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Capacity Expansion for Random Exponential Demand Growth with Lead Times

  • Sarah M. Ryan

    ()

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

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    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.

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    File URL: http://dx.doi.org/10.1287/mnsc.1030.0187
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    Article provided by INFORMS in its journal Management Science.

    Volume (Year): 50 (2004)
    Issue (Month): 6 (June)
    Pages: 740-748

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    Handle: RePEc:inm:ormnsc:v:50:y:2004:i:6:p:740-748
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    1. 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.
    2. 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.
    3. Bar-Ilan, Avner & Strange, William C, 1996. "Investment Lags," American Economic Review, American Economic Association, vol. 86(3), pages 610-22, June.
    4. Lieberman, Marvin B., 1989. "Capacity utilization: Theoretical models and empirical tests," European Journal of Operational Research, Elsevier, vol. 40(2), pages 155-168, May.
    5. Robert McDonald & Daniel Siegel, 1986. "The Value of Waiting to Invest," The Quarterly Journal of Economics, Oxford University Press, vol. 101(4), pages 707-727.
    6. Saman Majd & Robert S. Pindyck, 1985. "Time to Build, Option Value, and Investment Decisions," NBER Working Papers 1654, National Bureau of Economic Research, Inc.
    7. Stephen Nickell, 1977. "Uncertainty and Lags in the Investment Decisions of Firms," Review of Economic Studies, Oxford University Press, vol. 44(2), pages 249-263.
    8. Robert L. Smith, 1979. "Turnpike Results for Single Location Capacity Expansion," Management Science, INFORMS, vol. 25(5), pages 474-484, May.
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