crisis management concepts differ significantly in many countries and are conducted in the broader context of risk and crisis management. the primary and indisputable responsibility for protecting citizens and the fundamental values of society lies with the states. by improving awareness and understanding of the risks faced by states, decision-makers have a better position to agree on preventive measures to be taken and to prepare to avoid the most severe consequences of natural and human-made disasters. in the context of the responsibility of the state to prevent and resolve the effects of crises, special responsibility lies with the army, with an assessment of the comparative advantage of the military over other state bodies, but also the functional needs and opportunities for an effective response to non-military security threats (karović et al., 2010). one such security threat is certainly the pandemic caused by the covid-19 virus infection. it represents a new type of "enemy" that the serbian army has not yet encountered in its history. therefore, this research becomes more exciting and encourages and motivates further courses of study. the analysis of various scenarios, which represent the core of the study, is focused on determining all assumptions, possibilities, risks, and prospects for the use of units of the serbian army, based on risk assessment, on showing the level of exposure to viral infection in military missions. as a result of this project, the preparedness, level of exposure, and protection of serbian army members' are highlighted, and shortcomings are spotted. possible ways are considered for further suppression and security, while this paper gives new additional measures of security and safety of members in some future similar non-military threats. 2. covid-19 review and application of the serbian army in non-military security threats through swot analysis covid-19 is a disease caused by a coronavirus. coronaviruses are viruses that circulate among animals, but some of them can spread to humans. after they pass from animal to human, humans can distribute viruses among themselves. for example, the coronavirus of the respiratory syndrome sars originates from the viverridae, an animal from the order of beasts related to cats. discovered in china in 2003, it is genetically closely related to the covid-19 virus, and the two viruses have similar characteristics. in eight months, 33 countries reported more than 8,000 cases of sars. then one in ten infected people died of sars. covid-19 is sars-cov-2. it was detected in china, the city of wuhan, hubei province, at the end of 2019, the first case on november 17, 2019. year (ma josephina, 2020), while the first case in the territory of serbia arose on march 6, 2020. year (government of serbia, 2020). it is a new strain of coronavirus that has not been detected in humans before. although the virus originates from animals, it now spreads from person to person (human-to-human transmission). the virus is mainly transmitted by droplets when sneezing and coughing. preliminary research indicates that the average incubation period is 5-6 days, with a maximum of up to 14 days (chu et al., 2020). although people are most contagious when they have symptoms (similar to seasonal flu symptoms fever, sneezing, cough, muscle aches, fatigue). there are indications that some people can transmit the virus even though they have no signs or before use of the risk analysis approach n the serbian army integration process against covid-19 69 symptoms appear, which is not uncommon with other viral infections. in severe cases, severe pneumonia, acute shortness of breath syndrome, sepsis, and septic shock occur, which can cause the patient's death. older people and people with chronic diseases (such as high blood pressure, heart disease, diabetes, liver disorders, and respiratory diseases) have a higher risk of developing more severe forms of this disease. however, the exposure to this infection is not decreased for emergency and state services, including members of the serbian army. the serbian army is an organised armed force that defends the country from armed threats from outside and performs other missions and tasks, following the constitution, law, and principles of international law that regulate the use of force (law on the serbian army, 2019). the president of the republic or the minister of defense, upon the authorisation of the president of the republic, may decide that the serbian army shall assist the competent state body, i.e., organisation, the body of autonomous provinces and local self-government units, at their request, for protection of life and safety of people and property, for other reasons determined by law (official gazette of the republic of serbia, 2019). after the war in the 1990s, the serbian army actively participated in implementing the third mission of the army, i.e., assisted civilian authorities in the event of natural disasters, technicaltechnological and other accidents. the military usage for civilian purposes could be noticed during firefighting actions on several occasions in recent years, then during the floods of 2014 and 2019, and during the migrant crisis to help civilian structures conduct migrants through the territory serbia. however, the situation that caused the second state of emergency in the country in the 21st century after the prime minister's assassination in 2003 showed that the modern army had not encountered such a threat so far. the last time army was used in such a case, former jna, in this territory was in 1972, during the smallpox epidemic "variola vera," on securing temporary hospitals. the necessary measures applied by jna members were protective masks and steeled discipline, and the intensification of hygiene (radovanovic, 2017). the situation with the disease at that time did not seem to bring any experience, so the serbian army entered the fight against covid-19 practically unprepared. until the declaration of emergency on march 15, 2020, activities and tasks in the serbian army were going according to plan (official gazette of the republic of serbia, 2020). table 1. swot analysis strengths – s weaknesses w the medical and health care system is gradually improving the military medical academy. the covid-19 epidemic has spread to many regions in a short period. comprehensive progress of the military health system in terms of taking measures. (blumenthal et al., 2020). rumours of wider disinformation rapid and efficient cooperation of joint prevention and control of the military and civilian structures. (blumenthal et al., 2020). serbia's population density is 98.1 in / km2 lack of aid and labour supplies (ebrahim, 2020) lack of equipment and accommodation (rimmer, 2020) the public is upset and lacks awareness. simić, et al., /oper. res. eng. sci. theor. appl. 4 (1) (2021) 67-81 70 namely, for such a case of non-military security threat, there is no plan in the army. all forces are focused on helping civilian structures in extinguishing fires, assistance during floods, and select units of atomic-biological-chemical defence that are engaged in case of cbrn accident. in a way, the unpreparedness for "fighting" against covid-19 is understandable. hence the solution to why lessons and experiences were not learned from the epidemic of the 1970s. concerning the previous, swot analysis presents the situations, which refers to the assessment of various strengths (s), weaknesses (w), opportunities (o), threats (t), and other factors that affect a particular topic. it comprehensively, systematically, and accurately describes the scenario in which the issue is situated. this helps to formulate appropriate strategies, plans, and countermeasures, based on the results of the assessment (jasiulewicz-kaczmarek, 2016). this method can be used to identify favourable and unfavourable factors and conditions, target current problems, identify challenges and threats, and formulate strategic decision-making plans. this swot analysis (table 1) of covid-19 is based on the experience of the reaction to the sars epidemic from 2003, and the data as a basis are taken from the annual health statistics china for 2019 and adjusted for r. of serbia (china health statistics yearbook, 2019). based on the presented swot analysis, it can be concluded that the defence forces are extraordinary mild and that the weaknesses are too many. it can also be added that the serbian army is spread over the entire territory. due to the realisation of tasks, there is a need to connect personnel on specific charges, which was the case during the formation of a temporary hospital in the military institution "morovic." the lack of protective equipment can be singled out as a fundamental problem because with the existing resources, members are not adequately protected under regulations (eg. surgical masks in pharmacies do not have a long-lasting effect; according to some estimates, only 2-3 hours (chu et al., 2020). also, the chances that may only arise after a pandemic are reflected inexperience, not allowing the same omissions as during the epidemic of the 70s. as for threats, the most dangerous is related to the army members who are in an unenviable position, given their constant engagements and returns to their families after them. there is an increased risk of exposure to loved ones, regardless of government measures and curfews. based on the analysis, the fight against this type of "enemy" is shown in the following text. so far, the serbian army's application in the implementation of the third mission has shown that members of the army have not encountered this type of "enemy." role insecurity is one of the daily tasks of members of the army. during the opportunities – o threats t new research covid-19 (salvatore et al., 2020) impact on the daily life, work, and psychology of employees (barnes & sax, 2020) further improvement and inspection of the health system in the army (blumenthal et al., 2020) impact on the national economy (salvatore et al., 2020) opportunities for education for infectious diseases and gaining new experiences in combat (blumenthal et al., 2020) possible virus carriers to their families use of the risk analysis approach n the serbian army integration process against covid-19 71 security, standardised equipment is used following standardisation documents that are even stricter than management systems' standards. the standardisation documents are the standards of defence of the republic of serbia (sors), product quality regulations (pkp), and technical regulations in the field of protection (tpo) (official military gazette, 2018). the defence standard is a document that refers to specific items for the needs of defence and contains technical specifications and criteria that ensure that the material, products, processes, and services correspond to the purpose. the product quality regulation is a document that contains data important for quality in research, development, and production. at the same time, the tpo is a document related to facilities, devices, and plants for other processes, products, and services in the field of defence (official military gazette, 2018). the standards of defense of the republic of serbia (sors), formerly the standards of national defense (sno), are applied to every means, weapon, equipment in use, like the ones in the following figures. this case study will present three cases in the suppression of covid-19, as follows: provision of civilian hospitals, health centres, gerontology centres, and other public facilities of importance. during security, members were exposed to contact with staff employed in health facilities, controlled the entry and exit of patients, and performed their identification, as well as the passing of motor vehicles. establishment of temporary "covid" hospitals in sports halls and the military institution "morovic." the engagement of members in the formation of temporary hospitals was realised in all significant hotspots. they showed the most significant efforts during the construction of the hospital at the fair in belgrade. with a minimum of equipment (surgical mask and gloves), the assessment was that the members were protected during this task's realisation. figure 1. a member of the army during the construction of the covid hospital specialised units of the army realised disinfection of public areas and buildings. the members of the cbrn units had the best protection, but also the most challenging task, because by the nature of their work, they were simić, et al., /oper. res. eng. sci. theor. appl. 4 (1) (2021) 67-81 72 most exposed to chemical substances, and they were equipped with overalls, unique protective masks, and gloves at all times. figure 2. a member of the cbrn service on the task of disinfection 3. the methodological framework of the research research has the character of a theoretical-empirical procedure, where the design and implementation combine theoretical methods of scientific research and empirical methods. based on data from foreign and domestic literature, the descriptive method was used to present the viral pandemic situation as comprehensively as possible, both in the world and in the republic of serbia. when comparing the cases in which the army was engaged, a comparative analysis was used. the inductive-deductive method was used to draw lessons from foreign countries' experiences, primarily china and russia. when generalising certain phenomena related to covid-19 and the serbian army's use, the analytical-synthetic method was applied. the scientific significance of this project work lies in the new theoretical approach in defining the army's role in combating similar non-military security threats and assisting decision-makers with the advantages of this research; those are new adequate measures in case of possible recurrence. 4. case study so far, the serbian army's application has shown that members of the army have not encountered this type of "enemy." this case study will compare the levels of risk of exposure of members of the serbian army to covid 19 infection in three cases, by multicriteria decision using the topsis method, where issues are defined as options (a) and risks (k), after which alternatives will be ranked. appropriate conclusions will be drawn for better protection of employees during the performance of duties in these cases: use of the risk analysis approach n the serbian army integration process against covid-19 73 case 1: securing civilian hospitals, health centres, gerontology centres, and other critical public facilities. during security, members were exposed to contact with staff employed in health facilities, controlled the entry and exit of patients, and performed their identification, as well as the passing of motor vehicles. case 2: establishment of temporary "covid" hospitals in sports halls and the military institution "morović." the engagement of members in the formation of temporary hospitals was realised in all significant hotspots. they showed the most significant efforts during the construction of the hospital at the fair in belgrade. with a minimum of equipment (surgical mask and gloves), the assessment was that the members were protected during this task's realisation. case 3: disinfection of public areas and buildings carried out by specialised military units. the members of the cbrn units had the best protection, but also the most challenging task, because by the nature of their work, they were most exposed to chemical substances, and they were equipped with overalls, unique protective masks, and gloves at all times. after defining the cases and gathering information on the dangers posed by a viral infection, a risk assessment follows. one of the simplest methods used is to determine the level of risk. three levels of severity of consequences and three levels of probability of occurrence are defined, and then the level of risk is specified based on these data (table 2). table 2. defining risk levels consequences probability slightly dangerous dangerous extremely dangerous probable event medium risk high risk very high risk rare event low risk medium risk high risk sporadic event very low risk low risk medium risk based on the presented method of risk assessment and perception of the situation in the field, the risk assessment of the study case takes the probability of events: probable event, and based on the table, we see the consequences of events through a medium, high, and very high risk. a rare event is not taken as a reference, and also, the situation is not harmless, so a sporadic occurrence and a shallow risk are excluded (čerepnalkovska, 2016). based on the above, the risks and levels of risk are defined, which are shown in table 3: simić, et al., /oper. res. eng. sci. theor. appl. 4 (1) (2021) 67-81 74 table 3. defining risks and levels weighting coefficients risk medium risk high risk very high risk risk 1 level of protection of members of the armed forces 1 3 5 risk 2 possibility of infection risk 3 possibility of possible transmission to other members of the armed forces risk 4 possibility of possible transmission to their families risk 5 presence of chemicals risk 6 possibility of unwanted contact and conflict explanation of the level of risk (weighting coefficients) of the first case: the protection of members of the armed forces was assessed as "very high risk" because members use only surgical masks n95 or am-1002 and surgical gloves. the possibility of infection was assessed as "high risk" because members are exposed to potential patients at the entrance to public buildings, keeping a distance of 2 meters but with a personal identification check that requires a reduction in the prescribed space. the possibility of possible transmission was assessed as "very high risk" because members come to work after completing the task and then go to their homes. there is a possibility that they are potentially infected. persons on this task are not exposed to excessive effects of disinfectant chemicals. the possibility of unwanted contact and conflict was assessed as "high risk" because there are situations in which potentially infected people refused to cooperate and were brought to the brink of physical confrontation. explanation of the level of risk (weighting coefficients) of the second case: the level of protection of members of the armed forces was assessed as "very high risk" because members use only a surgical mask, improvised mask, and surgical gloves or work gloves (figure 1). the possibility of infection was assessed as "high risk" because the members are at a distance of fewer than 2 meters and a large concentration of people in one place. a possible transfer was assessed as "high risk" because members remain in contact after the task, during the rest and preparation for the next job but do not come into contact with their families. persons on this task are exposed to a specific effect of chemicals during the disinfection of established hospitals, and this risk is assessed as "high risk." the possibility of unwanted contact and conflict was assessed as "medium risk" because there are no other persons than members of the armed forces to implement this task. use of the risk analysis approach n the serbian army integration process against covid-19 75 explanation of the level of risk (weighting coefficients) of the third case: the level of protection of cbrn members was assessed as "medium risk" because they use special protective equipment for particular purposes (figure 2). the possibility of infection is assessed as "high risk" because members do not come into direct contact with the infected or potentially infected. a possible transfer was assessed as "high risk" because they are in constant contact with each other and go to their families after work. people on this task are most exposed to chemicals during disinfection because in addition to the use of chemicals, it is necessary to do the same, and this risk is assessed as "very high risk." the possibility of unwanted contact and conflict was assessed as "medium risk" because there are no persons other than cbrn members to implement this task. 4.1. technique for order preference by similarity to an ideal solution the technique for the order preference by similarity to ideal solution (topsis) was introduced by hwang and yoon (1981). the standard topsis method is based on the concept that the best alternative should have the shortest euclidian distance from the ideal solution, and at the same time, the farthest from the anti-ideal solution. topsis method can be implemented using the following steps: step 1: method starts with determination of a decision matrix x = (xij)m x n, in which element xij indicates the performance of alternative ai when it is evaluated in terms of decision criterion cj, (for i = 1, 2, 3,..., m and j = 1, 2, 3,..., n): c c 2 c n 1 x = xij = a  x x ... x  1  11 12 1n  ; a x x ... x  21 22 2n  2   a  x x ... x   m1 m2 mn  m step 2: determine the normalized decision matrix which elements are rij: x rij = ij , m  ij  x 2 i=1 step 3: obtain the weighted normalized decision matrix whose elements are vij by multiplying each column j of the normalized matrix by its associated weight wj: vij = rij  w j , (3) step 4: determine the positive ideal and the negative ideal solutions: (4) (1) (2) simić, et al., /oper. res. eng. sci. theor. appl. 4 (1) (2021) 67-81 76 where b and c are associated with the maximisation and minimisation criteria sets, respectively. step 5: calculate the separation measures (euclidean metric) from the positive ideal solution and the perfect negative solution. the separation of each alternative from the perfect positive solution is given as: + + ) 2 n si = (vij −v j j=1 the separation of each alternative from the negative ideal solution is given as: − − ) 2 . n si= (vij −v j j=1 step 6: calculate the relative closeness of the i-th alternative ai to the positive ideal solution: 𝑃𝑖 = 𝑆𝑖 − 𝑆𝑖 + + 𝑆𝑖 − the relative closeness pi can have values between (0, 1), whereby pi = 0 represents a negative ideal solution, while pi = 1 stands for a perfect positive solution. according to pi values, the alternatives can be ranked. the best option has the highest value, pi, because it is the closest to the positive ideal solution. since the last part of the paper defines alternatives (a) and criteria (k), it is necessary to determine the weights of the bars (risk), based on an exchange of opinions with occupational safety officers, for the application of the topsis method, according to the following: for k1 0.4 is considered the most important because it is the protection of human lives; for k2 0.2 presented as an important criterion because it entails other risks and possibilities of spreading the infection; for k3 0.1 presented as a medium-important criterion because there is a possibility of spreading the disease to military circles; for k4 0.15 presented as an essential criterion because employees, finishing their work, can spread the disease to their family members; for k5 0.1 it is considered not very important because only select units of the army work with chemicals; for k6 0.05 presented as the least important criterion because the cases are individual. (5) (6) (7) use of the risk analysis approach n the serbian army integration process against covid-19 77 figure 3. defining risk levels by alternatives the first step is the initial table-matrix of initial data with the assignment of coefficients, determination of values that are minimised and maximised, and assignment of weight values, which is shown in table 4. table 4. assignment of values and determination of max and min and weight values criteria k1 k2 k3 k4 k5 k6 0.4 0.2 0.1 0.15 0.1 0.05 alternatives min min min min min min a1 5 5 3 1 3 1 a2 3 5 4 2 3 3 a3 1 3 5 3 5 5 the values of the criteria are determined, where maximised-rewrite and minimised-convert to the max, as shown in table 5: table 5. criterion values obtained after minimisation and maximisation criteria k1 k2 k3 k4 k5 k6 0.4 0.2 0.1 0.15 0.1 0.05 alternatives min min min min min min a1 0 0 2 4 2 4 a2 2 0 1 3 2 2 a3 4 2 0 2 0 0 the next step is to determine the norm and to form a normalised matrix. the determination of weighted values follows this, and the obtained data are shown in table 6: simić, et al., /oper. res. eng. sci. theor. appl. 4 (1) (2021) 67-81 78 table 6. weighted values criteria k1 k2 k3 k4 k5 k6 0.4 0.2 0.1 0.15 0.1 0.05 alternatives min min min min min min a1 0 0 0.089 0.111 0.070 0.044 a2 0.178 0 0.044 0.083 0.070 0.022 a3 0.357 0.2 0 0.055 0 0 best max 0.357 0.2 0.089 0.111 0.070 0.044 best min 0 0 0 0.055 0 0 finally, the distance is calculated according to the shown values, and the alternatives are ranked, as shown in table 7. table 7. the final ranking of alternatives criteria s+ s the similarity to the solution rank a1 0.1345 a1 0.40987 a1 0.7528 1 a2 0.2006 a2 0.27436 a2 0.5775 2 a3 0.4098 a3 0.13454 a3 0.2471 3 based on the final rank of alternatives shown in table 7, it is concluded that members of the serbian army engaged in protecting hospitals and public institutions (alternative 1) were most exposed to covid-19 infection. the risk of their disease is the most significant, primarily due to daily exposure to potentially infected persons. in contrast, the lowest possibility of infection was present in members of the cbrn service (alternative 3) because they possessed the highest protection level. members of the army engaged in the formation of "covid" hospitals were ranked second because there was no one in their presence except themselves. a graphical representation of the final rank of alternatives is shown in figure 4. figure 4. graphical representation of the final rank of alternatives by the topsis method use of the risk analysis approach n the serbian army integration process against covid-19 79 5. conclusion this research showed the level of protection and risk of members of the serbian army. which were engaged in three cases, with some new security, which motivated the authors to examine the level of maximum risk exposure and identifies gaps and shortcomings, and proposes additional measures based on the research results. based on the case study and the application of multicriteria decision-making using the topsis method, the results showed that military members are most exposed to the possibility of contracting covid-19 virus infection, primarily due to low levels of protection and contact with potentially ill persons. cbrn members serve, thanks to their protective equipment and almost minimal contact with potentially infected people, they are the safest from the effects of a viral infection. members in the second case who were engaged in the formation of "covid" hospitals were assessed with a medium level of risk due to their spatial distribution in places where no viral agents were present. based on the research and case study, measures can be concluded and proposed to further prevent the spread of infection according to the following: ▪ provide sufficient quantities of surgical masks to ensure the condition of replacement every two hours, ▪ at the entrance to human accommodation (for pedestrians and vehicles), install and maintain disinfection barriers in the complexes (naclo, pinosteril 200, chlor, alcohol 70%), ▪ regularly disinfect the premises for housing and dining of people, ▪ perform regular personal and collective hygiene and accommodation and eating people, i.e., before eating to control the personal hygiene of all persons, ▪ during the execution of hospital security tasks, avoid close contacts with persons who show signs of acute respiratory diseases and strictly adhere to all prescribed measures, ▪ indirect communication with the civilian population, provide a distance of at least 2 meters, ▪ measure the members' temperature before performing the task, and send it to the ambulance if it occurs. ▪ use protective equipment (gloves and visor) when making the disinfectant mixture, ▪ after engaging in tasks, disinfect personnel and equipment. experiences that can be gained during this project's development are that the approach to the problem must be more serious and meaningful. it is necessary to look retroactively and see that preparation didn't exist for this type of "fight" and that for some future situations, all the people should be in the machine in a state of emergency. acknowledgement this research was financially supported by the ministry of education, science and technological development of serbia. simić, et al., /oper. res. eng. sci. theor. appl. 4 (1) (2021) 67-81 80 references barnes, m., sax p. 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(2016). a model for improving an integrated risk-based management system, faculty of technical sciences, university of novi sad, 26-31. © 2021 by the authors. it was submitted for possible open access publication under the terms and conditions of the creative commons attribution (cc by) license (http://creativecommons.org/licenses/by/4.0/). https://dx.doi.org/10.1016%2fs2352-4642(20)30235-2 use of the risk analysis approach in the serbian army integration process against covid-19 nikola simić*1, miladin stefanović2, goran petrović3, aleksandar stanković3 1. introduction 2. covid-19 review and application of the serbian army in non-military security threats through swot analysis 3. the methodological framework of the research 4. case study 4.1. technique for order preference by similarity to an ideal solution references plane thermoelastic waves in infinite half-space caused operational research in engineering sciences: theory and applications vol. 1, issue 1, 2018, pp. 76-90 issn: 2620-1607 eissn: 2620-1747 doi: https://doi.org/10.31181/oresta19012010175p * corresponding author e-mail addresses: adispuska@yahoo.com (a. puška), a.maksimovic22@gmail.com (a. maksimović), ilija.stojanovic@teol.net (i. stojanović) improving organizational learning by sharing information through innovative supply chain in agro-food companies from bosnia and herzegovina adis puška*, aleksandar maksimović, ilija stojanović institute for scientific research and development brcko district bosnia and herzegovina received: 21 october 2018 accepted: 02 december 2018 published: 19 december 2018 original scientific paper abstract: innovation is essential for long-term success in business and companies need to develop an innovative supply chain to respond to environmental and market challenges. it is necessary to develop knowledge through organizational learning in order to strengthen the ability of companies to innovate. an innovative supply chain is the basis for developing innovation in companies. to improve its market position companies should continuously receive high quality information from participants in the supply chain by sharing information. the complexity of relationships within supply chain affecting organizational learning is the subject of this study. we conducted an empirical study focusing our attention on agro-food companies in bosnia and herzegovina. a questionnaire was used as a data collection tool applying random systematic sampling and a total of 159 companies took part in this study. the empirical findings showed that sharing of information has a significant linkage with an innovative supply chain, but only in establishing partnerships with customers. we confirmed that an innovative supply chain is essential for development of organizational learning and agile supply chain. the findings could assist the managers of agro-food companies in bosnia and herzegovina to improve their business. this study provides guidance for improving business using supply chains. key words: sharing information, innovative supply chain, organizational learning, buyer-supplier relationships, structural equation model. improving organizational learning by sharing information through innovative supply chain in agro-food companies from bosnia and herzegovina 77 1. introduction innovation is a basis for creating an innovative supply chain and it is very important for success of small and large enterprises (bag, 2018). in order to implement an innovative supply chain any company should be oriented to set up strategic directions that will promote innovation in their business. an innovative supply chain also requires proper communication with suppliers and buyers. suppliers are an important element of an innovative supply chain because they are the source of innovative ideas and key technologies (wang, et al, 2011). the key segments in every supply chain are customers. if customers are not satisfied with the products, they will not buy them. customers are the driving force of innovative activities in the company. they are the reasons why companies innovates their business and products. it is necessary for customers to receive new enhanced products that are developed according to their requirements (wagner and bode, 2014). innovation in today’s dimensional business environment requires complex knowledge (bag, 2018). and scholars emphasize the key role of innovation and organizational learning in improving the company's competitive advantage (jiménezjiménez & sanz-valle, 2011). companies cooperate with suppliers in research and development, in production, and collect information from suppliers (kawai, et al, 2013). in cooperation with suppliers, companies innovate products to meet the increasing demands of customers. in this process information sharing is a key activity. through the establishment of a partnership relationship, companies receive information that helps them to reduce business uncertainty (tai & ho, 2010). the company receives from the customer the necessary information what they want and what are their needs. thanks to this information, the company can adapt to these needs and offer new or customized products. in these processes the exchange of information with partners becomes a precondition for developing innovative business in the company. when exchanging information with key partners, not only information is exchanged but also data and knowledge (kembro & näslund, 2014). through such information exchange, companies increase their organizational skills. this study is focused on complex interactions within supply chain. we especially analysed the way in which information is exchanged through buyersupplier relationships on an innovative supply chain, and how innovative supply chain acts on agility of the supply chain and organizational learning. this relationship was observed on the example of agro-food companies in bosnia and herzegovina. the importance of this paper can be found in the fact that it provides necessary information about how the buyer-supplier relationships are important for development of innovative supply chains and how influential on innovative supply chain are suppliers or customers through the exchange of timely information. we examined whether agro-food companies in bosnia and herzegovina how exchange information with customers and suppliers, and how they use this information when establishing an innovative supply chain in order to improve their organizational knowledge. understanding the way in which information is exchanged by developing an innovative supply chain and influencing organizational learning is the main significance of this study. based on the survey, we explored how companies use information sharing in business consolidation. the findings enable identification of a. puška, et al./oper. res. eng. sci. theor. appl. 1 (1) (2018) 76-90 78 major recommendations for companies in order to improve their competitiveness and market performance. the results obtained will assist managers of agro-food companies in bosnia and herzegovina to recognize the importance of sharing information in the operations of these companies. furthermore, the role of suppliers and customers in the sharing of information will be considered. on the basis of this finding, managers can learn how to improve their cooperation with them in order to improve the quality of information and accordingly to make supply chain more innovative. managers will also be given the answer whether an innovative supply chain is more agile and whether it increases the knowledge of the organization. based on this, the following research objectives are set: 1. to explore the application of information sharing and partner relationships with the buyers and suppliers to establish an innovative supply chain; 2. to study the impact of an innovative supply chain on agility and organizational learning in agro-food companies in bosnia and herzegovina; 3. to test the proposed model and examine the direct and indirect effects used in the model. 2. literature review we booked this section to present our research model, hypotheses and theoretical framework of the study. within the research model, several constructors were used: information sharing, buyer-supplier relationships, an innovative supply chain, an agile supply chain, and organizational learning. the mentioned constructors are explained in this part of the paper. this study highlighted the importance of sharing information in establishing partnerships and observed how sharing information and relationships with customers and suppliers affect the functioning of an innovative supply chain. we examined whether the sharing of information influences an innovative supply chain, or only in the course of establishing partnership relationships, innovation of the supply chain is also established. the study examined the individual impact of partner relationships with buyers and suppliers on the establishment of an innovative supply chain. we considered direct and indirect impacts of information sharing on an innovative supply chain. the findings will enable to understand these relationships in agro-food companies in order to improve an innovative supply chain by sharing information. the second part of the model explored the impact of an innovative supply chain on supply chain agility and organizational learning. this established relationship made it possible to understand whether an innovative supply chain contributes in improving speed of supply chain operations and whether it contributes to increasing company knowledge. this model will examine, in two different parts, the complex relations that prevail in agro-food companies in bosnia and herzegovina. the model represents a new perspective on the complexity of relationships within the supply chain. in order to carry out this study, the following steps were set in this study: 1. establishing the model based on the research constructors; improving organizational learning by sharing information through innovative supply chain in agro-food companies from bosnia and herzegovina 79 2. investigating relevant literature and set up the questionnaire; 3. passing the questionnaire and collecting data from agro-food companies in bosnia and herzegovina; 4. processing data and testing the model and hypotheses of this study; 5. presenting the findings; 6. highlighting the most important results of this study and give recommendations for future research. 2.1. sharing information one of the most important segments of partnership is the exchange of information. the exchange of information is exchange of important information between partners in the supply chain (lee & ha, 2018). during establishment of collaboration within supply chain, sharing information is an important dimension and is in the focus of all partners within the supply chain (chen, et al, 2011). during the exchange of information is necessary to implement two-way communication between partners. in doing so, not only information is exchanged, but also knowledge among partners. the exchange of information between the buyer and the supplier is of essential interest in building long-term trust based relationships (eckerd & hill, 2012). when exchanging information, it is crucial to determine the level of information sharing and the quality of information being exchanged. with true and precise information companies can respond to market changes. the efficiency of information sharing is not limited to the question "whether the information is shared or not," but also include the question "what kind of information is shared" and "when and how information is shared" (li et al., 2014). when sharing information, partners in the supply chain develop mutual trust and belief that their partner will not break the deal by unethical behavior (eckerd & hill, 2012). with increasing trust among partners, reduction of transaction costs and a greater exchange of information between partners occur (li, et al, 2017). trust among partners grows with the development of partner relationships (rogers & fells, 2018). it is therefore important to develop a mutual relationship between partners based on trust. with the exchange of information in the supply chain, trust among partners is raised. higher exchange reduces risk and uncertainty and increases the level of trust in relationships (nyaga, et al, 2010). based on all of the above, the following hypotheses of research are set: h1: sharing information has a significant positive impact on partner relationships with the suppliers h2: sharing information has a significant positive impact on partner relationships with customers h3: sharing information has a significant positive impact on innovativeness of supply chain. 2.2. buyer-supplier relationship researchers noted that partnerships with suppliers and customers have a role in achieving business results (faraz, et al, 2018). zacharia et al. (2011) emphasized a. puška, et al./oper. res. eng. sci. theor. appl. 1 (1) (2018) 76-90 80 that managing relationships with customer and suppliers is essential for success of the supply chain. the effects gained partner relationship for suppliers and customers are two-folded: the affective basis where the supplier is devoted to the customer, and the cognitive basis where the supplier acquires enough knowledge through the exchange of information to improve performance (shou, et al, 2013). it is therefore important that each company develops its buyer-supplier relationships. companies are ready to establish strong partnerships with key customers and suppliers. strong partnership is an opportunity to increase the success of partners rather than they work separately (faraz, et al, 2018). in order to achieve desired benefits it is necessary to build a strong relationship with key partners in the supply chain. the most important key partners for the company's business are customers and suppliers. chen & wu (2010) showed that the transaction costs of the company can be reduced by strengthening cooperation with customers and suppliers. in order to reduce production costs companies transfer their business processes through outsourcing to suppliers, thus the ability to manage relationships with suppliers becomes very important (faraz, et al, 2018). furthermore, in order to improve product's quality and other business parameters such as costs and delivery times, it is necessary to have an efficient and capable supplier (joshi, et al, 2016). during the establishment of relations communication, information sharing and joint activities facilitate knowledge transfer and assist suppliers to improve their innovation performance (kim, et al, 2017). having this in mind we set up the following hypotheses: h4: supplier relationship has a significant positive impact on innovativeness of supply chain. h5: customer relationship has a significant positive impact on innovativeness of supply chain. 2.3. innovative supply chain in order to offer new and more diversified products to customers, it is necessary to innovate in production and business processes (joshi, et al, 2016). innovation assists for companies to face with turbulent environment and it is a main driver of long-term success in the business (jiménez-jiménez & sanz-valle, 2011). companies strive to adopt technological innovations that should deliver better business results. without innovation, companies are not able to make adaptation to change. innovations trigger changes in the environment. it is necessary to build an innovative supply chain in the company. the main elements of an innovative supply chain are: supply chain of business processes, supply chain structure network, and supply chain technology (arlbjorn, et al, 2011). those companies oriented to build an innovative supply chain need to incorporate innovation in all processes of the company to meet the demands of the market. furthermore, an innovative supply chain needs to be based on continuous improvements. for establishing innovative supply chain, it is necessary to include suppliers and customers. suppliers are the source of innovative ideas and key technologies (wang, et al, 2011), while customers are the drivers of innovative activities in the company. in order to respond to customer demands, it is necessary to provide new enhanced products that have been developed according to these requirements (wagner & bode, 2014). by developing innovative supply chain, companies have a more flexible and faster response to the improving organizational learning by sharing information through innovative supply chain in agro-food companies from bosnia and herzegovina 81 demands placed on the market. having this in mind, the following hypotheses are posed in this study: h6: innovative supply chain has a significant positive impact on agile supply chain. h7: innovative supply chain has a significant positive impact on organizational learning. 2.4. agility agile supply chain is considered a key factor of success in the market. it allows companies to be more sensitive to signals on the market (chan, et al, 2017). the concept of agility was introduced as a means by which the company adjusts to changes in the market (gligor, et al, 2015). agility should be applied when demand is unstable and customer demands are complex and varied. the concept of an agile supply chain has been introduced due to the complexity of the market. agility is a mechanism that enables the company to establish a fast and flexible supply chain in terms of customizing customer requirements and market changes. an agile supply chain is defined as a strategic capability that enables the company to quickly feel and react to internal and external uncertainty through the effective integration of supply chain relationships (fayezi, et al, 2015). in order to create an agile supply chain it is necessary to have developed internal and external integrations in the company. internal and external integration affects the company's ability to introduce agility in the supply chain (fayezi, et al, 2016). it is therefore necessary to achieve synergy of different forms of flexibility from all sides in the supply chain to empower the company to respond effectively to a highly volatile marketplace (chan, et al, 2017). in order to improve the agility of the supply chain, it is necessary to apply company integrations that are accompanied by organizational learning (braunscheidel & suresh, 2009). based on this, the following hypothesis is posed in this study: h8: agile supply chain has a significant positive impact on organizational learning. 2.5. organizational learning organizational learning is a process that develops new knowledge through access to common experiences of people in the company and has the potential to influence the behavior of employees and improve the ability of companies (jiménezjiménez & sanz-valle, 2011). for the company, it is very important to create new competencies to deal with changes in the market and to adapt to the requirements of customers. with new knowledge, the company builds a competitive advantage. organizational learning can strengthen the company's ability to identify opportunities and seek new approaches to deal with changes in the environment. based on this, organizational learning is seen as the basis for achieving sustainable competitive advantage and for improving the efficiency of the enterprise (sanz-valle, et al, 2011). the basic assumption is that organizational learning plays a key role and enables companies to achieve speed and flexibility in the innovation process. organizational learning and innovation relate positively to each other (jiménezjiménez & sanz-valle, 2011). organizing learning contributes to improving company a. puška, et al./oper. res. eng. sci. theor. appl. 1 (1) (2018) 76-90 82 performance, competitiveness of the company, innovative activities, etc. (braunscheidel & suresh, 2009). therefore, it was important to investigate whether innovation and agility influenced the improvement of organizational learning. based on the theoretical framework and set hypotheses, we introduced a research model (figure 1). the applied research model has two segments. the first segment refers to the impact of sharing information on an innovative supply chain through partner relationships with suppliers and customers. the second segment refers to the examination of the impact of an innovative supply chain on an agile supply chain and on organizational learning. the proposed model has enabled the research whether an innovative supply chain had the role of a mediator in influencing the sharing of information on the agility of the supply chain and organizational learning. figure 1. research model 3. methodology in this section, we will present the basic set, sample survey and data collection procedures. we will show the results of non-response bias analysis of the collected data and will explain the operationalization of the research constructor. research for this study was carried out on the territory of bosnia and herzegovina. the research includes agro-food companies. according to the statistical business register from june 30th of june 2016 there are 1745 such companies in bosnia and herzegovina. the basic sample included those companies that are primarily engaged in the production or processing of food and beverages were taken including registered farms and cooperatives. however, this sample is consisted mainly from companies located in urban areas. if it was not possible for a company to determine whether it is doing business or performing business activity, the first one below is taken into consideration. data collection for this study was carried out from march to september 2016 and 149 companies took part in the survey. the basic characteristics of these companies are presented in table 1. improving organizational learning by sharing information through innovative supply chain in agro-food companies from bosnia and herzegovina 83 table 1. basic data about companies involved in the study companies' features frequency % size 1. micro 24 16.1 2. small 65 43.6 3. middle 43 28.9 4. big 17 11.4 number of employees 1. 1-9 47 31.5 2. 10-49 53 35.6 3. 50-99 19 12.8 4. 100-199 16 10.7 5. 200+ 14 9.4 age 1. before 1970 15 10.1 2. 1970-1989 16 10.7 3. 1990-2010 96 64.4 4. after 2010 22 14.8 ownership 1. private 145 97.3 2. state 0 0.0 3. mixed 4 2.7 possession of quality certificates 1. yes 99 66.4 2. no 50 33.6 primary activity 1. food production 61 40.9 2. production of milk and beverages 25 16.8 3. agricultural production 44 29.5 4. other production 19 12.8 a survey questionnaire was used during the research. the questionnaire was created in the following way. first, relevant papers were collected that dealt with the subject of this study. second, we identified the relevant papers which were used to create a questionnaire. third, the questionnaire was forwarded to four experts who gave suggestions on the issue. fourth, the survey questionnaire was corrected and sent to agro-food companies. we analysed within non-response bias analysis those companies that did not want to take a part in the survey. the reasons for non-participation were the following: lack of time, lack of approval from the administration, nonperformin registered activities, etc. on the basis of these answers it can be established that there is no valid reason why they did not participate in the research. so the collected data from this research were confirmed. on the basis of these answers we understood that there is no valid reason why they did not participate in the study. thus, the collected data from this study were confirmed. we used the questionnaire consisting of two parts. the first part of the questionnaire examined the basic characteristics of agro-food companies: size, number of employees, company's age, ownership of the company, sales revenues in 2015 (bam), possession of quality certificates and primary activity of the company. the second part of the questionnaire was measured research constructors: information sharing, supplier relationship, customer relationship, innovative supply a. puška, et al./oper. res. eng. sci. theor. appl. 1 (1) (2018) 76-90 84 chain, agile supply chain and organizational learning. these constructors were tested using the likert scale with five levels of agreement with the offered claims that ranged from "completely disagree" to "completely agree". for the measurement of research constructors, we used customized claims as follows: • information sharing chavez et al. (2015); • supplier relationship chavez, et al. (2015); • customer relationship baihaqi and sohal, (2013) and chavez, et al. (2015); • innovative supply chain mohezar & nor (2014) and lee, et al. (2014); • agile supply chain yang (2014) and gligor, et al. (2015); • organizational learning braunscheidela and suresh (2009). 4. results we used different statistical methods to examine established hypotheses and the model. cronbach's alpha (ca) was used to test the reliability of the measurement scale, average variance extracted (ave) was used to test discriminatory validity, square rot of ave and confirmatory factor analysis (cfa) was used to test the validity of the construction. the connectivity of the research constructors was tested using pearson's correlation coefficient while the model was tested by using structural equation model (sem). we conducted these statistical analyzes with the assistance of statistical programs lisrel 8.8 and spss 20. 4.1. scale validity and reliability before we tested the model, we performed cfa analysis and tested the reliability of the scale, the discriminatory validity and the relationship between the constructors. based on the cfa analysis performed (table 2), the findings showed that all claims have a good factor load (chi-square = 197.97; gfi = 0.88; agfi = 0.84, nfi = 0.93; nnfi = 0.97; cfi = 0.98; rmsr = 0.043; p = 0.043), thus the model has acceptable unidimensionality and convergent validity (prajogo, et al. 2012). our descriptive analysis (table 2) showed that the companies most agree with the claims related to the customer relationship constructor, while the least agree with the claims related to the supplier relationship constructor which is showed by the value of arithmetic mean. this analysis has shown that there is the largest dispersion in the responses related to the supplier relationship constructor, while the smallest dispersion has shown in the responses related to the customer relationship constructors which is indicated by the values of standard deviation (sd). during testing the internal consistency of the measurement scale, the findings showed that all values are greater than the critical value of .70 and range from .77 to .86 which proves the existence of consistent measurement scales. improving organizational learning by sharing information through innovative supply chain in agro-food companies from bosnia and herzegovina 85 table 2. scale validity and descriptives scale item description loading mean sd ca information sharing the information needed to improve cooperation are exchanged .69 3.67 .82 .86 partners share key knowledge about developing business processes and products .80 3.44 .88 information are exchanged with partners to assist planning of future activities .71 3.64 .86 communication with partners is timely, accurate, complete, adequate and reliable .62 3.75 .90 number of employees suppliers are involved to solve problems in the company .87 3.17 1.13 .83 it is being improved product quality with assistance of suppliers .64 3.67 .96 suppliers are involved in development of products and business processes .85 3.44 1.13 it is being cooperated with suppliers to improve business .83 3.21 1.05 customer relationship by interaction with customers, reliability and accountability are improved .47 4.28 .71 .77 ccustomer's satisfaction is measured often .65 3.94 .91 it is trying to determine future customer expectations .70 4.15 .86 innovative supply chain we use modern technology for product development .80 3.75 .99 .84 we are technologically competitive .77 3.62 .98 we use modern warehouses and means of transport .74 3.85 .94 agile supply chain we quickly respond to changes in the market .69 3.77 .84 .86 we adapt very quickly to customer demand .77 3.90 .83 we can quickly offer new products .70 3.66 .96 organizational learning we invest in the employees' promotion and learning .69 4.21 .79 .83 all employees have an embedded vision of the organization .76 4.00 .89 all employees are committed in achieving common goals of the organization. .68 3.95 .92 the results of cr constructors' reliability (table 3) showed that the values are above the critical .50 and range from .81 to .89 which proves that all constructors are reliable. the value of the ave indicator ranges from .59 to .74 which is above the critical value of .50, which confirms that the constructors have a good discriminatory a. puška, et al./oper. res. eng. sci. theor. appl. 1 (1) (2018) 76-90 86 value. the smallest value of square rot of ave is .771 which is greater than the absolute value of the correlation analysis, which fulfills the requirement of discriminatory validity of the model construction. correlation analysis showed that there is no significant connection in three cases. the least important is the relathionship between information sharing and agile supply chain (r = .049) constructors, while the largest connection was found between innovative supply chain and agile supply chain (r = .534). thus, it be concluded that the data collected are reliable and can be used to examine the research hypothesis and the research model. table 3. composite reliability corelation and average variance extracted construct cr ave a b c d e f a. information sharing .87 .62 .788 b. supplier relationship .81 .59 .292** .771 c. customer relationship .88 .65 .374** .451** .805 d. innovative supply chain .89 .74 .107 .296** .264** .857 e. agile supply chain .85 .66 .049 .310** .243** .534** .814 f. organizational learning .85 .66 .330** .360** .467** .157 .160 .810 note: **significance at 0.01 level, cr composite reliability; ave average-varianceextracted; the square root of ave is typed in bold italics along the diagonal 4.1. structural relationship we used sem analysis to examine the model. the findings showed that the model is reliable (chi-square = 242.33; gfi = 0.86; agfi = 0.82, nfi = 0.91; nnfi = 0.96; cfi = 0.96; rmsr = 0.058; p = 0.000). the results of model testing are presented in table 4. table 4. model results hypothesis path estimates t-value p-value results h1. information sharing → supplier relationship .43 4.59 .000 supported h2. information sharing → customer relationship .54 5.15 .000 supported h3. information sharing → innovative supply chain .19 1.67 .097 rejected h4. supplier relationship → innovative supply chain .18 1.86 .065 rejected h5. customer relationship → innovative supply chain .34 2.85 .005 supported h6. innovative supply chain → agile supply chain .41 4.42 .000 supported h7. innovative supply chain → organizational learning .43 3.81 .000 supported h8. agile supply chain → organizational learning -.03 -.28 .780 rejected the results obtained by examining the research hypotheses and the survey model showed that of eight total hypotheses, five hypotheses were accepted, while 3 improving organizational learning by sharing information through innovative supply chain in agro-food companies from bosnia and herzegovina 87 hypotheses were discarded. the hypotheses h1 and h2 are accepted, confirming that there is a significant connection between information sharing with supplier relationship (path = .43; t-value = 4.59; p-value = .000) and customer relationship (path = .54; t-value = 5.15; p-value = .000). hypothesis h3 has been rejected, which shows that there is no significant link between the sharing of information with an innovative supply chain (path = .19; t-value = 1.67; p-value = .097). there is no significant connection between the supplier relationship and the innovative supply chain (path = .18; t-value = 1.86; p-value = .065), which eliminates h4, while there is a significant relationship between customer relationship and innovative supply chain (path =. 34; t-value = 2.85; p-value = .005) supporting hypothesis h5. relation between innovative supply chain with constructors agile supply chain (path = .41; tvalue = 4.42; p-value = .000) and organizational learning (path = .43; t-value = 3.81; p-value = .000) show that there is a significant link between them, which confirms hypotheses h6 and h7. hypothesis h8 was discarded, which explained that there is no significant link between agile supply chain and organizational learning (path = .03; t-value = -.28; p-value = .780) 5. discussion this study focused on the role of sharing information in strengthening organizational learning. we did not study direct impact; rather we examined this issue through an innovative supply chain through the role of a mediator. the findings showed that sharing of information is not directly linked to innovative supply chain but rather through partner relations with the customer, wherein appeared another mediator. sharing information is crucial for establishing partnerships with customers and suppliers (lee & ha, 2018). partners will strengthen relationships if they develop trust among themselves through sharing of information. sharing information is a tool for sharing the necessary information that needs to be quality in order to improve operations of all partners in the supply chain. therefore, the impact of sharing information on partner relationships is explored. the findings showed that there is a significant correlation between sharing information and partner relationships with suppliers and customers. it is crucial for agro-food companies to have satisfied customer who will continue to buy their products. the company must find out what the customer wants and what his needs are. in order to reach information, the company must share information with key stakeholders. customer information helps the company to get to know their desires and needs, and information provided by suppliers helps the company to innovate the supply chain in order to meet these wishes and needs of customers. in order to offer new and varied products that are tailored to their customers' wishes and needs, companies must develop innovative production and business processes (joshi, et al, 2016). thus, we put the innovative supply chain in the focus of this study. the findings showed that the sharing of information does not have a direct connection with an innovative supply chain. however, when considering an indirect relationship through partner relationships with suppliers and customers, it has been proven that customers play an important role as a mediator between sharing information and an innovative supply chain (path = .184; p = .012), while suppliers do not have the role of a mediator (path = .077; p = .084). these findings suggest us that partner relationships with customers are crucial a. puška, et al./oper. res. eng. sci. theor. appl. 1 (1) (2018) 76-90 88 for establishing of innovative supply chain. after we examined the connection between sharing information and innovative supply chain, we also tasted the relationship between innovative supply chain and agile supply chain and organizational learning. the findings have shown that innovative supply chain is essential for supply chain to be agile-related and with organizational learning. based on these findings it can be concluded that agro-food companies in bosnia and herzegovina need an innovative supply chain to develop an agile supply chain. the results have shown that agro-food companies in bosnia and herzegovina need to develop an innovative supply chain to improve organizational learning in these companies. however, it is not necessary to have an agile supply chain to improve organizational learning. the obtained results of this study will assist agro-food companies in bosnia and herzegovina to improve organizational learning that is key issue for development of each company, because knowledge is the most important resource of the company. in order to enhance organizational learning of agro-food companies, they must first share information and develop partner relationships with customers enabling supply chain to be innovative. the study showed that an innovative supply chain is essential to improving organizational learning. 6. conclusion the study has shown that an innovative supply chain is necessary for development of organizational learning in the company. furthermore, this study has also shown that sharing information through partner relationships with customers is crucial in improving an innovative supply chain. the obtained results of this study will assist agro-food companies to improve their business and provide theoretical basis for understanding the relationships established in this research. in future studies it is possible to improve the model by including more constructors that are not involved and which could influence the improvement of organizational learning. moreover, the model enables research in other branches of industry in order to find out whether the same relations in these branches are matched. for future research, it is imperative to investigate which constructors are better linked to organizational learning. after that it is preferably to include those constructors in the model to give guidance on improving organizational learning. the study provided practical and theoretical basis for improving the knowledge on information sharing and an innovative supply chain for improvement of organizational learning. the used model will help agro-food companies in bosnia and herzegovina to organize their business in order to be more competitive on the market. references arlbjorn, j. s., de haas, h. & munksgaard, k. b. 