  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.
