Robust inventory control under demand and lead time uncertainty

In this paper a general methodology is proposed based on robust optimization for an inventory control problem subject to uncertain demands and uncertain lead times. Several lead time uncertainty sets are proposed based on the budget uncertainty set, and a set based on the central limit theorem. Robust optimization models are developed for a periodic review, finite horizon inventory control problem subject to uncertain demands and uncertain lead times. We develop an approach based on Benders' decomposition to compute optimal robust (i.e., best worst-case) policy parameters. The proposed approach does not assume distributional knowledge, makes no assumption regarding order crossovers, and is tractable in a practical sense. Comparing the new approach to an epigraph reformulation method, we demonstrate that the epigraph reformulation approach is overly conservative even when costs are stationary. The approach is benchmarked against the sample average approximation (SAA) method. Computational results indicate that the approach provides more stable and robust solutions compared to SAA in terms of standard deviation and worst-case solution, especially when the realized distribution is different than the sampled distribution.