Multiple (s, S) Policies and the n-Period Inventory Problem

In a previous paper the concept of a multiple (s, S, policy, generalizing the well-known (s, S) policy, was introduced, and it was shown that for a broad class of situations some multiple (s, S) policy would minimize costs when a single decision was to be made whether or not to order goods to add to inventory. In the present paper it is shown that when n such decisions must be made, some multiple (s, S) policy will minimize total (discounted) costs, though under slightly more restrictive conditions.