Simultaneous planning of purchase orders, production, and inventory management under demand uncertainty

This paper focuses on the issues of the purchase of bill of materials, production planning, and inventory management in materials and products warehouses under demand uncertainty, simultaneously. The purpose of this study is to determine the optimal volume of purchasing the raw materials from different vendors, transportation methods, and production planning over the time horizon so that with proper inventory management in the warehouses of materials and manufactured products, the total cost is minimized. This issue is defined as a multi-region, multi-supplier, multi-component, multi-product, and multi-period problem. There is a time interval between ordering and delivering the bill of materials, which depends on the region where the supplier is located. Customer demands are not predetermined, and robust optimization is employed to handle this uncertainty. Three numerical examples, based on increasing or decreasing the nominal customer demands, are presented to evaluate the robustness of the solutions and to examine the effect of conservatism level on the performance of the proposed model. Finally, the price and importance of proposed robust planning are evaluated based on random data.