11094 FACTA UNIVERSITATIS Series: Mechanical Engineering https://doi.org/10.22190/FUME231115032E © 2024 by University of Niš, Serbia | Creative Commons License: CC BY-NC-ND Original scientific paper ROUGH MULTI- PERIOD NETWORK DATA ENVELOPMENT ANALYSIS FOR EVALUATION OF SUPPLY CHAIN: A CASE STUDY OF SKILL TRAINING IN IRAN Sepideh Ebadi1, Ali Tajdin1, Iraj Mahdavi1, Hamed Fazlollahtabar2 1Department of Industrial Engineering, Mazandaran University of Science and Technology, Babol, Iran 2Department of Industrial Engineering, School of Engineering, Damghan University, Damghan, Iran Abstract. The existence of a comprehensive and complete model, along with accurate and reliable data, helps to evaluate the performance of the supply chain. Given the different layers and various performances in designing the supply chain, a method that can analyze and evaluate such network structure is required. Moreover, data and conditions’ uncertainty highlight the need for a method that can also include uncertainty in evaluation. In this paper, designing a multi-period network is carried out with rough data to embed in various layers and levels of supply chain. The supply chain performance evaluation is performed using rough network data envelopment analysis. Rough Network Data Envelopment Analysis (RNDEA) is a proper method since it analyzes all the current factors in evaluation; besides, it provides efficiency scores for inefficient decision- making units and boundary forecasting for these units on an efficient border. The study’s outcomes reveal the efficiency of different factors in the designed network. On the other hand, unlike common data envelopment analysis that indicates the maximum of a factor efficiency, the efficiency priority is calculated in the proposed rough network model, and divisional efficiency also is determined in each step. Key words: Network Data Envelopment Analysis, Rough Numbers, Multi-period, Performance Evaluation 1. INTRODUCTION Performance evaluation is essential because it acquaints us regarding the amounts of activities’ favorability and quality, creates a positive sign in societies, and improves the Received: November 15, 2023 / Accepted May 20, 2024 Corresponding author: Hamed Fazlollahtabar Department of Industrial Engineering, School of Engineering Damghan University, University Street, University Square, Damghan, Iran, Postal Code: 36716-41167 E-mail: h.fazl@du.ac.ir 2 S. EBADI, A. TAJDIN, I. MAHDAVI, H. FAZOLLAHTABAR services’ quality, particularly in dynamic environments. Recognizing various attitudes regarding performance evaluation indicate that evaluation discipline must be proportional to the growth and development of organizations and can respond to their various and numerous dimensions. On the other hand, if control and evaluation in a system are not carried out, communication with the internal and external environment of the organization is not established leading to make it impossible to performing the required reforms for the growth, development, and improvement of the organization’s activities. In two recent decades, there has been growing interest in evaluating the local governments’ performance worldwide [1]. Implementation and performing a performance evaluation system is one factor that ensures organizations’ growth and development. According to global competition, organizations continuously improve their quality processes to stay in competition. Companies concluded that competition enhancement supports them in detecting performance enhancement and provides cheaper