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International Journal of Modern Engineering Research (IJMER) www.ijmer.com Vol.2, Issue.6, Nov-Dec. 2012 pp-4189-4194 ISSN: 2249-6645 A Fuzzy Logic Multi-Criteria Decision Approach for Vendor Selection Manufacturing System Harish Kumar Sharma1 National Institute of Technology, Durgapur (WEST BENGAL) - 1713209Abstract: The success of an industry depends on decision making ( MCDM) are coherently derived tooptimization of product cost and for achieving above goal manage the problem ( Shyur &Shih, 2006).EvaluatingInternal selection should be efficient. In the present study vendors many criteria including quantitative, such as cost,an efficient Multi-Criteria Decision Making (MCDM) price as well as qualitative, a considerable number ofapproach has been proposed for quality evaluation and decision models have been developed based on the MCDMperformance appraisal in vendor selection. Vendor theory.selection is a Multi-Criteria Decision Making (MCDM) To resolve the problem, this paper suggestsproblem influenced by several parameters which are in evaluating vendor using a multiple levels multiple criterialinguistic. Multiple.Performance criteria/attributes. These decision making method under fuzzy logic methodcriteria attributes may be both qualitative as well as maintenance alternative for industries planning of the basisquantitative. Qualitative criteria estimates are generally of quantitative and qualitative factors formula are clearlybased on previous experience and perfomanance maker’s displayed. Classified to benefit and cost criteria has theopinion on suitability. Therefore to quantity the linguistic larger the better, ratings of vendor and importance weightsvariables fuzzy logic and set theory is used. The fuzzy set of all the criteria are assessed in linguistic valuestheory helps in vagueness of the system. a fuzzy decision represented by fuzzy numbers.approach is developed where are resourcing of vendors to Selection of fuzzy number & their membershipselect suitable vendor for materials is made MCDM method functions.has been illustrated in this reporting through a case study. Fuzzy logic of the scale function Averaging the fuzzy numbers as given by theKeywords: Vendor’s selection Fuzzy sets, Decision matrix, performance makers in terms linguistics variables.Rank, Multiple criteria decision making, weight Determinations of fuzzy normalize weight. Overall ranking of alternatives. I. Introduction Finally result of multi criteria decision making Iron and steel industry is an important basic In this paper the vendor selection by a MCDM forindustry for any industrial economy providing the primary these logic method identified a criteria based on product,material for construction, automobile machinery and other cost ,quality ,service etc. these criteria short out the vendorindustries. the importance of maintenance function has by using the performance makers P1,P2,P3,P4,P5, and PNincreased due to its role in keeping and improving the these performance makers gives the data in a logisticsavailability, product quality cost-effectiveness levels. variable weight of the criteria then we find the suitableMaintenance costs constitute an important part of the vendor materialoperating budget of manufacturing firms. Maintenanceselection is one of the most critical activities for many II. REVIEW OF PREVIOUS WORKindustries. The selection of an appropriate maintenance may [1]The vendor selection a focus area of researchreduce the purchasing cost and also improve since the 1966s.literature (Dickson,1966; Webercompetitiveness. ,1991)several dimensions are mentioned that are important It is impossible for a company to successfully for the multiple vendorproduce, low-cost, high-quality products without selectiondecision.nmaking,price,quality,delivery,performansatisfactory maintenance. The selection of appropriate ce,history,capacity,service Production facilities andmaintenance has been one of the most important function technical capabilities etc. the problem is how to selectfor a industries. If the relationship between a supplier and vendor that perform optimally on the desired dimensions.