FACTA UNIVERSITATIS Series: Mechanical Engineering Vol. 19, No 3, Special Issue, 2021, pp. 515 - 535 https://doi.org/10.22190/FUME210424060U © 2021 by University of Niš, Serbia | Creative Commons License: CC BY-NC-ND Original scientific paper A NEW INTEGRATED GREY MCDM MODEL: CASE OF WAREHOUSE LOCATION SELECTION Alptekin Ulutaş1, Figen Balo2, Lutfu Sua3, Ezgi Demir4, Ayşe Topal5, Vladimir Jakovljević6 1Sivas Cumhuriyet University, International Trade and Logistics Department, Turkey 2Fırat University, Industrial Engineering Department, Turkey 3School of Entrepreneurship and Business Administration, AUCA, Kyrgyzstan 4Piri Reis University, Management Information System Department, Turkey 5Niğde Ömer Halisdemir University, Business Department, Turkey 6University of Sidney, School of Mathematics and Statistics, Australia Abstract. Warehouses link suppliers and customers throughout the entire supply chain. The location of the warehouse has a significant impact on the logistics process. Even though all other warehouse activities are successful, if the product dispatched from the warehouse fails to meet the customer needs in time, the company may face with the risk of losing customers. This affects the performance of the whole supply chain therefore the choice of warehouse location is an important decision problem. This problem is a multi- criteria decision-making (MCDM) problem since it involves many criteria and alternatives in the selection process. This study proposes an integrated grey MCDM model including grey preference selection index (GPSI) and grey proximity indexed value (GPIV) to determine the most appropriate warehouse location for a supermarket. This study aims to make three contributions to the literature. PSI and PIV methods combined with grey theory will be introduced for the first time in the literature. In addition, GPSI and GPIV methods will be combined and used to select the best warehouse location. In this study, the performances of five warehouse location alternatives were assessed with twelve criteria. Location 4 is found as the best alternative in GPIV. The GPIV results were compared with other grey MCDM methods, and it was found that GPIV method is reliable. It has been determined from the sensitivity analysis that the change in criteria weights causes a change in the ranking of the locations therefore GPIV method was found to be sensitive to the change in criteria weights. Key words: Grey preference selection index, Grey proximity indexed value, Multi- criteria decision making, Warehouse location selection Received April 24, 2021 / Accepted August 26, 2021 Corresponding author: Alptekin Ulutaş Department of International Trade and Logistics, Sivas Cumhuriyet University, Sivas, Turkey E-mail: aulutas@cumhuriyet.edu.tr 516 A. ULUTAŞ, F. BALO, L. SUA, E. DEMIR, A. TOPAL, V. JAKOVLJEVIĆ 1. INTRODUCTION Warehouses are critical elements that affect the performance of an entire supply chain. In addition, warehouses are links between upstream suppliers and downstream customers throughout the entire supply chain. Warehouses can also be described as places where efficient using of space and equipment are made in. To react more quickly to client demands with reduced costs, efficient warehousing activities considerably decrease the order picking distance and processing time of item motion for order fulfillment within a warehouse [1]. No matter how successful the warehouse activities are, if the product dispatched from the warehouse fails to meet the customer needs in time, the company will risk losing customers. One of the most important factors in the timely delivery of the product is the location of the warehouse therefore enterprises need to develop effective solutions for the warehouse location selection problem which has a significant impact on logistics processes [2]. The problem of warehouse location selection requires a crucial strategic decision plan for the businesses profitably. Deciding on distribution warehouse locations is one of the most important issues to be considered in logistics problems. Choosing the right warehouse location provides competition and benefits for companies. At the same time, the location of the distribution warehouse is important in issues such as proximity to distribution locations, cost, and labor. Since there are usually more than one alternative and more than one criteria to be considered in the problem of selecting a warehouse location, this problem can be solved by using multi-criteria decision-making (MCDM) methods. MCDM methods are frequently used in the solution of assessment and sequencing problems including many conflicting criteria [3]. They are useful in determining the best alternative in a system with multiple alternatives and multiple criteria to be taken into account. Many real-world decision-making problems do not contain crisp data. Most of the data consist of uncertainty and vagueness. To deal with the uncertainty, different methodologies were developed such as fuzzy set theory, rough theory, D numbers, and grey theory. In the literature, these methodologies have mostly been used in combination with MCDM methods. For example, Ecer and Pamucar [4] have used fuzzy BWM (best worst method) to find the relative weights and fuzzy CoCoSo (combined compromise solution) with Bonferroni (CoCoSo’B) to rank alternatives in sustainable supplier selection problem. Ecer and Pamucar [5] assessed insurance companies according to their service quality in Covid- 19 by using intuitionistic fuzzy MARCOS (measurement of alternatives and ranking according to compromise solution). Shojaei and Bolvardizadeh [6] has used rough AHP (analytic hierarchy process) and rough TOPSIS (technique for order performance by similarity to ideal solution) for assessing suppliers in terms of sustainability in construction industry. Stević et al. [7] has used rough PIPRECIA (pivot pairwise relative criteria importance assessment) to evaluate tools in sustainable production and fuzzy MARCOS to rank forest companies. Pamucar et al. [8] ranked zero-carbon strategies in London transportation system with fuzzy BWM-D and TODIM (an acronym in Portuguese for interactive and multi criteria decision making)-D. Tian et al. [9] have used AHP and grey correlation TOPSIS for material selection problem in construction industry. Tadić et al. [10] assessed location alternatives for dry ports by using Delphi, AHP, and CODAS (combinative distance-based assessment) with grey numbers. A New Integrated Grey MCDM Model: Case of Warehouse Location Selection 517 Grey numbers’ major benefit is its adaptability in dealing with complicated scenarios. In addition, grey theory can be used successfully compared to fuzzy sets in terms of a small amount of data and limited and incomplete data [11-13]. If the upper and lower values of criteria (including uncertain data) are known, these criteria can be expressed in grey numbers. As they are known in this decision problem, a grey MCDM method is used in this study. Decision-makers can also make use of rough set theory to deal with uncertainty. However, in the rough set theory, crisp numbers can be used to handle uncertainty. On the contrary, in grey theory, uncertainty is handled by using interval values, which helps to take the data in a larger framework rather than compressing the data into crisp numbers. Therefore, in this study, the