Application of fuzzy TOPSIS method for the selection of Warehouse Location: A Case Study

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1 INTERDISCIPLINARY JOURNAL O CONTEORARY RESEARCH IN BUSINESS Application of fuzzy TOPSIS method for the selection of Warehouse Location: A Case Study Maysam Ashrafzadeh* Department of Industrial Engineering Najafabad Branch, Islamic Azad University, Isfahan, Iran Postal Code: , Unit 3, No 289, East Kakh Saadatabad St, Mir Ave, Isfahan, Iran arimah Mokhatab Rafiei Department of Industrial Engineering Isfahan University of Technology, Isfahan, Iran, Naser Mollaverdi Isfahani Department of Industrial Engineering Isfahan University of Technology, Isfahan, Iran, Zahra Zare Department of Industrial Engineering Najafabad Branch, Islamic Azad University, Isfahan, Iran Abstract Warehouse location selection is a multi-criteria decision problem including both quantitative and qualitative criteria and has a strategic importance for many companies. The conventional approaches to warehouse location selection problem tend to be less effective in dealing with the imprecise or vague nature of the linguistic assessment. Under many situations, the values of the qualitative criteria are often imprecisely defined for the decision-makers. To overcome this difficulty, fuzzy multi-criteria decision-making methods are proposed. In this paper, we present a multi-criteria decision making approach for selecting warehouse location under partial or incomplete information (uncertainty). The proposed approach comprises of two steps. In step, we identify the criteria for warehouse location selection. In step 2, experts provide linguistic ratings to the potential alternatives against the selected criteria. uzzy TOPSIS is used to generate aggregate scores selection of best alternative. This paper shows a successful application of fuzzy TOPSIS to a real warehouse location selection problem of a big company in Iran. Keywords: Warehouse location; Multi criteria decision making; uzzy TOPSIS. Introduction Warehouses are a key aspect of modern supply chains and play a vital role in the success, or failure of businesses today [24]. A warehouse is a commercial building for buffering and storing goods. Warehouses are utilized by manufacturers, importers, COPY RIHT 202 Institute of Interdisciplinary Business Research 655

2 INTERDISCIPLINARY JOURNAL O CONTEORARY RESEARCH IN BUSINESS exporters, retailers, transport businesses, etc. The location theory was first introduced by Weber (989) who considered the problem of locating a single warehouse in order to minimize the total travel distance between the warehouse and a set of spatially distributed customers. Indeed, he proposed a material index for the selection of the location according to which, if this index is greater than one, the warehouse should be installed in the vicinity of the source of raw material; otherwise, it must be close to the market [6]. The decision process in question encompasses the identification, analysis, evaluation and selection among alternatives. Such a decision is among the most critical decisions of distribution network design. The selection of a warehouse location among alternative locations is a multi-criteria decision making problem including both quantitative and qualitative criteria. Such decisions are of great importance to companies because they are costly and difficult to reverse, and entail a long-term commitment. They also have an impact on operating costs and revenues. or instance, a poor choice of location might result in excessive transportation costs, a shortage of qualified labor, loss of competitive advantage or some similar condition that would be detrimental to operations [47]. The general procedure for making location decisions usually consists of the following steps: Decide on the criteria that will be used to evaluate location alternatives Identify criteria that are important Develop location alternatives Evaluate the alternatives and make a selection The location of a warehouse is generally one of the most important and strategic decision in the optimization of logistic systems. It is a long-term decision and is influenced by many quantitative and qualitative criteria; however, some criteria are so important that they tend to dominate the decision dominate the decision in importance. Among the criteria taken into account in this paper are costs, labor characteristics, infrastructure and market. The conventional approaches to warehouse location selection problem tend to be less effective in dealing with the imprecise or vague nature of the linguistic assessment. In many situations, the values of the qualitative criteria are often imprecisely defined for decision-makers. In this paper, we present a multi criteria decision making approach to warehouse location selection under uncertain (fuzzy) circumstances. The rest of the paper is organized as follows: the literature review on warehouse/facility location selection is given in Section 2. In Section 3 and 4, we present the preliminaries of fuzzy set theory and fuzzy TOPSIS. In Section 5, we present the multi criteria decision making approach for warehouse location selection based on fuzzy TOPSIS. In Section 6, we present a case study and finally, in Section 7 we provide the conclusions and steps for future work. 2. Literature review Among supply chain studies, many papers on warehouse/facility location problem have been published. Vlachopoulou et al. [5] aim at developing a geographic decision support system for the warehouse site selection process, enabling the manager to use quantitative and qualitative criteria in order to classify alternative warehouses or visualize the best one. Sharma and Berry [45] consider the single stage capacitated warehouse location problem (SSCWLP) where goods are shipped from plants to COPY RIHT 202 Institute of Interdisciplinary Business Research 656

