Multi-Objective Mathematical Model for Supplier Selection and Order Allocation under Multi-Item Condition

Document Type : Original Article


1 Assistant Professor, Islamic Azad University, Arak.

2 MA., Islamic Azad University, Arak.


Suppliers play an important role in reducing costs and increasing product quality. Accordingly, assessment and selection of suppliers based on desired criteria, has become one of the fundamental headquarters of decision-making in supply chain management. Since now the suppliers have a significant impact on the success or failure of a company, purchases that previously was considered as a mere tactical tool, now is known as a strategic task. So, considering the importance of the subject, the aim of this study is providing a fuzzy approach in order to select multi-product and multi-purpose supplier and determine the economic order quantity in supply chain. Objectives considered in the above model include minimizing the total cost (including the purchase cost, cost of returned goods, control and order costs), maximizing quality (including the product’s quality and services provided by suppliers, and maximizing the amount of products received from suppliers on-time. To resolve the above issue, the Lp-Metric and Zimmermann fuzzy approach -due to dealing with uncertainty and getting more flexibility of decision-making- are applied. The results represent the best suppliers to purchase the products from and also optimized allocation to each of them.


1. Amid, A., Ghodsypour, S.H., & O’Brien, C. (2009). A weighted additive fuzzy multi-objective model for the supplier selection problem under price breaks in a supply Chain. International Journal of Production Economics, 121, 323-332.
2. Amid, A., Ghodsypour, S.H., & O’Brien, C. (2012). A weighted max–min model for fuzzy multi-objective supplier selection in a supply chain. International Journal of Production Economics, 131(1), 139-145.
3. Amid, A., Ghodsypour, S.H., & O’Brien, Ch. (2006). Fuzzy multi-objective linear model for supplier selection in a supply chain. International Journal of Production Economics, 104, 394–407.
4. Bagheri, F., & Tarokh, M.J. (2010). A fuzzy approach for multi-objective supplier selection. International Journal of Industrial Engineering & Production Research, 21(1), 1-9.
5. Chang, C. T. Ho, H. P. (2009). Global supplier selection using fuzzyanalytic hierarchy process and fuzzy goal programming.Quality and Quantity, Online Version.
6. Chopra, S., & Meindel, P. (2007). Supply chain Management – Strategy, Planning & Operation. 3rd, chapter 1, Pearson Prentice Hall.
7. Dalalah, D., Hayajneh, M., Batieha, F. (2011). A fuzzy multi-criteria decision making model for supplier selection. Expert Systems with Applications. 38, 8384-8391.
8. Demirtas, E.A., & Üstün, Ö. (2008). An integrated multi objective decision making process for supplier selection and order allocation. Omega, 36, 76 – 90.
9. Dickson, G. W. (1966). An analysis of vendor selection systems and decisions. Journal of Purchasing, 2(1), 5–17.
10. Elahi, B., Seyed-Hosseini, S.M., & Makui, A. (2011).A Fuzzy Compromise Programming Solution for Supplier Selection in Quantity Discounts Situation. International Journal of Industrial Engineering & Production Research, 22(2), 107-114.
11. Ghodsypour, S.H., O’Brien, C. (1997). An integrated method using the analytical hierarchy process with goal programming for multiple sourcing with discounted prices. In: Proceedings of 14th International Conference on Production Research (ICPR), Osaka, Japan.
12. Ghodsypour, S.H., & O’Brien, C. (1998). A decision support system for supplier selection using an integrated analytical hierarchy process and linear programming. International Journal of Production Economics, 56–57, 199–212.
13. Ghodsypour, S.H., & O’Brien, C. (2001). The total cost of logistic in supplier selection, under conditions of multiple sourcing, multiple criteria and capacity constraints. International Journal of Production Economics, 73, 15-27.
14. Hwang, C. L., Masud, A. S. Md. (1995). Multiple Objective Decision Making Methods and Applications. Springer, Berlin.
15. Ho, W., Xu, X., & Dey, P.K. (2010). Multi-criteria decision making approaches for supplier evaluation and selection: A literature review. European Journal of Operational Research, 22, 16-24.
16. Leenders / Fearon. (1997). Purchasing and supply management. IRWIN.Liao, Z., Rittscher, J. (2007). A multi-objective supplier selection model under stochastic demand conditions. International Journal of Production Economics, 105(1), 150–159.
17. Liao.J, & Rittscher J. (2007). Integration of supplier selection, procurement lot sizing and carrier selection under dynamic demand conditions. International Journal of Production Economics 107(2), 502-510.
18. Mollatayefeh, F., Talebi, D. (2012). Supliers Selection and Evaluation during Supply Chain by using Integrated Method of FAHP and Multi-Objectives Linear Programming. Journal of Industrial Management Perspective, 1(2), 27-42.
19. Ozkok, B. A., &Tiryaki, F. (2011). A compensatory fuzzy approach to multi-objective linear supplier selection problem with multiple-item. Expert Systems with Applications, 38, 11363–11368.
20. Rezaei, J. & Ortt.R. (2013) Supplier Segmentation Usage Fuzzy Logic. International Marketing Management, 42(4), 507 -517.
21. Sarfraz, A. (2011). An integrated multi objective decision making process for supplier selection with volume discounts. Proceedings on Industrial Engineering and Operations Management Kuala Lumpur, Malaysia, January, 22-24.
22. Seifbarghi, M., Pourebrahim, A., & Alidoost. M. (2011). A Comprehensive Fuzzy Multiobjective Supplier Selection Model under Price Brakes and Using Interval Comparison Matrices. Journal of Industrial and Systems Engineering, 4(4), 224-244.
23. Shahbandarzade, H., Paykam, A. (2015). Employment of a Weighted Fuzzy Multi-Objective Programming Model Method to Determine the Amount of Optimum Purchasing from Suppliers. Journal of Industrial Management Perspective, 5(18), 129-152.
24. Sharafi masole , A.,(2007) Select and Evalute of supplier with MCDM method, Car enginnering and depended industries (6), 1
25. Stadler, H., & Kilger, Ch. (2005). Supply chain management and advanced planning. Springer publications, Berlin.
26. Weber, C.A., Current, J.R., & Desai, A. (2000). An optimization approach to determining the number of vendors to employ. Supply Chain Management: an International Journal, 5(2), 90-98.
27. Zhang, Zhi., Lei, J., Cao, N., To, K., & Ng, K. (2004). Evaluation of supplier selection criteria and methods. Available at: [ %20]
28. Zimmermann, H.-J. (1978). Fuzzy programming and linear programming withseveral objective functions. Fuzzy Sets and Systems, 145–55.
29. Zouggari, A., & Benyoucef, L. (2012). Simulation based fuzzy TOPSIS approach for group multi-criteria supplier selection problem. Engineering Applications of Artificial Intelligence, 25, 507-519.