Serbian Serbian Journal of Management 11 (1) (2016) 15 - 27 Journal of Management www.sjm06.com

AN INTEGRATED FUZZY AHP AND TOPSIS MODEL FOR SUPPLIER EVALUATION

Željko Stevića*, Ilija Tanackovb, Marko Vasiljevića, Boris Novarlićc and Gordan Stojićb

aUniversity of East Sarajevo, Faculty of Transport and Traffic Engineering Doboj, Vojvode Mišića 52, 74 000 Doboj, bUniversity of , Faculty of Technical Sciences, Trg Dositeja Obradovića, 21 000 Novi Sad, cKP ''Progres'' ad, Doboj, Karađorđeva 10, 74 000 Doboj, Bosnia and Herzegovina

(Received 8 February 2016; accepted 5 April 2016)

Abstract

In today’s modern supply chains, the adequate suppliers’ choice has strategic meaning for entire companies’ business. The aim of this paper is to evaluate different suppliers using the integrated model that recognizes a combination of fuzzy AHP (Analytical Hierarchy Process) and the TOPSIS method. Based on six criteria, the expert team was formed to compare them, so determination of their significance is being done with fuzzy AHP method. Expert team also compares suppliers according to each criteria and on the base of triangular fuzzy numbers. Based on their inputs, TOPSIS method is used to estimate potential solutions. Suggested model accomplishes certain advantages in comparison with previously used traditional models which were used to make decisions about evaluation and choice of supplier.

Keywords: Fuzzy AHP, TOPSIS, Supplier evaluation, Multi-criteria decision making

1. INTRODUCTION Accordingly, decision makers are bearing great responsibility when modeling supply In day-to-day business, making decisions chain which includes the above mentioned. which will, on one side lessen the expenses, Their task can be manifested through and on the other side fulfill user’s needs, accomplishments of logistics triangle, which certainly represents a challenge. is made of expenses, time and quality.