3 INTERDISCIPLINARY JOURNAL O CONTEORARY RESEARCH IN BUSINESS warehouses and from warehouses to markets. The problem is to choose a set of points where warehouses are located so that the sum of warehouse location costs and transportation costs are minimized. In their study they consider different formulation styles due to eoffrion and raves [25] and Sharma [44] for the multistage warehouse location problem; and cast them in the formulation style of Sharma and Sharma [46] to obtain a variety of formulations of the problem SSCWLP. A public warehouses selection support system (PWSS) software has been built by Colson and Dorigo [7] to give the opportunity to industrial users of exploiting a classical data base on public warehouses, where several items of information are given on each warehouse located in a given country. Their software public warehouses selection support has two purposes: to select public warehouses according to several criteria and to exploit a database when some data are missing. They use multiple-criteria selections and rankings with a mixture of classical true continuous criteria and Boolean ones from a methodological point of view. Michel and Hentenryck [40] present a very simple tabu-search algorithm which performs amazingly well on the uncapacitated warehouse location problem. The algorithm uses a linear neighborhood. Drezner et al. [20] concern themselves with the optimal location of a central warehouse, when the possible locations and the number of warehouses are known. They solve the problem sequentially. irst, for any given central warehouse location, the problem is a pure inventory problem. They find the optimal policy for the inventory problem. They express the total inventory and transportation costs as a function of the central warehouse location. The next step is to optimize this total cost function over all possible central warehouse locations. Partovi [42] explains a new analytic model for facility location that takes into account both external and internal criteria that sustain competitive advantage. Partovi s model, which is based on quality function deployment (QD), also includes the analytic hierarchy process (AHP) and the analytic network process (ANP) concepts to determine the best location for a facility. The most well- known general heuristic methods for facility location problems are Tabu Search (TS), Simulated Annealing (SA), and enetic Algorithms (A). Arostegui et al. [2] compare the relative performance of TS, SA, and A on various facilities location problems. Hidaka and Okano [26] propose a simulation-based approach to the large-scale incapacitated warehouse/facility location problems, including a heuristic algorithm named Balloon Search. Tzeng and Chen [50] propose a location model based on a fuzzy multi objective approach. The model helps in determining the optimal number and sites of fire stations at an international airport, and also assists the relevant authorities in drawing up optimal locations for fire stations. Because of the combinatorial complexity of their model, a genetic algorithm is employed and compared with the enumeration method. Kuo et al. [35] develop a decision support system using the fuzzy sets theory integrated with analytic hierarchy process for locating a new convenience store. Chen [9] proposes a new multiple criteria decision-making method to solve the distribution center location selection problem under a fuzzy environment. In the proposed method, the ratings of each alternative and the weight of criterion are described by linguistic variables that can be expressed in triangular fuzzy numbers. The final evaluation value of each distribution centre location is also expressed in a triangular fuzzy number. COPY RIHT 202 Institute of Interdisciplinary Business Research 657

