Adaptive robust optimization for lot-sizing under yield uncertainty

Abstract

In manufacturing environments, uncertain production yield directly impacts the quality and feasibility of the production planning decisions. This paper investigates the use of adaptive robust optimization to hedge against uncertain yield when determining a production plan, and to react properly when updated information unfolds. We first derive a myopic adaptive robust policy for the inventory management problem, a special case of the lot-sizing problem where the setup and the production costs are omitted. We show that the policy is optimal under mild assumptions. Second, we address a multi-period single-item lot-sizing problem with a backorder and uncertain yield via adaptive robust optimization. We formulate an adaptive robust model based on the budgeted uncertainty set, where we exploit a linear approximation to transform the quadratic constraints into a mixed-integer linear program. We also propose a column and constraint generation algorithm to solve the adaptive model exactly. Finally, we demonstrate the performances of the proposed approaches and the value of the adaptive robust solutions through extensive numerical experiments.