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(2011). capabilities that enhance outcomes of an episodic supply chain collaboration. journal of operations management, 29(6), 591–603. © 2018 by the authors. submitted for possible open access publication under the terms and conditions of the creative commons attribution (cc by) license (http://creativecommons.org/licenses/by/4.0/). operational research in engineering sciences: theory and applications vol. 4, issue 2, 2021, pp. 1-12 issn: 2620-1607 eissn: 2620-1747 doi: https://doi.org/10.31181/oresta20402001k * corresponding author. navidkazemtashh@yahoo.com (n. kazemtash), h.fazl@du.ac.ir (h. fazlollahtabar), mabbas@ustmb.ac.ir (m. abbaspour) rough best-worst method for supplier selection in biofuel companies based on green criteria navid kazemitash 1, hamed fazlollahtabar 2*, mohammadmahdi abbaspour 3 1 department of management, faculty of economics and administrative sciences, university of mazandaran, babolsar, iran 2 department of industrial engineering, school of engineering, damghan university, damghan, iran 3 department of industrial engineering, mazandaran university of science and technology, babol, iran received: 03 march 2021 accepted: 13 may 2021 first online: 16 june 2021 research paper abstract. this paper concerns with the integration of rough set theory with the best worst method to evaluate information system performance within supplier selection problem of biofuel companies. first, a set of main criteria and sub-criteria are collected and then to include uncertainty in decision making, rough set theory is employed. the rough best worst method is applied for weighing and supplier evaluation with respect to information system performance and environmental impacts. further, a case study is conducted for biofuel company supplier selection and the results imply the effectiveness of the approach in tactical performance evaluation. the best criteria effective on the green supplier selection of iss performance is determined to be quality. key words: biofuel company; information systems; supplier selection; rough best worst method 1. introduction each organization performs specific and different activities and the cornerstone of each organization's activities is information. therefore, a proper information system (is) is essential to better manage the flow of information in the organization. (sweis, 2015). an organization must be able to make the right decisions to survive and improve, these decisions must be based on the proper processing of information within the organization and this information must be stored, processed and analyzed in a database, (is) is the database. (salmeron et al., 2001). information systems are kazemitash et al./oper. res. eng. sci. theor. appl. 4 (2) (2021) 1-12 2 made up of different parts, the most important of which are people and information. secondly, software and hardware for storing information and communication networks for transfer and sending information within the organization (kim & lee, 2004). information systems (is) have become essential for all organizations to survive in today’s technology-oriented environment. the number of companies and organizations are increasing which have invested widely in their is infrastructures to present better services and to produce more valuable products. anyway, it has been reasoned that not the (is) solution but their utilization provides the competitive advantages (zaied, 2012). thus, because of the aforementioned functions and importance of is, there are too many studies to emphasize the impact of iss on other contexts like health and medicine (sirintrapun & artz, 2016; sahay et al., 2018), transportation (chen et al., 2017), energy (sicilia et al., 2017), biology (miller, 2017), education (duman et al., 2015), environment (anjana et al., 2018), geography (wagner, 2017) and so many other disciplines. but one of the most important fields that the trace of iss has been seen is the selection of green suppliers. supplier selection is a significant task for modern companies considering the evolution and development of information systems. with respect to environmental factors, green supplier selection is now a substantial challenge for policy and decision makers requiring collecting and processing mass information (stevic et al., 2018; matic et al., 2019; stevic et al., 2020). it is necessary to make the supplier green. accordingly, many researchers have addressed the various aspects of the green suppliers selecting and specifically worked on the evaluation and ranking of the effective criteria which are important in choosing green suppliers (sureeyatanapas et al., 2018; trautrims et al., 2017; govindan et al., 2015). a comprehensive review on defining the relevant criteria effective of sustainable supplier selection problem was investigated in (durmić, 2019). banaeian et al. (2018) have selected the green supplier using the fuzzy group decision making methods. actually, they compared the result of three different techniquestopsis, vikor and gra methods in a fuzzy environment. sureeyatanapas et al (2018) used the topsis technique to simplify, choosing the suppliers based on the uncertain and unavailable information. further, they used to the rank order centroid (roc) method, to gather the weights of criteria to decrease the degree of subjectivity required from the decision makers. yazdani et al. (2017) represented an integrated approach through considering different environmental performance factors to select the green supplier. therefore, they used dematel technique to determine the internal-relationships between the customer requirements and used quality function deployment to make a central relationship matrix in order to identify degree of relationship between each pair of supplier selection criteria through the fuzzy extended ahp method. gupta & barua (2017) worked on the evaluation of supplier selection based on the green innovation abilities among the small and medium companies. jauhar & pant (2017) tended to develop an efficient system for sustainable supplier system through the combination of the data envelop analysis (dea) (despić et al. 2019) with differential evolution (de) algorithm and further with multi-objective differential evolution (mode) to overcome the inherent drawbacks of dea. and finally, hsu and hu (2009) applied hazardous substance management (hsm) to select the supplier through the analytic network process (anp). in their model, there were five criteria including rough best-worst method for supplier selection in biofuel companies based on green criteria 3 procurement management, r&d management, process management, incoming quality control and management system and 19 sub-criteria. to obtain sustainable development, the integration of environmental, economic and social performance turned into the complex challenge for them. because of above reasons, companies which buy their required materials and services from specific suppliers prefer to fulfill their expectations like low-cost, high-quality, short leadtime, and environmental criteria simultaneously (đalić et al., 2020; durmić et al., 2020; lee et al., 2009 fazlollahtabar & kazemitash, 2021). there are too many researches about green supplier selection (gss) and iss separately as two crucial parts of contemporary organizations, while except some limited studies in which (is) is considered as the effective factor for gss, there is not any research that investigate their relation. on the other hand, the second issue that is observed in the majority of the previous studies is using the complicated and timeconsuming techniques like dematel, ahp, anp, danp, topsis and vikor to compute the needed requirements (stevic et al., 2017). through the integrated rough best-worst method (rbwm) the local and global weights of criteria and sub-criteria will be obtained by the experts' opinions. next step is measuring the iss' performance in association with green supplier selection which are gained by the experts' opinions. ultimately, as a conclusion, companies could be able to focus on the specific is or iss which play the more important role in the green supplier selection processes and reinforce them if necessary. because of the complex condition of today's business, all companies need to have a long-term relationship with their partners, and it’s the reason why all corporations should be aware and alert to identify and select the supply resources. hence, it can show the extreme importance of supplier selection (gurel et al., 2015). the aim of this paper is evaluating of each single is on the green suppliers’ selection and actually finding the level of effectiveness of each is on the green supplier selection process. at the first step, it represents a localized gss model including eight criteria and 31 sub-criteria of green supplier selection, based on the gss experts' opinions (first problem). then it illustrates the performance of every is in relation with green supplier selection process using the rbwm (which computes the importance (weights) of every measure of gss model) and performance itemscores (which represents the effectiveness and performance of iss to select the green suppliers) of all existing iss in a company (second and third problem). 2. methods and materials the purpose of this study is evaluating the performance of various iss of a company, in green supplier selection process (gss). this aim is met by mcdm methods to gain the global weights of green supplier selection' sub-criteria, and another technique to rank the iss based on their performances in connection with the gss. it looks necessary to show the steps of rbwm as the mcdm method and itemscoring to rank the iss. best-worst method was proposed by rezaei (2015) that in comparison with other decision-making methods, bwm needs less data, since full pairwise comparison is not required providing a more consistent result. that is the main reason why it's applied in this study. also, rough set theory presented by kazemitash et al./oper. res. eng. sci. theor. appl. 4 (2) (2021) 1-12 4 pawlak (1982) is a mathematical tool to deal with uncertainty. further, the rough set theory is appropriate in practice characterized by a small amount of data. after the presentation of the model, the procedures of problems solving are demonstrated as techniques, step by step. the conceptual model is depicted in figure 1. figure 1. the conceptual model of green supplier selection's criteria and subcriteria as it's been pictured, there are three primitive operations in which 8 criteria and 31 sub-criteria have been selected by a number of organization's experts that have been extracted from the literature. then, the integrated rough bwm as the mcdm technique is started including three sub-sections in which the local weights of criteria, the local weights of sub-criteria and finally the global weights of sub-criteria are computed, respectively. as the last step, by determining the iss' performances regarding the meeting the green supplier selection criterion, the scores of the iss are calculated. ultimately, based on the computed final scores of iss, they are ranked. through this way, the determined goals of study are achieved, or indeed, the mentioned problems of the study are solved. rough best-worst method for supplier selection in biofuel companies based on green criteria 5 2.1. rough best-worst method given that best-worst is a new but well-known method. the steps of the (rbwm) are briefly mentioned as follow: step 1. determining the set of evaluation criteria. step 2. determining the most and the least significant criteria. step 3. determining the preferences of the most significant criterion (b) from set c; 1 2 ( , ,..., );1 e e e e b b b bn a a a a e m   (1) step 4. repeat step 3 for the worst criterion (w) and the set c ; 1 2 ( , ,..., );1 e e e e w w w nw a a a a e m   (2) step 5. determining the rough bo matrix for the average answers of the experts. * 1 2 1 2 1 2 1 2 2 2 1 [ , ,..., ; , ,..., ;...; , ,..., ] e m m k m m b b b b b b b bn bn bn n a a a a a a a a a a   (3) bo matrix *1 *2 *, ,..., m b b b a a a is obtained from the sequence ( ) e bj rn a . then, the average rough sequence is computed using equation (4). 11 2 1 1 ( ) ( , ,..., ) 1 m l el bj bj ee bj bj bj bj m u eu bj bj e a a m rn a rn a a a a a m              (4) where, e represents the e th expert ( 1, 2,..., )e m , ( ) e bj rn a represents the rough sequences. we thus obtain the averaged rough bo matrix of average responses: 1 2 1 [ , ,..., ]b b b bn na a a a  (5) step 6. determining the rough ow matrix of average expert responses. * 1 2 1 2 1 2 1 1 1 2 2 2 1 [ , ,..., ; , ,..., ;...; , ,..., ] e m m m w w w w w w w nw nw nw n a a a a a a a a a a   (6) the sequence for the worst criterion is also computed. 11 2 1 1 ( ) ( , ,..., ) 1 m l el jw jw ee jw jw jw jw m u eu jw jw e a a m rn a rn a a a a a m              (7) the average rough sequence is in hand: 1 2 1 [ , ,..., ]w w w nw na a a a  (8) kazemitash et al./oper. res. eng. sci. theor. appl. 4 (2) (2021) 1-12 6 step 7. calculation of the optimal rough weight coefficients of the criteria 1 2 [ ( ), ( ),..., ( )] n rn w rn w rn w from set c. ( )( ) ( ) ( ) ( ) ( ) jb bj jw j w rn wrn w rn a and rn a rn w rn w   (9) the previously defined limits will be presented in the following min-max model: 1 1 ( )( ) min max ( ) , ( ) ( ) ( ) . . 1 1 , 1, 2,..., , 0, 1, 2,..., jb bj jw j j w n l jj n u jj l u j j l u j j rn wrn w rn a rn a rn w rn w s t w w w w j n w w j n                            (10) model (10) is equivalent to the following model: 1 1 min . . ; ; 1 1 , 1, 2,..., , 0 , 1, 2,..., l u u l b b bj bj u l j j l u u lj j jw jw u l w w n l jj n u jj l u j j l u j j s t w w a a w w w w a a w w w w w w j n w w j n                                   (11) where ( ) [ , ]l u j j j rn w w w represents the optimum values of the weight coefficients, ( ) [ , ]l u b b b rn w w w and ( ) [ , ]l u w w w rn w w w represents the weight coefficients of the best and worst criterion respectively. by solving model (11) we obtain the optimal values of the weight coefficients for the evaluation criteria 1 2 [ ( ), ( ),..., ( )] n rn w rn w rn w and *  . for mcdm problems with more than one level of criteria such as this study, first of all, the weights for different levels should be obtained through the bwm steps. then, the weights of different levels have to be multiplied to determine the global weights (salimi & rezaei, 2018). to show this process clearly, in figure 2 the sub-steps of rough best-worst method for supplier selection in biofuel companies based on green criteria 7 every single technique, the order of them and major techniques and finally the output of them are observed. in figure 2, there are three main steps and their corresponding sub-steps from collecting the criteria and sub-criteria, purification, weighing, ranking and performance evaluation. figure 1. the proposed hybrid mcdm model 3. case study the proposed information system effectiveness model is tested to evaluate and rank the using iss in biofuel company. to ensure sustainability, new energies have recently attracted a lot of attention. so far, the supply chain and the select of supplier of these energies have been presented from different perspective. biofuel, as one of the types of renewable energy, has a significant amount of use in this type of fuel because this type of fuel can be obtained from the recycling of other materials. the optimal weights are obtained through the expert opinions, while the scores, are computed based on the data from a survey among the 100 experts of iss. kazemitash et al./oper. res. eng. sci. theor. appl. 4 (2) (2021) 1-12 8 3.1. weights of green supplier selection measures: to obtain the weights of the criteria and sub-criteria, the comparison data needed for bwm is gained by interviewing with 20 experts in the field of green supplier selection, individually. next, the weights of criteria and their sub-criteria are determined using bwm. finally, the overall weights for the criteria and sub-criteria are computed by using the aggregation (based on a simple average). table 1 shows the aggregated weights of the eight main criteria and the sub-criteria based on the inputs which are provided by the experts. based on these results, design for reduction or elimination of hazardous materials as the third sub-criteria of the green design (weight = 0.1176) has the most weight which illustrates the most effectiveness role which sub-criteria could play with respect to the green supplier selection, though the green product has the most amount of weight among the criteria. 3.2. green supplier selection item-scores of iss: as the first step, in a survey among the 50 iss' experts of the mentioned firm, their opinions about the iss performance and effectiveness with respect to the selection of green suppliers are provided, in which the respondents rated the 10 most common iss level based on items from different gss determined sub-criteria on a nine-point likert type scale. and finally, the last operation of this step is that the experts' opinions for every single sub-criterion are averaged. table 1. global rough weights for criteria and sub-criteria. criteria local weights sub-criteria local weights global weights of sub-criteria green design [0.1729,0.1786] design for resource efficiency [0.0878,0.0890] [0.0149,0.0162] design of products for reuse, recycle, and recovery of material [0.2336,0.2388] [0.0405,0.0417] design for reduction or elimination of hazardous materials [0.6731,0.6774] [0.1169,0.1181] service [0.0978,0.1107] rate of processing order [0.2323,0.2342] [0.0230,0.0238] service quality [0.7655,0.7679] [0.0757,0.0793] green image [0.0155,0.0451] ratio of green customers to total customers [0.8406,0.8429] [0.0285,0.0307] green purchase trend of customers [0.1573,0.1596] [0.0047,0.0063] quality [0.1233,0.1339] quality-related certificates [0.6303,0.6324] [0.0828,0.0854] capability of quality management [0.2520,0.2550] 0.0327,0.0345 reject rate [0.1141,0.1157] [0.0149,0.0156] environmental management [0.0884,0.1057] environmental protection policies/plans [0.1463,0.1481] [0.0136,0.0155] environment protection system [0.1091,0.1123] [0.0101,0.0122] rough best-worst method for supplier selection in biofuel companies based on green criteria 9 certification eup [0.4438,0.4460] [0.0429,0.0457] odc [0.0525,0.0566] [0.0048,0.0070] rohs [0.1133,0.1162] [0.0110,0.0119] wee [0.1275,0.1293] [0.0120,0.0340] green product [0.2409,0.2519] cost of component disposal [0.1367,0.1381] [0.0326,0.0353] green production [0.2909,0.2944] [0.0716,0.0728] green certifications [0.1176,0.1201] [0.0287,0.0303] green packaging [0.1328,0.1375] [0.0321,0.0349] recycle [0.1266,0.1285] [0.0301,0.0327] remanufacturing [0.0414,0.0439] [0.0100,0.0120] reuse [0.1451,0.1487] [0.0359,0.0365] delivery [0.1198,0.1271] order frequency [0.0857,0.0872] [0.0103,0.0206] order fulfillment rate [0.2518,0.2524] [0.0296,0.0318] lead time [0.1802,0.1819] [0.0215,0.0232] delivery efficiency [0.4783,0.4826] [0.0575,0.0590] cost [0.0891,0.0903] buying friendly materials [0.0825,0.0848] [0.0052,0.0096] compliance with sectorial pricing [0.1407,0.1440] [0.0112,0.0145] performance value/price [0.5254,0.5291] [0.0466,0.0479] transportation cost [0.2460,0.2467] [0.0214,0.0223] there are two different ways that it's possible to evaluate and investigate the performance of iss to support the gss process based on. in one hand, it's available to assess the performance of iss through their overall aggregations and rankings, so that the more overall aggregation, the better ranking. for instance, mis possesses the most overall aggregation (6.8800), so it’s the first information system as the best one. it means that it has the most effectiveness and best performance in related with gss. and after that, erp (6.7986), crm (6.6319), scm (6.5756), dss (6.3210), ec (6.1931), bi (6.0805), km (5.8977), oas (5.0642) and tps (4.7460) are placed in the following ranking respectively. on the other hand, it's possible to investigate the iss based on their scores and rankings in every single part (the aggregation of every criterion). for example, mis performance as the best one among the 10 mentioned iss, is placed as the first one in the quality criteria, the second one in three criteria, including environmental management, green product and cost criteria, the third one in the green design criteria, the fourth one in the green image criteria and the sixth one in the service criteria. as this way evaluates the performance of iss in every gss criteria, it’s the best one to compare two different iss which have close overall aggregations (not exact the same). for example, there is a slight difference between the overall aggregation of mis and erp which are 6.8800 and 6.7986 respectively, thus in the eyes of someone, it couldn't explain the superiority of mis rather than erp clearly. therefore, they rely on the second way to describe the differences and performance of every one in comparison with others. in this case, erp's performance (rank or actually aggregated score) is better than mis in three criteria in consist of service, delivery and green product in which the erp has the best performance, while in other criteria mis has better scores and rankings. kazemitash et al./oper. res. eng. sci. theor. appl. 4 (2) (2021) 1-12 10 the developed method in this paper can be employed to compare the gss with respect to iss performance; this way the position of iss in the final ranking can be considered. 4. conclusions this research tried to take into account the green supplier selection indices to allow each is to determine its overall weight. moreover, iss can improve their green supplier selection performance based on the importance of each perspective. more precisely, if an is wants be prominent in green product as the most important criteria in gss process, it should focus on and invest in green production, since the given information in table 1 display that the green 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(2012). an integrated success model for evaluating information system in public sectors. journal of emerging trends in computing and information sciences, 3(6), 814-825. © 2021 by the authors. submitted for possible open access publication under the terms and conditions of the creative commons attribution (cc by) license (http://creativecommons.org/licenses/by/4.0/). rough best-worst method for supplier selection in biofuel companies based on green criteria navid kazemitash 1, hamed fazlollahtabar 2*, mohammadmahdi abbaspour 3 1. introduction 2. methods and materials 2.1. rough best-worst method 3. case study 3.1. weights of green supplier selection measures: 3.2. green supplier selection item-scores of iss: 4. conclusions references plane thermoelastic waves in infinite half-space caused operational research in engineering sciences: theory and applications vol. 3, issue 3, 2020, pp. 65-83 issn: 2620-1607 eissn: 2620-1747 doi: https://doi.org/10.31181/oresta20303065w * corresponding author. swidjajanto@gmail.com (s. widjajanto), humiras.hardi@mercubuana.ac.id (h.h. purba), sansurijaqin@gmail.com (s.c. jaqin) novel poka-yoke approaching toward industry4.0: a literature review sugiri widjajanto1, humiras hardi purba 1, sansuri choesnul jaqin 1* 1 industrial engineering, universitas mercu buana jakarta, indonesia received: 05 august 2020 accepted: 19 october 2020 first online: 12 november 2020 review paper abstract: understanding quality in manufacturing starts with learning why errors happen and this could be improved by analysis with root causes related to human errors. human reliability influenced by equipment design or working environment will come to concept of poka-yoke (mistake proofing), and various means to reduce mistakes that have been greatly improved recently with latest sophisticated technology. this article will discuss poka-yoke technology related to the industry 4.0 (i4.0) or smart manufacturing concept. the method is to review research articles published within 2015-2020 with a keyword poka-yoke or mistake-proof or fault-proof and verify further whether their poka-yoke tools have implemented the i4.0 concept. the results obtained 50 selected articles, with 13 of them that already applied information technology, cloud computing, and augmented reality, which are considered as i4.0 tools. however, its application is not always satisfying concerning its suitability function, requirement of industries, culture, local regulation, and internal business concern, especially in terms of efficiency and cost. keywords: poka-yoke, mistake-proof, fault-proof, industry 4.0. 1. introduction there is a concept in quality management that prevents the human fault from occurring in production, which was introduced by shigeo shingo and named as poka-yoke (malega, 2018). it deals with mistake-proof or error-proof as per original wording yokeru (avoid) and poka (mistakes) (kurhade, 2015). the mistake can occur at any job at any type, e.g., misoperation, not performed as per protocol, using wrong tools, missing parts, having defects during assembling, using incorrect components, or inaccurate measurement (kurhade, 2015). currently, we are facing industry 4.0 or in short form as i4.0, and conventional industries will evolve to a smart and autonomous style (ahmed et al., 2019), and it will introduce and develop new tools that reduce human error at an early step of widjajanto et al./oper. res. eng. sci. theor. appl. 3 (3) (2020) 65-83 66 product and process development (lazarevic et al., 2019). it can be a communication strategy (tezel & aziz, 2017), or automation with a human touch (romero et al., 2019) or software application to avoid mistyping (hudori et al., 2017) or a smart decision tool (ahmed et al., 2019) or a computerized testing tool (bici et al., 2017) or using advanced technology like augmented reality to point out mistakes (dario antonelli & astanin, 2015). then, it comes to the question, how can poka-yoke and i4.0 supplement each other? and which i4.0 tools can support a poka-yoke method? the precondition for this literature study is looking at various lean approaches including mistake-proofing methods. indeed, there are many ideas of mistakeproofing methods with proper implementation according to their circumstances. however, there are insufficient published articles with this specific mistake-proof topic. 2. research methods this literature review is the best method to study and analyze from basic theory, tools, experience, and lessons learned from either academic or practical exercise. according to figure 1, this paper study starts with the initial collection as step number one of the total five steps. collecting from various publishers, i.e. science direct, research gate, proquest search, mdpi, springer open and google scholar within the year of 2015 until 2020. the keyword is "poka-yoke" or "mistake-proof" or "error-proof" or "fault-proof" for the industrial sector with the number of collected articles shown in table 1. figure 1 literature study framework table 1. number of articles at every stage stage article qty 1 99 2 84 3 64 4 50 5 50  stage 1. the initial collection, managed to collect 99 articles relevant to pokayoke. novel poka-yoke approaching toward industry-4.0: a literature review 67  stage 2. screening; omitted numbers of papers due to irrelevant research objects and kept 84 of them.  stage 3. collate information, also removing the number of papers when digging information inside, only selected 64 related to industrial and manufacturing.  stage 4. full-text article assessed, gained more knowledge and chosen 50 standing out.  stage 5. in-depth study for those remaining 50 articles. digesting more the article contents, it has been listed out all articles based on the industrial type or place of research, poka-yoke type, and country of the researcher. segregation based on poka-yoke type is mechanical, electronic, mechanicalelectronic (mix), it or system software, and the last is organizational, which is a focus on the development of protocol or procedure for the human-error problem. the summary of results based on the year of published papers is presented in figure 2. figure 2 collected articles & papers based on the publishing year analyzing the content from the final collected articles, there was a focus on a few aspects:  industrial type,  selected mistake-proof type (see figure 3),  implementation,  enablers and inhibitors. 2015 2016 2017 2018 2019 2020 0 5 10 15 20 widjajanto et al./oper. res. eng. sci. theor. appl. 3 (3) (2020) 65-83 68 figure 3 poka-yoke type based on theory, the poka-yoke implementation started in the automobile industry (in the 1960s as part of toyota production system (tps) in japan), and furthermore it was adopted by textile, construction, electronics, woods, services, and other industries in various countries. 3. results and discussion all articles and papers are elaborated in table 2, including the country of author, research object and respective result. surprisingly, the article published by the japanese is none at this literature study and this concern can be reserved for future research. 0 5 10 15 20 electronic it / software mechanical mechanical & electronic organizational 2015 2016 2017 2018 2019 2020 novel poka-yoke approaching toward industry-4.0: a literature review 69 table 2 mapping poka-yoke implementation from 50 articles no paper identity country of author research object result 1 (dahivale & lokhande, 2020) india rejection from reverse logistics and scrap after implementation of poka-yoke, rejection and scrap rates are significantly reduced to ‘zero’. 2 (solaimani & sedighi, 2020) netherland lean implement-ation including poka yoke in construction carry out and sustain the lean in construction and poka-yoke is part of them, particularly for safety. 3 (selvam & loganathan, 2019) india design & fabric-ation of hydraulic conduit connector improvement on quick releasing coupling. part of assembly is made noticeable. eventually, it raises a confidence level of the operator’s. 4 (muharam & latif, 2019) indonesia vibration signal for machine monitoring poka yoke device can observe machine condition, such as bearing abnormal alarm. furthermore, this system is also being used to see machinery and equipment condition. 5 (romero et al., 2019) italy jidoka/automation with human touch advised for step-by-step fully-automated operation deployment to let workers gain knowledge and change working culture towards semi-automated or fully automated operation, through development of stages and adopting jidoka systems, instead of immediate applying a fully automated solution. 6 (rösiö et al., 2019) sweden assessment manu-facturing system and poka yoke as part of diagnosable criteria develop assessment model to measure ability for modification and change variation of product and volume. 7 (putri & handayani, 2019) indonesia craft bag product quality (for cement powder) improvement with 3 poka yoke methods, i.e. warning, control & shutdown. 8 (hoellthaler et al., 2019) germany digitalization to support poka-yoke for a lean production system digital manner for tools and methods is indeed achievable, eventually reduces waste of time, cost and quality. 9 (attia et al., 2019) egypt poka yoke in clothes printing machines a mechanical poka yoke prototype is manufactured for diminishing problems. 10 (d. antonelli & stadnicka, 2019) italy identify potential mistakes either by human or robot. define proper mistake proofing (poka yoke) methods in an hrc (human-robot collaboration) assembly work cell. the best solution is to standardize the part and uniform the dimension. 11 (saputra et al., 2019) indonesia molding machine of plastic industry improvement is achieved gaining a value of 1.65 of spc through poka-yoke implementation. 12 (rubio-romero & pardo, 2019) spain perform an analysis of lean, faultproof and preventive activity in construction “personal-protective-equipment” or ppe is considered poka-yoke, and also warning sign with rfid and reflective railings. 13 (ahmed et al., 2019) australia svpd in design, process and inspection disseminate a smart system based on experimental expertise to support product development design, product planning that is able to enhance manufacturing process. widjajanto et al./oper. res. eng. sci. theor. appl. 3 (3) (2020) 65-83 70 14 (qeshmy et al., 2019) sweden aim to identify human error factors in an assembly line using augmented reality for smart factory. augmented-reality is not suitable if the aim is identification of human failure. the ar is not fully developed for the moment. 15 (bajjou & chafi, 2018) morocco survey in moroccan con-struction industry 61 % of the respondents are familiar with lean construction practices, and 68% are not familiar with poka-yoke. 16 (satolo et al., 2018) brazil to rank the tools of the lean poka yoke is rank 11 among lean tools like vsm, six-sigma, 5s, kaizen, etc. 17 (s. kumar et al., 2018) india sme with continuous improvement achieving by lean-kaizen approaching. however, found weakness in motivation of employees to eliminate wastes. 18 (gavriluţă et al., 2018) romania laboratory system for modern manu-facturing develop a laboratory situation and environment for a sophisticated industrial method, including a simulating flow of process and lean. 19 (soni & yadav, 2018) india review on produc-tivity improvement by poka yoke implementation application of poka yoke on a liner cutting machine to prevent possibility of liner mouth misalignment and increase the productivity. 20 (vinayagasundaram, r. velmurugan, 2018) india pick-to-light at compressor manufacturing implement poka yoke approaching for a zero-defect in an assembly line; pickers or operators are prompted by lights (hence the name pick-to-light). 21 (dawood et al., 2018) saudi arabia lean tools in a soft drink company, poka-yoke for variable missing operations, under fill, over fill, break ages. identify non-value adding activities, thereby enhancing productivity. step 1: detect the abnormality-(andon), step-2: stop the equipment or line by poka-yoke, step-3: fix and correct the immediate condition by poka-yoke, step 4: verify causes and install a counter measure poka-yoke. 22 (lilja, 2018) sweden tetrapak packaging machine using three sub-functions (physical, signaling and control) in the solution as all these functions seek to improve the environment around the assembler. 23 (malega, 2018) slovak business process and system in a general review poka yoke represents an excellent method for eliminating human errors in production process. 24 (prayogi et al., 2018) indonesia smart-key assembly in car manufacturing design two poka-yoke devices along with sensors that are integrated to the whole assembly system. 25 (sundaramali et al., 2018) india avoiding unneces-sary assembly of defective compo-nents and marking them the whole inspection from the beginning has involved poka yoke. 26 (pötters et al., 2018) germany shop floor process simulation for several methods including pokayoke identification of how to get optimal quality involves optimization experts in the company. this initial identification approach is carried out before the actual test is conducted. 27 (ardi et al., 2018) indonesia process of mounting actuator bracket the design with poka yoke overcomes the occurrence of bolt damage when installing the bracket. novel poka-yoke approaching toward industry-4.0: a literature review 71 28 (kurdve et al., 2018) sweden prototype for building wood modules with poka-yoke the eco-strategy can be used, but need more consideration to optimize the product life, optimize product function, and minimize environmental waste in the specification and concept phase. chosen material can be finalized during prototyping. 29 (kurdve, 2018) sweden assembly-line work instruction in digital manner with fault-proof safety & quality poka-yoke, standardized work instruction and using ready-assembly materials became solutions at husmuttern (wood-ware factory) although there is digital support available, but it does not fit with workers’ skills at wood-ware company. 30 (schaede et al., 2018) germany decision tree of cnc program with product parameters cnc is programmed for automatic with a limited parameter. decision tree is used to determine the best procedure. example implementation was presented, proving beneficial of automated cnc program. 31 (m. kumar et al., 2018) india adding real time production data as poka-yoke system plcs are equipped with servers for real-time fabrication data to ensure 100% inspection is carried out and sent to management. this is a poka-yoke method, so that operators cannot take a short-cut in production. 32 (erdogan et al., 2017) usa measure kaizen effectiveness in the wood industry provide the latest views on the use of kaizen and other improvement opportunities while staying focused on quality, safety, fault-proof and waste. 33 (lemahieu et al., 2017) usa lean in education highlighted lean in educational environment and delivering more efficient education and training. 34 (tezel & aziz, 2017) uk visual-management (vm) system in england construction project identify beneficial of visual-management system for a transportation construction project. potential of poka-yoke system for quality inspection and worker safety. 35 (b. kumar & kumar, 2017) india poka yoke on needle roller bearing poka yoke implementation has decreased a missing needle and obtained maximum efficient bearing. 36 (che-ani mn. et al., 2017) malaysia quality in process production quality has improved and ensured economic benefit by poka-yoke. 37 (ardi & abdurrahman, 2017) indonesia oxygen sensor machine functionality increase efficiency check of oxygen sensor machine by poka yoke system. rating errors reduced by 0.14% and mor hit 90% target. 38 (hudori et al., 2017) indonesia pallet package information at shipping dept poka yoke implementation for pallet package information. 39 (rojo abollado et al., 2017) uk optimize business process and change the information systems to support evolving of the business. overview of benefits that the implementation of digital workflow is doable in an aerospace company, along with detailed challenges of both digital workflows and human factor risks. 40 (bici et al., 2017) italy computer-aided-tolerancing-andinspection automatic measurement through specific algorithms is useful in guaranteeing measurement results involving many samples. 41 (isnain & karningsih, 2016) indonesia car body parts manufacturing implement poka yoke sensors at a press machine and finish wrapping. 42 (alghozali et al., 2016) malaysia vending machine product quality quality improvement in vending machine services by adopting the poka-yoke approach, adding date-based alarm warnings. widjajanto et al./oper. res. eng. sci. theor. appl. 3 (3) (2020) 65-83 72 43 (thareja, 2016) india real life or common use exemplars by citing various tools for correction, error proofing (poka yoke) of the processes is done. 44 (fauzan et al., 2016) indonesia printing processing with minimizing waste defect improvement suggestions were made as well as a poka yoke system as an effort to minimize waste defect. 45 (d. antonelli & stadnicka, 2016) italy mistake-proof solution by fuzzy logic for: 1. welding spot 2. kitting process 3. roller bearing seals propose a package to get the most suitable solution by using fuzzy-logic on kpi criteria. 46 (tak & wagh, 2015) india poka-yoke on punching machine problems can be managed by poka-yoke. 47 (singh & singh, 2015) india continuous improvement of north india manufacturing significantly increased oee reached 3.01%. 48 (shrigadi et al. 2015) india using a sensor on a particular place, then it can prevent mixing of different casting on a process line. if there is an incorrect casting, the sensor gives an alarm and the conveyor stops, so the operator changes the wrong one. 49 (dario antonelli & astanin, 2015) italy augmented-reality (ar) to improve welding quality using ar devices displayed welding point data. 50 (lazarevic et al., 2019) serbia literature review of poka yoke, 211 manuscripts with 50 examples poka-yoke's new approach is to recognize existing gaps and describe using experience in the field. novel poka-yoke approaching toward industry-4.0: a literature review 73 figure 4 country of author 3.1. brief results based on country around a quarter of the collected articles are published by authors from india as seen in figure 4. there are also authors from many european nations as well as asia followed by the us, australia, and africa. this representation of authors’ countries shows that a poka-yoke idea is spread all over the nations, see table 2 that maps all articles and figure 4. 3.2. review on poka-yoke type various articles & researchers on mapping all articles of table 2 are divided based-on five poka-yoke types as shown in table 3. table 3. poka-yoke type in respective articles poka-yoke type article author sum electronic (muharam & latif, 2019), (putri & handayani, 2019), (saputra et al., 2019), (vinayagasundaram, r. velmurugan, 2018), (dawood et al., 2018), (prayogi et al., 2018), (ardi et al., 2018; ardi & abdurrahman, 2017), (isnain & karningsih, 2016), (alghozali et al., 2016), (tak & wagh, 2015), (shrigadi et al., 2015). 12 mechanical (dahivale & lokhande, 2020), (selvam & loganathan, 2019), (attia et al., 2019), (soni & yadav, 2018), (sundaramali et al., 2018), (b. kumar & kumar, 2017), 7 3 1 1 2 1 1 1 2 1 1 2 2 1 2 5 2 1 1 1 1 3 1 1 1 3 2 1 1 2 2 1 0 2 4 6 8 10 12 14 australia brazil egypt germany india indonesia italy malaysia morocco netherland romania saudi arabia serbia slovak spain sweden uk usa 2015 2016 2017 2018 2019 2020 widjajanto et al./oper. res. eng. sci. theor. appl. 3 (3) (2020) 65-83 74 (che-ani mn. et al., 2017) mix mech-elect (rubio-romero & pardo, 2019), (lilja, 2018), (fauzan et al., 2016) 3 it / software (hoellthaler et al., 2019), (ahmed et al., 2019), (qeshmy et al., 2019), (pötters et al., 2018), (kurdve et al., 2018), (schaede et al., 2018), (m. kumar et al., 2018), (tezel & aziz, 2017), (hudori et al., 2017), (rojo abollado et al., 2017), (bici et al., 2017), (d. antonelli & stadnicka, 2016), (dario antonelli & astanin, 2015) 13 organizational (solaimani & sedighi, 2020), (romero et al., 2019), (rösiö et al., 2019), (d. antonelli & stadnicka, 2019), (bajjou & chafi, 2018), (satolo et al., 2018), (s. kumar et al., 2018), (gavriluţă et al., 2018), (malega, 2018), (kurdve, 2018), (erdogan et al., 2017), (lemahieu et al., 2017), (thareja, 2016), (singh & singh, 2015), (lazarevic et al., 2019) 15 organizational, as a category, includes methods, protocols, procedures, or an it / software concept which is a recent advanced tool, i.e. a device connected to the server database, remote control access, control system, and another computerized approaching. the electronics type, for instance, includes sensors, lights, electronic signs. mechanical includes stoppers, railing fences, bolts/nuts, etc. mix electronic and mechanical is sensors that are connected to mechanical actions. there are many different tools for respective purposes. however, the poka-yoke techniques have various names and they can be overlapped with each other. particular tools may have different implementation proposed by various researchers or different industries. many of these tools are used in conjunction with each other like visual control (andon) (dawood et al., 2018) and automation with a human touch (jidoka) (romero et al., 2019) as a poka-yoke tool. results in table 3 show that 15 articles are categorized as organizational because they did not specify actual implementation of the tool. furthermore, they are part of lean improvement strategy instead of poka-yoke alone. others are elaborated more in the next section based on the industry type and local or particular region condition. 3.3. review on industrial type the empirical study of poka-yoke approaching is grouped into several categories. this includes common industries as the specified or not specific industries mentioned in the article. there is also service and education under one group, and so on, as shown in figure 5. most of the research took place in the automotive industry, about 20% of the collected articles, then the machinery industry 16%. sme is only 2% while there are plenty of articles nowadays about small and medium enterprise industries, but very few about poka-yoke. novel poka-yoke approaching toward industry-4.0: a literature review 75 figure 5 industry type table 4. poka-yoke type versus researcher's country country electronic it / software mechanical mech & elect. organiza tional total australia 1 1 brazil 1 1 egypt 1 1 germany 3 3 india 3 1 5 3 12 indonesia 7 1 1 9 italy 3 2 5 malaysia 1 1 2 morocco 1 1 netherland 1 1 romania 1 1 ksa 1 1 serbia 1 1 slovak 1 1 spain 1 1 sweden 2 1 2 5 uk 2 2 usa 2 2 grand total 12 13 7 3 15 50 as per history that a poka-yoke tool was started in the automotive industry, it is not surprising that poka-yoke articles are mostly released from automotive industries with 20% out of 50 articles, see figure 5. it comes with various poka-yoke automotive 20% common 12% construction 8%education/ service 10% iron & steel 2% laboratory 2% machinery 16% packaging 8% plastic 2% sme 2% softdrink 2% textile 4% wood 6% electronics 4% aerospace manufacturing 2% widjajanto et al./oper. res. eng. sci. theor. appl. 3 (3) (2020) 65-83 76 types, such as electronic sensors (prayogi et al., 2018), a photo-electric detector (ardi & abdurrahman, 2017), a proximity sensor & push button (ardi et al., 2018), a sensor on a pressing machine (isnain & karningsih, 2016), a metal clip interlock (tak & wagh, 2015), and a sensor for casting (shrigadi et al., 2015). also, mechanical poka-yoke like different part dimensions & color code (che-ani mn. et al., 2017), it poka-yoke with computer visualization (qeshmy et al., 2019), and organizational poka-yoke with developing model (rösiö et al., 2019) and introducing volume flexibility, product flexibility and process flexibility (singh & singh, 2015). poka-yoke approaching in service & education articles are mostly started from conceptual until implementation, i.e. developing lean laboratory (gavriluţă et al., 2018), systematic poka yoke implementation (lazarevic et al., 2019), lean for education (lemahieu et al., 2017), shop floor simulation (pötters et al., 2018), and warning sign of vending service (alghozali et al., 2016). besides the automotive industry as originator, this poka-yoke is also suitable to be applied in the education and service area. looking at the construction sector, poka-yoke is implemented to cope with safety issues as ppe (personal protective equipment) (solaimani & sedighi, 2020) including a warning sign, reflective railing & rfid tag (rubio-romero & pardo, 2019) and utilize information technologies (it) in inspection and safety (tezel & aziz, 2017). however, there is irony from survey results in the construction sector where most of the respondents are not familiar with a poka-yoke method, about 68% out of 330 valid responses, even though the personal protective equipment (ppe) is a pokayoke tool in safety (bajjou & chafi, 2018). 3.4. review on research place and country in general, the relationship between mistake-proofing implementation and organization culture is bond to one another (satolo et al., 2018). different countries have different cultures, different labor capabilities, local industry policy, education, etc. that is the reason the mistake-proof tools vary significantly among the nations since they are developed based on the appropriate and specific approaching of respective local requirements, see fig. 3 and table 5. there is a factory in india that has poka-yoke approaching of engraved marking on scrap & disposal just to prevent someone sell the rejected ones to the black market (sundaramali et al., 2018). for sure, this will not be happening in a developed country like the uk or australia. on the other hand, there is a poka-yoke idea in a european factory to recognize a welding spot by using augmented reality (dario antonelli & astanin, 2015), which is for another country. this idea is costly and too much in terms of saving cost of optimization. regardless of industry type or country, the poka-yoke tool is generally part of lean manufacturing to optimize and eliminate waste. the lean will make organizations more efficient and effective, especially related to quality, reliability, flexibility, innovation and cost and ultimately achieving organizational goals (satolo et al., 2018). facing the challenging circumstance during the covid-19 outbreak, and raising concern about medical equipment industries, it can be an exciting future research concerning lean manufacturing as well as poka-yoke approaching. novel poka-yoke approaching toward industry-4.0: a literature review 77 3.5. novel poka-yoke with i4.0 approaching poka-yoke helps operators to avoid mistakes. regardless of what kind of technology is being used, the goal is to detect and eliminate abnormal conditions that lead to the prevention of product defects. this can be a sort of sequence forced on the execution process and which stops when there is an error. also, the same is done for i4.0 implementation. sophisticated technology at the moment, like auto-identification system that can ensure correct identification and digitalized product-id, allows to retrieve components and identify incorrect ones (mayr et al., 2018). it can be artificial intelligence (mayr et al., 2018) that can automatically be adjusted to ensure optimal product quality. there are also augmented reality head-mounted displays to improve quality inspection (d. antonelli & stadnicka, 2016; dario antonelli & astanin, 2015; qeshmy et al., 2019), and rfid-readers can be used for the safety barrier of contractor workers (rubio-romero & pardo, 2019). as a result of reviewing relevant literature, a simple matrix is shown in table 5 below figuring out i4.0 methods that can be utilized or support the novel poka-yoke approaching. table 5. possible i4.0 tools versus poka-yoke (mayr et al., 2018) industry 4.0 tools poka yoke human-computer interaction  virtual representation (e.g. vr, ar)  auto identification  digital object memory  cloud  real-time  big data  artificial intelligent  accordingly, several articles particularly relevant with the idea of i4.0 tools are collected and summarized in table 6 below. mostly, those are categorized under the it/software poka-yoke type (see table 3). there are usages of information technology for pallet information spreadsheet that can avoid mistyping during data entry (hudori et al., 2017), computer aided tolerancing & inspection (cat&i) to improve inspection (bici et al., 2017), implementation of digital workflow in aerospace manufacturing that removes many human errors (rojo abollado et al., 2017) and digitalization in making a prototype of building wood modules (kurdve et al., 2018). less satisfactory results occur when the i4.0 technology itself is not sufficiently mature or not suitable with the chosen industry, for instance, the augmented reality for welding spot inspection (dario antonelli & astanin, 2015) and for managing errors caused by the human on the assembly line of automotive industry (qeshmy et al., 2019). it can enhance the quality of manufacture; however, it needs further study for the overall process and cost constraint. cloud computing is introduced for an electronic industry with real-time production data working as a poka-yoke, so there is no chance to bypass the system (m. kumar et al., 2018). widjajanto et al./oper. res. eng. sci. theor. appl. 3 (3) (2020) 65-83 78 table 6 novel poka-yoke with i4.0 approaching researcher brief description (hoellthaler et al., 2019), germany digitalization of various methods and tools (including pokayoke) will look forward as industry 4.0 concepts. (ahmed et al., 2019), australia svpd (smart virtual product development) enhances quality and time as i4.0 concepts, poka-yoke is one of the enablers. (qeshmy et al., 2019), sweden design augmented reality and artificial intelligent to present any error occur and avoid wrong choices. (pötters et al., 2018), germany develop a model with shop floor simulation. this includes 5s, poka yoke, etc. (kurdve et al., 2018), sweden develop a system prototype for eco-friendly building modules including fault-proofing (poka-yoke). (schaede et al., 2018), germany new integrated cnc (computer numeric control) presented a promising human-error-free solution. (m. kumar et al., 2018), india cloud computerization for manufacture, particularly sme in india. poka-yoke is used for 100% inspection. (tezel & aziz, 2017), uk the it usage replaces conventional systems in the construction sector including a poka-yoke system for inspection and worker safety. (hudori et al., 2017), indonesia poka-yoke method is implemented in software application: 1) avoid errors or mistyping during data entry, 2) warning, 3) the same template as earlier design that the operator has been familiar with to reduce misunderstanding, 4) time saving, no manual entry. (rojo abollado et al., 2017), uk digital workflow systems eliminate human errors, and save time. this system can overcome the actions that are late or negate other tasks. (bici et al., 2017), italy cat&i (computer aided tolerancing & inspection) very useful in following:  avoiding errors of measurement points.  shape deviation analysis relevant, e.g. plastic shrinkage. (d. antonelli & stadnicka, 2016), italy propose a poka-yoke system to assist industrial problem solving by applying fuzzy logic. the mistake is detected during a production process of 1. welding spot 2. kitting process 3. roller bearing seals. (dario antonelli & astanin, 2015), italy sophisticated tool (augmented-reality) is applied to improve quality by error-free. introducing i4.0 technologies for novel poka-yoke tools depends on several factors, i.e. usability, selective data, end-user acceptance, ethical, regional requirements, and cost. the novel poka-yoke tools should be well-considered as part of improvements. the presented novel poka-yoke in table 6 is not a single tool for cost reduction. this should be part of lean manufacturing, which is a more complex solution. if i4.0 facility is implemented as “nice-to-have” solutions, it can be ended with novel poka-yoke approaching toward industry-4.0: a literature review 79 unsatisfactory results. based on reviewed articles, most of them try to develop a tool in conjunction with others to enhance results. strategically, every concept can be aligned with lean. and actually there are a lot of ways for improvement like condition-based monitoring that are integrated with a maintenance database system, remote visual management, cloud computing, etc. (mayr et al., 2018) based on organizational practices, lean tools that can be adopted successfully in a common industry are: standardization, control, training / learning, team-based organization, employee empowerment, adaptability, reward system, belief, commitment, communication, work methods, etc. (lazarevic et al., 2019). 4. conclusion implementation of i4.0 concept as a novel poka-yoke tool is an encouraged part of lean strategy. as for i4.0 perspective, everything is digital; business models, production systems, machines, operators, products and services. however, this must consider many factors, i.e. respective regional condition, social aspect, regulation and internal organization requirement with regard to business process and costeffectiveness and the most important is its functionality that appropriates with a respective industry. otherwise, it will undoubtedly end in dissatisfaction. there is a rule of thumb that the industry needs to measure their efforts of poka-yoke implementation as performance measurement. organizations need to conduct the right measures and then make encouragements if there is a wrong direction of chosen approaching. however, that information is hard to get, and only specific articles provide measurement values. for future research, production effectivity metrics need to be developed to justify the performance value before poka-yoke approaching against post-implementation. acknowledgement: the paper is a part of quality engineering study project in mercu buana university jakarta, indonesia. references ahmed, m. b., sanin, c., & szczerbicki, e. 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(2018). implementation of zero defect through poka yoke approaches. international journal of pure and applied mathematics, 119(17), 2319–2332. © 2020 by the authors. submitted for possible open access publication under the terms and conditions of the creative commons attribution (cc by) license (http://creativecommons.org/licenses/by/4.0/). operational research in engineering sciences: theory and applications vol. 4, issue 1, 2021, pp. 82-98 issn: 2620-1607 eissn: 2620-1747 doi: https:// doi.org/10.31181/oresta2040182c * corresponding author. tcakar@gelisim.edu.tr (t. cakar), bcavus@ibu.edu.mk (b. çavuş) supplier selection process in dairy industry using fuzzy topsis method tarik cakar *1, burcu çavuş 2 1 i̇stanbul gelisim university, engineering and architect faculty, industrial engineering department, turkey 2 international balkan university, engineering faculty, industrial engineering department, north macedonia received: 20 december 2020 accepted: 12 february 2021 published: 20 march 2021 research paper abstract: supplier selection is one of the most critical processes within the purchasing function. choosing the right supplier makes a strategic difference to an organization’s ability to reduce costs and improve the quality of products by helping to select the most suitable supplier. sütaş dairy company, which is entered to macedonia market in 2012. in the dairy company, there is only one purchasing manager who selects the farmers. importance weights of criteria are determined using his reference, and also the alternatives are evaluated according to each criterion. the most important criteria are product and other costs, the price is also playing an important role, but due to the small marketplace of macedonia, the prices are almost the same in every region. to select the dairy supplier in macedonia, fuzzy topsis technique is used. the main goal of using fuzzy logic in this study is to help decision-makers for identifying the importance of selection criteria and rank possible suppliers easily. since the supplier selection process is a multi-criteria decision making (mcdm) problem, after identify the weights and rankings in a fuzzy environment, topsis algorithm has been used in the rest of the problem. finally, fuzzy topsis methodology has been implemented successfully, and its result pointed out the most suitable suppliers. keywords: supplier selection, fuzzy topsis, dairy industry 1. introduction in today’s competitive world, supply chain management has a significance role in the companies’ plan due to survive and stay competitive. supply chain management is a management process that consists of getting raw materials by selecting the best supplier into the organization, work on the raw materials to produce end products, and also supply chain management involves customer satisfaction. since the procurement of raw material is the first and vital step of supply chain management, we may say that supplier selection has a numerous significant place in supply chain supplier selection process in dairy industry using fuzzy topsis method 83 management. also, organizations exist due to serve customers and satisfy their needs. because if there is not any customer, the organizations can not survive anymore. also, from another point of view, the businesses must stay competitive in the global marketing area not to lose their potential of consumers as well as their stakeholders. the common ground of all these goals of the organizations is passing through the select a suitable supplier. because a well-selected supplier can affect all needs and objectives of any organization, accordingly this study focuses on the selecting the best supplier and represent the supplier selection process in the dairy industry. supplier selection is a cross-functional group decision-making problem where the decision-makers from different parts of an organization. it is providing a long-term decision process due to it affects firm’s expectations from raw material to the end products and also regarding end products customers’ satisfaction. the role of purchasing managers (buyers) has become very important because supplier selection is an essential task within the purchasing function. however, since the supplier selection is a cross-functional group decision-making process, it involves different company departments, not only purchasing manager. on the hand, the purchasing department is influenced by several sets of factors such as individual, interpersonal, organizational, and environmental. on the other, supplier selection is a complicated process that may involve several and different types of criteria, a combination of different decision models, group decision-making, and various forms of uncertainty. therefore, the supplier selection process is one of multi-criteria decision making (mcdm) problems, and techniques for order performance by similarity to ideal solution (topsis), which is one of the known classical mcdm methods, may provide the basis for developing supplier selection models that can effectively overcome with these uncertainties. for this purpose, in this work topsis method is applied with its fuzzy renewal. moreover, according to benyoucef et al. (2003), there are two different aspects that characterize the supplier selection problem. the first aspect is the determination of a number of the suppliers by considering the characteristics of the company product and market and the second aspect is the selection of the best suppliers among existing alternatives. in this study, we consider the second aspect of the problem. therefore, we assume that the number of suppliers to be selected are already given. 2. literature review according to vinodh et al. (2011), supplier selection is a cross-functional group decision-making problem providing long-term decision for the company, and mazaher et al. (2013) mentioned that objective of supplier selection is to identify suppliers with the highest potential for meeting a firm’s needs consistently. professionals believe that supplier selection is an essential task within the purchasing function. therefore, the decision of supplier selection takes an essential place for the businesses. supplier or vendor selection processes are complicated by reason of various criteria have to be taken into account while decision making. from the beginning of the 1960’ s the analysis of criteria for the supplier selection and calculating their performance have been the focus of many academists, decisionmakers, and purchasing managers. cakar and çavuş /oper. res. eng. sci. theor. appl. 4 (1) (2021) 82-98 84 through define the selection criteria of suppliers, one of the most important study prepared by dickson (1966). dickson’s studies has based on a questionnaire sent to 273 buying managers and directors who are members of the national association of purchasing managers. as a result of this study, he identified 23 criteria that are still the main priorities of the supplier selection process and ranked concerning their importance. in the past, because cost reduction is the main priority for a decision-makers, the price was the key factor in choosing a supplier. however, the evolution of the industrial environment and hard competitive business world modified the degrees of the relative of these selection criteria and new criteria have to be taken into consideration by the decision-makers. for instance, weber et al. (1991) examined 74 supplier selection articles, which were published from 1966 to 1990, and also covered the dickson’s study. literature is very rich about supplier selection. in the nineties, ellram (1990) presented three principal criteria for supplier selection problem which are: 1) the financial statement of the supplier, 2) organizational culture and strategy of the supplier, and the last one 3) technological state of the supplier. also, for each criterion, the author defined several sub-criteria. like ellram’s principal criteria, barbarosoglu and yazgac (1997) proposed another three principal criteria: 1) the performance of the supplier, 2) technical capability and financial of the supplier, and 3) the quality system of the supplier, and each one have some sub-criteria. cherangi et al. (2004) conducted a cluster analysis of 110 research papers which are written in 1990-2001 regarding critical success factors. cherangi et al. compared their literature review with the literature review of weber et al. and updated the criteria. ho et al. (2010) assessed the 78 articles which were published the international magazines in 2000-2008. thiruchelvam and tookey (2011) examined 46 new articles, articles were written for engineering and manufacturing departments and published in international scientific magazines from 2000 to 2011. from the recent studies, johan and jimmy (2011) presented a review that was structured by four main headings such as the supplier selection process, buyingspecific factors, organizational factors, and inter-organizational factors, and each heading purposed sub-headings. supplier selection criteria for the identification of solution to problems to select the best supplier is the first and important step. however, after determining criteria, solution of the problem, in another word the process which leads to the best supplier, is important as much as criteria definition. therefore, another literature review was prepared with respect to used methods in supplier selection. there has been wide labor to develop decision techniques and methods for supplier selection. some previous reviews of these decision techniques have been prepared by holt (1998), ho et al. (2010), and agarwal et al. (2011). holt (1998) presented an article about the contractor evaluation and selection modeling methodologies. some of these methodologies are multiple regression, fuzzy set theory, multi-attribute analysis, and cluster analysis. the merits/demerits and previous/possible future applications of each methodology were also discussed. ho et al. (2010) examined 78 articles in 2000-2008. in this study, several individual and integrated approaches are proposed to solve supplier selection problems. according to its result, the most common of the integrated approach is analytic hierarchy processhierarchy process (ahp), and the most commons of the individual approach supplier selection process in dairy industry using fuzzy topsis method 85 are data envelopment analysis (dea), mathematical programming, and ahp. agarwal et al. (2011) have prepared a literature review which involves 68 articles written from 2000 to 2011 which were about multiple-criteria decision making methods. as the result of ho et al.’s study, this work also gave similar results and showed that the most commons of applied processes were dea, mathematical programming, and ahp. pearn et al. (2004) made sound the selection power analysis of the method using simulation and process capability. the certainty analysis provides useful information related to the sample size necessary for specified selection power. to tailor this method for in-plant applications and to select the better supplier and calculate the size of the difference between the two suppliers pearn et al. (2004) developed a two-phase selection procedure. because supplier selection abounds in the literature, only several methods mentioned above. however, the methods have been classified a little bit differently but mostly the same in the literature. one of the literature review on supplier selection was prepared by junyi et al. (2012). by using a methodological decision analysis in four aspects, including decision problems, decision-makers, decision environments, and decision approaches, they selected and reviewed 123 articles published in 2008-2012. to examine the research trend on uncertain supplier selection, they classified the articles into seven categories according to different uncertainties and 26 decision making techniques identified from three perspectives: firstly, mcdm techniques, secondly, mathematical programming (mp) techniques, and the last one artificial intelligence (ai) techniques. jadidi et al. (2009) used the topsis method and multi-objective mixed integer linear programming in order to solve the complicated problem, which is used to define the optimum quantities among the selected suppliers. rouyendegh et al. (2014) mentioned that supplier selection is mostly a complex multi-criteria problem which consists of qualitative and quantitative factors. therefore to deal with optimal decision making for selecting the best supplier and allocating order, applied the method of integrated fuzzy topsis and multi-choice goal programing (mcgp). firstly they used a fuzzy topsis to determine uncertain and imprecise judgment of decision-makers and, for the final supplier selection and order allocation, applied the mcgp model. tayyar et al. (2013) utilized ahp and vikor models to solve the problem of determining the best subcontractor among those which sew the orders of the worldwide known brands in the clothing sector through mcdm models. in addition, sachin and ravi, (2014) utilized a two-step method to identify and rank the solutions of knowledge management (km) adoption in the supply chain (sc) and overcome its barriers. at the first step, ahp was used to determine the weights of the barriers as criteria. at the second step, topsis was applied to obtain final ranking of the solutions of km adoption in sc. also, nydic and hill, (1992) and narasimahn, (1983) used ahp, and akman and aklan, (2006), fuzzy ahp to determine the best suppliers. a study published by yue, (2014) which aims to develop a new methodology for group decision-making (gdm) problems in an intuitionistic fuzzy environment. the weights of decision-makers were determined by using an extended topsis technique. the individual decisions of decision-makers were then converted into the group decision of alternatives. then the preference of alternatives was ranked by using an extended topsis technique. in order to show the major technical advances in the applied model, comparisons between the proposed method and other methods were studied. besides these approaches, three injection timing and three injector cakar and çavuş /oper. res. eng. sci. theor. appl. 4 (1) (2021) 82-98 86 protrusion settings were tested to study engine performance and exhaust emissions. the experimental results were evaluated using two multi-criteria decision-making techniques ahp and topsis and the optimal fuel type-injection timing-injector protrusion configuration was selected. another study proposed by izadikhah, (2009) by applying the topsis method to deal with fuzzy data for determining the best choice among all possible alternatives. in his approach, one of the yager indices, which were used for ordering fuzzy quantities in [0, 1], was applied to identify the fuzzy ideal solution and fuzzy negative ideal solution. the result of yager's index gave a procedure for choosing fuzzy ideal and negative ideal solutions directly from the data for observed alternatives. then, he proposed the hamming distance for calculating the distance between two fuzzy triangular numbers. demiral, (2013) used fuzzy linear programming in production planning among several optimization opportunities in the dairy industry. several reasons, such as an uncertain supply of milk and demand of dairy products and the results of the fuzzy linear programming model are more realistic than a linear programming model and more profitable in terms of the firm, made preferred the fuzzy linear programming. also, guan et al. took into account uncertain milk supply, price–demand curves and contracting, and applied multistage stochastic programming to a production planning problem for fonterra, a leading company in the new zealand dairy industry. they described a model for uncertain milk supply and a model for fonterra's supply chain. then presented a multistage stochastic quadratic programming model and a decomposition algorithm to compute an optimal sales policy, which is tested in simulation against a deterministic policy. jouzdani et al. (2013) proposed another study based on minimizing the costs of facility location, traffic congestion and transportation of raw/processed milk and dairy products under demand uncertainty by dynamic dairy facility location, and supply chain planning. they proposed a model which was dynamically incorporated possible changes in the transportation network, facility investment costs, the monetary value of time, and changes in the production process. zavadkas et al. (2020) studied on mcdm techniques for improving the sustainability engineering process. markovic et al. (2020) proposed a novel integrated subjective-objective mcdm model for alternative ranking in order to achieve business excellence and sustainability. gegovska et al. (2020) used fuzzymcdm technics and artificial neural networks for the green supplier selection process. matic et al. (2019) applied a new hybrid mcdm model: sustainable supplier selection in a construction company. puska et al. (2018) proposed a new way of applying interval fuzzy logic in group decision making for supplier selection. stevic et al. (2016) applied an integrated fuzzy ahp and topsis model for supplier evaluation. sahin et al. (2020) applied fuzzy topsis method for dry bulk carrier selection. jain et al. (2018) used fuzzy topsis and fuzzy ahp to select suppliers in the indian automotive industry. this study fills a gap in the literature by choosing a supplier in the dairy industry with a large number of specified criteria. although milk suppliers are similar due to their structure, there are differences among them, such as capacity, systematic work, technical structure, etc. determining these different criteria made it easier for us to decide among suppliers. this study determines the suppliers by solving a very supplier selection process in dairy industry using fuzzy topsis method 87 complex decision problem using the fuzzy-topsis method according to ten different criteria. 