IDEAS home Printed from
   My bibliography  Save this article

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

    Download full text from publisher

    File URL:
    Download Restriction: no

    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.
    Full references (including those not matched with items on IDEAS)


    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.

    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. 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.
    3. 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.
    4. 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.
    5. 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.


    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:inm:ormnsc:v:50:y:2004:i:6:p:740-748. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Mirko Janc). General contact details of provider: .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.