[2]manufacturing industries. Many studies have pointed out Weber et al.(1991) reviewed 74 vendor(supplier)that key is to set effective evaluation criteria for the supplier selection articles from 1966 to 1991 and showed that moreselection than 63% of them were in a multi criteria decision making. Vendor selection is a common problem for acquiring other researchers also endorsed using a weighted linearthe necessary materials to support the output of method of multiple for the VSP. Gaballa (1974) is theorganizations. The problem is to find and evaluate first author who applied mathematical programming to aperiodically the best or most suitable vendor for the vendor selection problem in a real case. He used a mixedorganization based on various vendor. Due to the fact that integer programming .model to minimize the totalthe evaluation always involves conflicting performance discounted price of it misallocated to the VSP. Webercriteria of vendors. The techniques of multiple criteria www.ijmer.com 4189 | Page
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International Journal of Modern Engineering Research (IJMER) www.ijmer.com Vol.2, Issue.6, Nov-Dec. 2012 pp-4189-4194 ISSN: 2249-6645and Current (1993) developed a multi objective MIP for normality with at least one element with degree ofvendor selection and order allocation among the selectedvendors .they applied the proposed model in a proposed x a x a model in a practical case.[3] Buffa and Jackson (1983) and a x b a xbSharma et al. (1989), respectively, used linear and non- b a b a linear mixed-integer goal programming (GP) for price, c x 1b x c x b x c x c a x d c x d service level, delivery and quality goals. Failure base maintenance (FBM) is performed when a failure or 0 c d breakdown occurs, no action is taken to detect the onset of or to present failure. The maintenance related costs are 0 usually high, but it may be considered cost effective incertain cases.[4] fuzzy multi agent system is proposed for (a) fA is a continuous mapping from R to [0, 1];ta-chung chu,Rangnath varma (2011),developed to depict (b) fA(x) = 0,∀ x ∈ (-∞,a ]the relationship among parent criteria and their sub-criteria (c) fA is strictly increase on [a, b];and criteria and the weight of all criteria,[5] amit karami (d) fA (x) = 1, x e [b, c];and zhiling Gua We demonstrate that the fuzzy logic (e) fA is strictly decreasing on [c, d];(f) fA(x) = 0,∀ x ∈[d,∞);approach provides a robust analysis for vendor selection, Where a, b, c and d are real numbers. We may let a -1, or a=b,[6]eleonona botani ,Antonio Rizzi (2007) An adapted multi or b=c or c=d or d= +1–criteria approach to suppliers and products selection Anapplication oriented to lead-time reduction. An extensive IV. OPERATIONS ON FUZZY NUMBERScase study is presented to show the practical application of Let A=(a1,b1,c1,d1) and B= (a2,b2,c2,d2) are twothe methodology trapezoidal fuzzy numbers. Then the operations [+,- ,×,÷] are expressed (Kaufmann and Gupta 1991) as. III. METHOD OF SOLUTION2.1 Fuzzy sets LetA fuzzy set A can denoted by Ai = {(x, fA(x)) |x U}, where A B a1 , b1 , c1 , d1 ) ( a2 , b2 , c2 , d 2 U is universe of discourse, x is an element in U, A is a a1 a2 , b1 b2 , c1 c2 , d1 d 2 fuzzy set in fA(x) is the membership function of A x(Kaufmann & gupta, 1991) the larger fA(x), the stronger the A B ( a1 , b1 , c1 , d1 ) ( a2 , b2 , c2 , d 2 )grade of membership for x in A a1 d 2 , c1 b2 , c1 b2 , d1 a2 2.2 Fuzzy numbersA real fuzzy number A is described as any fuzzy subset ofthe real line R with membership function fA which A B a1 , b1 , c1 , d1 ( a2 , b2 , c2 , d 2 )possesses the following properties (Dubois & Prade, 1978 a1 a2 , b1 b2 , c1 c2 , d1 d 2 Triangular L-R Fuzzy Number 1.0 A a1. b1 , c1 , d1 B a2 , b2 , c2 , d 2 0.9 0.8 Membership Value 0.7 0.6 a b c d 0.5 1 , 1 , 1 , 1 0.4 d 2 c2 b2 a2 0.3 0.2 µ (X) A 0.1 0.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Very Low Low More or Less Low Medium More or Less High High Very High A B C X (Input space) Trapezoidal L-R Fuzzy Number 1.0 0.9 0.8 Membership Value 0.7 0.6 0.5 Left Right 0.4 0.3 0.2 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0.1 WEIGHT 0.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 A B C D X (Input space) Fig. 2: Graphical representation of fuzzy numbers for linguistic variables. A fuzzy number is defined as a continuous fuzzy set that contains convexity with one distinct peak and For the selection of location, seven fuzzy numbers are taken www.ijmer.com 4190 | Page
