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

Abstract

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.