3. topsis method and its fuzzy extension in supplier selection problems, according to the characteristics of products, there can be differences between product types, which are procured by a supplier. for instance, some product types of a supplier can be more expensive when classed the products with similar types of product of other suppliers. if we give an example in the dairy industry, the supplied product is milk, and it can have more fat than other suppliers` milk. thus worth of a supplier can change with reference to each product it supplies. therefore, the significance worth of each supplier with regard to relevant product is determined via fuzzy technique for order preference by similarity to ideal solution (topsis). the classical topsis is developed by hwang and yoon in 1981 as an alternative method to the electre method. as mentioned previously, topsis is one of the mcdm methods, and it is based on calculating the distance of alternatives from the positive ideal solution and the negative ideal solution by using euclidean distance approach. therefore in the topsis method ideal solution should have shortest distance from the positive ideal solution and the farthest distance from the negative solution in the geometric sense. in this method, the alternatives are compared by identifying weights for each criterion, secondly normalizing scores for each criterion, and lastly, calculating the distance between each alternative and the ideal alternative, which is the best score in each criterion. the meaning of ideal alternative is related to criteria. for instance, considering the cost decision maker should take the lowest alternative whereas for profit, the decision-maker should choose the highest value as an ideal alternative. the terms used in the topsis are briefly defined as follows: criteria: criteria/attributes ( , 1, 2,..., ) j c j n= should provide a means of evaluating the levels of an objective. each alternative can be characterized by a number of criteria. alternatives: as mentioned in mcdm alternatives are synonymous with ‘options’ or ‘candidates’. alternatives ( , 1,..., ) i a i m= are different from each other. criteria weights: weight values ( ) j w show the relative importance of each criterion to the others.  | 1, 2,...,jw w j n= = (1) normalization: the purpose of normalization is to gain comparable scales, which allows comparisons across criteria and it transforms various criterion dimensions into non-dimensional criteria. to calculate the normalized value of ij x , the vector normalization approach divides the rating of each attribute by its norm. the equation of ij x , is in below: cakar and çavuş /oper. res. eng. sci. theor. appl. 4 (1) (2021) 82-98 88 2 1 , ij ij m ij i x r x = =  1,..., ;i m= 1,..., .j n= (2) topsis method is consisting of six steps, and within the presented steps, it is benefited from the study of hwang and yoon (1981) and yang and hung (2007). step 1: calculate normalized rating for each element in the decision matrix using the normalization the equation. step2: construct the weighted normalized ratings. the weighted normalized value ij v is calculated by equation below: , ij ij ij v w r= 1,..., ;i m= 1,..., .j n= (3) new matrix generated from the multiplication of the normalized decision matrix by its associated weight. step 3: determine the positive ideal *(a ) , and negative ideal (a )− solutions. the positive ideal solution equation is;  * * *1a ,..., v ,nv= (4) where  * (max | ), (min | ) 1,...,j ij ijiiv v j b v j c i m=   = . (5) the negative ideal solution equation is;  1a ,..., v ,nv − − − = (6) where  (min | ),(max | ) 1,...,j ij iji iv v j b v j c i m− =   = (7) where b is a set of benefit attributes (larger-the-better type) and c is a set of cost attributes (smaller-the-better type). step 4: calculate the distance measures for each alternative. the distance between alternatives can be measured by the n-dimensional euclidean distance. the separation from positive ideal solution, *a is given by the equation as in follow, * * 2 1 ( ) , n i ij j j s v v = = − 1,..., .i m= (8) similarly, the separation from the negative ideal solution, a− , is given by the equation below, supplier selection process in dairy industry using fuzzy topsis method 89 2 1 ( ) , n i ij j j s v v − − = = − 1,..., .i m= (9) step 5: calculate relative closeness to the ideal solution * i c ; * * ,i i i i s c s s − − = + 1,..., .i m= (10) in this step, the important point is that *0 1 i c  where * i c =0 when a a , i − = and * i c =1 when * i a a= step 6: rank preference order and according to preference rank order of * i c the best satisfied alternative can be decided. therefore, the best alternative is the one that has the closest distance to the ideal solution, which means the ideal solution is guaranteed to have the farthest distance to the negative ideal solution. further from the classical topsis method, uncertainty of the decision making environment is regarded by the fuzzy evaluations included in the fuzzy topsis process. similar to the topsis approach, in the fuzzy topsis, an optimal alternative that is nearest to the fuzzy positive ideal solution (fpis) and farthest from the fuzzy negative ideal solution (fnis). a detailed description and treatment of fuzzy topsis are discussed by many academicians (for instance, see: yang and hung (2007), govindan et al. (2013), saghafian and hejazi (2005), kilic(2012, 2013) and etc.) and we have adapted from dymova et al., (2013) and kilic (2013) the relevant steps of fuzzy topsis as presented below. the definitions of the related symbols used in the equations are as follows. the definitions of the symbols k: the number of decision-makers i: alternative j: criterion : ij x the rating of alternative “i” with respect to criterion j. : j w the importance of criterion j. : ij r normalized triangular fuzzy number : ij r matrix of normalized triangular fuzzy number : ij v weighted normalized triangular fuzzy number :v a matrix consisting of weighted normalized triangular fuzzy numbers ( , b , c ) : ij ij ij a the lower, middle and upper values in the triangular fuzzy numbers indicating the rating of alternative “i” with respect to criterion “j” cakar and çavuş /oper. res. eng. sci. theor. appl. 4 (1) (2021) 82-98 90 (w , w , w ) : ij ij ij the lower, middle, and upper values in the triangular fuzzy numbers indicating the importance of criterion j. step 1: in this step, the importance of criteria and the alternative ratings with respect to the criteria are evaluated by the decision-makers. each criterion is evaluated according to linguistic variables as shown in table 1, and each alternative is rated via table 2. step 2: table 1. shows linguistic variables and fuzzy triangular numbers for criteria evaluation. table 2. shows linguistic variables and fuzzy triangular numbers for criteria evaluation. alternative ratings ij x and criteria importance j w are computed by multiplying each data with their own weights. table 1. linguistic variables for criteria evaluation linguistic variable fuzzy numbers very low(vl) low (l) medium low (ml) medium (m) medium high (mh) high (h) very high (vh) (0,0,0.1) (0,0.1,0.3) (0.1,0.3,0.5) (0.3,0.5,0.7) (0.5,0.7,0.9) (0.7,0.9,1) (0.9,1,1) table 2. linguistic variables for alternative ratings linguistic variable fuzzy numbers very poor (vp) poor (p) medium poor (mp) fair (f) medium good (mg) good (g) very good (vg) (0,0,1) (0,1,3) (1,3,5) (3,5,7) (5,7,9) (7,9,10) (9,10,10) step 3: normalizing the decision matrix. an appropriate and method logically justified method for normalization of fuzzy decision matrices was developed in chen (2000), and if ( , 1, 2,..., , 1, 2,..., n, ) ij x i m j= = are triangular fuzzy numbers, then the normalization process can be performed by: [ ] ( , , ) , , , 1,...m; ij ij ijl m u ij mxn ij ij ij ij b j j j a b c r r r r r r i j k c c c + + +   =  = = =       (11) supplier selection process in dairy industry using fuzzy topsis method 91 where , max ( ); j i ij b c c j k + =  (12) if the criterion is a cost, the following equation is taken into consideration: ( , , ) , , , 1,...m; l m u i i i ij ij ij ij c ij ij ij a a a r r r r i j k c b a − − −  = = =       (13) where min ( ); . j i ij c a a j k − =  (14) because fuzzy set is in [0,1] range, this normalization provides that [0,1] ij r  for all i and j. step 4: the weighted normalized the fuzzy decision matrix is obtained. the definitions of the related symbols used in the equations are as follows. [ ] ij mxn v v= 1, 2,..., , 1, 2,..., n,i m j= = (15) . ij ij j v r w= (16) step 5: definition of fuzzy positive ideal solution and fuzzy negative ideal solution values. ã+ = {r̃1+, r̃2+,…,r̃n+} = {maxi {(rijl, rijm, riju)} | j ϵ km, mini{(rijl, rijm, riju)} | jϵ ku}, (17) ãˉ = {r̃1ˉ, r̃2ˉ,…,r̃nˉ } = {mini{( rijl, rijm, riju)} | jϵ km , maxi {(rijl, rijm, riju)} | j ϵ ku }. (18) step 6: the distances of each alternative from fuzzy positive and negative ideal solutions are calculated using the vertex method as follows: 𝑆𝑖 ∗ = ∑ 𝑤𝑗 (�̃�𝑗 + − �̃�𝑖𝑗 ) + ∑ 𝑤𝑗 (�̃�𝑖𝑗 − �̃�𝑗 −),𝑛𝑗𝜖𝐾𝑢 𝑛 𝑗𝜖𝐾𝑚 19) 𝑆𝑖 − = ∑ 𝑤𝑗 (�̃�𝑖𝑗 − 𝑟𝑗 −) + ∑ 𝑤𝑗 (�̃�𝑖𝑗 − �̃�𝑗 +)𝑖 = 1,2, … , 𝑚, 𝑗 = 1,2, … , 𝑛.𝑛𝑗𝜖𝐾𝑢 𝑛 𝑗𝜖𝐾𝑚 (20) 𝑆𝑖 ∗ = √ 1 3 [(�̃�𝑛 + − �̃�11) 2 + (�̃�𝑛 + − �̃�21) 2 + (�̃�𝑛 + − �̃�31) 2] 21) 𝑆𝑖 − = √ 1 3 [(�̃�11 − �̃�𝑛 −)2 + (�̃�21 − �̃�𝑛 −)2 + (�̃�31 − �̃�𝑛 −)2] (22) step 7: the fuzzy closeness coefficient i cc is computed as shown in the equation below, and the highest result is selected as the best alternative. * 1, 2,..., .i i i i s cc i m s s − − = = + (23) cakar and çavuş /oper. res. eng. sci. theor. appl. 4 (1) (2021) 82-98 92 4. application of fuzzy-topsis method in dairy industry in this section, we will apply fuzzy topsis method in the supplier selection problem in the dairy industry. sütaş dairy company is a newly built factory in macedonia. the company produces packaged and pasteurized milk, yogurt, ayran (yogurt drink), and other milk products. therefore there needs to be a daily milk supply, and to be competitive in the sector, and the company wants to choose the right suppliers and increase its efficiency. for this purpose, fuzzy topsis method will be used for the selection of suppliers. firstly we defined criteria with purchasing manager of the company, who is an expert on purchasing function, and decide to select suppliers. selection criteria have been determined by studying other similar supplier selection problems, and taking into account the specific structure of the dairy industry. the criteria are taken into consideration while supplier selection and they are as follows: 1. price: the price of raw milk when buying from farmers, and each farmer gives different values due to their local costs. however, the prices in every region of macedonia are almost the same. 2. product: it is raw milk which is bought from suppliers. also, it shows an alteration according to regions. 3. on time delivery: the delivered time of raw milk to the company from the first farmers. 4. capacity of supply: the capacity of raw milk which suppliers daily produce. 5. performance history: performance history of suppliers. 6. conflict problem solving capacity: it defines farmers’ ability to solve problems such as the sickness of animals. 7. location: the region where the suppliers are present. this criterion is considering to region of the supplier where the quality product can be supply. (i.e., air pollution, industrial area, capacity of farming and etc.) 8. transportation cost: the company is buying raw milk from different cities. therefore it causes costs, and we took into consideration. 9. technological capability: it is the power of using technology. 10. other costs: all costs except transportation cost. table 3. the evaluation for criterion importance weight criterion evaluation cr1 (price) mh cr2 (product) vh cr3 (on time delivery) h cr4 (capacity of supply) mh cr5 (performance history) ml cr6 (conflict problem solving capacity) m cr7 (location) m cr8 (transportation) ml cr9 (technological capability) m cr10 (other costs) vh supplier selection process in dairy industry using fuzzy topsis method 93 after defining criteria, they are evaluated by using linguistic terms. fuzzy linguistic terms of importance weight of the criteria are shown in table 3. alternative suppliers are determined as cities. there are six supplier cities, and their names as skopje, bitola, kumanovo, prilep, kocani, and tetovo-gostivar. tetovo and gostivar are presumed as one supplier. the linguistic values of alternatives related to criteria are presented in table 4. table 4. the evaluation of decision-makers for alternative ratings the linguistic terms of criteria are converted to triangular fuzzy numbers, and they will be used as weights in fuzzy topsis algorithm. fuzzified criteria can be seen in table 5. table 5. fuzzy weights of criteria crıterıon weıghts price (0.5,0.7,0.9) product (0.9,1.0,1.0) on time delivery (0.7,0.9,1.0) capacity of supply (0.5,0.7,0.9) performance history (0.1,0.3,0.5) conflict problem solving capacity (0.3,0.5,0.7) location (0.3,0.5,0.7) transportation (0.1,0.3,0.5) technological capability (0.3,0.5,0.7) other costs (0.9,1.0,1.0) to prepare a decision matrix, the linguistic terms of alternatives are defined as triangular fuzzy numbers, which can be seen in table 6. in the decision matrix, there are three cost criteria as well as seven benefit criteria, and they should be comparable values. for this purpose, each benefit criteria set, the highest value is taken, and all the other values are divided by this highest value. table 6. fuzzy decision matrix and fuzzy weights of criteria cr1 cr2 cr3 cr4 cr5 skopje (5,7,9) (5,7,9) (7,9,10) (7,9,10) (5,7,9) prilep (7,9,10) (3,5,7) (5,7,9) (5,7,9) (5,7,9) kumonovo (9,10,10) (5,7,9) (3,5,7) (5,7,9) (3,5,7) bitolo (5,7,9) (5,7,9) (5,7,9) (9,10,10) (7,9,10) kocani (9,10,10) (5,7,9) (5,7,9) (3,5,7) (3,5,7) tetova-gv (5,7,9) (7,9,10) (9,10,10) (9,10,10) (9,10,10) weight (0.5,0.7,0.9) (0.9,1.0,1.0) (0.7,0.9,1.0) (0.5,0.7,0.9) (0.1,0.3,0.5) suppliers cr1 cr2 cr3 cr4 cr5 cr6 cr7 cr8 cr9 cr10 skopje mg mg g g mg g f vg f mg prilep g f mg mg mg mg g f f f kumonovo vg mg f mg f mg mg g f f bitola mg mg mg vg g g mg mp mg f kocani vg mg mg f f mg g mg f f tetova-gostivar mg g vg vg vg g g g g f cakar and çavuş /oper. res. eng. sci. theor. appl. 4 (1) (2021) 82-98 94 cr6 cr7 cr8 cr9 cr10 skopje (7,9,10) (3,5,7) (9,10,10) (3,5,7) (5,7,9) prilep (5,7,9) (7,9,10) (3,5,7) (3,5,7) (3,5,7) kumonovo (5,7,9) (5,7,9) (7,9,10) (3,5,7) (3,5,7) bitolo (7,9,10) (5,7,9) (1,3,5) (5,7,9) (3,5,7) kocani (5,7,9) (7,9,10) (5,7,9) (3,5,7) (3,5,7) tetova-gv (7,9,10) (7,9,10) (7,9,10) (7,9,10) (3,5,7) weight (0.3,0.5,0.7) (0.3,0.5,0.7) (0.1,0.3,0.5) (0.3,0.5,0.7) (0.9,1.0,1.0) for the cost sets, the lowest value is selected, and it is divided by the rest values. as a result of those calculations, a normalized fuzzy decision matrix is obtained. it is shown in table 7. table 7. fuzzy normalized decision matrix cr1 cr2 cr3 cr4 cr5 skopje (0.56,0,71,1) (0.5,0.7,0.9) (0.7,0.9,1.0) (0.7,0.9,1.0) (0.5,0.7,0.9) prilep (0.5,0,56,0,71) (0.3,0.5,0.7) (0.5,0.7,0.9) (0.5,0.7,0.9) (0.5,0.7,0.9) kumonovo (0.5,0.5,0.56) (0.5,0.7,0.9) (0.3,0.5,0.7) (0.5,0.7,0.9) (0.3,0.5,0.7) bitolo (0.56,0,71,1) (0.5,0.7,0.9) (0.5,0.7,0.9) (0.7,0.9,1.0) (0.7,0.9,1.0) kocani (0.5,0.5,0.56) (0.5,0.7,0.9) (0.5,0.7,0.9) (0.3,0.5,0.7) (0.3,0.5,0.7) tetova-gv (0.56,0,71,1) (0.7,0.9,1) (0.9,1.0,1.0) (0.9,1.0,1.0) (0.9,1.0,1.0) cr6 cr7 cr8 cr9 cr10 skopje (0.7,0.9,1.0) (0.3,0.5,0.7) (0.1,0.1,0.11,) (0.3,0.5,0.7) (0.33,0.429,0.6) prilep (0.5,0.7,0.9) (0.7,0.9,1.0) (0.143,0.2,0.33) (0.3,0.5,0.7) (0.429,0.6,1) kumonovo (0.5,0.7,0.9) (0.5,0.7,0.9) (0.10,0.11,0.143) (0.3,0.5,0.7) (0.429,0.6,1) bitolo (0.7,0.9,1.0) (0.5,0.7,0.9) (0.2,0.33,1) (0.5,0.7,0.9) (0.429,0.6,1) kocani (0.5,0.7,0.9) (0.7,0.9,1.0) (0.11,0.143,0.2) (0.3,0.5,0.7) (0.429,0.6,1) tetova-gv (0.7,0.9,1.0) (0.7,0.9,1.0) (0.10,0.11,0.143) (0.7,0.9,1.0) (0.429,0.6,1) the next step is the fuzzy topsis method is to determine the weighted normalized fuzzy decision matrix. in this step, the normalized decision matrix is multiplied by the importance weights of criteria, as shown in table 8. table 8. fuzzy weighted normalized decision matrix cr1 cr2 cr3 cr4 cr5 skopje (0.28,0.497,0.9) (0.45,0.7,0.9) (0.49,0.81,1.0) (0.35,0.63,0.9) (0.05,0.21,0.45) prilep (0.25,0.392,0.639) (0.27,0.5,0.7) (0.35,0.63,0.9) (0.25,0.49,0.81) (0.05,0.21,0.45) kumonovo (0.25,0.35,0.504) (0.45,0.7,0.9) (0.21,0.45,0.7) (0.25,0.49,0.81) (0.03,0.15,0.35) bitolo (0.28,0.497,0.9) (0.45,0.7,0.9) (0.35,0.63,0.9) (0.35,0.63,0.9) (0.07,0.27,0.5) kocani (0.25,0.35,0.504) (0.45,0.7,0.9) (0.35,0.63,0.9) (0.15,0.35,0.63) (0.03,0.15,0.35) tetova-gv (0.28,0.497,0.9) (0.63.0.9,1.0) (0.63,0.9,1.0) (0.45,0.7,0.9) (0.09,0.3,0.5) cr6 cr7 cr8 cr9 cr10 skopje (0.21,0.45,0.7) (0.09,0.25,0.49) (0.01,0.03,0.055) (0.09,0.25,0.49) (0.297,0.429,0.6) prilep (0.15,0.35,0.63) (0.21,0.45,0.7) (0.0143,0.06,0.071) (0.09,0.25,0.49) (0.387,0.6,1) kumonovo (0.15,0.35,0.63) (0.15,0.35,0.63) (0.01,0.033,0.05) (0.09,0.25,0.49) (0.387,0.6,1) bitolo (0.21,0.45,0.7) (0.15,0.35,0.63) (0.02,0.099,0.1) (0.15,0.35,0.63) (0.387,0.6,1) kocani (0.15,0.35,0.63) (0.21,0.45,0.7) (0.011,0.0429,0.055) (0.09,0.25,0.49) (0.387,0.6,1) tetova-gv (0.21,0.45,0.7) (0.21,0.45,0.7) (0.01,0.033,0.05) (0.21,0.45,0.7) (0.387,0.6,1) after calculation of weighted normalized decision matrix, fuzzy positive ideal solution ( a+ ) and fuzzy negative ideal solution ( a− ) are determined. for fuzzy positive ideal solution the highest value of each benefit criteria column and the lowest value of each cost criteria column are taken into consideration. the determination of fuzzy negative ideal solution has a reverse situation and the values shown as follows: supplier selection process in dairy industry using fuzzy topsis method 95 * [(0.25,0.25,0.25),(1.0,1.0,1.0),(1.0,1.0,1.0),(0.9,0.9,0.9),(0.5,0.5,0.5), (0.7,0.7,0.7),(0.7,0.7,0.7),(0.01,0.01,0.01),(0.7,0.7,0.7),(0.297,0.297,0.297)] a = [(0.9,0.9,0.9),(0.27,0.27,0.27),(0.21,0.21,0.21).(0.15,0.15,0.15),(0.03,0.03,0.03), (0.15,0.15,0.15,),(0.09,0.09,0.09),(0.1,0.1,0.1),(0.09,0.09,0.09),(1.0,1.0,1.0)] a − = to calculate each alternative’s distance from fuzzy positive ideal solution and fuzzy negative ideal solution vertex method is used. the results are shown in table 9 and table 10. table 9. the distances from positive ideal solutions cr1 cr2 cr3 cr4 cr5 cr6 cr7 cr8 cr9 cr10 * s (skopje, * a ) 0.426 0.37 0.31 0.35 0.31 0.35 0.45 0.0284 0.45 0.191 * s (prilep, * a ) 0.343 0.54 0.44 0.45 0.31 0.38 0.32 0.0456 0.45 0.445 * s (kumonovo, * a ) 0.158 0.37 0.58 0.45 0.35 0.35 0.38 0.0266 0.45 0.445 * s (bitolo, * a ) 0.402 0.37 0.44 0.35 0.28 0.35 0.38 0.0733 0.38 0.445 * s (kocani, * a ) 0.158 0.37 0.44 0.56 0.35 0.35 0.32 0.0322 0.45 0.445 * s (tetova-gv, * a ) 0.402 0.22 0.22 0.28 0.26 0.43 0.32 0.0266 0.32 0.445 table 10. the distances from and negative ideal solutions cr1 cr2 cr3 cr4 cr5 cr6 cr7 cr8 cr9 cr10 * s (skopje, * a ) 0.427 0.45 0.22 0.53 0.26 0.36 0.25 0.0284 0.25 0.191 * s (prilep, * a ) 0.5 0.28 0.24 0.43 0.26 0.3 0.41 0.0456 0.25 0.445 * s (kumonovo, * a ) 0.542 0.45 0.32 0.43 0.2 0.3 0.35 0.0266 0.25 0.445 * s (bitolo, * a ) 0.427 0.45 0.24 0.53 0.31 0.36 0.35 0.0733 0.35 0.445 * s (kocani, * a ) 0.542 0.45 0.24 0.3 0.2 0.3 0.41 0.0322 0.25 0.445 * s (tetova-gv, * a ) cr1 cr2 cr3 cr4 cr5 cr6 cr7 cr8 cr9 cr10 using the total distance from fuzzy positive ideal solution and fuzzy negative ideal solution fuzzy closeness coefficient i cc is computed as shown in below. table 11. closeness coefficient and their rankings *s s − icc rankıng skopje 2.8094 2.963 0.5133 2 prilep 3.3806 2.65 0.4394 6 kumonovo 3.4016 2.794 0.4509 4 bitolo 3.0683 3.059 0.4992 3 kocani 3.3172 2.639 0.4430 5 tetova-gostivar 2.5216 3.354 0.5708 1 cakar and çavuş /oper. res. eng. sci. theor. appl. 4 (1) (2021) 82-98 96 after calculation of closeness coefficient, they are ranked from large to small values as in shown table 11. regarding the coefficient values, the best supplier is tetova-gostivar. 5. conclusion the supplier selection process is one of the most important activities in the supply chain management. in today’s competitive world, a company or any organization should have right supplier selection methodology to provide a sustainable system. however, it is known that available information regarding supplier selection problems is often uncertain and changeable. also, decision making for supplier selection becomes quite complicated because rather than the classical methods, which only focus on cost and profit, the supplier selection process is consisting of a wide range of factors such as product, quality, on time delivery time, etc. moreover, the supplier selection process is a kind of multi-criteria decision making problem. therefore, companies or organizations should have a strategic approach to choose the right suppliers considering all reasons that we mentioned. using fuzzy logic may help to overcome these problems while facing in the decision making process and as an extension of multi-criteria decision making methodology, fuzzy topsis is proposed in this study. the main purpose of the topsis algorithm is to find the best solution; in other words, which solution is the closest to positive ideal 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(2013), “selection of the best sub-contractor in clothing sector using ahp and vikor methods”, cbu sosyal bilimler dergisi vol. 11, no. 1. thiruchelvam, s. and tookey, j. (2011), “evolving trends of supplier selection criteria and methods”, international journal of automotive and mechanical engineering, 4:437-454. vinodh, s., r. anesh ramiya, and s. g. gautham, (2011), “application of fuzzy analytic network process for supplier selection in a manufacturing organisation.” expert systems with applications 38: 272–280. weber, c. a., current, j. r. and benton, w. c., (1991), “vendor selection criteria and methods”, european journal of operational research, 50 (1):2-18. yang, t. c., hung, c. (2007). “multiple-attribute decision making methods for plant layout design problem” robotics and computer-integrated manufacturing 23 126– 137 yue, z. (2014), “topsis-based group decision-making methodology in intuitionistic fuzzy setting”, information science. zavadkas, e.k., pamucar, d., stevic, z. et al. (2020), “multi-criteria decision making techniques for improvement sustainability engineering process”, symmetry, vol. 11, issue 6. © 2021 by the authors. it was submitted for possible open access publication under the terms and conditions of the creative commons attribution (cc by) license (http://creativecommons.org/licenses/by/4.0/). supplier selection process in dairy industry using fuzzy topsis method tarik cakar *1, burcu çavuş 2 1. introduction 2. literature review 3. topsis method and its fuzzy extension 4. application of fuzzy-topsis method in dairy industry 5. conclusion references operational research in engineering sciences: theory and applications vol. 4, issue 1, 2021, pp. 19-37 issn: 2620-1607 eissn: 2620-1747 doi: https:// doi.org/10.31181/oresta2040115h * corresponding author. malek.hassanpour@yahoo.com (m. hassanpour). an investigation of five generation and regeneration industries using dea malek hassanpour department of environmental science, ucs, osmania university, telangana state, india received: 04 november 2020 accepted: 03 january 2021 first online: 20 february 2021 research paper abstract: the data envelopment analysis (dea) has employed to figure out the efficiency of various engineering projects in the environment impact assessment (eia) plan and post-eia. the procedure allocated to comprise the input and output variables within industries by the present study. the study was used both weighing systems of the friedman test and the criteria importance through intercriteria correlation (critic) model in the estimation of dea. the objective of the research sought to find the efficiency of industries for the time interval before the establishment of industries and in the screening step of identification of projects. the findings manifested a classification of industries based on the dea model and in both weighing systems. using different weighing systems creates different categories via dea. overall, the dea model is an essential decision-making model in the screening step of eia. keywords: industries, recycling, eia, screening, projects, assessment 1. introduction the first use of plastic films in agriculture applications dates back to 1948. in recent years, with the increasing population and the declining trend of water resources, many countries have made extensive efforts to apply drip irrigation systems to avoid the risks associated with water shortages in agricultural production, modern agriculture, and water use (jha 2016; usman et al., 2016). plastics have used in various applications in agrarian usages. perhaps that is why polymer films, as one of the plastic applications in this field, are interpreted as a revolution that can be extended by expanding their use in all regions of the world to solve many problems related to drought and depletion of water resources. the main applications of polymer plastic films in agriculture are divided into the following. (1) mulch films (2) greenhouse and tunnel coverings (3) silage packaging films (4) solarizing films (5) geo-membranes, etc. from all these applications, greenhouse and tunnel coatings are the largest in terms of quantity consumption. the thickness of films used in this application is usually between 80 to 220 micrometers. they have used in one to hassanpour m/oper. res. eng. sci. theor. appl. 4 (1) (2021) 19-37 20 seven layers depending on the existing technologies in the countries. more than 80% of this market has accommodated by films made of light density poly-ethylene (ldpe), ethylene vinyl acetate, and ethylene butyl acrylate (difallah et al., 2018). today, the lifespan of these coatings varies between 6 months to ten years depending on the geographical location of the region, the polymers used in the greenhouse, and the formulation of various film stabilizers. the european standard din en 13206 has provided guidelines in thermoplastic coatings for use in agriculture and horticulture for measuring the lifespan, dimensions, mechanical properties, light, and the degree of impermeability of infrared waves. the greenhouse and tunnel coating market is a particular market that requires significant investments in massive extrusion lines to produce vast films. most of these films are produced by the blowing film process. problems in stabilizing these large bubbles are one reason why ldpe is used in the production of these films, instead of lldpe, due to the lower strength of the melt. in such cases, when co-extrusion lines are used, the technical complexity and quantity of investment increase significantly. the polymer films and coatings are affected by light, temperature, and chemical degradation during use. therefore, they need requirements that are strongly dependent on environmental parameters for a long lifespan. environmental parameters encompass the type of structure, its design, height, air conditioning, geographical parameters (sunlight and its intensity, temperature, rainfall, altitude, etc.), and chemicals used in the products (jumanne, 2016). it is impossible to achieve all these properties without the use of special additives and the generation of multilayer structures. that is why in recent years the tendency of developed countries has been more towards producing films of five layers and higher. with the development of metallocene catalyst technology, and plasma reactors, new generations of plastics materials, known as enhanced polymers and polymers made up of chemical vapor deposition, were introduced. this generation of plastic products has extraordinary properties compared to ordinary plastics due to their modern manufacturing technologies. these properties include high melt strength, impact resistance, excellent perforation resistance, high transparency, and unique thermal properties. these particular properties make modern plastic products ideal materials for such applications that require high performance (kado et al., 2004; peeters et al., 2014). another application of plastic materials in the framework of polyvinyl chloride (pvc) films are also discussed in this study is their use in the production of drippers in the sprinkler irrigation system, for which many industries have developed in iran. drip irrigation is the slow dispersion of water on the surface or under the soil in the form of separate, continuous, narrow streams or delicate sprays through droppers located along the water transfer line. the recent studies of the international committee on irrigation and drainage for the issues of drip irrigation show that one of the main difficulties in drip systems is the clogging of drippers in all countries of the world. the issue of obstruction is either due to the lack of use of water of good quality or improper selection of the treatment system, which results in uneven distribution of water along the sub-pipes. thus, it reduces irrigation efficiency. the risk of clogging the drippers also increases the cost of maintaining and operating the system, including controlling the drippers and replacing or repairing them (taylor and zilberman, 2017; gutiérrez et al., 2013; wang et al., 2016; raju et al., 2012). the agricultural waste has proliferated and vast quantities of agrarian straw and animal waste produced during recent years. so, investigations suggested setting up an effective recycling program via supporting and encouraging governmental policies an investigation of five generation and regeneration industries using dea 21 (gutiérrez et al., 2013; wang et al., 2016). the annual reports indicate that india has generated around 400 million tons of agrarian waste (raju et al., 2012). agrarian waste has been used in many applications, even utilized to remove dyes from wastewater by bharathi and ramesh (2013). the use of agricultural waste has applauded to generate bioethanol in various studies and cardboard in the current study (hossain et al., 2008). therefore, the industrial projects of discussed options posed to assess in eia. one of the most essential instruments on which to consider environmental considerations in the planning system is the eia. today, in many countries, the eia is one of the most critical strategic instruments of environmental management. to integrate environmental considerations in the planning and developing process at the highest levels, eia is considered as the most essential decision-making instrument. the environmental assessment in the service of sustainable development leads to progress towards sustainability and, consequently, improved the indicators of sustainable development including all economic, social, institutional, and environmental dimensions. protecting the environment, in which future generations should thrive in social life, is a public duty. it is necessary to raise awareness about this plan. it is essential to act strategically, not in the tactical field. in general, environmental assessment is defined as a method by which a correct understanding of the position, role, function, and effects of any natural or humanmade phenomenon in the environment is formed. thus, it is possible to determine the circumstances of the assessment that is related to the environment, its interaction, and the kind of processes and reactions between them. according to the international union of impact assessment, eia is a plan to reduce biophysical, social, and other impacts associated with the proposed development before the primary decision and executive action. analyzing the effects is a coherent scientific tool used to identify, summarize, and organize information related to the environmental impacts of policies, programs, and plans. in strategic & environmental assessment, the analysis and evaluation phase is one of the most critical parts of eia studies. in this section, the current situation and predicted effects on physical and chemical, biological, socioeconomic, and cultural environments are reviewed and analyzed. in fact, in this section, all information and forecasts, (both qualitatively and quantitatively), are standardized and presented in reviews and reports. in this section, according to the description of study services, to understand the significant and essential effects, all impacts are examined and analyzed according to their intensity, importance, and nature so that decisions be made based on them. today, there are several methods for evaluating and analyzing the effects of implementing policies and programs, each of which has its advantages and disadvantages (ieem, 2006). being able to implement these policies and practices may be contrary to today's conditions or nature. however, arrangements can be made for the necessary precautions and measures to be taken. the purpose of the monitoring program is to obtain information that identifies the effects and consequences of the various policies, programs, and activities. the monitoring program should provide a complete description of the techniques used. regarding sampling methods, the essential equipment should be presented in the monitoring program. therefore, it is indispensable that experts of environmental assessment and other relevant staff in various fields and disciplines must be recruited in this team who can evaluate the multiple dimensions of strategic hassanpour m/oper. res. eng. sci. theor. appl. 4 (1) (2021) 19-37 22 decisions, policies, and programs with a macro perspective. the following data are related to the project screening step according to the eia plan to underpin the efficiency score of five industries in iran (vallero, 2004; hassanpour, 2020; dubey and dai, 2006; bahrami et al., 2016; mansour and kesentini, 2008). our studies declare that there is no similar study investigating the efficiency of iranian industries in the screening step of the eia plan across iran. the motivation of the present research gets back to existing difficulties in the way of recently developed and outlined enterprises due to the sanctions approved against the iranian government. the objective of the paper was to figure out the efficiency of industries based on recent prices for the input and output variables of industries in the market of tehran, iran. 2. literature review the efficiency assessment based on the dea model takes into consideration the input and output variables. dea model measures productivity performance based on financial indicators. in this model, if we add other inputs and outputs (net sales, net profit margin, net profit/equity, net profit / total assets, etc.) to the model, different results may occur. for this reason, we can achieve the desired results based on the selected data in the model. statistics can sometimes provide us with this. the division of output to input values releases the dea rank. for example, the sustainability of suppliers has assessed via the fuzzy dea model. by the way, the variables allocated in 15 rows in inputs and outputs variables (zhou et al., 2016). the input and output variables introduced to the dea model based on the constant return to scale encompassed total outlays, co2 dissipation, the number of stations, weekly turn up, and the number of users in the investigation of two rail lines holding six and sixty stations in london, respectively (taboada and han 2020). chinese industries underwent an efficiency assessment using the dea model in seven years. it has been classified based on efficient and inefficient industries in the provinces (xiong et al., 2017). a study addressed the dea model as a potent instrument in economic prosperity assessment at national levels in energy and environment (sueyoshi et al., 2017). the precision and reality of the dea model (slacks-based measures) have investigated with other models. the comparison was reported with enough validity (shermeh et al., 2016). the dea model has been taken into consideration the efficiency and performance assessment of seven indian chemical industries. the findings classified efficient industries with an efficiency border range of the lowest to highest, around 0.713 to 1, respectively (anthony et al., 2019). a study introduced a type of dea model in assessing the seven operational research techniques in business tax. the model succeeded in offering responses of efficient industries and was extendable to similar models in this regard (santos et al., 2018). the efficiency assessment of wind turbines resulted in finding the inefficient cases regarding input variables of wind speed, wind power density, anemometer tower, and wind frequency and tower height and output variables of space between turbines, their directions, and the number of turbines in china (niu et al., 2018). bulak and turkyilmaz, (2014) evaluated 744 turkish suppliers at the efficiency level in a full list of input and output criteria and variables. the footprint of significant air pollutants emitted into the atmosphere by industrial sectors has assessed via the dea model in european union (zurano-cervello et al., 2018). in evaluating the agricultural enterprise, the dea model assigned to release the efficiency score based on financial indicators. the an investigation of five generation and regeneration industries using dea 23 excellent ranking system developed in the following calculations (fenyves et al., 2015). the performance assessment of both turkish and chinese companies used the dea model to detect the ranks, and, in the estimation, the canonical correlation analysis employed as a weighing system. the classification of efficient and inefficient industries paved the way for comparing the companies between two countries (bayyurt and duzu, 2008). the deareturns to scale model has assigned to assess the efficiency score of air transport sectors in 30 provinces in a matrix of 3×3 input and output variables in 2017 in china. according to the results, the majority of sectors appeared with full efficiency or very close values to the top efficiency border (song et al., 2020). andrejić and kilibarda (2016) employed the principal component analysis dea model for figuring out and improving the efficiency of distribution channels of products regarding 16 inputs and 17 outputs variables. the reasons for failure, efficiency fall, and circumstances of efficiency rise have discussed and offered options for expansion and improvement in the efficiency of distribution channels. the results pointed out to improvement of efficiency in four sections within the distribution channels. blagojević et al., (2020) used the fuzzy analytical hierarchical processes – dea model to investigate the performance of nine freight transport railways by selecting five main criteria. the border of efficiency determined in a range of around 0.242 to 1 in both systems of ccr and bcc. a study applied both models of ccr and bcc of the dea model and correlation analysis for determining the efficiency of five automotive companies based on financial statements in europe. findings revealed total efficiency for the mentioned cases (papouskova et al., 2020). dea model based on returns to scale in both systems of ccr and bcc has examined to realize and classify thirty-five indian small and medium-sized industries in facing lean and sustainability-oriented innovation. the score of efficiency placed the industries in a certain interval of 0.832 to 1, and most of them were efficient. a combination of both orientations helps the industries move towards sustainability (de et al., 2020). in brazil, the logistics modes of some projects outlined in transport and cargo handling operation have taken into consideration via the dea-ccr model consist of 12 alternatives, four inputs, and one output variable from 2008 to 2012. the results emerged with full efficiency for all years of study except for 2010. by the way, it offered some improvement options to escalate the efficiency score and impede falling in efficiency reported (lepchak and voese, 2020). by a combination of the entropyfuzzy piprecia-dea model and the presence of six inputs and five outputs, decisions have made in the field traffic safety of nine railways in bosnia and herzegovina. due to significant low efficiency and high risk in safety, two alternatives were held back in the following calculations. the sensitivity analysis has conducted to verify the findings by alteration in quantities of variables in a variety of scenarios (blagojevic et al., 2020). the dea-ccr model has taken into consideration for determining the efficiency of airlines due to a significant decline in efficiency score during the pandemic of covid-19 in asia. it used three inputs and three outputs key variables in the study. the findings proved a significant decline in the performance and efficiency of airlines. to evaluate the monthly performance of the egg generation in a poultry house, integration of dea (slacks-based measure)-critic-gray model has applied. a sample of 8000 chickens selected to breathe in proper conditions of feed and maintenance to evaluate the efficiency in various months of the year (15 months) in çukurova. in the study, three inputs and two outputs variables composed the framework of the data matrix to assess. a sensitivity analysis has done using four hassanpour m/oper. res. eng. sci. theor. appl. 4 (1) (2021) 19-37 24 models of multi-criteria decision-making to examine the validity of results. the final examination had shown a different classification in models for efficiency score (kucukonder et al., 2019). to figure out the efficiency score, the dea model has been considered in a variety of researches pertaining to financial variables and indicators during a specific time interval in the studies conducted by arab et al., (2015), kettiramalingam et al., (2017), raithatha and komera (2016), bagh et al., (2016) in the field of indian manufacturing companies, an indian cement industry, executive compensation relation between indian companies and fifty pakistani companies on the stock market respectively. 3. methodology 3.1. screening of projects by the current study, the initial data were picked up from the screening step of industrial projects by evaluator teams and were investigated to estimate the efficiency of industries (according to figure 1). to estimate the efficiency of industries via dea model was assumed 270 working days per year. the variables were multiplied in the working days. to calculate the costs was used the daily prices in the market of tehran, iran. figure 1. the evaluation steps of eia in iran and procedure conducted 3.2. weighing system of friedman test when the normal distribution of groups is individually uncertain for us, we use the friedman test as one of its essential applications. the blocks of values in the matrix are independent, and data are non-parametric. it is similar to the f test that indicates the samples of groups allocated together. it is also able to classify groups an investigation of five generation and regeneration industries using dea 25 hierarchically. the homogeneity of average weights between values in the friedman test depends on low fluctuations in data introduced into software for further processing (biju and prashanth, 2017; eisinga et al., 2017). the existing friedman test in the spss software was used to estimate the values of weights in the present study. there are a few empirical equations to describe the method, but this research has ignored to include them. 3.3. weighing system of critic the use of the weighing system of critic is encouraging because of its wide application in studies. it is classified in the list of correlation methods. the criterion xij consists of the membership function rij, which converts the existing quantities into an interval [1-0] to present the ideal point. the data matrix is configured with elements of rij with a standard deviation (σj) for the individual vector after translating the initial values. the values of weights are calculated for the assumed criteria by values of cj (vujicic et al., 2017). min max min ij ij i ij ij ij ii x x r x x − = − (1) (2) 1 j j m j j c w c = =  (3) 3.4. traditional dea model the main application of the dea model relies on distinguishing the efficient and inefficient alternatives (industries in this research). the framework of the dea model has been defined based on the division of the sum of weighted outputs variables to the sum of weighted inputs variables according to equation 4. the inputs and outputs variables were the costs of materials, the salary of employees, energy consumed, and industries' products for five industries in the present study, respectively. the vectors of both weighing systems of friedman test and critic were introduced into a matrix of data to sum the final values as productivity of alternatives. then the maximum value of productivity was selected to release the efficiency score (sergi et al., 2020). 1 1 s r m i urk yrk ekk vik xik = = =   (4) regarding an allocation of n dmus (alternatives) to be investigated, and individual dmu j (j=1,…,n) generates s various outputs via applying m different inputs, which are realized as yrj (r = 1,…,s) and xij (i = 1,….,m) respectively. to find out the efficiency (e) score of dmu k needs a division of the weighted sum of outputs over the weighted sum of inputs according to equation 4. by the way, vk =(v1k,…., hassanpour m/oper. res. eng. sci. theor. appl. 4 (1) (2021) 19-37 26 vmk) and uk = (u1k,…., usk) are input and output weighing vectors to evaluate dmu k, as urk and vik are multipliers of the inputs and outputs, respectively (vujicic et al., 2017; hassanpour, 2020). 4. result and discussion to start describing the applied processes in five generation and regeneration industries (drip irrigation system, mobile sprinkler for the home lawn, pvc film generation, cardboard generation of agricultural waste, and plastic waste recycling industries), was displayed their flow diagrams as below (figures 1.1 to 1.5). figure 1.1. diagram of layout units of drip irrigation system manufacturing in iran figure 1.2. diagram of layout units of mobile sprinkler generation industry for the home lawn in iran an investigation of five generation and regeneration industries using dea 27 figure 1.3. diagram of layout units of pvc film generation industry for the agricultural use in iran figure 1.4. the steps of cardboard generation of agricultural waste figure 1.5. the layout units of recycling of the plastic wastes hassanpour m/oper. res. eng. sci. theor. appl. 4 (1) (2021) 19-37 28 4.1. drip irrigation system manufacturing industry (dismi) in a drip irrigation system, the required water is transferred to the plants through a pipe and passing through different device components. this system typically includes a motor pump, a cyclone, a sand filter, a fertilizer tank, a control center, an optical filter, the main pipe, a water pipe, and a dripper. its wide application is for farms, gardens, and greenhouses. the production steps of drip irrigation components (pipes and dripper) are as follows: (1) polyethylene and additive materials are weighed and mixed in a blender (2) the output mixture enters into the extruder and takes the desired shape when it is leaving the extruder. (3) the pipe enters into the stabilizing bath, which is closed, and its pressure by the vacuum pump is slightly less than the atmospheric pressure. after leaving the tub, the pipes enter into the cold water. (4) this unit has two rows of conveyor-like plastic strips, placed at the bottom and top of the pipe, and pull it with friction force so that the pipe does not wrap after leaving the mold. (5) the pipe is cut to the desired length with a circular saw. when the pipe is cut, the saw moves with high speed in the direction of the pipe. after cutting, the tubes are assembled on the spool. (6) the impeller is made of plastic. (7) each of the 22 emitters is placed in a cardboard box in dimensions of 200 cm3, according to figure 1.1. the annual requirements of dismi have displayed in table 1. table 1. annual requirements of dismi (nominal capacity 1000 no+383.9t) the materials and equipment total annual rates $ materials demands hdpe 173t 204998 ldpe 224t pigment with the soot of 40% 16.600t single-layer of cardboard boxes 31250 no products dripper (according to standard 8072 and 8074 din); water supply pipe with a tolerable pressure of 10 atmospheres made of ldpe, heat resistance up to 80 and withstand cold up to 70 ċ with specific characteristics in the national standards of iran, numbers 1331; water supply pipe with a tolerable pressure of 110 atmospheres and made of hdpe, heat resistance up to 80 and withstand cold up to (70) ċ with specific characteristics in the national standards of iran, numbers 1331 and 2178 1000 no; 233.37t; 150.56t 4830572 employees staff 52 persons 83200 energy consumption required water 4590 m3 21062 power consumed 47520 kw required fuel (stoves) 1350 giga joule an investigation of five generation and regeneration industries using dea 29 4.2. mobile sprinkler for home lawn the home lawn sprinkler is a mobile piece and works with municipal water pressure, and is used to irrigate lawns and gardens to a limited extent. the sprinkler is classified as all-metal, all-plastic, and semi-plastic, which in this design, the type of semi-plastic was selected. it is made of cast iron in base and elbow, an aluminum fountain, and a plastic hose. it is designed in such a way that the fountain with water pressure in addition to spraying water in droplets, rotates around, and the elbow provides the possibility of irrigation under the beam. the stages of production of grass sprinklers are as follows: (1) lathing: the parts of the sprinkler mold, which are made of hexagonal profiles, wire, and aluminum pipes, are threaded according to the necessary processes of the lathing, drilling, and incorporating steps. (2) bending: the aluminum fountain tube will require a superior bending to perform the mechanism of circulation with underwater pressure where manual bending is used. (3) drilling: fountain pipe and cap need holes for spraying water, which is used to make a hole. (4) assembly of sprinkler parts: first, the cap is screwed on the fountain pipe, and then the pipes are closed inside the revolving base and then the feeder base and ribbed seal are installed on the revolving base. (5) casting: scrap iron is used for the production of the base of cast iron and elbow as a melting process which is prepared by a furnace and a mold. (6) the threading of the base and the elbow for installing the fountain is created in the product by a lathe. (7) the base and the elbow are degreased to be ready for dyeing. (8) dyeing is done with a pistol. (9) packaging: the last stage of production is the packaging of three sets of sprinklers, elbow base, and hose head inside the plastic and cardboard boxes, according to figure 1.2. the annual requirements of mobile sprinkler generation industries for the home lawn applications have displayed in table 2. table 2. annual requirements of mobile sprinkler generation industries for a home lawn application (nominal capacity of 81000 no) the materials and equipment total annual rates $ materials demands scrap metals 26700 kg 15000 al wires, d=20 mm 290 kg al pipes, d=22 mm 290 kg hexagonal al 6100 kg al pipes 4700 kg al wire 1t plastic labels 81000 no dye 3120 kg cardboard boxes 10*15*15 cm3 81000 no nylon bags 81000 no packaging carton in sizes of 45*45*50 mm3 1800 no plastic pipe heads 81000 no plastic washer, external d= 19 mm 81000 no steel washer, internal d= 21 mm 81000 no products a mobile sprinkler which works with municipal water pressure, with a fountain made of al, and a plastic hose head. it has good resistance to water in terms of erosion 81000 no 81000 hassanpour m/oper. res. eng. sci. theor. appl. 4 (1) (2021) 19-37 30 and abrasion. employees staff 9 persons 14400 energy consumption required water 1620 m3 7439.3 power consumed 14040 kw required fuel (stoves) 2160 giga joule 4.3. pvc film for agricultural use the steps for generating the pvc films in agricultural use are explained in the following (1) raw materials are weighed in proportion to the required. (2) these required pvc materials, emollients, and other additives which are required for mixing are introduced into the mixer. to achieve uniformity, the mixture is vigorously remixed by transferring into a strong mixer. (3) the mixture is conducted by a conveyor to a two-roller mill to perform another stage of mixing. the mixture is fed to the secondary two-roller mill to re-mix the constituents. (4) the mixed material is disembogued to the extruder. (5) using a conveyor belt, the mixture is transferred into a cylinder consisting of 4 rollers to bring the thickness to the dimensions referred as pvc film. (6) the temperature of the pvc film is reduced by passing through the dryer. the thickness of the pvc film is estimated via a measuring device which works based on beta rays. (7) for the pvc film to be rolled in terms of dimensions, its sides are cut, and its waste is returned to the initial mill. (8) pvc film is wrapped in a roll using the machine and the desired length. (9) the resulting rolls are packed using kraft paper, according to figure 1.3. the annual requirements of pvc film generation industries for agricultural use have displayed in table 3. table 3. annual requirements of pvc film generation industries for agricultural use in iran (nominal capacity 21600000 m2) the materials and equipment total annual rates $ materials demands pvc 3672t 416834.3 shaping materials 55t stabilizer 73t additives 37t paper in sizes of 0.5*2 m for packaging purposes 220000 no products pvc film, width = 1.8 m, thickness = 0.5-0.1 mm, the average weight of each m2 of pvc film = 92 g, the weight of each meter of pvc film = 170 g 21600000 m2 7714285.714 employees staff 46 persons 73600 energy consumption required water 270 m3 1708.5 power consumed 55620 kw required fuel (stoves) 27270 giga joule an investigation of five generation and regeneration industries using dea 31 4.4. cardboard generation of agricultural waste cardboard is a type of plywood that, due to the required strength and flexibility, is mainly used in the packaging industry, and each square meter should consist of more than 180 grams. the process of producing cardboard from agricultural waste is explained. (1) weighing: raw materials (agricultural waste and chemicals) are weighed to a certain proportion. (2) baking pulp: chemicals with agricultural waste are placed in a baking dick and are prepared at a lower temperature of 100 ℃ (3) washing the pulp: the pulp is coming out of the cooking pot is washed with water inside a washing cylinder in three steps. (4) sieving the pulp: after mixing and diluting, the clean pulp is pumped to centrifugal filters, and heavier particles like sands are separated from the pulp. the dryness percentage of the pulp is increased to about 100% by the thickening system. (5) de-colorization system: the pulp is mixed with chlorine solution in a blender with a retention time of 45 minutes. then it is conducted to the chlorine washing system. after re-dilution with hypochlorite solution, it is transferred to the final rinse and is transferred to the cardboard-making machine in several stages of de-colorization. (6) cardboard making: after passing through the de-colorization system, the paste is transferred to the cardboard making machine by a pump, and after withstanding the hammer pressures for separating the water from the suction pulp, it is sent to the drying part. (7) dryer: after the pulp passes through the cardboard-making machine, it is sent to the dryer tunnel, and inside this tunnel, hot air hits the cardboard and makes the cardboard to be dried. (8) ironing: since the cardboard loses its smoothness after leaving the dryer and its surface becomes uneven, in addition to flattening the surfaces by ironing with the pressure, it compresses the fibers and increases the strength of the cardboard. (9) cardboard cutting: after ironing the cardboard, the cardboard's dimensions are equalized by the cutting machine, and it reaches the desired dimensions. (10) packing: 100 pieces of cardboard are cut (80 by 120 cm2) and placed inside the packing plastics. the annual requirements of cardboard generation industries of agricultural waste have displayed in table 4. table 4. annual requirements of cardboard generation of agricultural waste (nominal capacity of 1350 kg) the materials and equipment total annual rates $ materials demands agricultural waste 2700t 111926.22 naoh 10800 kg naco3 5400 kg hypochlorite sodium 5400 kg ldpe 44400 m2 products the cardboard consists of 50-90% cellulose according to iranian standard number 1411 1350t 1400000 employees staff 46 persons 73600 energy consumption required water 9180 m3 42170 power consumed 85320 kw required fuel (stoves) 11070 giga joule hassanpour m/oper. res. eng. sci. theor. appl. 4 (1) (2021) 19-37 32 4.5. plastic waste recycling industries the steps for recovering plastic waste are as follows (1) waste classification: after collection, plastic waste should be classified according to the type of materials such as polypropylene and polyethylene, softness, and hardness. (2) crushing and grinding the scrapes in less than one inch. (3) washing: particles can be cleaned in water washing machines. it can be used either the sodium carbonate or ordinary detergent powders for this purpose. (4) dehydration and drying in a heated oven. (5) granulation: to prepare the pellets of plastic particles to use in downstream processes or to mix with first-hand materials, clean pellets of plastic particles must be in the form of granules, according to figure 1.5. the annual requirements of plastic waste recycling industries of agricultural waste have displayed in table 5. table 5. requirements of the plastic wastes recycling industry the materials and equipment total annual rates $ materials demands ldpe 1000t 108571.43 naco3 (0.5 g per kg wastes) 0.5t products granules of ldpe + ldpe milled 230t+400t 878787 employees staff 9 persons 14400 energy consumption required water 1620 m3 7743 power consumed 91530 kw required fuel (stoves) 2430 giga joule 4.6. dea assessment the friedman test was used to calculate the weights of criteria along with the weighing system of critic. according to the t-test analysis, there is no significant difference between the obtained weights in both systems. table 6 shows the values of weights in weighing systems. table 6. the values of weights in weighing systems industries/criteria materials demand products employees energy consumption friedman test wj 3 4 2 1 weighing system of critic wj 0.044233462 0.943349249 0.007437201 0.004980089 according to table 7, the obtained results in the dea score consist of a range between zero to one for the inefficient to efficient borders respectively. the number 1 denotes the fact that the industry is working with top efficiency and below that goes far from the efficiency border. the less value in the dea score, the less efficiency will have emerged. an investigation of five generation and regeneration industries using dea 33 table 7. dea score and rank industries/criteria productivity dea score dea rank based on the friedman test (1) 24.07893766 1 1 (2) 3.988217525 0.165630959 5 (3) 22.05008681 0.915741679 2 (4) 10.66364713 0.442862026 3 (5) 9.703456899 0.402985258 4 based on the critic system (1) 465.4 1 1 (2) 94.6 0.203288049 5 (3) 383.137 0.823245193 2 (4) 231.364 0.497131417 3 (5) 167.538 0.359988748 4 drip irrigation system (1), sprinkler generation (2), pvc film generation (3), cardboard generation of agricultural waste (4), plastic wastes recycling (5) the t-test analysis had shown a significant difference (p-value ≤ 0.028) for the criterion of employees in comparison with other variables (criteria) such as materials demand, product, and energy consumption. the null hypothesis test summary via a one-sample kolmogorov smirnov test retained the null hypothesis for the variables. but the same hypothesis had revealed a significant difference around 0.002 among four variables via related samples friedman's two-way analysis of variance by ranks and the distribution of materials demand, product, employee, and energy consumption was the same. due to a significant rise in the price of raw materials required by industries, dependence on procuring raw materials of industries (in many cases), and devaluation of the iranian currency, there is a need for a significant rise in the price of industrial products. on the other hand, due to the decrease in purchasing power, the industries will move towards inefficiency. with a slight increase in the selling price of the products of the industries, the efficiency score will decrease too. also, with the rise in employees' salaries in the industry, there will be a further decrease in efficiency of industries. so, the stakeholders tend to either reduce the salaries of employees or lay off the number of employees. due to the variability in energy consumption in units with the same nominal capacity, the results are not comparable to operating companies. because the initial estimates in the project screening phase will change with the pattern of energy consumption in the industry after the construction of the industries. the quantity of energy consumption can be the same, but the costs will vary depending on the type of energy applied. on the other hand, finding industries with the exact specifications will raise the lack of cooperation from managers. to prove the fall and rise in efficiency score of industries before and during the period of sanction we can only rely on reports of inflation rate in iran. the inflation rate and the rise in the price of goods are monthly announced by the incharge bodies in iran. to estimate the efficiency score of industries was used real data. conducting a sensitivity analysis via manipulated and sophisticated data for the costs of energy & materials streams before and during the period of sanction will make the real results meaningless. the other limitations of the present research refer to the provision of initial data, the collaboration of in-charge organizations with the hassanpour m/oper. res. eng. sci. theor. appl. 4 (1) (2021) 19-37 34 research centers, fluctuations in the market for the costs of materials & energy demands in industries, and raising the daily prices. 5. conclusion the present research attempted to find the efficiency of 5 industries based on the input variables of materials demand, employees' number, energy consumed, and the output variable of products generated. the dea method applies to industries with the same nominal capacity. it can allocate them in a particular decision-making situation concerning the fact that the whole inventory of availability is the same for them in the screening step. but the efficiency will be changed for the same industries with different nominal capacities. it means by assessing an industry from one particular group, we can decide for the same group of industries with the same nominal capacity. on the other hand, we are aware the running technologies are the same among certain groups and stakeholders used the same processes and technologies in their manufacturing units in iran. any development and progress will happen in the post-eia after the complete establishment of industries, and the efficiency will change according to a rise in the variables interfering in dea estimation and during a time interval (years) of operation. however, it needs to point out that due to the ongoing pandemic prevalence of covid-19 in our world, the efficiency scores of all sectors are decreasing. this situation is valid for the global economy. this fact should be taken into account as well as the current situation in iran. future studies can be discussed for changing the actual prices of input and output variables and can be compared with existing reports to find the significant differences and conduct a sensitivity analysis in a variety of scenarios. using novel models of dea either individually or integrated with other multi-criteria decision-making models is also encouraging to find efficient enterprises. the tabulated data can be used to estimate the financial statements of mentioned industries and develop any financial estimation model in this regard. also, the sustainability of industries can be taken into consideration by selecting various criteria from concepts presented by the text in decision-making theory. acknowledgment: this research was considered as part of the ph.d. research work (entitled; evaluation of 405 iranian industries). the funding information does not apply to the present paper. any opinions, findings, and conclusions expressed in this publication are those of the author and necessarily reflect the current views and policies. references anthony, p., behnoee, b., hassanpour, m., pamucar, d. 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(2018). eco-efficiency assessment of eu manufacturing sectors combining input-output tables and data envelopment analysis following production and consumption-based accounting approaches. journal of cleaner production, 174, 1161-1189. © 2021 by the authors. submitted for possible open access publication under the terms and conditions of the creative commons attribution (cc by) license (http://creativecommons.org/licenses/by/4.0/). https://cyberleninka.ru/journal/n/russian-journal-of-agricultural-and-socio-economic-sciences https://cyberleninka.ru/journal/n/russian-journal-of-agricultural-and-socio-economic-sciences an investigation of five generation and regeneration industries using dea malek hassanpour 1. introduction 2. literature review 3. methodology 3.1. screening of projects 3.2. weighing system of friedman test 3.3. weighing system of critic 3.4. traditional dea model 4. result and discussion 4.1. drip irrigation system manufacturing industry (dismi) 4.2. mobile sprinkler for home lawn 4.3. pvc film for agricultural use 4.4. cardboard generation of agricultural waste 4.5. plastic waste recycling industries 4.6. dea assessment 5. conclusion references operational research in engineering sciences: theory and applications vol. 4, issue 1, 2021, pp. 99-114 issn: 2620-1607 eissn: 2620-1747 doi: https://doi.org/10.31181/oresta2040199l * corresponding author mtarique181@gmail.com (m. tarique lakhiar), mtl.eng17@gmail.come-mail (m. tahir lakhiar), abdhalid@uthm.edu.my (a. halid abdullah) occupational health and safety performance in high-rise building projects in pakistan: a systematic literature review muhammad tarique lakhiar 1*, muhammad tahir lakhiar 2, abd halid abdullah 1 1 faculty of civil and environmental engineering, universiti tun hussein onn malaysia, batu pahat, johor, malaysia 2 school of engineering, monash university, subang jaya, selangor, malaysia received: 09 february 2021 accepted: 08 march 2021 first online: 20 march 2021 review paper abstract: the building industry contributed an impressive share in pakistan's growth sector, where the construction industry contributes almost 2.74% of the gdp of pakistan. in most metropolitan cities, the trend of building multi-story structures is at increase. however, this construction industry is a prominent accident-prone industry where laborers generally work in an unsafe environment. these projects suffer from fatal and non-fatal accidents as labor health and security are not a prime aim in the construction industry despite all employees still dealing with safety issues. this research examines the occupational safety and health (osh) performance in high-rise building projects in pakistan. this review focuses on adopting qualitative approaches, using the comprehensive literature approach for seeking current practice in health and safety and ohs laws in pakistan's building industry. finally, it proposes a realistic strategy for developing a safe environment at workplaces. research indicates that pakistan's construction sector should consider workers' safety as a priority, update and enforce safety laws at the workplace to enrich ohs conditions in the pakistani construction sector. keywords: building industry, accident prevention, safety culture, fall protection system, pakistan engineering council 1. introduction pakistan is considered one of the underdeveloped countries that have recently undergone instant development in building activities throughout the past decade, with almost 3 million laborers working in the building industry. however, building industry employees constitute 7.6% of the total workforce, whereas construction lakhiar et al./oper. res. eng. sci. theor. appl. 4 (1) (2021) 99-114 100 fatal and non-fatal accidents account for 17.3% of the entire crew (pakistan bureau of statistics, 2018). even with these frightening figures, few or no strenuous efforts are expended by government authorities or private agencies to improve pakistani construction workers' safety conditions (raheem and hinze, 2012). similarly, the majority of the opposing under-developing countries, around numerous hurdles and threats that pakistan is experiencing to elevate and execute legislative system in the building sector. the existing safety acts in pakistan are not exclusive to the building sector. they are accomplished by the factories act of 1934, the workmen's compensation act of 1923, and the minimum wage ordinance of 1961. these laws mainly deal with the work-related safety and health complications of industrial personnel. moreover, the health and safety clauses are generally made as part of contract documents in the pakistan building industry. still, they are commonly not imposed in reality because of carelessness and illiteracy amongst the workforces for their privileges, ensuing in inferior safety execution (zahoor et al. 2016. pakistan bureau of statistics (2018) has reported that about 36.6 % 36.7% of the whole manpower is utilized in the service sector (which includes the construction sector) (figure. 1a), the construction sector of pakistan is positioned third amongst the entire economic sectors and 1st amongst the service sectors relative to the share of reported occupational injuries/diseases (figure. 