Inventory management with random supply and imperfect information: A hidden Markov model

In most of the papers on inventory models operating in a random environment, the state of the environment in each period is assumed to be fully observed with perfect information. However, this assumption is not realistic in most real‐life situations and we provide a remedy in this paper by assuming that the environment is only partially observed with imperfect information. We accomplish this by analyzing two formulations of single‐item models with periodic‐review and random supply in a random environment. In the first one, supply is random due to random capacity of production and random availability of transportation. We show that state‐dependent base‐stock policy is optimal if the capacity and all costs are observed, while demand and availability are unobserved. In the second model, we consider a model with random availability only with fixed‐ordering cost. We show that state‐dependent (s,S) policy is optimal if the availability process is observable.