Robust optimization for lot-sizing problems under yield uncertainty

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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. To address this issue, we propose a multiperiod single-item lot-sizing problem with backorder under yield uncertainty via a robust optimization methodology. First, we formulate the robust model based on the budgeted uncertainty set. The resulting model optimizes under the worst-case perspective to ensure the feasibility of the proposed plan for any realization of the uncertain yield. Second, we derive the properties of the optimal robust policies for the special cases under a box uncertainty, which helps us obtain a dynamic program with polynomial complexity. Finally, extensive computational experiments show the robustness and effectiveness of the proposed model through an average and worst-case analysis. The results demonstrate that the robust approach immunizes the system against uncertainty. In addition, a comparison with the stochastic models shows that the robust model balances the costs to reduce the backorders at the expense of more often producing a larger amount of goods.

, 23 pages

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