Supplier Selection by Using Multi Criteria Decision Making Methods

International Journal of Engineering Research and General Science Volume 2, Issue 6, October-November, 2014 ISSN 2091-2730 Supplier Selection by Using Multi Criteria Decision Making Methods P.Murali1, V. Diwakar Reddy2, A. Naga Phaneendra3 Department of Mechanical Engineering, Sri Venkateswara University college of Engineering, Tirupati, India Email – muralikrishna.781@gmail.com; phani.34suriya@gmail.com Abstract— In the present study an efficient multi criteria decision making (MCDM) approach has been proposed for quality evaluation and performance appraisal in supplier selection. Supplier selection is a multi-criteria decision making problem influenced by multiple performance criteria.These criteria’s/attributes may be both qualitative as well as quantitative .Qualitative criteria estimates are generally based on previous experience and expert opinion on a suitable conversion scale.This conversion is based on human judgment.Therefore predicted result may not be accurate always because the method does not explore real data.These are analyzed by TOPSIS(Technique for order preference similarity to ideal solution), PROMETHEE(Preference Ranking Organization Method for Enrichment Evaluations) etc. In solution of MCDM problems there should be a common trend is to convert quantitative criteria values into an equivalent single performance index called Multi attribute performance index. MCDM methods helps to choose the best alternatives where many criteria have come into existence ,the best one can be obtained by analyzing the different scope for the criteria, weights for the criteria. Keywords— Supplier Selection, MCDM, Qualitative, Quantitative, Weights for the Criteria,Multi attribute performance index, TOPSIS,PROMETHEE. INTRODUCTION In any Industry decisions are being made from various criteria’s, so the decision can be made by providing weights are obtain from expert groups. MCDM is pertaining to structure and solve decision and planning problems involving multiple criteria [1].The main objective of this survey is to support decision makers where there are huge choices exist for a problem to be solved. This survey on multi criteria decision understands the need of MCDM,many works have been proposed in determining the best optimal solution for a problem using different methods in it. PROPOSED METHODOLOGIES The proposed methodology for supplier selection problem, composed of TOPSIS method, consists of three Steps .They are as follows: (1) Identify the criteria to be used in the model; (2) weigh the criteria by using expert views; (3) Evaluation of alternatives with TOPSIS and determination of the final rank. In the first Step, with the help of going over expertise of experts and their relevant specialized literature, we try to recognize variables and effective criteria in supplier selection and the criteria which will be used in their evaluation is extracted. Thereafter, list of qualified suppliers are deter-mined and. In the last stage of the first step, the decision criteria are approved by decision-making team. After the approval of decision criteria, we assigned weights on them by organizing experts’ sessions in the second step. In the last stage of this step, calculated weights of the criteria are approved by decision making team. Finally, ranks are deter-mined, using TOPSIS method in the third step. TOPSIS METHOD TOPSIS(Technique for order preference similarity to ideal solution) method was introduced for the first time by Yoon and Hwang and was appraised by surveyors and different operators. As large number of potential available vendors