grey extensions of MCDM (PSI and PIV) methods are proposed to solve the warehouse selection problem. This study proposes an integrated grey MCDM model including GPSI (grey preference selection index) and GPIV (grey proximity indexed value) to determine the most appropriate warehouse location for a supermarket. While the GPSI method is used to determine the weights of the criteria, the GPIV method is used to evaluate the performance of the alternatives and to rank these alternatives. PSI's main benefit is that, unlike other MCDM approaches, it does not need assigning a relative priority between criteria [14]. Compared to other MCDM methods, PIV has comparatively straightforward and effective with simple computing steps, and minimizes rank reversal issues [15-16]. The flow of methodology is demonstrated in Fig. 1. Fig. 1 The steps of grey MCDM methodology for location selection Criteria Weights • Creating a grey decision matrix • Developing normalized grey decision matrix • Finding mean grey normalized values • Calculating the grey preference values • Determining the grey deviation values • Finding the grey weights Alternative Ranking • Forming the grey decision matrix • Normalizing the grey decision matrix • Multiplying values in normalized matrix with grey weights of criteria • Developing grey weighted proximity index • Computing crisp overall proximity values • Ranking alternatives Sensitivity Analysis • Using four different criteria weigth sets • Ranking alternatives with new weights 518 A. ULUTAŞ, F. BALO, L. SUA, E. DEMIR, A. TOPAL, V. JAKOVLJEVIĆ This study aims to make three contributions to the literature. First, PSI and PIV methods combined with grey theory will be introduced for the first time in the literature. There is no study that combined grey theory with PSI and PIV methods to the best of our knowledge. Combining these two methods with grey theory will aid to effectively handle the uncertainties in the problem. Second, GPSI and GPIV methods will be combined and used to select the best warehouse location. It has not been seen in the literature that GPSI and GPIV methods are used together in solving any MCDM problems. The study is organized as follows. In Section 2, the literature review is made concerning the warehouse location selection, PSI and PIV methods. In Section 3, the methodology of GPSI and GPIV methods is presented. In Section 4, the results of the proposed model are indicated. In Section 5, the results of GPSI are compared with the results of other grey MCDM, which are grey TOPSIS [17], grey WASPAS (weighted aggregated sum-product assessment) [18], and grey COPRAS (complex proportional assessment method) [19] and grey weights of criteria are changed using 4 different scenarios and sensitivity analysis is performed. In the last section, a brief conclusion is indicated. 2. LITERATURE REVIEW In this section, first, the studies that solve the problem of selecting the warehouse location with MCDM methods will be presented, then, studies using PSI and PIV methods will be demonstrated. 2.1. Warehouse Location Selection Problem The problem of warehouse location selection has been discussed many times in the literature. For example, Lee [20] discussed cost, Hakimi and Kuo [21] discussed maximizing profitability, Korpela and Lehmusvaara [22] developed a customer-oriented approach and used AHP and mixed integer programming model. In another study, Korpela et al. [23] used AHP and DEA (data envelopment analysis) with distribution time, quantity and quality of distributions, emergency distributions, frequency situations, special requests and capacity criteria. Ho and Emrouznejad [24] developed an application for users to select a warehouse location. Kuo et al. [25], Tabari et al. [26], Chen [27], Kahraman et al. [28], Karmaker and Saha [29] discussed warehouse location selection problem only with fuzzy methodologies. They examined scenario-based examples of wrong decisions that can be made in warehouse selection in terms of economic losses. Stevenson [30] and Frazelle [31] explained warehouse centers as a factor of commercial success and competition. Demirel et al. [32] discussed the critical success factors in warehouse selection in terms of logistics management and optimization. In this study, it was revealed that decision-making processes are extremely important in case of success and failure in the selection of warehouse location. At the same time, it was concluded that a balance should be struck between cost and effectiveness in potential locations in organizational terms. In this context, the warehouse selection model was first modeled by Kuehn and Hamburger [33]. In this study, cost minimization has been aimed with mathematical modeling techniques. Efroymson and Ray [34] and Khumawala [35] selected warehouse locations with the classical linear programming model in their studies. The location problem has been created by Weber and Friedrich [36] and Tellier [37] by minimizing the distances to the final distribution locations. Owen and Daskin [38] dealt with a comprehensive mathematical A New Integrated Grey MCDM Model: Case of Warehouse Location Selection 519 problem in their work. In this study, benefit and cost values have been considered as the main criteria. On the other hand, various criteria and methodologies have been used by introducing the MCDM methodology. Badri [39] used the AHP method together with linear programming. This study has been focused on 4 main criteria. These criteria are benefits, costs, risks and opportunities. Vlachopoulou et al. [40] suggested a geographic decision support system to choose warehouse location with geographic criteria. Kabak and Keskin [41] proposed geographical information systems (GIS) and AHP models for potential warehouse locations. Nine criteria have been proposed in this study. Yerlikaya et al. [42] suggested an AHP - CRITIC (the criteria importance through intercriteria correlation) –VIKOR (visekriterijumska optimizacija i kompromisno resenje) based approach. In the study, they used cost, speed, safety criteria. Mihajlovic et al. [43] studied fruit warehouse location selection based on AHP and WASPAS. Ma et al. [44] handled the choices of warehouse location utilizing an Integrated Multi-Attribute Decision Making Method based on the cumulative prospect theory. It has been determined a strategic ranking of decision- making schemes by presenting a cumulative foreground theory. Pamučar and Božanić [45] selected location from the suggested choices using a Single- Valued Neutrosophic (SVNN) based MABAC (Multi Attributive Border Approximation Area Comparison) model. It was aimed to select the ideal logistics center location by applying an optimization routine reducing transport costs and improving the business performance, competitiveness and profitability. Tuzkaya et al. [46] used AHP to rank locations to reduce costs and maximize profit. Uysal and Tosun [47] developed a grey theory-based method to solve warehouse location problem and compared the results of ELECTRE (elimination et choix traduisant la realité) and TOPSIS decision-making models. Özcan et al. [48] set the criteria for the most optimal warehouse location in a retail sector and applied grey theory, ELECTRE, TOPSIS and AHP. In this study, the authors considered five criteria, which are stock holding capacity, unit price, mean distance to shops, mean distance