4 INTERDISCIPLINARY JOURNAL O CONTEORARY RESEARCH IN BUSINESS 3. Preliminaries of fuzzy set theory To deal with vagueness of human thought, Zadeh [54] first introduced the fuzzy set theory, which was oriented to the rationality of uncertainty due to imprecision or vagueness. A major contribution of fuzzy set theory is its capability of representing vague data. The theory also allows mathematical operators and programming to apply to the fuzzy domain. A fuzzy set is a class of objects with a continuum of grades of membership. Such a set is characterized by a membership (characteristic) function, which assigns to each object a grade of membership ranging between zero and one. With different daily decision making problems of diverse intensity, the results can be misleading if the fuzziness of human decision making is not taken into account [49]. uzzy sets theory providing a more widely frame than classic sets theory, has been contributing to capability of reflecting real world [23]. uzzy sets and fuzzy logic are powerful mathematical tools for modeling: uncertain systems in industry, nature and humanity; and facilitators for common-sense reasoning in decision making in the absence of complete and precise information. Their role is significant when applied to complex phenomena not easily described by traditional mathematical methods, especially when the goal is to find a good approximate solution [5]. uzzy set theory is a better means for modeling imprecision arising from mental phenomena which are neither random nor stochastic. Human beings are heavily involved in the process of decision analysis. A rational approach toward decision making should take into account human subjectivity, rather than employing only objective probability measures. This attitude, towards imprecision of human behavior led to study of a new decision analysis filed fuzzy decision making [37]. A tilde will be placed above a symbol if the symbol represents a fuzzy set. Some related definitions of fuzzy set theory adapted from (Buckley [7], Dubois and Prade [2], Kaufmann and upta [3], Klir and Yuan [34], Pedrycz [43], Zadeh [54], Zimmermann [55]) are presented as follows: Definition. A fuzzy set M in a universe of discourse X is characterized by a membership function µ ( x ) that maps each element x in X to a real number in the interval [0, ]. The function value M µ ( x) is termed the grade of membership of x in M. The nearer the value of µ ( x) to unity, the higher M M the grade of membership of x in M. Definition 2. A triangular fuzzy number (TN), M is shown in ig.. A triangular fuzzy number is denoted simply as ( l / m, m / u ) or ( l, m, u ). The parameters l, m and u, respectively, denote the smallest possible value, the most promising value and the largest possible value that describe a fuzzy event. Each triangular fuzzy number has linear representations on its left and right side such that its membership function can be defined as: µ( x/ M) = 0 ( x l) ( m_ l) ( u x) ( u _ m) 0 x < l l x m m x u x > u (3-) COPY RIHT 202 Institute of Interdisciplinary Business Research 658

5 INTERDISCIPLINARY JOURNAL O CONTEORARY RESEARCH IN BUSINESS A fuzzy number can always be given by its corresponding left and right representation of each degree of membership: l( y) r( y ( M, M ) = l + ( m l) y, u + ( m_ u) ) ( y) [ 0, ] M = y (3-2) Where l (y) and r (y) denote the left side representation and the right side representation of a fuzzy number, respectively. Many ranking methods for fuzzy numbers have been developed in the literature. These methods may give different ranking results and most methods are tedious in graphic manipulation requiring complex mathematical calculation. The algebraic operations with fuzzy numbers can be found in Kahraman et al. [30]. 4. uzzy TOPSIS Technique for Order Performance by similarity to Ideal solution (TOPSIS), one of the most classical methods for solving MCDM problem, was first developed by Hwang and Yoon [27]. It is based on the principle that the chosen alternative should have the longest distance from the negative-ideal solution i.e. the solution that maximizes the cost criteria and minimizes the benefits criteria; and the shortest distance from the positive-ideal solution i.e. the solution that maximizes the benefit criteria and minimizes the cost criteria. In classical TOPSIS the rating and weight of the criteria are known precisely. However, under many real situations crisp data are inadequate to model real life situation since human judgments are vague and cannot be estimated with exact numeric values [27]. To resolve the ambiguity frequently arising in information from human judgments fuzzy set theory has been incorporated in many MCDM methods including TOPSIS. In fuzzy TOPSIS all the ratings and weights are defined by means of linguistic variables. A number of fuzzy TOPSIS methods and applications have been developed in recent years. Chen and Hwang [] first applied fuzzy numbers to establish fuzzy TOPSIS. Triantaphyllou and Lin [48] developed a fuzzy TOPSIS method in which relative closeness for each alternative is evaluated based on fuzzy arithmetic operations. Liang [38] proposed uzzy MCDM based on ideal and anti-ideal concepts. Chen [8] considered triangular fuzzy numbers and defined crisp Euclidean distance between two fuzzy numbers to extend the TOPSIS method to fuzzy DM situations. Chu [4] and Chu and Lin [6] further improved the methodology proposed by Chen [8]. Chen and Tsao [3] are to extend the TOPSIS method based on Interval-valued fuzzy sets in decision analysis. Jahanshahloo et al. [28] and Chu and Lin [5] extended the fuzzy TOPSIS method based on alpha level sets with interval arithmetic. Chen and Lee [2] extended fuzzy TOPSIS based on type-2 fuzzy TOPSIS method in order to provide additional degree of freedom to represent the uncertainties and fuzziness of the real world. uzzy TOPSIS has been introduced for various multi-attribute decision-making problems. Yong [53] used fuzzy TOPSIS for plant location selection and Chen et al. [0] used fuzzy TOPSIS for supplier selection. Kahraman et al. [29] utilized fuzzy TOPSIS for industrial robotic system selection. Wang and Chang [52] applied fuzzy TOPSIS to help the Air orce Academy in Taiwan choose optimal initial training COPY RIHT 202 Institute of Interdisciplinary Business Research 659