* Corresponding author: [email protected] DOI:10.5937/sjm11-10452 16 Ž.Stević / SJM 11 (1) (2016) 15 - 27 Satisfying these needs that are placed in front The AHP method was previously used to of decision makers requires systematic address the problem of supplier selection, approach which is mirrored in expenses’ whether in the conventional form or in a reduce in every sub-system of logistics, combination with fuzzy logic, for example in shortening of time needed for certain (Nydick & Hill, 1992; Chen et. al., 2006; operations accomplishments, as well as Stević et al., 2015b), supplier selection in entire process needed for realization of industry (Barbarosoglu & Yazgac, 1997), goods delivery. Besides, company must supplier selection for the textile company strive to enlarge the quality of product itself, (Ertugrul & Karakasoglu, 2006), the area of so the end user is satisfied with provides production (Chan & Kumar, 2007), the area services, what would make him a loyal user. of production TFT-LCD (Lee, 2009), Due to above mentioned, it is necessary, electronic procurement (Benyoucef & during the first phase of logistics, ie. Canbolat, 2007), in washing machine purchasing logistics, to commit good company (Kilincci & Onal, 2011), in a gear evaluation and choice of supplier, what can motor company (Ayhan, 2013), suppliers for largely influence the forming of product’s white good manufacturers (Kahraman et. al., final price and in that way accomplish 2003), while Ho, along with co-authors in significant effect in complete supply chain. It (Ho et. al. 2010) conducted a literature is possible to accomplish the above review of the application of multi-criteria mentioned if evaluation is being done based analysis in the mentioned field. There are on multi-criteria decision making that other areas where this method is applied, for includes large number of criteria and expert’s example catering services evaluating estimation of their relative significance, (Kahraman et. al., 2004), evaluating and since one of the most important selecting a vendor in a supply chain model characteristics of multi-criteria decision (Haq & Kannan, 2006), evaluating and making is that different criteria can not have selection of computers (Srichetta & equal importance (Stević et. al., 2015a). Thurachon, 2012), evaluation of impact of Multi-criteria analysis is rapidly safety training programme (Raja Prasad & expanding, especially during the past several Chalapathi Venkata, 2013). years, and therefore, big number of problems is being solved nowadays using methods from that area. It is being used for solving 2. RESEARCH problems of diferent nature, it is also greatly accepted and used in the area of management AHP is often used in combination with and logistics, where certain decisions are other methods, as evidenced by (Stević et al., being made exactly on the base of multi- 2015c) where the authors are using AHP in criteria methods. There is a great number of their work to assess the difficulty of criteria, methods belonging to the area of multi- and Topsis method for obtaining the final criteria decision making, and the most often ranking of alternatives or combination fuzzy used, at least when dealing with supplier AHP and Topsis method (Ballı & Korukoğlu, choice, are the AHP and TOPSIS methods, 2009; Mahmoodzadeh et al., 2007), that are used in this paper for evaluation of combination fuzzy AHP and fuzzy Topsis supplier. (Sun, 2010; Zeydan et al., 2011; Shukla et Ž.Stević / SJM 11 (1) (2016) 15 - 27 17 al., 2014; Bronja & Bronja, 2015). hierarchy. More details on the analytic For the purpose of suppliers’ evaluation, hierarchy process are found in the book of this paper uses the combination of methods (Saaty & Vargas, 2012). of mulit-criteria analysis. Fuzzy analitical- Some of the key and basic steps in the hierarchy proccess (FAHP) had been used AHP methodology according to (Vaidya & for determination of significance of criteria, Kumar, 2006) are as follows: to define the which compares criteria based on fuzzy problem, expand the problem taking into scales for comparison, while Topsis method account all the actors, the objective and the was used for alternatives’ ranking. outcome, identification of criteria that influence the outcome, to structure the 2.1. Conventional AHP method problem previously explained hierarchy, to compare each element among them at the Analytic hierarchy process is created appropriate level, where the total of nx(n- Thomas Saaty (Saaty, 1980) and according to 1)/2 comparisons is necessary, to calculate him (Saaty, 2008) AHP is a measurement the maximum value of own vector, the theory which is dealing with pairs comparing consistency index and the degree of and which relies on expert opinion in order consistency. to perform the priority scale. With AHP AHP in a certain way solves the problem according (Saaty, 1988), it is possible to of subjective influence of the decision-maker identify the relevant facts and connections by measuring the level of consistency (CR) existing between them. Parts of AHP and notifies the decision maker thereof. If the method are problem decomposition, where level of consistency is in the range up to the goal is located at the top, followed by 0.10, the results are considered valid. Some criteria and sub-criteria, and at the end of the authors take even greater degree of hierarchy are potential solutions, explained consistency as valid, which of course is not in more details by (Saaty, 1990). recommendable. This coefficient is In (Saaty, 1986) is defined the axioms recommended depending on the size of the which the AHP is based on: the reciprocity matrix, so we may find in the papers of axiom. If the element A is n times more (Anagnostopoulos et al., 2007) that the significant than the element B, then element maximum allowed level of consistency for B is 1/n times more significant than the the matrices 3x3 is 0.05, 0.08 for matrices element A; Homogeneity axiom. The 4x4 and 0.1 for the larger matrices. If the comparison makes sense only if the elements calculated CR is not of the satisfactory value, are comparable, e.g. weight of a mosquito it is necessary to repeat the comparison to and an elephant may not be compared; have it within the target range (Saaty, 2003). Dependency axiom. The comparison is granted among a group of elements of one 2.2. Chang’s extent analysis level in relation to an element of a higher level, i.e. comparisons at a lower level When it comes to decision making using depend on the elements of a higher level; fuzzy AHP method, various approaches were Expectation axiom. Any change in the developed as expanded fuzzy AHP method structure of the hierarchy requires re- based on triangular fuzzy numbers (Chang, computation of priorities in the new 1996; Zhu et al., 1999), fuzzy preference 18 Ž.Stević / SJM 11 (1) (2016) 15 - 27 programming developed by (Mikhailov, ଵ ଶ ௠ (1) ܯ௚௜ǡܯ௚௜ǡܯ௚௜ǡ݅ ൌ ͳǡʹǡ ǥ ݊Ǥǡ 2003), logarithmic fuzzy preference j programming originated from the above where M g , j 1 , 2 ,... m ., are fuzzy triangular mentioned access by its expanding, numbers. Chang's expanded analysis which was developed by (Wang & Chin, includes following steps: 2011). Step 1: Values of fuzzy extension for the The theory of fuzzy sets was first i-th object are given by the equation:

