Inventory models with unreliable suppliersin a random environment

We consider infinite‐horizon periodic‐review inventory models with unreliable suppliers where the demand, supply and cost parameters change with respect to a randomly changing environment. Although our analysis will be in the context of an inventory model, it is also appropriate for production systems with unreliable machines where planning is done on a periodic basis. It is assumed that the environmental process follows a Markov chain. The stock‐flow equations of the inventory system subject to environmental fluctuations is represented using a two‐dimensional stochastic process. We show that an environment‐dependentorder‐up‐to level (i.e., base‐stock) policy is optimal when the order cost is linearin order quantity. When there is also a fixed cost of ordering, we show that a two‐parameter environment‐dependent (s, S) policy is optimal under reasonable conditions. We also discuss computational issues and some extensions.