Inventory models with unreliable suppliers in a random environment

We consider infinite-horizon periodic-review inventory models with unreliab le suppliers where the demand, supply and cost parameters change with respe ct to a randomly changing environment. Although our analysis will be in the context of an inventory model, it is also appropriate for production syste ms 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 fluctuatio ns is represented using a two-dimensional stochastic process. We show that an environment-dependent order-up-to level (i.e., base-stock) policy is opt imal 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 compu tational issues and some extensions.