Inventory models with unreliable suppliers in 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-dependent order-up-to level (i.e., base-stock) policy is optimal when the order cost is linear in 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.