Optimality of (s, S) Policies in the Infinite Horizon Dynamic Inventory Problem

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.