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Optimal Joint Inventory and Transshipment Control Under Uncertain Capacity

Kelley School of Business, Indiana University, Bloomington, Indiana 47405
Ross School of Business, University of Michigan, Ann Arbor, Michigan 48109
Ross School of Business, University of Michigan, Ann Arbor, Michigan 48109
hux{at}indiana.edu
duenyas{at}umich.edu
roman.kapuscinski{at}umich.edu

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 the optimal policy is most likely to yield significant benefits compared to simple policies.

Subject classifications: dynamic programming; application; inventory/production; uncertainty/stochastic; reliability; capacity; uncertainty.
History: Received July 2004; revision received December 2006; accepted December 2006.