in the current marketing environment, a full ANP (Analytic Network Process) decision process becomes impractical in some cases [11]. To avoid an unreasonably large number of pair-wise comparisons, we choose TOPSIS as the ranking technique because of its concepts ease of use. A general TOPSIS process with six activities is listed below. STEP 1: Establish a decision matrix for the ranking. The structure of the matrix can be expressed as follows 533 www.ijergs.org International Journal of Engineering Research and General Science Volume 2, Issue 6, October-November, 2014 ISSN 2091-2730 B 1 D= … F1 P11 F2 P12 … … … Fn P1n … … … --------------------------- (1) Pm1 Pm2 … Pmn Where Bi denotes the alternatives i, i = 1...,m; Fj represents jth attribute or criterion, j = 1...,n, related to ith alternative; Pij is a crisp value indicating the performance rating of each alternative Bi with respect to each criterion Fj. Bn STEP 2: Calculate the normalized decision matrix Q= [Sij]. The normalized value Sijis calculated as Sij = 𝑷𝒊𝒋 i=1….n;j=1……m 𝒏 𝑷 𝟐 𝒋=𝟏 𝒊𝒋 ------------------ (2) STEP 3: Calculate the weighted normalized decision matrix by multiplying the normalized decision matrix by its associated weights. The weighted normalized value vij is calculated as: Vij=Wij*Sij, J=1……n;i=1……….m; -----------(3) Where wj represents the weight of the jth attribute or criterion. STEP 4: Determine the PIS (Positive Ideal Solution) and NIS (Negative Ideal Solution) respectively: V+= (v1+……vn+ ) = ((Max vij 1 j ∈ J),(Min vij 1 j∈ J1)) V- =(v1-…..…..vn-) = ((Min vij 1 j∈ J),(Max vij 1 j ∈ J1)) Where J is associated with the positive criteria and J' is associated with the negative criteria STEP 5: Calculate the separation measures, using the m-dimensional Euclidean distance. The separation measure𝐸𝑖+ of each alternative from the PIS is given as: Ei+= + 2 𝑛 𝑗=1 (𝑣ij − 𝑣𝑗 ) , i = 1…….m -------- (4) Similarly, the separation measure 𝐸𝑖− of each alternative from the NIS is as follows: 𝐸𝑖 − = − 2 𝑛 𝑗=1(𝑣ij − 𝑣𝑗 ) , i = 1…….m ------- (5) STEP 6: Calculate the relative closeness to the idea solution and rank the alternatives in descending order. The relative closeness of the alternative Ai with respect to PIS V+ can be expressed as: 𝐻𝑖 ∗ = ℇ𝑖 − ℇ𝑖 + + ℇ𝑖 − --------- (6) Where the index value of Hi* lies between 0 and 1. The larger the index value, the better the performance of the alternatives. CASESTUDY To apply this methodology, we have solved simulated numerical problem. Assume that the management of Lanco industry Srikalahasthi wants to choose their best suppliers. Based on proposed methodology, three steps are applied for assessment and selection of suppliers. In this part we deal with application of these steps. After forming decision making team, step 1 starts developing an updated pool of supplier selection criteria for the industry, using those accepted criteria given in the literature, as well as those criteria recommended by the experts. In this numerical example, the criteria are selected as shown in Table 1. Although, the criteria considered in supplier evaluation are condition-industry specific. Selection of criteria is totally industry specific and based on each case and the criteria are changed and replaced. Opinions of decision makers on criteria were aggregated and weights of all criteria have been calculated by organizing the expert meeting. Its results have Assuming 4 suppliers are included in the evaluation process, information of each of suppliers has been mentioned in Table 2. After normalizing information and considering weight of criteria in them, negative and positive separation measures, based on normalized Euclidean distance for each supplier is calculated and then final weight of each supplier is calculated. 