to movement flexibility, and primary suppliers, when evaluating four warehouse location alternatives. In another study, Ashrafzadeh et al. [49] used fuzzy TOPSIS to choose the best warehouse location for an Iranian company. They considered fifteen criteria in the evaluation of five alternatives. Dey et al. [50] proposed an integrated fuzzy MCDM to solve warehouse location selection problem in a supply chain. García et al. [51] utilized AHP method to choose the ideal warehouse location for perishable agricultural products. They took into account six criteria, which are costs, distance, needs, security, acceptance and accessibility, in the evaluation of three alternatives. Aktepe and Ersöz [2] used AHP, MOORA (multi-objective optimization method by ratio analysis) and VIKOR methods to address warehouse location selection problem for a company. Six criteria were used in the evaluation of eleven alternatives. Dey et al. [52] proposed three fuzzy MCDM methods, namely fuzzy TOPSIS, fuzzy MOORA and fuzzy simple additive weighting to choose a warehouse location. Additionally, to evaluate the objective criteria, the classical normalization technique is used. Silva et al. [53] used SMARTER and lexicographic method to rank products and assign them to the locations of warehouse storage. Mangalan et al. [54] utilized weighted MOORA method to optimize warehouse site. The results of the proposed method and TOPSIS method were compared to prove the applicability of the proposed method. Temur [55] proposed cloud based design optimization technique tackling high uncertainty. This technique was used in a warehouse location problem in order to indicate the feasibility and performance of this technique. Dey et al. [56] developed a novel multi-criteria group decision-making to determine the best warehouse location for an 520 A. ULUTAŞ, F. BALO, L. SUA, E. DEMIR, A. TOPAL, V. JAKOVLJEVIĆ Indian company. Four criteria, which are space availability, transportation facility, cost and availability of markets, were considered in the evaluation process. Raut et al. [57] used AHP to determine the best sustainable warehouse location among four alternatives while considering eleven criteria. The most important criterion was determined as governmental policies, and regulations among eleven criteria. Emeç and Akkaya [3] integrated fuzzy VIKOR and stochastic AHP methods to address warehouse location problem for a supermarket. Seventeen criteria were considered when determining the best location among four alternatives. Micale et al. [58] proposed an interval extension of MCDM methods, which are ELECTRE TRI and TOPSIS, to solve storage location assignment problem for an Italian company. Canbolat et al. [59] used decision tree and MABAC methodologies for warehouse location selection. Ehsanifar et al. [60] prioritized and ranked ten criteria using UTASTAR methodology. The most commonly used criteria in the current studies are cost minimization, profitability and geographical factors. 2.2. Literature Related to PSI Method Some recent studies, carried out on PSI method (developed by Maniya and Bhatt [61]), in the literature are summarized in Table 1. Table 1 Literature related to PSI method Authors Methods Application Area Vahdani et al. [62] Interval-Valued Fuzzy PSI Application in Human Resource Management Attri and Grover [63] PSI Illustrative Examples Chamoli [64] PSI For an experiment, the determination of optimum roughness parameters Akyüz and Aka [65] PSI Manufacturing performance measurement in the glass industry Petković et al. [66] PSI Illustrative Examples Madić et al. [67] PSI In determining of laser cutting process conditions Tuş and Adalı [68] CRITIC, PSI, and CODAS In solving of a personnel selection problem for a textile firm Jha et al. [69] PSI In determining of optimum composite combination Pathak et al. [70] PSI and Metaheuristic method In determining of optimum value for parameters of scanning process Ulutaş [71] Fuzzy PSI and Fuzzy ROV In solving of a green supplier selection problem for a textile company 2.3. Literature Related to PIV Method Many MCDM methods [72-78] have been developed in recent years. PIV is one of the newly developed (by Mufazzal and Muzakkir [15]) MCDM methods and it minimizes the rank reversal problem. There are few studies about this method in the literature. Khan et al. [16] used PIV method to indicate the efficacy and applicability of this method. To do this, two illustrative examples related to the e-Learning websites selection were analyzed and the results of PIV method were compared with the results of other MCDM methods A New Integrated Grey MCDM Model: Case of Warehouse Location Selection 521 (COPRAS, VIKOR, AHP, WEDBA and WDBA). In another study, Yahya et al. [79] integrated Entropy and PIV methods to use for multi-response optimization. Nine experiments were evaluated while considering two criteria, which are Zeta potential and viscosity. As it can be observed from literature review, there are limited studies about PSI and PIV methods, and they are mostly used for different decision problems other than location selection. For location selection problem, most of the studies in the literature used crisp MCDM methods, such as AHP and TOPSIS. This clearly shows that there is a gap in the application of new MCDM methods on location selection problem. Additionally, in this study, unlike most of the studies in the literature; costs will be handled in two types, which are holding costs (HC) and transportation costs (TC). In addition, geographical features of the supplied materials, which are distance to customers (DC), distance to suppliers (DS), distance to producers (DP), delivery time (DT), and distance to the opponents (DO), have been handled separately. The criteria list has been enriched by considering different criteria such as capacity of storage (CS), development rate (DR), and transportation diversity (TD). Besides, environmental conditions, specifically infrastructure (I) and climatic conditions (CC), have been used in the selection of the warehouse location. Unlike the most of the studies, 12 different criteria were considered in this study. In the most of the studies, linear programming and cost-benefit optimization, and crisp MCDM methodologies were used to select warehouse location. Also, fuzzy sets were also commonly used in the literature. Fuzzy sets have been used in problems with uncertainty, and they address the problem with linguistic expressions. However, in the case of the small amount of data and limited and incomplete data, the fuzzy set theory is not sufficient. In this context, it is thought that the study will fill the following gaps in the literature: ▪ Few studies in the literature have used grey MCDM methods for warehouse location selection. ▪ There are no grey extensions of the two MCDM methods (PSI and PIV) that have few computations steps and reach a solution quickly. 3. METHODOLOGY In this study, a grey model consisting of GPSI and GPIV methods is proposed for the solution of the warehouse location problem. While the GPSI method is used to determine the weights of the criteria, the GPIV method is used to evaluate the performance of the alternatives and to rank these alternatives. 