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International Journal of Modern Engineering Research (IJMER) www.ijmer.com Vol.2, Issue.6, Nov-Dec. 2012 pp-4189-4194 ISSN: 2249-6645to describe the level of performance on decision criteria, to Step – 4:avoid difficulties for an performance makers indistinguishing subjectively between more than seven The normalized weight for each criteria (Ci) isalternatives Salty (1977) obtained as Wj, Where J=1, 2… n. The normalized weightTable 1 shows the fuzzy numbers associated with the for each criterion is obtained by dividing the Defuzzifiedcorresponding linguistic variables and the same is scores of each criterion by the total of all the criteria.graphically represented in figure3. Rating of Suitable Locations: In similar way as procedure adopted for theTable 1: Fuzzy numbers and corresponding linguistic calculation of weight criteria, the rating of suitable locationvariables is derived as: Linguistic Variable Fuzzy Number • Locations suitable on each of the criteria are to VL (Very low) (0.0, 0.0, 0.1, 0.2) be rated in the linguistic variables by the performance makers, which is converted into L (low) (0.1, 0.2, 0.3, 0.4) fuzzy numbers and the same is represented in the matrix form (Fuzzy Decision Matrix). ML/LL (more or less low ) (0.2, 0.3, 0.4, 0.5) • The average fuzzy score matrix for each M ( Medium) (0.4, 0.5, 0.5, 0.6) locations are obtained. MH/LH (more or less high) (0.5, 0.6, 0.7, 0.8) • The crisp score (Defuzzified value) for each location are obtained and same is represented in H( High) (0.6, 0.7, 0.8, 0.9) the matrix form as Xij, where i= 1,2 , m and J= VH (Very high) (0.8, 0.9, 1.0, 1.0) 1,2, , n. Where, m is the number of locations, n is the number of criteria. • Total aggregated score for locations againstStep – 1: each criteria is obtained asThe linguistic variables assigned by the experts for eachcriteria is translated into fuzzy numbers and the same is TS = {Xij} {Wj}represented in the matrix (Fuzzy Decision Matrix). v11v12 v1 j v1m w1 Step – 2: Let Ajar be the fuzzy number assigned to an vendor AI by v21v22 v2 j v2 m w2 the Perfomanance makers (Pk) for the decision criterion. TS v w tCj, the average of fuzzy numbers is given as vi1vi 2 vij vim w j Aij 1 a j i1 a j i 2 ...... a j ik ; k p vn1vn 2 vnj vnm wn =1,2………….p. On the basis of the total score obtained for each location against decision criteria, overall scores are The average fuzzy score matrix for each criteria is obtained, using simple average method, which provideobtained. final ranking of locations. V. CASE STUDY Step – 3: Steel industries purposed methodology allows theThe crisp score (Defuzzified values) for each criteria is experts to rank the suitable vendor reelection for aobtained. Defuzzification of fuzzy numbers is an operation magnum steel limited Gwalior (India) companies on thethat produces a non fuzzy crisp value. Defuzzified value is basis of different decision criteria in a more realisticgiven by the following equation (Kaufman and Gupta, manner. The advantage of fuzzy set theory facilitates the1991). assessment to be made on the basic of linguistic manner, which corresponded to the real lie situations in a muchTrapezoidal fuzzy number better way for simplicity five perfomanance makers E1, E a b c d E2,, E3, E4, E5 vendor selection projects, were consulted 4 to get the linguistic variables in terms of importance of each of the delusion criteria used to rank the vendor forTriangular fuzzy number each criteria’s (V1, V2, V3, V4, V5). E a 2b c 1. material cost(C1) 2. Semi –Raw material cost (C2) 4 www.ijmer.com 4191 | Page
