Optimality of ( s , S ) Policies in the Infinite Horizon Dynamic Inventory Problem
Donald L. Iglehart · Management Science · 1963
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.