Capacity expansion under a service-level constraint for uncertain demand with lead times

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2009-01-01
Authors
Marathe, Rahul
Ryan, Sarah
Ryan, Sarah
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Ryan, Sarah
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Abstract

For a service provider facing stochastic demand growth, expansion lead times and economies of scale complicate the expansion timing and sizing decisions. We formulate a model to minimize the infinite horizon expected discounted expansion cost under a service-level constraint. The service level is defined as the proportion of demand over an expansion cycle that is satisfied by available capacity. For demand that follows a geometric Brownian motion process, we impose a stationary policy under which expansions are triggered by a fixed ratio of demand to the capacity position, i.e., the capacity that will be available when any current expansion project is completed, and each expansion increases capacity by the same proportion. The risk of capacity shortage during a cycle is estimated analytically using the value of an up-and-out partial barrier call option. A cutting plane procedure identifies the optimal values of the two expansion policy parameters simultaneously. Numerical instances illustrate that if demand grows slowly with low volatility and the expansion lead times are short, then it is optimal to delay the start of expansion beyond when demand exceeds the capacity position. Delays in initiating expansions are coupled with larger expansion sizes.

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<p>This is the peer reviewed version of the following article: [Marathe, R. R. and S. M. Ryan, “Capacity Expansion under a Service Level Constraint for Uncertain Demand with Lead Times,” Naval Research Logistics, 56(3), 250-263 (2009), which has been published in final form at<a target="_blank"> http://dx.doi.org/10.1002/nav.20334</a>. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving.</p>
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