Optimal dynamic production and inventory transshipment policies for a two-location make-to-stock system

Inventory sharing through transshipment has attracted a great deal of attention from researchers and practitioners due to its potential for increasing service levels while simultaneously decreasing stock levels. In this paper, we analyze the optimal production and transshipment policy for a two-location make-to-stock queueing system with exponential production and interarrival times. A key feature of our model is that we allow transshipments to be triggered by both demand arrivals and production completions. Thus, transshipment is used to achieve production flexibility through inventory reallocation, as well as to fill emergency demands. We also consider capacity issues in transshipment by modeling each location as a single-server, make-to-stock queueing system. In this setting, we prove that the optimal production policy for each location belongs to the hedging point family of policies, while the optimal demand filling policy belongs to the state-dependent rationing family of policies. We analyze the structural properties of the optimal policy and provide conditions under which the optimal policy can be simplified. Given the complex nature of the optimal policy, we develop three easy-to-implement heuristics that work very well for a large range of cost parameters.