introduced by (Zadeh, 1965), whose ିଵ ௡ ௝ ୬ ୫ ௝ application enables decision makers to ܵ௜ ൌ σ௝ୀଵ ܯ௚௜ ൈቂσσ୧ୀଵ ୨ୀଵ ܯ௚௜൧ (2) effectively deal with the uncertainties. Fuzzy sets used generally triangular, trapezoidal In order to obtain expression

and Gaussian fuzzy numbers, which convert ିଵ ୬ ୫ ௝ uncertain fuzzy numbers numbers. Fuzzy set ቂσσ୧ୀଵ ୨ୀଵ ܯ௚௜൧ (3) is according to (Xu & Liao, 2014) a class of objects characterized by function of it is necessary to perform additional fuzzy belonging, in which each object is getting a operations with "m" values of the extended grade of belonging to the interval (0,1). analysis, which is represented by the Triangular fuzzy numbers, which were used following expressions: in this work are marked as (lij, mij, uij). The ௡ ௝ ௠ ௠ ௠ (௚௜ ൌ൫σ௝ୀଵ ݈௝ ǡ σ௝ୀଵ ݉௝ǡ σ௝ୀଵ ݑ௝൯ (4ܯ parameters (lij, mij, uij) are the smallest σ௝ୀଵ possible value, the most promising value and ௡ ௡ ௝ ௡ ௡ ௡ (௚௜ ൌ ሺσ௜ୀଵ ݈௜ ǡ σ௜ୀଵ ݉௜ǡ σ௜ୀଵ ݑ௜ሻ (5ܯ highest possible value that describes a fuzzy σσ௜ୀଵ ௝ୀଵ event, respectively. Chang's extended analysis, despite the Then it is necessary to calculate the papers of (Wang et al., 2008; Fazlollahtabar inverse vector:

et al., 2010) who criticize this method, is ିଵ ଵ ଵ ଵ widely used for decision making in various ቂσσ୬ ୫ ܯ௝ ൧ ൤ ǡ ǡ ൨ (6) ୧ୀଵ ୨ୀଵ ௚௜ σ೙ ௨ σ೙ ௠ σ೙ ௟ fields. ೔సభ ೔ ೔సభ ೔ ೔సభ ೔ According to (Xu & Liao, 2014), one of Step 2: Possibility degree Sb > Sa is the disadvantages of the expanded AHP defined: analysis is considered to be not taking into ͳǡ ݂݅݉௕ ൒݉௔ Ͳǡ ݂݈݅௔ ൒ݑ௕ ܸሺܵ௕ ൒ܵ௔ሻ ൌ൞ account the consistency degree, i.e. failure to ௟ ି௨ (7) ݁ݏݓ݅ݎǡ ݋ݐ݄݁ ್ ೌ calculate its value. However, it can be ሺ௠್ି௨್ሻିሺ௠ೌି௟ೌሻ calculated by taking the crisp value.

Lets assume that X = {x1, x2,...,xn} is where „d“ ordinate of a largest cross-section