1b). the governing authority is generally exhausted in executing the laws efficiently in underdeveloped countries like pakistan. work dangers are not identified and either observed with not as much hazardous (larcher and sohail, 1999). most underdeveloped countries have executed several safety regulating systems to minimize the frequency of accidents. the governing organizations like osha in the usa and hong kong labor department are persistently endeavoring to attain 0 % of causality rate (choudhry et al. 2009). likewise, several safety encouragement plans are often publicized to lessen the frequency of accidents (choudhry et al. 2008). in contrast, safety is not much properly considered in underdeveloping countries, such as pakistan. accident statistics are neither maintained nor regularly reported to the government department (raheem and issa, 2016). safety rules barely exist, the regulatory authority is mostly ineffective, and work hazards are not assessed accurately (ali, 2006). the pakistan engineering council (pec), which is that the principal controlling agency for construction in pakistan, has not set detailed guidelines and safety regulations for the industry. moreover, a major difference is observed between big and small contractors against their safety performance. only the large firms have safety policies, conduct safety training, and appoint safety staff on their job sites (raheem and hinze, 2013). figure 1a. distribution of total labor force occupational health and safety performance in high-rise building projects in pakistan: a systematic literature review 101 figure 1b. accidents relative to reported injuries/diseases the construction workers usually face serious threats and safety issues while building high-rise structures. building laborers are usually more subjected to falling, plant movement, heavy machinery, electroshock, and loud noises. the factors time, cost, and quality are often the key factors perceived to be ahead of safety. health problems are still considered subordinate and take a back seat on the building site. many organizations have not developed robust accident management plans but instead focusing on optimizing income. (choudhry et al. 2008). thus, laborers are more liable to face numerous hazards, such as harsh weather conditions and safety problems at high altitudes (dropping from elevation, colliding with items at workplace). these may be the reason for serious work-related wounds among building workers throughout the globe. most building incidents happened due to a fall from a height, accompanied by electrocution and shifting activities (zahoor et al. 2016). lack of personal protective equipment (ppe), ineffective training, unrealistic construction time, and missing appropriate anchoring points are the main causes of falls from height at construction sites (choudhry et al., 2014). in the last seven years, no noteworthy reduction in injury rate has been detected, as the injury rate remained nearly constant at over 14% (pakistan bureau of statistics, 2018). most occupational incidents in the pakistani building industry are due to falls from a height, accompanied by uplifting activity, electric shocks, and hit by objects (choudhry et al. 2014). however, building projects are still suffering from casualties even with the following safety criteria, mostly due to falling from height and electrocution (choudhry et al. 2014). whereas falling from height is the main cause of incidents that happen in the construction of tall buildings (hassan, 2012). the main causes for safety non-compliance are generally summarized as; desire for earning more profit, misinterpretation that putting investment on safety raises the project budget, absence of a controlling authority, labors’ unawareness, poor governing system, lack of safety training, and shortage of safety equipment’s, political influence, and meeting deadlines (farooqui, 2012). 2. literature review this study adopted a qualitative approach to analyze workplace safety and health performance in high-rise construction in pakistan. it exposes the facts without lakhiar et al./oper. res. eng. sci. theor. appl. 4 (1) (2021) 99-114 102 tossing the information away. this study focused on a thorough analysis of the literature relating to workplace protection and health in high-scale pakistan and their potential applications to improve occupational health and safety standards in the pakistani buildings industry. it was intended to sum up the latest occupational safety and health efficiency of high-rise buildings in pakistan and to review prevailing ohs laws and regulations and their application in the sector. for a paper retrieval of the ohs performance in pakistan, a systemic method involving three steps, as seen in figure 2, has been adopted. a systematic desktop search was performed in scopus under the 'article title/abstract/keyword' search area. the keywords for the search were safety culture, safety practices, construction safety, ohs, pakistan. their title/abstract /keyword section was deliberately picked to be for further review with these particular words. other databases were also explored to access the relevant articles, such as google, scholar science direct, ebsco, scopus, web of science, and google. in short, the best source for looking for the conference papers and proceedings was google. a further step was to search the proceedings using the same search engines for 14 global osh conferences. for the next step, profiles were investigated in research gate, academia, and google scholar to find out scholars who are intensively interested in ohs research in pakistan. consequently, the snowball technique was eventually used for the finding of the corresponding articles by reviewing the reference portion of all the articles found. the papers that could not be downloaded were accessed via e-mail from the researchers. figure 2. research methodology 2.1. nature of the construction industry in pakistan underdeveloped countries should focus on executing safety, health, and environmental management systems in the building industry to carry projects deprived of injuries and scale back worksite dangers. in developing countries, like pakistan, the safety regulation hardly exists; and most of the laws are not suitable for building industry, and those laws are unsatisfactory, inefficient, or outdated. generally, the administrative body is weak in imposing safety laws efficiently, and site hazards are either not evaluated at all or observed that these job risks are tolerable to worker safety (ali, 2006). various building firms across the globe are occupational health and safety performance in high-rise building projects in pakistan: a systematic literature review 103 executing health, safety, and environmental management systems to prevent damages, eradicate illness, and offer a harmless work atmosphere on building projects. on the other hand, there is no legislative safety system in pakistan to impose safety in the building industry without having any particular governing authority for ohs management, likewise osha in the usa (choudhry et al. 2008). as the only regulatory body, the pakistan engineering council (pec) has yet to enforce health standards to be followed by construction stakeholders (farooqui et al., 2007). however, pec doesn't have the power and administrative authority to establish and enforce safety-related legislation. the majority of clients seek fast speed and high efficiency of building work in the region at the lowest feasible expense, and the project budgets do not specifically contain protection funds (farooqui, 2012). the health efficiency of large and small contractors also varies considerably. many of the major firms listed with the pec in category c-a have detailed safety policies that offer some form of training to staff that retain safety personnel in their workplaces. contrary to that, small firms usually do not have protection on their agenda, and there are dangerous environments on many building sites, and often injuries and fatalities occur to staff (choudhry et al. 2008a). however, at different work sites of contractors, training programs for the safety of laborers haven't been introduced yet, no safety-related training conducted for entirely new workers, work-related risks never identified, and never called and conducted any safety meetings. furthermore, the absence of immediate availability of medical services, inferior housekeeping, and unhygienic conditions tend to exist on isolated projects. although safety clauses are included in contract documents, they are not strictly implemented. likewise, construction firms are mostly failed to prescribe these clauses due to the nonexistence of the regulatory authorities. pec also organizes safety education seminars and obligatory short courses on continuing professional development (cpd), which are only available for engineers. however, no instruction for construction managers and staff are offered (choudhry and zahoor, 2016). the kind of work conducted at worksites in pakistan are labor-intensive and relies entirely on the mostly nonprofessional and non-qualified workers, which usually poses an enormous risk of special damages (farooqui et al. 2007a). underdeveloped countries such as pakistan are witnessing serious potential accidents due to intense work and rely heavily on professional and unskilled staff from diverse educational backgrounds. similarly, the bulk of accidents in the pakistani building industry are attributed to falls from height and a few more to lifts, electric shocks, and safety training is the most neglected aspect in the construction industry. (choudhry and zahoor, 2016). generally, laborers and managers have different opinions about accident reporting mechanisms. as explained by masood et al. (2012), any accident that happened at the site is reported from the perspective of managers. still, laborers possess a different belief and commonly not in agreement with the managers. likewise, stakeholders are only concerned with productivity, while safety is not given much preference. significant health and safety disparities among developing and under-developed nations contain inexistence, inadequate compliance, weak risk management, and lack of ohs awareness programs and safety regulations (zahoor et al., 2017). this worsening condition contributes to serious worksite injuries and a significant shortage of site staff, reduced work morale, delays in building progress, and disputes between stakeholders (haseeb et al. 2011). building work is the country's riskiest task because it entails wounding and death on sites in pakistan. lakhiar et al./oper. res. eng. sci. theor. appl. 4 (1) (2021) 99-114 104 2.2. status of occupational safety in the construction industry in underdeveloped nations, health at work remains overlooked due to overlapping social, economic, and political problems. following worldwide progress on os&h problems, around 2.3 million deaths from workplace injuries and workrelated disease are reported, 317 million suffer serious disabilities, and 160 million become sick, most of whom in less developing countries belong to rural regions (azhar et al. 2015). employees in less-developed nations have often had a large chance of injury/disease in jobs because of bad working standards and social security. in remote regions in less developed nations, the condition is much worse because of insufficient health care services. for less-developed nations, workplace injuries/diseases are a major expense to the national social insurance program (rundmo and hale, 2003). due to poor health safety infrastructure. work accidents are the primary causes of an economic downturn (brown, 2003). the ilo reports that the overall burden of work accidents and illnesses constitutes 4 percent of the national gdp on average (international labor organization, 2009). proper social insurance programs are not integrated into less-developed countries, especially rural ones, and there is a reality of constraints and low-quality information; hence a standard data study is useful in assessing the efficiency of the country's occupational health safety systems (smith, 2001). moreover, in the least developed countries where workers are involved in dangerous jobs, mainly in agriculture, construction, fishing, and mining, work-related damage and death are greater (international labor organization, 2013). social safety at low levels faces a high risk for adverse occupational exposure. according to the pakistan economic survey 2013-14, pakistan is the 10th largest country in the world in terms of the labor force, and its rural population accounts for 67.5% of the total population involved in agriculture activities (pakistan bureau of statistics, 2014). workers' health and safety in pakistan are miserable due to several causes, for instance, inadequate healthcare services, lack of relevant ohs regulations, and uneducated workers. evidently, in pakistan, no institutional program is in place to monitor incidents and causes associated with jobs. there is also a lack of obtainable statistics, meaning that most accidents are not reported to the labor department. ohs is not the country's highest priority because of a shortage of funding and the lack of technical skills. at the provincial level, the saeed ahmed awan centre for the development of working conditions & environment and the directorate general of labor welfare of punjab province is responsible for offering medical and technical expertise for employee safety. punjab recently revealed the first labor policy (dawn news, 2015), and baluchistan established an agreement on labor law and industrial reform (international labor organization, 2015). in addition, since the independence of pakistan in 1947, the ilo has been collaborating with the government of pakistan to resolve issues at work, workers' rights, and raise labor conditions. pakistan has signed 36 ilo conventions, with eight of them were main agreements. since thousands of employees are subjected daily to hazardous chemical compounds, pakistan has a high prevalence of workplace diseases and injuries. most workers are not aware of the distinction between preventive measures during their jobs. the majority of the workforce is not trained to cope with the threats presented by manufacturing and production processes. there are no clear safety laws for various industries throughout the country to cope with employees’ health and security problems. the nation needs essential facilities and professional staff to provide ohs workforce services. a occupational health and safety performance in high-rise building projects in pakistan: a systematic literature review 105 significant number of employees would also be in danger if possible; efforts to strengthen the osh management are not made (ahasan, 2001). 2.3. causes and effects of occupational accidents in the construction industry every year 3.7% of the labor in pakistan undergo occupational injuries/diseases that result in the loss of working time (pakistan bureau of statistics, 2008). although its literacy rate of only 57.7 percent is reasonably acceptable, pakistan is considered a country that lacks a security culture, mainly attributed to a lack of effective legislation (farooqui, 2012). most building industry injuries are caused by height dropping (zahoor et al. 2016). the key causes of such incidents involve failure for fall security and sufficient anchorages on construction sites, insufficient preparation, excessive building time, and health ignorance among the workers (choudhry et al., 2014). drop from the top is the main cause of injuries, whilst other causes include electrical action, trapped between machines and objects (nawaz et al. 2013). the ignored safety measures that trigger accidents in high-rise buildings are recognized as having no ear defenders, no boots, and no face masks if needed (farooqui et al. 2008). the lack of coordination and comport ability, safety knowledge, consumer engagement, and health legislation are responsible for safety non-compliance (khan, 2013). significant reasons for safety violation are summed up: misunderstanding of the fact that safety improvements raise the costs of the project, ineffective regulatory bodies, political interference, unreasonable timelines, overtime, health ignorance, and lack of collaboration among employees (raheem et al. 2011). untrained employees and a higher unemployment rate are potential sources of injuries. these incidents lead to higher building costs, such as charging for the jobs of extra workers, temporary stoppages, and delays in time (jafri, 2012). moreover, accidents have adverse impacts on the morality of employees. 2.4. safety culture in the construction industry of pakistan safety culture (sc) is well-defined as the safety expectations, standards, and customs shared by the followers of an industry. it can be explicated that these fundamental values and standards that distress the performance of individuals in industries. present pieces of training in management establishes that there is an intensifying acknowledgment of the effect of sc on variation execution accomplishment. for the disintegrated existence of the regulatory atmosphere and the erraticism of safety perception, the construction industry in pakistan hasn't been able to develop a sound safety culture (raheem et al., 2012). though stakeholders/owners in the building industry in pakistan are generally aware of protection objectives and their value to the sector, they do not have engagement, collaboration, experience, and knowledge of instruments to enforce the safety culture in their projects (farooqui et al. 2008). formal safety management practices between stakeholders/owners are rare, and thus incidents leading to loss of production, delays in development, and cost overruns occur in projects. it has also been concluded that, because of a lack of dedication and institutional processes, the managers, partners, and investors in the pakistan building industry are not able enough to sustain a secure project. the key challenges encountered by contractors in introducing and enhancing protection are – in descending order of importance – the lack of the following: staff collaboration and behavior, experience and competence with protection management strategies, safety lakhiar et al./oper. res. eng. sci. theor. appl. 4 (1) (2021) 99-114 106 understanding and knowledge, owner involvement, and a safety regulatory system (farooqui et al. 2008). 2.5. ohs training institutes in pakistan the saeed ahmed awan centre for improvement of working conditions and environment’ in lahore city of punjab province; in pakistan, it is a leading center offering professional services in the areas of ohs and the workplace environment founded by the labour & human resource department, government of the punjab, pakistan. several private institutes provide ohs training facilities on a commercial basis in pakistan: 1. pakistan institute of management (pim) has established its offices in karachi, lahore, islamabad, and quetta. it is awarding diploma certificates of osh after four months of training. 2. pakistan safety institute (psi) is a karachi-based commercial organization providing training, auditing, and consulting services in the field of health and safety, fire safety, and construction safety. 3. occupational safety and loss prevention (osalp) is a lahore-based commercial organization, providing training in the fields of quality assurance, health, safety, security, and environment. 4. safety trends international (sti) is a karachi-based private institute providing nebosh and iosh training. 5. descon, a well renowned lahore and karachi based company, is providing osh training to its employees at its descon technical institute (dti). they also provide training on a commercial basis. 6. occupational training institute (oti) is based in lahore and providing osh training on a commercial basis. 7. vivid institute of occupational safety and health (viosh) has its training offices in eight cities of pakistan. it provides osh training courses like osha, iosh, nebosh, particularly in the construction and petroleum sectors. 8. horizon institute of occupational safety and health (hiosh) has established its branches in lahore, rawalpindi, attock and peshawar. it is providing training for iosh and nebosh certifications. 9. center of risk, safety, health and environment (core) is a karachi based institute, providing training for nebosh international general certification and for iosh managing safely and iosh working safely certifications. in fact, as explained above, a variety of private companies offer ohs trainings on a commercial basis. this is essential to remember that construction employees are not strictly required to undergo any health training at workplaces because they are allowed to work on building projects without any health certification. therefore, only construction workers who prepare for an overseas job are involved in receiving a safety training program. occupational health and safety performance in high-rise building projects in pakistan: a systematic literature review 107 3. development of construction health and safety guidelines presently, pakistan construction industry has not had any proper occupational health and safety laws. even though several ohs laws such as workmen’s compensation act 1923, factories act 1934, and minimum wage ordinance, 1961 are established, they were basically applicable for over-all industries and do not specifically fulfil the criteria of safety compliance in the building industry. therefore, a prominent need to modify the factories act 1934 or to generate completely advance safety legislation. moreover, to improve the construction safety culture in the construction industry, current safety regulations, and safety performance, the higher education commission of pakistan collaborated with department of state, usa under pakistan-us science and technology cooperation program funded a capacity building project. the purpose of this project was to set up a knowledgebased centre. the construction management and safety research centre (cmsrc) was instituted at national university of sciences and technology (nust) in 2012 to step up and encourage safety research in construction, training and education to enrich safety rules and policies in building industry by engaging academia, public organizations, industry, regulatory agencies, and the regulatory bodies. the project team has submitted a request to the ministry of education, training and standards for higher education to set up the “pakistan occupational safety and health agency (posha)”. one of the functions of this department is to gather data on health and safety results on an annual basis. the plan is currently being reviewed by the appropriate department (azhar et al. 2012). 4. construction health and safety education and training for the achievement of occupational health and safety programmes, successful ohs training is necessary as it enhances behavioral skills, associated information, and or attitudes and stimulates accident forecasting, particularly for new employees. to increase workplace ohs efficiency both at the level of the worker and the organization, management should develop a regular, rigorous health and safety curriculum for new workers and provide an instructor for them (vredenburgh, 2002). memon et al. (2013) suggest that management support, teamwork, effective supervision, safety education and training, regular safety meetings, effective communication, and setting realistic goals can effectively enhance the safety performance. hassan (2012) suggests that the safety situation can be improved by the effective enforcement of ohs laws, incorporating safety credit points in the contractors’ licensing, appointing safety inspectors for site monitoring, allocating sufficient safety budget, providing personal protective equipment (ppe), and effective safety training. while conducting surveys with three different questionnaires for the managers, workers and national culture, mohamed et al. (2009) established a link between national culture and safety behavior (mohamed et al. 2009). in addition, it has been suggested to use wireless sensors for intelligent real-time monitoring of workers in the confined spaces (riaz et al. 2014). raheem and issa (2016) emphasize to incorporate more specific safety clauses in the contract documents and include safety plan as a mandatory part of the bidding process. they suggest starting with the safety induction training for all the workers, supervisors and managerial staff. lakhiar et al./oper. res. eng. sci. theor. appl. 4 (1) (2021) 99-114 108 4.1. accident reporting and investigation through background facts, injuries are caused by horrific incidents: machinery failures, unsafe working techniques, and poor maintenance. updating people about such unpleasant incident would be useful in identifying reasons for minimizing the possibility of such incidence. to accomplish this aim, almost all misses, fatal and nonfatal accidents must be documented, it does not matter how minor they might appear. the accidents reporting phenomenon varies from company to company, as the procedures vary, so all information would be provided to administrators quickly so that the incidents could be further investigated (fahad et al. 2019). the effective method to track accidents is by a particular method of reporting. the method must provide a well-defined summary of incident, persons and work included, damages received, healthcare services given, and of the evidence provided if there is also, if possible, photos of the concerned region should also be added. consequently, at every building site, it should always be demanded and assessed to maintain an injury record at the site where all forms of minor accidents including such cuts, damaging incidents such as attributing disabilities and fatalities has to be included and evaluated by the safety official (fahad et al. 2019). fortunately, the reporting of an injury is not sufficient to mitigate the chances of recurrence, and it must be determined as quickly as possible after an accident has been reported. the investigation process should be carefully examined to include all facets and concerns that have arisen in order to determine the root causes of incidents. 4.2. temporary platform structure scaffolding is a temporary framework used in the design, renovation, and reconstruction of homes, bridges, and all other manmade structures to sustain a work team and materials. scaffolding is a vital trade in the construction of buildings by offering platforms that allow workers to maintain their job at a high altitude. drop hazards are the leading cause of workplace accidents, responsible for almost half a year of all construction accidents. osha, (2002) reports that about 65 percent of contractors work on scaffolds each year. this could lead to hazardous conditions for construction staff and projects around the world without knowledge of the dangers of scaffolding. get professionally qualified to recognize electrocution, fall, and dropping objects and techniques for treating these hazards when using a scaffold. the proper use of the scaffold must also be included in the training, how to handle materials, and the load capacity of the scaffold. once you can use the scaffold, make sure that the qualified individual inspects the scaffold so that it is in good working order. when working on scaffolds, always use a sturdy, durable, non-skid work pair of boots and lanyard. if the scaffold is used inappropriately, please inform the supervisor straight away. connect the machine to a secure level, which does not permit more than six feet of free fall before stopping (osha, 2002). 4.3. personal protective equipment (ppe) it is very necessary to wear ppe for workplace safety and for further various security reasons. it is designed for the defense of the body from disruptive impacts, electric threats, heating, and chemical agents for the wearer's whereas, wearer's apparel, masks, gloves, or other devices are produced to shield the body from injury. personal protective equipment (ppe) is needed by the occupational safety and health administration (osha) in the united states to mitigate worker risks and hazards occupational health and safety performance in high-rise building projects in pakistan: a systematic literature review 109 where engineering and administrative controls are inadequate to minimize such exposures to the required standard (osha, 2006). in addition, the building firm must define the statutory conditions for ppe in the construction sites and safety policy. the ohs manager will regularly review the needed volume of ppe on the job. ohs officials will perform routine checks for faulty ppe that are not in usage by staff. for review, replacement, and follow-up activities for the ppe, a checklist should be created. ppe used by all laborers of subcontractors must be checked and must meet the prime contractor's relevant requirements. 4.4. fall protection system generally, workers would choose the fall safety systems that are more consistent with the job type. flying objects are common at building sites as workers use power equipment or perform activities that include pressing, dragging, or prying (keng and razak, 2014). then researchers like hamid, majid, and singh (2008) reaffirmed that the most frequent form of the building site incident is caused by falling from a height or dropping objects. incidents involving falling or flying objects may expose staff to minor injuries, like cuts and abrasions, and, rarely, even more, severe injuries, including concussions or blindness. more risks may be taken in accidents caused by falling items, particularly for workers who work under scaffolds or other places. in another study, the u.s. department of labor (dol) reports falling as one of the main causes of traumatic workplace mortality, responsible for 8 percent of all traumarelated workplace deaths. for a fact, if a worker is 4 feet or taller, the worker would be at risk and will be secured. as a result, dosh (2007) emphasized that fall protection equipment must be used and applied anywhere an individual would be at risk of falling by 2 meters. 5. improving the existing regulatory infrastructure for worker health and safety while construction activities have risen in the last decade, the pakistani building industry is suffering largely because of the absence of a viable legislative framework due to unsafe working conditions. owing to the delicate existence of the regulatory structure, temperamental and weak morale have become norms for the construction industry (ali, 2006). the behavior of labor at the workplace reveals a significant challenge to the compliance of safety laws in pakistan. therefore, corporate control has marginal consequences, and the government pays no attention to health. nawaz et al. (2013) recommend reformulating and implementing safety laws and by-laws, disseminating safety awareness, determining an accident reporting mechanism, and ensuring the provision of safety training as well as ppe to all the workers. in this connection, draft regulations to improve the existing health and safety legislative framework are submitted by azhar and choudhry (2016) to pec for approval and implementation (azhar and choudhry, 2016). in order to improve safety standard in the building industry, researchers have recommended the pec to: modify the contract documents, allocate explicit safety budget at the time of bidding, giving due weightage to safety performance in the processes of contractor licensing and renewal along with the professional credit points, and employ safety professionals on all the projects (raheem and hinze, 2013). in addition, the development of a database is lakhiar et al./oper. res. eng. sci. theor. appl. 4 (1) (2021) 99-114 110 emphasized to record the number of injuries/fatalities against the completed and ongoing construction projects at the industry level (sheikh and ali, 2013). 6. conclusion this paper addressed problems relating to the study of workplace safety and health performance in the construction of high-rise buildings in pakistan. furthermore, the difference in safety culture development in western nations and strategies and methods of encouraging the health and safety of buildings is also addressed. in order to minimize the occupational risk, a comprehensive analysis of the literature indicates that safety implementation in the construction sector of pakistan should be considered. to ensure the ohs in pakistan's construction industry, attempts must be made by both parties (government and entrepreneurs) to upgrade the working environment and to minimize risks for construction workers. building safety and health research are in the development stage in pakistan. there are also numerous articles that have been published in the area of ohs in pakistan. it promises that several conferences are held annually to completely recognize and upgrade conditions in the construction sector; nonetheless, it is incredibly hard to obtain online details on these conferences. this situation makes it very hard for researchers to determine and understand working environments and recommend additional changes. this article is an attempt to examine and recognize pakistan's health and safety practices. study results show that construction companies are hesitant to disclose occupational incident-related records, aside from not showing and reporting workplace regulations that further jeopardize worker health and safety. therefore, the selection criteria of pec contractors is based exclusively on financial potential, not success in health and safety. while in its legal contracts, pec has incorporated safety clauses, due to the lack of administrative authorization, these are not enforced. to create alertness among its staff, pec is also arranging cpd webinars and seminars; however, training of workers is not taken into account. consequently, the following steps are recommended to pec to increase ohs knowledge at construction workplaces, thus pec must launch safety awareness campaigns; set up regulating authority; develop clients' procurement and records of bids on the allocation of safety allowances; incorporate safety credit points into the evaluation criteria of the contractors, and establish a realistic system for reporting and investigating incidents. references ahasan, m. r., & partanen, t. 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(2017). modelling the relationship between safety climate and safety performance in a developing construction industry. a cross-cultural validation study. international journal of environmental research and public health, 14(4), 351. zahoor, h., chan, a.p.c., utama, w.p. and gao, r. (2016). a research framework for investigating the relationship between safety climate and safety performance in the construction of multi-storey buildings in pakistan. procedia engineering, vol. 118, pp. 581-589. © 2021 by the authors. submitted for possible open access publication under the terms and conditions of the creative commons attribution (cc by) license (http://creativecommons.org/licenses/by/4.0/). occupational health and safety performance in high-rise building projects in pakistan: a systematic literature review muhammad tarique lakhiar 1*, muhammad tahir lakhiar 2, abd halid abdullah 1 1. introduction 2. literature review 2.1. nature of the construction industry in pakistan 2.2. status of occupational safety in the construction industry 2.3. causes and effects of occupational accidents in the construction industry 2.4. safety culture in the construction industry of pakistan 2.5. ohs training institutes in pakistan 3. development of construction health and safety guidelines 4. construction health and safety education and training 4.1. accident reporting and investigation 4.2. temporary platform structure 4.3. personal protective equipment (ppe) 4.4. fall protection system 5. improving the existing regulatory infrastructure for worker health and safety 6. conclusion references operational research in engineering sciences: theory and applications vol. 4, issue 2, 2021, pp. 36-54 issn: 2620-1607 eissn: 2620-1747 doi: https://doi.org/10.31181/oresta20402036f * corresponding author. dimas.mhfathurohman (fathurohman), humiras.hardi@mercubuana.ac.id (h. h. purba), aristrimarjoko@gmail.com (a. trimarjoko) value stream mapping and six sigma methods to improve service quality at automotive services in indonesia dimas mukhlis hidayat fathurohman 1, humiras hardi purba 1, aris trimarjoko 2* 1 department of industrial engineering, mercu buana university, jakarta, indonesia 2 department of industrial engineering, sekolah tinggi teknologi yuppentek, tangerang, banten, indonesia received: 16 february 2021 accepted: 26 april 2021 first online: 24 june 2021 research paper abstract: automotive service industry currently holds an important role in helping to increase customer satisfaction. various strategies are carried out to win the competition for increasing customer satisfaction. quality service combined with the right instruments can be used to increase customer satisfaction and loyalty. customer satisfaction is the key to success in the manufacturing and service industries. service quality is an important attribute and it is a key factor in service industries. improving lead time service in automotive toyota dealer service industries is the focus of this research. value stream mapping succeeded in identifying problems that were happening as an impact of waiting for services, washing processes, and length of service processes. the dmaic (define, measure, analyze, improve and control) method assisted by tools of quality successfully analyzed and gave recommended corrective actions to reduce the lead time of express maintenance service from 120.06 minutes to 64.00 minutes or improved 53% per service cycle, and succeeded in increasing the capability of the service process from 1.96 sigma to 3.80 sigma. quality of service can be improved to get customer satisfaction, increase company profitability, and increase the competitiveness of companies in maintaining the sustainability of the industry in the future. keywords: service quality, lead time, value stream mapping, dmaic 1. introduction global competition in the increasingly stringent industry requires business people to get effective strategies to meet customer satisfaction. customer satisfaction is a value stream mapping and six sigma methods to improve service quality at automotive services in indonesia 37 feeling of consumers for the product or service that has been used (kuhlang et al. 2011). customer satisfaction can be formed if the organization might be able to provide product characteristics or attributes following customer expectations (pyzdek, 2003). thus, it can be interpreted that customer satisfaction is one of the important attributes in the industrial world, especially the service industry. based on this fact, the service industry must be able to identify important elements and be able to make improvements to receive intended customer satisfaction. the automobile services industry in indonesia is a type of automotive industry or commonly referred to as a dealer that provides sales, repair, and sales for four-wheeled vehicle parts. the results of a survey conducted by jd power 2018, jandhagi et al. (2011) in indonesia found an important finding namely low customer satisfaction caused by scheduling appointments via digital channels that are very low, with a percentage value of 7% of customers who schedule their service appointments via its website or through smartphone applications. an automobile service company is a service industry that serves sales, maintenance, repair, and supply of vehicle part services. the service operation branch also provides spare parts and workshops that provide special maintenance and repair services for vehicles. it consists of three main divisions, which are sales department, service department, and spare parts department. the key element in determining the level of service quality is after-sales customer satisfaction. the quality of after-sales services provided by car dealers has a great influence on customer satisfaction to maintain long-term relationships with their customers and many businesses. have changed their strategic focus to emphasize customer retention (rego et al. 2013). the high after-sales service lead time in automobile services in toyota dealers in indonesia is 120.06 minutes in one service cycle, higher than the lead time charged at 60 minutes. it is a problem that must be resolved so that customer satisfaction, which is an important attribute in the service industry can be met. by mapping the aftersales service process in automotive services toyota dealer using value stream mapping, it is expected that the actual conditions of current service processes can be identified and found, which processes are causing the high after-sales service lead time that occurs. by assisting various tools of quality in the six sigma method, it is also expected to be able to provide analysis and recommendations for corrective actions so that the quality of service is in line with expectations and can be improved. it is believed that good service quality will result in customer satisfaction and will have an impact on the reuse of products and services that have been used and help improve company's image through product information and services to other customers (gijo et al. 2012, thompson, 2005, lam et al. 2004, venkamteswaran and padmanaban, 2018). six sigma is a systemic and structured method with dmaic stages (define, measure, analyze, improve, and control) that has been proven effective in identifying, measuring, analyzing, and providing recommendations for improvement of problems that occurred (causevic & golub, 2019). researched at portugal automotive industry using dmaic (define, measure, analyze, improve and control) cycle for process improvement could decrease 0.98% on the indicator of work-off generated by the production system, the financial impact could save over 165,000 € per annum (costa et al. 2017). omar & mustafa (2014) stated that the adoption of six sigma does not only mean a process improvement but it is a business strategy that uses a systematic approach to increase productivity, corporate financial benefits, and customer fathurohman et al./oper. res. eng. sci. theor. appl. 4 (2) (2021) 36-54 38 satisfaction (pucheta et al. 2019). other research in automotive that selected as observed machine dmaic could reduce the machine breakdown time from 111 became 85 minutes/month and breakdown quantity from 4.7 became 3.5 times/month and increase the availability value from 90.8% became 96.0% and the impact was increasing oee (overall equipment effectiveness) value from 87% became 92% (rozak et al. 2020). in the united kingdom 2012, the six sigma method had succeeded in reducing the waiting time from 24 minutes to 11 minutes or more than 50% of pathology department service processes in the healthcare industry (hussain et al. 2014). other studies had also successfully revealed that the implementation of six sigma can improve the attitude of health workers better (53%), compared to government employees (18%) (sethi et al. 2018). based on the facts from previous studies, it is proven that the implementation of value stream mapping and six sigma combined with other tools of quality successfully resolve various problems and succeeded in enhancing customer satisfaction and company profits. 2. literature review customer satisfaction is the lifeblood of every company, so customer satisfaction is one important element in improving the performance of a company or organization (nagi & altarazi, 2017). customer satisfaction can be formed if the customers get what is expected from a product or service they use (croft & kovach, 2012, pyzdek, 2003). customer satisfaction is a comparison between the actual performance in products and the expected performance (caesaron & simatupang, 2015). customer satisfaction is a response from the comparison of product performance with several standards before, during, and after consumption (minh & huu, 2016, srivasnavar & bhatnagar, 2013, barrios & jimenez, 2016). especially in the service industry, customer satisfaction is closely related to the level of service quality in which there is a direct interaction between the system, the operator, and the customer, where process the customer can feel directly the quality of services which at the same time can provide an assessment of the quality of the service without passing through other stages of the process. service quality is the main process in the service organization/industry that prioritizes the achievement of service quality that meets or even exceeds customer expectations (barrios & jimenez, 2016). other research stated that the success of industry without exception a service industry is very dependent on human resources and processes owned so that in the service industry the improvement of human resource competencies and continuous process improvement are important factors as well as determinants of the industry to gain its success (vijay, 2014). identification of ongoing process conditions including in the service industry which aims to find opportunities for continuous process improvement is an important activity so that quality of service that can meet customer expectations can be realized. some various methods and tools can help identify the ongoing process to get the opportunity for improvement as intended. this research seeks to combine value stream mapping and six sigma methods with the help of other tools of quality in identifying, measuring, and analyzing the processes that occur in automotive after-sales services in indonesia, it is hoped that the processes currently running can be identified and value stream mapping and six sigma methods to improve service quality at automotive services in indonesia 39 opportunities for improvement can be found in efforts to improve quality services that can meet or exceed expectations and certainly increase customer satisfaction. the identification of ongoing process conditions is very important in the strategy of quality improvement in the industrial world both in the manufacturing and service industries. especially in the service industry, the quality of service that can be felt simultaneously in the process becomes very important to always be identified and evaluated quickly and effectively so that the quality of service and the image of the organization in customer perspectives can be maintained. value stream mapping is a device that has been widely used by various industries including the service industry in identifying and analyzing the conditions of ongoing processes to find opportunities for further improvement. value stream mapping can optimize the power sources by eliminating non-value of added activities to improve productivity and sense of competitiveness (george, 2003). value stream mapping is a successful method that is used internationally, usually applied in a single project that has a high innovative impact and is developed towards continuous improvement with a systematic process management approach (kuhlang et al. 2011). the value stream mapping method has successfully identified the operational conditions through the study of takt time and succeeded in reducing the process lead time from 7.6 to 3.2 days or a 73% reduction in the automotive industry cycle time in india (chang & wang, 2007). value stream mapping has also succeeded in identifying bottleneck processes and reducing waiting time by up to 27% (otim & grover, 2006). referring to the various studies, it can be understood that the value stream mapping method is very effective in identifying ongoing processes to obtain opportunities for improvement and can improve the productivity and quality of processes and products in both manufacturing and service industries. six sigma is a comprehensive, flexible and measurable system for achieving, maintaining, and maximizing increasingly competitive business success. six sigma is a quality improvement approach that is systematically effective for improving organizational performance based on the use of various statistical analysis techniques (pande & holpp, 2002). in general, six sigma has two meanings, namely six sigma as a philosophy for continuous improvement in reducing defective products and six sigma as a technical tool in measuring the number of defects per 1 million products produced. six sigma in technical methods has a statistical. approach orientation to the calculation of product defects. the goal is to reduce the variance process by eliminating the entire defects interfering with customer satisfaction (peng & wang, 2006). for the service industry, six sigma is a business improvement methodology that maximizes shareholder value by achieving the fastest rate of increase in customer satisfaction, cost, quality, processing speed, and investment capital (haviana & hernadewita, 2019). six sigma is a version, philosophy, strategy, and a set of tools to improve process and service quality, for services-based industries, where customer needs are the main focus, and their needs often seem unpredictable (ebrahimi & keykavossi, 2018). six sigma is a systemic and structured method with dmaic (define, measure, analyze, improve, and control) steps. it has been proven effective in identifying, measuring, analyzing, and providing recommendations for improvement that have a focus on reducing the variety of processes and products that can increase customer satisfaction, profitability, and competitiveness of the company (elbireer et al. 2011, fathurohman et al./oper. res. eng. sci. theor. appl. 4 (2) (2021) 36-54 40 jona than, 2013, trimarjoko et al. 2019). the researches showed that most service organizations in the uk have been implementing six sigma for more than three years. the company's average sigma quality level is around 2.8 around 98,000 defects per million opportunities (dpmo). management commitment and involvement, customer focus and six sigma integration with business strategy are important factors in implementing six sigma (syafwiratama et. al. 2016). the implementation of the six sigma method can reduce shipping delays and lead time in the small and medium scale industries in the united kingdom and increase the sigma level from 1.44 to 2.09 sigma (otim & grover, 2006). the application of the six sigma method proves that the average waiting time for maternal and child hospital services decline from 6.89 days to 4.08 days and the standard deviation dropped from 1.57 days to 1.24 days. in this way, the hospital will serve pregnant women faster, reducing the risk of perinatal and maternal death (omar & mustofa, 2014). the combination of value stream mapping and six sigma methods can reduce the lead time of a delivery process at the automotive dealers in mexico from 50,499.5 minutes (35.06 days) to close to 30,240 minutes or even 20,160 minutes or down 60.17% (parasuraman & grewal, 2000). other research in india using value stream mapping and six sigma methods showed that lead time has been reduced by 14.88%, processing time 14.71%, and waste of material movement 37.97%. as proposed in the model, wip (work in process) inventories have decreased by 17.76% and labor 17.64%. furthermore, it will generate 161,800 rupees profit per year. and get a net savings of 145,560 rupees per year (shahin, 2006). referring to these studies, it shows that six sigma methods in the service industry combined with other methods are very effective in identifying, analyzing, and improving processes and products to get better service quality and also able to increase the profit and competitiveness of the industry by 37.97%. referring to these studies, the six sigma method in the service industry combined with other methods is very effective in identifying, analyze and improve processes and products to get better service quality and can increase the profitability and competitiveness of the industry. 3. case study automotive toyota dealers service in indonesia have a problem with high aftersales service lead time is 120.06 minutes in one service cycle, which is higher than the lead time charged by 60 minutes for a type of expres maintenance service. by combining value stream mapping and six sigma based on other tools of quality, it is expected that the problem of high after-sales lead time in the automotive toyota dealer services industry can be identified and get improvement recommendations so that the problem can be solved effectively and efficiently. the proposed implementation framework is an integrated approach of lean and six sigma and is shown in figure 1. it is based on the traditional five phases of the dmaic six sigma improvement model: (define, measure, analyze, improve, and control). each phase of the dmaic: define, measure, analyze, improve and control methodology utilizes several six sigma tools to improve the mobile order fulfillment process. in this study, both qualitative and quantitative data were collected from multiple sources. qualitative data were obtained from direct observations in the field and unstructured interviews with team leaders, experienced team members, and systems experts, while quantitative data were obtained from the company’s historical records. several tools value stream mapping and six sigma methods to improve service quality at automotive services in indonesia 41 and techniques, such as a pareto chart, value stream mapping (vsm), cause-andeffect analysis, process capability analysis, a control chart, and 5w + 1h analysis, were used through the dmaic (define, measure, analyze, improve and control) methodology. all statistical analysis of data (at a 5% level of significance) and graphical presentations were performed using minitab statistical software. identification scope and objectives input from case organization literatures review define (describe the problem) : 1. identify critical to quality characteristics 2. finalize problem description activity through pareto analyze . measure (establish baseline performance) : 1. data collection 2. test normality & exixtence of special cause of variation & process capability analysis 3. four block diagram current condition analyze (identify the root cause) : cause and effect analysis improve (select the best solution) : 1. further analysis of root cause by 5w + 1 h 2. establish improvement planning martrix control (sustain the gain) : 1. test normality & exixtence of special cause of variation & process capability analysis 2. four block after improvement 3. evaluation value stream mapping after improvement 3. documentation and standardization of all methods 4. process monitoring and controling analysis value stream mapping current condition figure 1. implementation framework value stream mapping has been widely used in various companies both manufacturing and services that are useful for knowing the condition of the ongoing process and very effective in knowing which of all sub-processes (workstations) are bottlenecks and have an impact on current problems. these conditions are termed as current stage conditions, while value stream mapping can also be reused in mapping a series of processes after repairs called future stage conditions so that with the improved results value stream mapping can also be identified. fathurohman et al./oper. res. eng. sci. theor. appl. 4 (2) (2021) 36-54 42 receiving binning issuing reception production final inspection washing call customer sub depot regional c/t = 542 second ope rat or = 8 distance = 0 c/t = 2067 second ope rat or = 6 distance = 30 m c/t = 115 second ope rat or = 1 distance = 10 m c/t = 606 second ope rat or = 2 distance = 25 m c/t = 383 second ope rat or = 1 distance = 0 m total l/t lt = 120,06 minutes sparepare demand/po appointment maintain reminder activity customer lt=90 minutes l/t = 60 minutes total l/t lt = 154 minutes l/t = 4 minutes pkb pkb pkb pkb pkb service process service preparation sps c 2 days 30 minutes 10 minutes appointment preparation 3 days waiting time 127 second waiting time 2704 second waiting time 382 second waiting time 10 minutes waiting time 30 minutes waiting time 5 minutes waiting time 10 minutes waiting time 5 minutes 1 day waiting time issuing 10 minutes 15 minutes t t t t i lt = 2.12 minutes lt = 9.04 minutes lt = 45.08 minutes lt = 34.45 minutes lt= 4.59 minutes lt = 1.92 minutes lt = 6.37 minutes lt = 10.10 minutes lt = 6.39 minutes waiting time 275 second figure 2. value stream mapping current condition value stream mapping and six sigma methods to improve service quality at automotive services in indonesia 43 figure 2 explains value stream mapping (vsm) that illustrates the current condition of the process that is ongoing (before improvement). the condition was analyzed to find out which workstations were causing the high lead time. based on value stream mapping current condition as obtained in figure 2, the average lead time process in the automotive totota dealer services industry was a minimum of 46 ~ 65 minutes, a maximum of 263 ~ 389 minutes with an average of 120.06 minutes for a type of express maintenance service. its condition exceeded the company's target of 60 minutes, using value stream mapping the value stream mapping for general description can be explained in table 1. table 1. evaluation of the actual time of overall workstations current condition order type service count (valid) work process (minute) total lead time em (express maintenance) w a it in g r e ce p ti o n is t p ro ce ss r e ce p ti o n is t w a it in g s e rv ic e p ro ce ss s e rv ic e a n o th e r jo b o rd e r w a it in g f in a l in sp e ct io n p ro ce ss f in a l in sp e ct io n w a it in g w a sh in g w a sh in g p ro ce ss c a ll c u st o m e r timeactual target evaluation 2.12 9.04 45.08 34.45 0.00 4.59 1.92 6.37 10.10 6.39 120.06 0.00 10.00 0.00 30.00 0.00 0.00 5.00 0.00 10.00 5.00 60.00 x v x x v x v x x x x note : x: unable to meet the target. v: able to meet the target. referring to the evaluation of each workstation contained in the express maintenance (em) process, in this case, the process of handling after-sales customer complaints in the automotive toyota dealer services, the results showed that up to 80% were not able to meet the target of the company so that the overall total lead time was not be fulfilled. therefore, further analysis is needed to get the total lead time following the company's target. the application of the six sigma method is based on theoretical studies that had been found and had been proven effective in solving problems in various industries both manufacturing and service industries. six sigma with its structured stages will be used in solving the problem of high aftersales/express maintenance lead time in the automotive. services industry in this study. the six sigma analysis used in this study was: 3.1. define phase the define stage was the first stage. in this stage, the problem description activity was carried out, determining critical to quality (ctq) and the target to be achieved. from the data collection and mapping process with value stream mapping, it is known that the problem that occurred was the high after-sales lead time on average of 120.06 minutes of the specified target was 60.0 minutes. as for the data obtained, we floated in the pareto diagram to find out the critical to quality that occurred, while the pareto diagram is shown in figure 3. based on the pareto diagram in figure 3 it explained that 80% of the longest express maintenance lead time was on the waiting service 49.15 minutes or 56%, washing process 12.27 minutes difference to the target or 14% and process (service) 10.45 minutes, so based on the pareto diagram critical to quality of this research was as many as 3 types, i.e. waiting for fathurohman et al./oper. res. eng. sci. theor. appl. 4 (2) (2021) 36-54 44 service, service process, and washing process. the target to be achieved in this research was lead maintenance express maintenance service time of 60.0 minutes. lead time 49,15 40,45 22,27 10,27 6,47 5,88 5,63 3,35 percent 34,3 28,2 15,5 7,2 4,5 4,1 3,9 2,3 cum % 34,3 62,5 78,0 85,1 89,6 93,7 97,7 100,0 process o th er ca ll c us to m er w ai tin g w as hi ng pr oc es s fi na l i ns pe ct io n pr oc es s re ce pt io ni st pr oc es s w as hi ng pr oc es s se rv ic e w ai tin g se rv ic e 160 140 120 100 80 60 40 20 0 100 80 60 40 20 0 l e a d t im e p e r c e n t figure 3. pareto diagram analysis of the express maintenance process 3.2. measure phase measure phase was the second stage. in this step, the capability of the express maintenance process was calculated, aimed to find out the current condition of the process under this study. from data collection which had been obtained, to be then calculated the capability of the process as follows: 360300240180120600 lsl usl ls l 71 target * u s l 210 s ample m ean 141.015 s ample n 400 s td ev (within) 67 s td ev (o v erall) 67.73 p rocess d ata z.bench 0,53 z.ls l 1,04 z.u s l 1,03 c pk 0,34 z.bench 0,51 z.ls l 1,03 z.u s l 1,02 p pk 0,34 c pm * o v erall c apability p otential (within) c apability p p m < ls l 65000,00 p p m > u s l 135000,00 p p m total 200000,00 o bserv ed p erformance p p m < ls l 148011,48 p p m > u s l 151592,60 p p m total 299604,08 e xp. within p erformance p p m < ls l 150629,60 p p m > u s l 154213,21 p p m total 304842,81 e xp. o v erall p erformance w ithin ov erall figure 4. the capability process of z bench st express maintenance value stream mapping and six sigma methods to improve service quality at automotive services in indonesia 45 360300240180120600 lsl usl ls l 71 target * u s l 210 s ample m ean 141.015 s ample n 400 s td ev (within) 67.8915 s td ev (o v erall) 67.73 p rocess d ata z.bench 0,51 z.ls l 1,03 z.u s l 1,02 c pk 0,34 z.bench 0,51 z.ls l 1,03 z.u s l 1,02 p pk 0,34 c pm * o v erall c apability p otential (within) c apability p p m < ls l 65000,00 p p m > u s l 135000,00 p p m total 200000,00 o bserv ed p erformance p p m < ls l 151205,38 p p m > u s l 154789,43 p p m total 305994,81 e xp. within p erformance p p m < ls l 150629,60 p p m > u s l 154213,21 p p m total 304842,81 e xp. o v erall p erformance w ithin ov erall figure 5. the capability process of z bench lt express maintenance from the calculation of z bench st (sigma level) and the value of z bench lt, it can be plotted into four block diagrams as an illustration of improvement direction from the control and technology side, by calculating z shift with the following result from calculating and converting defect per million opportunity (dpmo) to sigma level 1.96 sigma. so that the capabilities of the running process can be plotted in the four-block diagrams in figure 6, as follows. a c b d control technology 1,5 4,5 poor good z shift z st (0,34, 1.96) 5,02 figure 6. four block diagram current condition fathurohman et al./oper. res. eng. sci. theor. appl. 4 (2) (2021) 36-54 46 figure 6 explains that the condition of the sigma level of the ongoing process in terms of control is good but in terms of technology is still very bad. so that effective improvement is needed to get a better sigma level. 3.3. analyze phase referring to value stram mapping define and measure phases it is known that the high lead time express maintenance (em) was caused by 3 processes, namely: waiting for service, service process, and washing service. by using the cause-effect diagram, the problems of processes were analyzed to get what was the dominant cause of the 3 processes. the cause-effect diagram of the problem is shown in figure 7 below: the maintenance process was caused by: 1. equipment factor the condition of the equipment used by express maintenance mechanics was only 40% in good condition and suitable for use, 24% was damaged, 7% was lacking and 29% was missing or not yet used. utilizing the tools which were broken and lacking was temporarily displaced by stalls express maintenance 1 and 2 tools whereas, for devices that did not exist, em had not used them. they still used standard tools that were periodically serviced. 2. material factors the rapidity of providing spare parts for regular service. for the procurement stock of spare parts, consumers still often waited due to the availability of spare following periodic service manuals. 3. management factors the length of time express maintenance service takes place was because mechanical mechanics received work orders that had complaints either express maintenance booking or express maintenance walk-in (direct coming). express maintenance work should have as few complaints as possible due to the distribution of improper mechanical task dividers for cars coming in for service and the lack of digging information from the booking service staff. 4. environmental factors em mechanics should look for cars that needed to be serviced in the service parking area because cars were mixed with other cars which were not included as the express maintenance (em) service customers. moreover, when the car park was full, it was placed in another parking area, making it more difficult for mechanics to find the cars. the fact that an indicator to search the cars was only a periodic service indicator without a sign or special identity of express maintenance also made it hard to identify the cars. value stream mapping and six sigma methods to improve service quality at automotive services in indonesia 47 lead time service used the sam e tools bad of procurement tools less of tools still conventional tools decrease of efficiency tools waiting for take additional parts standard operation procedur isn t done waiting supporting part mechanic missunderstanding service will need type of booking service and walking service come at the same tim e search of vehicle will be service parking area not organized figure 7. cause and effect diagram analysis fathurohman et al./oper. res. eng. sci. theor. appl. 4 (2) (2021) 36-54 48 3.4. improve phase activities in this stage were to determine the proposed improvement of the root of the causes that have been carried out at the analyze stage by conducting a brainstorming using 5w + 1h and the improvement matrix plan of the service process and washing process that becomes the problem in this study. a large amount of lead time in services at the dealer had been found. it might likely occur due to the long duration of handling throughout the service process, and many miscommunication errors. thus, it will be one of the main points for improvement in the next step of the dmaic improvement cycle. with the following improvements: the improvement in the production area or service process aimed to reduce the service process time from the actual time before repairing 34.45 minutes while the expected target is 30 minutes. the improvement steps taken by the small group activity express maintenance team (sga em) were as follows: failure1: provide special parking wait express maintenance service. failure 2: provide parts with standard operation procedure (sop) pre-picking rack. failure 3: provide material with standard operation procedure pre-picking. failure 4: loss of manpower with the addition of man power. by carrying out the corrective footsteps as mentioned above, it is expected that the high maintenance lead time of 120.06 minutes can be reduced to the target of 60.00 minutes per service cycle. 3.5. control phase the control stage was the last in the six sigma method, where this stage the process capability (sigma level) calculation was conducted again after the improvement. observation activities as in the measuring stage were still applied. sigma level could be calculated by using minitab software that could also by calculating z shift with the following result from calculating and converting defect per million opportunity (dpmo) to sigma level 3.80 sigma. a c b d technology 1,5 4,5 poor 5,02 (0,36, 3.80) good control figure 8. four block diagram after improvement figure 8 shows the results of improvement in this study. it has better results than the conditions before the improvement. then, to get the stability of the express maintenance process, the documentation of improvement was made into a work fathurohman et al./oper. res. eng. sci. theor. appl. 4 (2) (2021) 36-54 49 standard in the form of 1. making a work squance sheet (wss), was a written work procedure that was a detailed job in detail. 2. stick work squance sheet (wss) in areas related to wss attached to areas that had been improvised, placing work squance sheet (wss) in a location that was visible and readable by officers in their respective areas. 3. socializing work squance sheet (wss) socialization and improvement programs were conducted when the regular all small group activity (sga) meetings are held every month. also, it was socialized at the machine shop roll call, which was routinely held on tuesday and thursday. every morning roll call, each smal group activity can report the progress of the repairs that have been made. furthermore, to find out the lead time analysis of the express maintenance process after improvement, this mapping was carried out again after the improvement using value stream mapping in figure 9. figure 9 explains value stream mapping (vsm) that illustrates condition after improvement process. figures 2 and 9 value stream mapping are the same, both the flow process and the location map, only the difference is that the results of the lead time have been made improvements to the work process. value stream mapping (vsm) shows the condition of the process that is being express maintenance after a repair, as for the general description can be explained in table 3: table 3. evaluation of the overall actual time of work stations at after improvement order type service count (valid) work process (minute) total lead time em (express maintenance) w a it in g r e ce p ti o n is t p ro ce ss r e ce p ti o n is t w a it in g s e rv ic e p ro ce ss s e rv ic e a n o th e r jo b o rd e r w a it in g f in a l in sp e ct io n p ro ce ss f in a l in sp e ct io n w a it in g w a sh in g w a sh in g p ro ce ss c a ll c u st o m e r timeactual target evaluation 1.57 7.53 13.00 23.70 0.00 3.63 1.25 5.46 3.45 4.45 64.00 0.0 10.00 0.00 30.00 0.00 0.00 5.00 0.00 10.00 5.00 60.00 x v x v x x v x v v note : x: unable to meet the target. v: able to meet the target. fathurohman et al./oper. res. eng. sci. theor. appl. 4 (2) (2021) 36-54 50 receiving binning issuing reception production final inspection washing call customer sub depot regional c/t = 454 second ope rat or = 2 c/t = 1422 second ope rat or = 5 c/t = 75 second ope rat or = 1 c/t = 207 second ope rat or = 4 c/t = 267 second ope rat or = 1 total l/t lt = 64 minutes sparepare demand/po appointment maintain reminder activity customer lt=90 minutes l/t = 60 minutes total l/t lt = 154 minutes l/t = 4 minutes pkb pkb pkb pkb pkb service process service preparation sps c 2 days 30 minutes 10 minutes appointment preparation 3 days waiting time 10 minutes waiting time 30 minutes waiting time 5 minutes waiting time 10 minutes waiting time 5 minutes 1 day 15 minutes t t t t i lt = 1.57 minutes lt = 7.53 minutes lt = 1.25 minutes lt= 3.63 minutes lt = 23.70 minutes lt = 13.00 minutes lt = 5.46 minutes lt = 3.45 minutes lt = 4.45 minutes figure 9. value stream mapping after improvement fathurohman et al./oper. res. eng. sci. theor. appl. 4 (2) (2021) 36-54 51 table 3. evaluation of the overall actual time of work stations at future conditions. based on the results of the current stream mapping mapping, three dominant factors are causing the express maintenance service duration of the vehicle flow, namely: waiting service 13.00 minutes, washing process 3.45 minutes, and service process 23.70 minutes with an average completion process reaching 64 minutes. the state map after improvement was created to show the condition after repair. improvements in processing time and waiting time resulted from the dominant length of work for the express maintenance service, namely the washing process, service process, and cycle time service. the improvement state map that has been created will be a reference for the current state map which requires corrective action to achieve the next future. all of this is done continuously to achieve the ideal conditions of express maintenance services. 