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Capacity Expansion for Random Exponential Demand Growth with Lead Times

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  • Sarah M. Ryan

    (Department of Industrial and Manufacturing Systems Engineering, Iowa State University, Ames, Iowa 50011-2164)

Abstract

The combination of demand uncertainty and a lead time for adding capacity creates the risk of capacity shortage during the lead time. We formulate a model of capacity expansion for uncertain exponential demand growth and deterministic expansion lead times when there is an obligation to provide a specified level of service. The service level, defined in terms of the ratio of expected lead-time shortage to installed capacity, is guaranteed by timing each expansion to begin when demand reaches a fixed proportion of the capacity position. Under this timing rule, the optimal facilities to install can be determined by solving an equivalent deterministic problem without lead times. Numerical results show the effects of the demand parameters and lead-time length on the expansion timing. The interaction of timing with expansion size is explored for the case when continuous facility sizes are available with economies of scale.

Suggested Citation

  • Sarah M. Ryan, 2004. "Capacity Expansion for Random Exponential Demand Growth with Lead Times," Management Science, INFORMS, vol. 50(6), pages 740-748, June.
    • Handle: RePEc:inm:ormnsc:v:50:y:2004:i:6:p:740-748
    DOI: 10.1287/mnsc.1030.0187
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    1. Ward Whitt, 1981. "The Stationary Distribution of a Stochastic Clearing Process," Operations Research, INFORMS, vol. 29(2), pages 294-308, April.
    2. Majd, Saman & Pindyck, Robert S., 1987. "Time to build, option value, and investment decisions," Journal of Financial Economics, Elsevier, vol. 18(1), pages 7-27, March.
    3. Porteus, Evan L. & Angelus, Alexandar & Wood, Samuel C., 2000. "Optimal Sizing and Timing of Modular Capacity Expansions," Research Papers 1479r2, Stanford University, Graduate School of Business.
    4. Bar-Ilan, Avner & Strange, William C, 1996. "Investment Lags," American Economic Review, American Economic Association, vol. 86(3), pages 610-622, June.
    5. James C. Bean & Julia L. Higle & Robert L. Smith, 1992. "Capacity Expansion Under Stochastic Demands," Operations Research, INFORMS, vol. 40(3-supplem), pages 210-216, June.
    6. Lieberman, Marvin B., 1989. "Capacity utilization: Theoretical models and empirical tests," European Journal of Operational Research, Elsevier, vol. 40(2), pages 155-168, May.
    7. Robert McDonald & Daniel Siegel, 1986. "The Value of Waiting to Invest," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 101(4), pages 707-727.
    8. Stephen Nickell, 1977. "Uncertainty and Lags in the Investment Decisions of Firms," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 44(2), pages 249-263.
    9. Robert L. Smith, 1979. "Turnpike Results for Single Location Capacity Expansion," Management Science, INFORMS, vol. 25(5), pages 474-484, May.
    10. John R. Birge, 2000. "Option Methods for Incorporating Risk into Linear Capacity Planning Models," Manufacturing & Service Operations Management, INFORMS, vol. 2(1), pages 19-31, August.
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    Cited by:

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