number of objects, and U = {u1, u2,...,um} is in point D between μSa andi μSb as shown in number of aims. figure 1. According to the methodology of extended analysis set up by Chang, for each object an extended goal analysisis is made. Values of the extended analysis "m" for each object can be represented as follows: Figure 1. Intersection between Sa and Sb Ž.Stević / SJM 11 (1) (2016) 15 - 27 19 To compare S1 and S2, both values V(S1 solution, where the cost criteria are ≥ S2) i V(S2 ≥ S1) are needed. maximized and benefit criteria are Step 3: Level of possibility for convex minimized. fuzzy number to be greater than „k“ convex The following are the steps of the number Si (i =1,2,...,k) can be defined as algorithm for solving the multi-criteria tasks follows: of TOPSIS method: Initial matrix: ᇱ (ሺܵ௜ ൒ܵଵǡܵଶǡǥǡܵ௞ሻ ൌ ‹ ܸሺܵ௜ ൒ܵ௞ሻǡൌݓ ሺܵ௜ሻ (8ܸ (ൌฮݔ௜௝ฮ௠௫௡ (12ܺ ᇱ ݀ ሺܣ௜ሻ ൌ ‹ ܸሺܵ௜ ൒ܵ௞ሻǡ݇ ്݅ǡ݇ൌͳǡʹǡǥǡ݊ (9) Step 1: Normalization of the initial The weight vector is given by the matrix: following expression: ԡܺԡ ՜ ԡܴԡ (13) ᇱ ᇱ ᇱ ᇱ ் ܹ ൌሺ†ሺܣଵሻǡ† ሺܣଶሻǡǥǤǡ†ሺܣ௡ሻሻ ǡ (10) ܴൌฮݎ௜௝ฮ௠௫௡ (14) Step 4: Through normalization, the ௫೔ೕ weight vector is reduced to the phrase: ܴ௜௝ ൌ (15) σ೘ మ ට ೔సభ ௫೔ೕ ் ܹൌሺ†ሺܣଵሻǡ†ሺܣଶሻǡǥǤǡ†ሺܣ௡ሻሻ ǡ (11) Step 2: Weighting of the normalized where W does not represent fuzzy number. matrix: There is a significant number of publications dealing exactly with ԡܴԡ ՜ ԡܸԡ (16) comparison of conventional AHP and fuzzy (௜௝ฮ (17ݎAHP, such as (Davoudi & Sheykhvand, ܸൌฮݒ௜௝ฮൌฮܹԢ௝ ή 2007; Özdağoğlu & Özdağoğlu, 2007; Zhang, 2010; Kabir & Hasin 2011; Step 3: Forming the positive ideal and Nooramin et al., 2012; Aggarwal & Singh, negative ideal solution: 2013). A+ - the positive ideal solution, which has 2.3. TOPSIS method all best features regarding all criteria: ­ ½ A §max v j K'· i §min v j K"· The Technique for Order Preference by ®¨ ij  ¸ ¨ ij  ¸¾ ¯© i ¹ © i ¹¿ Similarity to Ideal Solution (TOPSIS) was     first proposed by (Hwang & Yoon, 1981). ^`v1 ,v2 ,...,v j ,...,vn , i 1,m (18) The basic idea for this method is to choose K'Ž K o K' is a subset of K consisting of the alternative, which is as close to the max type criteria. positive ideal solution as possible and as far K''Ž K o K'' is a subset of K consisting of from the negative ideal solution as possible. min type criteria. The positive ideal solution is a solution with maximized benefit criteria and minimized A¯ - the negative ideal solution, which has cost criteria. The negative ideal solution is a all worst features regarding all criteria: 20 Ž.Stević / SJM 11 (1) (2016) 15 - 27 supplier in production and retail trade  ­§ · § ·½ A ®¨min vij j  K'¸ i ¨max vij j  K"¸¾ surrounding. Criteria’s were given in 74 © i ¹ © i ¹ ¯ ¿ documents published between 1966 and     ^`v1 ,v2 ,...,v j ,...,vn , i 1,m (19) 1991. Group of authors came to conclusion that following criteria are dominant: quality, Step 4: Calculating the distance delivery and price; while geographic (Euclidean distance) of each alternative from location, financial status and production the positive ideal and negative ideal solution: capacities belong to secondary group of + S1 - distance of an alternative from the factors. Then, (Verma & Pullman, 1998) positive ideal solution commenced examination among big number of managers with the aim to examine in ܵ ା σ௡ ା ଶ ௜ ൌ ට ௝ୀଵሺݒ௜௝ െݒ௝ ሻ (20) which way to make compromise during supplier selection. Their research pointed ¯ S1 - distance of an alternative from the out that managers are paying the most negative ideal solution attention to the quality as the most important suppliers’s attribute, before delivery and ି ௡ ି ଶ ௜ ൌ ටσ௝ୀଵሺݒ௜௝ െݒ௝ ሻ (21) price. Research about influence of criteria inܵ the supply chain is continuing on during the Step 5: Calculating the relative closeness beginning of this century as well, so (Karpak of an alternative to the ideal solution: et al., 2001) took reliability of delivery as a

