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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)


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

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    References listed on IDEAS

    1. 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.
    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 610-622, 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. 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.
    7. Robert L. Smith, 1979. "Turnpike Results for Single Location Capacity Expansion," Management Science, INFORMS, vol. 25(5), pages 474-484, May.
    8. 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:

    1. Georgiadis, Patroklos & Athanasiou, Efstratios, 2013. "Flexible long-term capacity planning in closed-loop supply chains with remanufacturing," European Journal of Operational Research, Elsevier, vol. 225(1), pages 44-58.
    2. repec:eee:joaced:v:28:y:2010:i:2:p:85-102 is not listed on IDEAS
    3. Patrick Afflerbach & Manuel Bolsinger & Maximilian Röglinger, 2016. "An economic decision model for determining the appropriate level of business process standardization," Business Research, Springer;German Academic Association for Business Research, vol. 9(2), pages 335-375, August.
    4. Ornella Tarola, 2010. "Public Utilities: Privatization without Regulation," Czech Economic Review, Charles University Prague, Faculty of Social Sciences, Institute of Economic Studies, vol. 4(1), pages 062-078, March.
    5. repec:eee:eneeco:v:70:y:2018:i:c:p:132-142 is not listed on IDEAS
    6. Julka, Nirupam & Baines, Tim & Tjahjono, Benny & Lendermann, Peter & Vitanov, Val, 2007. "A review of multi-factor capacity expansion models for manufacturing plants: Searching for a holistic decision aid," International Journal of Production Economics, Elsevier, vol. 106(2), pages 607-621, April.
    7. Li, X. & Zuidwijk, R.A. & de Koster, M.B.M. & Dekker, R., 2016. "Competitive Capacity Investment under Uncertainty," ERIM Report Series Research in Management ERS-2016-005-LIS, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam.


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