products than efficient production competitors [2]. The competitiveness of organizations depends on their performance levels. For such cases, it is crucial to have a measurement and evaluation system that provides sets of indicators and reliable information for reflecting their goals and performance evaluation. In preparing and implementing organizational policies, performance evaluation is a key section. As a principle, each organization must evaluate its performance capacities as far as possible. Several factors influence the countries’ growth and development. Based on the performed studies in this regard, efficiency lead to the enhancement of economic development speed. Hence, enhancing organizations’ performance and efficiency is an inevitable necessity for survival in today’s global market. The mentioned issue is not exclusive to a particular sector or industry and includes all economic sectors within a limited period [3]. The performance measurement system is critical in business management since it provides the required information for decision-making proceedings. Therefore, measuring the proper cases at the appropriate time is critical in the supply chain. Nevertheless, companies often fail in maximizing the limpid strategies benefits due to their failure to develop required performance measurement indicators for inefficiencies evaluation and efficiency improvement [4]. 2. LITERATURE REVIEW The customers’ requirements have become more differentiated and diverse, along with the intensification of competitiveness in the market more than ever. In this regard, companies seeking the main market competition must convert the unit operation into a status in which suppliers, customers, and partners can cooperate in various aspects. Accordingly, the necessity of supply chain management is gradually enhanced. In these market spaces, competition between companies converts to competition among supply chains gradually [5]. Nowadays, competition among supply chains has replaced competition among individual companies. Hence, assessing the supply chain efficiency is one of the critical and fundamental issues since the management of each process is impossible without its efficiency assay. One of the most interesting fields in Data Envelopment Analysis (DEA) is the analysis of the efficiency of the network and multi-stage systems [6]. The supply chain performance issues are evaluated using DEA. In common DEA models (to be used for evaluating the Rough Multi- Period Network Data Envelopment Analysis for Evaluation of Supply Chain… 3 efficiency of decision-maker units), there are several inputs and outputs. Ignoring the intermediate products and link activities is one of the problems of these models [7]. There is extensive literature for assessing and evaluating the performance or efficiency of various systems using DEA. A summary of performed researches for evaluating the supply chain performance is provided in Table 1. Table 1 Summary of evaluation methods for the supply chain performance Year Important variables Research Methods Title Reference 2012 Fuzzy number, Non radial model, Performance evaluation, Intermediate production NDEA Evaluating performance supply chain by a new non- radial network DEA model with fuzzy data [8] 2014 Economic performance, Environmental performance, Dual-role factors, Undesirable outputs, Fuzzy set NDEA A novel network data envelopment analysis model for evaluating green supply chain management [9] 2014 Financial factors, Performance Indicators, Intellectual capital, Responsiveness, Cooperation