ௌ ష criteria for choice making while (Bhutta & ܥ ൌ ೔ ௜ ௌ షାௌ శ (22) Huq, 2002) used four criteria for evaluation ೔ ೔ of suppliers: price, quality, techniology and Ͳ൑ܥ௜ ൑ͳ (23) service. Criteria applied in this study are: price of Step 6: Ranking of alternatives: materials, pipe length, delivery time, way of Ranking of Ci values arranged in payment, mode of delivery and quality hat descending order (from the highest to lowest are still in operation are marked with C1-C6 value) corresponds to the ranking of Ai respectively. Therefore, there are three alternatives (from the best to worst). criteria, quantitatively expressed and three criteria which are qualitative, as shown in 2.4. Input parameters in model Figure 2. Prices of materials, pipe length, delivery Literature and various publications time and transportation distance are the dealing with these or issues similar to ones quantitative criteria that are easily expressed from this paper, there can be found great as they represent stabil measures, ie. specific number of criteria for supplier evaluation. values. However, one question arises: how to make Price of materials indicates the money right selection from certain group, which value of goods established by the supplier will assist in finding the best solution. Some based on investment in the form of materials, authors (Weber et al. 1991) tried to answer energy, labor, etc. this question at the end of last century, so Pipe length is a parameter that is they examined criteria for selection of expressed in meters and which in this case Ž.Stević / SJM 11 (1) (2016) 15 - 27 21

Figure 2. The hierarchical structure of the model plays an important role due to the fact that In contrast to the above, the remaining customers often require delivery of pre- criteria are qualitative, they represent soft insulated pipes with precisely defined length, masurers and are not so easy to express, so which allows easier use. they should be presented by a descriptive Delivery time is the time interval between mark. the moment of getting the order and the time Payment represent compensation in of availability of goods to the customer. It is money for delivered goods as determined most commonly expressed in days, but can between the contract parties. During be in other time units as well. research, it was established that payment can

