Document Type : Original Article


1 Ph.D, Tarbiat Modares University.

2 Professor, Tarbiat Modares University.

3 Associate Professor, Tarbiat Modares University.

4 Assistant Professor, Tarbiat Modares University.


This research aims to design a bi-level optimization model for a supply chain that integrates decentralized quantitative and qualitative decisions at strategic and tactical levels. The manufacturer, as upper-level decision-maker, offers quantity discounts to encourage customers to order more quantity. At the lower level, customers tend to obtain economies of scale by aggregating their orders through cooperative purchasing.  This is one of the first studies that investigate the model of customer expectations with the optimization model of manufacturers at the same time with real data from the supply chain in order to find the optimal solutions to the problem of the medical equipment supply chain in Iran. In addition, there have been no studies to date that consider quantitative discount strategies for the seller and customer behavior in a bi-level planning model simultaneously. The results and analyses reveal that the designed bi-level model compared to the one-level model for the customer and the manufacturer is more suited to the real world and will lead to a long-term relationship between the parties through customer participation. Research suggestions and directions for future research are also provided.


Main Subjects

  1. Alidoost, F., Bahrami, F. & Safari, H. (2020). Multi-Objective Pharmaceutical Supply Chain Modeling in Disaster (Case Study: Earthquake Crisis in Tehran). The Journal of Industrial Management Perspective, 10(3), 99-123. (In Persian)
  2. Amiri, M., & Pahlavani Ghomi, M. (2016). Presenting a Bi-Level Model for Pricing and Order Planning in Three Level Supply Chain. Modern Researches in Decision Making, 1(1), (In Persian).
  3. Amirtaheri, O., Zandieh, M. & Dorri., B. (2016). Design of Bi-Level Programming Model for a Decentralized Production-Distribution Supply Chain with Cooperative Advertising. Industrial Management Studies 41, 1-38. (In Persian)
  4. Avraamidou, S, & Efstratios N. (2017). A Multiparametric Mixed-Integer Bi-Level Optimization Strategy for Supply Chain Planning Under Demand Uncertainty. IFAC-PapersOnLine, 50(1), 10178–83.
  5. Bard, J. F. (1991). Some Properties of the Bilevel Programming Problem. Journal of Optimization Theory and Applications, 68(2), 371–78.
  6. Caramia, M., & Renato, M. (2016). A Decomposition Approach to Solve a Bilevel Capacitated Facility Location Problem with Equity Constraints. Optimization Letters, 10(5), 997–1019.
  7. Chen, M., Lixuan, N., Jiangjiang, H., Yan, Y., Yuan, X., Mi, T., & Chunlin, J. (2020). Prospects for Development of Group Purchasing Organizations (GPOs) in China within the Context of National Centralized Drug Procurement. June 2016, 2016–19.
  8. Chu, Y., Fengqi, Y., John, M. W., & Anshul, A. (2015). Integrated Planning and Scheduling under Production Uncertainties: Bi-Level Model Formulation and Hybrid Solution Method. Computers and Chemical Engineering, 72, 255–72.
  9. Feng, C., Yanfang, M., Gengui, Z., & Ting, N. (2018). Stackelberg Game Optimization for Integrated Production-Distribution-Construction System in Construction Supply Chain. Knowledge-Based Systems, 157, 52–67.
  10. Gang, J., Yan,T, Benjamin, L., Jiuping, X., Wenjing, S., & Liming, Y. (2015). A Multi-Objective Bi-Level Location Planning Problem for Stone Industrial Parks. Computers and Operations Research, 56, 8–21.
  11. Hansen, P., Brigitte, J., & Gilles, S. (1992). New Branch-And-Bound Rules For Linear Bilevel Programming. SIAM Journal on Scientific and Statis-Tical Computing 13(5), 1194–1217.
  12. Hansen, P., Yuri, K., & Nenad, M. (2004). Lower Bounds for the Uncapacitated Facility Location Problem with User Preferences. Les Cahiers Du GERAD.
  13. Hwang, C.L., & K Yoon. (1981). Multiple Attribute Decision Making Methods and Application. Springer-Verlag, New York.
  14. Jayaraman, R., Kamal, T., Kun Soo, P., & Jaywon, L. (2014). Impacts and Role of Group Purchasing Organization in Healthcare Supply Chain. IIE Annual Conference and Expo 2014, no. February: 3842–51.
  15. Kolyaei, M., Azar, A. & Rajabzadeh, A. (2019). Design of Two Phrase Robust Mathematical Model for Green Supply Chain. Organizational Resources Management Researchs, 8(4), (In Persian).
  16. Kolyaei, M., Azar, A. & Rajabzadeh ghatari, A. (2018). Design of An Integrated Robust Optimization Model for Closed-Loop Supply Chain and Supplier and Remanufacturing Subcontractor Selection. Journal of Decision Engineering, 2(7), (In Persian).