6 INTERDISCIPLINARY JOURNAL O CONTEORARY RESEARCH IN BUSINESS aircraft in a fuzzy environment. Benitez et al. [4] presented a fuzzy TOPSIS approach for evaluating dynamically the service quality of three hotels of an important corporation in ran Canaria Island via surveys. Kahraman et al. [29] proposed a fuzzy hierarchical TOPSIS model for the multi-criteria evaluation of the industrial robotic systems. Ashtiani et al. [3] used interval-valued fuzzy TOPSIS method is aiming at solving MCDM problems in which the weights of criteria are unequal, using intervalvalued fuzzy sets concepts. Ekmekcioglu et al. [22] used a modified fuzzy TOPSIS to select municipal solid waste disposal method and site. Kutlu and Ekmekcioglu [36] used fuzzy TOPSIS integrated with fuzzy AHP to propose a new MEA failure modes & effects analysis which overcomes the shortcomings of traditional MEA. Kaya and Kahraman [32] proposed a modified fuzzy TOPSIS for selection of the best energy technology alternative. Kim et al. [33] used fuzzy TOPSIS for modeling consumer s product adoption process. The various steps of fuzzy TOPSIS are presented as follows: Step : Assignment of ratings to the criteria and the alternatives. Let us assume there are J possible candidates called A = { A, A2,... Aj} which are to evaluated against n criteria C = { C, C2,... C j}. The criteria weights are denoted by w i ( i =,..., m). The performance ratings of each decision maker D k ( k =,..., K) for each alternative A j ( j =,..., n) with respect to criteria C i ( i =,..., m) are denoted by R = x ( i =,..., m; j =,..., n; k,..., K) with membership function ( x) k k = µ. R k Step 2: Compute aggregate fuzzy ratings for the criteria and the alternatives. If the fuzzy ratings of all decision makers is described as triangular fuzzy number Rk = ( ak, bk, ck ), k =,..., K, then the aggregated fuzzy rating is given by R = ( a, b, c), k =,..., K, where; a K = min k k K = k { a } b = b c = max c } k k { k (4-) th If the fuzzy rating and importance weight of the k decision maker are x = ( a, b, c ) and w k = ( wjk, wjk2, wjk3), i =,..., m; j =,..., n respectively, then the aggregated fuzzy ratings ( x ) of alternatives with respect to each criteria are given by x = ( a, b, c ) where a K = min k k K = k { a } b = b c = maxc } ( k (4-2) The aggregated fuzzy weights w ) of each criterion are calculated as w = ( w, w, w ) where: k { k K j = min jk j2 jk2 j3 max{ jk3 k K k = k { w } w = w w w } w = (4-3) j k k k j j2 j3 k Step 3: Compute the fuzzy decision matrix. The fuzzy decision matrix for the alternatives (D) C C2 C3 C4 and the criteria (W ) is constructed as follows: COPY RIHT 202 Institute of Interdisciplinary Business Research 660

7 INTERDISCIPLINARY JOURNAL O CONTEORARY RESEARCH IN BUSINESS A x A 2 x2 D = A 3... A 4 xm (4-4) x x x m x n x2n, i =,..., m;... xmn j =,..., n W = ( w, w,..., w ) (4-5) 2 n Step 4: Normalize the fuzzy decision matrix. The raw data are normalized using linear scale transformation to bring the various criteria scales into a comparable scale. The normalized fuzzy decision matrix R is given by: [ r ], i =,..., m; j = n R = m n,..., (4-6) Where a b c r,, = and c j = maxc c c c i j j j ( benefit criteria) (4-7) a a a r j j j,, = and a j = mina c b a i (cost criteria) (4-8) Step 5: Compute the weighted normalized matrix. The weighted normalized matrix V for criteria is computed by multiplying the weights ( w j ) of evaluation criteria with the normalized fuzzy decision matrix r V (4-9) [ v ] m n, i =,..., m; j =,..., n where v = r (.) w j = Step 6: Compute the fuzzy positive ideal solution (PIS) and fuzzy negative ideal solution (NIS). The PIS and NIS of the alternatives are computed as follows: A + = v (4-0) A = v (4-), v { v }, i =,..., m; j n v n where v,..., ), j = max,..., ( 2 3 = i, v { v }, i =,..., m; j n v n where v,..., ), j = min,..., ( 2 = i COPY RIHT 202 Institute of Interdisciplinary Business Research 66

