Optimal Policy for Inventory Management with Periodic and Controlled Resets

TL;DR

This paper characterizes the structure of optimal inventory policies with periodic resets, showing they follow a four-threshold pattern under mild conditions, and provides computational insights for practical scenarios.

Contribution

It introduces sufficient conditions ensuring a four-threshold optimal policy structure for inventory resets, generalizing the classic $(s, S)$ policy, and analyzes non-convex value functions.

Findings

Optimal policies follow a four-threshold structure.

Conditions for policy structure are mild and broadly applicable.

Computational experiments illustrate policy effectiveness in various scenarios.

Abstract

Inventory management problems with periodic and controllable resets occur in the context of managing water storage in the developing world and retailing limited-time availability products. In this paper, we consider a set of sequential decision problems in which the decision-maker must not only balance holding and shortage costs but discard all inventory before a fixed number of decision epochs, with the option for an early inventory reset. Finding optimal policies using dynamic programming for these problems is particularly challenging since the resulting value functions are non-convex. Moreover, this structure cannot be easily analyzed using existing extended definitions, such as $K$-convexity. Our key contribution is to present sufficient conditions that ensure the optimal policy has an easily interpretable structure that generalizes the well-known $(s, S)$ policy from the operations literature. Furthermore, we demonstrate that the optimal policy has a four-threshold structure under these rather mild conditions. We then conclude with computational experiments, thereby illustrating the policy structures that can be extracted in several inventory management scenarios.