  17. Kumar, R. L., Ganapathy, R. G., & Manoj, K. T. (2020). Quantitative Approaches for the Integration of Production and Distribution Planning in the Supply Chain: A Systematic Literature Review. International Journal of Production Research, no. May, 1–27.
  18. Ma, Y, Fang ,Y, Kai K, & Xuguang .W. (2016). A Novel Integrated Production-Distribution Planning Model with Conflict and Coordination in a Supply Chain Network. Knowledge-Based Systems, 105, 119–33.
  19. Maldonado-Pinto, S., Martha-Selene C-R., & José-Fernando C-V. (2016). Analyzing the Performance of a Hybrid Heuristic for Solving a Bilevel Location Problem under Different Approaches to Tackle the Lower Level. Mathematical Problems in Engineering, 2016, 1–10.
  20. Marvel, Howard P., & Huanxing Yang. (2008). Group Purchasing, Nonlinear Tariffs, and Oligopoly. International Journal of Industrial Organization, 26(5), 1090–1105.
  21. Naser Sadrabady, A.R., Mirghafori, S. H., & Salar, S. S. (2014). Group Decision Making Using a Fuzzy Approach for Evaluating the Supply Chain Flexibility of Yazdbaf Factory. The Journal of Industrial Management Perspective, 3(4), 165-187. (In Persian)
  22. Piorunowska-Kokoszko, J. (2015). Group Purchasing Organization (Gpo) As a Means of Business Costs Savings. Journal of Positive Management 6(1), 56-70.
  23. Rego, N., João C., & Jorge P de S. (2014). A Hybrid Approach for Integrated Healthcare Cooperative Purchasing and Supply Chain Configuration. Health Care Management Science, 17(4), 303–20.
  24. Saranwong, S., & Chulin, L. (2016). Product Distribution via a Bi-Level Programming Approach: Algorithms and a Case Study in Municipal Waste System. Expert Systems with Applications, 44, 78–91.
  25. Saranwong, S., & Chulin L. (2017). Bi-Level Programming Model for Solving Distribution Center Problem: A Case Study in Northern Thailand’s Sugarcane Management. Computers and Industrial Engineering, 103, 26–39.
  26. Scaparra, M. P., & Church R. L. (2008). A Bilevel Mixed-Integer Program for Critical Infrastructure Protection Planning. Computers and Operations Research, 35(6), 1905–23.
  27. Schneller, Eugene S., & Eugene S Schneller. (2009). The Value of Group Purchasing - 2009: Meeting the Needs for Strategic Savings. Health Care.
  28. Sebatjane, M., & Olufemi A. (2019). Economic Order Quantity Model for Growing Items with Incremental Quantity Discounts. Journal of Industrial Engineering International, 15(4), 545–56.
  29. Shateri, H. R., Amoozad Mahdiraji, H. & Mokhtarzade, N. (2020). A Comparison of the Buyback, Rebate and Quantity Flexible Contracts in Multi Echelons Supply Chains with Probabilistic Demand and Game Theory Approach. The Journal of Industrial Management Perspective, 9(2), 131-151. (In Persian)
  30. Sinha, A., Pekka M., & Kalyanmoy D. (2018). A Review on Bilevel Optimization: From Classical to Evolutionary Approaches and Applications. IEEE Transactions on Evolutionary Computation, 22(2), 276–95.
  31. Tella, E, & Veli Matti ,V. (2005). Motives behind Purchasing Consortia. International Journal of Production Economics, 93–94 (SPEC.ISS.): 161–68.
  32. Tsai, J. F. (2006). An Optimization Approach for Supply Chain Management Models with Quantity Discount Policy. European Journal of Operational Research, 177(2), 982–94.
  33. Vicente, L. N., & Paul H. Calamai,. (1994). Bilevel and Multilevel Programming: A Bibliography Review. Journal of Global Optimization 5(3), 291–306..
  34. Weinstein, B. (2006). The Role of Group Purchasing Organizations (GPOs) in the U.S. Medical Indutry Supply Chain. Estudios de Economía Aplicada, 24(3), 789–802.
  35. Wilhelm, W. E. (1999). Strategic, Tactical and Operational Decisions in Multi-National Logistics Networks : A Review and Discussion of Modeling Issues Accepted for Publication on September 8, 1999 by the International Journal of Production Research, 38(7), 1501-1523.
  36. Wu, Sh., & Zhongzhen ,Y. (2018). Optimizing Location of Manufacturing Industries in the Context of Economic Globalization: A Bi-Level Model Based Approach. Physica A: Statistical Mechanics and Its Applications 501, 327–37.
  37. Yue, D., & Fengqi Y. (2017). Stackelberg-Game-Based Modeling and Optimization for Supply Chain Design and Operations: A Mixed Integer Bilevel Programming Framework. Computers and Chemical Engineering 102, 81–95.
  38. Zhou, M., Bin, D., Songxuan, M., & Xumei, Z. (2017). Supply Chain Coordination with Information Sharing: The Informational Advantage of GPOs. European Journal of Operational Research, 256(3), 785–802.
  39. Zhou, X., Rui, L., Yan, T., Benjamin, L., & Witold, P. (2018). Data Envelopment Analysis for Bi-Level Systems with Multiple Followers. Omega (United Kingdom), 77, 180–88.