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The optimal ordering policy for a n-period dynamic inventory problem in which the ordering cost is linear plus a fixed reorder cost and the other one-period costs are convex is characterized by a pair of critical numbers, (s n, S n) ; see Scarf, 4. In this paper we give bounds for the sequences s n and S n and discuss their limiting behavior. The limiting (s, S) policy characterizes the optimal ordering policy for the infinite horizon problem. Similar results are obtained if there is a time-lag in delivery.
Donald L. Iglehart (Tue,) studied this question.
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