**Eugene A. Feinberg
Department of Applied Mathematics and Statistics
State University of New York at Stony Brook
Stony Brook, NY 11794-3600
631-632-7189**

** Mark E. Lewis
School of Operations Research & Industrial Engineering
Cornell University
226 Rhodes Hall, Ithaca, NY 14853
607-255-0757**

For general state and
action space Markov decision processes, we present sufficient
conditions for

the existence of solutions of the average cost optimality inequalities.
These conditions also imply the

convergence of both the optimal discounted cost value function and
policies to the corresponding objects

for the average costs per unit time case. Inventory models are natural
applications of our results. We

describe structural properties of average cost optimal policies for the
cash balance problem; an inventory

control problem where the demand may be negative and the decision-maker
can produce or scrap

inventory. We also show the convergence of optimal thresholds in the
finite horizon case to those under

the expected discounted cost criterion and those under the expected
discounted costs to those under the

average costs per unit time criterion.