Optimal Joint Inventory and Transshipment Control under Uncertain Capacity

In this paper, we address the optimal joint control of inventory and transshipment for a firm that produces in two locations and faces capacity uncertainty. Capacity uncertainty (e.g., due to downtime, quality problems, yield, etc.) is a common feature of many production systems but its effects have not been explored in the context of a firm that has multiple production facilities. We first characterize the optimal production and transshipment policies and show that uncertain capacity leads the firm to ration the inventory that is available for transshipment to the other location and characterize the structure of this rationing policy. Then we characterize the optimal production policies at both locations which are defined by state-dependent produce-up-to thresholds. We also describe sensitivity of the optimal production and transshipment policies to problem parameters and, in particular, explain how uncertain capacity can lead to counterintuitive behavior, such as produce-up-to limits decreasing for locations that face stochastically higher demand. We finally explore, through a numerical study, when applying the optimal policy is most likely to yield significant benefits compared to simple policies. In particular, we consider two simple straw policies: 1) a policy that disallows transshipment and 2) a policy that disallows rationing and forces the two locations to transship inventory to satisfy the other location’s shortage.