3.1. Grey Preference Selection Index Step 1: The linguistic values shown in Table 2 will be assigned by the experts as the performance values of the alternatives in the criteria. These performance values are converted to grey values with the help of Table 2, thus forming a grey decision matrix (⨂𝐹). ⨂𝐹 = [⨂𝑓𝑖𝑗 ]𝑚×𝑛 (1) In Eq. (1), ⨂𝑓𝑖𝑗 (⨂𝑓𝑖𝑗 = [𝑓𝑖𝑗 𝑙 , 𝑓𝑖𝑗 𝑢 ]) indicates grey performance value of 𝑖th alternative on 𝑗th criterion. 522 A. ULUTAŞ, F. BALO, L. SUA, E. DEMIR, A. TOPAL, V. JAKOVLJEVIĆ Table 2 Linguistic and grey performance values Linguistic Performance Values Grey Performance Values Very High [9, 10] High [7, 9] Medium [5, 7] Low [3, 5] Very Low [1, 3] Step 2: By utilizing Eq. (2) (beneficial criteria) and Eq. (3) (cost criteria), ⨂𝐹 can be normalized as below. ⨂𝑘𝑖𝑗 = ⨂𝑓𝑖𝑗 𝑚𝑎𝑥(⨂𝑓𝑖𝑗) = [ 𝑓𝑖𝑗 𝑙 𝑚𝑎𝑥(𝑓𝑖𝑗 𝑢) , 𝑓𝑖𝑗 𝑢 𝑚𝑎𝑥(𝑓𝑖𝑗 𝑢) ] (2) ⨂𝑘𝑖𝑗 = 𝑚𝑖𝑛(⨂𝑓𝑖𝑗) ⨂𝑓𝑖𝑗 = [ 𝑚𝑖𝑛(𝑓𝑖𝑗 𝑙 ) 𝑓𝑖𝑗 𝑢 , 𝑚𝑖𝑛(𝑓𝑖𝑗 𝑙 ) 𝑓𝑖𝑗 𝑙 ] (3) In Eqs. (2) and (3), ⨂𝑘𝑖𝑗 indicates the normalized version of ⨂𝑓𝑖𝑗 . Step 3: By using Eq. (4), the mean grey normalized value (⨂�̅�𝑖𝑗 ) of each criterion is calculated as, ⨂�̅�𝑖𝑗 = ∑ ⨂𝑘𝑖𝑗 𝑚 𝑖=1 𝑚 = [ ∑ 𝑘𝑖𝑗 𝑙𝑚 𝑖=1 𝑚 , ∑ 𝑘𝑖𝑗 𝑢𝑚 𝑖=1 𝑚 ] (4) Step 4: For each criterion, the grey preference value (⨂𝛿𝑗 = [𝛿𝑗 𝑙, 𝛿𝑗 𝑢 ]) is computed with Eq. (5). ⨂𝛿𝑗 = ∑ (⨂𝑘𝑖𝑗 − ⨂�̅�𝑖𝑗 ) 2 = [∑ (𝑘𝑖𝑗 𝑙 − �̅�𝑖𝑗 𝑙 )2,𝑚𝑖=1 ∑ (𝑘𝑖𝑗 𝑢 − �̅�𝑖𝑗 𝑢 )2𝑚𝑖=1 ] 𝑚 𝑖=1 (5) Step 5: By Eq. (6), the grey deviation value (⨂𝛾𝑗) for each criterion is obtained. ⨂𝛾𝑗 = [𝛾𝑗 𝑙, 𝛾𝑗 𝑢 ] = |1 − ⨂𝛿𝑗 | = [|1 − 𝛿𝑗 𝑢|, |1 − 𝛿𝑗 𝑙|] (6) Step 6: The grey weight (⨂𝑤𝑗 = [𝑤𝑗 𝑙 , 𝑤𝑗 𝑢 ]) of each criterion is computed with Eq. (7). ⨂𝑤𝑗 = ⨂𝛾𝑗 ∑ ⨂𝛾𝑗 𝑛 𝑗=1 = [ 𝛾𝑗 𝑙 ∑ 𝛾𝑗 𝑢𝑛 𝑗=1 , 𝛾𝑗 𝑢 ∑ 𝛾𝑗 𝑙𝑛 𝑗=1 ] (7) After computing the grey weight of each criterion, these grey weights are dispatched into GPIV. 3.2. Grey Proximity Indexed Value GPIV method consists of four steps shown as follows. Step 1: In Eq. (1), the grey decision matrix is formed. The values in this matrix are normalized by using Eq. (8). ⨂𝑒𝑖𝑗 = [𝑒𝑖𝑗 𝑙 , 𝑒𝑖𝑗 𝑢 ] = ⨂𝑓𝑖𝑗 √∑ (⨂𝑓𝑖𝑗) 𝑚 𝑖=1 2 = [ 𝑓𝑖𝑗 𝑙 √∑ (𝑓𝑖𝑗 𝑢)𝑚𝑖=1 2 +∑ (𝑓𝑖𝑗 𝑙 )𝑚𝑖=1 2 , 𝑓𝑖𝑗 𝑢 √∑ (𝑓𝑖𝑗 𝑢)𝑚𝑖=1 2 +∑ (𝑓𝑖𝑗 𝑙 )𝑚𝑖=1 2 ] (8) A New Integrated Grey MCDM Model: Case of Warehouse Location Selection 523 In Eq. (8), ⨂𝑒𝑖𝑗 is the normalized of ⨂𝑓𝑖𝑗 . Step 2: These normalized values are multiplied by grey weights of criteria (obtained in GPSI) with Eq. (9). ⨂𝑡𝑖𝑗 = [𝑡𝑖𝑗 𝑙 , 𝑡𝑖𝑗 𝑢 ] = ⨂𝑤𝑗 × ⨂𝑒𝑖𝑗 = [𝑤𝑗 𝑙 × 𝑒𝑖𝑗 𝑙 , 𝑤𝑗 𝑢 × 𝑒𝑖𝑗 𝑢 ] (9) Step 3: Grey weighted proximity index (⨂𝑔𝑖𝑗 = [𝑔𝑖𝑗 𝑙 , 𝑔𝑖𝑗 𝑢 ]) is computed for beneficial (Eq. (10)) and cost criteria (Eq. (11)) as follows. ⨂𝑔𝑖𝑗 = 𝑚𝑎𝑥(⨂𝑡𝑖𝑗 ) − ⨂𝑡𝑖𝑗 = [𝑚𝑎𝑥(𝑡𝑖𝑗 𝑙 ) − 𝑡𝑖𝑗 𝑢 , 𝑚𝑎𝑥(𝑡𝑖𝑗 𝑢 ) − 𝑡𝑖𝑗 𝑙 ] (10) ⨂𝑔𝑖𝑗 = ⨂𝑡𝑖𝑗 − 𝑚𝑖𝑛(⨂𝑡𝑖𝑗 ) = [𝑡𝑖𝑗 𝑙 − 𝑚𝑖𝑛(𝑡𝑖𝑗 𝑢 ), 𝑡𝑖𝑗 𝑢 − 𝑚𝑖𝑛(𝑡𝑖𝑗 𝑙 )] (11) Step 4: Grey (⨂𝑑𝑖 = [𝑑𝑖 𝑙, 𝑑𝑖 𝑢]) and crisp (𝑑𝑖 ) overall proximity values are computed respectively with Eqs. (12) and (13). ⨂𝑑𝑖 = ∑ ⨂𝑔𝑖𝑗 𝑛 𝑗=1 = [∑ 𝑔𝑖𝑗 𝑙 , ∑ 𝑔𝑖𝑗 𝑢 ,𝑛𝑗=1 𝑛 𝑗=1 ] (12) 𝑑𝑖 = 𝑑𝑖 𝑙 +𝑑𝑖 𝑢 2 (13) Finally, alternative with the least crisp overall proximity value is designated as the best alternative. 4. APPLICATION The application of the integrated grey MCDM model is performed in a supermarket, which has over ten years of experience in the sector. During the Covid-19 pandemic, there were delays due to restrictions on transportation of the business. In addition, there has been an increase in costs in terms of warehouse and workforce during the pandemic. In order to overcome these problems, the supermarket chain decided to develop a project. At this point, consultancy service was received for logistics and crisis management. This study was carried out for 6 weeks with five experts who are the general manager of the supermarket chain, the director of logistics and transportation department, and 3 people from the consultancy company. The owner of the supermarket chain has 25 years of experience in the field of business graduate. The logistics director of the supermarket chain has a PhD in the logistics field and has 20 years of experience. In addition, 3 people in the consultancy company are industrial engineers with over 15 years of experience in the fields of engineering and logistics. Criteria were determined by literature review. In the 6-week meetings, the criteria in the literature were discussed with 5 experts, new criteria were added and removed. While determining the criteria, the cost criteria have been expanded to holding cost and transportation cost due to increasing in the costs during pandemic. Unlike the literature review, criteria such as infrastructure and climate conditions have been added. In addition, the criteria were developed by examining the distance functions in detail. Totally, twelve criteria were identified for utilizing in warehouse location selection. These criteria are Holding Cost (HC), Transportation Costs (TC), Distance to Customers (DC), Distance to Suppliers (DS), Distance to Producers (DP), Delivery Time (DT), Distance to Opponents (DO), Capacity of Storage (CS), Development Rate (DR), Transportation Diversity (TD), Infrastructure (I) and Climatic Conditions (CC). The first 524 A. ULUTAŞ, F. BALO, L. SUA, E. DEMIR, A. TOPAL, V. JAKOVLJEVIĆ six criteria are assigned as cost criteria and the others are assigned as beneficial criteria. The expert team identified five suitable alternatives for the warehouse location. The grey data of the first criterion were collected from expert team as actual data. The unit of this grey data is US Dollars and represents the holding cost per month. The expert team did not give the TC criterion as actual grey data for commercial reasons. For, TC and the other criteria, the grey data were determined together by the expert team and using the linguistic values shown in Table 2. The grey decision matrix was formed with all collected data. This matrix is presented in Table 3. Table 3 The Grey decision matrix Criteria Locations HC TC DC Location 1 [340, 380] [3, 5] [7, 9] Location 2 [420, 440] [5, 7] [5, 7] Location 3 [320, 360] [5, 7] [3, 5] Location 4 [430, 460] [5, 7] [3, 5] Location 5 [330, 350] [7, 9] [3, 5] Criteria Locations DS DP DT Location 1 [5, 7] [3, 5] [3, 5] Location 2 [3, 5] [1, 3] [5, 7] Location 3 [5, 7] [1, 3] [5, 7] Location 4 [3, 5] [1, 3] [7, 9] Location 5 [7, 9] [3, 5] [5, 7] Criteria Locations DO CS DR Location 1 [5, 7] [7, 9] [3, 5] Location 2 [3, 5] [5, 7] [7, 9] Location 3 [5, 7] [5, 7] [3, 5] Location 4 [3, 5] [7, 9] [7, 9] Location 5 [5, 7] [7, 9] [1, 3] Criteria Locations TD I CC Location 1 [5, 7] [3, 5] [1, 3] Location 2 [7, 9] [5, 7] [5, 7] Location 3 [5, 7] [5, 7] [5, 7] Location 4 [7, 9] [5, 7] [5, 7] Location 5 [5, 7] [3, 5] [3, 5] By means of Eqs. (2) and (3), the grey decision matrix is normalized. The normalized grey decision matrix is presented in Table 4. A New Integrated Grey MCDM Model: Case of Warehouse Location Selection 525 Table 4 The normalized grey decision matrix (for GPSI) Criteria Locations HC TC DC Location 1 [0.842, 0.941] [0.6, 1] [0.333, 0.429] Location 2 [0.727, 0.762] [0.429, 0.6] [0.429, 0.6] Location 3 [0.889, 1] [0.429, 0.6] [0.6, 1] Location 4 [0.696, 0.744] [0.429, 0.6] [0.6, 1] Location 5 [0.914, 0.970] [0.333, 0.429] [0.6, 1] Criteria Locations DS DP DT Location 1 [0.429, 0.6] [0.2, 0.333] [0.6, 1] Location 2 [0.6, 1] [0.333, 1] [0.429, 0.6] Location 3 [0.429, 0.6] [0.333, 1] [0.429, 0.6] Location 4 [0.6, 1] [0.333, 1] [0.333, 0.429] Location 5 [0.333, 0.429] [0.2, 0.333] [0.429, 0.6] Criteria Locations DO CS DR Location 1 [0.714, 1] [0.778, 1] [0.333, 0.556] Location 2 [0.429, 0.714] [0.556, 0.778] [0.778, 1] Location 3 [0.714, 1] [0.556, 0.778] [0.333, 0.556] Location 4 [0.429, 0.714] [0.778, 1] [0.778, 1] Location 5 [0.714, 1] [0.778, 1] [0.111, 0.333] Criteria Locations TD I CC Location 1 [0.556, 0.778] [0.429, 0.714] [0.143, 0.429] Location 2 [0.778, 1] [0.714, 1] [0.714, 1] Location 3 [0.556, 0.778] [0.714, 1] [0.714, 1] Location 4 [0.778, 1] [0.714, 1] [0.714, 1] Location 5 [0.556, 0.778] [0.429, 0.714] [0.429, 0.714] To give an example of the calculation of the values shown in Table 4, the HC (Eq. 3) grey normalized values of Location 1 are found as follows. ⨂𝑘11 = ⨂𝑓11 𝑚𝑎𝑥(⨂𝑓𝑖𝑗 ) = [ 𝑚𝑖𝑛(𝑓𝑖𝑗 𝑙 ) 𝑓11 𝑢 , 𝑚𝑖𝑛(𝑓𝑖𝑗 𝑙 ) 𝑓11 𝑙 ] = [ 320 380 , 320) 340 ] = [0.842 , 0.941] The grey preference values (⨂𝛿𝑗), grey deviation values (⨂𝛾𝑗 ) and grey weights (⨂𝑤𝑗 ) are calculated by using Eqs. (5-7), respectively. Table 5 presents the results. 