4. result the combination of value stream mapping and six sigma used in this study proved effective and succeeded in reducing the lead time of express entertainment services in the automotive services in toyota dealer. that would be seen by reviewing the results of the comparison of the four block diagrams, before and after improvements to the car service that can experience an increase in terms of technology. thus, it means resolving the problem using the define, measure, analyze, improve and control (dmaic) method in the automobile totota dealer service succeeded in increasing the process capability from 1.96 to 3.80 sigma, mapping process using value stream mapping analysis was seen to be able to reduce the length of service time and waiting time of each process in the car service with a total lead time to 64.0 minutes from 120.06 minutes or can reduce the express maintenance service lead time by 53%. 5. conclusion this study aims to improve car dealer services by reducing the express maintenance lead time in the automobile toyta dealer services. for this reason, it is necessary to know the stages of the process that results in dealer service issues ranging from acceptance to submission back to the customer and can be analyzed and prevented from occurring problems. value stream mapping helps to define key process stages to make improvements to the problems that occur in each stage of the process. this research uses an integrated value stream mapping (vsm) and six sigma mechanism that tries to unravel the problem that is happening the express maintenance service in the automotive toyota dealer services industry in indonesia, namely a high lead time of 120.06 minutes from the management target of 60.00 minutes. by assisting the value stream mapping method, it was able to identify which part of the series of processes caused the problem and managed to find out the total lead time that was running at 120.06 minutes and after repairing the value stream it was also found that the total lead time express maintenance decreased to 64.00. six sigma method with dmaic (define, measure, analyze, improve and control) steps were also carried out in this study with the help of other tools of quality such as pareto diagrams, process capability with four block diagrams, cause-effect diagram analysis of 5w + 1h also and succeeded in measuring, analyzing, repairing and fathurohman et al./oper. res. eng. sci. theor. appl. 4 (2) (2021) 36-54 52 controlling the process of express maintenance so that total lead time of the process can be derived as above and can raise the sigma level of the express maintenance process from 1.96 sigma to 3.80 sigma. in general, 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(2014). reducing and optimizing the cycle time of patients discharge process in a hospital using six sigma dmaic spproach. international journal for quality research, 8(2) 169–182. © 2021 by the authors. submitted for possible open access publication under the terms and conditions of the creative commons attribution (cc by) license (http://creativecommons.org/licenses/by/4.0/). value stream mapping and six sigma methods to improve service quality at automotive services in indonesia dimas mukhlis hidayat fathurohman 1, humiras hardi purba 1, aris trimarjoko 2* 1. introduction 2. literature review 3. case study note : x: unable to meet the target. v: able to meet the target. 3.1. define phase 3.2. measure phase 3.3. analyze phase 3.4. improve phase 3.5. control phase note : x: unable to meet the target. v: able to meet the target. 4. result 5. conclusion references operational research in engineering sciences: theory and applications vol. 3, issue 3, 2020, pp. 101-122 issn: 2620-1607 eissn: 2620-1747 doi: https://doi.org/10.31181/oresta20303101k kysem24@gmail.com; semakayapinar@munzur.edu.tr evaluation of the effect of covid-19 on countries’ sustainable development level: a comparative mcdm framework sema kayapinar kaya department of industrial engineering, munzur university, tunceli, turkey received: 02 november 2020 accepted: 01 december 2020 first online: 06 december 2020 original scientific paper abstract: the extent of the outbreak of coronavirus disease (covid-19) had a major impact on health, social life, economic and environmental activities in almost every country over the world. it has disrupted the sustainable development of countries and brought many uncertainties for their future capabilities. in this study, the effects of the covid-19 on oecd countries' sustainable development were investigated, and the sustainable development performance of the countries was evaluated by the multiattributive ideal-real comparative analysis (mairca) method. data for the second quarter of 2020 and the same quarter of the previous year is considered. then, the results obtained by the mairca method were compared with two different multi-criteria decision-making (mcdm) methods called mabac (multi‐attributive border approximation area comparison) and waspas (weighted aggregated sum product assessment). the effectiveness and validity of the results obtained from these methods were tested with spearman's correlation coefficient. finally, to examine the effect of covid-19 on the indicators of sustainable development, a non-parametric wilcoxon signed-rank test was applied. as a result, it was concluded that covid-19 negatively affected the sustainable development of countries. however, sustainable development performances of developed countries have been observed to be better than developing countries. keywords: pandemic, covid-19, sustainability, mairca, multi-criteria decision making 1. introduction in december 2019, chinese center for disease control and prevention and wuhan city health authorities reported an unknown pneumonia outbreak in wuhan city, hubei province, china. on january 7, 2020, the center detected a new type of coronavirus that has never been seen in humans from the lower respiratory tract samples of patients (wang et al., 2020; li et al., 2020). samples from the first patients kaya/oper. res. eng. sci. theor. appl. 3 (3) (2020) 101-122 102 were tested with many known pathogens. the new type of coronavirus showed similarity to respiratory diseases such as severe acute respiratory syndrome (sarscov) and middle east respiratory syndrome (mers) (lai et al., 2020). symptoms of the new type of coronavirus include fever, cough, shortness of breath, and dyspnea. however, these symptoms differ from person to person. while most infected people develop mild to moderate symptoms, some patients experience severe pneumonia, pulmonary edema, and multiple organ failure, leading to death. this infectious virus has been officially named as severe acute respiratory syndrome coronavirus 2 (sars-cov-2) by the world health organization (who). who used the term covid-19 to describe the disease caused by the virus (who, 2020). this disease, the first case of which appeared in china in the last days of 2019, later began to occur in countries such as japan, south korea, and thailand (chen et al., 2020). the disease spread rapidly around the world in january 2020, and cases of virus began to be reported in several countries in europe, north america, and asiapacific (cdc, 2020; hui et al., 2020; bedford et al., 2020). on march 11, 2020, who declared covid-19 as a global pandemic (who, 2020). at the time of writing this paper, the covid-19 epidemic affected 213 countries and regions worldwide, infected more than 11 million 600 thousand people and the number of people who died globally has exceeded 530 thousand (covid-19 virus pandemic, 2020). after who announced that the epicenter of the covid-19 outbreak was europe in the spring of 2020, the loss of life caused by covid-19 increased in many countries, especially in italy, france, spain, and the united kingdom. again, at the time of writing this paper, it was announced by who that the new epicenter of covid-19 was the continent of america and asia. it was also reported that the pandemic risk continues largely; the usa, with more than 7 million cases, and india, with 6 million cases, have been the two countries in the world with the most covid-19 cases. the number of deaths in both countries is increasing day by day and 200 thousand people in the usa and 96 thousand people in india died due to covid-19 (coronavirus update, 2020). although the covid-19 pandemic was initially seen as a global health crisis, the situation has changed as the extent of the pandemic increased, and covid-19 has become a deep political, economic, social, and environmental crisis in every country it touched. due to the pandemic, in almost 90% of the world a wide range of social isolation and curfews have been implemented, many businesses have been closed, and domestic and international transportation services have been disrupted. social restrictions and home isolation negatively affected many sectors especially production, health, transportation, tourism, real estate, education, energy, banking, etc. (deloitte | annual turkish m&a review, 2019). even in the largest economies of the world, an economic contraction is foreseen that exceeds the estimates. according to international monetary fund (imf) report titled "great isolation" dated april 14, 2020, the world is expected to experience the biggest global economic crisis since the "great depression" in 1929. in the report published by imf, the growth expectation of the global economy has been revised as 3% shrinkage instead of 3.3% growth for 2020, and it is expected that global trade will decrease by 11% and oil prices by 42%. due to the pandemic, a great decrease has occurred in the production and service sector and this made developing countries face high inflation and increasing unemployment. the gross domestic product, one of the most important economic indicators, fell by 1.8% in the oecd region in the first quarter of 2020 (world economic outlook, 2020). evaluation of the effect of covid-19 on countries’ sustainable development level: a comparative mcdm framework 103 however, it is not exactly known how dramatic the effects of the covid-19 outbreak on the global economy will be. in the world economic forum report, it was stated that in addition to the economic problems, many countries would face many multidimensional problems in tourism, the housing market, demand for commercial products, transportation, unemployment, education, energy consumption, and impact on social life (world economic outlook, 2020). tourism and service transportation is one of the sectors heavily hit by covid-19. transportation and transport activities have almost come to a halt during the quarantine process. the world travel and tourism council stated that 50 million jobs operating in the global tourism and travel industry are at risk (news article | world travel & tourism council (wttc), 2020). with the decrease in production in the pandemic period, the amount of energy needs to be decreased, as a result of which a decrease in energy production and investment was experienced. the positive aspect of the pandemic is that despite the decline in energy investments, renewable energy has resisted and continued to grow against the pandemic (iea, 2020). even though the disruption of the education process of children was prevented by initiating the distance / online education processes in the quarantine process, the discount / free meal application given in schools in many countries, which is especially important for disadvantaged people, was disrupted, and some of the students suspended their education as they could not connect to the internet, and this situation brought about socio-economic inequalities. as can be seen, the pandemic is a multidimensional global crisis that affects the economic, social, and environmental factors of the countries and disrupts its sustainable development. the united nations (un) stated that all the work done during and after this crisis should focus on building more resilient, equal, inclusive, and sustainable economies in the face of the challenges we face. also, it was emphasized that the countries' recovery and sustainable development goals should be taken into consideration more than ever before to cope with the shocks that may be encountered in the pandemic in the future (undp, 2020). only a few studies have addressed the threat of the coronavirus pandemic to the sustainable development levels of countries. this paper attempts to investigate how the covid-19 pandemic has changed the level of sustainable development for developed and less developed countries. additionally, mcdm has become widely used in different sustainable development context over the past few years (perez-gladish et al., 2020). for this purpose, this study is to evaluate and compare the level of sustainable development of the oecd countries by using the mairca model. mairca is an effective mcdm method that takes into account the concept of the positive and negative ideal solution. the results obtained with the mairca method were compared with new multi-criteria decision-making methods such as mabac and waspas. the efficacy and validity of the results obtained in the three methods were tested with spearman's correlation coefficient. finally, the wilcoxon signed-rank test was performed to examine the impact of covid-19 on the indicators of sustainable development. the rest of the paper is organized as follows: in section 2, literature review on mairca has presented. the steps of the mairca method is explained in section 3. evaluation of the effect of covid-19 on countries’ sustainable development level based on the mairca method is given in the fourth section. the results obtained to test the effectiveness and validity of mairca method are illustrated in section 5. next kaya/oper. res. eng. sci. theor. appl. 3 (3) (2020) 101-122 104 section, the results of the non-parametric wilcoxon signed-rank test are presented. results and some limitations are discussed in detail in section 7.. 2. literature review mairca is a popular method within the group of mcdm methods which is developed by professor dragan pamucar in the logistics research centre at the university of defence in belgrade (pamucar et al., 2014). mairca is easy to use in computation procedure and its calculation steps are similar to the ideal and non-ideal solution approach in the technique for order of preference by similarity to ideal solution (topsis) method. (gul and ak, 2020). the mairca model is a considerable new decision-making method that can be very successfully combined with different mcdm methods. related literature has been evaluated over the years. gigović et al. (2016) aimed to determine the appropriate location for the ammunition depots by using the geographic information system (gis) and mairca methods together. to do this, the priority weights criteria of depots were determined by dematel-anp, and then the ranking of alternative regions was performed by mairca. in the study by (pamučar et al., 2017a), using a hybrid approach, the tenderers of the public procurement tender were evaluated by means of rough number based on dematel, anp, and mairca methods. in another study, pamucar et al. (2018) used the full consistency method (fucom) and mairca integrated methods in the location selection of level crossings to reduce the number of traffic accidents. pamučar et al. (2019) defined six alternatives in determining the landing departure point of the vehicles in combat operations and they ranked their priorities with mairca using interval-valued fuzzy-rough numbers. in their research, badi and ballem (2018) evaluated the supplier selection process by applying the integration of the rough numbers with the best-worst method (bwm) and mairca methods. as a result, it is determined that the cost, quality, and company profile are the three most important criteria. chatterjee et al. (2018) evaluated the suppliers' performances considering the green supply chain criteria with the help of rough dematel, analytic network process (anp) and mairca methods. pamucar et al. (2018) performed the location selection for a multi-model logistics facility that took into account sustainability criteria with the help of dematel-mairca methods. based on the two main criteria that affect the ergonomic risk level, ekinci and can (2018) developed the critic-mairca method to achieve a combined risk level by taking into consideration the evaluation results made for the sub-criteria of these main criteria. boral et al. (2020) listed the types of errors seen in the production facility of a small and medium-sized (sme) company operating in the automobile industry using the fuzzy mairca method. ulutaş (2019) used the step-wise weight assessment ratio analysis (swara) and mairca integrated method in the selection of the catering company. aycin (2020) used the criteria importance through intercriteria correlation (critic) and mairca methods in the selection of personnel to work in the it department of a company operating in the logistics industry. arsić et al. (2019) made a menu evaluation for a restaurant with bwm and rough mairca methods. in the study by (chatterjee et al., 2020), the mairca method was used to evaluate the alternatives in lightweight environmentally friendly materials in the automotive industry. pirbasti et al. (2020) selected the waste disposal facility location of eight hospitals using a hybrid approach with fuzzy swara and gis-mairca. in the study by evaluation of the effect of covid-19 on countries’ sustainable development level: a comparative mcdm framework 105 pamučar and savin (2020), bwm and mairca methods were utilized together for the selection of military land vehicles, taking into account the 11 criteria defined. gul and ak (2020) used bwm and mairca methods under fuzzy conditions to analyze potential risks in the marble factory. the relative importance of the three risk factors in the traditional fine-kinney method was calculated with fuzzy bwm, and the identified risks were ranked by fuzzy mairca. 3. mairca method mairca, which has been added to mcdm literature by gigovic et al., 2016, is a method based on defining the gaps between ideal and empirical ratings. by the addition of the gaps for each criterion, the total gap for decision alternatives is obtained. at the end of the application process, the alternative that is the closest to the ideal ratings according to most of the criteria, or in other words, the alternative with the lowest total gap value is determined as the best alternative (gigović et al., 2016; pamučar et al., 2017). the mairca method has an implementation process consisting of eight steps (pamucar et al., 2018). step 1: creating the initial decision matrix (x): the criteria(cj) values obtained from each alternative (ai) are shown in equation (1). 𝐶1 𝐶2 … 𝐶𝑛 𝑋 = [ 𝑥11 𝑥12 … 𝑥1𝑛 𝑥21 𝑥22 … 𝑥2𝑛 ⋮ ⋮ ⋱ ⋮ 𝑥𝑚1 𝑥𝑚2 … 𝑥𝑚𝑛 ] (0) step 2: determining the priorities of alternatives: the absence of a priority in the alternative selection process of the decision-maker is an assumption of the method, m as the total number of alternatives, i. the priority of the alternative 𝑃𝑟𝐴𝑖 is calculated as shown in equation (2). 𝑃𝑟𝐴𝑖 = 1 𝑚 ; ∑ 𝑃𝑟𝐴𝑖 𝑚 𝑖=1 = 1 𝑖 = 1, 2, … , 𝑚 (2) the decision-maker is equidistant to any alternative. therefore, all priorities are equal, as shown in equation (3). 𝑃𝑟𝐴1 = 𝑃𝑟𝐴2 = ⋯ = 𝑃𝑟𝐴𝑚 (3) stage 3: construction of the theoretical rating matrix (𝑻𝒑): the elements of the matrix (𝑡𝑝𝑖𝑗 ) are calculated by multiplying the priorities of alternatives (𝑃𝑟𝐴𝑖 ) and the criterion weights (𝑤𝑗 ), as shown in equation (4). kaya/oper. res. eng. sci. theor. appl. 3 (3) (2020) 101-122 106 𝑻𝒑 = [ pra1. w1 pra1. w2 … pra1. wn pra2. w1 pra2. w2 … pra2. wn ⋮ ⋮ ⋱ ⋮ pram. w1 pram. w2 … pram. wn ] (4) stage 4: defining the real rating matrix (𝑻𝒓): in order to obtain 𝑇𝑟 matrix, theoretical grading matrix 𝑇𝑝 and initial decision matrix 𝑋 are used. matrix elements should be calculated by using equation (5) for maximization criteria and equation (6) for minimization criteria. trij = tpij . ( xij − xij − xij + − xij −) (5) trij = tpij . ( xij − xij + xij − − xij +) (6) 𝑥𝑖𝑗 + is the highest value of the criterion from the alternative (𝑥𝑖𝑗 + = max (𝑥1, 𝑥2, … , 𝑥𝑚 )), 𝑥𝑖𝑗 − is the lowest value of the criterion from the alternative (𝑥𝑖𝑗 − = min (𝑥1, 𝑥2, … , 𝑥𝑚 )). the actual rating matrix to be obtained as a result of calculations is shown in eq. (7). 𝐶1 𝐶2 … 𝐶𝑛 𝑇𝑟 = [ tr11 tr12 … tr1n tr21 tr22 … tr2n ⋮ ⋮ ⋱ ⋮ trm1 trm2 … trmn ] (7) stage 5: computation of total gap matrix (g) with the help of gap matrix (𝐺), equation (8), the difference between the theoretical rating matrix (𝑇𝑝) and the actual grading matrix (𝑇𝑟 ) is obtained as shown in eq. (9). 𝑔𝑖𝑗 = 𝑡𝑝𝑖𝑗 − 𝑡𝑟𝑖𝑗 𝑔𝑖𝑗 ∈ [0, ∞) (8) 𝐺 = 𝑇𝑝 − 𝑇𝑟 = [ 𝑔11 𝑔12 … 𝑔1𝑛 𝑔21 𝑔22 … 𝑔2𝑛 ⋮ ⋮ ⋱ ⋮ 𝑔𝑚1 𝑔𝑚2 … 𝑔𝑚𝑛 ] (9) stage 6: determining the total gap with alternatives if theoretical rating (𝑡𝑝𝑖𝑗 ) and real rating (𝑡𝑟𝑖𝑗 ) of an alternative (𝐴𝑖 ) for a criterion (𝐶𝑗 ) are equal and different from zero, the gap will be zero (𝑔𝑖𝑗 = 0). in this case, this alternative (𝐴𝑖) would be the ideal alternative (𝐴𝑖 +) for this criterion (𝐶𝑗 ). if the theoretical rating (𝑡𝑝𝑖𝑗 ) of an alternative (𝐴𝑖) for a criterion (𝐶𝑗 ) equals zero (𝑡𝑝𝑖𝑗 = 𝑡𝑟𝑖𝑗 = 𝑔𝑖𝑗 = 0), then the gap for the alternative (𝐴𝑖 ) for the criterion (𝐶𝑗 ) is (𝑔𝑖𝑗 = 0). in this case, this alternative (𝐴𝑖 ) will be the worst alternative (𝐴𝑖 −) for this criterion (𝐶𝑗 ). evaluation of the effect of covid-19 on countries’ sustainable development level: a comparative mcdm framework 107 stage 7: calculation of the value (𝑸𝒊) of the final criteria functions of alternatives the value of the criteria functions is calculated to take advantage of equation (10) for each alternative. 𝑄𝑖 = ∑ 𝑔𝑖𝑗 𝑛 𝑗=1 , 𝑖 = 1, 2, … , 𝑚 (10) 𝑄𝑖 values are ranked from small to a large value, and alternatives are obtained. 4. evaluate the effects of the covid-19 pandemic on sustainable development performance of oecd countries the organization for economic co-operation and development, or oecd in short, is an international platform that works jointly to solve the economic, social, and management problems of member countries. this establishment was founded in paris in 1961 and was originally established with 20 countries. later, the number of oecd member countries increased to 37 with the participation in developmentally and socioeconomically different countries (our global reach oecd, 2020). the main purpose of oecd is to support countries in ensuring sustainable economic growth, increasing employment, raising living standards, ensuring economic stability and contributing to the growth of world trade. member states of the organization constitute 63 percent of gdp, three-quarters of world trade, 95 percent of world official development aid and more than half of world energy consumption in today's world (what is oecd, 2020). in the study, colombia, luxemburg, israel and new zealand were excluded from this study due to the unavailability of some data for this method. the impact of covid19 on the sustainable development performances of a total of 33 oecd countries were analyzed using mairca considering the data of the second quarter (q2) of 2020 and the data of the same quarter of the previous year (2019). to test the validity and effectiveness of this method, the ranking results of mairca were compared with the results obtained from novel mcdm models such as mabac and waspas. additionally, the wilcoxon signed-rank test is conducted to determine whether the sustainable development indicators of oecd countries differ between the q2/2019 and q2/2020. the general framework of this study is summarized in figure 1. kaya/oper. res. eng. sci. theor. appl. 3 (3) (2020) 101-122 108 figure 1. general framework of study sustainable development indicators of oecd countries have been determined in line with the sustainable development goals of oecd, the european union, and the united nations and literature review. in addition, all the indicators used in this study collect data from oecd and iea database identify sustainable development indicators comparison and sensitivity analysis using the mabac and waspas method explore assumptions for the statistical hypothesis test comparison of data for the same quarter of two different year discuss the result of wilcoxon signed-rank test step 1: describe the problem and identify indicators step 2: mairca method step 3. sensitivity analysis step 4. wilcoxon test evaluation of the effect of covid-19 on countries’ sustainable development level: a comparative mcdm framework 109 were designed to take into account all dimensions, namely the economy, environment, and social, which constitute the sustainable development model. eight different sustainable development indicators comprising total electricity production, renewable energy production, merchandise trade, customer price index (cpi), analytical house price indicators (rent price), gross domestic product (gdp), producer price index (ppi), unemployment rate, aged 15 and over were selected in this study. the indicators were analyzed for their ability to measure the economic, environmental and social dimensions of sustainable development. data on economic and social indicators (i3, i4, i5, i6, i7, i8) were obtained from the oecd databases, and environmental indicators (i1 and i2) were obtained from reports published by the international energy agency (iea). definitions, indices, and periods considered in the study regarding indicators of sustainable development are shown in table 1. table 1. indicators of sustainable development not. indicator unit quarter / year references i1 total electricity production gwh q2/2019 q2/2020 (ding et al., 2016); (sustainable development goals, 2020) i2 renewable energy production gwh q2/2019 q2/2020 (mateusz et al., 2018); (kothari et al., 2010); (sustainable development goals, 2020); (sathaye et al., 2011) i3 merchandise trade us dollar, billions q2/2019 q2/2020 (ding et al., 2016); (sustainable development goals, 2020) i4 customer price index index, 2015=100 q2/2019 q2/2020 (gaspar et al., 2017); (sustainable development goals, 2020) i5 analytical house rent price indicators index q2/2019 q2/2020 (zavadskas et al., 2017); (sustainable development goals, 2020) i6 gross domestic product annual growth rate (%) q2/2019 q2/2020 (bali swain and yang-wallentin, 2020); (balcerzak and pietrzak, 2016); (ding et al., 2016): (gaspar et al., 2017); (sustainable development goals, 2020) i7 producer price index index, 2015=100 q2/2019 q2/2020 (sustainable development goals, 2020) i8 the unemployment rate, aged 15 and over % q2/2019 q2/2020 (bali swain and yang-wallentin, 2020); (balcerzak and pietrzak, 2016); (ding et al., 2016); (mateusz et al., 2018); (gaspar et al., 2017) total electricity production (i1): electricity generated different type of energy resources such as fossil fuels, nuclear power plants, hydropower plants (excluding pumped storage), geothermal systems, solar panels, biofuels, wind, etc. renewable energy production (i2): renewable energy is the energy received from the energy flow that exists in the natural processes that continue continuously. they are hydro energy, wind, solar, geothermal, and other renewable energy sources. merchandise trade (i3): goods that add or subtract from the stock of material resources of a country by entering (imports) or leaving (exports) its economic territory. kaya/oper. res. eng. sci. theor. appl. 3 (3) (2020) 101-122 110 customer price index (i4): defined as the change in the prices of a basket of goods and services that are typically purchased by specific groups of households. analytical house rent price indicators (i5): house price indices (rent prices), are index numbers that measure the rent prices of residential properties over time. gross domestic product (i6): the standard measure of the value-added created through the production of goods and services in a country during a certain period. producer price index (i7): the rate of change in the prices of products sold as they leave the producer. the unemployment rate, aged 15 and over (i8): the number of unemployed people as a percentage of the labor force, where the latter consists of the unemployed plus those in paid or self-employment. table 2. initial decision matrix indicators countries i1 i2 i3 i4 i5 i6 i7 i8 australia 21041 4304 69.61 106.6 102.5 1223934.95 111.1 5.231 austria 6357 5842 44.75 106.7 114.4 469791.799 105.1 4.500 belgium 6891 1376 112.24 107.9 103.9 553085.807 113.5 5.467 canada 47322 31979 114.90 107.7 104.6 1723905.35 106.4 5.567 chile 6804 2560 17.06 111.1 117.8 445180.531 108.8 6.980 czech republic 6613 925 50.17 108.1 109.7 406561.381 103.0 1.967 denmark 2292 1955 27.84 103.1 104.9 308065.246 105.9 4.933 estonia 489 137 4.11 109.9 130.7 45784.7699 109.7 4.867 finland 5202 2999 18.65 103.4 108.2 254103.301 104.7 6.800 france 44439 9888 145.44 104.4 100.6 2908013.64 103.3 8.500 germany 45887 20169 371.46 105.5 105.4 4150471.67 105.4 3.067 greece 3117 1227 9.66 101.9 92.1 306790.238 104.7 17.333 hungary 2258 358 30.36 109.4 123.4 307584.948 115.0 3.433 iceland 1660 1660 1.28 109.4 120.0 18920.8022 99.0 3.367 ireland 2293 625 42.61 102.1 115.9 413134.441 100.6 5.200 italy 22141 10296 133.67 103.0 101.0 2335523.24 103.5 10.000 japan 73035 36284 181.29 101.7 99.3 5356221.8 101.0 2.367 korea 43570 3031 136.20 104.9 104.0 2150833.19 102.7 4.000 latvia 402 244 3.94 109.4 107.0 55221.0561 110.5 6.367 lithuania 282 206 8.41 110.4 126.0 96063.1159 107.2 6.100 mexico 27884 5347 117.21 117.9 110.0 2388177.33 126.3 3.549 netherlands 9374 1796 176.64 106.0 108.2 930705.86 109.4 3.333 norway 9770 9502 26.31 110.6 107.6 331933.394 114.0 3.433 poland 12052 1848 66.00 105.7 112.8 1204174.54 109.7 3.333 portugal 4037 2176 16.89 104.2 107.5 339634.903 104.8 6.600 slovak republic 2264 695 22.21 106.0 101.3 181242.251 103.7 5.767 slovenia 1419 588 11.31 105.4 118.4 75067.7421 103.1 4.367 spain 20784 8803 84.80 104.6 103.0 1790431.14 105.3 14.200 sweden 12703 7655 40.11 106.8 104.1 519697.892 112.1 6.533 switzerland 5744 3551 61.12 102.0 102.1 569152.648 100.4 4.455 turkey 23989 14407 44.52 158.2 141.4 2330974.19 186.2 13.867 united kingdom 23914 8185 108.49 107.8 103.8 2948323.99 111.5 3.767 united states 332986 74378 408.63 108.0 115.3 19900185.1 106.94 3.633 aim max max max min min min min min evaluation of the effect of covid-19 on countries’ sustainable development level: a comparative mcdm framework 111 in this study, one of the expert is an engineer with expertise in regional development at the ankara development agency in turkey, and the others are two academics working in the economics and business department of the university. in line with the opinion received from three experts, as a result of interview with experts, the sustainable indicator should equal the importance weight. in the application of the mairca method, data of 33 oecd countries are obtained from the oecd and iea databases. the initial decision matrix for the second quarter of 2020 and the aim of each indicator are presented in table 2. due to the nature of the method, the decision-maker should not have a priority in the choice of an alternative. since there are 33 alternative countries (n), the priority (𝑃𝑟𝐴𝑖 ) of each alternative is calculated as shown in equation 2. 𝑃𝑟𝐴𝑖 = 1 𝑛 = 1 33 = 0.030 (11) 𝑃𝑟𝐴1 =𝑃𝑟𝐴2 = 𝑃𝑟𝐴3 = 𝑃𝑟𝐴4 =……………………=𝑃𝑟𝐴33 =0.030 (12) the theoretical rating matrix was calculated by eq. (3) and eq. (4), respectively. matrix elements are obtained by multiplying the chosen alternative preferences (𝑃𝑟𝐴𝑖 ) and the coefficients (𝑤𝑖 ) of the weights of the indicators. experts assumed that the indicator weights were of equal coefficient. the theoretical rating matrix (𝑇𝑝) is shown in table a1 (appendix). after this matrix was calculated, the real evaluation matrix (𝑇𝑟 ) was created, as given in table a2 (appendix). the actual evaluation matrix element is found by multiplying the theoretical rating matrix element with the normalized start matrix element. the normalized initial matrix was calculated using the eq. (6) and eq. (7). the total gap matrix (g) was obtained by subtracting the real rating matrix (𝑡𝑟𝑖𝑗 ) from the theoretical rating matrix (𝑡𝑝𝑖𝑗 ), as shown in eq. (8) and eq. (9). it is preferred that the gap value be close to zero. the gap matrix is shown in table a3 in annex. in the last step of the method, by using the total gap matrix in table a3 (appendix), the criterion function values of decision alternatives were calculated by using equation (10). the function values (𝑄𝑖 ) of the criteria obtained for the second quarter of 2019 with the mairca method and the ranking of the oecd countries are shown in table 3. similar steps were followed using data from the second quarter of 2020, when covid-19 started to spread worldwide, and the ranking of the sustainability performances of oecd countries obtained by mairca method for the second quarter of 2019 and 2020 is shown in figure 1. according to the results given in table 3, the country with the best sustainability performance among oecd countries is the united states. this country is followed by japan, germany, canada, korea, and the netherlands, respectively. kaya/oper. res. eng. sci. theor. appl. 3 (3) (2020) 101-122 112 table 3. the ranking of oecd countries using the mairca method (q2/2020) countries qi rank countries qi rank united states 0.0090 1 slovak republic 0.0136 18 germany 0.0091 2 austria 0.0137 19 japan 0.0095 3 portugal 0.0138 20 korea 0.0114 4 finland 0.0138 21 netherlands 0.0117 5 sweden 0.0139 22 france 0.0119 6 slovenia 0.0139 23 switzerland 0.0121 7 latvia 0.0146 24 united kingdom 0.0123 8 iceland 0.0146 25 italy 0.0123 9 mexico 0.0147 26 belgium 0.0127 10 spain 0.0148 27 canada 0.0129 11 hungary 0.0148 28 czech republic 0.0130 12 greece 0.0150 29 australia 0.0131 13 estonia 0.0153 30 denmark 0.0133 14 lithuania 0.0157 31 ireland 0.0133 15 chile 0.0166 32 norway 0.0135 16 turkey 0.0249 33 poland 0.0135 17 the sustainability performance rankings of the countries in the second quarter of 2020, in which the covid-19 pandemic spread worldwide, were compared in the same period of the previous year, as shown in figure 2. according to the results obtained with mairca in the second quarter of 2020, the usa belongs to the best sustainable development level among alternative countries. this country is followed by germany, japan, korea and the netherlands, respectively. countries with the worst sustainable development performance of the same period, the lowest ranking countries in terms of sustainability performance, are turkey (33rd), chile (32nd), lithuania (31st), estonia (30th), and greece (29th). to examine how the covid-19 pandemic has affected the sustainable development goals of oecd countries, data from the same period of the previous year were used and the mairca method was resolved again. the comparison of the sustainable performance levels for both quarters is shown in figure 2. accordingly, the country with the highest sustainable development performance in april-may-june 2019 was america, followed by japan, germany, canada and korea, respectively. in the ranking results, canada ranked 4th in 2019, ranked 11th during the pandemic period. the pandemic has been shown to seriously affect canada's level of sustainable development. it can be seen that for hungary, turkey, greece, lithuania, australia, denmark, norway, poland, sweden, in terms of development sustainability, rankings are stable. evaluation of the effect of covid-19 on countries’ sustainable development level: a comparative mcdm framework 113 figure. 2. comparison of sustainability performance rankings (q2/2019-q2/2020) 5. sensitivity analysis the reliability of the results obtained from the mairca model should be tested to ensure the validity of the selected alternatives. for this purpose, the reliability and validity of the model were analyzed by using the mabac method and waspas method. results obtained with mairca, mabac and waspas methods are quite similar to each other. a comparison of results obtained using three mcdm methods are illustrated in figure 3 and figure 4, respectively. as can be seen from figure 3, in all three methods, the united states has the best sustainable development performance. in the second quarter of 2019, japan, germany, canada and korea have the same rank in all three methods. the spearman correlation coefficient was used to determine the relationships between these methods. the spearman correlation coefficient is used to measure the similarity between two group rankings. this method with a higher spearman's rank relationship coefficient is accepted to be more significant than one with a lower spearman's rank connection coefficient since it has better concurrences with other mcdm methods (gang kou, yanqun lu, yi peng, & yong shi, 2012). spearman correlation coefficients for both years are shown in table 4. according to the validity results, the correlation coefficient is above 87.2% and it has a high correlation. this confirms that the mairca method is in agreement with other mcdm methods and its results are reliable. 0 5 10 15 20 25 30 35 q2/2019 q2/2020 kaya/oper. res. eng. sci. theor. appl. 3 (3) (2020) 101-122 114 figure 3. the ranking of oecd countries (q2/2019) figure 4. the ranking of oecd countries (q2/2020) table 4. correlation values of methods spearman's coefficient mabac waspas average value mairca (q2/2019) 1.000 0.872 0.936 mairca (q2/2020) 0.644 0.881 0.762 0 5 10 15 20 25 30 35 mairca mabac waspas 0 5 10 15 20 25 30 35 a u st ra li a a u st ri a b e lg iu m c a n a d a c h il e c z e c h r e p u b li c d e n m a rk e st o n ia f in la n d f ra n c e g e rm a n y g re e c e h u n g a ry ic e la n d ir e la n d it a ly ja p a n k o re a l a tv ia l it h u a n ia m e x ic o n e th e rl a n d s n o rw a y p o la n d p o rt u g a l s lo v a k r e p u b li c s lo v e n ia s p a in s w e d e n s w it z e rl a n d t u rk e y u n it e d k in g d o m u n it e d s ta te s mairca mabac waspas evaluation of the effect of covid-19 on countries’ sustainable development level: a comparative mcdm framework 115 6. wilcoxon signed-rank test the non-parametric wilcoxon signed-rank test was applied to determine whether there is a significant difference between the second quarter of 2020 and the same quarter of the previous year in terms of the indicators of the sustainable development of oecd countries. it can be clearly seen in table 5, p values of all indicators are less than 0.05 value. according to wilcoxon test hypothesis, if p-value is less than zero, the null hypothesis is rejected and it is concluded that there is a significant difference between the period (april-june 2019) and (april-june 2020). accordingly, table 5 shows that as the p values of “total electricity production (i1), renewable energy production (i2), merchandise trade (i3), customer price index (i4), analytical house rent price indicators (i5), gdp (i6)", producer price index (i7), unemployment rate, aged 15 and over (i8) are less than 0.05, results demonstrated that there are differences between before and during the covid-19 pandemic. test results are clearly expressed in table 5 and 6, respectively. table 5. wilcoxon signed-rank test results i1(2020) i1(2019) i2(2020) i2(2019) i3(2020) i3(2019) i4(2020) i4(2019) i5(2020) i5(2019) i6(2020 i6(2019) i7(2020) i7(2019) i8(2020) i8(2019) z -3.815b -2.10b -5.012b -2.124c -3.293c -5.012b -3.475c -3.726c p 0.000 0.036 0.000 0.034 0.001 0.000 0.001 0.000 a. wilcoxon signed-rank test, b. based on positive ranks, c. based on negative ranks as seen in table 6, the total electricity production of 26 oecd countries decreased in the second quarter of 2020. it is observed that the covid-19 pandemic has negatively affected the energy production of oecd countries. however, this situation has changed in the amount of renewable energy generation. in the second quarter of 2020, which was heavily affected by the pandemic, the amount of renewable energy production of 22 countries increased compared to the second quarter of the previous year. it is interesting to note that covid-19 pandemic has a positive effect on renewable energy goals. the global covid-19 novel coronavirus pandemic has severe negative impacts on the global economy. gdp is an important indicator to bring coherence to the sustainable development goals. when the result on house rent prices were analyzed, the consumer price index of 27 countries increased compared to the second quarter of 2019. according to table 6, merchandise trade and gdp of all oecd countries plunged in the second quarter of 2020 as compared to the same period last year. the covid-19 has prevented countries from achieving their sustainable development goals. the producer price index means the average change over time in selling prices received by domestic producers of goods and services. the producer price index of 29 countries decreased compared to the same quarter of the previous year. the other important sustainable development indicator is the unemployment rate; the test result indicates that the unemployment rate of 26 countries has increased compared to the same period of the previous year. coronavirus has hit unemployment in oecd countries. the results found that all sustainable development indicators, except renewable energy production, have been severely affected by the covid-19 pandemic. kaya/oper. res. eng. sci. theor. appl. 3 (3) (2020) 101-122 116 table 6. cash ratio ranks number mean rank sum of ranks i1 (2019) – i1(2020) total electricity production negative ranks 26 19.00 494.0 positive ranks 7 9.57 67.0 i2 (2019) – i1(2020) renewable energy negative ranks 11 14.82 163.0 positive ranks 22 18.09 398.0 i3 (2019) – i1(2020) merchandise trade negative ranks 33 17.00 561.0 positive ranks 0 0.00 0 i4 (2019) – i1(2020) cpi negative ranks 12 12.54 150.5 positive ranks 20 18.88 377.5 i5 (2019) – i1(2020) rent price negative ranks 4 20.00 80.0 positive ranks 27 15.41 416.0 i6 (2019) – i1(2020) gdp negative ranks 33 17.00 561.0 positive ranks 0 0.00 0.0 i7 (2019) – i1(2020) producer price index negative ranks 29 17.59 475.0 positive ranks 6 14.33 86.0 i8 (2019) – i1(2020) unemployment rate negative ranks 7 10.29 72.0 positive ranks 26 18.81 489.0 7. results and limitations world economies have faced serious health problems and socio-economic crises due to the covid-19 pandemic. the covid-19 pandemic continues to threaten life, to suppress the world economy, and to have a profound impact on social and environmental issues. national and international community organizations emphasized that countries should pay more attention to sustainable development goals in the post-covid-19 recovery phase in order to reduce the destructive effect of the covid-19 crisis. in this study, the effect of the covid-19 pandemic on the sustainable development of oecd countries was investigated with a novel mcdm method. for this purpose, the mairca method was used to rank the sustainability performance of oecd countries and test its validity and reliability with mabac and waspas methods. moreover, statistical analysis was implemented and obtained results were discussed in view of sustainable development. the analysis leads to the following conclusions: united states, germany, japan, france, and south korea are with the best development performance while countries with the worst performance are turkey, chile, lithuania, and estonia for the same quarter of 2019 and 2020. developed countries are in the top position in the ranking of sustainable development performance compared to developing countries, and this situation did not change with the appearance of the covid-19 pandemic; the rankings score was the same. in order to test the validity and effectiveness of the mairca method, the ranking results of mairca were compared with the results obtained from novel mcdm models such as mabac and waspas. it has been observed that all mcdm methods used give effective results to determine the ranking of countries under a sustainable development level. furthermore, a non-parametric wilcoxon signedrank test was used to determine whether the direction of changes of each sustainable development indicator was different between the pre-covid-19 and covid-19. evaluation of the effect of covid-19 on countries’ sustainable development level: a comparative mcdm framework 117 accordingly, results demonstrated that there were significant differences between before and during the covid-19 pandemic. importantly, our results provide evidence that, except for renewable energy production, all sustainable indicators have adversely been affected by the covid-19 pandemic. however, this study has revealed that covid 19 has had an innovator effect by changing the direction of energy production resources. the pandemic has tripped the scale in favor of renewable energy. there are a number of limitations for this study. one of the main limitations is the missing dataset. due to the continuing covid-19 pandemic, there are missing and uncompleted sustainable development indicators such as the "number of hospital beds", "attendance at school", "inequality in education", "life expectancy", "gender inequality", etc. further study will reevaluate with a different type of sustainable indicators. another limitation of the study is that it only takes into account the impact of the pandemic on oecd countries' sustainable development performances. in the future study, new research is planned with different countries included in opec, g20, and bric countries. appendix table a1. theoretical evaluation matrix (tp) countries i1 i2 i3 i4 i5 i6 i7 i8 australia 0.0038 0.0038 0.0038 0.0038 0.0038 0.0038 0.0038 0.0038 austria 0.0038 0.0038 0.0038 0.0038 0.0038 0.0038 0.0038 0.0038 belgium 0.0038 0.0038 0.0038 0.0038 0.0038 0.0038 0.0038 0.0038 canada 0.0038 0.0038 0.0038 0.0038 0.0038 0.0038 0.0038 0.0038 chile 0.0038 0.0038 0.0038 0.0038 0.0038 0.0038 0.0038 0.0038 czech republic 0.0038 0.0038 0.0038 0.0038 0.0038 0.0038 0.0038 0.0038 denmark 0.0038 0.0038 0.0038 0.0038 0.0038 0.0038 0.0038 0.0038 estonia 0.0038 0.0038 0.0038 0.0038 0.0038 0.0038 0.0038 0.0038 finland 0.0038 0.0038 0.0038 0.0038 0.0038 0.0038 0.0038 0.0038 france 0.0038 0.0038 0.0038 0.0038 0.0038 0.0038 0.0038 0.0038 germany 0.0038 0.0038 0.0038 0.0038 0.0038 0.0038 0.0038 0.0038 greece 0.0038 0.0038 0.0038 0.0038 0.0038 0.0038 0.0038 0.0038 hungary 0.0038 0.0038 0.0038 0.0038 0.0038 0.0038 0.0038 0.0038 iceland 0.0038 0.0038 0.0038 0.0038 0.0038 0.0038 0.0038 0.0038 ireland 0.0038 0.0038 0.0038 0.0038 0.0038 0.0038 0.0038 0.0038 italy 0.0038 0.0038 0.0038 0.0038 0.0038 0.0038 0.0038 0.0038 japan 0.0038 0.0038 0.0038 0.0038 0.0038 0.0038 0.0038 0.0038 korea 0.0038 0.0038 0.0038 0.0038 0.0038 0.0038 0.0038 0.0038 latvia 0.0038 0.0038 0.0038 0.0038 0.0038 0.0038 0.0038 0.0038 lithuania 0.0038 0.0038 0.0038 0.0038 0.0038 0.0038 0.0038 0.0038 mexico 0.0038 0.0038 0.0038 0.0038 0.0038 0.0038 0.0038 0.0038 netherlands 0.0038 0.0038 0.0038 0.0038 0.0038 0.0038 0.0038 0.0038 norway 0.0038 0.0038 0.0038 0.0038 0.0038 0.0038 0.0038 0.0038 poland 0.0038 0.0038 0.0038 0.0038 0.0038 0.0038 0.0038 0.0038 portugal 0.0038 0.0038 0.0038 0.0038 0.0038 0.0038 0.0038 0.0038 slovak republic 0.0038 0.0038 0.0038 0.0038 0.0038 0.0038 0.0038 0.0038 slovenia 0.0038 0.0038 0.0038 0.0038 0.0038 0.0038 0.0038 0.0038 spain 0.0038 0.0038 0.0038 0.0038 0.0038 0.0038 0.0038 0.0038 sweden 0.0038 0.0038 0.0038 0.0038 0.0038 0.0038 0.0038 0.0038 kaya/oper. res. eng. sci. theor. appl. 3 (3) (2020) 101-122 118 switzerland 0.0038 0.0038 0.0038 0.0038 0.0038 0.0038 0.0038 0.0038 turkey 0.0038 0.0038 0.0038 0.0038 0.0038 0.0038 0.0038 0.0038 united kingdom 0.0038 0.0038 0.0038 0.0038 0.0038 0.0038 0.0038 0.0038 united states 0.0038 0.0038 0.0038 0.0038 0.0038 0.0038 0.0038 0.0038 table a2. real evaluation matrix (tr) countries i1 i2 i3 i4 i5 i6 i7 i8 australia 0.0002 0.0002 0.0006 0.0035 0.0030 0.0036 0.0033 0.0030 austria 0.0001 0.0003 0.0004 0.0035 0.0021 0.0037 0.0035 0.0032 belgium 0.0001 0.0001 0.0010 0.0034 0.0029 0.0037 0.0032 0.0029 canada 0.0005 0.0016 0.0011 0.0034 0.0028 0.0035 0.0035 0.0029 chile 0.0001 0.0001 0.0001 0.0032 0.0018 0.0037 0.0034 0.0026 czech republic 0.0001 0.0000 0.0005 0.0034 0.0024 0.0037 0.0036 0.0038 denmark 0.0000 0.0001 0.0002 0.0037 0.0028 0.0037 0.0035 0.0031 estonia 0.0000 0.0000 0.0000 0.0032 0.0008 0.0038 0.0033 0.0031 finland 0.0001 0.0001 0.0002 0.0037 0.0025 0.0037 0.0035 0.0026 france 0.0005 0.0005 0.0013 0.0036 0.0031 0.0032 0.0036 0.0022 germany 0.0005 0.0010 0.0034 0.0035 0.0028 0.0030 0.0035 0.0035 greece 0.0000 0.0001 0.0001 0.0038 0.0038 0.0037 0.0035 0.0000 hungary 0.0000 0.0000 0.0003 0.0033 0.0014 0.0037 0.0031 0.0034 iceland 0.0000 0.0001 0.0000 0.0033 0.0016 0.0038 0.0038 0.0034 ireland 0.0000 0.0000 0.0004 0.0038 0.0020 0.0037 0.0037 0.0030 italy 0.0002 0.0005 0.0012 0.0037 0.0031 0.0033 0.0036 0.0018 japan 0.0008 0.0018 0.0017 0.0038 0.0032 0.0028 0.0037 0.0037 korea 0.0005 0.0001 0.0013 0.0036 0.0029 0.0034 0.0036 0.0033 latvia 0.0000 0.0000 0.0000 0.0033 0.0026 0.0038 0.0033 0.0027 lithuania 0.0000 0.0000 0.0001 0.0032 0.0012 0.0038 0.0034 0.0028 mexico 0.0003 0.0003 0.0011 0.0027 0.0024 0.0033 0.0026 0.0034 netherlands 0.0001 0.0001 0.0016 0.0035 0.0026 0.0036 0.0033 0.0035 norway 0.0001 0.0005 0.0002 0.0032 0.0026 0.0037 0.0031 0.0034 poland 0.0001 0.0001 0.0006 0.0035 0.0022 0.0036 0.0033 0.0035 portugal 0.0000 0.0001 0.0001 0.0036 0.0026 0.0037 0.0035 0.0026 slovak republic 0.0000 0.0000 0.0002 0.0035 0.0031 0.0038 0.0036 0.0029 slovenia 0.0000 0.0000 0.0001 0.0035 0.0018 0.0038 0.0036 0.0032 spain 0.0002 0.0004 0.0008 0.0036 0.0030 0.0035 0.0035 0.0008 sweden 0.0001 0.0004 0.0004 0.0035 0.0029 0.0037 0.0032 0.0027 switzerland 0.0001 0.0002 0.0006 0.0038 0.0030 0.0037 0.0037 0.0032 turkey 0.0003 0.0007 0.0004 0.0000 0.0000 0.0033 0.0000 0.0009 united kingdom 0.0003 0.0004 0.0010 0.0034 0.0029 0.0032 0.0032 0.0033 united states 0.0038 0.0038 0.0038 0.0034 0.0020 0.0000 0.0034 0.0034 table a3. total gap matrix countries i1 i2 i3 i4 i5 i6 i7 i8 australia 0.0036 0.0036 0.0032 0.0003 0.0008 0.0002 0.0005 0.0008 austria 0.0037 0.0035 0.0034 0.0003 0.0017 0.0001 0.0003 0.0006 belgium 0.0037 0.0037 0.0028 0.0004 0.0009 0.0001 0.0006 0.0009 canada 0.0033 0.0022 0.0027 0.0004 0.0010 0.0003 0.0003 0.0009 chile 0.0037 0.0037 0.0036 0.0006 0.0020 0.0001 0.0004 0.0012 czech republic 0.0037 0.0037 0.0033 0.0004 0.0014 0.0001 0.0002 0.0000 denmark 0.0038 0.0037 0.0035 0.0001 0.0010 0.0001 0.0003 0.0007 estonia 0.0038 0.0038 0.0038 0.0005 0.0030 0.0000 0.0005 0.0007 finland 0.0037 0.0036 0.0036 0.0001 0.0012 0.0000 0.0002 0.0012 evaluation of the effect of covid-19 on countries’ sustainable development level: a comparative mcdm framework 119 france 0.0033 0.0033 0.0024 0.0002 0.0007 0.0006 0.0002 0.0016 germany 0.0033 0.0028 0.0003 0.0002 0.0010 0.0008 0.0003 0.0003 greece 0.0038 0.0037 0.0037 0.0000 0.0000 0.0001 0.0002 0.0038 hungary 0.0038 0.0038 0.0035 0.0005 0.0024 0.0001 0.0007 0.0004 iceland 0.0038 0.0037 0.0038 0.0005 0.0021 0.0000 0.0000 0.0003 ireland 0.0038 0.0038 0.0034 0.0000 0.0018 0.0001 0.0001 0.0008 italy 0.0035 0.0033 0.0026 0.0001 0.0007 0.0004 0.0002 0.0020 japan 0.0030 0.0019 0.0021 0.0000 0.0006 0.0010 0.0001 0.0001 korea 0.0033 0.0036 0.0025 0.0002 0.0009 0.0004 0.0002 0.0005 latvia 0.0038 0.0038 0.0038 0.0005 0.0011 0.0000 0.0005 0.0011 lithuania 0.0038 0.0038 0.0037 0.0006 0.0026 0.0000 0.0004 0.0010 mexico 0.0035 0.0035 0.0027 0.0011 0.0014 0.0005 0.0012 0.0004 netherlands 0.0037 0.0037 0.0022 0.0003 0.0012 0.0002 0.0005 0.0003 norway 0.0037 0.0033 0.0036 0.0006 0.0012 0.0001 0.0007 0.0004 poland 0.0037 0.0037 0.0032 0.0003 0.0016 0.0002 0.0005 0.0003 portugal 0.0037 0.0037 0.0036 0.0002 0.0012 0.0001 0.0003 0.0011 slovak republic 0.0038 0.0038 0.0036 0.0003 0.0007 0.0000 0.0002 0.0009 slovenia 0.0038 0.0038 0.0037 0.0002 0.0020 0.0000 0.0002 0.0006 spain 0.0036 0.0033 0.0030 0.0002 0.0008 0.0003 0.0003 0.0030 sweden 0.0036 0.0034 0.0034 0.0003 0.0009 0.0001 0.0006 0.0011 switzerland 0.0037 0.0036 0.0032 0.0000 0.0008 0.0001 0.0001 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the creative commons attribution (cc by) license (http://creativecommons.org/licenses/by/4.0/). evaluation of the effect of covid-19 on countries’ sustainable development level: a comparative mcdm framework sema kayapinar kaya 1. introduction 2. literature review 3. mairca method 4. evaluate the effects of the covid-19 pandemic on sustainable development performance of oecd countries 5. sensitivity analysis 6. wilcoxon signed-rank test 7. results and limitations appendix references operational research in engineering sciences: theory and applications vol. 4, issue 2, 2021, pp. 124-139 issn: 2620-1607 eissn: 2620-1747 doi: https://doi.org/10.31181/oresta20402124r * corresponding author. mangeyram@geu.ac.in (m. ram), vash.tyagi@gmail.com (v. tyagi) reliability characteristics of railway communication system subject to switch failure mangey ram 1, vaishali tyagi2* 1 department of mathematics, computer science and engineering, graphic era, dehradun, uttarakhand, india and institute of advanced manufacturing technologies, peter the great st. petersburg polytechnic university, saint petersburg, russia 2 department of mathematics and statistics, kanya gurukul campus, gurukul kangri, haridwar, uttarakhand, india received: 20 march 2021 accepted: 23 june 2021 first online: 08 july 2021 research paper abstract. in the present study, a railway communication system (rcs) reliability model is developed based on system failure. the proposed rcs has control centre and stations which are arranged in such a manner that failure of control centre or a single station stops the working of overall system i.e., all switches must be working for communication to be available. to improve the reliability of the proposed communication system, a ring architecture is employed. in this architecture one additional communication path is connected in parallel configuration. provision of two path of communication ensures that failure of one path will not cause a communication failure and communication will be available through additional path. all failures of rcs are exponentially distributed. mathematical modelling of the system is carried out using markov process by which the differential equations are generated. these differential equations are further used to evaluate the reliability measures like availability, reliability, mean time to failure of the proposed rcs. likewise, sensitivity analysis is done to determine the impact of failures on rcs’s performance measures. the proposed markov process-based model gives the information about the failure and working of the multistate railway communication system. finally, numerical results are provided with graphs to demonstrates the usefulness of the findings. key words: railway communication system; reliability; mean time to failure; markov process; sensitivity 1. introduction in the present day’s society demands inexpensive, more secure, and timesaving public transport. railway transportation systems attracts a lot of passengers because reliability characteristics of railway communication system subject to switch failure 125 of their capacity of transporting the people with high luxury, great comfort and large get-up-and-go efficacy (ai et al., 2014). a lot of people choose trains for travelling because of the easy understanding, experience and comfort that the rail transport gives. railway communications systems are needed to develop the communication between train and path equipment for traffic management and dealing with continuous high-data-rate traveler services, hypermedia dispatching video transmissions, railway mobile ticketing, and the internet of things (iot) for railways (ai et al., 2015; guan et al., 2017). the security of railway’s employees, passengers and of the general public are the first requirements and is of specific significance in the railway industry. railway industry looking for many aspects to improve the security / safety and the reliability of the railway systems. a railway system is a very large and complex stochastic dynamic system. this system is already interesting by itself. large, stochastic complex systems are generally examined with deterministic methods. many authors have written about deterministic optimization of railway systems over the last twenty years. a lot of research has been done in the context of the different techniques to increase the reliability of a railway communication system. aggarwal (1975) obtained reliability expression for communication system. marquez et al. (2003) discussed about the improvement of a way to deal the use of remote monitoring to the reliability centred maintenance of railway attendances. tao et al. (2007) used fault tree analysis method for rcs, in which main factors affecting the failure of rcs are determined by minimum cut set analysis. de felice and petrillo (2011) proposed a methodological approach based on human reliability analysis (hra) and failures modes, effects criticality analysis (fmeca) to calculate the reliability of railway transportation system. hra gives a logical analysis of factors affecting human performance, prompts suggestions for improvement. lin (2015) proposed an advanced finite state markov chain channel model for high-speed railway fading channels and derived the expression of state transition probabilities under different speed modes. unterhuber et al. (2016) provided a summary of communication systems in trains and discussed about possible direction for future wireless network. also, authors identified the gaps for station classification in railway environment, total velocity, and relative velocity for radio broadcast measurement. he et al. (2017) studied the propagation characteristics for rapid railway communication system including metropolitan, rural and tunnel with straight and curved route. zhang et al. (2018) proposed a markov model for railway communication system and used multi-link transmission communication technique to improve the capacity of rcs. kumar and kumar (2019) evaluated the reliability, and mean time to failure of the wireless communication system regarding its component failure. authors also identified the critical component by sensitivity analysis. song (2019) described a communication-based train control system and discussed the different constraints that affects the working of communication system. authors also evaluated system availability and performance by applied stochastic petri nets. in this research article, a railway communication system with control centre and stations is considered. the considered multi-state repairable system having control centre and stations in such a manner that for communication, all switches must be in working condition. failure in control centre and any of one station arises a communication failure. to improve the reliability of the proposed communication ram and tyagi/oper. res. eng. sci. theor. appl. 4 (2) (2021) 124-139 126 system, an additional path is connected in parallel configuration. in the proposed model of rcs, probability of each transition states is obtained and reliability measures such as system availability, system reliability, mean time to failure (mttf), and sensitivity of reliability have been computed. the rest of the paper is categorised as follows. the description of the proposed rcs with requisite assumptions and notations are presented in section 2. in section 3, the set of differential equations is constructed based on markov process and also probability of each state is calculated using laplace transformation. in section 4, the numerical calculations to compute the reliability measures of rcs such as availability, reliability, mean time to failure, and sensitivity analysis is given. in section 5, the behaviour of the reliability measures is discussed with the help of tables and graphs. finally, section 6 gives the concluding remark to highlight the significant and some future prospects of the present work. 2. system modelling in this study, a railway communication system with control centre and stations is considered. in this system a communication which is provided in the control centre as well as in each of the stations which are connected in a series configuration. it can be seen in the diagram that all switches must be working for the communication system to be function. if there is a failure in switch at any station, there will be a communication failure at those stations as well as at all stations beyond that point i.e., all switches must be working to continue communication. further one additional communication path is connected in parallel configuration to improve the reliability of proposed system. adding an additional path means that the communication will be available after failure of any one of the paths. on failure of both path’s switches, the communication system will be failed. figure 1. reliability block diagram of railway communication system to study and formulation of the system, following assumptions and notations are made (table 1): • the communication system consists of two paths namely path 1 and path 2, in which each path has a control centre and 3 stations. • the proposed communication system has main three states full operation, degradation states and failure state. • at time t = 0, control centre and stations are in fully operation state and communication system is available. reliability characteristics of railway communication system subject to switch failure 127 • this study assumes that the failure rates of path 1 units and path 2 units are statistically independent, constant and are exponentially distributed with failure rates λc1, λ1, and λc2, λ2. • failure of one path will not cause a communication failure. • repair service is always available to repair the failed unit, i.e., as soon as an operating unit fail, it is instantaneously detected and sent for repair. • when a failed unit is repaired it considered to be a new one. table 1. notations t time variable λc1 failure rate of path 1 control centre λc2 failure rate of path 2 control centre λ1 failure rate of all stations of path 1 λ2 failure rate of all stations of path 2 pi(t) the state probability of the system at instant ‘t’ for i = 0 to 7 pi (x, t) the failed state probability of the system at instant ‘t’ and an elapsed repair time x for i = 8 to 21 x elapsed repair time μ (x) repair rate for repaired state figure 2. transition diagram ram and tyagi/oper. res. eng. sci. theor. appl. 4 (2) (2021) 124-139 128 3. governing equations the following set of equations have been derived for the proposed communication system by using markov process. original state 21 1 2 1 2 0 80 ( ) ( , ) i i c c p t μp x t dx t  =   + + + + =    (1) degraded states ( )1 2 1 2 1 1 2 0( ) ( )c c p t c c p t t   +  +  +  +  =  +    (2) 1 1 2 2 1 ( ) ( )c p t p t t   +  +  =    (3) 2 2 3 1 1 ( ) ( )c p t p t t   +  +  =    (4) 1 2 1 4 2 0 ( ) ( )c c p t p t t   +  +  +  =    (5) 1 1 5 2 4 ( ) ( )c p t c p t t   +  +  =    (6) 1 2 2 6 1 0 ( ) ( )c c p t p t t   +  +  +  =    (7) 2 2 7 1 6 ( ) ( )c p t c p t t   +  +  =    (8) failed states ( , ) 0, 8, 9,...20, 21 i μ p x t i t x    + + = =    (9) boundary conditions 8 2 1 (0, ) ( )p t c p t=  (10) 9 1 1 (0, ) ( )p t c p t=  (11) 10 1 2 (0, ) ( )p t p t=  (12) 11 1 2 (0, ) ( )p t c p t=  (13) 12 2 3 (0, ) ( )p t p t=  (14) 13 2 3 (0, ) ( )p t c p t=  (15) 14 1 4 (0, ) ( )p t p t=  (16) reliability characteristics of railway communication system subject to switch failure 129 15 1 4 (0, ) ( )p t c p t=  (17) 16 1 5 (0, ) ( )p t p t=  (18) 17 1 5 (0, ) ( )p t c p t=  (19) 18 2 6 (0, ) ( )p t p t=  (20) 19 2 6 (0, ) ( )p t c p t=  (21) 20 2 7 (0, ) ( )p t p t=  (22) 21 2 7 (0, ) ( )p t c p t=  (23) initial condition 0 (0) 1 (0) 0, 1, 2,..., 21 i p p i = = = (24) after taking the laplace transform from equations (1) to (23), one can get the following set of equations:   21 1 2 1 2 0 80 ( ) ( , ) i i s c c p s μp x s dx  = + + + + =  (25)   ( )1 2 1 2 1 1 2 0( ) ( )s c c p s c c p s+ + + + =  + (26)  1 1 2 2 1( ) ( )s c p s p s+ + =  (27)  2 2 3 1 1( ) ( )s c p s p s+ + =  (28)  1 2 1 4 2 0( ) ( )s c c p s p s+ + + =  (29)  1 1 5 2 4( ) ( )s c p s c p s+ + =  (30)  1 2 2 6 1 0( ) ( )s c c p s p s+ + + =  (31)  2 2 7 1 6( ) ( )s c p s c p s+ + =  (32) ( , ) 0, 8, 9,...20, 21 i s μ p x s i x   + + = =   (33) 8 2 1 (0, ) ( )p s c p s=  (34) 9 1 1 (0, ) ( )p s c p s=  (35) 10 1 2 (0, ) ( )p s p s=  (36) 11 1 2 (0, ) ( )p s c p s=  (37) 12 2 3 (0, ) ( )p s p s=  (38) ram and tyagi/oper. res. eng. sci. theor. appl. 4 (2) (2021) 124-139 130 13 2 3 (0, ) ( )p s c p s=  (39) 14 1 4 (0, ) ( )p s p s=  (40) 15 1 4 (0, ) ( )p s c p s=  (41) 16 1 5 (0, ) ( )p s p s=  (42) 17 1 5 (0, ) ( )p s c p s=  (43) 18 2 6 (0, ) ( )p s p s=  (44) 19 2 6 (0, ) ( )p s c p s=  (45) 20 2 7 (0, ) ( )p s p s=  (46) 21 2 7 (0, ) ( )p s c p s=  (47) now, solving equation (25) (33) with the help of (34) (47), the following state transition probabilities are obtained: 0 1 2 1 2 1 ( ) ( ) ( ) ( ) ( ) ( ) p s s c c s s u s v s w s =  + + + + − + +  (48) 1 2 1 0 1 2 1 2 ( ) ( ) ( ) c c p s p s s c c  + = + + + + (49) 2 1 2 2 0 1 1 1 2 1 2 ( ) ( ) ( ) ( )( ) c c p s p s s c s c c   + = + + + + + + (50) 1 1 2 3 0 2 2 1 2 1 2 ( ) ( ) ( ) ( )( ) c c p s p s s c s c c   + = + + + + + + (51) 2 4 0 1 2 1 ( ) ( )p s p s s c c  = + + + (52) 2 2 5 0 1 1 1 2 1 ( ) ( ) ( )( ) c p s p s s c s c c   = + + + + + (53) 1 6 0 1 2 2 ( ) ( )p s p s s c c  = + + + (54) 1 1 7 0 2 2 1 2 2 ( ) ( ) ( )( ) c p s p s s c s c c   = + + + + + (55) 2 1 2 8 0 1 2 1 2 ( ) 1 ( ) ( ) ( ) ( ) c c c s s p s p s s c c s    + − =   + + + +   (56) 1 1 2 9 0 1 2 1 2 ( ) 1 ( ) ( ) ( ) ( ) c c c s s p s p s s c c s    + − =   + + + +   (57) reliability characteristics of railway communication system subject to switch failure 131 1 2 1 2 10 0 1 1 1 2 1 2 ( ) 1 ( ) ( ) ( ) ( )( ) c c s s p s p s s c s c c s     + − =   + + + + + +   (58) 1 2 1 2 11 0 1 1 1 2 1 2 ( ) 1 ( ) ( ) ( ) ( )( ) c c c s s p s p s s c s c c s     + − =   + + + + + +   (59) 1 2 1 2 12 0 2 2 1 2 1 2 ( ) 1 ( ) ( ) ( ) ( )( ) c c s s p s p s s c s c c s     + − =   + + + + + +   (60) 2 1 1 2 13 0 2 2 1 2 1 2 ( ) 1 ( ) ( ) ( ) ( )( ) c c c s s p s p s s c s c c s     + − =   + + + + + +   (61) 1 2 14 0 1 2 1 1 ( ) ( ) ( ) ( ) s s p s p s s c c s    − =   + + +   (62) 1 2 15 0 1 2 1 1 ( ) ( ) ( ) ( ) s s p s p s s c c s    − =   + + +   (63) 2 1 2 16 0 1 1 1 2 1 1 ( ) ( ) ( ) ( )( ) c s s p s p s s c s c c s     − =   + + + + +   (64) 2 1 2 17 0 1 1 1 2 1 1 ( ) ( ) ( ) ( )( ) c c s s p s p s s c s c c s     − =   + + + + +   (65) 1 2 18 0 1 1 1 2 1 1 ( ) ( ) ( ) ( )( ) s s p s p s s c s c c s    − =   + + + + +   (66) 1 2 19 0 1 2 2 1 ( ) ( ) ( ) ( ) c s s p s p s s c c s    − =   + + +   (67) 1 1 2 20 0 2 2 1 2 2 1 ( ) ( ) ( ) ( )( ) c s s p s p s s c s c c s     − =   + + + + +   (68) 2 1 1 21 0 2 2 1 2 2 1 ( ) ( ) ( ) ( )( ) c c s s p s p s s c s c c s     − =   + + + + +   (69) the probabilities of up and down states are as follows: 1 2 2 1 2 1 1 2 2 1 1 2 2 1 1 2 0 2 1 1 1 1 2 1 2 2 2 1 1 ( ) ( ) ( ) ( ) ( ) ( ) 1 1 ( ) ( ) ( ) up c c s c c s c s c s c c p s p s c c s c s c c s c    +    + + + +   + + + + + + + + + + +   =          + + +    + + + + + + +      (70) ram and tyagi/oper. res. eng. sci. theor. appl. 4 (2) (2021) 124-139 132 1 2 1 2 1 2 1 1 1 11 2 1 2 2 11 1 2 2 2 2 2 2 0 2 2 1 1 2 1 1 1 1 2 1 1 1 1 1 ( ) ( ) ( ) ( ) ( ) 1 ( ) ( ) ( ) ( ) ( ) ( ) ( down c c c s c s cc c cs c c s c s c s s p s p s c c c cs s c c s c s c       +  + + + +  +  +  +  +    +     +  +  +  +   +  +  +  +  +    −  =        +  + + +   +  +  +  +  +  +  +    1 1 1 2 2 2 2 1 2 2 2 2 2 ) ( ) ( ) c c c c s c c s c s c                            +  + +  +  +  +  +  +  +  +        (71) where, 1 2 1 2 1 2 1 1 1 11 2 1 2 2 11 2 1 2 2 2 2 2 ( ) ( )( ) ( ) ( ) ( ) ( ) c c c s c s cc c u s cs c c s c s c       +  + +  +  +  +  +  +    =      +  +  +  +   + +  +  +  +  +   2 1 2 1 2 1 1 1 2 1 1 1 1 1 ( ) ( ) ( ) ( ) c c c v s c s c c s c s c       =  + + +  + + + + + + +  1 2 1 1 2 2 2 1 2 2 2 2 2 2 ( ) ( ) ( ) ( ) c c c w s c s c c s c s c       =  + + +  + + + + + + +  4. numerical calculations for computing the reliability measures of the proposed railway communication system, following failure and repair rates will be assumed as given by table 2. table 2. assumed failure and repair rate of proposed railway communication system. failure and repair rate/per hour λ1 = 0.009 λc1 = 0.06 λ2 = 0.007 λc2 = 0.03 μ = 1 4.1. availability the availability of the proposed system is computed by substituted the values of failure and repair rates as given in table 2, in equation (70), after putting these values, availability of the proposed rcs in terms of time t is given as follows: ( 0.9887 ) ( 0.2075 ) ( 0.0779 ) ( 0.0439 ) ( ) 0.01158 0.05608 0.00085 0.00277 0.95911 t t t t a t = e e e e − − − − + − − + (72) now after varying time from 0 to 50 with the interval of 5 units of time, one can get the numerical values of availability of the proposed system which are demonstrates by table 3. reliability characteristics of railway communication system subject to switch failure 133 table 3. availability of the proposed system time (t) availability 0 1.00000 5 0.97611 10 0.96398 15 0.95991 20 0.95867 25 0.95838 30 0.95829 35 0.95815 40 0.95811 45 0.95808 50 0.95801 0 10 20 30 40 50 0.95 0.96 0.97 0.98 0.99 1.00 1.01 a v a il a b il it y time (t) figure 3. availability of the proposed system as time vary from 0 to 50 units 4.2. reliability for the proposed system, reliability is calculated by substitute the values of failures as given in table 2 and repair rate equal to zero in equation (70), after substitute these failures and repairs values, the reliability function in terms of t is given by ( 0.0370 ) ( 0.6900 ) ( 0.1060 ) ( ) 0.30057 0.64938 (0.06123 0.05005) t t t r t e e t e − − − = + + + (73) now varying time t from 0 to 10 unit with an interval of 1 unit, one can analyzed the reliability behavior of proposed system as tabulated in table 4 and shown in figure 4. ram and tyagi/oper. res. eng. sci. theor. appl. 4 (2) (2021) 124-139 134 table 4. reliability of the system time (t) reliability 0 1.00000 1 0.91938 2 0.76281 3 0.60074 4 0.45978 5 0.34658 6 0.25947 7 0.19404 8 0.14553 9 0.10976 10 0.08341 0 2 4 6 8 10 0.0 0.2 0.4 0.6 0.8 1.0 r e li a b il it y time (t) figure 4. reliability of the system w.r.t. time 4.3. mean time to system failure the mean time to failure is calculated by taking μ = 0 and limit 0→s (tyagi et al., 2021) in equation (70). so, the mttf of the proposed system in terms of failure rate is given by equation (74). 