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

► We study inventory models with random demand and supply in a partially observed random environment. ► The first model assumes no fixed-ordering cost and the supplier has random capacity/availability. ► A state-dependent base-stock policy is optimal in the first model if the capacity is observable. ► The second model has fixed-ordering cost and the supplier has infinite capacity. ► A state-dependent (s,S) policy is optimal for inventory problems in the second model.