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This paper considers the dynamic inventory model with a discrete demand. There is a constant lead time, backlogging of excess demand, a fixed set-up cost, and holding and shortage costs whose negatives are unimodal. The criterion is the long-run average cost. A value iteration method with discount factor approaching to 1 is studied. This value iteration method supplies policies of the (s,S) type and convergent upper and lower bounds on the minimal average cost. Further, the average cost of the (s n ,S n ) policy found at then-th iteration lies between the corresponding upper and lower bound. Also, for alln sufficiently large the (s n ,S n ) policy is average cost optimal. Computational considerations are given for the special case of linear holding and shortage costs.

An iterative method for approximating average cost optimal (s,S) inventory policies