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International Journal of Modern Engineering Research (IJMER) www.ijmer.com Vol.2, Issue.6, Nov-Dec. 2012 pp-4189-4194 ISSN: 2249-66453. Transportation cost (C3) 30 33 30 0 94. Inventory and storage cost (C4) C5 0.6 0.7 0.8 0.93 0.80 0.2535. Production Process cost (C5) 70 67 70 0 96. On time delivery (C6) C6 0.5 0.6 0.7 0.80 0.67 0.2117. Percentage waste items (C7) 60 34 20 0 88. Flexibility in service (C8) C7 0.2 0.3 0.4 0.50 0.35 0.1109. Financial position (C9) 00 00 00 0 010. Inspection (quality control) (C10) C8 0.5 0.6 0.7 0.83 0.67 0.211 41 20 20 1 8Table. 2 show the linguistic variables assigned by the C9 0.4 0.5 0.6 0.72 0.59 0.184Perfomanance makers to each of the decision criteria are 22 80 42 0 1define in the table -1 C10 0.4 0.5 0.6 0.72 0.60 0.190 70 67 70 0 7Table 3: Linguistic variables assigned by the Perfomanance maker’s Rating of alternatives (venders) on criterion (Xi j) Criteria perfomanance maker’s Suitability of venders against each criteria are to be rated and linguistic variables are assigned by the experts to the E1 E2 E3 E4 E5 venders table-3 are define in table-1 the linguistic variables C1 H M H H VH are converted into fuzzy numbers C2 H H H VH H Table 5: Linguistics variables for alternatives C3 MH H H VH VH C1 V1 M L M L M C4 MH MH M M M V2 H M VH H M C5 M M MH M M V3 VH M M VH VH C6 H H VH H M V4 VH VH H VH VH C7 MH VH M MH M V5 H H M H H C2 V1 VH VH VH VH VH C8 M MH MH M M V2 H H H VL L C9 VH H VH M H V3 H VH VH VH VH C10 MH MH M VH M V4 M M VH H VH V5 VH VH M H HThe average fuzzy scores, defuzzifled values and C3 V1 L M M M Mnormalized weight of criteria are obtained and given in table3 V2 L M H M H Table 3: Normalized weight of criteria V3 H VH H H VH criter Parameter of average fuzzy Defu Norma V4 VH H H H VH ia scores zz lized V5 M VH H VH H ifled weight C4 V1 VH VH M H H Valu VL M M H VH e V2 V3 VH VH H H M C1 0.6 0.7 0.8 0.89 0.80 0.250 V4 M H H VH M 70 67 70 0 0 V5 VH H M VH VH C2 0.4 0.5 0.6 0.72 0.60 0.190 70 67 70 0 6 C5 V1 M H M L M C3 0.6 0.7 0.8 0.92 0.80 0.253 V2 H L VL L M 70 68 70 0 7 V3 M M VL H H C4 0.5 0.6 0.7 0.78 0.66 0.209 V4 H VH M M H www.ijmer.com 4192 | Page
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International Journal of Modern Engineering Research (IJMER) www.ijmer.com Vol.2, Issue.6, Nov-Dec. 2012 pp-4189-4194 ISSN: 2249-6645 V5 H M H M VH V2 0.480 0.530 0.633 0.730 0.593 C6 V1 VH H VL H M V3 0.470 0.567 0.670 0.720 0.607 VH H M M H V4 0.330 0.433 0.530 0.450 0.436 V2 V5 0.400 0.500 0.600 0.700 0.550 V3 L VL M VL L C4 V1 0.733 0.830 0.930 0.980 0.868 V4 L L L H H V2 0.267 0.370 0.470 0.520 0.407 V5 VH H H H VH V3 0.400 0.500 0.600 0.700 0.550 C7 V1 VL M L VL L V4 0.400 0.500 0.600 0.700 0.550 V2 VL M M M H V5 0.533 0.630 0.730 0.801 0.494 V3 M M VL VL L C5 V1 0.200 0.300 0.400 0.500 0.350 V2 0.730 0.833 0.930 0.980 0.856 V4 H H L L VL V3 0.670 0.767 0.870 0.920 0.807 V5 H VH VH M M V4 0.470 0.470 0.567 0.720 0.557 C8 V1 VH M L H H V5 0.530 0.633 0.730 0.820 0.679 V2 VL VL L M M C6 V1 0.470 0.567 0.670 0.720 0.607 V3 H M H H H V2 0.470 0.567 0.670 0.700 0.602 V4 L M H M H V3 0.130 0.233 0.330 0.460 0.289 V5 M M H H H V4 0.530 0.630 0.730 0.820 0.678 C9 V1 L M L L L V5 0.470 0.570 0.670 0.720 0.608 V2 H M H M L C7 V1 0.730 0.830 0.930 0.950 0.860 V3 L M VH H M V2 0.530 0.630 0.730 0.820 0.678 V4 M VL L L L V3 0.400 0.500 0.600 0.700 0.550 V5 H H M M VL V4 0.330 0.430 0.500 0.670 0.483 C10 V1 H VL L VL VL V5 0.530 0.630 0.730 0.820 0.678 V2 L H H H M C8 V1 0.470 0.570 0.670 0.720 0.608 V3 L L VL VL VL V2 0.730 0.830 0.930 0.980 0.868 V4 M L VL M VL V3 0.670 0.767 0.870 0.890 0.800 V5 M L VL M H V4 0.470 0.470 0.567 0.620 0.532 V5 0.530 0.633 0.730 0.820 0.679 Table 6: Average fuzzy scores and Defuzzified scores C9 V1 0.470 0.567 0.670 0.720 0.606criteria Vendo Average Fuzzy scores Defuzz r ied V2 0.470 0.567 0.670 0.720 0.607 score V3 0.130 0.233 0.330 0.460 0.289C1 V1 0.670 0.767 0.870 0.890 0.799 V4 0.530 0.630 0.730 0.820 0.678 V2 0.470 0.567 0.670 0.710 0.605 V5 0.470 0.570 0.670 0.720 0.608 V3 0.670 0.767 0.870 0.880 0.797 C10 V1 0.730 0.830 0.930 0.960 0.863 V4 0.530 0.633 0.730 0.800 0.674 V2 0.530 0.630 0.730 0.830 0.680 V5 0.670 0.767 0.870 0.900 0.802 V3 0.400 0.500 0.600 0.700 0.550C2 V1 0.530 0.633 0.730 0.820 0.679 V4 0.330 0.430 0.500 0.640 0.476 V2 0.200 0.300 0.400 0.500 0.350 V5 0.530 0.630 0.730 0.820 0.678 V3 0.730 0.833 0.930 0.980 0.869 V4 0.467 0.567 0.667 0.767 0.617 V4 0.670 0.767 0.870 0.910 0.805 V5 333 0.433 0.530 0.620 0.479 V5 0.600 0.700 0.800 0.900 0.750C3 V1 0.530 0.633 0.730 0.850 0.686 www.ijmer.com 4193 | Page