Table 1. Comparison criteria by three experts

C1 C2 C3 C4 C5 C6 C1 E1 (1,1,1) (2/3,1,2) (1/2,2/3,1) (1/2,1,3/2) (1/2,1,3/2) (2/3,1,2) E2 (1,1,1) (2/3,1,2) (2/3,1,2) (1,3/2,2) (1/2,1,3/2) (2/3,1,2) E3 (1,1,1) (1/2,2/3,1) (2/5,1/2,2/3) (1/2,1,3/2) (1/2,1,3/2) (2/7,1/3,2/5) C2 E1 (1/2,1,3/2) (1,1,1) (2/3,1,2) (1,3/2,2) (1,3/2,2) (1,1,1) E2 (1/2,1,3/2) (1,1,1) (1,1,1) (3/2,2,5/2) (1,3/2,2) (1,1,1) E3 (1,3/2,2) (1,1,1) (2/3,1,2) (3/2,2,5/2) (3/2,2,5/2) (2/5,1/2,2/3) C3 E1 (1,3/2,2) (1/2,1,3/2) (1,1,1) (3/2,2,5/2) (3/2,2,5/2) (1/2,1,3/2) E2 (1/2,1,3/2) (1,1,1) (1,1,1) (3/2,2,5/2) (1,3/2,2) (1,1,1) E3 (3/2,2,5/2) (1/2,1,3/2) (1,1,1) (2,5/2,3) (2,5/2,3) (1/2,2/3,1) C4 E1 (2/3,1,2) (1/2,2/3,1) (2/5,1/2,2/3) (1,1,1) (1,1,1) (2/3,1,2) E2 (1/2,2/3,1) (2/5,1/2,2/3) (2/5,1/2,2/3) (1,1,1) (1/2,1,3/2) (2/5,1/2,2/3) E3 (2/3,1,2) (2/5,1/2,2/3) (1/3,2/5,1/2) (1,1,1) (1,1,1) (2/7,1/3,2/5) C5 E1 (2/3,1,2) (1/2,2/3,1) (2/5,1/2,2/3) (1,1,1) (1,1,1) (1/2,2/3,1) E2 (2/3,1,2) (1/2,2/3,1) (1/2,2/3,1) (2/3,1,2) (1,1,1) (1/2,2/3,1) E3 (2/3,1,2) (2/5,1/2,2/3) (1/3,2/5,1/2) (1,1,1) (1,1,1) (2/7,1/3,2/5) C6 E1 (1/2,1,3/2) (1,1,1) (2/3,1,2) (1/2,1,3/2) (1,3/2,2) (1,1,1) E2 (1/2,1,3/2) (1,1,1) (1,1,1) (3/2,2,5/2) (1,3/2,2) (1,1,1) E3 (5/2,3,7/2) (3/2,2,5/2) (1,3/2,2) (5/2,3,7/2) (5/2,3,7/2) (1,1,1) 22 Ž.Stević / SJM 11 (1) (2016) 15 - 27 be done as advance, postponed with bank responses of the experts (Lee, 2009), this is guarantee, or percentage of total amount as shown in Table 2. Example calcuation of advance, and the rest is paid postponed, what geometric mean for C12 is: can be shown in following way: bad, n- = (2/3x2/3x1/2)1/3=0,606 acceptable, good and excellent. n = (1x1x2/3)1/3=0,874 Way of delivery represents a qualitative n+ = (2x2x1)1/3=1,587 criteria that can be expressed as good, To determine Fuzzy combination average and bad, depending of the fact expansion for each one of the criteria, first n whether the transport is calculated in the j we calculate ¦ M gi value for each row of the price of material – is it free of charge, or matrix. j 1 delivery of goods is to be done by vehicles of C1=(1+0.606+0.511+0.630+0.5+0.503; examined company. If it is the second option 1+0.874+0.693+1.145+1+0.694; distances of suppliers must be taken into 1+1.587+1.817+1.651+1.5+1.17)=(3.75; consideration, as well as expences caused by 5.406; 8.725) etc. n n that. j The ¦ ¦ M gi value is calculated as: The quality of materials is the level of i 1 j 1 fulfilling the requirements of regulations and (3.75; 5.406; 8.725)+(5.585; 7.407; 9.576) standards, on the one hand and the level of +(6.262; 8.427; 10.535)+(3.631; 4.348; fulfilling customer's expectations on the 5.912)+(3.825; 4.646; 6.564)+(6.464; 8.554; other side. It can be described as good, very 10.703)=(29.517; 38.788; 52.015) good, excellent and outstanding. 1 n ª n m º Upon criteria establishing, the expert j j Then, Si ¦ M gi u «¦ ¦ M gi » team comprised of three members compared j 1 ¬« i 1 j 1 ¼» them on the base of triangular fuzzy scale S1 = (3.75; 5.406; 8.725) x (1/52.015; (Chang, 1996) which is shown in Table 1. 1/38.788; 1/29.517) = (0.072; 0.139; 0.296) etc. Now, the V values (preference order) are 3. RESULTS АND DISCUSSION calculated using these vectors.

Fuzzy important weight of the criteria is 0.107  0.296 V S1 t S2 0.784 calculated by taking geometric mean of the 0.139  0.296  0.191 0.107 Table 2. Fuzzy important weight of the criteria calculated by taking geometric mean

C1 C2 C3 C4 C5 C6 (0.606,0.874, (0.511,0.693, (0.630,1.145, (0.503,0.694, C (1,1,1) (0.5,1,1.5) 1 1.587) 1.817) 1.651) 1.170) (0.630,1.145 (1.310,1.817, (1.145,1.651, (0.737,0.794, C (1,1,1) (0.763,1,1.587) 2 1.651) 2.31) 2.154) 0.874) (0.909,1.442, (1.651,2.154, (1.442,1.957, (0.630,0.874, C (0.630,1,1.31) (1,1,1) 3 1.957) 2.657) 2.466) 1.145) (0.606,0.784, (0.431,0.550, (0.376,0.464, (0.794,1, (0.424,0.550, C (1,1,1) 4 1.587) 0.763) 0.606) 1.145) 0.811) (0.464,0.606, (0.405,0.511, (0.415,0.529, C (0.667,1,2) (0.874,1,1.26) (1,1,1) 5 0.874) 0.693) 0.737) (0.855,1.442, (1.145,1.260, (0.874,1.145, (1.233,1.817, (1.357,1.890, C (1,1,1) 6 1.990) 1.357) 1.587) 2.359) 2.41) Ž.Stević / SJM 11 (1) (2016) 15 - 27 23 0.12  0.296 V S t S 0.693 1 3  0.157  0.097