Factor Analysis A network data envelopment analysis model for supply chain performance evaluation: real case of Iranian pharmaceutical industry [10] 2018 Performance, Humanitarian disasters NDEA Developing a new chance constrained NDEA model to measure the performance of humanitarian supply chains [11] 2018 Performance, Stochastic data NDEA Developing a new chance constrained NDEA model to measure performance of sustainable supply chains [12] 2019 Performance, Process, Consulting, Educational Services NDEA Multi-period network data envelopment analysis to measure efficiency of a real business [13] 2020 Overall weights, Efficiency, Intuitionistic Fuzzy, Ranking Intuitionistic Fuzzy ANP -NDEA Efficiency Measurement for Hierarchical Network Systems Using Network DEA and Intuitionistic Fuzzy ANP [14] There are several applications of DEA in evaluating the efficiency of training units [15]. DEA is a strong performance evaluation method when the Decision-Making Units (DMUs) are homogeneous [16]. This method can solve problems with different inputs and outputs 4 S. EBADI, A. TAJDIN, I. MAHDAVI, H. FAZOLLAHTABAR without pre-defined weights; hence, it is used more than other performance evaluation methods [17]. This method has been used in various fields such as transportation, supply chain, production [18], training, insurance [19], financial affairs [20], and energy systems [21, 22]. Estimating the system’s general efficiency based on initial inputs and final outputs and bypassing the role of the internal structure of production processes are problems of the traditional DEA method. Some production processes produce intermediate products that are used as input for the next step of the final output production [23]. Chen et al. [24] performed a study and recommended a novel Fuzzy BWM-DEA approach for selecting the smart product service module. Providing the applicable model for evaluating the performance of supply chain networks was the purpose in [25]. In this work, the rough set theory has been used to construct a model for evaluating the performance of the supply chain in uncertain conditions. This model creates a novel point of view for utilizing a performance evaluation model to support managerial decision- making in a dynamic environment and uncertain conditions. 3. PROBLEM DEFINITION AND MODELLING In DEA, various methods are used to assess and evaluate efficiency and performance [26]. In multi-stage supply chains, outputs of a process stage are used as inputs of subsequent stages and have intermediate status. Therefore, the structure of the network data envelopment analysis (NDEA) model is evolved. Several researchers extensively applied the series-DEA model [2]. The considered supply chain system is in series. In most situations that DMUs have a two-step structure, the outputs of the first step are used as input for the next step. The existing DEA multi-step models in literature can be classified into two categories: closed system models and open system models [27]. In closed system DEA models, the intermediate outputs have remained without change from one step to another step. Contrary, in open DEA system models, intermediate outputs of a step are partial inputs of the next step [28]. Various models of DEA have been extended in recent years to use in distinct fields. Selection of models or appropriate models is one of the crucial steps before evaluating the studied units. Thereby, evaluating the efficiency of these types of network structures is critical. The system’s general efficiency