526 A. ULUTAŞ, F. BALO, L. SUA, E. DEMIR, A. TOPAL, V. JAKOVLJEVIĆ Table 5 The GPSI method’s results Criteria Results HC TC DC ⨂𝛿𝑗 [0.039, 0.059] [0.037, 0.178] [0.063, 0.298] ⨂𝛾𝑗 [0.941, 0.961] [0.822, 0.963] [0.702, 0.937] ⨂𝑤𝑗 [0.087, 0.101] [0.076, 0.101] [0.065, 0.098] Criteria Results DS DP DT ⨂𝛿𝑗 [0.055, 0.270] [0.021, 0.533] [0.037, 0.178] ⨂𝛾𝑗 [0.730, 0.945] [0.467, 0.979] [0.822, 0.963] ⨂𝑤𝑗 [0.067, 0.099] [0.043, 0.103] [0.076, 0.101] Criteria Results DO CS DR ⨂𝛿𝑗 [0.097, 0.099] [0.060, 0.060] [0.357, 0.357] ⨂𝛾𝑗 [0.901, 0.903] [0.940, 0.940] [0.643, 0.643] ⨂𝑤𝑗 [0.083, 0.095] [0.087, 0.098] [0.059, 0.067] Criteria Results TD I CC ⨂𝛿𝑗 [0.060, 0.060] [0.097, 0.099] [0.260, 0.260] ⨂𝛾𝑗 [0.940, 0.940] [0.901, 0.903] [0.740, 0.740] ⨂𝑤𝑗 [0.087, 0.098] [0.083, 0.095] [0.068, 0.077] To give an example of the calculation of the values shown in Table 5, the grey deviation values (⨂𝛾1) and the grey weights (⨂𝑤1) of HC are computed by Eqs. (6) and (7) respectively as follows. ⨂𝛾1 = [𝛾1 𝑙 , 𝛾1 𝑢 ] = [|1 − 𝛿1 𝑢|, |1 − 𝛿1 𝑙 |] = [|1 − 0.059|, |1 − 0.039|] = [0.941, 0.961] ⨂𝑤1 = ⨂𝛾1 ∑ ⨂𝛾𝑗 𝑛 𝑗=1 = [ 0.941 0.961 + 0.963 + 0.937 … . +0.740 , 0.961 0.941 + 0.822 + 0.702 … . +0.740 ] = [0.087, 0.101] The grey weights of criteria (⨂𝑤𝑗 ) found in the GPSI method are transferred to the GPIV method. Eq. (8) is applied to the grey decision matrix, which is shown in Table 3, in order to develop the normalized grey decision matrix for GPIV. This matrix is presented in Table 6. A New Integrated Grey MCDM Model: Case of Warehouse Location Selection 527 Table 6 The normalized grey decision matrix for GPIV Criteria Locations HC TC DC Location 1 [0.279, 0.311] [0.153, 0.254] [0.400, 0.514] Location 2 [0.344, 0.360] [0.254, 0.356] [0.286, 0.400] Location 3 [0.262, 0.295] [0.254, 0.356] [0.171, 0.286] Location 4 [0.352, 0.377] [0.254, 0.356] [0.171, 0.286] Location 5 [0.270, 0.287] [0.356, 0.458] [0.171, 0.286] Criteria Locations DS DP DT Location 1 [0.269, 0.376] [0.303, 0.505] [0.153, 0.254] Location 2 [0.161, 0.269] [0.101, 0.303] [0.254, 0.356] Location 3 [0.269, 0.376] [0.101, 0.303] [0.254, 0.356] Location 4 [0.161, 0.269] [0.101, 0.303] [0.356, 0.458] Location 5 [0.376, 0.484] [0.303, 0.505] [0.254, 0.356] Criteria Locations DO CS DR Location 1 [0.294, 0.411] [0.302, 0.388] [0.163, 0.272] Location 2 [0.176, 0.294] [0.216, 0.302] [0.381, 0.490] Location 3 [0.294, 0.411] [0.216, 0.302] [0.163, 0.272] Location 4 [0.176, 0.294] [0.302, 0.388] [0.381, 0.490] Location 5 [0.294, 0.411] [0.302, 0.388] [0.054, 0.163] Criteria Locations TD I CC Location 1 [0.228, 0.319] [0.176, 0.294] [0.061, 0.184] Location 2 [0.319, 0.410] [0.294, 0.411] [0.307, 0.429] Location 3 [0.228, 0.319] [0.294, 0.411] [0.307, 0.429] Location 4 [0.319, 0.410] [0.294, 0.411] [0.307, 0.429] Location 5 [0.228, 0.319] [0.176, 0.294] [0.184, 0.307] The normalized values are multiplied by the grey weights of criteria with the aid of Eq. (9). The grey weighted proximity values are calculated with Eqs. (10) and (11). For example, the grey weighted proximity values of Location 1’s HC criterion are computed by Eq. (11) as follows. ⨂𝑔11 = ⨂𝑡11 − 𝑚𝑖𝑛(⨂𝑡𝑖𝑗 ) = [𝑡11 𝑙 − 𝑚𝑖𝑛(𝑡𝑖𝑗 𝑢 ), 𝑡11 𝑢 − 𝑚𝑖𝑛(𝑡𝑖𝑗 𝑙 )] = [0.024 − 0.029, 0.031 − 0.023] = [−0.005, 0.008] Calculated all grey weighted proximity values are shown in Table 7. 528 A. ULUTAŞ, F. BALO, L. SUA, E. DEMIR, A. TOPAL, V. JAKOVLJEVIĆ Table 7 The grey weighted proximity values Criteria Locations HC TC DC Location 1 [-0.005, 0.008] [-0.014, 0.014] [-0.002, 0.039] Location 2 [0.001, 0.013] [-0.007, 0.024] [-0.009, 0.028] Location 3 [-0.006, 0.007] [-0.007, 0.024] [-0.017, 0.017] Location 4 [0.002, 0.015] [-0.007, 0.024] [-0.017, 0.017] Location 5 [-0.006, 0.006] [0.001, 0.034] [-0.017, 0.017] Criteria Locations DS DP DT Location 1 [-0.009, 0.026] [-0.018, 0.048] [-0.014, 0.014] Location 2 [-0.016, 0.016] [-0.027, 0.027] [-0.007, 0.024] Location 3 [-0.009, 0.026] [-0.027, 0.027] [-0.007, 0.024] Location 4 [-0.016, 0.016] [-0.027, 0.027] [0.001, 0.034] Location 5 [-0.002, 0.037] [-0.018, 0.048] [-0.007, 0.024] Criteria Locations DO CS DR Location 1 [-0.015, 0.015] [-0.012, 0.012] [0.004, 0.023] Location 2 [-0.004, 0.024] [-0.004, 0.019] [-0.011, 0.011] Location 3 [-0.015, 0.015] [-0.004, 0.019] [0.004, 0.023] Location 4 [-0.004, 0.024] [-0.012, 0.012] [-0.011, 0.011] Location 5 [-0.015, 0.015] [-0.012, 0.012] [0.011, 0.030] Criteria Locations TD I CC Location 1 [-0.003, 0.020] [-0.004, 0.024] [0.007, 0.029] Location 2 [-0.012, 0.012] [-0.015, 0.015] [-0.012, 0.012] Location 3 [-0.003, 0.020] [-0.015, 0.015] [-0.012, 0.012] Location 4 [-0.012, 0.012] [-0.015, 0.015] [-0.012, 0.012] Location 5 [-0.003, 0.020] [-0.004, 0.024] [-0.003, 0.020] By using Eq. (12), grey overall proximity value (⨂𝑑𝑖 ) for each location alternative is computed. The crisp overall proximity value (𝑑𝑖 ) for each location alternative is computed by Eq. (13). For example, the grey overall proximity values and crisp overall proximity value for Location 1 are computed by Eqs. (12) and (13) respectively as follows. ⨂𝑑1 = ∑ ⨂𝑔𝑖𝑗 𝑛 𝑗=1 = [−0.005 + −0.014 + −0.002 … . +0.007 , 0.008 + 0.014 + 0.039 … . +0.029] = [−0.085, 0.272] 𝑑1 = 𝑑1 𝑙 + 𝑑1 𝑢 2 = −0.085 + 0.272 2 = 0.094 The same operations are repeated for other location alternatives. The results and the rankings of location alternatives are indicated in Table 8. A New Integrated Grey MCDM Model: Case of Warehouse Location Selection 529 Table 8 The results of GPIV Results Locations ⨂𝑑𝑖 𝑑𝑖 Rankings Location 1 [-0.085, 0.272] 0.094 4 Location 2 [-0.123, 0.225] 0.051 2 Location 3 [-0.118, 0.229] 0.056 3 Location 4 [-0.130, 0.219] 0.045 1 Location 5 [-0.075, 0.287] 0.106 5 According to Table 8, the warehouse locations are listed as follows; Location 4, Location 2, Location 3, Location 1 and Location 5. Thus, Location 4 is designated as the best warehouse location. 