On some optimality conditions and their equivalence in time-dependent inventory models

Abstract

The paper considers a deterministic, time-and-review-continuous, finite horizon inventory model with general time-dependent demand, holding cost, shortage cost and replenishment rate functions. It gives conditions for the optimal ordering schedule, for a fixed number of replenishments, which reduce the effort for its finding to a simple one-dimensional search. The paper also proves equivalence relationships between the derived optimality conditions and the corresponding ones for special cases of the general model where some of its component functions tend to infinity. It concludes with a discussion concerning the uniqueness of the optimal number of replenishments, and the convergence of the optimal ordering schedule for an infinite time horizon.