V S1 t S4 1

V S1 t S5 1 0.124  0.296 V S t S 0.677 1 6  0.157  0.097 The priorities of weights are calculated using: d'=(C1)min(0.784; 0.693; 1; 1; 0.677)=0.677 d'=(C2)min(1; 0.887; 1; 1; 0.870)=0.870 Figure 3. Ranking of alternatives d'=(C3)min(1; 1; 1; 1; 0.983)=0.983 d'=(C4)min(0.826; 0.541; 0.432; 0.941; demands, changes of criteria importance, as 0.411)=0.411 well as company’s needs, current rank of d'=(C5)min(0.888; 0.618; 0.513; 1; 0.492)= alternatives could change, even in near 0.492 future; what requires constant monitoring of d'=(C6)min(1; 1; 1; 1; 1; 1)=1 own performanses and performanses of After the equation is applied (10), weight potential suppliers. values are obtained, and from the equation (11) normalized weights of criteria are received: 4. CONCLUSION W'=(0.677; 0.870; 0.983; 0.411; 0.492; 1) W=(0.15; 0.20; 0.22; 0.09; 0.11; 0.23) Estimation of supplier’s value for After determination of criteria, it is clear companies dealing with production, that the third and the sixth criteria are almost especially ones without big storage area for equally relevant, ie. for the company which material stocks necessary for production is subject of research, delivery time and proccess represents a key strategic issue. In material quality represents the most order to make possible timely, high-quality important criteria during the evaluation of and favorable production, it is necessary to potential suppliers. By applying previously look into market from diferent aspects. described steps of Topsis method, results Among most important ones is the aspect of represented by the following figure were end user, ie. demands the end user have obtained. while making decision about product On figure 3, it is visible that the purchasing. alternative, ie. supplier no. 2 has the highest Logistic of purchasing nowadays plays value and represent the best solution very important role in the supply chain, its according to previously conducted steps. optimization enables company to achieve Remaining alternatives, without alternative significant efect on entire logistics system. no. 5 which is the poorest solution, could as When it comes to purchasing the requred well in certain circumstances compete for materials, it is necessary to take care of great primary supplier. Depending on market amount of criteria with potential influence on 24 Ž.Stević / SJM 11 (1) (2016) 15 - 27 forming the final product’s price, as well as methodology, chose five suppliers which on position in the market obtained by are compeeting for the job of securing the company. Therefore, evaluation of suppliers purchase system, out of wich supplier no. 5 using the combination of multi-criteria can for sure be excluded from combination methods, can bring clearer picture about all because it represents far weaker solution in potential suppliers, their advantages and comparison with other suppliers. weaknesses. Effective flow of materials requires In its work, expert team which is integral efficient operating, where applying of these part of the company where the research methods can be of significant help. was done, based on previously described

ИНТЕГРИСАНИ “FUZZY AHP” И “TOPSIS” МОДЕЛ ЗА ВРЕДНОВАЊЕ ДОБАВЉАЧА

Жељко Стевић, Илија Танацков, Марко Васиљевић, Борис Новарлић и Гордан Стојић

Извод

У данашњим савременим ланцима снабдевања адекватан избор добављача представља питање од стратешког значаја за целокупно пословање компанија. Циљ рада је извршити вредновање добављача применом интегрисаног модела који подразумева комбинацију fuzzy AHP (aналитичко хијерархијски процес) и TOPSIS методе. На основу шест критеријума експертски тим који је формиран врши поређење критеријума, те се одређивање њиховог значаја врши примењујући fuzzy AHP методу. Поређење добављача према сваком критеријуму на основу троугаоних fuzzy бројева такође извршава експертски тим и на основу њихових улазних података приступа се вредновању потенцијалних решења применом TOPSIS методе. Предложеним моделом остварују се одређене предности у односу на претходне традиционалне моделе на бази којих су се доносиле одлуке о вредновању и избору добављача.

Kључне речи: Fuzzy AHP, TOPSIS, вредновање добављача, вишекритеријумско одлучивање

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