Optimal Policy for Inventory Management with Periodic and Controlled Resets

Problem definition: Inventory management problems with periodic and controllable resets occur in the context of managing water storage in the developing world and dynamically optimizing endcap promotion duration in retail outlets. 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. Methodology/results: Finding optimal policies for these problems through dynamic programming presents unique challenges because of the nonconvex nature of the resulting value functions. Moreover, this structure cannot be readily analyzed even with extended convexity definitions, such as K-convexity. Managerial implications: Our key contribution is to present sufficient conditions that ensure the optimal policy has an easily interpretable structure, which generalizes the well-known $(s,S)$ policy from the operations management literature. Furthermore, we demonstrate that, under these rather mild conditions, the optimal policy exhibits a four-threshold structure. We then conclude with computational experiments, thereby illustrating the policy structures that can be extracted in various inventory management scenarios.

Funding: This work was supported by the National Science Foundation [Grant CMMI-1847666] and the Division of Graduate Education [Grant DGE-2125913].

Supplemental Material: The online appendix is available at https://doi.org/10.1287/msom.2022.0318.