5. DISCUSSION The GPIV results are compared with the results of other grey MCDM methods, which are grey TOPSIS, grey WASPAS, and grey COPRAS, to test whether the GPIV results are accurate. The coefficients of Spearman’s correlation for all these grey MCDM are indicated in Table 9. Table 9 Spearman correlation coefficients Grey MCDM GPIV Grey TOPSIS Grey WASPAS Grey COPRAS GPIV 1.000 0.700 1.000 1.000 Grey TOPSIS - 1.000 0.700 0.700 Grey WASPAS - - 1.000 1.000 Grey COPRAS - - - 1.000 According to Table 9, GPIV method has reached the same results as grey WASPAS and grey COPRAS methods. Although the correlation coefficient between the grey TOPSIS and GPIV methods is lower than the other correlation coefficients, the first two locations (Location 4 and Location 2) are obtained as the same ranked according to the results of both methods. As a result, it has been proved that GPIV method has reached correct results when compared with other grey MCDM methods. Compared with other grey MCDM methods, it was observed that the GPIV method is easier and have fewer steps. In order to track the change in the rankings of the locations with regard to the change in criteria weights, the sensitivity analysis is performed. Four sets of criteria weights are designated for this analysis. Table 10 indicates these sets. 530 A. ULUTAŞ, F. BALO, L. SUA, E. DEMIR, A. TOPAL, V. JAKOVLJEVIĆ Table 10 Criteria weights sets Sets Criteria Set 1 Set 2 Set 3 Set 4 HC [0.210, 0.250] [0.350, 0.380] [0.150, 0.180] [0.120, 0.150] TC [0.030, 0.060] [0.030, 0.060] [0.050, 0.060] [0.060, 0.080] DC [0.070, 0.080] [0.070, 0.080] [0.090, 0.100] [0.050, 0.080] DS [0.070, 0.090] [0.070, 0.090] [0.080, 0.090] [0.060, 0.100] DP [0.050, 0.060] [0.050, 0.060] [0.060, 0.080] [0.050, 0.105] DT [0.060, 0.070] [0.060, 0.070] [0.080, 0.100] [0.170, 0.180] DO [0.090, 0.095] [0.070, 0.080] [0.085, 0.090] [0.080, 0.090] CS [0.060, 0.080] [0.010, 0.020] [0.080, 0.090] [0.080, 0.095] DR [0.050, 0.080] [0.040, 0.050] [0.060, 0.070] [0.070, 0.090] TD [0.060, 0.080] [0.040, 0.050] [0.080, 0.090] [0.080, 0.090] I [0.090, 0.105] [0.020, 0.030] [0.060, 0.065] [0.030, 0.040] CC [0.040, 0.070] [0.100, 0.120] [0.050, 0.060] [0.020, 0.030] These weights of criteria are utilized to perform the sensitivity analysis. The results are indicated in Fig. 2. Fig. 2 The sensitivity analysis’s results As it can be observed from sensitivity analysis, there is a change in the ranking of all locations. Location 3 is designated as the best location in Set 1 and Set 2, however, Location 4 and Location 2 are designated as the best locations in Set 3 and Set 4 respectively. As a result, the change in criteria weights causes a change in the ranking of the locations. Thus, GPIV method was found to be sensitive to the change in criteria weights. Although the proposed methods have achieved accurate results with easy calculations, the methods have individual limits. The solution efficiency of the PSI method decreases as the number of alternatives increases [67]. Also, since the PSI method does not take into account the correlation between the criteria, it stands weak compared to the CRITIC method in finding 0 1 2 3 4 5 6 Set 1 Set 2 Set 3 Set 4 R a n k in g s Sets Location 1 Location 2 Location 3 Location 4 Location 5 A New Integrated Grey MCDM Model: Case of Warehouse Location Selection 531 the objective weights of the criteria. The limits mentioned for the PSI method are also valid for the GPSI method. Both GPSI and GPIV methods work with grey data. In a situation where there is no grey data and the uncertainty is higher, it may be difficult to reach the correct results and both methods may not work. In addition, both methods do not have a membership function as in fuzzy numbers. This will cause the proposed model to deal with uncertainty in less detail compared to comprehensive fuzzy (interval type 2, intuitionistic, spherical, and fermatean) methods. In addition, in the proposed method, only the objective weights of the criteria are considered. Subjective weights of criteria can also be obtained using grey MCDM methods (such as Grey AHP, Grey SWARA, and Grey FUCOM), and stronger and more consistent results can be obtained by combining objective and subjective weights of criteria. 6. CONCLUSION This study proposes an integrated grey MCDM model including GPSI and GPIV to determine the most appropriate warehouse location for a supermarket. While the GPSI method is used to determine the weights of the criteria, the GPIV method is used to evaluate the performance of the alternatives and to rank these alternatives. This study aims to make three contributions to the literature. PSI and PIV methods combined with grey theory will be introduced for the first time in the literature. In addition, GPSI and GPIV methods will be combined and used to select the best warehouse location. In this study, the performances of five location alternatives were measured by considering twelve criteria. According to the results of GPIV, Location 4 is designated as the best warehouse location. In this study, the results of the GPIV method and other grey MCDM methods were compared. Accordingly, it was found that GPIV method reached the correct results. In addition, a sensitivity analysis was performed by changing the weights of the criteria. It has been observed that the change in criteria weights causes a change in the ranking of the locations. Thus, GPIV method was found to be sensitive to the change in criteria weights. This study has been carried out for the selection of warehouse location during the Covid-19 pandemic. In this context, the criteria considered has been expanded. These criteria can be used in conjunction with other methodologies to compare results. It is expected that the GPSI based GPIV methodology proposed for the first time in this study will be used in future studies therefore will become widespread and cited in the literature. In the proposed method, only the objective weights of the criteria are considered. Future studies use grey MCDM methods (such as Grey AHP, Grey SWARA, and Grey FUCOM) to obtain subjective weights of criteria after that they can combine objective and subjective weights of criteria to obtain stronger and more consistent results. Future studies may utilize the proposed model to address other MCDM problems, such as energy sources selection, supplier selection and third-party logistics provider selection etc. Particularly, the number of studies on the logistics center location selection problem is few in the literature [80-83]. Therefore, the proposed model can be utilized to solve this problem. 532 A. ULUTAŞ, F. BALO, L. SUA, E. DEMIR, A. TOPAL, V. JAKOVLJEVIĆ REFERENCES 1. Pang, K.W., Chan, H.L., 2017, Data mining-based algorithm for storage location assignment in a randomised warehouse, International Journal of Production Research, 55(14), pp. 4035–4052. 2. Aktepe, A., Ersöz, S., 2014, AHP-VIKOR ve MOORA yöntemlerinin depo yeri seçim probleminde uygulanması, Endüstri Mühendisliği Dergisi, 25(1–2), pp. 2–15. 3. Emeç, Ş., Akkaya, G., 2018, Stochastic AHP and fuzzy VIKOR approach for warehouse location selection problem, Journal of Enterprise Information Management, 31(6), pp. 950–962. 4. Ecer, F., Pamucar, D., 2020, Sustainable supplier selection: A novel integrated fuzzy best worst method (F- BWM) and fuzzy CoCoSo with Bonferroni (CoCoSo’B) multi-criteria model, Journal of Cleaner Production, 266, 121981. 5. Ecer, F., Pamucar, D., 2021, MARCOS technique under intuitionistic fuzzy environment for determining the COVID-19 pandemic performance of insurance companies in terms of healthcare services, Applied Soft Computing, 104, 107199. 6. Shojaei, P., Bolvardizadeh, A., 2020, Rough MCDM model for green supplier selection in Iran: a case of university construction project, Built Environment Project and Asset Management, 10(3), pp. 437-452. 7. Stević, Ž., Karamaşa, Ç., Demir, E., Korucuk, S., 2021, Assessing sustainable production under circular economy context using a novel rough-fuzzy MCDM model: a case of the forestry industry in the Eastern Black Sea region, Journal of Enterprise Information Management. Article in press. 