Average-Cost Optimality of a Base-Stock Policy for a Multi-Product Inventory Model with Limited Storage

We consider a stochastic multi-product inventory model with a ware-housing constraint with the objective of minimizing the expected long-run average cost. Using the vanishing discount approach, a dynamic programming equation and the corresponding verification result are established. The structure of optimal policies is analyzed when ordering cost of the commodities is linear and the inventory/backlog cost is convex. The optimal policy is shown to be a base-stock policy, in contrast to a modified base-stock policy optimal in the discounted cost version of the problem