On the Optimality of (S,S) Inventory Policies: New Conditions and a New Proof

摘要

Scarf has shown that the (s,S) policy is optimal for a class of discrete review dynamic nonstationary inventory models. In this paper a new proof of this result is found under new conditions which do not imply and are not implied by Scarf's hypotheses. We replace Scarf's hypothesis that the one period expected costs are convex by the weaker assumption that the negative of these expected costs are unimodal. In addition, the bounds on the optimal parameter values given by Veinott and Wagner are established for the present case. The bounds in a period are easily computed, and depend only upon the expected costs for that period. Moreover, simple conditions are given which ensure that the optimal parameter values in a given period equal their lower bounds. This result is exploited to derive a planning horizon theorem. (Author)