Robust optimization approach for an aggregate production-distribution planning in a three-level supply chain

An aggregate production-distribution (P-D) planning generates an aggregate plan for regular time, overtime, outsourcing, hiring, and firing that takes into account distributing, inventory holding, backordering, and machine capacity for a definite planning horizon. A large number of P-D problems require decisions to be made in the presence of uncertainty. Previous research on this topic mainly utilized either stochastic programming or fuzzy programming to cope with the uncertainty. This may lead into huge challenges for supply chain managers that use non-robust P-D planning in uncertain environments. Moreover, there has been little discussion about robust optimization approach in aggregate P-D problems so far.Therefore, the aim of this paper is to develop robust optimization in P-D planning in order to minimize the total cost of a three-level supply chain including multiple production facilities, multiple distribution centers, and multiple customer zones with uncertain parameters in terms of a limited set of discrete future economic scenarios. These scenarios are associated with probabilities in an industrial case study. In addition, a trade-off between solution robustness and model robustness using specified weight is studied, and a sensitivity analysis for this trade-off is implemented. Finally, the applicability of the proposed methodology is demonstrated.