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International Journal of Modern Engineering Research (IJMER) www.ijmer.com Vol.2, Issue.6, Nov-Dec. 2012 pp-4189-4194 ISSN: 2249-6645 The total scores for each vendor can be calculated matrix as follows VII. ACKNOWLEDGEMENT V V2 V3 V4 V5 Wj Authors would like to thank to Vimal steel 1 corporation ltd., for providing data’s to create decision C1 0.800 0.605 0.797 0.674 0.802 0.250 criteria & also thank to Perfomanance maker’s for C2 0.679 0.350 0.869 0.805 0.750 0.190 providing linguistic variables to apply fuzzy multi criteria C3 0.686 0.593 0.607 0.436 0.550 0.253 decision approach for selecting the best vendor for a companies. C4 0.868 0.407 0.550 0.550 0.494 0.209 C5 0.350 0.856 0.807 0.557 0.679 0.254 REFERENCES C6 0.607 0.602 0.289 0.678 0.608 0.213TS [1] Alexios-patapios kontis and vassilionvyagotis, C7 0.860 0.678 0.550 0.483 0.678 0.110 supplier Selection problem multi-criteria approaches C8 0.608 0.808 0.800 0.532 0.629 0.212 based on DEA,international Scientific Advances in C9 0.606 0.607 0.289 0.678 0.608 0.185 Management & Applied Economics, vol1.1,no.2,207- C10 0.863 0.680 0.550 0.476 0.678 0.190 219(2011) [2] Shyur &Shih, 2006.Evaluating vendors many criteria Including quantitative, as well as qualitative, a considerable Number of decision making EuropeanTotal scores for vender (V1) on criteria is obtained as- Journal of Operation Research, Vol.50, 5-10(2009)(0.800×0.250)+(0.679×0.190)+(0.686×0.253)+(0.868×0.20 [3] Kaufmann, A.,& Gupta, M.M, Introduction to Fuzzy9)+(0.350×0.254)+(0.607×0.213)+(0.860×0.110)+(0.608×0 Arithmetic theory & application, Van No strand.212)+(0.606×0.185)+(0.863×0.190)= 1.4035 Reinhold, Newyork.vol.1; 5-18 (1991)Similarly, total scores for venders (V2), (V3),(V4),(V5)are [4] Dickson, Weber, Multi objective linear model forobtained and provided in table-7In the selection of suitable Vendor Selection criteria and methods, Europeanvendor for any company , initial investment, qualitative Journal ofcriteria each has equal weight age. Hence t h e final Operational Research, Vol.50, 2-18(1991)s c o r e s a n d r a n k i n g o f venders are given in table.6 [5] Buffa and Jackson and Sharma, Multi decision making used linear and non-linear programming, Total Table 7: Final scores and ranging of venders. Quality Environmental Management Vol.3 (4); 521-Vendors V1 V2 V3 V4 V5 530(1994) Final [6] Tu-chung Chu, Rangnath varma, Evaluating suppliersScores 1.4035 1.2859 1.29900 1.2489 1.3353 via a multiple criteria decision making method under Rank 1 4 000001 3 5 2 fuzzy Enviroment, nternationalJournalofcomputers&Industrial VI. RESULTS CONCLUSION Engineering vol, 62; 653-660(2012) This paper, presented the fuzzy multi criteria [7] Swanson’s., 2001.Linking maintenance strategiesdecision approach, the order odd ranking of vendor’s for To performance. International Journal of Productionthe company’s are as V1>V5>V3>V2>V4. The result Economics70, 237-244. (2001)show V1 is the best location for the company. Has been [8] Shyur &Shih, 2006.Evaluating vendors many criteriahighlighted to solve multi-criteria decision making Including quantitative, as well as qualitative, aproblems through a case study of vendor selection. The considerable Number of decision making EuropeanStudy demonstrates the effectiveness of the said MCDM Journal of Operational Research,Vol.50,5-10(2009)techniques in solving such a vendor selection problem. www.ijmer.com 4194 | Page
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