On optimal policies for production-inventory systems with compound Poisson demand and setup costs

In this paper, we consider a single-item, one-machine production-inventory system with compound Poisson demand. The production facility may be on or off. While on, the production rate is constant, and, while off, the production rate is zero. System costs consist of switching costs and inventory and backlogging costs. We provide conditions when (s, S)-policies are optimal under the long-run average expected cost criterion. These conditions are met in particular, but not necessarily, when the inventory costs are convex. The developed method in the proof is easy to apply to more general cases. Moreover, the method allows us to compute optimal policies very efficiently.