534 www.ijergs.org International Journal of Engineering Research and General Science Volume 2, Issue 6, October-November, 2014 ISSN 2091-2730 Table 1. Selecting criteria for supplier evaluation and Weight Code Criteria D1 D2 D3 D4 D5 D6 D7 D8 (Material Quality) (On time delivery) (Ordering cost) (Product price) (Financial stability) (Delivery lead time) (Technical Capability) (Transportation cost) (Rejection of defective product) (Production facilities and capacity) D9 D10 Weight (%) 0.20 0.08 0.07 0.15 0.10 0.09 0.07 0.05 0.08 0.11 Step-1 developing decision matrix; Table2. Supplier's information Criteria Suppliers D1 (%) D2 (%) D3 (₹) D4 (₹) D5 (Grad) D6 (Day) D7 (%) D8 (₹) D9 (%) D10(Grad) 1 2 3 4 95 90 135 2800 5 12 46 650 0.02 5 94 96 150 3500 3 15 52 470 0.03 4 96 94 145 3000 6 14 38 550 0.01 6 90 91 140 3100 3 10 40 700 0.02 7 Step-2 Calculating the normalized decision matrix 𝑆𝑖𝑗 = Table 3. Normalized decision matrix information of Suppliers SupplierCriteria 1 2 3 4 D1 0.51 0.50 0.51 0.48 D2 0.49 0.52 0.51 0.49 D3 0.47 0.53 0.51 0.49 D4 0.45 0.56 0.48 0.50 D5 0.56 0.34 0.68 0.34 D6 0.47 0.58 0.54 0.39 D7 0.52 0.59 0.43 0.45 D8 0.54 0.39 0.46 0.58 D9 0.47 0.71 0.24 0.47 D10 0.45 0.36 0.53 0.62 535 𝑃𝑖𝑗 𝑃ij 2 www.ijergs.org International Journal of Engineering Research and General Science Volume 2, Issue 6, October-November, 2014 ISSN 2091-2730 Step-3 calculating the weighted normalized decision matrix; Vij = Wij * Sij Table 4. Weighted normalized decision matrix information of Suppliers Criteria Supplier 1 2 3 4 D1 0.1020 0.1000 0.1020 0.0960 D2 0.0392 0.0416 0.0408 0.0392 D3 0.0329 0.0371 0.0357 0.0343 D4 0.0675 0.0840 0.0720 0.0750 D5 0.0560 0.0340 0.0680 0.0340 D6 0.0423 0.0522 0.0486 0.0351 D7 0.0364 0.0413 0.0301 0.0315 D8 0.270 0.0195 0.0230 0.0290 D9 0.0376 0.0568 0.0192 0.376 D10 0.0495 0.0396 0.0583 0.0682 Step-4 Determining the PIS (Positive Ideal Solution) and NIS (Negative Ideal Solution). V+ = {.1020, .0416, .0371, .0840, .0680, .0522, .0413, .0290, .0568, .0396} V- = {.0960, .0392, .0329, .0675, .0340, .0351, .0301, .0195, .0192, and .0682} Step-5 Calculating separation measure 𝐸𝑖+Calculating separation measure 𝐸𝑖− Table 5. Positive separation measure of SuppliersTable 6. Negative separation measure of Suppliers Ei+ = Supplier 1 2 3 4 + 2 𝑛 𝑗 =1 (𝑣ij − 𝑣𝑗 ) Supplier 0.0320 0.0353 0.0462 0.0534 1 2 3 4 𝐸𝑖 − = − 2 𝑛 𝑗=1(𝑣ij − 𝑣𝑗 ) 0.0367 0.0544 0.0388 0.0219 Step-6 Separation measures and the relative closeness coefficient; RESULTS Table 7. Relative Closeness Coefficient of Suppliers Suppliers Closeness Coefficient ∗ Supplier 1 Supplier 2 Supplier 3 Supplier 4 𝐻𝑖 = ℇ𝑖 − ℇ𝑖 + + ℇ𝑖 − 0.534 0.606 0.456 0.290 Rank 2 1 3 4 Therefore, the relative closeness coefficients are determined, and four suppliers are ranked. Obtained results have been mentioned in Table-7. Thus, supplier 2 has the best score amongst 4 suppliers. PROMETHEE METHOD STEP 1: Normalize the decision matrix using the following equation: 536 www.ijergs.org International Journal of Engineering Research and General Science Volume 2, Issue 6, October-November, 2014 ISSN 2091-2730 Rij= [Xij-min(Xij)] / [max(Xij)-min(Xij)] (i=1,2,3……, j=1,2….m) -------- (7) Where Xij is the performance measure of ith alternative with respect to jth criteria. STEP 2: Calculate the evaluative difference of ith alternative with respect to other alternative. This step involves the calculation of differences in criteria values between different alternative pairwise. STEP 3:Calculate preference function, Pj (i, i’) Pj (i, i’) =0 if Rij<=Ri’j Pj (i, i’)= (Rij-Ri’j) if Rij >Ri’j STEP 4: The aggregate preference function taking in to accountthe criteria weight. Aggregate preference function, mm Π(i,i’)= [ Σ Wj * Pj (i ,i’)] / Σ Wj --------------- (8) j=1 j=1 Where Wj is the relative importance (weight) of jth criteria STEP 5: Determine the leaving and entering outranking flows as follows: Leaving or positive flow for ith alternative n ф+ (i) = 1/n-1 Σ Π(i,i’) (i is not equal to i’) i’=1 ---------------------------- (9) Entering or negative flow for ith alternative n ф- (i)= 1/n-1 Σ Π(i,i’) (i is not equal to i’) i’=1 ----------------------- (10) Where n is the number of alternatives. Here each alternative faces (n-1) other alternatives. The leavingflow express how much an alternative dominates the other alternative,while the entering flow denotes how much an alternative’s dominated by other alternatives. Based on these outrankingflows, the PROMETHEE-1 method provide a partial preorderof the alternatives, whereas the PROMETHEE-2 method give the complete pre order by using the net flow, though it losses much information of preference relations. Calculate the net outranking flow for each alternative. ф (i) = ф+ (i) – ф-(i)-------------------------- (11) Determine the ranking of all the considered alternatives depending on the values of ф (i). The higher value of ф (i), the better is alternative.Thus the best alternative is the one having the highest ф (i) value. CASE STUDY As a case study, the supplier selection problem in a Lanco IndustrySrikalahasthi has been studied.The attributes for supplier selection are cost (Rs), insertion loss(db), volume (cc), and Weight (kg). The targeted values of eachcriterion correspond to the elements of reference data series for comparison [9]. The target to minimize cost, achieve high insertionloss and less volume, less weight. For cost, volume and weightlower the better criteria (LB) and for insertion loss higher thebetter criteria (HB) have been selected . Table 8.Objective data for supplier selection problem Supplier Criteria Supplier 1 Supplier 2 Supplier 3 Supplier 4 537 Cost (Rs) 0.590 0.745 0.590 0.590 Insertion Loss(db) 0.745 0.665 0.745 0.665 Volume (cc) 0.500 0.745 0.590 0.590 www.ijergs.org Weight (Kg) 0.500 0.745 0.665 0.590 International Journal of Engineering Research and General Science Volume 2, Issue 6, October-November, 2014 ISSN 2091-2730 Table 9. Normalized decision matrix Supplier Criteria Cost (Rs) Insertion Loss(db) Volume (cc) Weight (kg) Supplier 1 0 1 0 0 Supplier 2 1 0 1 1 Supplier 3 0 1 0.3673 0.6734 Supplier 4 0 0 0.3673 0.6734 Table 10. Preference functions for all the pairs of alternative Suppliers pair Criteria Cost (Rs) Insertion Loss(db) Volume (cc) Weight (Kg) (1,2) 0 1 0 0 (1,3) 0 0 0 0 (1,4) 0 1 0 0 (2,1) 1 0 1 1 (2,3) 1 0 0.6327 0.3266 (2,4) 1 0 0.6327 0.6327 (3,1) 0 0 0.3627 0.6734 (3,2) 0 1 0 0 (3,4) 0 0 0 0.3061 (4,1) 0 0 0.3673 0.3673 (4,2) 0 0 0 0 (4,3) 0 0 0 0 Table 11. Aggregate preference function Suppliers Supplier 1 Supplier 2 Supplier 3 Supplier 4 Supplier 1 - 0.300 0 0.300 Supplier 2 0.700 - 0.57859 0.61074 Supplier 3 0.1214 0.300 - 0.03214 Supplier 4 0.08926 0 0 - Table 12. Leaving and Entering flows for different supplier Suppliers Leaving Flow Entering Flow Supplier 1 0.200 0.30355 Supplier 2 0.62978 0.2000 Supplier 3 0.15118 0.19286 Supplier 4 0.02975 0.31429 538 www.ijergs.org International Journal of Engineering Research and General Science Volume 2, Issue 6, October-November, 2014 ISSN 2091-2730 RESULTS Table 13. Net Outranking Flow values for different supplier Suppliers Net out Ranking Flow Supplier Ranking Supplier 1 0.1036 3 Supplier 2 0.4298 1 Supplier 3 0.0417 