8 INTERDISCIPLINARY JOURNAL O CONTEORARY RESEARCH IN BUSINESS Step 7: Compute the distance of each alternative from PIS and NIS. The distance ( d i, d i ) of each weighted alternative i =,..., m from the PIS and the NIS is computed as follows: n ( v v, ), i = m di = dv j,..., j= (4-2) n ( v v, ), i = m di = dv j,..., j= (4-3) Where d v ( a, b) is the distance measurement between two fuzzy numbers a and b. Step 8: Compute the closeness coefficient ( CC i) of each alternative. The closeness coefficient CC i represents the distances to the fuzzy positive ideal solution ( A * ) and the fuzzy negative ideal solution ( A ) simultaneously. The closeness coefficient of each alternative is calculated as: di CCi =, i =,..., m + d + d (4-4) i i Step 9: Rank the alternatives. In step 9, the different alternatives are ranked according to the closeness coefficient CC i in decreasing order. The best alternative is closest to the PIS and farthest from the NIS. Warehouse location selection under uncertainty The proposed framework for warehouse location selection under uncertainty consists of two steps: Selection of evaluation criteria. Evaluation and selection of best alternative using selected criteria. These steps are presented in detail as follows. Criteria selection The first step involves selection of criteria for warehouse location. In this study, 5 criteria were used for the selection of warehouse location. These criteria were selected from the studies of Min and Melachrinoudis [4], Alberto [] and MacCarthy and Atthrirawong [39], Demirel et al. [8] and Dogan [9]. The definitions of the criteria are summarized as follows:. Labor costs: Labor costs are the criterion that changes with respect to the life conditions at alternative locations. COPY RIHT 202 Institute of Interdisciplinary Business Research 662

9 INTERDISCIPLINARY JOURNAL O CONTEORARY RESEARCH IN BUSINESS 2. Transportation costs: Transportation costs vary according to the economic structure of the alternative regions, transportation facilities and alternative transportation types as air, land, railroad, and marine. 3. Handling costs: Handling costs, which is caused by the storage of the goods, are the costs that are composed of capital, work power, equipment and risk costs and vary from a region to another region. 4. Land cost: Land cost is considered as a criterion that differs from one region to another. The cost of land for a warehouse is one of the major costly elements in this investment. 5. Skilled labor: This criterion defines the ideal personnel for a work, who has qualities to perform such work and who is trained, qualified. This is one of the requirements in order to perform a work timely and in a qualified manner. The skilled labor may not be at the desired level at each location. 6. Availability of labor force: Availability of labor force is a criterion that changes based on the level of development in the region, training levels, and population structure. 7. Land availability: Land availability is a criterion that changes according to the structure of the alternative regions. 8. Climate: Climate is a criterion that varies from a region to another. Significant climate fluctuations and severe weather conditions disrupt the business as well as affecting human efficiency. 9. Existence of modes of transportation: This criterion has an importance based on the availability of different transportation types in the location. 0. Telecommunication systems: Telecommunication systems are a criterion that defines the communication facilities and communication technologies of the warehouse with the customer nodes, the producers or the suppliers.. Quality and reliability of modes of transportation: This criterion defines the transportation service between the customer nodes, suppliers, and the warehouse, to be performed in a reliable and qualified way based on the different transportation modes. Reliable and quality service means timely delivery, delivery to the correct location and undamaged delivery of the goods. 2. Quality and reliability of utilities: Quality and reliability of utilities are considered as a criterion that differs from one region to another and is a criterion that changes based on the level of development in the region. 3. Proximity to customers: This criterion defines the distance of the warehouse location to the customer nodes. 4. Proximity to suppliers or producers: This criterion defines the distance of the warehouse location to the suppliers and the producers. 5. Lead times and responsiveness: This criterion defines the ability and the period to fulfill an order. These criteria are shown in Table. To express the criteria easier, the symbols in Table were generated. Alternatives evaluation and selection using fuzzy TOPSIS The second step involves allocation of linguistic ratings to the 5 criteria and the potential alternatives for each of the criteria by the decision makers or experts. The alternative ratings for each of the criteria from Table 2 and the criteria ratings are provided from Table 3. The linguistics terms are then transformed to fuzzy triangular numbers. Then, fuzzy TOPSIS (Section 4) is applied to aggregate the criteria and the COPY RIHT 202 Institute of Interdisciplinary Business Research 663

