Average Cost Optimality in Inventory Models with Markovian Demands and Lost Sales

Abstract:  This paper is concerned with long-run average cost minimization of a stochastic inventory problem with Markovian demand, fixed ordering cost, convex surplus cost, and lost sales.  The states of the Markov chain represent different possible states of the environment.  Using a vanishing discount approach, a dynamic programming equation and the corresponding verification theorem are established.  Finally, the existence of an optimal state-dependent (s,S) policy is proved.