is decomposed into two steps in the structure of a two-step network. Kao reformed the DEA standard model considering the multi-step series relationship in general processes [29]. In the two-step structure problem, j𝜖J={1, …, n} is the index set of the n DMUs; j0𝜖J denotes the evaluated DMU; xij is the vector of stage -1 external inputs i used by DMU j; zpj is the vector of intermediate measures p for DMU j; yrj is the vector of stage-2 final outputs r produced by DMU j; v=(v1, …, vm) is the vector of weights of the stage-1 external inputs; w=(w1, …, wq) is the vector of weights for the intermediate measures; u=(u1, …, us) is the vector of weights of the stage-2 0utputs. Suppose a case where each DMU converts the x external inputs to y final outputs through z intermediate indicators with a two-step process. Nothing except first step inputs are entered in these initial settings, and nothing except second step outputs are not exited from the system. E1(vrs) j is the efficiency of the first stage for DMU j. Commonly, the efficiency of DMUj in the first step is defined as follows: Rough Multi- Period Network Data Envelopment Analysis for Evaluation of Supply Chain… 5 𝐸𝑗 1(𝑣𝑟𝑠) = ∑ 𝑤𝑝 𝑧𝑝𝑗 𝑞 𝑝=1 ∑ 𝑣𝑖𝑥𝑖𝑗 𝑚 𝑖=1 (1) The efficiency of DMU j in the second step is defined as follows: 𝐸𝑗 2(𝑣𝑟𝑠) = ∑ 𝑢𝑟𝑦𝑟𝑗 𝑠 𝑟=1 ∑ 𝑤𝑝𝑧𝑝𝑗 𝑞 𝑝=1 (2) The overall efficiency of DMU j is defined as follows: 𝐸𝑗 (𝑣𝑟𝑠) = ∑ 𝑢𝑟𝑦𝑟𝑗 𝑠 𝑟=1 ∑ 𝑣𝑖𝑥𝑖𝑗 𝑚 𝑖=1 (3) After simplification, we have Model I as follows: 𝑚𝑎𝑥 𝐸𝑘 (𝑣𝑟𝑠) = ∑ 𝑢𝑟𝑦𝑟𝑘 𝑠 𝑟=1 (4) s.t. ∑ 𝑣𝑖𝑥𝑖𝑘 = 1𝑚 𝑖=1 (5) ∑ 𝑤𝑝𝑧𝑝𝑗 − ∑ 𝑣𝑖𝑥𝑖𝑗 ≤ 0, 𝑗 = 1,… , 𝑛𝑚 𝑖=1 𝑞 𝑝=1 (6) ∑ 𝑢𝑟𝑦𝑟𝑗 − ∑ 𝑤𝑝𝑧𝑝𝑗 ≤ 0, 𝑗 = 1,… , 𝑛 𝑞 𝑝=1 𝑠 𝑟=1 (7) 𝑣𝑖 ≥ 0, 𝑖 = 1,… ,𝑚 (8) 𝑤𝑝 ≥ 0, 𝑝 = 1,… , 𝑞 (9) 𝑢𝑟 ≥ 0, 𝑟 = 1,… , 𝑠 (10) Since the designed model of the problem is examined in real conditions in different periods, designing the evaluation model as a multi-period is required due to assessing the evaluation output in different periods, and the requirement of revision or improvement is planned for each period exclusively [30]. Model II: Periods are added to examine the mathematical model of NDEA as multi- period in Model I; therefore, the proposed model having period index t is given below: 𝑚𝑎𝑥 𝐸𝑘 (𝑣𝑟𝑠) = ∑ 𝑢𝑟𝑡𝑦𝑟𝑘𝑡 𝑠 𝑟=1 (11) s.t. ∑ 𝑣𝑖𝑡𝑥𝑖𝑘𝑡 = 1𝑚 𝑖=1 (12) ∑ 𝑤𝑝𝑡𝑧𝑝𝑗𝑡 − ∑ 𝑣𝑖𝑡𝑥𝑖𝑗𝑡 ≤ 0, 𝑗 = 1,… , 𝑛𝑚 𝑖=1 𝑞 𝑝=1 (13) ∑ 𝑢𝑟𝑡𝑦𝑟𝑗𝑡 − ∑ 𝑤𝑝𝑡𝑧𝑝𝑗𝑡 ≤ 0, 𝑗 = 1,… , 𝑛 𝑞 𝑝=1 𝑠 𝑟=1 (14) 𝑣𝑖 ≥ 0, 𝑖 = 1,… ,𝑚 (15) 𝑤𝑝 ≥ 0, 𝑝 = 1,… , 𝑞 (16) 𝑢𝑟 ≥ 0, 𝑟 = 1,… , 𝑠 (17) 6 S. EBADI, A. TAJDIN, I. MAHDAVI, H. FAZOLLAHTABAR 3.1 Rough Network Data Envelopment Analysis In recent decades, the performance evaluation with rough network data envelopment analysis is attracted scholars worldwide. The outputs and inputs in rough envelopment analysis are interval numbers obtained based on the up and down approximate of the rough set theory. The rough network data envelopment analysis (RNDEA) process has been used in this research due to subjective and ambiguous skill learners’ judgments and opinions regarding obtained feedback from the training process. There are studies that made use of uncertainty in evaluation processes in supply chain and production scheduling [31]. Further, possibility theory using correlation study was applied in mechanical specification analysis [32]. The following steps of the RNDEA process are presented. According to the rough data envelopment analysis model, the envelopment analysis model with rough multi- period network data is defined as follows: 𝑀𝑎𝑥 𝑒̃ 𝑘 = ∑ 𝑢𝑟𝑡⌈𝑦𝑟𝑘𝑡 𝐿 , 𝑦𝑟𝑘𝑡 𝑈 ⌋𝑠 𝑟=1 (18) s.t. ∑ 𝑣𝑖𝑡⌈𝑥𝑖𝑘𝑡 𝐿 , 𝑥𝑖𝑘𝑡 𝑈 ⌋𝑚 𝑖=1 = 1 (19) ∑ 𝑤𝑝𝑡⌈𝑧𝑝𝑗𝑡 𝐿 , 𝑧𝑑𝑗 𝑈 ⌋ 𝑞 𝑝=1 ∑ 𝑣𝑖𝑡⌈𝑥𝑖𝑗𝑡 𝐿 , 𝑥𝑖𝑗𝑡 𝑈 ⌋ ≤ 0 , 𝑗 = 1,2, … , 𝑛𝑚 𝑖=1 (20) ∑ 𝑢𝑟𝑡⌈𝑦𝑟𝑗𝑡 𝐿 , 𝑦𝑟𝑗 𝑈 ⌋𝑠 𝑟=1 − ∑ 𝑤𝑝𝑡⌈𝑧𝑝𝑗𝑡 𝐿 , 𝑞 𝑝=1 𝑧𝑝𝑗𝑡 𝑈 ⌋ ≤ 0 , 𝑗 = 1,2, … , 𝑛 (21) 𝑢𝑟𝑡 , 𝑤𝑝𝑡 , 𝑣𝑖𝑡 ≥ 𝜀 > 0 (22) Here, yL rjt and yU rjt are the lower and upper limits of network outputs, respectively, obtained from the calculation of the rough number. Moreover, zL pjt and zU pjt are the lower and upper limits of the input of the second sub-system. xL ijt and xU ijt are lower and upper limits of inputs of the first sub-system in the network series. urt, wpt, and vit are the weights of the network’s inputs and outputs. In this model, the p index indicated the p-th decision-making unit. Furthermore, all weights are considered greater than a very small positive number (𝜀). The method of modeling in pessimistic state is as follows: 𝑀𝑎𝑥 𝑒̃𝑝 𝐿 = ∑ 𝑢𝑟𝑡𝑦𝑟𝑘𝑡 𝐿 𝑟 (23) s.t. ∑ 𝑣𝑖𝑡𝑥𝑖𝑘𝑡 𝑈 𝑖 = 1 (24) ∑ 𝑢𝑟𝑡𝑦𝑟𝑗𝑡 𝐿 𝑟 −∑ 𝑤𝑝𝑡𝑧𝑝𝑗𝑡 𝑈 𝑝 ≤ 0 (25) ∑ 𝑢𝑟𝑡𝑦𝑟𝑗𝑡 𝑈 −∑ 𝑤𝑝𝑡𝑧𝑝𝑗𝑡 𝐿 𝑝 ≤ 0, 𝑗 = 1,2, … , 𝑛, 𝑗 ≠ 𝑝𝑟 (26) ∑ 𝑤𝑝𝑡𝑧𝑝𝑗𝑡 𝐿 − ∑ 𝑣𝑖𝑡𝑥𝑖𝑗𝑡 𝑈 𝑖𝑝 ≤ 0 (27) ∑ 𝑤𝑝𝑡𝑧𝑝𝑗𝑡 𝑈 𝑝 − ∑ 𝑣𝑖𝑡𝑥𝑖𝑗𝑡 𝐿 𝑖 ≤ 0, 𝑗 = 1,2, … , 𝑛, 𝑗 ≠ 𝑝 (28) 𝑢𝑟 , 𝑤𝑑 , 𝑣𝑖 ≥ 𝜀 > 0 (29) The method of modeling in optimistic state is as follows: 𝑀𝑎𝑥 𝑒̃𝑝 𝑈 = ∑ 𝑢𝑟𝑡𝑦𝑟𝑘𝑡 𝑈 𝑟 (30) Rough Multi- Period Network Data Envelopment Analysis for Evaluation of Supply Chain… 7 s.t. ∑ 𝑣𝑖𝑡𝑥𝑖𝑘𝑡 𝐿 𝑖 = 1 (31) ∑ 𝑢𝑟𝑡𝑦𝑟𝑗𝑡 𝑈 𝑟 −∑ 𝑤𝑝𝑡𝑍𝑧𝑝𝑗𝑡 𝐿 𝑝 ≤ 0 (32) ∑ 𝑢𝑟𝑡𝑦𝑟𝑗𝑡 𝐿 −∑ 𝑤𝑝𝑡𝑧𝑝𝑗𝑡 𝑈 𝑝 ≤ 0, 𝑗 = 1,2, … , 𝑛, 𝑗 ≠ 𝑝𝑟 (33) ∑ 𝑤𝑝𝑡𝑧𝑝𝑗𝑡 𝑈 − ∑ 𝑣𝑖𝑡𝑥𝑖𝑗𝑡 𝐿 𝑖𝑝 ≤ 0 (34) ∑ 𝑤𝑝𝑡𝑧𝑝𝑗𝑡 𝐿 𝑝 − ∑ 𝑣𝑖𝑡𝑥𝑖𝑗𝑡 𝑈 𝑖 ≤ 0, 𝑗 = 1,2, … , 𝑛, 𝑗 ≠ 𝑝 (35) 𝑢𝑟 , 𝑤𝑑 , 𝑣𝑖 ≥ 𝜀 > 0 (36) 4. NUMERICAL IMPLEMENTATION The employment rate is critical among the policymakers in various countries, given the population growth, the unskillfulness of many people (even academic graduates), and eventually the unemployment of mass ranges of society. By reviewing the researches conducted in the field of designing education supply chains, it was observed that the supply chain for higher education and post-graduate education had been established, but so far there was no supply chain for skill training in the literature. It is due to the more or less encountering of most countries (from industrial societies to third world developing countries) with unemployment problems in different ways. Skill training can be considered the main priority of the educational system as an essential tool for cultivating and enhancing the efficiency and productivity of human forces to reform and solve unemployment and economic development. There are two steps in the supply chain of skill training. Generally, it can be mentioned that the outputs of a process step are considered the inputs of the next step, and it has intermediate status. Therefore, the structure of the present study is a two-step network. Only three main levels are considered to evaluate this chain as follows: First level (suppliers), Second level (training process), and Third level (consumers). The components of the first level: higher education graduates, educational and educational aids equipment, supplies equipment, training workshop, training course, the cost of center overhead, training support force, training content, training portal, welfare; The components of the second level: Consultation and guidance of career, training scheduling, designing of training model, training forms, and theoretical and operational evaluation; The components of the third level): results of employment, final products. This research was carried out for five popular standards in the industry cluster and skill training field. For this purpose, five influential provinces in Iran with higher amount of population, including Alborz, East Azerbaijan, Isfahan, Razavi Khorasan, and Tehran are investigated. Initially, the collected data in five provinces were converted to rough data using related input data to factors’ performance in different layers in the first period. The summary is given in Tables 2, 3, and 4. 