A Weighted Robust Two-Stage Stochastic Optimization Model for Supplier Selection and Order Allocation under Uncertainty

Document Type : Original Article


1 M.A., Department of Industrial Engineering, Electronic Branch, Islamic Azad University, Tehran, Iran.

2 Assistant Professor, Department of Industrial Engineering, Electronic Branch, Islamic Azad University, Tehran, Iran.

3 Assistant Professor, Department of Industrial Engineering, South Tehran Branch, Islamic Azad University, Tehran, Iran.



This paper presents an integrated model as a combination of fuzzy analytical hierarchy process (FAHP), scenario-based two-stage stochastic programming and robust optimization approaches for the problem of supplier selection and order allocation under supply risk conditions. Uncertainties in the supply of materials are considered under three scenarios: increased sanctions, stability of sanctions, and sanctions removal. In the first step, the main qualitative factors for the selection of suppliers are identified and a specific weight is assigned to each supplier through FAHP. In the second step, these weights are introduced as inputs to a two-stage stochastic programming model and affect the second-stage variables. In the third step, we use the Mulvey formulation and then linearize the resulted robust two-stage stochastic model. The model is a integer linear programming model solved by CPLEX for a case study and the results are discussed. Finally, a sensitivity analysis is performed on the parameters of the robust model and the balance between the total cost and the unfulfilled demand is shown.