10 INTERDISCIPLINARY JOURNAL O CONTEORARY RESEARCH IN BUSINESS alternative ratings to generate an overall score for warehouse location selection. The highest score is selected as the best alternative for warehouse location. Case Study Entekhab industrial group, a big company in Iran, wants to decide on where it will locate its new warehouse. The alternative locations have been determined by the five experts ( D, D2, D3, D4 andd5 ) of the company: Isfahan ( A ), Arak ( A 2 ), Rasht ( A 3 ), Urmia ( A 4 ), Tabriz ( A 5 ).The criteria used for evaluation are same as presented in Table. The committee used linguistic assessments (Tables 2 and 3) to rate the 5 criteria (Table ) and the five alternatives ( A, A2, A3, A4 anda5 ). The results are shown in Tables 4 and 5 respectively. Then, the aggregated fuzzy weights ( W ) of each criterion are calculated using Eq. (4-3) and the aggregate fuzzy weights of the alternatives are computed using Eq. (4-2). The results are presented in Table 6 and 7 respectively. In the next step, we perform normalization of the fuzzy decision matrix of alternatives using Eqs. ((4-6), (4-7) and (4-8)). Next, the fuzzy weighted decision matrix for the five alternatives is constructed using Eq. (4-9). Then, the fuzzy positive ideal solution ( A * ) and the fuzzy negative ideal solutions ( A ) are computed using Eqs. (4-0), (4-) for the five alternatives. Then, the distance dv(.) of each alternative from the fuzzy positive ideal matrix ( A * ) and fuzzy negative ideal matrix ( A ) are determined according to Eqs. (4-2) and (4-3) as given in Tables 8. using distances * d i and d i (Eq. (4-4)), we compute the closeness coefficient ( CC i) of the five alternatives. The final results are shown in Table 9. By comparing the CC i values of the five alternatives (Table 9), we find that A > A2 > A5 > A4 > A3. Therefore, alternative Isfahan ( A ) is recommended as warehouse location. Conclusion A warehouse location selection is a multi-criteria decision-making problem including both quantitative and qualitative. In this paper, we present a multi-criteria decision making approach for warehouse location selection under fuzzy environment. The proposed approach comprises of two steps. In step, the criteria for warehouse location selection are identified. These criteria are labor costs, transportation costs, handling costs, land cost, skilled labor, availability of labor force, land availability, climate, existence of modes of transportation, telecommunication systems, quality and reliability of modes of transportation, quality and reliability of utilities, proximity to Customers, proximity to producer, lead times and responsiveness. In step 2, the experts provide linguistic ratings to the criteria and the alternatives. uzzy TOPSIS is used to aggregate the ratings and generate an overall performance score for measuring each alternative. The alternative with the highest score is selected as the best warehouse location selection. The warehouse location selection problem in this paper can be solved by fuzzy AHP and the obtained results can be compared for further research. COPY RIHT 202 Institute of Interdisciplinary Business Research 664

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14 INTERDISCIPLINARY JOURNAL O CONTEORARY RESEARCH IN BUSINESS Tables and igures µ M l( y) M r( y) M 0 l m u M igure. A triangular fuzzy number, M Table : Warehouse selection criteria. Criteria Symbol Labor costs C Transportation costs C 2 Handling costs C 3 Land cost C 4 Skilled labor C 5 Availability of labor force C 6 Land availability C 7 Climate C 8 Existence of modes of transportation C 9 Telecommunication systems C 0 Quality and reliability of modes of transportation C Quality and reliability of utilities C 2 Proximity to Customers C 3 Proximity to producer C 4 Lead Times and responsiveness C 5 Table 2: Linguistic terms for alternative ratings. Linguistic term Membership function Very Poor (VP) (0,0,) Poor (0,,3) Medium Poor () (,3,5) air () (3,5,7) Medium ood () (5,7,9) ood () (7,9,0) Very good (V) (9,0,0) COPY RIHT 202 Institute of Interdisciplinary Business Research 668

