Technical Note—Time Inconsistency of Optimal Policies of Distributionally Robust Inventory Models

In this paper, we investigate optimal policies of distributionally robust (risk averse) inventory models. We demonstrate that if the respective risk measures are not strictly monotone, then there may exist infinitely many optimal policies that are not base-stock and not time consistent. This is in a sharp contrast with the risk neutral formulation of the inventory model where all optimal policies are time consistent. This also extends previous studies of time inconsistency in the robust setting.