8. Pamucar, D., Deveci, M., Canıtez, F., Paksoy, T., Lukovac, V., 2021, A Novel Methodology for Prioritizing Zero-Carbon Measures for Sustainable Transport, Sustainable Production and Consumption, 27, pp. 1093-1112. 9. Tian, G., Zhang, H., Feng, Y., Wang, D., Peng, Y., Jia, H., 2018, Green decoration materials selection under interior environment characteristics: A grey-correlation based hybrid MCDM method, Renewable and Sustainable Energy Reviews, 81, pp. 682-692. 10. Tadić, S., Krstić, M., Roso, V., Brnjac, N., 2020, Dry Port Terminal Location Selection by Applying the Hybrid Grey MCDM Model, Sustainability, 12(17), 6983. 11. Liu, S., Lin, Y., 2006, Grey information: Theory and practical applications, Springer Science & Business Media, London. 12. Bai, C., Sarkis, J., 2010, Integrating sustainability into supplier selection with grey system and rough set methodologies, International Journal of Production Economics, 124(1), pp. 252–264. 13. Xia, X., Govindan, K., Zhu, Q., 2015, Analyzing internal barriers for automotive parts remanufacturers in China using grey-DEMATEL approach, Journal of Cleaner Production, 87, pp. 811–825. 14. Attri, R., Grover, S., 2015, Application of preference selection index method for decision making over the design stage of production system life cycle, Journal of King Saud University-Engineering Sciences, 27(2), pp. 207-216. 15. Mufazzal, S., Muzakkir, S.M., 2018, A new multi-criterion decision making (MCDM) method based on proximity indexed value for minimizing rank reversals, Computers & Industrial Engineering, 119, pp. 427-438. 16. Khan, N.Z., Ansari, T.S.A., Siddiquee, A.N., Khan, Z.A, 2019, Selection of E-learning websites using a novel Proximity Indexed Value (PIV) MCDM method, Journal of Computers in Education, 6(2), pp. 241-256. 17. Oztaysi, B., 2014, A decision model for information technology selection using AHP integrated TOPSIS- Grey: The case of content management systems, Knowledge-Based Systems, 70, pp. 44–54. 18. Zavadskas, E.K., Turskis, Z., Antucheviciene, J., 2015, Selecting a contractor by using a novel method for multiple attribute analysis: Weighted Aggregated Sum Product Assessment with grey values (WASPAS- G), Studies in Informatics and Control, 24(2), pp. 141–150. 19. Zavadskas, E.K., Kaklauskas, A., Turskis, Z., Tamošaitiene, J., 2008, Selection of the effective dwelling house walls by applying attributes values determined at intervals, Journal of Civil Engineering and Management, 14(2), pp. 85–93. 20. Lee, C., 1993, The multiproduct warehouse location problem: Applying a decomposition algorithm, International Journal of Physical Distribution and Logistics Management, 23, pp. 3-13. 21. S.L. Hakimi, S.L., Kuo, C.C.,1991, On a general network location allocation problem, European Journal of Operational Research, 108, pp. 135-142. 22. Korpela, J., Lehmusvaara, A., 1999, A customer oriented approach to warehouse network evaluation and design, International Journal of Production Economics, 59, pp. 135-146. 23. Korpela, J., Lehmusvaara, A., Nisonen, J., 2007, Warehouse operator selection by combining AHP and DEA methodologies, International Journal of Production Economics, 108, pp. 135-142. 24. Ho, W., Emrouznejad, A., 2009, Multi-criteria logistics distribution network design using SAS/OR, Expert Systems with Applications, 36, pp. 7288-7298. about:blank#bb0105 A New Integrated Grey MCDM Model: Case of Warehouse Location Selection 533 25. R.J. Kuo, R.J, Chi, S.C., Kao, S.S., 2002, A decision support system for selecting convenience store location through integration of fuzzy AHP and artificial neural network, Computers in Industry, 47, pp. 199-214. 26. Tabari, M., Kaboli, A., Aryanezhad, M.B., Shahanaghi, K, Siadat, A., 2008, A new method for location selection: A hybrid analysis Applied Mathematics and Computation, 206, pp. 598-606 27. Chen, C., 2001, A fuzzy approach to select the location of the distribution center, Fuzzy Sets and Systems, 118, pp. 65-73. 28. Kahraman, C., Ruan, D., Doğan, I., 2003, Fuzzy group decision-making for facility location selection, Information Sciences, 157, pp. 135-153 29. Karmaker, C., Saha, M., 2015, Optimization of warehouse location through fuzzy multi-criteria decision making methods, Decision Science Letters, 4(3), pp. 315–334 30. Stevenson, W.J., 1993, Production/operations management, McGraw-Hill Company, New York. 31. Frazelle, E., 2002, Supply chain strategy: the logistics of supply chain management, McGraw-Hill Education, New York. 32. Demirel, T., Demirel, N.Ç., Kahraman, C., 2010, Multi-criteria warehouse location selection using Choquet integral, Expert Systems with Applications, 37(5), pp. 3943–3952 33. Kuehn, A.A., Hamburger, M.J., 1963, A heuristic program for locating warehouses, Management Science, 9(4), pp. 643–666. 34. Efroymson, M., Ray, T., 1966, A branch-bound algorithm for plant location, Operations Research, 14(3), pp. 361–368. 35. Khumawala, B.M., 1972, An efficient branch and bound algorithm for the warehouse location problem, Management Science, 18(12), pp. 718–731. 36. Weber, A., Friedrich, C.J., 1929, Alfred Weber’s theory of the location of industries, Chicago, Ill., The University of Chicago Press, Chicago. 37. Tellier, L.N., 1972, The Weber problem: solution and interpretation, Geographical Analysis, 4(3), pp. 215–233. 38. Owen, S.H., Daskin M.S., 1998, Strategic facility location: a review, European Journal of Operational Research, 111(3), pp. 423–447. 39. Badri, M.A., 1999, Combining the analytic hierarchy process and goal programming for global facility location-allocation problem, International Journal of Production Economics, 62(3), pp. 237–248. 40. Vlachopoulou, M., Silleos, G., Manthou, V., 2001, Geographic information systems in warehouse site selection decisions, International Journal of Production Economics, 71(1– 3), pp. 205–212. 41. Kabak, M., Keskin, İ., 2018, Hazardous materials warehouse selection based on GIS and MCDM, Arabian Journal for Science & Engineering, 43(6), pp. 3269–3278. 42. Yerlikaya, M.A., Tabak, Ç., Yıldız, K., 2019, Logistic location selection with Critic-Ahp and Vikor integrated approach, Data Science and Applications, 2(1), pp. 21– 25. 43. Mihajlović, J., Rajković, P., Petrović, G., Ćirić, D., 2019, The selection of the logistics distribution center location based on MCDM methodology in southern and eastern region in Serbia, Operational Research in Engineering Sciences: Theory and Applications, 2(2), pp. 72–85. 44. Ma, Y., Su, X., Zhao, Y., 2018, Hybrid multi-attribute decision making methods: an application, Tehnički Vjesnik, 25(5), pp. 1421–1428. 45. Pamučar, D., Božanić, D., 2019, Selection of a location for the development of multimodal logistics center: application of single-valued neutrosophic MABAC model, Operational Research in Engineering Sciences: Theory and Applications, 2(2), pp. 55–71. 46. Tuzkaya, G., Önüt, S., Tuzkaya, U.R., Gülsün, B., 2008, An analytic network process approach for locating undesirable facilities: an example from Istanbul, Turkey, Journal of Environmental Management, 88(4), pp. 970–983. 47. Uysal, F., Tosun, Ö., 2014, Selection of sustainable warehouse location in supply chain using the grey approach, International Journal of Information and Decision Sciences, 6(4), pp. 338– 353. 