15 INTERDISCIPLINARY JOURNAL O CONTEORARY RESEARCH IN BUSINESS Table 3: Linguistic terms for criteria ratings. Linguistic term Membership function Very Low (VL) (0,0,) Low (L) (0,,3) Medium Low (ML) (,3,5) Medium (M) (3,5,7) Medium High (MH) (5,7,9) High (H) (7,9,0) Very High (VH) (9,0,0) Table 4: Linguistic assessments for the 5 criteria. Criteria Decision makers D D 2 D 3 D 4 D 5 C ML MH MH ML M C 2 H VH VH H H C 3 H MH H H MH C 4 MH H MH MH M C 5 MH MH MH M MH C 6 ML M M ML ML C 7 MH H MH MH MH C 8 ML ML ML M ML C 9 MH H MH MH MH C 0 M H M H H C VH VH VH VH VH C 2 ML MH M M ML C 3 H H VH H VH C 4 VH VH H H H C 5 VH H H H VH Table 6: Aggregate fuzzy criteria weight Criteria Weight C (,5,9) C 2 (5,8.8,0) C 3 (3,6.2,9) C 4 (3,7.4,0) C 5 (5,8.8,0) C 6 (,5.4,9) C 7 (,4.6,9) C 8 (5,8.2,0) C 9 (7,9.4,0) C 0 (7,9.4,0) C (3,5.8,9) C 2 (3,6.6,9) C 3 (5,8.8,0) C 4 (3,7.4,0) C 5 (3,7.4,0) C 6 (3,7,0) COPY RIHT 202 Institute of Interdisciplinary Business Research 669

16 INTERDISCIPLINARY JOURNAL O CONTEORARY RESEARCH IN BUSINESS COPY RIHT 202 Institute of Interdisciplinary Business Research 670 C5 C4 C3 C2 C C0 C9 C8 C7 C6 C5 C4 C3 C2 C Criteria V V D V V V D2 D3 V D4 V V D5 A D D2 D3 D4 D5 A2 D D2 D3 D4 D5 A3 D D2 D3 D4 D5 A4 D D2 D3 D4 D5 A5 Alternative Table 5: Linguistic assessments for the three alternatives.

17 INTERDISCIPLINARY JOURNAL O CONTEORARY RESEARCH IN BUSINESS Table 7: Aggregate fuzzy decision matrix Criteria Alternative A A 2 A 3 A 4 A 5 C (5,8.6,0) (3,5.8,9) (3,5.8,9) (3,5.8,9) (3,7,0) C 2 (5,8.2,0) (3,6.2,9) (3,5.4,9) (3,6.2,9) (3,6.6,9) C 3 (5,8.2,0) (3,6.2,9) (3,6.2,9) (3,6.6,9) (3,6.6,9) C 4 (,3.4,7) (,4.6,7) (,4.2,7) (,4.2,7) (,4.6,7) C 5 (5,8.8,0) (3,7,0) (3,6.2,9) (3,5.8,9) (3,6.6,9) C 6 (5,8.2,0) (5,7,9) (3,5.8,9) (3,6.6,9) (5,7,9) C 7 (5,8.2,0) (3,5.4,9) (3,6.2,9) (3,6.2,9) (3,6.6,9) C 8 (5,8.2,0) (5,7.8,0) (3,6.6,9) (3,5.8,9) (3,6.6,9) C 9 (7,9.4,0) (5,7.4,0) (3,6.2,9) (3,6.2,9) (5,7.4,0) C 0 (3,6.6,9) (3,5.8,9) (3,5,7) (3,5.4,9) (3,5.4,9) C (5,8.6,0) (5,7.4,0) (3,6.2,9) (3,6.2,9) (5,7,9) C 2 (5,8.2,0) (5,7,9) (3,5.8,9) (3,5.8,9) (3,6.6,9) C 3 (5,8.6,0) (3,6.6,9) (3,6.6,0) (3,6.6,0) (5,8.2,0) C 4 (7,9.6,0) (5,7.8,0) (3,6.2,9) (3,5.4,9) (3,5.4,9) C 5 (7,9.4,0) (5,7.4,0) (3,6.6,0) (3,6.6,0) (5,8.2,0) Table 8: Distance d v A, A ) and d v A, A ) for alternatives. ( ( Criteria d + d - A A 2 A 3 A 4 A 5 A A 2 A 3 A 4 A 5 C C C C C C C C C C C C C C C Table 9: Closeness coefficient ( CCi ) of the three alternatives A A 2 A 3 A 4 A 5 d i d i CC i COPY RIHT 202 Institute of Interdisciplinary Business Research 67