A Note on the Optimality of (S,s) Policies in Inventory Theory

Abstract

In this paper a proof of Herbert Scarf's on the optimality of ( S , s ) policies in inventory theory is extended to cases where differentiability of cost functions may not be available. In addition to an ordering cost composed of a unit cost plus a reorder cost all that is needed in the proof is that the expected holding and shortage cost function be convex.