1. Chan, F.T.S., & Kumar, N. (2007). Global supplier development considering risk factors using fuzzy extended AHP based approach. Omega, 35, 417-431.
2. Gunasekaran, A., & Ngai, E.W.T. (2004). Virtual supply chain management. Production Planning and Control, 15(6), 584–595.
3. Gunasekaran, A., & Ngai, E.W.T. (2004). Information systems in supply chain integration and management. European Journal of Operational Research, 159, 269–295.
4. Weber, C.A., Current, JR, & Benton, W.C. (1991) Vendor selection criteria and methods. European Journal of Operational Research, 50(1), 2-18.
5. Bertsimas, D., & Sim, M. (2004). The Price of Robustness. Operations research. 52(1), 35–53.
6. Alem, D.J., &Morabito, R. (2012). Production planning in furniture settings via robust optimization. Computers & Operations Research, 39(2), 139-150.
7. Dahel, N-E. (2003). Vendor Selection and Order Quantity Allocation in Volume Discount Environments. Supply Chain Management: An International Journal, 8(4), 335-342.
8. Shahbandarzadeh, H., & Paykam, A. (2015). Employment of a Weighted Fuzzy Multi-Objective Programming Model to Determine the Amount of Optimum Purchasing from Suppliers. Journal of Industrial Management Perspective, 5(2), 129-152 (In Persian).
9. Cebi, F., Otay, I. (2015). A two-stage fuzzy approach for supplier evaluation and order allocation problem with quantity discounts and lead timeInformation Sciences 339143-157.
10. Trapp, A. C., & Sarkis, J. (2016). Identifying Robust portfolios of suppliers: a sustainability selection and development perspective. Journal of Cleaner Production, 112, 2088-2100.
11. Hasani, P., Mohammaditabar, D. (2018). A Multi Period Lot-Sizing Model in Three-Echelon Supply Chain by Considering Payment Methods and Joint Replenishment of Inventory Items. Journal of Industrial Management Perspective, 8(3), 141-165 (In Persian).
12. Eydi, A., & Bakhtiari, M. (2016). Evaluating and Selecting Two-Layers of Suppliers in Green Supply Chain using Hierarchical Fuzzy Topsis based on Alpha Levels. Journal of Industrial Management Perspective, 6(2), 91-121. (In Persian)
13. Abdel-Baset, M., Chang, V., Gamal, A., & Smarandache, F. (2019). An integrated neutrosophic ANP and VIKOR method for achieving sustainable supplier selection: A case study in importing field. Computers in Industry, 106, 94-110.
14. Dotoli, M., Epicoco, N., Falagario, M., & Sciancalepore, F. (2016). A stochastic cross‚Äźefficiency data envelopment analysis approach for supplier selection under uncertainty. International Transactions in Operational Research, 23(4), 725-748.
15. Fallah Lajimi, H., Mohammadi Kani, S., & Rasooli Khatir, Z. (2019). Applying of Piecewise Linear Value Functions in LARG Suppliers Ranking: Multi-Criteria Decision Making Mixed Approach. Journal of Industrial Management Perspective, 9(1), 115-140 (In Persian).
16. Xia, W., & Wu, Z. (2007). Supplier Selection with multiple criteria in volume discount environments. Omega-The International journal of Management Science, 35(5), 494-504.
17. Burke, G.J., Carrillo, J., Vakharia, A.J., (2008). Heuristics for sourcing from multiple suppliers with alternative quantity discounts. European Journal of Operational Research, 186 (1), 317-329.
18. 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(2), 323-33.
19. Wang, T., Yang, Y., (2009). A Fuzzy model for supplier selection in quantity discount environments. Expert Systems with applications, 36(10): 12179-12187.
20. Mafakheri, F., Breton, M., & Ghoniem, A. (2011). Supplier selection-order allocation: A two-stage multiple criteria dynamic programming approach. International Journal of Production Economics132(1), 52-57.
21. Ayhan, M.B., Kilic, H.S. (2015). A two stage approach for supplier selection problem in multi-item/multi-supplier environment with quantity discounts. Computers and Industrial Engineering 85(3), 1-12.
22. Chai, J., & Ngai, E. W. (2019). Decision-making techniques in supplier selection: Recent accomplishments and what lies ahead. Expert Systems with Applications, 112903.
23. Li, L., & Zabinsky, Z.B. (2011). Incorporating uncertainty into a supplier selection problem. International Journal of Production Economics, 134(2), 344-356.
24. Hammami, R., Temponi, C., & Frein, Y. (2014). A scenario-based stochastic model for supplier selection in global context with multiple buyers, currency fluctuation uncertainties, and price discounts. European Journal of Operational Research, 223, 159-170.
25. Hosseini, S., Morshedlou, N., Ivanov, D., Sarder, M. D., Barker, K., & Al Khaled, A. (2019). Resilient supplier selection and optimal order allocation under disruption risks. International Journal of Production Economics, 213, 124-137.
26. Vahidi, F., Torabi, S. A., & Ramezankhani, M. J. (2018). Sustainable supplier selection and order allocation under operational and disruption risks. Journal of Cleaner Production, 174, 1351-1365.
27. Babbar, C., & Amin, S. H. (2018). A multi-objective mathematical model integrating environmental concerns for supplier selection and order allocation based on fuzzy QFD in beverages industry. Expert Systems with Applications, 92, 27-38.
28. Rabieh, M., Azar, A., Modarres Yazdi, M., Fetanat Fard Haghighi, M. (2011). Designing a Multi-Objective Resource-Based Mathematical Modeling: An Approach to Supply Chain Risk Reduction (Case Study: Iran Khodro Supply Chain). Journal of Industrial Management Perspective, 1(1), 57-77 (in Persian).
29. Babaei, M., & Omrani, H. (2017). Robust optimization approach for supplier selection under lean procurement. International journal of industrial engineering and production management, 28(3), 459-469 (In Persian).
30. Yahyazade, Y., Olfat, L., & Amiri, M. (2016). Robust optimization approach for Supplier selection and order allocation in an uncertain environment. Industrial Management Studies, 14(40), 25-52. (In Persian)
31. Fu, Y., Lai, K. K., & Liang, L. (2016). A robust optimisation approach to the problem of supplier selection and allocation in outsourcing. International Journal of Systems Science, 47(4), 913-918.
32. Farrokh, M., Azar, A., & Jandaghi, G. (2016). Developing a Robust Fuzzy Programming Approach for Closed Loop Supply Chain Design. Journal of Industrial Management Perspective, 6(2), 9-43 (In Persian).
33. Kim, J., Do Chung, B., Kang, Y., & Jeong, B. (2018). Robust optimization model for closed-loop supply chain planning under reverse logistics flow and demand uncertainty. Journal of Cleaner Production, 196, 1314-1328.
34. Sanayei, A., Mousavi, S.F., & Yazdankhah, A. (2010). Group decision making process for supplier selection with VIKOR under fuzzy environment. Expert System with Applications, 37, 24–30.
35. Kara, S. S. (2011). Supplier selection with an integrated methodology in unknown environment. Expert Systems with Applications, 38(3), 2133-2139.
36. Memari, A., Dargi, A., Jokar, M. R. A., Ahmad, R., & Rahim, A. R. A. (2019). Sustainable supplier selection: A multi-criteria intuitionistic fuzzy TOPSIS method. Journal of Manufacturing Systems, 50, 9-24.
37. Mulvey, J., Vanderbei, R., & Zenios, S. (1995). Robust optimization of large-scale systems. Operations Research, 43, 264– 81.
38. Chang, D. Y. (1996). Applications of the extent analysis method on fuzzy AHP. European journal of operational research, 95(3), 649-655.