4 Supplier 4 0.2846 2 Therefore, Net out Ranking Flow for different Suppliers are determined, and four Suppliers are ranked. Thus Supplier 2 has best score amongst 4 Suppliers. CONCLUSION For an Industry it is necessary to maintain the good coordination between management and supplier in terms of material quality, quantity, cost and time. By above mathematical treatment it is clear that the supplier selection for an Industry involves multiple criteria which show the important role in selection of suppliers. It allows the decision makers to rank the candidate alternative more efficiently and easily. The present study explores the use of PROMETHEE and TOPSIS methods in solving a supplier selection problem and the results obtained can be valuable to the decision maker in framing the supplier selection strategies. REFERENCES: [1] William Ho, Xiaowei Xu, Prasanta K. Dey. Multi-criteria decision making approaches for supplier evaluation and selection, European Journal of Operational Research (2010), Volume: 202, Issue: 1, Publisher: Elsevier, Pages: 16-24. [2] Albadvi, A., Chaharsooghi, S. K., & Esfahanipour, A. (2007). Decision making in stock trading: An application of PROMETHEE. European Journal of Operational Research, 177, 673–683 [3] Brans, J. P., Vincke, P. H., & Mareschall, B. (1986). How to select and how to rank projects: The PROMETHEE method. European Journal of Operational Research, 14, 228–238. [4] Charles A. Weber, John R. Current, W.C. Benon. Vendor selection criteria and methods, European Journal of Operational Research 50 (1991) 2-18, North Holland. [5] Chen-Tung Chen, Ching-Torng Lin, Sue-Fn Huang, A TOPSIS approach for supplier evaluation and selection in supply chain management. International Journal of Production Economics, Volume 102, Issue 2, August 2006, Pages 289–301. [6] C. Elanchezhian B, Vijaya Ramnath, Dr. R. Kesavan, Vendor Evaluation Using Multi Criteria Decision Making, International Journal of Computer Applications (0975 – 8887) Volume 5– No.9, August 2010. [7] H.K. Sim and Mohamed K. Omar, W.C. chee, N.T. gan, ―A Survey on supplier Selection Criteria in the Manufacturing Industry in Malaysia‖. The 14th Asia Pacific Regional Meeting on International Foundation for Production Research, Melaka, 7-10 December 2010. [8] J.p. Brans, Ph. Vincke, B. Mareschal, "How to select and how to rank projects: The PROMETHEE method", European journal of operational research 24(1986) 228-238. [9] Mohammad Saeed Zaeri, Amir Sadeghi, Amir Na-deri, Abolfazl Kalanaki, Reza Fasihy, Seyed Masoud Hosseini Shorshani, and Arezou Poyan, Application of multi criteria decision making technique to evaluation suppliers in supply chain management, African Journal of Mathematics and Computer Science Research Vol. 4 (3), pp. 100-106, March, 2011. [10] M. behzadian, R.B. kazemzadeh, A. Albadvi, M. Aghdasi, "PROMETHEE: a comprehensive literature review on methodologies applications", European journal of operational research 200 (2010) 198-215. [11] M.Diaby, J.M.Martel, "Preference structure modelling for multi-objective decision making: A goal programming approach". Journal of Multi-Criteria Decision Analysis 6 (1997) 150–154. [12] Pragati Jain and Manisha Jain, Fuzzy TOPSIS Method in Job Sequencing Problems on machines of un-equal efficiencies, Canadian Journal on Computing in Mathematics, Natural Sciences, Engineering and Medicine Vol. 2 No. 6, June 2011. [13] Vijay Manikrao Athawale, Shanker Chakraborty, ―Facility location selection using PROMETHEE method‖. Proceedings of the 2010 international conference on industrial engineering and operations management Dhaka, Bangladesh, January 9-10, 2010 539 www.ijergs.org