1 2 2 1 2 1 1 2 2 1 1 2 2 1 1 2 1 2 1 2 2 1 1 1 1 2 1 2 2 2 1 1 ( ) ( ) ( ) ( )1 ( ) 1 1 ( ) ( ) ( ) c c c c c c c c mttf c c c c c c c c    +    + + + +    + + +  +  +  + +   =   + + +        + + +     +  + +  +      (74) now setting all failure rates values as given by table 2 and vary each failure rate one by one from 0.001 to 0.04 in equation (74) to get the mttf of the proposed system with respect to variation in the failure rates. the variation in mttf can be reliability characteristics of railway communication system subject to switch failure 135 seen from table 5 and corresponding figure 5 shows the behaviour of mttf regarding variation in failure rates. table 5. mttf of the system variation in failure rates mttf λc1 λc2 λ1 λ2 0.001 68.6161 51.82156 22.35057 24.79149 0.003 62.38204 45.53850 21.65165 24.28984 0.005 57.63895 41.19976 21.29690 23.84834 0.007 53.85080 37.98025 21.12371 23.45672 0.009 50.71749 35.46688 20.45672 23.10686 0.02 39.53540 27.40036 19.61863 21.69336 0.04 29.23630 20.75466 19.01606 20.24722 0.06 23.45672 17.10419 17.34855 19.39883 0.08 19.65024 14.65523 17.21551 18.81630 0.1 16.92906 12.85991 16.70574 18.37954 0.02 0.04 0.06 0.08 0.10 10 20 30 40 50 60 70  c1  c2  1  2 m t t f variation in failure rates figure 5. mttf with respect to variation in failure rates 4.4. sensitivity of reliability in reliability sensitivity study, the effect of failure rates on reliability has been studied. the reliability function is the dependent variable. it’s dependent because it depends on failures rates. those failure rates are the independent variable. sensitivity of reliability is obtained by partial differentiation of reliability function with respect to all the failure rates. now putting all failure rates as given by table 2 and repair rate equal to zero in these derivatives, one can get the table 6 and corresponding figure 6. ram and tyagi/oper. res. eng. sci. theor. appl. 4 (2) (2021) 124-139 136 table 6. sensitivity of reliability of the proposed communication system time (t) sensitivity of reliability 1 ( )r t c   2 ( )r t c   1 ( )r t  2 ( )r t  0 0 0 0 0 1 -0.08468 -0.08575 -0.01886 -0.03526 2 -0.30679 -0.31133 -0.06439 -0.12756 3 -0.62535 -0.636 -0.123 -0.25976 4 -1.00731 -1.02689 -0.18454 -0.41824 5 -1.42634 -1.45771 -0.24159 -0.59228 6 -1.86164 -1.90766 -0.28897 -0.77354 7 -2.29709 -2.36052 -0.32325 -0.95566 8 -2.72038 -2.80387 -0.34243 -1.13384 9 -3.12234 -3.22838 -0.34555 -1.3046 10 -3.49642 -3.62729 -0.33251 -1.4655 0 2 4 6 8 10 -4.0 -3.2 -2.4 -1.6 -0.8 0.0 s e n si ti v it y o f re li a b il it y time (t)  c1  c2  1  2 figure 6. sensitivity of reliability with respect to time 5. result discussion in this paper, different reliability characteristics have been calculated and analysed for the railway communication system. some results related to these reliability characteristics are given below: (i) from table 3 and figure 3, one can see the behaviour of the availability of the proposed rcs. availability of the rcs decreases with increases in the value of time t. at initially, i.e., time t = 0, availability is 1 and after 50 units of time, reliability characteristics of railway communication system subject to switch failure 137 system availability is 0.9580. from figure 3, one can see that the availability graph is constant for the time period 35 units to 50 units. (ii) table 4 and corresponding figure 4 give an idea about the behaviour of the reliability of proposed railway communication system regarding time t for various system failure rates. from table 4 and figure 4, it is easily seen that the reliability of the proposed system decreases rapidly as increment in time t. at initially, reliability is one and after 10 units of time, reliability is 0.08341. (iii) from table 5, it is easily seen that the mttf of the proposed system continuously decreases as all the failure rates λ1, λc1, λ2, λc2 increases. with respect to all stations failure rates mttf is decreases in a uniform manner but with respect to control centre failure rates it decreases rapidly. figure 5 demonstrates that the mttf is high with variation in the failure rate of the first control centre and lowest regarding failure rates of path 1 stations which means failure rate of all stations of path 1 has more frequent downtime and disruption as compare to other failure rates. (iv) further, from table 6 and figure 6, one can see the behaviour of the failure rates on system reliability. the reliability of the rcs is more influenced by the variation in the second control centre failure rate which means second control centre failure rate causes the stronger change in reliability of the proposed system as time increases. 6. conclusion the present study discussed the performance of a railway communication system regarding sits component failure, and a procedure to evaluate the system’s reliability measures. in order to numerically analyzed the performance of the composed system, markov process has been applied. in the proposed railway communication system, the reliability is more influenced by failure rate of second control centre, thus the system reliability can be increased by a slight improvement in the failure rate of second control centre. in future work one can extend this investigation by using link-lk between switches so that communication is available even if there are multiple failures. references aggarwal, k. k., gupta, j., & misra, k. 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(2015). control and data signaling decoupled architecture for railway wireless networks. ieee wireless communications, 22(1), 103-111. zhang, b., zhong, z., he, r., dahman, g., ding, j., lin, s., ai, b., & yang, m. (2018). measurement-based markov modeling for multi-link channels in railway communication systems. ieee transactions on intelligent transportation systems, 20(3), 985-999. zimmermann, a. (2013, december). reliability modelling and evaluation of dynamic systems with stochastic petri nets (tutorial). in proceedings of the 7th international conference on performance evaluation methodologies and tools (pp. 324-327). https://doi.org/10.4108/icst.valuetools.2013.254370. zimmermann, a., & hommel, g. (2003, april). a train control system case study in model-based real time system design. in proceedings international parallel and distributed processing symposium (pp. 8-pp). ieee. france. © 2021 by the authors. submitted for possible open access publication under the terms and conditions of the creative commons attribution (cc by) license (http://creativecommons.org/licenses/by/4.0/). https://doi.org/10.4108/icst.valuetools.2013.254370 reliability characteristics of railway communication system subject to switch failure mangey ram 1, vaishali tyagi2* 1. introduction 2. system modelling 3. governing equations 4. numerical calculations 4.1. availability 4.2. reliability 4.3. mean time to system failure 4.4. sensitivity of reliability 5. result discussion 6. conclusion references plane thermoelastic waves in infinite half-space caused operational research in engineering sciences: theory and applications vol. 1, issue 1, 2018, pp. 91-107 issn: 2620-1607 eissn: 2620-1747 doi: https://doi.org/10.31181/oresta19012010191f e-mail address: hfazl@du.ac.ir operations and inspection cost minimization for a reverse supply chain hamed fazlollahtabar department of industrial engineering, school of engineering, damghan university, damghan, iran received: 23 october 2018 accepted: 03 december 2018 published: 19 december 2018 original scientific paper abstract: reverse supply chain is a process dealing with the backward flows of used/damaged products or materials. reverse supply chain includes activities such as collection, inspection, reprocess, disposal and redistribution. a well-organized reverse supply chain can provide important advantages such as economic and environmental ones. in this study, we propose a configuration in which quality assurance is a substantial operation to be fulfilled in the reverse chain so that to minimize the total costs of the reverse supply chain. a mathematical model is formulated for product return in reverse supply chain considering quality assurance. we consider a multilayer, multi-product for the model. control charts with exponentially weighted moving average (ewma) statistics (mean and variance) are used to jointly monitor the mean and variance of a process. an ewma cost minimization model is presented to design the joint control scheme based on performance criteria. the main objective of the paper is minimizing the total costs of reverse supply chain with respect to inspection. key words: reverse supply chain; quality inspection; mathematical model. 1. introduction and related works with the increase in environmental consciousness, reverse supply chain and reverse supply chain management have received significant attention from both business and academic research during the past few years. according to the american reverse logistics executive council, reverse logistics is defined as rogers and tibben-lembke (1998): “the process of planning, implementing, and controlling the efficient, cost effective flow of raw materials, in process inventory, finished goods and related information from the point of consumption to the point of origin for the purpose of recapturing value or proper disposal.” a reverse logistics system comprises a series of activities, which form a continuous process to treat return products until they are properly recovered or disposed of. these activities include collection, cleaning, disassembly, test and sorting, storage, transport, and recovery operations. the latter can also be represented as one or a combination of several fazlollahtabar/oper. res. eng. sci. theor. appl. 1 (1) (2018) 91-107 92 main recovery options, like reuse, repair, refurbishing, remanufacturing, cannibalization and recycling (dekker and van der laan, 1999; beaulieu et al., 1999; thierry et al., 1993). also, these options are to be reclassified into three broad categories such as reuse, recycling, and remanufacturing. in reuse, the returned product can be used more than once in the same form after cleaning or reprocessing. on the other hand, recycling denotes material recovery without conserving any product structure. finally, remanufacturing is an industrial process in which wornout products are restored to like-new condition. the design/redesign of the supply chain with return flows has become a challenge for many companies. this is an important area of research as it helps lowering costs, while improving coordination and customer service (guide et al., 2003). for instance, nike, the shoe manufacturer encourages consumers to bring their used shoes to the store where they had purchased them. these shoes are then shipped back to nike’s plants and made in to basketball courts and running tracks. by donating the material to the basketball courts and donating funds for building and maintaining these courts, nike has enhanced the value of its brand rogers and tibben-lembke (1998).furthermore, according to other advocators’ opinions, effective reverse supply chain activities can enhance relationships with consumers and supply chain partners, can be a source of significant cost savings, and can even function as a profit center (stock et al., 2003). for the last decade, increasing concerns over environmental degradation and increased opportunities for cost savings or revenues from returned products prompted some researchers to formulate more effective reverse logistics strategies. these researchers including salema et al. (2007) have proposed a milp model to analyze the problem of closed loop supply chains. they consider multi-product returns with uncertain behavior but limit their consideration of demand for returned products to factories and not to secondary markets or spare markets. thus a supplier network which may be required to remanufacture a new product to meet the market demand is not considered. also, this model is not suitable for modular products. del castillo and cochran (1996) presented a pair of linear programs and a simulation model to optimally configure the reverse logistics network involving the return of reusable containers in such a way that the number of reusable containers was maximized. however, they did not take into account transportation issues related to reverse logistics. patti et al. (2008) have formulated a mixed integer goal programming model for analyzing paper recycling network. the model assumes five echelons and studies the inter-relationship between cost reduction, product quality improvement through increased segregation at the source, and environmental benefits through waste paper recovery. the model also assists in determining the facility location, and route and flow of different varieties of recyclable wastes. aras et al. (2008) developed a non-linear model and tabu search solution approach for determining the locations of collection centers and the optimal purchase price of used products in a simple profit maximizing reverse logistics network. initiating product recovery network design efforts, thierry (1997) introduced a linear program to design product distribution and product recovery networks involving the collection of used copying machines. however, his model did not address the location issue of where the product recovery (resale of products after remanufacturing and refurbishment) process should be installed and at what capacity. krikke (1998) proposed a network graph and a mixed integer program to operations and inspection cost minimization for a reverse supply chain 93 optimize the degree of disassembly and evaluate product recovery options in collecting used copying machines and redistributing them after refurbishment, while determining the location and capacity of remanufacturing, central stocking, and disposal facilities. similarly, krikke et al. (1999) developed a mixed integer program to determine the locations of shredding and melting facilities for the recovery and disposal of used automobiles, while determining the amount of product flows in the reverse logistics network. jayaraman et al. (1999) presented a mixed integer program to determine the optimal number and locations of remanufacturing facilities for electronic equipment. jayaraman et al. (2003) extended their prior work to solve the two-level hierarchical location problem involving the reverse logistics operations of hazardous products. they also developed heuristic concentration procedures combined with heuristic expansion components to handle relatively large problems with up to 40 collection sites and 30 refurbishment sites. despite their success in solving large-sized problems, their model and solution procedures are still confined to a single period problem and are not designed to deal with the possibility of making trade-offs between freight rate discounts and inventory cost savings resulting from consolidation of returned products. lee and dong (2008) developed an milp model for integrated logistics network design for end-of-lease computer products. they consider a simple network with a single production center and a given number of hybrid distribution-collection facilities to be opened which they solve using tabu search. however, all of researches are found for some cost in reverse logistics that contain and define some centers (govindan, and nicoleta popiuc, 2014; cardoso et al., 2013; chuang et al., 2014; huang et al., 2013; soleimani, and govindan, 2014). reformulation of supply chain network from nonlinear to a similar piecewise linear programming model was investigated by diabat and theodorou (2015), diabat (2016), and al-salem et al. (2016). also, optimization approaches employed in the literature for closed loop or green supply chains included both certain and uncertain namely, stochastic programming, robust optimization, genetic algorithm, hybrid particle swarm-genetic algorithm and other metaheuristics (diabat and al-salem, 2015; diabat and deskoores, 2016; alshamsi and diabat, 2017; hiassat et al. 2017; zohal and soleimani, 2016; wang et al. 2016). our study focuses on a general framework and propose total cost minimization model in reverse supply chain considering quality assurance. according to the importance of reverse supply chain for saving cost and improvement of customer loyalty and futures sales we design a framework and a mathematical model for costs in a multilayer multi-product in reverse supply chain system. the main contributions of the paper are, including ewma control chart for inspection process of returned products, making use of process capability index for quality assurance purpose, and cost optimization for integrated operations and inspections model for a multi-layer and multi-product reverse supply chain. the main advantage of the proposed model is to include quality control in the cost minimization decision, i.e., a tradeoff between cost minimization and quality maximization. thus, managers can keep cost and quality at the same time. this decision is challenging in real production system. another advantage is the proposed reverse supply chain in which inspection of return products are fulfilled in a comprehensive control mechanism. this paper is organized as follows. in the next section, quality inspection and the proposed ewma control chart for inspection process are explained. in section 3, a fazlollahtabar/oper. res. eng. sci. theor. appl. 1 (1) (2018) 91-107 94 general framework and problem definition for reverse supply chain integrated with the inspection cost monitoring are proposed. section 4 proposes the mathematical model of the reverse supply chain. section 5 gives the numerical results and the required analysis. finally conclusions are addressed in the last section. 2. quality inspection statistical process control (spc) is an effective method of monitoring a process through the use of control charts. control charts enable the use of objective criteria for distinguishing background variation from events of significance based on statistical techniques. much of its power lies in the ability to monitor both process center and its variation about that center. by collecting data from samples at various points within the process, variations in the process that may affect the quality of the end product or service can be detected and corrected, thus reducing waste as well as the likelihood that problems will be passed on to the customer. with its emphasis on early detection and prevention of problems, spc has a distinct advantage over quality methods, such as inspection, that apply resources to detecting and correcting problems in the end product or service. 2.1. ewma control charts we assume that the observations for the process variable x are independent and normally distributed. when the process is in control, the mean and variance of x is μ0 and 2 0  , respectively. at any sampling instant t, the sample mean and variance are computed from 1 / n t it i x nx   (1) and 2 2 1 ( ) / ( 1) n tt it i s x x n     (2) where tx and 2 t s are the sample mean and variance at time t, and n is the fixed sample size, 2n  . using tx and 2 t s , the chart statistics are calculated as 1 (1 )tt m m tz x z     (3)  2 20 1max ln( ), ln( ) (1 )t v t v ty s y      (4) 0 , 1 m v    (5) 0 0 z  (6) operations and inspection cost minimization for a reverse supply chain 95 2 0 0 ln( )y  (7) where m  and v  are the smoothing constants associated with the ewma chart for mean (ewma-m) and variance (ewma-v), respectively. the statistic t z is used in the ewma-m chart, and t y is associated with the ewma-v chart. 2.2. process monitoring by ewma when ewma schemes are used for process monitoring, not only the current observations of x but also the observations from previous samples are taken into account. in the computation of the test statistic, more recent samples are given a larger weight than the ones taken earlier. the user can increase the weight given to the last sample by increasing the value of the smoothing constant. lucas and saccucci (1990) described the properties of the ewma-m chart in detail. we use the lower and upper control limits (lclm and uclm) computed based on the asymptotic in-control standard deviation of the ewma chart statistic z such that 0 m m z lcl l   (8) 0 m m z ucl l   (9) where 0.5 0 ( / (2 ) ) z m m n     , and m l is the control limit parameter. thus, whenever t z is outside the interval (lclm and uclm), the process is considered to be out of control and a search for assignable cause is conducted. due to the natural variation of the process, out-of-control signals may also occur while the process is in control. however, when there is a shift in process mean and/or variance, the chart will generate an out-of-control signal much more quickly. to monitor the process dispersion, a number of authors have previously studied the control charts based on ewma of lns2 (crowder and hamilton, 1992; gan, 1995; acosta-mejia et al., 1999). the particular dispersion chart we adopt in this study is referred to as ewma-v which has the lower and upper control limits as follows: 2 0 2 0 ln( ) ln( ) v v v y lcl ucl l       (10) where 2 / ( 1) / 2 / (2 )y v vn     , /  (0) is the trigamma function, and v l is the control limit parameter. the trigamma function is the second logarithmic derivative of the gamma function (0) , i.e., / 2 2( ) ln ( ) /u d u du   , u>0 . we consider an upper one-sided ewma-v chart which is well-suited for detecting the increases in the process standard deviation. an increase in the process standard deviation would fazlollahtabar/oper. res. eng. sci. theor. appl. 1 (1) (2018) 91-107 96 either reflect an undesirable special cause or the impact of an undesirable process change (either purposeful or unpurposeful); a decrease in process variation would indicate the effect of a process improvement. ewma-v chart yields an out-of-control signal when t y exceeds uclv. the statistical properties of the combined ewmam/ewma-v control scheme have been explored in morais and pacheco (2000). to illustrate the smoothing effect of exponential weighting, we plot the values of and zt for 40 samples generated via simulation in figure 1. the observations constituting the first 20 samples are generated from the in-control process distribution with mean=0, variance=1. the samples 21 through 40 are based on the out-of-control process distribution with mean=0.5, variance=1.5; we also set n=4, in this simulation experiment. the values of  2ln ts and yt (with ) obtained from the same simulation run are displayed in figure 2. the lower and upper control limits shown in these charts are based on lm= lv= 2.5. figures 1 and 2 show that the time series of exponentially weighted sample statistics (zt and yt) exhibit less variability than the original series ( and  2ln ts ) from which they are derived. figure 1. ewma control chart for mean – plot of and test statistic zt operations and inspection cost minimization for a reverse supply chain 97 figure 2. ewma control chart for variance – plot of  2ln ts and test statistic yt 3. problem definition the reverse supply chain under study is multi-layer and multi-product. in the designed model, the returned products after collecting and inspecting are divided into two groups of disassembling and not disassembling products. some of the products that don’t need to be disassembled will be transmitted to the inspecting center right after collecting centers. then, considering to the variety of products and the request of manufacturing centers they will be sent directly to be remanufactured. in the remanufacturing process, according to the production center's demand, the parts which can be used again, after inspecting center will be sent to the remanufacturing center and after compounding with the other parts will be changed into new products and can return to the distribution chain to assure the quality of the product.. the quality assurance is based on the ewma control chart for the product in inspection centers. the configuration of the problem is shown in figure 3. supplier manufacturer customer quality inspection return product measuring cp criterion figure 3. framework for reverse supply chain fazlollahtabar/oper. res. eng. sci. theor. appl. 1 (1) (2018) 91-107 98 in this paper the reverse supply chain model has been considered for returned products with the purpose of minimizing the reverse supply chain costs considering the quality inspection process. the main assumptions included in the study are:  the quantity of inspection and manufacturing are determined.  some products will transport straightly from customers to the inspection centers. and the required indices are as follows: k index of inspection centers f index of manufacturing centers m index of products for the ewma based inspection process, a comprehensive cost function is developed. 3.1. cost of monitoring in ewma we denote the time between two consecutive samples (sampling interval) by fm h . it is assumed that the in-control time for the process is distributed exponentially with mean . we allow the possibility that both the process mean and variance may change when an assignable cause occurs. when the process is out of control, the mean of x becomes and the standard deviation of x shifts to . using the lorenzen and vance (1986) framework, the expected cost per unit time (hour), c, associated with the control scheme consisting of ewma-m and ewma-v charts is in lorenzen and vance):     / ( ) 0 1 1 1 1 2 2 / 0 / 1 / (1 ) / ( ) 1 0 1 1 2 ( ) / 1 / ( ) 1 1 1 2 2 / 1 / c c c n e h arl t t m km m m m m fm m mf m mf m s f arl rmc m m m mf s arl n e h arl t t km mf m m m m m fm m mf mf a b n h n e h arl t t m m m mf km m m m fm m mf m mf m k                                                       (1 ) / ( )1 0 1 1 2s arl n e h arl t tm mf m m m m m fm m mf mf        (11) the effective parameters in the proposed inspection cost function are listed below: c0 cost per hour due to nonconformities produced while the process is in control c1 cost per hour due to nonconformities produced while the process is out of control  expected time between the occurrence of the assignable cause and the time of the last sample taken before the assignable cause = [1 (1 ) exp( )] / [ (1 exp( ))]h h h        e time to sample and chart one item arl0 average run length while in control arl1 average run length while out of control t1 expected time to discover the assignable cause operations and inspection cost minimization for a reverse supply chain 99 t2 expected time to repair the process 1  =1 if production continues during inspection, =0 if production ceases during inspection 2  =1 if production continues during repair, =0 if production ceases during repair s expected number of samples taken while in control = exp( )] / [1 exp( )]h h    the traditional approach to the economic design of control charts involves calculation of the expected cost per hour by dividing the expected cost per cycle by the expected cycle length. each cycle is made up of two parts: (a) an in-control interval, and (b) an out-of control interval following that. the cost function is derived by dividing the sum of costs incurred during the in-control and out-of-control segments by the expected cycle length. the expected lengths of the in-control and out-of-control intervals, e(iin) and e(iout), are 1 0 0 ( ) (1/ ) (1 ) / in e i st arl    (12) 1 1 2 ( ) ( ) out e i ne h arl t t      (13) the in-control interval is composed of the expected time until failure and the expected time spent for investigating false alarms. the expected length of the incontrol interval depends on whether the production continues during inspection or not. the out-of-control interval includes the time from the occurrence of the assignable cause to the next sampling instant ( )fm mh  , the time until an out-ofcontrol signal 1( 1)fmh a rl  , the time to collect and chart a sample (ne), the time to discover the assignable cause (t1), and the time to repair the process (t2). after an assignable cause is found and corrective action is taken, the process mean and variance are restored to their in-control values 0  and 2 0  , and the cycle restarts. the decision variables are , , , , ,fm m v m vn h l l   . as defined previously, average run length is the expected number of samples taken before an out of control signal is observed. to minimize false alarms and react swiftly to out-of-control conditions, large values for arl0 and small values for arl1 are desirable. arl0 and arl1 depend on all decision variables except h. 4. mathematical formulation we want to demonstrate a model in reverse supply chain so that to minimize the chain costs. we aim to minimize total operations and inspection costs for the proposed reverse supply chain. the required parameters are reviewed as shown in table 1: fazlollahtabar/oper. res. eng. sci. theor. appl. 1 (1) (2018) 91-107 100 table 1. the parameters of the mathematical model km u capacity of inspection center k for product m fm h capacity of manufacturing center f for product m fm dm manufacturing center's demand f for product m kfm cspm unit cost of transportation from inspection center k into the manufacturing center f for product m km focp fixed opening cost for inspection centers k and product m fm rmc unit cost of remanufacturing in manufacturing center f for product m 0m c cost per hour due to nonconformities produced while the process is in control for product m 1m c cost per hour due to nonconformities produced while the process is out of control for product m mk f cost per false alarm for inspection centers k and product m mk a fixed cost per sample for inspection centers k and product m mk b cost per unit sampled for inspection centers k and product m m s expected number of samples taken while in control for product m m  expected time between the occurrence of the assignable cause and the time of the last sample taken before the assignable cause for product m m n number of sample for product m m e time to sample and chart one item for product m 0m a rl average run length while in control for product m 1m a rl average run length while out of control for product m 1mf t expected time to discover the assignable cause for manufacturing center f and product m 2mf t expected time to repair the process for manufacturing center f and product m 1mf  1 if production continues during inspection, and 0 if production ceases during inspection for manufacturing center f and product m 2mf  1 if production continues during repair, and 0 if production ceases during repair for manufacturing center f and product m me  smoothing constants associated with the ewma chart for mean v  smoothing constants associated with the ewma chart for variance and finally the decision variables are listed below: qkfm amount shipped from inspection center into the manufacturing center f for product m βkm 1, if inspection center k is open for product m and 0, otherwise operations and inspection cost minimization for a reverse supply chain 101 µfm the product m flow amount in manufacturing center f θkm the product m flow amount in inspection center k cpkp process capability for product m in inspection center k the formulation of the mathematical model is given below: 1 1 1 1 1 1 1 k f m k m f m k f m k m f m min z csrm q focp rmc c kfm kfm km km fm fm                (14) by attention to the definition of indices, parameters and decision variables; the objective function is defined to be minimizing the costs of transportation and inspection of products, the fixed opening cost of centers and operations costs on products in reverse supply chain. constraints: 1 . . , f kfm km km km f q u cp k m    (15) this constraint is stating that the amount of shipping products from any inspection centers (if it is opened) into the manufacturing centers should be equal or smaller than the capacity of the same inspection centers for each product considering product process capability index. . . , km km km km u cp k m   (16) this constraint is stating that the amount of a product which is in the inspection center should be equal or smaller than the capacity of the same inspection center with respect to the quality assurance measure. , fm fm h f m   (17) this constraint states that the amount of product in each manufacturing center should be equal or smaller than the capacity of the same manufacturing center.    k k fmkfm mfdmq 1 , (18) mfdm fmfm , (19) these two constraints guarantee the demand fulfillment in manufacturing and inspection centers for products. (7) and (8) are the quality assurance inequalities to confine the model to satisfy the products’ quality. (9) and (10) enforce the binary and nonnegativity restrictions on the corresponding decision variables. ( ) ( ) , 6 in out km km e i e i cp k m     (20) fazlollahtabar/oper. res. eng. sci. theor. appl. 1 (1) (2018) 91-107 102 if the upper and lower specification limits of the process are usl and lsl, the estimated variability of the process (expressed as a standard deviation) is , then commonly accepted process capability index for product m in inspection center k is cpkm. estimates what the process is capable of producing if the process mean were to be centered between the specification limits. assumes process output is approximately normally distributed.     / ( ) 0 1 1 1 1 2 2 / 0 / 1 / (1 ) / ( ) 1 0 1 1 2 ( ) / 1 / ( ) 1 1 1 2 2 / 1 / c c c n e h arl t t m km m m m m fm m mf m mf m s f arl rmc m m m mf s arl n e h arl t t km mf m m m m m fm m mf mf a b n h n e h arl t t m m m mf km m m m fm m mf m mf m k                                                       (1 ) / ( )1 0 1 1 2s arl n e h arl t tm mf m m m m m fm m mf mf        (21) this function computes the inspection cost. , , , 0 , , kfm fm km km q cp k f m    (22) mk km ,}1,0{  (23) in these relations, the sign and type of decision variables are emphasized. 5. numerical example in this section, we solve an example to show the validity of the proposed mathematical model. the multi-layer and multi-product supply chain considered here has 3 inspection centers, 3 manufacturing centers, and 4 products. here, the other inputs are: 299 211 111 485 350 375 425 270 460 289 360 115 km u           412 965 592 978 520 666 632 711 483 786 842 822 fm h           125 235 482 116 455 142 471 192 260 368 269 453 fm dm           11 44 27 18 38 25 22 32 49 kfm cspm           45 85 44 96 46 75 61 93 58 89 69 81 km focp           12 44 28 42 18 48 33 15 29 50 39 27 fm rmc           12 18 24 14 13 19 22 11 15 20 23 25 km ocp           implementing the model in lingo optimization software package, the following outputs are obtained: q113=592; q223=632; q333=842; q234=822  13=592;632=23  ;  33=842;  34=822; http://en.wikipedia.org/wiki/specification_%28technical_standard%29 http://en.wikipedia.org/wiki/standard_deviation operations and inspection cost minimization for a reverse supply chain 103  11=299;  13=111;350=21 ;  23=425;  31=460;  11=  13=  21=  23=  31=1. 5.1. analysis in the following analysis we assume production continues during the search for an assignable cause, but it ceases during repair, 1 1  , 0 2  . we use the following values of parameters: 0.01،0.05 )θϵ ) p e b a w f parameter 0 1 200 0 20 0 0.5 1 5 250 500 value let  be the ratio of the out-of-control standard deviation to in-control standard deviation, i.e. 0 1     . the optimal values of design parameters for given different shift values  and  are listed in table 1 for the joint ewma scheme with k = 0.1. note that, cost values from the proposed cost function is also computed in table 2. regarding the decision variables, especially for large shifts, sample size and sampling interval have been found to be relatively more robust than other variables to changes in initial values. one of the reasons behind the observed sensitivity of control limits and smoothing constants to starting values may be the additional flexibility provided by using two charts rather than a single chart. the change in one variable, say ml , is compensated by a change in another variable, say vl , and hence, different combinations of variables essentially lead to the same impact on the total cost. if only a single chart was used, due to a smaller set of decision variables, the number of alternative combinations of variables resulting in approximately same value of the total cost would probably be less, and therefore, the search would be more likely to converge to the same values of decision variables at termination regardless of the initial values. table 2. optimal economic design for the reverse supply chain v l ml v me n h c    2.67 2.45 0.11 0.29 7 20.00 24.51 1 0.5 0.01 1.83 2.80 0.77 0.80 11 10.65 32.26 1.5 1.69 3.13 0.86 0.99 6 6.14 39.10 2 3.12 2.53 0.15 0.83 10 15.63 28.54 1 1 1.88 2.67 0.99 0.76 7 8.10 34.98 1.5 1.69 3.09 0.84 0.81 5 5.19 41.92 2 2.80 2.73 0.05 0.88 6 9.40 33.64 1 1.5 2.04 2.75 0.81 0.85 5 5.53 39.43 1.5 1.63 3.02 0.86 0.84 4 4.14 46.45 2 fazlollahtabar/oper. res. eng. sci. theor. appl. 1 (1) (2018) 91-107 104 2.27 2.96 0.11 0.85 4 5.27 40.21 1 2 3.98 3.00 0.41 0.82 4 4.41 45.70 1.5 1.53 2.94 0.89 0.83 3 3.43 52.68 2 1.38 3.90 0.11 0.68 2 20.00 25.36 1 0.5 0.05 1.37 2.28 0.98 0.85 9 15.57 45.60 1.5 1.52 2.90 0.74 0.94 5 4.87 65.77 2 3.88 2.20 0.09 0.73 8 19.98 38.38 1 1 1.65 2.34 0.94 0.80 6 7.64 54.33 1.5 1.44 2.74 0.92 0.83 4 3.89 73.92 2 3.19 2.44 0.86 0.82 5 7.41 53.15 1 1.5 1.80 2.56 0.93 0.87 4 4.26 67.90 1.5 1.41 2.77 0.88 0.93 3 3.03 87.20 2 2.24 2.65 0.96 0.86 3 4.51 72.10 1 2 1.78 2.63 0.66 0.78 3 3.37 86.35 1.5 1.45 2.86 0.99 0.77 3 2.63 105.52 2 5.2. managerial implications as we know, defects of a product, causes extra charges of substituting with a perfect one and etc. according to the obtained results and model analysis, managers can make important decisions in order to advance the goals. quicker planning on more efficient products for timely delivery and recycling is important. in terms of timely delivery, it is also possible to plan, considering the return rate of the product with the highest return rate, that too many material and product other are ecofriendly for precautionary reasons. investing more on high-performance return products is another aspect for managers to decide. from the point of view of investing in return product with more efficiency, return product with reliability greater than other materials can be mentioned. 6.conclusions this paper concerned with inclusion of quality inspection in the process of reverse supply chain items’ collection and re-manufacturing. we configured a reverse supply chain and modeled a minimization formulation to handle several cost operations within the return flow of the products. the major contribution of the work was to consider inspection operation as a quality assurance focal element. the presented model was an integer linear programming model for multi-layer, multiproduct reverse supply chain that minimizes the products operation costs and inspection costs among different centers in layers for variety of products. we have studied the joint economic design of ewma control charts for monitoring the mean and variance of a process. in our numerical examples we have observed that, in general, both the optimal sample size and sampling interval decrease as the size of shifts in mean and/or variance increases. the outputs implied that the proposed model is helpful in industrial system as it encompasses both cost and quality. the quality was monitored in ewma control chart and then formulated as a 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(2016). advanced cross-entropy in closed-loop supply chain planning. journal of cleaner production, 135, 201-213. zohal, m., & soleimani, h. (2016). developing an ant colony approach for green closed-loop supply chain network design: a case study in gold industry. journal of cleaner production, 133, 314337. © 2018 by the authors. submitted for possible open access publication under the terms and conditions of the creative commons attribution (cc by) license (http://creativecommons.org/licenses/by/4.0/). plane thermoelastic waves in infinite half-space caused operational research in engineering sciences: theory and applications operational research in engineering sciences: theory and applications vol. 2, issue 1, 2019, pp. 1-14 issn: 2620-1607 eissn: 2620-1747 doi: https://doi.org/10.31181/oresta1901001b * corresponding author. e-mail addresses: ibrahim.badi@hotmail.com (i. badi). aa_shahed@yahoo.com (a. abdulshaed) ranking the libyan airlines by using full consistency method (fucom) and analytical hierarchy process (ahp) ibrahim badi*a, ali abdulshahedb a mechanical engineering department, misurata university, libya b electrical engineering department, misurata university, libya received: 12 november 2018 accepted: 16 january 2019 first online: 03 march 2019 original scientific paper abstract. performance measurement and evaluation of the airlines are a key point for improving their performance. this evaluation can help achieving the airline targets. the aim of this paper is to evaluate and compare the performance of four libyan airlines by considering five main areas of performance; the airline reliability, employees, management, customer's satisfaction and tangibles. in this work, a hybrid method which combined the full consistency method (fucom) and analytical hierarchy process (ahp) in one system has been used to assess the four libyan airlines. in the ahp method, the number of the required pairwise comparisons are increases dramatically with the number of the elements to be compared. the more the comparisons are the higher is the likelihood that the decision maker will introduce erroneous data. in this regard, the problem has been solved by means of using integer, decimal values from the predefined scale for the pairwise comparison of the criteria. the results show that the reliability is the most important performance area followed by satisfaction. among the four investigated airlines, libyan wings were ranked first with a total 0.392 score. key words: libyan airlines, ahp, fucom, mcdm. 1. introduction in today’s competitive market within the airline industry, delivering high-quality service has become a global marketing need. one of the key elements for airline modern industry is the evaluation of performance and effectiveness. this can support achieving the company objectives, and compare their performance with the similar best practices' businesses. in order to achieve these higher-quality levels, badi & abdulshahed /oper. res. eng. sci. theor. appl. 2 (1) (2019) 1-14 2 airlines need to develop a methodology to make this measurement in a profitable manner. the air transport industry plays an important role in africa, while it provides the essential links for the economic and physical integration in the continent. the network of the other transportation service could be inadequate. despite the great potential and the rapid growth of air transport, africa’s share in the global air transport industry stills insignificant. the state of air transport industry in africa is about 2.85% and 2% of global revenue passenger kilometer and global airport income respectively, and about 1% of global airlines’ cargo (njoya, 2016). furthermore, only around 20% of intercontinental traffic between africa and the rest of the world is controlled by african airlines. (amankwah-amoah, 2018). there are many internal and external elements that lead to the limited competitiveness of the african airlines. some of these external factors are slow implementation of the yd and protection of state-owned airlines, which have leads to the unfair competition. furthermore, the internal factors such as limited economies of scale and quality of service have affected the ability of competition of some airlines (amankwah-amoah, 2018). none of the above-mentioned studies have considered libyan airlines in their investigation. this study responds to this need by using a list of key performance indicators to assess a number of aspects of airline's performance. the aim of this work is to use a set of key performance indicators to measures and evaluate the performance of libyan airlines. a questionnaire survey was used to gather expertise opinions across libya. the responses to the questionnaire were then analyzed and studied with a new method which companies the analytic hierarchy process (ahp) methodology and full consistency method (fucom) in one system. the fucom technique was used to determine the relative weight of the kpis and then ranked the libyan airlines using ahp according to their kpis. the paper is organized as follows. section 2 presents a literature review on mcdm methods. section 3 presents the full consistency method fucom. in section 4, the case study is presented and discussed, where sixteen indicators were used to determine the performance of the airlines. section 5 presented the determination of the weights using fucom method and compares it to results obtained by the ahp method, and ranks the libyan airlines using ahp method. finally, section 6 presents the conclusion remarks that emerged from the analysis of the case study. 2. literature review multi criteria decision making mcdm methods are gaining more popularity in many fields such as logistics, supply chain management, energy, urban development, waste management, and passenger satisfaction measurement (pamučar and ćirović, 2015); (tsafarakis et al., 2018, milosavljević et al., 2018); (petrović and kankaraš, 2018); (liu et al., 2018); (vesković et al., 2018); (pamučar et al., 2018a). mcdm methods generally work as a decision support tool to the problems containing multiple and conflicting objectives. one of the most popular methods in mcdm techniques is analytic hierarchy process (ahp) (zietsman and vanderschuren, 2014), which introduced by thomas l. saaty ranking the libyan airlines by using full consistency method (fucom) and analytical hierarchy process (ahp) 3 in 1977 (saaty, 1980). according to (mardani et al., 2016), ahp and its modified forms are the most commonly used methods for evaluating of transportation systems. ahp is based on the following four main components: • define the problem and determine the type of information required • structure the problem as a hierarchy • conduct pairwise comparisons among all criteria at every level within the hierarchy • compute the relative weights of the criteria barros and wanke (barros and wanke, 2015) used two-stage topsis method and neural networks to analyses the african airlines efficiency. because of its location, libya has a good opportunity to be a strategic air transport hub. maertenz et al (maertens et al., 2014) focused on the traffic between africa and europe and evaluates the prospects of an air transport operation in libya. they developed a weighted average distance penalty (wadp) indicator and applied it to tripoli airport as a potential hub location. recently, eshtaiwi et al. (eshtaiwi et al., 2018) developed a set of kpi’s to evaluate the performance of the libyan airports. the grey theory model has been used to evaluate the libyan airports (eshtaiwi et al., 2017). mahtani and garg (mahtani and garg, 2018) adopts a multi-criteria decision making (mcdm) approach based on the technique of fuzzy analytical hierarchy processing (ahp). the results indicate that that financial factors are the most critical and categorized as a major influence on the commercial stability of the airlines. results also show that annual inflation and gdp growth rate in the country has a major influence on the sustainability of the airlines in india. karman and akman (karaman and akman, 2018) used the analytical hierarchical process (ahp) to turkish airline industry to assess and weigh the csr program criteria among multiple alternatives. questionnaires based on the pairwise comparison, answered by a number of experts working in different major airline companies, are used to assess the relative importance of related factors. then, fuzzy linguistic variables are adopted to rank the selected csr programs of airliner companies. the results indicate that csr paradigm in the airline industry is envisaged within a restricted economic realm besieging social and environmental dimensions, rather than within the totality of systemic efforts towards multi-faceted issues. high-quality service has become a requirement in the market among air carriers, and helps companies to gain and maintain customer loyalty. it also leads to creating competitive pressure among air carriers (chen et al., 2011). tsafarakis et al. (tsafarakis et al., 2018) suggested a model for airline passenger satisfaction measurement and service quality improvement. in this context, no research has been done regarding the airline’s performance measurements in libya. 3. the full consistency method fucom fucom (pamučar et al., 2018b) is a new mcdm method for determination criteria weights. the problems of multi-criteria decision-making are characterized by the choice of the most acceptable alternative out of a set of the alternatives presented on the basis of the defined criteria. a model of multi-criteria decisionmaking can be presented by a mathematical equation badi & abdulshahed /oper. res. eng. sci. theor. appl. 2 (1) (2019) 1-14 4 ( ) ( ) ( )1 2max , ,..., , n 2nf x f x f x    , with the condition that  1 2, ,..., mx a a a a = ; where n represents the number of the criteria, m is the number of the alternatives, fj represents the criteria ( 1, 2,...,ј n= ) and a represents the set of the alternatives ai ( 1, 2,...,i m= ). the values ij f of each considered criterion j f for each considered alternative i a are known, namely ( ) ( ), , ; 1, 2,..., ; 1, 2,...,ij j if f a i j i m j n=  = = . the relation shows that each value of the attribute depends on the jth criterion and the ith alternative. real problems do not usually have the criteria of the same degree of significance. it is therefore, necessary that the significance factors of particular criterion should be defined by using appropriate weight coefficients for the criteria, so that their sum is one. determining the relative weights of criteria in multi-criteria decision-making model is always a specific problem inevitably accompanied by subjectivity. this process is very important and has a significant impact on the final decision-making result, since weight coefficients in some methods crucially influence the solution. therefore, particular attention in this paper is paid to the problem of determining the weights of criteria, and the new fucom model for determining the weight coefficient of criteria is proposed. this method enables the precise determination of the values of the weight coefficients of all the elements mutually compared at a certain level within the hierarchy, simultaneously satisfying the conditions of the comparison consistency. in real life, pairwise comparison values / ij i j a w w= (where aij shows the relative preference of criterion i to criterion j) are not based on accurate measurements, but rather on subjective estimates. there is also a deviation of the values ij a from the ideal ratios / i j w w (where i w and j w represents criteria weights of criterion i and criterion j). if, for example, it is determined that a is of much greater significance than b, b of greater importance than c, and c of greater importance than a, there is inconsistency in problem solving and the reliability of the results decreases. this is especially true when there are a large number of the pairwise comparisons of criteria. fucom reduces the possibility of errors in a comparison to the least possible extent due to: (1) a small number of comparisons (n-1) and (2) the constraints defined when calculating the optimal values of criteria. fucom provides the ability to validate the model by calculating the error value for the obtained weight vectors by determining dfc. on the other hand, in the other models for determining the weights of criteria (the bwm, the ahp models), the redundancy of the pairwise comparison appears, which makes them less vulnerable to errors in judgment, while the fucom methodological procedure eliminates this problem. in the following section, the procedure for obtaining the weight coefficients of criteria by using fucom is presented. step 1. in the first step, the criteria from the predefined set of the evaluation criteria  1 2, ,..., nc c c c= are ranked. the ranking is performed according to the significance of the criteria, i.e. starting from the criterion which is expected to have ranking the libyan airlines by using full consistency method (fucom) and analytical hierarchy process (ahp) 5 the highest weight coefficient to the criterion of the least significance. thus, the criteria ranked according to the expected values of the weight coefficients are obtained: (1) (2) ( ) ... j j j k c c c   (1) where k represents the rank of the observed criterion. if there is a judgment of the existence of two or more criteria with the same significance, the sign of equality is placed instead of “>” between these criteria in the expression (1) step 2. in the second step, a comparison of the ranked criteria is carried out and the comparative priority ( / ( 1)k k  + , 1, 2,...,k n= , where k represents the rank of the criteria) of the evaluation criteria is determined. the comparative priority of the evaluation criteria ( / ( 1)k k  + ) is an advantage of the criterion of the ( )j k c rank compared to the criterion of the ( 1)j k c + rank. thus, the vectors of the comparative priorities of the evaluation criteria are obtained, as in the expression: (2) ( )1/ 2 2/3 / ( 1), ,..., k k   + = (2) where / ( 1)k k  + represents the significance (priority) that the criterion of the ( )j k c rank has compared to the criterion of the ( )j k c rank. the comparative priority of the criteria is defined in one of the two ways defined in the following part: a) pursuant to their preferences, decision-makers define the comparative priority / ( 1)k k  + among the observed criteria. thus, for example, if two stones a and b, which, respectively, have the weights of 300 a w = grams and 255 b w = grams are observed, the comparative priority ( /a b  ) of stone a in relation to stone b is / 300 / 255 1.18 a b  = = . also, if the weights a and b cannot be determined precisely, but a predefined scale is used, e.g. from 1 to 9, then it can be said that stones a and b have weights 8 a w = and 7 b w = . respectively. then the comparative priority ( /a b  ) of stone a in relation to stone b can be determined as / 8 / 7 1.14 a b  = = . this means that stone a in relation to stone b has a greater priority (weight) by 1.18 (in the case of precise measurements), i.e. by 1.14 (in the case of application of measuring scale). in the same manner, decision-makers define the comparative priority among the observed criteria / ( 1)k k  + . when solving real problems, decision-makers compare the ranked criteria based on internal knowledge, so they determine the comparative priority / ( 1)k k  + based on subjective preferences. if the decision-maker thinks that the criterion of the ( )j k c rank has the same significance as the criterion of the ( 1)j k c + rank, then the comparative priority is / ( 1) 1 k k  + = . badi & abdulshahed /oper. res. eng. sci. theor. appl. 2 (1) (2019) 1-14 6 b) based on a predefined scale for the comparison of criteria, decision-makers compare the criteria and thus determine the significance of each individual criterion in the expression (1). the comparison is made with respect to the first-ranked (the most significant) criterion. thus, the significance of the criteria ( ( )j kc  ) for all of the criteria ranked in step 1 is obtained. since the first-ranked criterion is compared with itself (its significance is (1) 1 jc  = ), a conclusion can be drawn that the n-1 comparison of the criteria should be performed. for example: a problem with three criteria ranked as c2>c1>c3 is being subjected to consideration. suppose that the scale   ( ) 1, 9 j kc   is used to determine the priorities of the criteria and that, based on the decision-maker’s preferences, the following priorities of the criteria 2 1 c  = , 1 3.5 c  = and 3 6 c  = are obtained. on the basis of the obtained priorities of the criteria and condition / ( 1) 1 k k k k w w  + + = we obtain following calculations 2 1 3.5 1 w w = i.e. 2 1 3.5w w=  , 1 3 6 3.5 w w = i.e. 1 3 1.714w w=  . in that way, the following comparative priorities are calculated: 2 1/ 3.5 / 1 3.5 c c  = = and 1 3/ 6 / 3.5 1.714 c c  = = (expression (2)). as we can see from the example shown in step 2b, the fucom model allows the pairwise comparison of the criteria by means of using integer, decimal values or the values from the predefined scale for the pairwise comparison of the criteria. step 3. in the third step, the final values of the weight coefficients of the evaluation criteria ( )1 2, ,..., t n w w w are calculated. the final values of the weight coefficients should satisfy the two conditions: (1) that the ratio of the weight coefficients is equal to the comparative priority among the observed criteria ( / ( 1)k k  + ) defined in step 2, i.e. that the following condition is met: / ( 1) 1 k k k k w w  + + = (3) (2) in addition to the condition (3), the final values of the weight coefficients should satisfy the condition of mathematical transitivity, i.e. that / ( 1) ( 1) / ( 2) / ( 2) k k k k k k    + + + +  = . since / ( 1) 1 k k k k w w  + + = and 1 ( 1) / ( 2) 2 k k k k w w  + + + + = , that 1 1 2 2 k k k k k k w w w w w w + + + +  = is obtained. thus, yet another condition that the final values of the weight coefficients of the evaluation criteria need to meet is obtained, namely: ranking the libyan airlines by using full consistency method (fucom) and analytical hierarchy process (ahp) 7 / ( 1) ( 1) / ( 2) 2 k k k k k k w w   + + + + =  (4) full consistency i.e. minimum dfc (  ) is satisfied only if transitivity is fully respected, i.e. when the conditions of / ( 1) 1 k k k k w w  + + = and / ( 1) ( 1) / ( 2) 2 k k k k k k w w   + + + + =  are met. in that way, the requirement for maximum consistency is fulfilled, i.e. dfc is 0 = for the obtained values of the weight coefficients. in order for the conditions to be met, it is necessary that the values of the weight coefficients ( )1 2, ,..., t n w w w meet the condition of / ( 1) 1 k k k k w w   + + −  and / ( 1) ( 1) / ( 2) 2 k k k k k k w w    + + + + −   , with the minimization of the value  . in that manner the requirement for maximum consistency is satisfied. based on the defined settings, the final model for determining the final values of the weight coefficients of the evaluation criteria can be defined. ( ) / ( 1) ( 1) ( ) / ( 1) ( 1) / ( 2) ( 2) 1 min . . , , 1, 0, j k k k j k j k k k k k j k n j j j s t w j w w j w w j w j       + + + + + + = −   −    =     (5) by solving the model (5), the final values of the evaluation criteria ( )1 2, ,..., t n w w w and the degree of dfc (  ) are generated. 4. the case study expectations and actual services delivered to the customer could be used as a definition for service quality. many activities can be used as a measure for service quality functions performed by the airlines such as ticket reservation, purchasing, check-in, comfortable and safe travelling and value-added services, such as on-board services, seat comfort, and cleanliness, luggage transportation, promotional incentives, including frequent membership programs and miles rewards, lost baggage handling and services for delayed passengers. thus, service quality badi & abdulshahed /oper. res. eng. sci. theor. appl. 2 (1) (2019) 1-14 8 categories can be seen as a combination of various subjective and objective factors, which are difficult to evaluate appropriately. for the purpose of assessing the libyan airlines, sixteen indicators were used, as shown in fig. 1. in this paper we follow the indicators suggested by (perçin, 2018), which categorized the indicators into five groups as follows: • reliability: this category typically includes flight schedule and frequency, on-time performance and flight safety and security. • employees: the attitude among the employees towards the customers affects customers' expectations of airline service quality. therefore, employee courtesy, responsiveness and neat appearance will probably positively influence passengers' perceptions of the airline. • management: a good management system is necessary for providing highquality services to the customers. therefore, service efficiency, service diversification and flight crew competence help airlines to satisfy customer needs. • satisfaction: this category includes the ability of the employees for handling customer complaints and solving problems regarding reservations, check-in, ticketing, baggage, flight delays, cancellations, and boarding situations. nevertheless, the airline's competitive strengths can affect by the employee inability or unwillingness to handle customer complaints. • tangibles: some other indicators like in-flight services such as airplane comfort and cleanliness, on-board entertainment (movies, magazines, etc.) and on-board services (meals and drinks) are of an important role on passenger satisfaction and perception of an airline's service quality. figure 1. performance indicators for airlines service quality measurement c1: reliability c2: employees c3: management c4: satisfaction c5: tangibles c11: flight schedule and frequency c12: on-time performance c13: flight safety and security c21: courtesy of employees c22: responsiveness of employees c23: neat appearance of employees c31: service efficiency c32: service diversification c33: competence of flight crew c41: handling of customer complaints c42: efficiency of checking-in service c43: ease of ticket purchase/reservation c51: comfort and cleanliness of airline c52: on-board entertainment c53: on-board services c44: accuracy of baggage delivery ranking the libyan airlines by using full consistency method (fucom) and analytical hierarchy process (ahp) 9 there are 13 airlines operates in libya. the four major airlines are: libyan airlines: it operates scheduled passenger and cargo services within libya and to europe, middle east and north africa. it founded on 1964. the company is100% owned by the government. afriqyiah airways: it is a state-owned airline. it founded on 2001. it is operated domestically and to europe, africa, asia, and middle east. libyan wings: it started operations in 2015. it is operated domestically and to two destinations (turkey and tunisia). buraq air: founded in 2001. it operates scheduled domestic and international services to europe, north africa, and the middle east. 5. results and analysis 5.1. results by ahp method table 1 shows the pairwise comparison of the main indicators, with consistency ratio (cr) equal to 10% (saaty, 1990). table 1: pairwise comparison of the main categories c1 c2 c3 c4 c5 ωj c1 1 5 4 3 7 0.503 c2 1/5 1 ½ 1/3 1 0.077 c3 1/4 2 1 1/2 2 0.132 c4 1/3 3 2 1 3 0.216 c5 1/7 1 ½ 1/3 1 0.071 cr=0.010 5. 2. determining the weight of the main criteria using the fucom method step 1. in the first step, the decision-makers performed the ranking of the criteria: c1> c4> c3> c2 >c5. step 2. in the second step (step 2b), the decision-maker performed the pairwise comparison of the ranked criteria from step 1. the comparison was made with respect to the first-ranked c2 criterion. the comparison was based on the scale  1,9 . thus, the priorities of the criteria ( ( )j kc  ) for all of the criteria ranked in step 1 were obtained (table 2). table 2. priorities of criteria criteria c1 c4 c3 c2 c5 ( )j kc  1 2.7 5 5.5 5.8 badi & abdulshahed /oper. res. eng. sci. theor. appl. 2 (1) (2019) 1-14 10 based on the obtained priorities of the criteria, the comparative priorities of the criteria are calculated: 1 4/ 2.7 / 1 2.7 c c  = = , 4 3/ 5 / 2.7 1.852 c c  = = , 3 2/ 5.5 / 5 1.1 c c  = = , 2 5/ 5.8 / 5.5 1.055 c c  = = . step 3. the final values of weight coefficients should meet the following two conditions: a) the final values of the weight coefficients should meet the condition (3), i.e. that 1 4 2.7 w w = , 4 3 1.852 w w = , 3 2 1.1 w w = , 2 5 1.055 w w = . b) in addition to the condition (3), the final values of the weight coefficients should meet the condition of mathematical transitivity, i.e. that 1 3 2.7 1.852 5 w w =  = , 4 2 1.852 1.1 2.037 w w =  = , 3 5 1.1 1.055 1.16 w w =  = . by applying the expression (5), the final model for determining the weight coefficients can be defined as: 31 4 2 4 3 2 5 31 4 3 2 5 5 1 min 2.70 , 1.852 , 1.1 , 1.055 , . . 5.00 , 2.037 , 1.16 , 1, 0, j j j ww w w w w w w ww w s t w w w w w j         =  −  −  −  −     −  −  −     =      by solving this model, the final values of the weight coefficients ( )0.520, 0.094, 0.104, 0.192, 0.090 t and dfc of the results 0.00016 = are obtained. the value of the criteria according to the marks given at the beginning is shown in table 4. the model is solved using the lingo17 software. from obtained results it can be concluded that the most important criterion is c1, followed by the criterion c4. table 3 presents the weight of the kpas and kpis. in terms of key performance areas, reliability have got the most important weight with a value of 0.506. the satisfaction ranked next with a value of 0.216, followed by the management with value of 0.0.131. employees perspective (0.091) is ranked the fourth most important area, while the tangibles (0.059) is the least important performance area. in kpis terms, on-time performance (0.289) is regarded as the most important indicator. flight safety and security is the second most important key performance indicator with a value of 0.115. ranking the libyan airlines by using full consistency method (fucom) and analytical hierarchy process (ahp) 11 table 3: criteria weights crieria sub-criteria weights (ahp) weights (fucom) c1: reliability 0.506 0.520 c11: flight schedule and frequency 0.072 0.068 c12: on-time performance 0.289 0.306 c13: flight safety and security 0.145 0.146 c2: employees 0.076 0.094 c21: courtesy of employees 0.016 0.021 c22: responsiveness of employees 0.042 0.050 c23: neat appearance of employees 0.018 0.023 c3: management 0.131 0.104 c31: service efficiency 0.082 0.063 c32: service diversification 0.018 0.016 c33: competence of flight crew 0.031 0.025 c4: satisfaction 0.216 0.192 c41: handling of customer complaints 0.053 0.039 c42: efficiency of checking-in service 0.047 0.033 c43: ease of ticket purchase/reservation 0.021 0.028 c44: accuracy of baggage delivery 0.94 0.098 c5: tangibles 0.071 0.090 c51: comfort and cleanliness of airline 0.024 0.029 c52: on-board entertainment 0.007 0.009 c53: on-board services 0.040 0.052 the results obtained during this work can help the libyan airlines to compare their performance against others in the future based on the values of the evaluated kpis. furthermore, the results can be used as a bases for the airlines to perform internal benchmarking by comparing the performance of different areas with itself during a period of time. the hybrid method which combined the fucom method and ahp analysis has been used to select the best practices for the libyan airlines as follows: libyan wings ranked first with the highest importance weight of 0.392. afriqiyah airlines ranked second with a value of 0.261, followed by libyan airlines with a value of 0.202, and at last buraq airlines with score of 0.145, respectively. these scores illustrated that libyan wings is the most efficient airlines in libya according to the experts’ opinions. fig. 2 illustrates the performance of the four airlines in the five key performance areas. in this regards, libyan wings airline has the best performance in every area in comparison to the other airlines. on the other hand, buraq airline has a low performance in management area. buraq airline has the lowest individual score in three dimensions. pairwise comparisons judgements in the ahp (see table 2) assume that the decision-maker can compare any two elements at the same level within the hierarchy and provide a numerical value for the ratio to their importance. however, a major disadvantage is that the number of the required comparisons increases quadratically with the number of the elements to be compared. thus, in the proposed badi & abdulshahed /oper. res. eng. sci. theor. appl. 2 (1) (2019) 1-14 12 method, the assessment of the priorities from the pairwise comparison intervals will be formulated as integer, decimal values or the values from the predefined scale for the pairwise comparison with the criteria, in this regard the proposed method will maximize the decision-maker’s satisfaction with a specific crisp priority vector. figure 2: performance of the libyan airlines 6. conclusion this paper used a set of key performance indicators to measure the performance of libyan airlines. the value obtained in this research can be used by the libyan airlines to benchmark their performance with other airlines which operates in similar environments. full consistency method (fucom) and analytical hierarchy process (ahp) method has been combined in one system in order rank the performance measures. the advantages of fucom model is that allows the pairwise comparison of the criteria by means of using integer, decimal values or the values from the predefined scale for the pairwise comparison of the criteria. the results showed that the reliability of the airline and the satisfaction areas are the most important area measures. considering airlines ranking, libyan wings airline is the highest ranked airline followed by afriqiah airline, libyan airline, and at last buraq airline. the model can be used as a decision support tool to improve the airlines performance. through this paper are demonstrated advantages of fucom method in comparison with ahp. 7. references amankwah-amoah, j. 