48. Özcan, T., Çelebi, N., Esnaf, Ş., 2011, Comparative analysis of multi-criteria decision making methodologies and implementation of a warehouse location selection problem, Expert Systems with Applications, 38(8), pp. 9773–9779. 49. Ashrafzadeh, M., Rafiei, F.M., Isfahani, N.M., Zare, Z., 2012, Application of fuzzy TOPSIS method for the selection of warehouse location: A Case Study, Interdisciplinary Journal of Contemporary Research in Business, 3(9), pp. 655–671. 50. Dey, B., Bairagi, B., Sarkar, B., Sanyal, S.K., 2013, A hybrid fuzzy technique for the selection of warehouse location in a supply chain under a utopian environment, International Journal of Management Science and Engineering Management, 8(4), pp. 250–261. 534 A. ULUTAŞ, F. BALO, L. SUA, E. DEMIR, A. TOPAL, V. JAKOVLJEVIĆ 51. García, J.L., Alvarado, A., Blanco, J., Jiménez, E., Maldonado, A.A., Cortés, G., 2014, Multi-attribute evaluation and selection of sites for agricultural product warehouses based on an analytic hierarchy process, Computers and Electronics in Agriculture, 100, pp. 60–69. 52. Dey, B., Bairagi, B., Sarkar, B., Sanyal, S.K., 2016, Warehouse location selection by fuzzy multi-criteria decision making methodologies based on subjective and objective criteria, International Journal of Management Science and Engineering Management, 11(4), pp. 262–278. 53. Silva, D.D., Vasconcelos, N.V.C., Cavalcante, C.A.V., 2015, Multicriteria decision model to support the assignment of storage location of products in a warehouse, Mathematical Problems in Engineering, Article ID 481950. 54. Mangalan, A.V., Kuriakose, S., Mohamed, H., Ray, A., 2016, Optimal location of warehouse using weighted MOORA approach, In 2016 International Conference on Electrical, Electronics, and Optimization Techniques (ICEEOT), pp. 662–665, IEEE. 55. Temur, G.T., 2016, A novel multi attribute decision making approach for location decision under high uncertainty, Applied Soft Computing, 40, pp. 674–682. 56. Dey, B., Bairagi, B., Sarkar, B., Sanyal, S.K., 2017, Group heterogeneity in multi member decision making model with an application to warehouse location selection in a supply chain, Computers & Industrial Engineering, 105, pp. 101–122. 57. Raut, R.D., Narkhede, B.E., Gardas, B.B., Raut, V., 2017, Multi-criteria decision making approach: A sustainable warehouse location selection problem, International Journal of Management Concepts and Philosophy, 10(3), pp. 260–281. 58. Micale, R., La Fata, C.M., La Scalia, G.A, 2019, Combined interval-valued ELECTRE TRI and TOPSIS approach for solving the Storage Location Assignment Problem, Computers & Industrial Engineering, 135, pp. 199–210. 59. Canbolat, Y.B., Chelst, K., Garg, N., 2007, Combining decision tree and MAUT for selecting a country for a global manufacturing facility, Omega 35(3), pp. 312–325. 60. Ehsanifar, M., Wood, D.A., Babaie, A., 2021, UTASTAR method and its application in multi-criteria warehouse location selection, Operations Management Research, 14, pp. 202–215. 61. Maniya, K., Bhatt, M.G., 2010, A selection of material using a novel type decision-making method: Preference Selection Index method, Materials & Design, 31(4), pp. 1785–1789. 62. Vahdani, B., Mousavi, S.M., Ebrahimnejad, S., 2014, Soft computing-based preference selection index method for human resource management, Journal of Intelligent & Fuzzy Systems, 26(1), pp. 393–403. 63. Attri, R., Grover, S., 2015, Application of Preference Selection Index method for decision making over the design stage of production system life cycle, Journal of King Saud University-Engineering Sciences, 27(2), pp. 207–216. 64. Chamoli, S., 2015, Preference Selection Index approach for optimization of V down perforated baffled roughened rectangular channel, Energy, 93, pp. 1418–1425. 65. Akyüz, G., Aka, S., 2015, An Alternative approach for manufacturing performance measurement: Preference Selection Index (PSI) Method, Business and Economics Research Journal, 6(1), pp. 63–77. 66. Petković, D., Madić, M., Radovanović, M., Gečevska, V., 2017, Application of the performance selection index method for solving machining MCDM problems, Facta Universitatis-Series Mechanical Engineering, 15(1), pp. 97–106. 67. Madić, M., Antucheviciene, J., Radovanović, M., Petković, D., 2017, Determination of laser cutting process conditions using the Preference Selection Index method, Optics & Laser Technology, 89, pp. 214–220. 68. Tuş, A., Adalı, E.A., 2018, CODAS ve PSI yöntemleri ile personel değerlendirmesi, Alphanumeric Journal, 6(2), pp. 243–256. 69. Jha, K., Chamoli, S., Tyagi, Y.K., Maurya, H.O., 2018, Characterization of biodegradable composites and application of Preference Selection Index for deciding optimum phase combination, Materials Today: Proceedings, 5(2), pp. 3353–3360. 70. Pathak, V.K.,Singh, R., Gangwar, S., 2019, Optimization of three-dimensional scanning process conditions using Preference Selection Index and metaheuristic method, Measurement, 146, pp. 653–667. 71. Ulutaş, A., Topal, A., Bakhat, R., 2019, An Application of fuzzy integrated model in green supplier selection, Mathematical Problems in Engineering, Article ID 4256359. 72. 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), pp. 3016-3028. 73. Gigović, L., Pamučar, D., Bajić, Z., Milićević, M., 2016, The combination of expert judgment and GIS- MAIRCA analysis for the selection of sites for ammunition depots, Sustainability, 8(4), 372. 74. Pamučar, D., Stević, Z., Sremac, S., 2018, A New Model for Determining Weight Coefficients of Criteria in MCDM Models: Full Consistency Method (FUCOM), Symmetry, 10(9) 393. A New Integrated Grey MCDM Model: Case of Warehouse Location Selection 535 75. Žižović, M., Pamucar, D., 2019, New model for determining criteria weights: Level Based Weight Assessment (LBWA) model, Decision Making: Applications in Management and Engineering, 2(2), pp. 126-137. 76. 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. 77. Žižović, M., Pamučar, D., Albijanić, M., Chatterjee, P., Pribićević, I., 2020, Eliminating rank reversal problem using a new multi-attribute model—the rafsi method, Mathematics, 8(6), 1015. 78. Ulutaş, A., Stanujkic, D., Karabasevic, D., Popovic, G., Zavadskas, E. K., Smarandache, F., Brauers, W. K., 2021, Developing of a Novel Integrated MCDM MULTIMOOSRAL Approach for Supplier Selection, Informatica, 32(1), pp. 145-161. 79. Yahya, S.M., Asjad, M., Khan, Z.A, 2019, Multi-response optimization of TiO2/EG-water nano-coolant using Entropy based Preference Indexed Value (PIV) method, Materials Research Express, 6(8), 0850a1. 80. Tomić, V., Marinković, D., Marković, D., 2014, The selection of logistic centers location using multi- criteria comparison: case study of the Balkan Peninsula, Acta Polytechnica Hungarica, 11(10), pp. 97-113. 81. Ulutaş, A., Karaköy, Ç., Arıç, K. H., Cengiz, E., 2018, Çok Kriterli Karar Verme Yöntemleri İle Lojistik Merkezi Yeri Seçimi, İktisadi Yenilik Dergisi, 5(2), pp. 45-53. 82. Pamucar, D. S., Pejcic Tarle, S., Parezanovic, T., 2018, New hybrid multi-criteria decision-making DEMATELMAIRCA model: sustainable selection of a location for the development of multimodal logistics centre, Economic research-Ekonomska istraživanja, 31(1), pp. 1641-1665. 83. Yazdani, M., Chatterjee, P., Pamucar, D., Chakraborty, S., 2020, Development of an integrated decision making model for location selection of logistics centers in the Spanish autonomous communities, Expert Systems with Applications, 148, 113208.