8 S. EBADI, A. TAJDIN, I. MAHDAVI, H. FAZOLLAHTABAR Table 2 Rough output related to the first layer DMU x1 x2 x3 x4 L U L U L U L U Motoring 40.02 42.56 147.16 152 334.06 343.85 31.97 35.43 Electricity 22.5 25.5 246.14 251.25 278.75 286.25 22.04 25.95 Turning 16.43 18.97 156.14 165.93 237.5 252.5 16.02 18.56 Welding 26.70 29.12 123.75 131.25 157.16 162 24.62 28.02 Cartography 8.75 10.25 56.77 60.81 31.70 35.29 10.22 12.18 DMU x5 x6 x7 x8 L U L U L U L U Motoring 34.5 37.5 133.75 138.64 207.5 222.5 3.75 4.72 Electricity 22.04 25.95 89.56 93.02 128.62 135.20 3.75 4.72 Turning 18.29 20.70 59.85 63.56 133.75 141.25 5.27 6.25 Welding 33.38 28.56 93.27 97.97 137.72 140.64 3.75 5.25 Cartography 9.29 11.70 41.43 43.97 64.41 67.75 4.75 6.25 DMU x9 x10 L U L U Motoring 31.62 36.70 31.62 36.70 Electricity 21.29 23.70 21.97 25.43 Turning 16.16 18.83 17.29 19.70 Welding 21.89 26.85 23.52 27.89 Cartography 11.29 13.70 10.08333 13.08 Uncertainty of data and conditions determines the need for a method that can apply uncertainty in evaluation. As a result, the design of a multi-period network is done with raw data to embed suitable factors in different layers and levels. Evaluation of supply chain performance is done through the rough network data envelopment analysis method. Rough Network Data Envelopment Analysis (RNDEA) is a suitable method because it analyzes all factors in the evaluation. Considering that employment is one of the important and discussed issues of policy makers in different countries of the world and most of the countries are more or less facing the issue of unemployment. On the other hand, due to the fact that there is a deep and inferable link between education and employment, and education is considered an important factor in economic growth and employment, addressing the issue of education, especially skill training, which has not been addressed so far, is an inevitable necessity. This is why one of the important priorities in educational investments is the development and expansion of skill-based education. Rough Multi- Period Network Data Envelopment Analysis for Evaluation of Supply Chain… 9 Table 3 Rough output related to the second layer DMU z1 z2 z3 L U L U L U Motoring 979.58 994.58 4.58 5.41 986.77 1001.14 Electricity 338 342.83 5.27 6.25 338.31 345.43 Turning 258.5 264.16 5.12 5.87 262.85 267.68 Welding 455.43 474.14 9.70 13.29 465.85 475.39 Cartography 172.18 184.89 3.75 5.25 179.06 188.85 DMU z4 z5 L U L U Motoring 33 37.83 986.14 995.93 Electricity 21.29 23.70 334.04 341.79 Turning 14.56 18.02 257.64 266.93 Welding 24.70 28.29 468.45 475.70 Cartography 11.29 13.70 184.06 193.85 Table 4 Rough output related to the third layer DMU y1 y2 y3 y4 L U L U L U L U Motoring 83 87.83 104.18 108.22 64.06 73.85 168.60 175.97 Electricity 27.43 32.14 40.12 44.87 22.72 27.68 53.60 60.97 Turning 22.66 13.83 25.60 31.81 17.60 21.64 42.04 47.12 Welding 37.18 43.29 53.37 57.62 33.77 37.81 83 87.83 Cartography 22.39 27.02 29.97 33.43 17.12 20.70 42.45 47.54 By providing informal skill training along with high formal training, a very effective step can be taken in the development of human resource employment. Therefore, due to increasing the efficiency and effectiveness of