Optimality of (s, S) policies in inventory models with Markovian demand

This paper is concerned with a generalization of classical inventory models (with fixed ordering costs) that exhibit (s, S) policies. In our model, the distribution of demands in successive periods is dependent on a Markov chain. The model includes the case of cyclic or seasonal demand. The model is further extended to incorporate some other realistic features such as no ordering periods and storage and service level constraints. Both finite and infinite horizon nonstationary problems are considered. We show that (s, S) policies are also optimal for the generalized model as well as its extensions.