Optimal policies for inventory systems with finite capacity and partially observed Markov-modulated demand and supply processes

We analyze a single-item periodic-review inventory system with random yield and finite capacity operating in a random environment. The primary objective is to extend the model of Gallego and Hu (2004) to the more general case when the environment is only partially observable. Although our analysis is specific to inventory systems, it can also be applied to production systems by replacing the fixed capacity supplier with a fixed capacity producer. Using sufficient statistics, we consider single-period, multiple-period and infinite-period problems to show that a state-dependent modified inflated base-stock policy is optimal. Moreover, we show that the multiple-period cost converges to the infinite-period cost as the length of the planning horizon increases.