training in skill-oriented organizations, checking the progress towards the set educational goals, correct formulation of educational policies, identifying the components that need more attention and obtaining information in order to make the right decisions, it is necessary to enforce the training performance evaluation. Having a chain of training for this type of training can help a lot in training a capable and trained workforce ready to work in the society. Designing a performance evaluation model for skill training that leads to sustainable political, economic, social, cultural and environmental development is an undeniable necessity. Considering the special and important role of skill training in increasing people's skills and employment, designing and evaluating the supply chain of these trainings is considered very important. The need to evaluate the performance of the education supply chain is important because it increases 10 S. EBADI, A. TAJDIN, I. MAHDAVI, H. FAZOLLAHTABAR the efficiency and effectiveness of education. The findings of the research show the efficiency of various factors in the stages of the designed network. In addition, it provides efficiency scores for inefficient decision-making units and boundary prediction for these units in an efficient boundary. Then, performance evaluation is carried out using input data and the proposed RNDEA model. The outputs of each step of efficiency evaluation in the rough form in the first period are indicated in Table 5. Table 5 Output for period 1 Rank Rough DMU NO 5 [0.285,0.571] Motoring 1 1 [0.639,1] Electricity 2 3 [0.450,0.767] Turning 3 4 [0.346,0.648] Welding 4 2 [0.633,0.855] Cartography 5 Notably, the mentioned process is repeated; performance evaluation is performed in different periods, and an improvement solution is provided. The results of this study show the effectiveness of different factors in the stages of network design. By designing the performance evaluation model of the skill training supply chain network, we tried to identify the best performance for the supply chain. 5. CONCLUSION Based on the outputs table, the best efficiency is related to the electrical field due to having the maximum efficiency in the first, second, and third layers. Besides, the lowest efficiency is related to motoring. Thereby: Electricity > Cartography > Turning > Welding > Motoring; It can be described that these results were obtained given the supply chain components of skill training that are used in this research and declared in the numerical example section. Moreover, the following reasons can be pointed out for the low efficiency of debated fields: lack of updated proper workshop equipment based on the requirement of the labor market, no existence of sufficient consumer goods due to the budget deficit, not the proportion of knowledge and experience of instructors with skill artisan and updated changes of technology, lack of insurance of employed skill learners in the repair shop, also skill learners that established their considered business, and lack of providing accurate information in employment tracking to the staff of career monitoring. Another point is that most skill courses in electrical, building cartography, order-oriented turning and welding, and proportion to work market requirements. In contrast, the most presented periods in the motoring field are supply-oriented. Thereby, most of the skilled learners participate in four required fields in the market, leading to employment. 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