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(2014). analytic hierarchy process assessment for potential multi-airport systems–the case of cape town. journal of air transport management, 36, 41-49. operational research in engineering sciences: theory and applications vol. 4, issue 1, 2021, pp. 115-135 issn: 2620-1607 eissn: 2620-1747 doi: https://doi.org/10.31181/oresta20401156j * corresponding author. antras1209@gmail.com (ž. jokić), dbozanic@yahoo.com (d. božanić), dpamucar@gmail.com (d. pamučar) selection of fire position of mortar units using lbwa and fuzzy mabac model željko jokić*, darko božanić, dragan pamučar military academy, university of defence in belgrade, serbia received: 18 february 2021 accepted: 26 march 2021 first online: 28 march 2021 original scientific paper abstract: the paper presents a hybrid model based on the lbwa method and the fuzzy mabac method, applied when selecting firing positions' locations of the serbian army's mortar units. using a questionnaire, the experts determined the criteria for choosing the firing position. the lbwa method is used to determine the weighting coefficients of the criteria, while the fuzzy mabac method is used to determine the most favorable location of the firing position by choosing between six specific options alternatives. by changing the value of the elasticity coefficients, the sensitivity analysis of the developed model was performed, and by applying the spearman coefficient, it was determined that there is an ideal positive correlation of ranks. key words: lbwa, mabac, fuzzy numbers, mortar units, firing position. 1. introduction the entire twentieth and the beginning of the 21st century were marked by dizzying technological developments that could not but include the military industry. the impact of technological development on armaments and military equipment also conditioned a change in the armed conflicts' physiognomy. modern combat conflicts are characterized by: sudden and rapid actions of forces from a distance, with mass use of armored and mechanized units and special forces on land, frequent use of helicopter landings, strong air support, and constant possibility and the threat of using weapons of mass destruction. however, there are means of military equipment which, despite the stated technological development, have not undergone significant changes during all this time, and even without them, no major armed conflict can be imagined. from its appearance in 1904, in the russo-japanese war, to the present day, mortars have undergone small changes. they are produced in various calibers, of which the most common are 60 mm, 81-82 mm, and 120 mm, as traction or self-propelled. with the mailto:antras1209@gmail.com mailto:dbozanic@yahoo.com jokić et al./oper. res. eng. sci. theor. appl. 4 (1) (2021) 115-135 116 possibility of shooting in a vertical path, they are suitable for shooting from bays, ravines, and from the back slope. mortar units are the basis of the infantry battalion's fire support in performing all types of combat operations. with their firepower and the possibility of quick maneuver, they can bring an advantage on the field, provided they are used correctly, which, above all, depends on the correct choice of the location of the combat schedule elements. the article discusses the choice of the location of the battalion fire group fire position (bfg) formed by the company-platoon of 120 mm mortars. the ultimate goal of the article is to apply a model that will support the decision-maker in choosing the location of the firing position, which would significantly reduce the response time and the possibility of making an inadequate decision. with the relatively newer lbwa method, the weight coefficients of the criteria for the selection of the location of the firing position (fp) will be determined. experts in the subject area identified eight criteria, based on the applicable rules and instructions, on which the choice of the location of the firing position directly depends. the choice of the specific location of the firing position, between the six options, will be solved by applying the fuzzy mabac method. 2. the place and role of mortars in contemporary combat actions the 120 mm mortar is an accompanying infantry weapon, intended for neutralizing and destroying manpower and firepower, creating smoke curtains, blinding observation posts and firing points, illuminating battlefields, opening passages through wire barriers and minefields, and demolishing light fortification barriers at distances of about 6500 m (military encyclopedia, 1973). according to the formation of mb 120 mm, mortar companies or platoons are formed, depending on whether it is an infantry or mechanized battalion. during combat operations, when operating within a battalion, a company-platoon of 120 mm mortars forms a battalion fire group of temporary composition. at the decision of the commander, the battalion fire group may be attached to another unit or perform tasks for the needs of a higher unit. the tasks of the battalion fire group, during the execution of combat operations, derive from the purpose of the 120 mm mortar (military encyclopedia, 1973): neutralization and destruction of the enemy's manpower, firepower and fire support, fight against enemy landings, neutralization of enemy observation posts and observation posts, neutralization of enemy command posts and communication centers, demolition and destruction of field-type fortifications and opening of passages in obstacles, smoking and lighting of certain areas and rooms. when conducting combat operations, bfg possesses elements of the combat schedule, which is part of the combat schedule of the battalion in which it operates, ie the unit it supports. the combat schedule of the bfg consists of an observation post, a firing position and a place of means of transport. the command part has an selection of fire position of mortar units using lbwa and fuzzy mabac model 117 observation post, and the fire part has a fire position. before possessing the stated elements of the combat schedule, the selection of optimal regions-locations for the execution of the obtained task is performed. as the topic of the paper is the choice of the location of the firing position in the future, the paper will not deal with the observation post. the fire position (fp) is a region on the land where people, tools, ammunition and traction equipment are deployed in order to perform a fire task (kurtov et al., 2014). according to the purposes, fp can be: basic, reserve, temporary, next and false, while according to the degree of shelter: sheltered, semi-sheltered and discovered (unprotected). there are no works in the domestic and foreign literature that deal exclusively with the problem of choosing the firing position for mortar units. in addition to the rules and manuals that deal with mortars from the point of view of construction, some authors in works such as department of the army (2017), jenzen-jones (2015), consider mortars from the aspect of their application. the choice of the location of the basic vp for mortar units belongs to the group of location problems, which are considered in the literature in different ways, both by the type of location and by the applied methods. the problem of the location of military facilities was discussed by karatas et al. (2019). božanić & pamučar (2010) select the location of the bridge crossing using fuzzy logic. also, pamučar et al. (2019) select the optimal location for water barriers using the interval-valued fuzzy-rough numbers and mairca methods. sennaroglu & celebi (2018) use the ahp, promethee and vikor methods to select the location of the military airport. pamučar et al. (2016) selected the firing position of the brigade artillery group in the defensive operation using a hybrid model fuzzy ahp topsis and a fabricated satie scale. hamurcu & eren (2019) using multi-criteria decision-making using the ahp and topsis methods select the best motorcycle route in ankara. stoilova (2020) using the ahp and simus optimal railway route in case of an emergency. liang et al. (2020) address the problem of route selection for perishable goods vehicles. xu et al. (2020) solve a similar problem by multi-criteria analysis. darbari et al. (2016) using multi-criteria analysis determine the optimal locations for the collection and disposal of recycled electrical equipment. ortiz-astorquiza et al. (2018) conduct a comprehensive overview of problems with the location of accommodation facilities. a similar problem is addressed by küçükaydın & aras (2020) using the fuzzy c-means cluster. contreras & o’kelly (2019) address the problem of hub location when designing networks in transportation and telecommunications systems. the hybrid model ahp and promethee, abdel-basset et al. (2021) are used to select the location of coastal wind farms. pan et al. (2021) are conducting a case study on the selection of the most suitable pedestrian overhead bridge location for the installation of elevators in singapore using an adaptive bayesian network. 3. description of the method the hybrid model, applied when solving the problem of choosing the location of fp mortars, consists of lbwa and fuzzy mabac method. the lbwa method is used to determine the weight coefficients of the criteria, while the fuzzy mabac method is used to determine the most favorable location of the mortars position. figure 1 shows the scheme of the model. jokić et al./oper. res. eng. sci. theor. appl. 4 (1) (2021) 115-135 118 phase 1 defining criteria phase 2 – calculation of weight coefficients of criteria phase 4 sensitivity analysis phase 3 choosing the best alternative expert evaluation expert evaluation, lbwa method fuzzy mabac change weighting coefficients, spearman coefficient figure 1. model scheme 3.1. level based weight assessment (lbwa) model the model of weight assessment based on levels (lbwa) was presented for the first time in their work by žižović & pamučar in 2019. although a relatively new method, lbwa has so far been applied in several papers in solving various problems. after the first presentation of the method, božanić et al. (2020) use a hybrid lbwa ir-mairca model of multi-criteria decision-making for weapon selection. fuzzy lbwa – macbeth – rafsi was used to develop a multi-criteria model for the sustainable reorganization of the health system in the emergency situation caused by the covid-19 pandemic (pamučar et al., 2020b). the choice of the way passengers arrive at the airport in istanbul was made, also by applying the fuzzy lbwa-waspash model (pamučar et al., 2020a). lbwa is a subjective model for determining weighting coefficients. advantage of lbwa metod over other is in next keys (žižović & pamučar, 2019): (1) calculation of weighting coefficients can be realized with a small number of comparison criteria; (2) a simple algorithm of the lbwa method; (3) а simple mathematical apparatus is used to obtain the weighting coefficients; (4) after realized comparisons of criteria, the coefficient of elasticity enables additional corrections of the values of weight coefficient. criteria must be defined before applying the lbwa method. if the number of criteria is denoted by n, then a set of criteria is available  1 2, , , ns c c c= . after that, the lbwa method is approached through the following steps (žižović & pamučar, 2019): step 1. determining the most significant criterion. the most important criterion is the one that, in the opinion of experts, has the greatest influence. selection of fire position of mortar units using lbwa and fuzzy mabac model 119 step 2. grouping the criteria by levels of significance in relation to the most significant criterion, according to the following: level 1 s : from the set s, at the level of s1, criteria are grouped that are of equal importance as c1 or are up to twice less significant than c1; level 2 s : from the set s, at the level of s2, the criteria are grouped exactly two times less significant than c1 or are up to three times less significant than c1; level s3: ... by applying the previously, the decision-maker is grouping criteria according levels of significance. if the significance of the criteria j c marks with ( ) j s c , wherein  1, 2, ,j n , then we have 1 2 ks s s s=    , where for each level  1, 2, ,i k , it is true that it is     1 2 , , , : ( ) 1 si i i i j j s c c c c s i s c i= =    + (1) also, for everyone  , 1, 2, ,p q k such that it is p q the intersection of the sets is p q s s =  . step 3. within the formed subsets, criteria according to significance are compared. each criterion pi i c s from the set   1 2 , , , si i i i s c c c= is assigned an integer  0,1, , pi i r , that the most important criterion 1 c is assigned a number 1 0i = . if it is pi c more significant than qi c than it is p q i i , and if it is pi c of the same importance as qi c , than it is p q i i= . expression (2) gives the maximum value of the scale for comparing the criteria r.  1 2max , , ,= kr s s s (2) step 4. based on the defined maximum value of the scale for comparing the criteria, coefficient of elasticity is determined 0 r n which should satisfy the condition that 0 r r . step 5. the calculation of the criterion influence function is realized in the following way: 0 0 ( ) p p i i r f c i r i =  + (3) where i is the number of levels / subsets into which the criterion is classified, r0 represents the coefficient of elasticity, while  0,1, , pi i r represents the value assigned to the criterion pi c within the observed level. step 6. calculation of optimal values of weight coefficients of criteria: jokić et al./oper. res. eng. sci. theor. appl. 4 (1) (2021) 115-135 120 1 2 1 1 ( ) ( ) = + + + n w f c f c (4) the values of the weighting coefficients of the other criteria: 1 ( ) j j w f c w=  (5) where in 2,3, ,j n= , and n the total number of criteria. if expert decision-making is performed, as previously stated, after each expert determines the values of weighting coefficients, the aggregation of individual judgments according to the considered criterion (aij) is started (blagojević et al., 2017). in the aij method, to obtain the group coefficient, the weighted geometric mean method is used, which is calculated as the nth root of the product of all elements of the data set using expression (6): 1 1 2 1 * *...* = = =  n n n jc j j jn j i w w w w w (6) where in 1jc w combined weighting factor for the criterion c1, 1jw expert weighting factor (e1) and n number of weighting coefficients according to the given criterion. 3.2 fuzzy sets in classical set theory, the membership of elements in a set is estimated in a binary sense according to the bivalent condition the element either belongs or does not belong to the set (chatterjee & stević, 2019). however, it is not always possible to make a clear division, especially of complex phenomena, which cannot be easily described by traditional mathematical methods, especially when the goal is to find an approximately good solution (bojadziev & bojadziev, 1996). modeling using fuzzy sets has been shown to be an effective way of formulating decision-making problems, where available input information is subjective or imprecise (zimmermann, 1998). fuzzy sets are sets whose elements have membership degrees. the theory of obscure sets was first introduced by zadeh (1965), whose application enables decision-makers to deal effectively with uncertainties. since then, fuzzy sets have been used by many researchers in solving various problems alone or in combination with other methods of multi-criteria decisionmaking. thus, kushwaha et al. (2020) and panchal et al. (2019a, 2019b) use fuzzy fmea to assess risk and improve safety in various engineering systems. also pamučar et al. (2016) use fuzzy logic system of type 2 to assess the risk of natural and other disasters in the republic of serbia while božanć et al. (2015) in risk assessment when overcoming water obstacles in a defense operation. similar to the previous one, gopal & panchal (2021) use the fuzzy lambda-tau (λ-τ) approach in the dairy processing industry. the lambda-tau fuzzy method was also applied when determining the time interval of regular maintenance of a coal-fired thermal power plan (panchal et al., 2020) as well as when analyzing the performance problems of a chemical process plan (panchal & srivastava, 2019). fuzzy sets are used mainly with triangular (tfn), trapezoidal and gaussian fuzzy numbers. a fuzzy set ã is a set of ordered pairs consisting of elements x of the selection of fire position of mortar units using lbwa and fuzzy mabac model 121 universal set h and a certain degree of affiliation μã(h), shape ã={ (x, μã(x))︱xx, μã(x)[0,1](zadeh, 1965). the membership function of the μã fuzzy set ã is the mapping μã: x → [0,1], where ã is a subset of the universal set h. due to its fairly simple membership function, the triangular fuzzy number is one of the most commonly used fuzzy numbers, is defined by the following form: 1 , 1 , 0, otherwise  − − −    − = −   +     a m x m l x m l x m m x m u u (7) fuzzy number is denoted as ( , , )=a l m u . the value of m mark the basic value of the fuzzy number, a l deviation from the left, that is, u to the right of the modal value. a very important concept associated with the application of fuzzy numbers is the dephasing process, which converts a fuzzy number into a real number. several methods for performing dephasification can be found in the literature. the most widely used dephasification procedure is the centroid method, which is also known as the center of gravity or the kwong method (kwong & bai, 2003). the triangular fuzzy of the number ã = (l, m, u) is translated into a real number using the following expression: ( 4 * ) 6 + + = l m u m (8) 3.3. fuzzy mabac method multi-attributive border approximation area comparasion (mabac) the mabac method is a reliable tool for rational decision-making (pamučar & ćirović, 2015). so far, it has been used in a large number of works independently or in one of the modifications. alinezhad & khalili (2019) in their book, among others, deal with the mabac method. sun et al. (2017) use the mabac method to determine the priority of patient care. using a modified rough method, ahp-mabac, sharma et al. (2018) determined the priority stations in the indian railways. some authors combine the basic mabac motor with fuzzy sets q-rofs (wang, 2020). wei et al. (2019) apply the mabac meter in ranking medical equipment suppliers. božanić et al. (2016) applied the mabac method in support of decision-making on the use of force in a defensive operation. liang et al. (2019) use the mabac method when assessing risk. also, using this method, some authors selected the most suitable route of new lines in road and railway traffic (luo et al., 2019). when defining the new interval-valued fuzzy-rough numbers (ivfrn) method, pamučar et al. (2018) modified the bwm (best – worst method) and mabac methods. mishra et al. (2020) select a programming language using the mabac method. due to its consistency mentioned earlier, the mabac method can be found in many more papers. тhe fuzzy mabac method solves the problem in three steps (bobar et al., 2020): jokić et al./oper. res. eng. sci. theor. appl. 4 (1) (2021) 115-135 122 step 1. forming the initial decision matrix ( x ). the first thing is to do assessment m alternatives according to n criteria. alternatives are shown in vector form ( )1 2, ...,=i i i ina x x x . 1 2 1 11 12 1 2 11 22 2 1 2 ... ... ... ... ... ... ... ...      =       n n n m m m mn c c c a x x x a x x x x a x x x (9) step 2. normalization the initial matrix ( x ) 1 2 1 11 12 1 2 11 22 2 1 2 ... ... ... ... ... ... ... ...      =       n n n m m m mn c c c a n n n a n n n x a n n n (10) elements of a normalized matrix ( n ) are determined by the equation: a) for benefit (max) type criteria − + − − = − ij i ij i i x x n x x (11) b) for cost (min) type criteria ij i ij i i x x n x x + − + − = − (12) step 3. calculate the elements from the weighted matrix ( v ). * ij i ij i v w n w= + (13) ij n is the elements of a normalized matrix ( n ), and i w is the weighting coefficients of the criteria. using equation (19) we receive a weighted matrix 11 12 1 21 22 2 1 2 ... ... ... ... ... ... ... n n m m mn v v v v v v v v v v      =       (14) step 4. determining the matrix of the approximate boundary area ( g ). selection of fire position of mortar units using lbwa and fuzzy mabac model 123 boundary approximation area (baa) is determined based on the expression: 1/ 1 m m i ij j g v =   =      (15) after calculating the value i g for each criterion, a matrix of boundary approximate domains is formed g .   1 2 1 2 ... ... n n c c c g g g g= (16) step 5. the calculation of the distance of the alternatives from the boundary approximate domain is obtained as follows: 11 12 1 21 22 2 1 2 ... ... ... ... ... ... n n m m mn q q q q q q q q q q      =       (17) q v g= − (18) alternative i a may belong to the boundary approximate domain ( g ), upper approximate area ( g + ) or the lower approximate domain ( g − ). belonging to an alternative i a area of approximation ( g , g + or g − ) is determined on the basis of the equation (19). 0 0 0 ij i ij ij g if q a g if q g if q + −    =   (19) step 6. ranking alternatives. through the sum of the distances of the alternatives from the boundary approach area ( i q ) the calculation of the values of the criterion functions for alternatives was received. the final value of the criterion functions of the alternatives was received by calculating the sum of the elements of the matrix q by rows. 1 , 1, 2,..., , 1, 2,..., n i ij j s q j n i m = = = = (20) 4. application of the hybrid model of multi-criteria decision making the lbwa – fuzzy mabac hybrid model consists of four phases. in the first phase of the model, based on expert assessment, the criteria are defined. in the second phase, the calculation of the weight coefficients of the criteria is realized using expert jokić et al./oper. res. eng. sci. theor. appl. 4 (1) (2021) 115-135 124 assessment and the lbwa method. in the third phase, the best alternative is selected using the fuzzy mabac method. the last phase includes the sensitivity analysis of the developed model and the correlation of ranks. 4.1. criteria for choosing the firing position in the first phase, the criteria are defined that in the further work directly affect the choice of the best alternative, ie. optimal locations for the firing position. defining criteria and their weighting coefficients represents an important phase for decisionmaking models (pamučar et al., 2016). due to the complexity of the problem in defining the selection criteria, experts were hired. experts identified eight criteria for the considered problem, which are listed from c1 to c8. the criteria for selecting the location of the fire position (fp) of the battalion fire group (bfg), which is formed by a company of 120 mm mortars, were defined on the basis of expert opinion, and the data from the rules served as the basis for the survey. the selection of the most favorable location of bfg is made on the basis of eight criteria: c1 distance to the target, expressed in meters (ideal location is generally defined at 1/3 of the range of the weapon from the front end of its own forces when the unit is in attack, or 2/3 when in defense). c2 the ability to observe the firing position by the enemy. in the professional literature, the stated criterion is defined as the shelter of the firing position, and on that basis, the division into sheltered, semi-sheltered and discovered (un sheltered) firing position was made. the detected firing position allows direct aiming at the target. on it the enemy can spot people and tools. the semi-sheltered firing position makes it impossible for the enemy to visually spot people, but it can detect it by smoke and flash when firing a mine. the sheltered firing position prevents the enemy from observing from the ground or detecting the firing position by the smoke and flash of a fired mine. c3 masking conditions (terrain characteristics that enable successful masking of bfg and movement of parts or the whole bfg). c4 soil bearing capacity terrain characteristics on which the accuracy of shooting depends. when shooting from too hard ground, the ground bounces off the ground, while on soft ground it collapses, which requires additional soil reinforcement. c5 the size of the parallax expressed in thousands of parts of the angle. the parallax of the target is the angle between the line of sight and the line of fire. if it is in the range from 0-00 to 3-00 it is small, from 3-00 to 5-00 it is medium and over 5-00 it is large. c6 distance of the observation post from the firing position. the distance of the observation post from the firing position directly affects the duration and accuracy of the correction. the smaller the distance, the more precise the correction will be, and thus the faster it will be completed. based on that, there is a division into near and far observatories. the observation post is close if it is within 10% of the shooting distance. selection of fire position of mortar units using lbwa and fuzzy mabac model 125 c7 access conditions. the approach conditions directly affect the speed of the firing position, and thus the time of preparation of the unit for opening fire. having in mind the mass of individual parts of the 120 mm mortar, it is not at all negligible whether the tools can be brought by motor vehicle to the firing position or the handlers have to carry them by hand. c8 distance to own units. the duration of the correction also depends on the distance of the firing position to one's own units. the closer the units are to the firing position, the easier it is to make a correction, and thus in a shorter time. the set of criteria cj consists of two subsets, a subset of the benefit type criteria, which means that a higher value of the criterion is more desirable, ie. better, denoted by c + and a subset of cost-type criteria, which means that a smaller value is more desirable, ie. better marked with c -. in this particular case, the subset of criteria c+ includes criteria c2, c3, c4 and c7, while the subset of criteria cincludes criteria c1, c5, c6 and c8. the values of criteria c1 and c8 are shown as numerical values while the values of criteria c2 are shown through a linguistic scale from 1 to 5 as seen in table 1. table 1. linguistic descriptors for criterion c2 linguistic descriptor discovered (ds) semi-sheltered (ss) sheltered (s) assigned numeric value 1 3 5 the values of criteria c3, c4, c5, c6 and c7 are presented as fuzzy linguistic descriptors (table 2, table 3 and table 4). table 2.fuzzy linguistic descriptors for criteria c3, c4, c7 linguistic condition fuzzy number bad (b) (0, 1, 3) good (g) (2, 3, 5) excellent (e) (4, 5, 5) table 3. fuzzy linguistic descriptor for criterion c5 linguistic condition fuzzy number small (s) (0, 2, 3.5) medium (m) (2.5, 4, 5.5) large (l) (4.5, 6, 7.5) table 4: fuzzy linguistic descriptor for criterion c6 linguistic condition fuzzy number close (c) (0, 450, 600) remote (r) (480, 640, 1000) 4.2. calculation of weight coefficients of criteria using lbwa method in the second phase, the calculation of the weight coefficients of the criteria is performed using the lbwa method, in the previously described manner. after the selection of the most important criteria by the experts, the determination of the weighting criteria is presented in this text. determination of weighting coefficients is shown for one expert (e1). as 11 experts participated in the research, in the end the jokić et al./oper. res. eng. sci. theor. appl. 4 (1) (2021) 115-135 126 aggregation of weight coefficients from all of them was performed and the weight coefficients were obtained, which were further used when choosing the firing position of the 120 mm mortar using the mabac method. step 1: for the most important, the e1 expert chose criterion c2. step 2: the criteria are classified into three levels: s1 = {c2,c8, s2 = {c1,c6,c4, s3 = {c7,c5,c3. step 3: based on expression (2), the maximum value of the scale for comparing the criteria is defined r = max {|s1|, |s2|, |s3| = 3 based on the comparison of criteria according to their significance, c2 gets the value i2 = 0 as the most significant criterion, while other criteria according to their importance in their sub-levels, get the following values: s1: i8=1; s2: i1=1, i6=2, i4=4; s3: i7=1, i5=3, i3=3. step 4: based on the defined maximum value of the scale for comparing the criteria r = 3, the coefficient of elasticity r0 = 4 is defined. step 5: using expression (3), the influence functions of the criteria were calculated: 2 8 1 6 4 7 5 3 4 4 ( ) 1, ( ) 0.8, 1* 4 0 1* 4 1 4 4 4 ( ) 0.444, ( ) 0.4, ( ) 0.333, 2 * 4 1 2 * 4 2 2 * 4 4 4 4 4 ( ) 0.308, ( ) 0.267, ( ) 0.267 3* 4 1 3* 4 3 3* 4 3 f c f c f c f c f c f c f c f c = = = = + + = = = = = = + + + = = = = = = + + + step 6: using expression (4), the weight coefficient of the most influential criterion was obtained 2 1 0.262 1 0.8 0.444 0.4 0.333 0.308 0.267 0.267 w = = + + + + + + + while the values of weight coefficients of the remaining criteria were obtained by applying the expression (5): 1 3 8 0.262 * 0.444 0.116, 0.262 * 0.267 0.209, ... 0.262 * 0.8 0.209. w w w = = = = = = based on the previous, the vector of expert weight coefficients (e1) was obtained: selection of fire position of mortar units using lbwa and fuzzy mabac model 127 wj1=(0.116, 0.262, 0.070, 0.087, 0.070, 0.105, 0.081, 0.209). using the expression (6), the aggregation of weight coefficients obtained from the experts was performed, on the basis of which a vector of weight coefficients was formed: wj =(0.187, 0.234, 0.072, 0.104, 0.094, 0.085, 0.067, 0.156). after determining the weight coefficients of the criteria, it is possible to move on to the next phase of the model. 4.3. choosing the best alternative using the fuzzy mabac method the third phase of the model involves selecting the best alternative for the firing position using the fuzzy mabac method as described previously. the paper discusses six potential locations-alternatives to the firing position of the mortar unit. the characteristics of the considered locations were obtained by the intelligence-reconnaissance work of the superior command. step 1. the first step is to form the initial matrix according to expression (9), which is shown in tables 5 and 6. table 5 shows the initial decision matrix. numerical and linguistic values are given for the considered alternatives according to the stated criteria. table 5. initial decision matrix alt. criteria c1 (min) c2 (max) c3 (max) c4 (max) c5 (min) c6 (min) c7 (max) c8 (min) a1 5850 s e g s c g 1000 a2 4925 ss g e m r e 950 a3 3762 ds g e l r e 1250 a4 4558 ss b g m c g 1187 a5 5321 s e b s c b 1530 a6 4789 s g g l r g 1987 wi 0.187 0.234 0.072 0.104 0.094 0.085 0.067 0.156 linguistic values, in table 6, are quantified into numerical ones. criterion c2 is shown as a real number after quantification while criteria c3 to c7 are shown as triangular fuzzy numbers. table 6. quantification of the initial decision matrix alt criteria c1 (min) c2 (max) c3 (max) c4 (max) c5 (min) c6 (min) c7 (max) c8 (min) a1 5850 5 (4, 5, 5) (2, 3, 5) (0, 2, 3.5) (0, 450, 600) (2, 3, 5) 1000 a2 4925 3 (2, 3, 5) (4, 5, 5) (2.5, 4, 5.5) (480, 640, 1000) (4, 5, 5) 950 a3 3762 1 (2, 3, 5) (4, 5, 5) (4.5, 6, 7.5) (480, 640, 1000) (4, 5, 5) 1250 a4 4558 3 (0, 1, 3) (2, 3, 5) (2.5, 4, 5.5) (0, 450, 600) (2, 3, 5) 1187 a5 5321 5 (4, 5, 5) (0, 1, 3) (0, 2, 3.5) (0, 450, 600) (0, 1, 3) 1530 a6 4789 5 (2, 3, 5) (2, 3, 5) (4.5, 6, 7.5) (480, 640, 1000) (2, 3, 5) 1987 jokić et al./oper. res. eng. sci. theor. appl. 4 (1) (2021) 115-135 128 step 2. normalization of initial matrix elements (x). normalization of elements from the confirmed initial decision matrix was performed using expressions (11) and (12), and the results are shown in table 7. table 7. normalized matrix (n) alt. criteria c1 (min) c2 (max) c3 (max) … c7 (max) c8 (min) a1 0 1 (0.8, 1, 1) … (0.4, 0.6, 1) 0.952 a2 0.443 0.500 (0.4, 0.6, 1) … (0.8, 1, 1) 1 a3 1.000 0.000 (0.4, 0.6, 1) … (0.8, 1, 1) 0.771 a4 0.619 0.500 (0, 0.2, 0.6) … (0.4, 0.6, 1) 0.771 a5 0.253 1.000 (0.8, 1, 1) … (0, 0.2, 0.6) 0.441 a6 0.508 1.000 (0.4, 0.6, 1) … (0.4, 0.6, 1) 0 step 3. calculation of elements from a weighted matrix (v). the elements from the weighted matrix (v) are calculated on the basis of expression (13) which is shown in table 8. table 8. difficult normalized matrix (v) alt. criteria c1 (min) c2 (max) c3 (max) … c7 (max) c8 (min) a1 0.187 0.468 (0.130, 0.144, 0.144) … (0.094, 0.107, 0.134) 0.305 a2 0.270 0.351 (0.101, 0.115, 0.144) … (0.120, 0.134, 0.134) 0.312 a3 0.374 0.234 (0.101, 0.115, 0.144) … (0.120, 0.134, 0.134) 0.267 a4 0.303 0.351 (0.072, 0.087, 0.115) … (0.094, 0.107, 0.134) 0.277 a5 0.234 0.469 (0.130, 0.144, 0.144) … (0.067, 0.080, 0.107) 0.225 a6 0.282 0.469 (0.101, 0.115, 0.144) … (0.094, 0.107, 0.134) 0.156 step 4. determination of the boundary approximate domain matrix (g) the boundary approximate area was obtained by applying expression (15), which is shown in table 9. table 9. boundary approximate domain matrix baa criteria c1 (min) c2 (max) c3 (max) … c7 (max) c8 (min) gi 0.269 0.379 (0.104, 0.118, 0.139) … (0.096, 0.110, 0.129) 0.251 step 5. calculating the distance of the alternative from the area of the approximate boundary for the matrix elements ( q ) the distance of alternatives from baa was obtained by applying expressions (18) and (19), table 10. selection of fire position of mortar units using lbwa and fuzzy mabac model 129 table 10. matrix distance alternatives from baa alt. criteria c1 (min) c2 (max) c3 (max) … c7 (max) c8 (min) a1 -0.082 0.089 (-0.009, 0.026, 0.040) … (-0.035,-0.003, 0.038) 0.054 a2 0.001 -0.028 (-0.038,-0.003, 0.040) … (-0.009, 0.024, 0.038) 0.062 a3 0.105 -0.145 (-0.038,-0.003, 0.040) … (-0.009, 0.024, 0.038) 0.017 a4 0.034 -0.028 (-0.067,-0.032, 0.012) … (-0.035,-0.003, 0.038) 0.026 a5 -0.035 0.089 (-0.009, 0.026, 0.040) … (-0.062,-0.030, 0.011) -0.026 a6 0.013 0.089 (-0.038,-0.003, 0.040) … (-0.035,-0.003, 0.038) -0.094 step 6. ranking alternatives. to make it easier to represent the final rank of the alternatives using expression (8) the triangular fuzzy number is translated into a real number. according to expression (20), by calculating the sum of the elements of the matrix q by rows, the final values of the criterion functions of the alternatives were obtained, which is shown in table 11. table 11. rank of alternatives by mabac method alt. criteria qj ran k c1 (min) c2 (max) c3 (max) c4 (max) c5 (min) c6 (min) c7 (max) c8 (min) a1 -0.082 0.089 0.022 -0.002 0.027 0.012 -0.002 0.054 0.120 1 a2 0.001 -0.028 -0.002 0.032 0.001 -0.011 0.021 0.062 0.077 2 a3 0.105 -0.145 -0.002 0.032 -0.024 -0.011 0.021 0.017 -0.006 5 a4 0.034 -0.028 -0.030 -0.002 0.001 0.012 -0.002 0.026 0.011 4 a5 -0.035 0.089 0.022 -0.044 0.027 0.012 -0.028 -0.026 0.019 3 a6 0.013 0.089 -0.002 -0.002 -0.024 -0.011 -0.002 -0.094 -0.032 6 based on the obtained results, it is concluded that alternative a1 is ranked first, ie that the ranking of alternatives is as follows: a1 > a2 > a5 > a4 > a3 > a6. 4.4. sensitivity analysis the fourth phase includes testing the sensitivity of the applied model, in order for the decision-maker to receive confirmation of the quality of the obtained solution, ie to determine how changes in the weight of criteria lead to changes in alternative ranks (tešić & božanić, 2018; durmić et al., 2020). checking the stability of the used methods of multi-criteria decision-making is an indispensable step in the process of developing a model to support decision-making (pamučar et al., 2017). stability was examined by changing the weight coefficients wi, ie by changing the value of the coefficient of elasticity r0, whose value in the work is r0 = 4. table 12 shows the influence of the value of r0 on the change in the rank of the alternative: jokić et al./oper. res. eng. sci. theor. appl. 4 (1) (2021) 115-135 130 table 12: rank alternative depending on r0 alt. r0 = 4 r0 = 5 r0 = 6-9 r0 = 10-20 a1 1 1 1 1 a2 2 2 2 2 a3 5 5 5 4 a4 4 4 3 3 a5 3 3 4 5 a6 6 6 6 6 based on table 12, it can be noticed that with the change of the weight coefficient, ie the coefficient of elasticity, the model shows stability. three alternatives (a1, a2 and a6) retain the rank regardless of the value of r0 while the other alternatives suffer changes of rank for r0 = 5, r0 = 6 and r0 = 10. for the values r0 = 7, r0 = 8 and r0 = 9, the rank is identical as for r0 = 6. also, for r0 = 11-20 the rank is identical as for r0 = 10. in order to establish the correlation of the ranks obtained by changing r0, the spearman coefficient was used as in expression (20): n 2 i i 1 2 6 d s 1 n(n 1) == − −  (21) where di represents the difference of rank according to the given r0 and rank in the corresponding r0, and n the number of ranked alternatives. the spiraman coefficient belongs to the value interval [-1,1] (radovanović et al., 2020). when the ranks of the alternatives completely match the spearman coefficient is 1 (“ideal positive correlation”), when the ranks are completely opposite the spearman coefficient is -1 (“ideal negative correlation”), ie when s = 0 the ranks are uncorrelated. the values of the spearman coefficient for the considered problem are shown in table 13. table 13: spearman coefficient values r0 = 4 r0 = 5 r0 = 6-9 r0 = 10-20 r0 = 4 1 1 0.94 0.83 r0 = 5 1 0.94 0.83 r0 = 6-9 1 0.94 r0 = 10-20 1 from the results shown in table 13, it can be concluded that the values of the spearman coefficient for all values of r0 are extremely high, ie that there is an ideal positive correlation of ranks. there is no deviation from the ideal positive correlation as well as the negative correlation. based on the above, it is possible to conclude that the model has sufficient sensitivity. 5. conclusion on a hybrid model based on the lbwa and fuzzy mabac method, the paper explains the process of creating a multi-criteria decision model. through a multicriteria model, the paper solves the problem of choosing the location of the firing selection of fire position of mortar units using lbwa and fuzzy mabac model 131 position for mortar units of company size mb 120 mm, which has not been considered in this way in the existing literature so far. the paper describes in detail the steps of the lbwa and fuzzy mabac methods. the experts determined eight criteria for influencing the choice of firing position. further, the experts identified the most significant criterion, defined the levels of significance and determined the values of the criteria by levels. part of the criteria, of the linguistic type, obtained numerical values using fuzzy linguistic and linguistic descriptors. as the best choice-alternative, the mabac method suggests the a1 alternative. alternative a1 in relation to the others, has the largest battle of criteria belonging to the above approximate domain. as the last phase, the sensitivity analysis of the presented model was performed in the paper, by changes in the weight coefficients of the criteria (by changing the coefficient of elasticity) from r0 = 4 to r0 = 20. the results of the analysis indicate sufficient stability of the model. the first-ranked alternative a1 retains the first position regardless of the growth of the coefficient of elasticity r0. also, the spearman coefficient has a great value, which shows that there is an ideal positive correlation of ranks. based on the existing literature, the lbwa method has not been combined with the mabac method so far. based on the results, presented in the model, it is 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(2019). new model for determining criteria weights: level based weight assessment (lbwa) model. decision making: applications in management and engineering, 2(2), 126-137. © 2021 by the authors. submitted for possible open access publication under the terms and conditions of the creative commons attribution (cc by) license (http://creativecommons.org/licenses/by/4.0/). selection of fire position of mortar units using lbwa and fuzzy mabac model željko jokić*, darko božanić, dragan pamučar 1. introduction 2. the place and role of mortars in contemporary combat actions 3. description of the method 3.1. level based weight assessment (lbwa) model 3.2 fuzzy sets 3.3. fuzzy mabac method multi-attributive border approximation area comparasion (mabac) 4. application of the hybrid model of multi-criteria decision making 4.1. criteria for choosing the firing position 4.2. calculation of weight coefficients of criteria using lbwa method 4.3. choosing the best alternative using the fuzzy mabac method 4.4. sensitivity analysis 5. conclusion references operational research in engineering sciences: theory and applications vol. 4, issue 2, 2021, pp. 79-101 issn: 2620-1607 eissn: 2620-1747 doi: https://doi.org/10.31181/oresta20402079n * corresponding author. mgnaikc@gmail.com (m. gopal naik), kravande58@gmail.com (k. ravande), salimousavi.d32@gmail.com (s.a mousavi dehmourdi) modeling a multi-criteria decision support system for prequalification assessment of construction contractors using critic and edas models m. gopal naik, ravande kishore, seyed ali mousavi dehmourdi* department of civil engineering, uce, osmania university, telangana state, india received: 16 february 2021 accepted: 26 april 2021 first online: 01 july 2021 research paper abstract: contractor prequalification assessment in the construction industry is an essential part of the project development process because contractors play a pivotal role in the extension of projects and resources. the main objective of the present study is comprised prequalification assessment for classifying contractors by applied the edas method for recognizing the contractors' potential before competitive tendering and obtaining bids. first, an inclusive, detailed list of 56 sub-factors under 5 main factors for project prequalification was compiled following a thorough literature review, and review of contractors by experts of bandar imam khomeini municipality who already have done projects with contractors. second, used the critic method for obtained the weighing and importance of each factor. third, classified the contractors by applied the edas system for recognizing the contractors' potential before competitive tendering and obtaining bids. finally, the prequalification assessment process was developed to obtaining the rank of each contractor and help the stakeholders to select the right contractors. the effectiveness of the present approach was tested by applying it to a case study of the prequalification assessment of four construction companies' in bandar imam khomeini municipality, khuzestan, iran. it is worth mentioning that the prequalification assessment by the proposed approach is approved by the project stakeholders and is consistent with their expectations. it can be concluded that based on relevant ranking and weighing of companies that procedure can be extended to the same studies in this regard, and the contribution of the present study is to propose a support system for prequalification and identification of contractors' ability, before assigning projects to companies for success in projects. keywords: support system, contractor prequalification, mcdm, critic, edas mailto:salimousavi.d32@gmail.com https://link.springer.com/article/10.1007/s11269-008-9288-y#auth-1 gopal naik et al./ oper. res. eng. sci. theor. appl. 4(2) (2021) 79-101 80 1. introduction construction plays a key role in any economy; henceforth, it is important to push forward and support the construction industry for developing the countries suffering from under development. the gross output of the construction industry is the value of all the buildings and works produced by the industry in a given period of time, normally a year. in the world as a whole, it is probably about 10 percent of gross national product (xu et al., 2020). in most developing economies around the world, the construction industry plays a significant role in the economy and can be hailed by the government as a platform to stimulate national economic transformation towards the status of a developed country (mat isa et al., 2015). in the concern of developing the countries, the construction industry is typically the alarm for financial growth and the main producer of skilled occupations. important challenges in presentation, productivity, labor, and sustainability contains undermined industry reliability and growth. despite extensive studies, the development of the industry has shown slow progress. it is almost certain that the existing construction studies have contributed a lot to sympathetic the major causes and consequences of construction issues. therefore, poor presentation in construction developments remains a worldwide marvel (yap et al., 2019). the construction industry in iran is challenged with other glitches such as unpredictability in the cost of material, wobbliness in production and investment laws and guidelines, the frailty of transportation infrastructure, international sanctions etc. furthermore, the selection of suitable contractors also is a major crisis for the entire world and majorly for iran construction industries (poloie et al., 2012). construction contractors play an important part in any construction projects, for the successful or unsuccessful release of projects, that's why contractor selection is the most critical decision for project. the selection process should embrace the investigation of contractors’ potential to deliver a service of an acceptable standard, on time, and budget (topcu, 2004). khuzestan province is the major oil-producing region of iran, and is also one of the wealthiest provinces in iran. khuzestan ranks third among iran's provinces in gdp. the highest construction budget in the whole country was allocated to khuzestan, iran in 2019. the government construction budget was $ 226,732,000 for the khuzestan province in 2019. the municipality’s construction budget of khuzestan province allocated around $ 125,224,000 in 2019 in khuzestan province, iran. according to the interview of the mayor of bandar imam khomeini, 350 active construction projects were running there in 2017. one of the main functions of the plan and budget organization (pbo) is to take the assessment of iranian contractors, considering criteria and capacity qualifying in five grade terms of throughput and from large to small ranked as follows, contractors ranking from level one to level five. numerous factors are influential in determining the rank and grade of a contracting company. educational and work records of the board members and staff of the company, work records of the company, the status of financial accounts, etc. therefore, this paper tries to make a support system for the prequalification of contractors within the enterprise, that an organization or client can recognize the potential of the contractor before competitive tendering and obtaining bids. prequalification is an important part of the process of finding the right contractor for the project. therefore, this research attempts to make certain distinctions and classification between contractors, which are at the same level. based on the author's point of view, there is a difference between the contractor who has five years’ https://link.springer.com/article/10.1007/s11269-008-9288-y#auth-1 modeling a multi-criteria decision support system for prequalification assessment of construction contractors using critic and edas models 81 experience with that who has only one-year experience where both of them are in the same rank; thus offering a particular classification between contractors who are at the same rank is requirement. the necessity in the system for the prequalification assessment of construction contractors (iran) gets back to the lack of relevant study comprising of the need to put the required qualifications in a frame for the identification of contractors' ability, before assigning projects to companies. therefore, our efforts were focused to propose a support system for the assessment of construction contractors. success in any construction project majorly depends on choosing the right contractors, contractor prequalification is a process that is widely used to select responsible and competent contractors to perform the construction contract and provide the desired results with minimal damage, because potential contractors are measured and judged according to a set of common criteria, the contractor's prequalification can be considered as a multi-criteria decision issue (nieto-morote & ruz-vila, 2012). the present study focuses on exploring support system for the prequalification assessment of contractors by offering a review of literature to identifying the various assessment criteria of construction contractor. first, various assessment criteria of construction contractor are identified from available literature and categorized to secure the five prominently used performance measures of a firm, namely: general information, financial aspect, technical and equipment information, management information, professional experience information of companies in the framework of a questionnaire. developing a frame for contractors' prequalification assessment through mcdm practices is an essential step for project owner's for recognizing the potential of construction contractors to address their variable future needs. few studies discuss how prequalification assessments are essential for sustaining the competitive advantage of a construction project as a whole, and no proper classifications and guidelines exist to classify contractors holding the same rank. hence, this study focuses on: i. identifying various construction contractor assessment criteria from the existing literature. ii. recognizing the contractors' potential before the tender process. iii. classifying contractors, which are holding the same rank. the most important message from this research is prequalification of contractors within the enterprise, that an organization or client can recognize the potential of the contractor before the tender process. contractor selection is a critical activity that plays a major role in the success of the projects؛ and prequalification is an important part of the contractor selection process of finding the right contractor for the project. 2. literature review awad & fayek (2012) recognized and categorized the most significant assessment factors that guarantee applicants and brokers considerations when assessing a particular construction project for runway purposes. they used many data collection methods such as interviews, questionnaires, and interacting meetings, with highly experienced experts, which were conducted to compile a comprehensive and detailed list of the evaluation criteria. for solution methodology, they used fuzzy logic and expert systems mutual to grow a decision support system for applying in contractor and project assessment. they asserted that the strategic system could gopal naik et al./ oper. res. eng. sci. theor. appl. 4(2) (2021) 79-101 82 assist contractors to self-assess and to recognize areas for promotion to better get an attachment for construction projects. ng (2001) demonstrated the performance and presentation of the method by analyzing with the theoretical system, which is called case-based reasoning system that can help expert and decision-makers to additional reliable, prompt decisions for the contractor's prequalification dimension and offer as a new case for formulating factors for the contractor's prequalification for expert judgment. experimental results show that the satisfied and the case-based reasoning system is appropriate for modeling the scope of the contractor's prequalification. el-sawalhi et al., (2007) established a state-of-the-art system for prequalification based on combining the merits of the ahp, neural network, and genetic algorithm in one consolidated model, which is able to overcome the limitations of the published system. they used this method in the gaza strip and west bank and all sub-criteria will be tested via an email questionnaire to reach a consensus for achieving that prequalification that is suitable to be adopted. the proposed genetic-neural network model will overcome most of the disadvantages of published models, particularly the accuracy of the model outputs and the prediction of the contractor’s performance. nieto-morote and ruz-vila, (2012) researched a case study for the rehabilitation project of a building at the university polytechnic of cartagena is presented to illustrate the use of the proposed model and linguistic assessment or exact assessment of the performance of the contractors on qualitative or quantitative criterion, respectively, they suggested system provides a systematic scaffold for contractor assessment in a fuzzy environment that can be easily extended to the analysis of other classification problems in project management. kishore et al., (2020) developed a framework for construction subcontractor’s selection, they used ahp and saw method for analyzing data, in a real case study in iran khuzestan's presence, for collecting quantitative data from main contractors and subcontractors applied a prequalification assessment, finally, the result showed the priority in subcontractors' selection as hejrat manesh izeh (i), khesht sazan karoun (ii), yeganeh saze omid (iii), sakht karan moongasht (iv), darya sanat khavarmianeh (v), omran mehragane yosef (vi) respectively. jafari (2013) investigated the central aims of prequalification to recognize an array of appropriate contractors that are required for postqualification steps and further considerations, proposed a novel contractor prequalification model with the goal of deciding this issue, he used quality function deployment to involve the ‘voice of the project owners’ through the prequalification of contractors in the construction projects, this model employs the quality function placement system and reflects the project owner’s needs and the contractor’s abilities, used a numerical example and found that the thought of the project goals or the project owner’s needs and prospects can influence contractor prequalification. khosrowshahi (1999) suggested the artificial neural network as the most suitable technique to grade contractors, because of its competence to process the noisy data, and thus reliable for building a non-linear association among the score of the individual criterion and its impact on the decision to be made. ka chi lam and yu, (2011) developed a novel technique for contractor prequalification, which is called the multiple kernel learning method, hence, the capability of the multiple kernel learning method was compared with support vector machine models through a case study, from the outcome, it has been shown that both method perform well in classification, and multiple kernel-learning model is better than support vector machine models. https://link.springer.com/article/10.1007/s11269-008-9288-y#auth-1 modeling a multi-criteria decision support system for prequalification assessment of construction contractors using critic and edas models 83 sönmez et al., (2002) investigated a contractor prequalification problem to show how the evidential reasoning approach can overcome this issue; used the dumpstershafer theory to obtain partial evidence for an acceptable conclusion, finally the proposed method, the evidential reasoning approach, makes the concept of degree of belief. sacks and harel (2006) proposed an economical game theory approach for understanding the behavior of subcontractors in assigning resources to projects and the influences on workflow constancy applied in gaming theory. the study asserted that impractical scheduling and over-commitments of subcontractors in manifold projects jeopardize the relations between the supervisors or managers and the subcontractors and thus, achieving success in projects. finally suggested into thought subcontractors' behaviors across organizational, social, and technical aspects as pre-qualification criteria in instruction to control possible achievement goals in projects. banaitiene and banaitis, (2006) studied on the criteria employed for contractor selection and assessment of bid tender offer in lithuania and abroad, which analyzes issues related to the evaluation of contractors' qualifications, the data was collected from the questionnaire survey, the outcomes presented that the proposals are based on experts' estimates of the weight of contractors' evaluation criteria. finally, the finding indicated three main weights of contractor evaluation criteria such as (i) bid price (ii) legal activity (iii) contractor adequacy. kukoyi et al., (2021) determined the prequalification of selecting construction project contractors using health and safety criteria cronbach’s alpha was used to test the reliability of the questionnaire used for data collection, the results show that health and safety is not a clients’ goal or a project value hence, health and safety are not viewed as a vital pre-qualification criterion for contractor selection. acheamfour et al., (2019) declared that contractors’ prequalification models that considered clients’ objectives only focused on cost, time, and quality as criteria for selection. furthermore, associating the lowest bidder with a satisfactory project outcome is not the best act. duarte and sousa, (2020) developed a simple and fast supply chain partner prequalification process, which agrees to a questionnaire, an automatic assessment, and a classification method, used the prequalification questionnaire and the questionnaire consists of grouped questions, the main achievement was the managers' lack of familiarity with analysis and improvement techniques, the difficulty of defining quality. landy et al., (2020) figuring out the service quality factors that are considered more important in the construction sector, the procedure was documental and based on a review of articles obtained from major scientific databases, the result shows that in all cases, the traditional models of service quality were used as guidelines to explain and adapt to specific contexts, overall, the results indicate a generalized conservative approach that characterizes this sector. acheamfour et al., (2019) investigated the impact of contractors prequalification on construction project delivery with empirical arguments and has given some recommendations regarding success in construction project delivery performance in terms of time and quality in the adoption of due process, not minding the cost of the project, the contractual qualification building projects’ time delays, finances the fund’s credentials and project characteristics and cost increases are closely linked to contractors' qualifications criteria. patil et al., (2020) evaluated five criteria along with their sub criteria for contractor prequalification, such as technical considerations, management considerations, financial considerations, reputation gopal naik et al./ oper. res. eng. sci. theor. appl. 4(2) (2021) 79-101 84 considerations and health, safety and environmental considerations, figuring out the top three causes of inadequate contractor prequalification, the outcome shows serves as the fundamental for further experiential studies on contractor prequalification criteria. (adedokun, 2020) identified the significant factors for the selection of contractors in construction projects, for data collection used 120 questionnaire surveys adopted, observed that capital bid, financial status, experience, the experience of technical personnel, and client-contractor relationship are the most important sub-factors for contractors’ prequalification. (khoso et al., 2020) investigated the most suitable criteria for the pre-qualification process for pakistan construction projects, data collection gathered through interviews and floating several questionnaires, for data analysis applied computer software, observed that the most important factors are experience and past performance, financial stability, personnel capabilities, equipment capabilities, and managerial capabilities. doloi (2009) studied prequalification criteria in contractor selection and impacts of contractor selection on project success, selected criteria (43 cases) for evaluating project performance through multiple linear regression models, applied a questionnaire survey and expert opinion to data collection. jaskowski et al., (2010) based on the questionnaire survey tried to find the right contractor in the prequalification step, applied an example that illustrates this approach to determine criteria weights for bidder assessment, the findings passed through the pairwise comparison, ahp weighing system, and fuzzy set theory with the emergency of pertinent outcomes in the assay. the outcomes demonstrated that the offered fuzzy ahp method is superior to the classic ahp in terms of developed excellence of criteria prioritization. rashvand et al., (2015) developed a comprehensive contractor assessment system that directly addresses the contractor's abilities and practices as a critical element at the prequalification stage, analyzed data based on an analytic network project model, the results showed that this model evaluated scores that are the effectiveness of a contractor's management ability. k c lam et al., (2000) introduced a model to support contractor prequalification selection using artificial neural networks. the prequalification assessment of the contractor has been done via an extension of the multi-kernel learning model based on the questionnaire. the following step verified results via sensitivity analysis of a few decision support systems that were actually algorithms measurement (ka chi lam & yu, 2011). korytárová et al., (2015) completed the research based on 345 tenders for public works contracts in the czech republic and compared the results with the projects in poland from 2013-2014, the data collected from official databases; the significant differences appeared in two areas of professional experiences and economic and financial qualifications. a study used the support vector regression model to select the contractor with relevant results for 250 virtual contractors. awad and fayek (2012) used questionnaires, face-to-face and individual interviews, and interacting group meetings, with highly experienced experts for contractor selection. therefore, 38 alternatives and 32 prequalification cases were chosen to configure the dimensions of the decision-making system with an accuracy of up to 84.0%, and developed a new pre-qualification method using a quality function deployment technique based on availability and requirements of the project and contractor. attar et al., (2013) proposed a method to support vector machine that has been based on the forecast of a contractor's deviation from a client's objectives, for analyzing the https://link.springer.com/article/10.1007/s11269-008-9288-y#auth-1 modeling a multi-criteria decision support system for prequalification assessment of construction contractors using critic and edas models 85 system, contractor prequalification for two hundred and fifty contractors was solved, they believe that the suggested system had a great generalization in linear, nonlinear, noisy, and inductive environments. the results showed that support vector machines could reliably perform even with a small amount of training data. contractors’ prequalification models that considered clients’ objectives only focused on cost, time, and quality as criteria for selection; furthermore, associating the lowest bidder with a satisfactory project outcome is not the best practice, insights on various prequalification criteria can have positive impacts on projects (acheamfour et al., 2019). chen et al., (2021) proposed an integrated subjective-goal approach to calculate criterion weights and to put into effect an electre iii-based method that incorporates that consists of hflts opportunity distributions, which permit treating the indetermination, imprecision, and uncertainty embedded in value determinations of alternative-criterion selections whilst comparing bids. prasetia and imaroh (2020) developed an approach for carrying out an evaluation of the contractor's selection/providers in the upstream oil and gas industry with the goal of enforcing green supply chain management with the ahp method, the result shows that the two most important criteria are environmental criteria and health and safety criteria. marović et al., (2021) developed an analytic hierarchy process (ahp) together with promethee for selecting the optimal contractor, the result of their synergy were proposed that: (i) allows the incorporation of opposing stakeholders’ demands; (ii) increases the transparency of decision-making and the consistency of the decision-making process; (iii) enhances the legitimacy of the outcome. kukoyi et al., (2021) determining the reasons for clients contending with contractors that are not committed to health and safety, using a questionnaire for data collection, and mean scores for data analysis, finally provided information on influence clients to have to respect health and safety as a prequalification criterion and towards construction workers’ health and safety. dehmourdi et al., (2021) studied the impact of the crisis in construction projects, using the critic method to the weighting of crisis factors and waspas method to find out the most influential crisis factors and made a case study of ‟khuzestan province (iran), finally, observed that most influential crisis factors in the khuzestan construction industry are the economic crisis, followed by the market and real estate. okifitriana latief (2021) developed the quality management system (qms) for the construction services procurement process to improve the quality of contractor performance in universities indonesia, used the survey, and statistical analysis for data analysis, and finally developed a quality management system for the construction services procurement process in universities indonesia. afshar et al., (2017) proposed a practical prequalification technique for contractor assessment that uses interval type-2 fuzzy sets to report both linguistic imprecision and differences of opinions, they solve a numerical example has been presented to exemplify how the prequalification technique is carried out using type-1 and type-2 fuzzy sets. associating the outcomes shows the effect of preserving the erraticism of the evidence in the chain of reasoning. the contractor prequalification assessment is a screening instrument by the in-charge staff, client, and project supervisor based on a certain and defined framework where lots of criteria and factors are allocated to be processed by a variety of mcdm models (russell & skibniewski, 1988). topcu (2004) provided a new framework based on the mcdm models for the construction contractor and suggested to the turkish public sector, the system suggested that three key goals have been produced for gopal naik et al./ oper. res. eng. sci. theor. appl. 4(2) (2021) 79-101 86 assortments as cost, time, and quality, they asserted this model can be used as a decision support system by the project owners in order to recognize the most appropriate contractor that will be given the contract. nassar and hosny (2013) 294 projects passed through the prequalification assessment for contractor selection in uae, the mcdm models of the ahp and fuzzy algorithm used to categorize the companies for the projects pertain to quantitative and qualitative measures. keshavarz ghorabaee et al., (2015) proposed a new approach for the edas, in the suggested approach of the system; according to positive and negative distances from the mean solution to evaluate the options, to prove the performance of the proposed method in the multi-criteria cataloguing issue, it is mentionable for better understanding they used a mutual example, asserted that the proposed method could be used for multi-criteria decision-making problems, associated the proposed method with vikor, topsis, saw, and copras as a numerical example. they observed that the suggested method is steady at dissimilar weights and is consistent with other methods. kazan and ozdemir (2014) studied financial ratios of economical statements of the fourteen-large scale conglomerates, which traded on ise, used the critic weights method to calculate nineteen criteria over three periods (2009-2011), and found their financial ratio weights. then among multicriteria decision-making methods, the topsis method was employed to measure and evaluate the performances of 14 large-scale ise-listed conglomerates. kahraman et al., (2017) suggested that the intuitive fuzzy edas method used to evaluate the options for selecting a solid waste disposal site; comparative analysis and sensitivity are also included. sensitivity analysis is also given to show how strong decisions are made intuitively through fuzzy edas. liang et al., (2018) evaluated a case of the cleaner production performance for four gold mines is provided to explain the application of the proposed method, first determined the comprehensive criteria weights obtained from the combined criteria weights extended swara model, a systematic comparison analysis with other existent methods is conducted to reveal the advantages of our method, in the last phases obtaining the ranking orders results indicate that the integrated edas-electre method is suitable and effective for gold mines to evaluate their cleaner production performance, and has important reference values for the cleaner production management and operation. adalı and işık (2017) evaluated four contract builder options using the critic method and maut methods. for achieving the importance of criteria used critic method, while the complete ranking of the contract builder options obtained using maut, and then the output it is important to work with the right contract manufacturer to gain a competitive advantage, they believe critic and maut solve the problems of selecting a contractor for a textile company. žižović et al., (2020) proposed a new method in modifying the (critic) method, which waterfalls underneath objective methods for decisive factors weight constants, by presenting a new procedure of combination of weight constant values in the critic-m method, a more complete sympathetic of data in the initial decision matrix was made possible, foremost to additional objective values of weight constants, therefore, the relations between information in the initial decision matrix are obtainable in a more objective solution. maheshwari et al., (2021) developed a finite element model for a ventilated brake disc is developed to numerically simulate the fatigue life and axial deflection, for data analyses and compare the various design parameter combinations, multi-criteria decision-making such as aras, edas, copras, fea, mcdm and topsis are used. applied topsis to optimize process https://link.springer.com/article/10.1007/s11269-008-9288-y#auth-1 modeling a multi-criteria decision support system for prequalification assessment of construction contractors using critic and edas models 87 parameters of the vibration-assisted turning process; also investigated edas method in a broad range of technological systems to engineering problems. (ghorabaee et al., 2018). mousavi-nasab and sotoudeh-anvari (2017) reviewed application of mcdm techniques including edas in the field of material selection. similarly, copras (complex proportional assessment) is an advanced mcdm methodology, which is based on the evaluation of alternatives to the solution of the problem proportionately. zavadskas et al., (2019) introduced a new technique based on edas in the minkowski space (edas-m), which was the modified extension of conventional edas approach. to develop the proposed plan, they used critic method for obtaining the objective criteria weights, applied seven unusual methods for comparing their plan to validate the efficiency and effectiveness of the proposed method. developed the fuzzy evaluation based on distance from average solution (fuzzy edas) method for resolving the air-handling unit and the heating, ventilating and air conditioning system and its supplier collection problem for a green multifunctional shopping center project located in russia, sensitivity analysis was approved out to show the constancy of the consequences (polat & bayhan, 2020). the foremost aim for the applied edas method is to allow both the calculating the criteria weights and ranking the alternatives in a simple and easy way. if other mcdm methods such as copras, fuzzy aras, vikor, moora, were chosen, they should have been integrated with the criteria weighting methods such as ahp, which would complicate the problem (stević et al., 2018). 