A Robust Optimization Approach for an Integrated Production Distribution Planning in a Supply Chain

Document Type : Original Article


1 Professor, Allameh Tabatabaei University.

2 M.Sc., Faculty of Management and Accounting, Islamic Azad University, Qazvin.

3 M.Sc., Islamic Azad University, Qazvin Branch.


The aim of this paper is to develop a mixed-integer non-linear programming (MINLP) for an integrated production–distribution problem in a three-level supply chain, consisting of multiple manufacturers, multiple distributors and multiple consumers at each level. In the particular case of this problem, customer’s demand and transportation costs are uncertain and robust optimization approach is utilized. First, a deterministic MINLP model is designed for this supply chain network. Then, the robust counterpart of the proposed model is presented by using the recent extensions in robust optimization theory. Finally, a numerical example with different scenarios and uncertainty levels is proposed, and their results are discussed.


1. Fahimnia, B., Luong, L. H. S. & Marian, R. (2008a). An integrated model for the optimization of a two-echelon supply network. Journal of Achievements in Materials and Manufacturing Engineering, 31(2), 477–484.
2. Park, B., Choi, H. & Kang, M. (2007). Integration of Production and Distribution Planning Using a Genetic Algorithm in Supply Chain Management”, Analysis and Design of Intelligent Systems using Soft Computing Techniques, Berlin Heidelberg, Springer,416-426.
3. Park, Y. B. (2005). An integrated approach for production and distribution planning in supply chain management. International Journal of Production Research, 43(6), 120-135.
4. Beamon, B. M. (1998). Supply chain design and analysis: models and methods”, International Journal of Production Economics, 55(3), 281–294.
5. Chen, Z. L. & Vairaktarakis, G. L. (2005). Integrated Scheduling of Production and Distribution Operations. Management Science, 51(4), 614-628.
6. Sahinidis, N. V. (2004). Optimization under uncertainty: state-of-the-art and opportunities”, Computers and Chemical Engineering, 28(6), 971–983.
7. Al-e-hashem, S. M. J. M., Malekly, H. & Aryanezhad, M. B. (2011). A multi-objective robust optimization model for multi-product multi-site aggregate production planning in a supply chain under uncertainty. Int. J. Production Economics, 134(1), 28–42.
8. Lim, S. J., Jeong S. J., Kim K. S., & Park, M. W. (2006). A simulation approach for production–distribution planning with consideration given to replenishment policies. The International Journal of Advanced Manufacturing Technology, 27, 593–603.
9. Leung, S. C. H., Tsang, S. O. S., Ng, W. L. & Wu, Y. (2007). A robust optimization model for multi-site production planning problem in an uncertain environment. European Journal of Operational Research, 181(1), 224–238.
10. Nishi, T., Konishi, M., & Ago, M. (2007). A distributed decision-making system for integrated optimization of production scheduling and distribution for aluminum production line”, Computers & Chemical Engineering31, 1205–1221.
11. Elahipanah, M., and Farahani R. Z. (2008). A genetic algorithm to optimize the total cost and service level for just-in-time distribution in a supply chain. International Journal of Production Economics, 111, 229-43
12. Selim, H., Araz, C., and Ozkarahan, I. (2008). Collaborative production–distribution planning in supply chain: a fuzzy goal programming approach. Transportation Research Part E: Logistics and Transportation Review44, 396–419.
13. Zanjani, M. K., Ait-Kadi, D. & Nourelfath, M. (2010). Robust production planning in a manufacturing environment with random yield: A case in sawmill production planning. European Journal of Operational Research, 201(3), 882–891.
14. Aghezzaf, E.-H., Sitompul, C. & Najid, N. M. (2010). Models for robust tactical planning in multi-stage production systems with uncertain demands. Computers & Operations Research, 37(5), 880-889.
15. Chiu, S. W. (2010). Robust planning in optimization for production system subject to random machine breakdown and failure in rework. Computers & Operations Research, 37(5), 899-908.
16. Aghezzaf, E.-H., Sitompul, C. & Broecke, F.V.D. (2011). A robust hierarchical production planning for a capacitated two-stage production system. Computers & Industrial Engineering, 60(2), 361–372.
17. Pishvaee, M. S., Rabbani, M. & Torabi, S. A. (2011). A robust optimization approach to closed-loop supply chain network design under uncertainty. Applied Mathematical Modeling, 35(2), 637–649.
18. Wei, C., Li, Y. & Cai, X. (2011). Robust optimal policies of production and inventory with uncertain returns and demand. Int. J. Production Economics, 134(2), 357–367.
19. Tuzkaya, U. R. & Önüt, S. (2008). A fuzzy analytic network process based approach to transportation-mode selection between Turkey and Germany: A case study”, Information Sciences, 178(1), 3133–3146.
20. Ben-Tal, A., Golany, B., Nemirovski, A. & Vial, J.-P. (2005). Supplier-Retailer Flexible Commitments Contracts: A Robust Optimization Approach. Manuf. Service Operation Management, 7(3), 248–271.
21. Ben-Tal, A., Chung, B. D., Mandala, S. R. & Yao, T. (2011). Robust optimization for emergency logistics planning: Risk mitigation in humanitarian relief supply chains. Transportation Research Part B, 45(8), 1177–1189.
22. Aliev, R. A., Fazlollahi, B., Guirimov, B. G. & Aliev, R. R. (2007). Fuzzy-genetic approach to aggregate production–distribution planning in supply chain management. Information Sciences, 177, 4241–4255.
23. Tawarmalani, M. & Sahinidis, N. V. (2005). A polyhedral branch-and-cut approach to global optimization. Mathematical Programming103(2), 225-249.
24. Hasani, A., & Hosseini, S.M.H., (2014). A Comprehensive Robust Bi-objective Model and a Memetic Solution Algorithm for Designing Reverse Supply. Journal of Indusrial Mangement Perspective, 16, 31-54 (In Persian).
25. Rabieh, M., Azar, A., Modarres, M., & Fetanat, M., (2011). Mathematical Modeling for Multi Objective Robust Sourcing Problem: An Approach in Reduction of Supply Chain Risk (Case study: IKCO Supply Chain). Journal of Indusrial Mangement Perspective, 1, 57-77. (In Persian)
26. Rabieh, M., & Fadaei, A., (2015). Fuzzy Robust Mathematical Model for Project Portfolio Selection and its Solving through Multi Objective Differential Evolutionary Algorithm. Journal of Indusrial Mangement Perspective, 19, 65-90 (In Persian).