Optimal replenishment and transshipment management with two locations

We study the problem of optimally managing an inventory system with backorders over a finite time horizon where the objective is minimization of expected total discounted costs. The system consists of two locations each stocking the same product. At the beginning of each time period decisions are made about replenishment at each location and about any quantity to transship between the locations before demand is observed. Leveraging the L♮‐convexity of the problem's cost function; we characterize the optimal replenishment and transshipment policy for this system. More specifically, we show the optimal policy can be described using switching curves monotone in the system state. We also discuss two extensions. For a lost‐sales model, we establish L♮‐convexity and apply it to characterize the optimal policy, simplifying the analysis found in previous work. In the other extension, we investigate the optimal policy for a partial transshipment problem where only one location orders from the external supply source and then transships to the other location.