#### 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.