A robust optimization approach to model supply and demand uncertainties in inventory systems

Abstract

In this article, we simultaneously consider supply and demand uncertainties in a robust optimization (RO) framework. First, we apply the RO approach to a multi-period, single-station inventory problem where supply uncertainty is modeled by partial supply. Our main finding is that solving the robust counterpart is equivalent to solving a nominal problem with a modified deterministic demand sequence. In particular, in the stationary case the optimal robust policy follows the quasi-(s, S) form and the corresponding s and S levels are theoretically computable. Subsequently, the RO framework is extended to a multi-echelon case. We show that for a tree structure network, decomposition applies so that the optimal single-station robust policy remains valid for each echelon in the tree. We conduct extensive numerical studies to demonstrate the effectiveness of the proposed robust policies. Our results suggest that significant cost benefits can be realized by incorporating both supply and demand uncertainties.