3. methodology the solution methodology applied for the present study is the critic method for obtaining the importance and influence of contractor assessment factors and the edas system for recognizing the contractors' potential before competitive tendering and obtaining bids. a questionnaire was designed to collect the initial matrix of data. to determine the weight of each criterion used as per the weighing system of critic concerning the variables. the members who participated to complete the assessment program were those who were in close connection with the contractor and supervisors of the project, around 4 members. in the present case study, four construction companies including daghigh koshan sepahan, hejrat manesh eizeh, hemat talash, and omran mehran mongasht were assessed to get the contractor prequalification ranking levels. in addition, the contractors participated in tendering the project and evaluated in the bandar imam khomeini municipality, khuzestan, iran. for obtaining the importance of each sub-factor using the critic method and for classifying and ranking of the contractors by applying the edas system for recognizing the contractors' potential before competitive tendering and obtaining bids. the studied contractors are from the same competence ranking (rank 5) obtained from in-charge the plan and budget organization (pbo) of iran. previous performance evaluation completed by staff who have related information with these companies in ways such as the director of the technical department, supervisor engineer, resident engineer, and consultant engineer. the sub-factors and main factors of assessment comprising the general ability, financial ability, technical and gopal naik et al./ oper. res. eng. sci. theor. appl. 4(2) (2021) 79-101 88 equipment ability, management ability, and professional experience of companies consists of 56 cases in this regard. many studies have analyzed construction contractor assessment in terms of their advantages and have produced conceptual frameworks. however, in iran scenario, additional research is needed to identify the potential of contractors who in the same rank, before competitive tendering and obtaining bids. this study proposes to: i. identify the essential contractors prequalification assessment factors from existing literature; ii. conduct a questionnaire-based survey from bandar imam khomeini municipality, khuzestan, iran experts to identify the importance of each factor; iii. conduct a second questionnaire-based survey with the same experts as respondents to obtain the potential of the four contractor; iv. apply critic system to find the total grade of the each factor; v. identify the rank and potential of each contractor through edas method. 3.1. critic method the mcdm models have always been associated with two factors and issues, one is the weighting of criteria and the other is the ranking of options. these two categories are complementary to each other, sometimes by one method and sometimes by a combination of methods. in this method, the data are analyzed based on the degree of interference and conflict between the factors or criteria. critic method of processing causes the role of each factor to be applied correctly in the results of the calculations. in the critic method, for each evaluation criterion, there is a range of variations of the measured values between the pixels (options), which are expressed in the form of a membership function. each of the components formed for the criteria used has statistical parameters such as standard deviation. these parameters represent the degree of difference in the relevant standard values. the critic method steps 1 to 3 as follows: step 1: the decision matrix x is formed, it shows the performance of different alternatives with respect to various criteria. (1) step 2: decision matrix is normalized data using the equation 1: (2) normalized performance value each sub-factors number step 3: while determining the criteria weights, both standard deviation of the criterion and its correlation between other criteria are included. (3) https://link.springer.com/article/10.1007/s11269-008-9288-y#auth-1 modeling a multi-criteria decision support system for prequalification assessment of construction contractors using critic and edas models 89 quantity of information contained standard deviation for determine the importance of each sub-factor used equation number 3. (4) 3.2. edas method the edas method is the best solution is the distance from the average solution. this method does not need to calculate the positive and negative ideals, but consider two criteria for evaluating the desirability of options; the first is a positive distance from the mean (pda) and the second is a negative distance from the mean (nda). these measures can show the difference between each option and the median solution. options are evaluated according to higher pda values and lower nda values. higher pda values or lower nda values indicate that the option is better (keshavarz ghorabaee et al., 2015). step 1: select the most important criteria that describe alternatives. step 2: construct the decision-making matrix (x), shown as follows where denotes the performance value of alternative on criterion. step 3: determine the average solution according to all criteria, shown as follows: (5) where, (6) step 4: calculate the positive distance from average (pda) and the negative distance from average (nda) matrixes according to the type of criteria (benefit and cost), shown as follows: if criterion is beneficial (7) (8) and if criterion is non-beneficial, (9) (10) gopal naik et al./ oper. res. eng. sci. theor. appl. 4(2) (2021) 79-101 90 where and denote the positive and negative distances of alternative from an average solution in terms of criterion, respectively. step 5: determine the weighted sum of pda and the weighted sum of nda for all alternatives, shown as follows: (11) (12) where is the weight of criterion. step 6: normalize the values of sp and sn for all alternatives, shown as follows: (13) (14) step 7: calculate the appraisal score (as) for all alternatives, shown as follows: (15) 4. results and discussion contractor prequalification assessment in the construction industry is an essential part of the project development process because contractors play a pivotal role in the extension of projects and resources. table 1. sub criteria of general information sub criteria critic daghigh koshan hejrat manesh hemat talash omran mehran sub criteria of general information weight appraisal score (as) 1 follow the extent of rules and regulations 0.0163 0.719 0.507 0.878 0.719 2 follow the extent of standard and specification 0.0163 0.629 0.507 0.548 0.2057 3 completeness of documents of firm 0.0163 0.629 0.169 0.125 0.360 4 quality of documents plans and drawings 0.0133 0.527 0.098 0.477 0.587 5 use the value engineering 0.0163 0.822 0.615 0.175 0.240 6 observance the health, safety, environment, and energy 0.0163 0.822 0.120 0.292 0.144 https://link.springer.com/article/10.1007/s11269-008-9288-y#auth-1 modeling a multi-criteria decision support system for prequalification assessment of construction contractors using critic and edas models 91 7 observance of rules 0.0163 0.091 0.676 0.878 0.205 8 environmental, labor and social security 0.0157 0.325 0.334 0.590 0.197 9 stability of board members and specialist staff 0.0163 0.476 0.094 0.585 0.449 prequalification is an important part of the process of selecting the right contractor for the project. whereas multiple criteria may contribute to prequalification measures, it is important to identify the essential assessment criteria. based on the on the present case study the following results are determined. table 1 shows the criteria of general information, appraisal score of each contractor, and total critic score of each criteria. according to result of critic method, the importance of most criteria in general information section almost match with each other. table 2. sub criteria of financial information sub criteria critic daghigh koshan hejrat manesh hemat talash omran mehran sub criteria of financial information weight appraisal score (as) 1 financial position of the contractor 0.0163 0.339 1.000 0.702 0.450 2 the liquidity of contractor 0.0232 0.130 0.172 0.624 0.292 3 total assets of contractor 0.0163 0.091 0.604 0.798 0.206 4 securities other than shares 0.0133 0.075 0.415 0.358 0.588 5 timely payment of wages of employees, agents, and subcontractors 0.0199 0.580 0.206 0.000 0.175 6 insurance to all facilities, equipment, and personnel against possible accidents 0.0163 0.476 0.348 0.439 0.540 7 shares and equity contractors in the bourse 0.0157 0.604 0.162 0.211 0.628 8 insurance technical provisions in the site of the contractor 0.0163 0.646 0.121 0.293 0.360 9 macroeconomic and financial developments in of contractor experience account 0.0163 0.476 0.716 0.251 0.000 10 balance sheet vulnerabilities of 0.0173 0.667 0.538 0.266 0.218 gopal naik et al./ oper. res. eng. sci. theor. appl. 4(2) (2021) 79-101 92 contractor 11 capital ratios of contractor 0.0163 0.494 0.508 0.251 0.000 12 standalone bank credit ratings which contractor has account 0.0227 0.127 0.484 0.610 0.333 from the table 2 it is observed the criteria of financial information, appraisal score of each contractor, and total critic score of each criteria. it is observed that the liquidity of contractor (sub criteria number 2) has most influential in this section. table 3. sub criteria of technical and equipment information sub criteria critic daghigh koshan hejrat manesh hemat talash omran mehran sub criteria of technical and equipment information weight appraisal score (as) 1 site preparation 0.0163 0.494 0.508 0.702 0.450 2 site amenities 0.0186 0.386 0.000 0.625 0.234 3 transportation facilities contractor 0.0232 0.130 0.687 0.416 0.205 4 provide communication and access ways 0.0227 0.000 0.705 0.610 0.714 5 status of site technical office 0.0227 0.229 0.588 0.174 1.000 6 quality of specifications standards 0.0163 0.091 0.121 0.251 0.514 7 using new technology 0.0227 1.000 0.588 0.348 0.000 8 quality and quantity of construction machines 0.0163 0.339 0.423 0.000 0.240 9 quality and quantity materials control 0.0163 0.629 0.423 0.251 0.450 10 quality operation in mechanical 0.0163 0.091 0.716 0.549 0.144 11 quality operation in electrical 0.0163 0.548 0.508 0.798 0.000 12 contractor performance in laboratory 0.0157 0.457 0.116 0.422 0.432 13 take timely action for shortage and problems 0.0163 0.494 0.325 0.439 0.540 14 provide timely report 0.0327 0.987 0.484 0.878 0.960 15 provisional hand0.0173 0.436 0.179 0.000 0.255 https://link.springer.com/article/10.1007/s11269-008-9288-y#auth-1 modeling a multi-criteria decision support system for prequalification assessment of construction contractors using critic and edas models 93 over timely 16 having suitable and sufficient equipment and machinery to carry out construction 0.0173 0.097 0.370 0.532 0.477 from the table 3 it is noted the criteria of technical and equipment information, appraisal score of each contractor, and total critic score of each criteria. from the table 4 it is observed the criteria of management information, appraisal score of each contractor, and total critic score of each criteria. table 4. sub criteria of management information sub criteria critic daghigh koshan hejrat manesh hemat talash omran mehran sub criteria of management information weight appraisal score (as) 1 efficiency, accuracy and effectiveness planning of contractor's methods 0.0227 0.000 0.168 0.222 0.800 2 performance and effectiveness of the contractor's methods for organization and control the project 0.0173 0.436 0.138 0.266 0.153 3 performance and effectiveness of the contractor methods for quality and quality assurance 0.0163 0.411 0.348 0.702 0.450 4 status of human resource management 0.0163 0.476 0.484 0.251 0.360 5 stability in the organization and the executive team the contractor 0.0173 0.524 0.449 0.310 0.545 6 coordination of contractor with covenants and other relevant factors 0.0157 0.000 0.487 0.527 0.197 7 coordination of contractor with subcontractor 0.0163 0.091 0.121 0.293 0.851 8 performance and abilities contractor project management 0.0227 0.127 0.392 0.976 0.333 9 performance and abilities contractor site 0.0227 0.762 0.995 0.610 0.714 gopal naik et al./ oper. res. eng. sci. theor. appl. 4(2) (2021) 79-101 94 management 10 methods of contractor procurement 0.0163 0.629 0.716 0.439 0.000 11 performance of contractor program 0.0163 0.629 0.604 0.549 0.240 from table 5 it is seen the criteria of professional experience information, appraisal score of each contractor, and total critic score of each criteria. it is worth mentioning that the criteria number 7, (good experience in previous works) was most influential in this section. table 5. sub criteria of professional experience information sub criteria critic daghigh koshan hejrat manesh hemat talash omran mehran sub criteria of professional experience information weight appraisal score (as) 1 executive experience in the field and field the desired work 0.0163 0.000 0.508 0.293 0.450 2 classified documents and documentation of the work done in the previous project 0.0163 0.091 0.651 0.659 0.450 3 native contractor or the project experience 0.0163 0.339 0.484 0.878 0.514 4 creativity and innovation in previous projects 0.0163 0.548 0.538 0.549 0.514 5 on-going communication and coordination with the client and monitoring devices 0.0163 0.494 0.282 0.176 0.654 6 awards and appreciation official letters 0.0163 0.091 0.716 0.176 0.180 7 good experience in previous works 0.0227 0.471 0.168 0.813 0.333 8 quality of provided previously project 0.0186 0.104 0.482 1.000 0.615 the t-test and paired test statistical analysis confirmed no significant differences between both values of w for the ahp and critic models. figure 1 displays the comparison of the values of w of ahp and critic. figure 2 shows the sequence number diagram for both w values of the ahp and the critic model. the friedman test calculated the ranks for both w values as ahp (1.45) and critic weighing system as 1.55 with a chi-square value of around 0.643. the distribution of weights of ahp was normal with a mean 0.02 and standard deviation 0.01 via a one-sample kolmogorov-smirnov test in the null hypothesis (null hypothesis retained). https://link.springer.com/article/10.1007/s11269-008-9288-y#auth-1 modeling a multi-criteria decision support system for prequalification assessment of construction contractors using critic and edas models 95 figure 1. one-sample kolmogorov-smirnov test. figure 2. the sequence number diagram for both w values of ahp and critic model the sequence number diagram revealed that the expansion of w values does not follow a parallel trend but it is a linear development. the concept of a linear development refers to high overlapping between both w values when it goes to move with parallel lines. figures 3 and 4 present the w values released in the ranking system of edas for both companies. gopal naik et al./ oper. res. eng. sci. theor. appl. 4(2) (2021) 79-101 96 figure 3. the w values released in the ranking system of edas for both companies figure 4. the w values released in the ranking system of edas for both companies the findings of the edas model appeared in table 6. the findings proved reasonable values in the ranking system with regard to this fact that the initial properties about companies were very close together. it needs to explain that the authors examined the various mcdm models to get the relevant response in this https://link.springer.com/article/10.1007/s11269-008-9288-y#auth-1 modeling a multi-criteria decision support system for prequalification assessment of construction contractors using critic and edas models 97 regard. however, the propinquity between findings caused us to fail and we could not realize the ranks for the companies. table 6.the final ranking of companies in the edas model rank values score company 3 22.38356729 daghigh koshan sepahan 2 23.86945084 hejrat manesh eizeh 1 26.03712557 hemattalash 4 21.8705158 omran mehran mongasht 5. conclusion the mcdm models facilitated the differentiation of the ranks between variables, criteria, and alternatives. the weighing systems also help to sort out the criteria based on values. a questionnaire was used to collect the initial data of research and was processed in the edas and critic systems; it can be used to collect various kinds of data for the same objective. an inclusive, detailed list of 56 sub-factors under 5 main factors for project prequalification was compiled following a thorough literature review, and review of contractors by experts of bandar imam khomeini municipality who already have done projects with contractors, and then used the critic method for obtained the weighing and importance of each factor and classified the contractors by applied the edas system for recognizing the contractors' potential before competitive tendering and obtaining bids. by the present research, it was attempted to rank four companies in order to conduct a prequalification assessment. an inclusive, detailed list of 56 sub-factors under 5 main factors for project prequalification was compiled following a thorough literature review, and review of contractors by 4 experts who already have done projects with contractors, and then using the critic method for obtained the weighing of each factor and classifying contractors by applied the edas system for recognizing the contractors' potential before competitive tendering and obtaining bids. the present research proposed herein a new approach to prequalification that accounts for multiple criteria when assessing the best contractor. the proposed support system was developed to help the tender holder, owner or client, and stakeholders to select the right contractors, and to afford a systematic and organized approach to the multifaceted issues. the effectiveness of the present approach was tested by applying it to a case study of the prequalification assessment of four construction companies' in bandar imam khomeini municipality, khuzestan, iran. it is worth mentioning that the prequalification assessment by the proposed approach is approved by the project stakeholders and is consistent with their expectations. note that, albeit the proposed method is a generalized approach and can be applied to a variety of projects, applying more pragmatic cases to approve the proposed approach is complicated because of the limited accessibility of project sources, the requirement to more adjust boundaries. the contribution of the present study proposed as a support system for prequalification and identification of contractors' ability, before assigning projects to companies for success in projects. the future research orientation can be oriented towards developing new mcdm models, weighing systems, and expansion in the content of questionnaires. gopal naik et al./ oper. res. eng. sci. theor. appl. 4(2) (2021) 79-101 98 acknowledgment this paper was conducted as part of the corresponding author ph.d. in department of civil engineering, uce, osmania university, telangana state (entitled; an investigation on construction crisis framework based on the multiple criteria 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(2019). a novel extended edas in minkowski space (edas-m) method for evaluating autonomous vehicles. studies in informatics and control, 28(3), 255–264. žižović, m., miljković, b., & marinković, d. (2020). objective methods for determining criteria weight coefficients: a modification of the critic method. decision making: applications in management and engineering, 3(2), 149–161. © 2021 by the authors. submitted for possible open access publication under the terms and conditions of the creative commons attribution (cc by) license (http://creativecommons.org/licenses/by/4.0/). modeling a multi-criteria decision support system for prequalification assessment of construction contractors using critic and edas models m. gopal naik, ravande kishore, seyed ali mousavi dehmourdi* 1. introduction 2. literature review 3. methodology 3.1. critic method 3.2. edas method 4. results and discussion 5. conclusion acknowledgment references operational research in engineering sciences: theory and applications vol. 4, issue 1, 2021, pp. 38-66 issn: 2620-1607 eissn: 2620-1747 doi: https://doi.org/10.31181/oresta2040123t * corresponding author: dilbagh panchal e-mail addresses: mohitmied@gmail.com (m. tyagi), panchald@nitj.ac.in (d. panchal), dk18102010@gmail.com (d. kumar), waliaravinder@yahoo.com (r. walia) modeling and analysis of lean manufacturing strategies using ism-fuzzy micmac approach mohit tyagi 1, dilbagh panchal 1*, deepak kumar 2, r. s. walia 3 1department of industrial and production engineering, dr b r ambedkar national institute of technology jalandhar, punjab, india 2 department of mechanical engineering, delhi technological university, delhi, india 3 department of production and industrial engineering, pec university, chandigarh, india received: 01 december 2020 accepted: 12 february 2021 first online: 20 february 2021 original scientific paper abstract: the current research work deals with an identification of different lean strategies and extraction to relevant strategies after discussion with experts and gives the answer of a question “how lean manufacturing strategies can help the organization to enhance the efficiency of the organization with great effectiveness?” in this research work, thirty-six lean strategies have been identified and out of which thirteen lean strategies were filtered in respect of highly importance value by factor analysis using software spss 21. further, to identify and analyze the inter-relationship among filtered strategies, an interpretive structural modeling (ism) with fuzzy matriced’ impacts croise´s multiplication applique´e a un classement (micmac) approach has been used. fuzzy micmac help to understand the dependence and driver’s power of the lean strategies. the mutual importance of extracted strategies has been discussed through developing the ism model and the individual assessment of each strategy with each of the other strategies has been derived using the fuzzy micmac approach. key words: lean manufacturing system (lms), lean strategies; factor analysis, spss 21, ism methodology, fuzzy micmac 1. introduction in the present scenario, it has been observed that the manufacturing firms are facing many challenges worldwide like quality, productivity, time management etc. to overcome these challenges forced the world’s manufacturing firms to develop new manufacturing methods and concepts in the competitive market. among them one of the main concepts is execution of lean manufacturing strategies in the production system. the concept of lean manufacturing system (lms) was initiated by a japanese automobile industry toyota in mid-20th century was well known for production https://doi.org/10.31181/oresta2040123t mailto:dk18102010@gmail.com modeling and analysis of lean manufacturing strategies using ism-fuzzy micmac approach 39 system. the aim of toyota production system was to enhance and raise the productivity with cost-reduction of the product by reducing waste or non-value added ventures (womack et al., 1990; srinivasaraghavan & allada, 2006). it defines the production process and procedures to improve the working environment of the shop floor consequently it also helps in increasing the overall productivity of company (narasimhan et al., 2006; kusrini et al., 2014). it can provide the essential extended term performance to automobile companies by refining the organization of cost effectiveness, elimination of wastage and also environmental risks over the improvement of experiences for endless organizational progress. lean manufacturing can implement the various set of activities for better performance of a company (yusup et al., 2015; al-tit, 2017). there are different techniques generally accessing in the industry for effective outcomes. application of lean manufacturing strategies can lead to continuous improvement in industrial field. the concept of lean can be implemented in any business organization along with the industries. different types of tool are being used from past several decades in order to get error free production from production unit. it is a tool that provides effective results to withstand the competition in prevailing different segments in the market aiming to remove all others unnecessary parameters from production unit (schiele & mccue, 2010). it uses very small inventory for manufacturing of product at high productivity. that’s why, it can be seen as a very popular tool or technique used by most of big industries and firms. lean management is meant for respect of humanity, it does not under estimate the capacity of people working in the company. moreover, it will help people to be more effective and appreciate their work. lean management maintains the production and levelise all stages of production in the company (ahlstrom, 2004; nenni et al., 2014). many errors occur during production like breakdown, lot reject etc. it can provide the framework to remove all these errors during the production. it can analyze the production procedure to find out the causes occur during production. lean can help in maintaining the documentation of work process or procedure of production and establish the standards of the manufacturing for the company for present and future production (jasti & kodali, 2016). many articles have focused on lean manufacturing strategies and lean integrated production system (hackman & wageman, 1995; mckone et al., 2001). this research purposes to pinpoint several lean strategies and features through comprehensive textual review to analyze them through interpretive structural modeling (ism). a model based on ism technique is developed to frame the immediate connection between various considered strategies. then the fuzzy micmac technique is performed to measure the inter-dependent power of different lean strategies. the results of present effort will assist the managers to improve the efficiency of their firm in this competitive market. in the current study, an ism approach with fuzzy micmac analysis has been applied due to its various importances over the other mcdm approaches. this approach provides a model based on that the dependence and driving nature of any factor/measures/strategies which is missing with the application of other mcdm approaches. furthermore, the micmac analysis under uncertain environment (fuzzy) provide the cluster based analysis through four sectors (dependent, independent, linkage or individual) which provides a platform to the manager or policy makers to emphasize on strategies or factors according to the policy notion of the concerned organization. tyagi et al./oper. res. eng. sci. theor. appl. 4 (1) (2021) 38-66 40 the organization of this research article is as follow: section one gives a brief introduction on the various lean strategies and their importance in present manufacturing scenario, section two encloses the inclusive literature review and the based that important lean strategies have been extracted, section three illustrates the methodology which has been applied on the selected strategies in order to obtain the interrelationship among them, the conclusion drawn from the present research and its managerial implications in manufacturing environment have been expressed in section four and five respectively. in the last, section six shows the limitation and future scope of the present study. 2. literature review the goal of lms is to reduce inventory and increase human efficiency and handling industrial stocks which are in accordance to consumer needs and the products are manufactured effectively and efficiently (bhim et al., 2010). increasing resource effectiveness by excluding superfluous consumption denotes the logical extension from lean manufacturing to lean and manufacturing. a simulation based methodology for monetary valuation was studied by greinacher et al., (2015) of lean and green manufacturing organizations as non-monetary green parameters. thus, economical efficiency is an indispensable evaluating factor in the application of lean and green manufacturing strategies. salleh et al., (2012) studied the forming process for simulation of combined total quality management along with lean manufacturing activities. wahab et al., (2013) established a theoretical model to evaluate leanness in manufacturing unit. in this research, a concept based model for leanness element in the manufacturing unit has been made and deliberate in two prime levels i.e. dimensions and factors. additionally, the model also demonstrations how lean parameters of an organization or manufacturing system corelating different forms of wastes. hartini & ciptomulyono (2015) examined the effect of lean and sustainable production system to improve organization performance. onyeocha et al., (2015) worked on assessment of multi-product lean manufacturing system with assembly and changing demand. many of the suggestions recommended that lean production system is favorable for sustainable production system; most influentially, it would help in perspective environment and cost-effective aspects. duraccio et al., (2014), arslankaya & atay (2015) observed and apply the maintenance management with the lean manufacturing methods at the maintenance workshop for removing the losses caused by breakdowns in order to improve production and motivate the personnel. youssouf et al., (2014) worked on the optimization of strategies lean six sigma. lean manufacturing with ergonomic working environment in the automobile sector is another very effective concept to enhance the working condition, improve productivity, improving production processes, and eliminate the waste (berlin et al., 2014; dos santos et al., 2015). the key area of ergonomics is to improve and relate the man alteration methods to their work and competent and harmless ways in order to enhance the welfare, safety, health, prosperity and thus to accumulate efficiency and productivity of the organization (dul & neumann, 2009). mohammaddust et al., (2017) developed the robust lean model for alternative risk mitigation strategies. rohani & zahraee (2015) studied lean manufacturing technique termed as value stream mapping (vsm) for enhancing the assembly line of an industry. to attain this modeling and analysis of lean manufacturing strategies using ism-fuzzy micmac approach 41 goal, lean strategies were applied in order to construct vsm for identification, disposal of wastages and improved performance of the organization. susilawati et al., (2015) used the fuzzy logic based process to quantify the level of lean activity in industry. mandal & deshmukh (1994) researched about the vendor selection procedure of the company dependent on different parameters using ism. ism methodology is a very popular technique to define the direct relationship among different enablers or barriers. lee et al., (2011) analysed that the lean manufacturing is very popular technique in the field of production system from past several decades. kanban system among them is the most important lean manufacturing principles for lean production system along with reduced cost and marginal inventories. the objectives are (i) to define the working of the kanban system successfully across organizations globally and (ii) categorizing factors obstructing small and medium enterprises from executing kanban in lean manufacturing system (rahman et al., 2013). shah & ward (2003) observed the outcomes of three dependent issues, plant dimensions, plant life and unionization position, on the chance of applying different manufacturing industrial practices that are main facets of lms. lee et al., (2011) analyzed the process-advantages, expenses, and threats for identifying techniques by making use of integrated ism and fuzzy analytic order of procedure. shuaib et al., (2016) studied on enablers of smart organization and developed the integrated ism model with fuzzy micmac. dewangan et al., (2015) examined the enablers for advancement of innovation in the indian manufacturing segment and direct relationship has been analyzed among different enablers with help of ism and fuzzy micmac. charan et al., (2008) explored the barriers in supply chain performance measurement system and implementation in indian context. ism technique to analysis the enablers and barriers of green supply chain management (gscm) has been used by many researcher, some of them are as follows (diabat & govindan, 2011; gorane & kant, 2013; faisal, 2010; mudgal et al., 2010; singh et al., 2010; talib et al., 2011; tyagi et al., 2015; wang et al., 2015; tyagi et al., 2017). kannan et al. (2009) applied the combined study of ism and fuzzy topsis approach to examine and considering the 3-p reverse logistic providers. diabat & govindan (2011) have suggested the ism approach to examination the drivers influencing the application of gscm. prasad et al., (2020) developed a novel framework based on lean manufacturing concept for continuous improvement in indian textile industry. palang & dhatrak (2020) implemented define, measure, analysis, improve and control (dmaic), failure mode and effect analysis (fmea), industry 4.0 and kaizen approaches for developing the lean manufacturing concept based model in order to improve the productivity of the industry. yadav et al., (2020) proposed hybrid fuzzy analytical hierarchy process (fahp) decision making trial and evaluation laboratory (dematel) approaches based lean manufacturing concept for enhancing the improvement capabilities of companies under developing economies. guillen et al., (2020) proposed a structured methodology based on lean manufacturing principles for improving facility management. tortorella et al., (2021) proposed lean automation based model for examining improvement pathway of an industry. from the reviewed literature it has been noted that the application of ismmicmac approaches was not yet been reported by any researcher in order to identify and analyze the inter-relationship among filtered strategies for the considered lean manufacturing case. to bridge this, gap the current work presents the application of tyagi et al./oper. res. eng. sci. theor. appl. 4 (1) (2021) 38-66 42 ism-micmac approaches based framework to enhance the efficiency of the considered organization. 3. research methodology on the basis of discussion with experts and literature review lean manufacturing strategies were identified and a developed questionnaire was floated among the experts for the collection of the data. factor analysis was performed, and appropriate strategies were filtered and further brainstorming session was conducted for their acceptance or rejection. after the acceptance of filtered strategies ism and fuzzy micmac approaches were applied and analysis was carried for reaching appropriate decision. the flow diagram on the research work plan denoted in figure 1 is carried out in unique view. however, a step by step explanation of ism approach is also given below. the interpretive structural modeling (ism) used to create a composite system into an envisioned ordered arrangement. it is used for studying and solving complex problems to help in decision-making (warfield, 1974; jain & raj, 2015). it is based on computer-assisted method that usually used to conclude the multiplex situations by providing a sensible and reasonable path of action (kannan et al., 2009). initial phase of the ism method is used to pin-point lean strategies, drivers or other alternatives, which concerns the research complication. then a theoretically feasible derived relation is selected (thakkar et al., 2006). ism methodology involves several steps as follows (kannan &haq, 2007; sharma & garg, 2010). identify and enlist the diverse strategies of lean manufacturing system. i. creating a relative relationship between different lean manufacturing strategies. ii. development of a fundamental self-interaction matrix (ssim) to lean manufacturing strategies which show interactions among lean manufacturing strategies under the ambit. iii. creating reachability matrix using ssim and then transitivity of the matrix is evaluated. iv. a flow chart is drawn on the basis of reachability matrix. v. interpret the subsequent relationship digraph into an ism by switching lean strategies with statements verify for conceptual difference and essential improvements made and contextual correlation was developed among diverse lean manufacturing strategies. modeling and analysis of lean manufacturing strategies using ism-fuzzy micmac approach 43 figure 1. flow chart illustrating research direction discussion with the experts based on literature review identification of lean manufacturing strategies questionnaire development and dispatching to field experts data collection from field experts factor analysis / principal component analysis filtration of appropriate strategies brain storming sessions if collecting and visualizing expert’s opinion ism methodology result and discussion conclusion ok not ok fuzzy micmac stage 2 stage 1 tyagi et al./oper. res. eng. sci. theor. appl. 4 (1) (2021) 38-66 44 4. proposed research methodology implementation based results in accordance to the literature survey and after consultation with the field professionals, thirty-six lean manufacturing strategies were acknowledged. then, a questionnaire was designed using google form and forwarded on google doc. numerous views of different field professionals were collected. to analyze the lean strategies, the experts from indian automobiles companies situated near delhi ncr and academicians from several organizations were communicated for the view of lean manufacturing strategies. encompassing expertise in the field of manufacturing and strategies formulation have been considered to collect their opinions regarding the implementation of lean strategies in indian automobile companies in order to improve their performance. to analyze the lean strategies, an ism approach with fuzzy micmac has been applied, for the same qualitative input from the experts (four groups having five to six experts in each group) have been taken to develop the structural self-interaction matrix. here concept of fuzzy set is used to consider the vagueness of the collected data for high accuracy in the decision results. before implementing the ism approach, a factor analysis has also been carried in order to extract the significant strategies based on their factor loading values. factor analysis (fa) is a dynamic means for statistical mitigation and conveying the nearby events of diverse strategies by deciding the normal elements in view of the account of perceived correlations (hayton, 2004). primarily, a questionnaire has been designed by5-point likert type scale for thirty-six lean strategies and was send to the one hundred and fifty field professionals to gather their view regarding the significance of lean strategies. out of one hundred and fifty, fifty-seven replies were acknowledged, which reveals the 38% response rate. when the response rate is greater than 30%, it is appropriate to execute the reliability examination as suggested by malhotra & grover (1998). the received stats are deemed as reliable, only if the cronbach alpha coefficient(α)ranges from0.7to 1. gliem & gliem (2003) mentions the rules as follows: α> 0.9 signifies outstanding, α > 0.8 signifies good, α >0 .7 signifies satisfactory, α > 0.6 signifies questionable, α > 0.5 signifies poor, and α < 0.5 signifies unacceptable”. in the present research work, score of the cronbach alpha coefficient comes as 0.794, hence the collected data can be considered as reliable. then factor analysis is done for the clarification of appropriate lean strategies by same software. table 1 shows cumulative variances of different lean strategies and thirteen lean strategies contributed to about 77.648 % of the total variance and have eigen values greater than threshold value of 1. the component matrix was observed to extract thirteen lean strategies based on the variable loaded in the software. the listed of extracted lean strategies is shown in table 2. to understand the dominance thirteen extracted lean strategies over the total identified strategies a scree plot has been structured, as shown in figure 2. the scree plot makes an elbow after the thirteenth component, which means that each succeeding factor accounts for smaller and smaller accounts of the total variance. modeling and analysis of lean manufacturing strategies using ism-fuzzy micmac approach 45 figure 2 scree graph for different components table 1 total variance explained component initial eigenvalues extraction sums of squared loadings rotation sums of squared loadings total % of variance cumulative % total % of variance cumulative % total 1 5.838 16.216 16.216 5.838 16.216 16.216 2.764 2 3.311 9.196 25.412 3.311 9.196 25.412 2.745 3 2.894 8.038 33.450 2.894 8.038 33.450 2.608 4 2.386 6.628 40.078 2.386 6.628 40.078 2.557 5 2.107 5.854 45.932 2.107 5.854 45.932 2.547 6 1.882 5.229 51.161 1.882 5.229 51.161 2.420 7 1.741 4.836 55.997 1.741 4.836 55.997 2.220 8 1.604 4.456 60.453 1.604 4.456 60.453 1.971 9 1.533 4.258 64.712 1.533 4.258 64.712 1.750 10 1.396 3.878 68.590 1.396 3.878 68.590 1.742 11 1.198 3.329 71.919 1.198 3.329 71.919 1.595 12 1.060 2.946 74.865 1.060 2.946 74.865 1.578 13 1.002 2.784 77.648 1.002 2.784 77.648 1.458 14 .903 2.510 80.158 15 .814 2.261 82.419 16 .786 2.184 84.603 17 .727 2.019 86.622 18 .688 1.911 88.533 19 .625 1.735 90.268 20 .497 1.380 91.648 21 .476 1.323 92.971 22 .431 1.197 94.168 tyagi et al./oper. res. eng. sci. theor. appl. 4 (1) (2021) 38-66 46 23 .361 1.002 95.170 24 .346 .962 96.131 25 .305 .848 96.980 26 .233 .649 97.628 27 .190 .529 98.157 28 .180 .501 98.658 29 .135 .375 99.034 30 .112 .312 99.346 31 .081 .225 99.571 32 .065 .180 99.751 33 .041 .115 99.866 34 .032 .089 99.955 35 .011 .031 99.986 36 .005 .014 100.000 table 2 extracted lean strategies sr. no. lean strategies sources s1. line improvement activity (salleh et al., 2012; chai et al., 2012) s2. ability to adjust capacity rapidly within a short time period (stecke& kim, 1988; ward &duray, 2000) s3. alternative supply chain networks (harland, 1996; hugo &pistikopoulos, 2005; mohammaddust et al., 2017) s4. focus on market orientation (venkatraman&ramanu jam, 1987) s5. development programs or past performance record (brown & cousins, 2004) s6. proper machine utilization (nordin et al., 2010) s7. minimizing work in progress (riezebos et al., 2009; onyeocha et al., 2015) s8. ability to provide innovation design (zhao et al., 2006; le dain et al., 2011) s9. recycling of raw materials and defective parts (thierry et al., 1995; wang et al., 2008) s10 higher collaboration for better production planning (seifert, 2003; kenne et al., 2007; chinprateep&boondisk ulchok, 2010) s11. monitoring the implementation schedules step by step (ballard & howell, 1998; guo et al., 2015; soroush, 2015) s12. training of employees to develop multi skills (wang et al., 2008; heimerl&kolisch, 2010) s13. handling of appropriate variations in customer orders (anand& ward, 2004) modeling and analysis of lean manufacturing strategies using ism-fuzzy micmac approach 47 now, after extracting the significant lean manufacturing strategies, a step by step implementation of ism approach has been made as given below: 4.1 structural self-interaction matrix (ssim) the ssim is used to understand the related relationship between the diverse identified lean strategies in table 3 by making use of professional’s view. the matrix delivers the pair-wise connection of each lean strategy. the signs [v, a, x and o] are applied for linking of lean strategies (a, b). v strategy ‘a’ will assistance to enhance strategy ‘b’ a -strategy ‘a’ will assistance to enhance strategy ‘b’ x -strategy ‘a’ and ‘b’ will assistance to enhance each other o strategy ‘a’ and ‘b’ are independent table 3 ssim lean strategies s.no. lean strategies 13 12 11 10 9 8 7 6 5 4 3 2 1 s1. line improvement activity v a a a o v v v a v a a s2. ability to adjust capacity rapidly within a short time period v a a a o a v x o a a s3. alternative supply chain networks v o a o x a v v o a s4. focus on market orientation v v v a v v o v v s5. development programs or past performance record v a v x v v v v s6. proper machine utilization a a a a o o v s7. minimizing work in progress o a a a v a s8. ability to provide innovation design x a a a o s9. recycling of raw materials and defective parts a a o o s10 higher collaboration for better production v a v tyagi et al./oper. res. eng. sci. theor. appl. 4 (1) (2021) 38-66 48 planning s11. monitoring the implementation schedules step by step x a s12. training of employees to develop multi skills v s13. handling of appropriate variations in customer orders 4.2 reachability matrix the formulation of the initial reachability matrix is the subsequent stage in ism methodology. the transformation into initial reachability matrix as depicted in table 4 is obtained by the dual linking of the lean strategies in ssim given in table 3 by means of binary system. the transformation is prepared with the assistance of the below mentioned rules: when (a, b) in the set implies v, assign the value of (a, b) within the reachability matrix as 1 and assign the (b, a) value as 0. when (a, b) in the set implies a, assign the value of (a, b) within the reachability matrix as 0 and assign the (b, a) value as 1. when (a, b) in the set implies x, assign the value of (a, b) within the reachability matrix as 1 and assign the (b, a) value as 1. when (a, b) in the set implies o, then assign the (a, b) result within the reachability matrix as 0 and assign the (b, a) value as 0. table 4 initial reachability matrix sr. no. lean strategies 1 2 3 4 5 6 7 8 9 10 11 12 13 s1. line improvement activity 1 0 0 1 0 1 1 1 0 0 0 0 1 s2. ability to adjust capacity rapidly within a short time period 1 1 0 0 0 1 1 0 0 0 0 0 1 s3. alternative supply chain networks 1 1 1 0 0 1 1 0 1 0 0 0 1 s4. focus on market orientation 0 1 1 1 1 1 0 1 1 0 1 1 1 s5. development programs or past 1 0 0 0 1 1 1 1 1 1 1 0 1 modeling and analysis of lean manufacturing strategies using ism-fuzzy micmac approach 49 performance record s6. proper machine utilization 0 1 0 0 0 1 1 0 0 0 0 0 0 s7. minimizing work in progress 0 0 0 0 0 0 1 0 1 0 0 0 0 s8. ability to provide innovation design 0 1 1 0 0 0 1 1 0 0 0 0 1 s9. recycling of raw materials and defective parts 0 0 1 0 0 0 0 0 1 0 0 0 0 s10 higher collaboration for better production planning 1 1 0 1 1 1 1 1 0 1 1 0 1 s11. monitoring the implementation schedules step by step 1 1 1 0 0 1 1 1 0 0 1 0 1 s12. training of employees to develop multi skills 1 1 0 0 1 1 1 1 1 1 1 1 1 s13. handling of appropriate variations in customer orders 0 0 0 0 0 1 0 1 1 0 1 0 1 by applying the transitivity rule the initial matrix was converted into final matrix in table 5, which suggests that the lean strategy ‘l’ is interrelated to ‘m’ and ‘m’ is interrelated to ‘n’, it is considered that l will be interrelated to n. the set that indicates the transitivity is noticeable with the symbol (*). table 5 final reachability matrix sr. no. lean strategies 1 2 3 4 …….. 9 10 11 12 13 s.p s1. line improvement activity 1 1* 1* 1 …….. 1* 0 1* 1* 1 12 s2. ability to adjust capacity rapidly within a short time period 1 1 0 1* …….. 1* 0 1* 0 1 9 tyagi et al./oper. res. eng. sci. theor. appl. 4 (1) (2021) 38-66 50 s3. alternative supply chain networks 1 1 1 1* …….. 1 0 1* 0 1 10 s4. focus on market orientation 1* 1 1 1 …….. 1 1* 1 1 1 13 s5. development programs or past performance record 1 1* 1* 1* …….. 1 1 1 0 1 12 s6. proper machine utilization 1* 1 0 0 …….. 1* 0 0 0 1* 6 s7. minimizing work in progress 0 0 1* 0 …….. 1 0 0 0 0 3 s8. ability to provide innovation design 1* 1 1 0 …….. 1* 0 1* 0 1 9 s9. recycling of raw materials and defective parts 1* 1* 1 0 …….. 1 0 0 0 1* 7 s10 higher collaboration for better production planning 1 1 1* 1 …….. 1* 1 1 1* 1 13 s11. monitoring the implementation schedules step by step 1 1 1 1* …….. 1* 0 1 0 1 10 s12. training of employees to develop multi skills 1 1 1* 1* …….. 1 1 1 1 1 13 s13. handling of appropriate variations in customer orders 1* 1* 1* 1* …….. 1 1* 1 0 1 12 12 12 11 9 …….. 13 5 10 4 12 4.3 level partition in order to filter out the reachability and antecedent sets, reachability matrix has been partitioned by applying the concept of level partition as shown in tables 6 and 7. in table 6, a complete process has been explained for level partition based on reachability and antecedent sets in respect of each filtered strategy. modeling and analysis of lean manufacturing strategies using ism-fuzzy micmac approach 51 however, in table 7, a complete summary of levels has been given. the reachability set includes the lean strategy itself along with lean strategies that it would affect while the antecedent set includes the lean strategy itself along with other lean strategies that may impact it. then, different levels are obtained by the intersection for all lean strategies of these sets. the lean strategy whose reachability and antecedent set are identical, is placed in the uppermost level of the order. the uppermost level lean strategies are the ones that would not lead other lean strategies to overcome their own level in this order. after identifying the topmost level of lean strategies, they are uninvolved in contemplation while the same procedure is reiterated to find out the successive levels. this method is applied till the level of each lean strategy is obtained. these levels play a major role in building the ism model. table 6 level partition (iteration i) lean strateg ies reachability set antecedent set interaction level s1. 1,2,3,4,5,6,7,8,9,1 1,12,13 1,2,3,4,5,6,8,9, 10,11,12,13 1,2,3,4,5,6,8,9, 11,12,13 s2. 1,2,4,6,7,8,9,11,13 1,2,3,4,5,6,8,9, 10,11,12,13 1,2,4,6,8,9,11, 13 s3. 1,2,3,4,6,7,8,9,11, 13 1,3,4,5,7,8,9,1 0,11,12,13 1,3,4,7,8,9,11, 13 s4. 1,2,3,4,5,6,7,8,9,1 0,11,12,13 1,2,3,4,5,10,11 ,12,13 1,2,3,4,5,10,11 ,12,13 s5. 1,2,3,4,5,6,7,8,9,1 0,11,13 1,4,5,10,13 1,4,5,10,13 s6. 1,2,6,7,9,13 1,2,3,4,5,6,8,9, 10,11,12,13 1,2,6,9,13 s7. 3,7,9 1,2,3,4,5,6,7,8, 9,10,11,12,13 3,7,9 i s8. 1,2,3,6,7,8,9,11,13 1,2,3,4,5,8,10, 11,12,13 1,2,3,8,11,13 s9. 1,2,3,6,7,9,13 1,2,3,4,5,6,7,8, 9,10,11,12,13 1,2,3,6,7,9,13 i s10 1,2,3,4,5,6,7,8,9,1 0,11,12,13 4,5,10,12,13 4,5,10,12,13 s11. 1,2,3,4,6,7,8,9,11, 13 1,2,3,4,5,8,10, 11,12,13 1,2,3,4,8,11,13 s12. 1,2,3,4,5,6,7,8,9,1 0,11,12,13 1,4,10,12 1,4,10,12 s13. 1,2,3,4,5,6,7,8,9,1 0,11,13 1,2,3,4,5,6,8,9, 10,11,12,13 1,2,3,4,5,6,8,9, 10,11,13 tyagi et al./oper. res. eng. sci. theor. appl. 4 (1) (2021) 38-66 52 table 7 level partition (final iteration) lean strategies reachability set antecedent set interaction level s1. 1,2,3,4,5,6,8,11, 12,13 1,2,3,4,5,6,8,10,11,12, 13 1,2,3,4,5,6,8,11,1 2,13 ii s2. 1,2,4,6,8,11,13 1,2,3,4,5,6,8,10,11,12, 13 1,2,4,6,8,11,13 ii s3. 3,4,8,11, 3,4,5,8,10,11,12 3,4,8,11, iii s4. 4,5,10,12 4,5,10,12 4,5,10,12 iv s5. 4,5,10, 4,5,10 4,5,10 iv s6. 1,2,6,13 1,2,3,4,5,6,8,10,11,12, 13 1,2,6,13 ii s7. 3,7,9 1,2,3,4,5,6,7,8,9,10,11, 12,13 3,7,9 i s8. 8,11 3,4,5,8,10,11,12 8,11 iii s9. 1,2,3,6,7,9,13 1,2,3,4,5,6,7,8,9,10,11, 12,13 1,2,3,6,7,9,13 i s10 4,5,10,12 4,5,10,12 4,5,10,12 iv s11. 3,4,8,11 3,4,5,8,10,11,12 3,4,8,11 iii s12. 12 12 12 v s13. 1,2,3,4,5,6,8,10, 11,13 1,2,3,4,5,6,8,10,11,12, 13 1,2,3,4,5,6,8,10,1 1,13 ii figure 3 model based on ism modeling and analysis of lean manufacturing strategies using ism-fuzzy micmac approach 53 the above flow charts illustrated in figure 3 depicts the diverse lean strategies and their inter-dependence. in the flowchart, the adopted influential steps have been distributed into 5 levels for the progress of the organization. training of employees to develop multi skills (s35) is most significant lean strategy which pushes all the former strategies which effect in positive incorporation of lean and every organization need to focus on this strategy. with continuous and systematic training, personnel become competent in new techniques that assist in building up several abilities which further help to steer the organization at higher level. the foundation of this ism model is built up by level 5 strategies (s12). training of employees to develop multi skills (s12) escorts the three strategies at level 4 i.e. focus on market orientation (s4), development programs or past performance record (s5) and higher collaboration for better production planning (s10). these three strategies have solid connection among them based on the performance data of the past or improvement programs which plays a role in finding out the shortcomings of concluding products or new demands of consumers centered by concentrated on the inclination of the market. this would assist the manufacturing unit in teaming up with other personnel, hence enhancing productivity. at level 3 strategies, alternative supply chain networks (s3), ability to provide innovation design (s8) and monitoring the implementation schedules step by step (s11) ushered by level 4. regular training and focusing on market orientation helps the employees to create the ability of innovative designing according to the demand that further come out to give alternative sully chain networks. this is also helps in monitoring the implementing schedules steps by steps. level 2 drive the further four strategies i.e. line improvement activity (s1), ability to modify capacity quickly within a short time interval (s2), proper machine utilization (s6) and handling of appropriate variations in customer orders (s13). strategies at level 2 have very strong connectivity with each other. if there is proper machine utilization and improved line activity, it can create ability to adjust the capacity quickly within short period of time that helps to handle the variations in customers’ orders. minimizing work in progress (s7) and recycling of raw materials and defective parts (s9) at first level directed by second level are the preferred products of the figures. aforementioned two strategies acquiring the uppermost rank of this orderly representation make use of proper machine utilization and improved line activity results in minimizing work in process with minimal defective parts which gives desired best quality products and increases the productivity of the organization. 4.4 fuzzy micmac analysis micmac can be elaborated as “matriced impacts croises-multipication applique and classment” or in simple way it is define as “cross-impact matrix multiplication applied to classification” (jain & raj, 2016; qureshi et al., 2008). this analysis involves the different steps as follows: i: creating the binary direct relationship matrix ii: constructing the fuzzy direct reachability matrix iii: producing the stabilized fuzzy micmac matrix tyagi et al./oper. res. eng. sci. theor. appl. 4 (1) (2021) 38-66 54 here, fuzzy concept is used in order to consider the uncertainties or vagueness in the collected data useful for high accuracy in the decision results. 4.5 creating the binary direct relationship matrix to make the binary direct relationship matrix, it is required to transform the convectional micmac analysis into fuzzy micmac analysis using binary system (0 & 1). to make an analysis stronger through considering the uncertainty in the collected raw data, fuzzy set theory (panchal & kumar, 2014; stojić et al., 2018; chatterjee & stević, 2019; panchal et al., 2018; panchal et al., 2019; petrović et al.,2019; đalić et al., 2020; pająk, 2020; kushwaha et al., 2020; zavadskas et al., 2020) has been utilized. the binary direct relationship matrix is shown below in table 8. table 8 binary direct relationship matrix sr. no. lean strategies 1 2 3 4 5 6 7 8 9 10 11 12 13 d.p s1. line improvement activity 0 0 0 1 0 1 1 1 0 0 0 0 1 5 s2. ability to adjust capacity rapidly within a short time period 1 0 0 0 0 1 1 0 0 0 0 0 1 3 s3. alternative supply chain networks 1 1 0 0 0 1 1 0 1 0 0 0 1 6 s4. focus on market orientation 0 1 1 0 1 1 0 1 1 0 1 1 1 9 s5. development programs or past performance record 1 0 0 0 0 1 1 1 1 1 1 0 1 8 s6. proper machine utilization 0 1 0 0 0 0 1 0 0 0 0 0 0 2 s7. minimizing work in progress 0 0 0 0 0 0 0 0 1 0 0 0 0 1 s8. ability to provide innovation design 0 1 1 0 0 0 1 0 0 0 0 0 1 4 s9. recycling of raw materials and defective parts 0 0 1 0 0 0 0 0 0 0 0 0 0 1 s10 higher collaboration 1 1 0 1 1 1 1 1 0 0 1 0 1 9 modeling and analysis of lean manufacturing strategies using ism-fuzzy micmac approach 55 for better production planning s11. monitoring the implementation schedules step by step 1 1 1 0 0 1 1 1 0 0 0 0 1 7 s12. training of employees to develop multi skills 1 1 0 0 1 1 1 1 1 1 1 0 1 10 s13. handling of appropriate variations in customer orders 0 0 0 0 0 1 0 1 1 0 1 0 0 4 dependence power 6 7 4 2 3 9 9 7 7 2 5 1 9 table 9 possibility of numerical values of the reachability possibility of reachability no very low low medium high very high complete value 0 0.1 0.3 0.5 0.7 0.9 1 4.6 constructing the fuzzy direct reachability matrix the values given in table 9 are made use in the binary direct relationship matrix for developing the fuzzy direct reachability matrix. the understanding of micmac analysis is augmented by making use of fuzzy theory which is why possibility of interaction is used to interpret the immediate connection among different lean strategies as represented in table 9. therefore, fuzzy direct reachability is developed and as depicted in table 10. table 10 fuzzy direct reachability matrix s.no. lean strategies 1 2 3 4 ….. 9 10 11 12 13 s1. line improvement activity 0 0 0 0 ….. 0 0 0 0 0.1 s2. ability to adjust capacity rapidly within a short time period 0 0 0 0 …… 0 0 0 0 0.3 s3. alternative supply chain networks 0.3 0 0 0 ….. 0.9 0 0 0 0.3 s4. focus on market orientation 0 0.9 0.7 0 …… 0.9 0 0.3 0 0.5 s5. development 0 0 0 0 0 0 0 0 0.1 tyagi et al./oper. res. eng. sci. theor. appl. 4 (1) (2021) 38-66 56 programs or past performance record …… s6. proper machine utilization 0 0 0 0 …… 0 0 0 0 0 s7. minimizing work in progress 0 0 0 0 …… 0 0 0 0 0 s8. ability to provide innovation design 0 0 0 0 …… 0 0 0 0 0 s9. recycling of raw materials and defective parts 0 0 0 0 …… 0 0 0 0 0 s10 higher collaboration for better production planning 0.5 0.5 0 0 ……. 0 0 0.5 0 0.9 s11. monitoring the implementation schedules step by step 0.1 0.1 0 0 …….. 0 0 0 0 0 s12. training of employees to develop multi skills 0.5 0.5 0 0 ……. 0 0 0.5 0 0.7 s13. handling of appropriate variations in customer orders 0 0 0 0 …….. 0.3 0 0 0 0 the subset values are given in table10 is used as the base for constructing stabilized fuzzy micmac matrix. multiplication of the obtained matrix is done many a times unless the orders of dependence and driving power become constant. with reference to the mentioned theory, the result obtained could be a fuzzy matrix, after the multiplication of two fuzzy (kandasamy et al., 2007) interval values. the following multiplication method is used to get the required result for multiplying of two fuzzy matrixes, mn = max {min (mij, nij)} where, m = [mij] and n = [nij] are two fuzzy matrices. for solving the above equation, the program is written in the ‘c’ language to attain the accuracy. the result obtained is illustrated in figure 4 and the required stabilized fuzzy micmac matrix is given in table 11. modeling and analysis of lean manufacturing strategies using ism-fuzzy micmac approach 57 figure 4 stabilized fuzzy micmac matrix table 11 stabilized fuzzy micmac matrix s.no. lean strategies 1 2 3 4 …… 9 10 11 12 13 driving power s1. line improvement activity 0.5 0.5 0.5 0.5 …… 0.5 0.3 0.3 0.5 0.5 6.1 s2. ability to adjust capacity rapidly within a short time period 0.5 0.5 0.5 0.5 …… 0.5 0.3 0.3 0.5 0.5 6.1 s3. alternative supply chain networks 0.5 0.5 0.5 0.5 …… 0.5 0.3 0.3 0.5 0.5 6.1 s4. focus on market orientation 0.5 0.5 0.5 0.5 …… 0.5 0.3 0.3 0.5 0.9 6.9 s5. development programs or past performance record 0.5 0.5 0.5 0.5 …… 0.5 0.3 0.3 0.5 0.5 6.3 s6. proper machine utilization 0.5 0.5 0.5 0.5 …… 0.5 0.3 0.3 0.5 0.5 6.1 s7. minimizing work in progress 0.1 0.1 0.1 0.1 …… 0.1 0.1 0.1 0.1 0.1 1.3 s8. ability to provide innovation design 0.5 0.5 0.5 0.5 …… 0.5 0.3 0.3 0.5 0.9 6.5 s9. recycling of raw materials 0.1 0.1 0.1 0.1 …… 0.1 0.1 0.1 0.1 0.1 1.3 tyagi et al./oper. res. eng. sci. theor. appl. 4 (1) (2021) 38-66 58 and defective parts s10 higher collaboration for better production planning 0.5 0.5 0.5 0.5 …… 0.5 0.3 0.3 0.5 0.7 6.3 s11. monitoring the implementation schedules step by step 0.5 0.5 0.5 0.5 …… 0.5 0.3 0.3 0.5 0.5 6.1 s12. training of employees to develop multi skills 0.5 0.5 0.5 0.5 …… 0.5 0.3 0.3 0.5 0.7 6.5 s13. handling of appropriate variations in customer orders 0.5 0.5 0.5 0.5 …… 0.5 0.3 0.3 0.5 0.5 6.5 dependence power 5.7 5.7 5.7 5.7 …. 5.7 3.5 3.5 5.7 6.9 stabilized matrix as shown in table 11 is categorized into four cluster in accordance to driving power and dependence power. the summing up values of rows in the stabilized fuzzy micmac matrix is driving power and summing up values columns in the stabilized fuzzy micmac matrix is the dependence power. the cluster representation is shown in figure 5. figure 5 driving and dependence power graph modeling and analysis of lean manufacturing strategies using ism-fuzzy micmac approach 59 cluster 1: lean strategies belonging to the particular group should have low driving and dependence power. strategies in this group have no relation to each other. they are neither influence nor influenced by any others strategies. there is no lean strategy in our research that fall in this cluster. this is called autonomous cluster cluster 2: in this cluster, lean strategies are having low driving power and high dependence power. it characterizes lean strategies that are dependent on others strategies. the dependency of these lean strategies shows that they need all other lean strategies for the implementation of lean strategies into the system. lean strategy (s7) minimizing work in progress and lean strategy (s9) recycling of raw materials and defective parts and are categorized in this cluster. this is called dependence cluster cluster 3: lean strategies in this group are having very high driving power and high dependence power. this cluster denotes lean strategies which have very robust relation to each other’s. most of lean strategies in current research fall in this group. if there is a change in any lean strategy it will immediately affect the other lean strategy. most of the lean strategies of present study fall in this cluster. total eight strategies are categorized that are line improvement activity (s1), ability to adjust capacity quickly within a short time period (s2), alternative supply chain networks (s3), focus on market orientation (s4), development programs or past performance record (s5), proper machine utilization (s6), ability to provide innovation design (s8), training of employees to develop multi skills (s12) and handling of appropriate variations in customer orders (s13). this is called linkage cluster. cluster 4: lean strategies belonging to this group have low dependence power but very high driving power. lean strategy which are categorized in this group are higher collaboration for better production planning (s10) and monitoring the implementation schedules step by step (s11). this is called independent cluster. 5. managerial implications of the work to prevail over the various tasks that emerge during production time and to improve the efficiency of their organization, managers require flexible attitudes to take the worthwhile decision for the growth of organization. the current research reveals that manager is required to emphasize on diverse lean strategies liable on the condition at different level. training of employees is the primary need of the organization which accelerates the others strategies effectively in every field. apart from this strategy, managers need to focus on secondary strategies at different level also as illustrated in figure 2. driving and dependence graph illustrated in figure 3 would help the managers to decide whether the applied strategies are driving in nature or dependent on others. most of strategies fall in cluster 3 managers have to focus more on this category. strategies in this category are very crucial for application of lean manufacturing in the organization. also, each and every strategy serves its role in the performance of the organization at its level. therefore, this study helps the managers for implementation of various lean strategies into the organization. tyagi et al./oper. res. eng. sci. theor. appl. 4 (1) (2021) 38-66 60 6. conclusion it is understood that no single strategy is enough for implementation of lean manufacturing for enhancement of the efficiency organization. after factor analysis out of thirty-six lean strategies thirteen were extracted using software spss 21 and analyzed by structural modeling and then used to construct the ism based model which helps to understand the direct relationship among various lean strategies. “training of employees to develop multi skills(s12)” has been identified as the most crucial strategy which drives all the other strategies for the success of lean. minimizing work in progress (s7) and recycling of raw material and defective parts (s9) were level one, strategies whose success is dependent on other factors. apart from the relationship among various lean strategies, it was also essential to express the role of individual strategy also. it was observed that most of the selected strategies have very high driving power and dependence power as well. no lean strategy was identified which fall in the autonomous cluster. higher collaboration for better production planning (s10) and monitoring the implementation schedules step by step (s11) have been identified as the independent strategies which have high driving power and low dependence power. also, minimizing work in progress (s7) and recycling of raw materials and defective parts (s9) were categorized in dependence cluster as they have low driving power and high dependence power. organization across the globe now wants to make their system more define for every aspect. the present research contribution gives the optimistic correlation between different lean strategies to maintain their organization systematically. the present research assists the managers or industrialists in decision making for the implication of particular lean strategy during the production. the outcomes of this research may also be helpful for managers to comprehend the indirect and direct relationship among various lean strategies in order to provide a path to improve the efficiency of their enterprise in this competitive market. as an advantage of lean system in manufacturing organization, it is most valuable to identify and asses the importance of strategies related to lean system but it is not easy or feasible to implement the all strategies at a time in any industry or organization. for the same, a need arises to explore the strategies based on their dependence and driving behavior in order to implement and improve the lean manufacturing system of an organization. by keeping this view in mind, this study has been performed. 6.1 limitations and future scope of the work in this study, initially thirty-six lean strategies were identified on the basis of literature review; however, thirteen lean strategies have been extracted by using factor analysis. in ism approach, there is no restriction in consideration on numbers of lean strategies, therefore more numbers of lean strategies can also be considered. moreover, as the numbers of lean strategies increases, ism model will become more complex. to drive the analysis, data have been gathered only from the automobiles industries situated at delhi ncr. in future, data can also be gathered from the automobile industries situated at different locations of india and comprehensive study can also be implemented. to compare the outcomes of present research, the other multi-faceted decision building approaches like fuzzy dematel and sem can be considered. modeling and analysis of lean manufacturing strategies using ism-fuzzy micmac approach 61 references ahlstrom, p. 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(2006). decision sciences research in china: a critical review and research agenda—foundations and overview. decision sciences, 37(4): 451-496. © 2021 by the authors. submitted for possible open access publication under the terms and conditions of the creative commons attribution (cc by) license (http://creativecommons.org/licenses/by/4.0/). modeling and analysis of lean manufacturing strategies using ism-fuzzy micmac approach mohit tyagi 1, dilbagh panchal 1*, deepak kumar 2, r. s. walia 3 1. introduction 2. literature review 3. research methodology 4. proposed research methodology implementation based results 4.1 structural self-interaction matrix (ssim) 4.2 reachability matrix 4.3 level partition 4.4 fuzzy micmac analysis 4.5 creating the binary direct relationship matrix 4.6 constructing the fuzzy direct reachability matrix 5. managerial implications of the work 6. conclusion 6.1 limitations and future scope of the work references