Robust optimization for lot-sizing problems under yield uncertainty

Abstract

Production yield can be highly volatile and uncertain, especially in industries where exogenous and environmental factors such as the climate or raw material quality can impact the manufacturing process. Thus, for production planning, it is necessary to take into account the production yield uncertainty to obtain robust and efficient plans. In this paper, we consider lot-sizing problems under yield uncertainty. We propose a multi-period, single-item lot-sizing problem with backorder and yield uncertainty via a robust optimization methodology. First, we formulate a robust model under a budgeted uncertainty set, which is optimized under the worst case perspective to ensure the feasibility of the proposed plan for any realization of the yield described by the uncertainty set. Second, we analyze the structure of the optimal lot-sizing solution, and we derive the optimal robust policy for the special case of the inventory management problem under a box uncertainty. These results help us develop a dynamic program with polynomial complexity for the lot-sizing problem with stationary yield rate. Finally, extensive computational experiments show the robustness and effectiveness of the proposed model through an average and worst case analyses. The results demonstrate that the robust approach immunizes the system against uncertainty. Moreover, a comparison of the robust model with the nominal model, the deterministic model with safety stock, and the stochastic model shows that the robust model balances the costs better by reducing the backorders at the expense of more often producing a larger amount of goods.