Near-optimal ( r, Q) policies for a two-stage serial inventory system with Poisson demand

Abstract

We consider a two-stage serial inventory system whose cost structure exhibits economies of scale in both stages. In the system, stage 1 faces Poisson demand and replenishes its inventory from stage 2, and the latter stage in turn orders from an outside supplier with unlimited stock. Each shipment, either to stage 2 or to stage 1, incurs a fixed setup cost. We derive important properties for a given echelon-stock ( r, Q) policy for an approximation of the problem where all states are continuous. Based on these properties, we design a simple heuristic algorithm that can be used to find a near-optimal ( r, Q) policy for the original problem. Numerical examples are given to demonstrate the effectiveness of the algorithm.