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Dynamic Capacity Expansion for a Service Firm with Capacity Deterioration and Supply Uncertainty

Department of Industrial and Operations Engineering, University of Michigan, Ann Arbor, Michigan 48109, and School of Economics and Management, Tsinghua University, Beijing, China
Sauder School of Business, University of British Columbia, Vancouver, British Columbia, Canada V6T 1Z2
School of Business and Management, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong
xchao{at}umich.edu
hong.chen{at}sauder.ubc.ca
imzheng{at}ust.hk

Motivated by the challenges faced by the telecom industry during the past decade, in this paper we study a dynamic capacity expansion problem for service firms. There is a random demand for the firm's capacity in each period: the demand in excess of the capacity is lost, and revenue is generated for the fulfilled demand. At the beginning of each period, the firm Edits ok?might increase its capacity through purchasing equipment for immediate delivery, which is constrained by a random supply limit, or it might sign a future contract for equipment delivery in the following period. We assume that the firm's capacity might partially become obsolete due to natural deterioration or technology innovation. We aim at characterizing optimal capacity expansion strategies and comparing the profit functions as well as the optimal control policies of different options. Specifically, we show that the optimal capacity expansion policy for the current period is determined by a base-stock policy. Compared with the case where no future contracts are available, the optimal control parameters of capacity expansion are always smaller. We further show that when the obsolescence rate is deterministic, the optimal policy for capacity expansion through future contracts is also a base-stock type. The results are extended to the cases with stochastically dependent capacity supply limits and stochastically dependent demand processes, which establish the robustness of the optimal policy in various market conditions.

Subject classifications: capacity expansion; future contracts; base-stock policy; submodularity; stochastic order.
History: Received November 2005; revision received October 2007; accepted November 2007.