IDEAS home Printed from https://ideas.repec.org/a/inm/ormnsc/v50y2004i6p740-748.html
   My bibliography  Save this article

Capacity Expansion for Random Exponential Demand Growth with Lead Times

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/mnsc.1030.0187
    Download Restriction: no
    File URL: https://libkey.io/10.1287/mnsc.1030.0187?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

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

    Citations

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


    Cited by:

    1. Rahul R. Marathe & Sarah M. Ryan, 2009. "Capacity expansion under a service‐level constraint for uncertain demand with lead times," Naval Research Logistics (NRL), John Wiley & Sons, vol. 56(3), pages 250-263, April.
    2. 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.
    3. Haoying Sun & Subodha Kumar, 2020. "A Manufacturer's New Product Preannouncement Decision and the Supplier's Response," Production and Operations Management, Production and Operations Management Society, vol. 29(10), pages 2289-2306, October.
    4. Snead, Kenneth & Stott, David & Garcia, Andy, 2010. "The causes of misapplied capacity related manufacturing costs and corresponding reporting implications: A conceptual perspective," Journal of Accounting Education, Elsevier, vol. 28(2), pages 85-102.
    5. Gregory Dobson & Hsiao-Hui Lee & Edieal Pinker, 2010. "A Model of ICU Bumping," Operations Research, INFORMS, vol. 58(6), pages 1564-1576, December.
    6. 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.
    7. 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.
    8. Li, Xishu & Zuidwijk, Rob & de Koster, M.B.M, 2023. "Optimal competitive capacity strategies: Evidence from the container shipping market," Omega, Elsevier, vol. 115(C).
    9. Dawei (David) Zhang & Barrie R. Nault & Xueqi (David) Wei, 2019. "The Strategic Value of Information Technology in Setting Productive Capacity," Information Systems Research, INFORMS, vol. 30(4), pages 1124-1144, December.
    10. Van-Anh Truong & Robin O. Roundy, 2011. "Multidimensional Approximation Algorithms for Capacity-Expansion Problems," Operations Research, INFORMS, vol. 59(2), pages 313-327, April.
    11. Chen, Siyuan & Zhang, Qi & Wang, Ge & Zhu, Lijing & Li, Yan, 2018. "Investment strategy for underground gas storage facilities based on real option model considering gas market reform in China," Energy Economics, Elsevier, vol. 70(C), pages 132-142.
    12. Woonghee Tim Huh & Robin O. Roundy & Metin Çakanyildirim, 2006. "A general strategic capacity planning model under demand uncertainty," Naval Research Logistics (NRL), John Wiley & Sons, vol. 53(2), pages 137-150, March.
    13. Perera, Sandun & Gupta, Varun & Buckley, Winston, 2020. "Management of online server congestion using optimal demand throttling," European Journal of Operational Research, Elsevier, vol. 285(1), pages 324-342.
    14. Torres-Rincón, Samuel & Sánchez-Silva, Mauricio & Bastidas-Arteaga, Emilio, 2021. "A multistage stochastic program for the design and management of flexible infrastructure networks," Reliability Engineering and System Safety, Elsevier, vol. 210(C).
    15. 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.
    16. Xiuli Chao & Hong Chen & Shaohui Zheng, 2009. "Dynamic Capacity Expansion for a Service Firm with Capacity Deterioration and Supply Uncertainty," Operations Research, INFORMS, vol. 57(1), pages 82-93, February.
    17. Gwang Seok Kim & Young Hoon Lee, 2021. "Speed and Sustainability When Entering New Market," Sustainability, MDPI, vol. 13(22), pages 1-20, November.
    18. 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.
    19. Sergio Chayet & Wallace J. Hopp, 2008. "Risk‐sensitive sizing of responsive facilities," Naval Research Logistics (NRL), John Wiley & Sons, vol. 55(3), pages 218-233, April.
    20. Alexandar Angelus & Evan L. Porteus, 2008. "An Asset Assembly Problem," Operations Research, INFORMS, vol. 56(3), pages 665-680, June.
    21. Gupta, Varun & Perera, Sandun, 2021. "Managing surges in online demand using bandwidth throttling: An optimal strategy amid the COVID-19 pandemic," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 151(C).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Alexandar Angelus & Evan L. Porteus, 2008. "An Asset Assembly Problem," Operations Research, INFORMS, vol. 56(3), pages 665-680, June.
    2. Rahul R. Marathe & Sarah M. Ryan, 2009. "Capacity expansion under a service‐level constraint for uncertain demand with lead times," Naval Research Logistics (NRL), John Wiley & Sons, vol. 56(3), pages 250-263, April.
    3. Bar-Ilan, Avner & Strange, William C., 1998. "A model of sequential investment," Journal of Economic Dynamics and Control, Elsevier, vol. 22(3), pages 437-463, March.
    4. Lim, Terence & Lo, Andrew W. & Merton, Robert C. & Scholes, Myron S., 2006. "The Derivatives Sourcebook," Foundations and Trends(R) in Finance, now publishers, vol. 1(5–6), pages 365-572, April.
    5. Lei Zhu & ZhongXiang Zhang & Ying Fan, 2011. "An evaluation of overseas oil investment projects under uncertainty using a real options based simulation model," Economics Study Area Working Papers 121, East-West Center, Economics Study Area.
    6. Rena Sivitanidou, 1999. "Does the Theory of Irreversible Investments Help Explain Movements in Office-Commerical Construction?," Working Paper 8659, USC Lusk Center for Real Estate.
    7. Fredrik Armerin & Han-Suck Song, 2021. "A framework for modelling cash flow lags," SN Business & Economics, Springer, vol. 1(10), pages 1-13, October.
    8. Laarni T. Bulan, 2005. "Real options, irreversible investment and firm uncertainty: New evidence from U.S. firms," Review of Financial Economics, John Wiley & Sons, vol. 14(3-4), pages 255-279.
    9. Saphores, Jean-Daniel & Gravel, Éric & Bernard, Jean-Thomas, 2003. "Environmental Impact Assessment and Investment under Uncertainty. An Application to Power Grid Interconnection," Cahiers de recherche 0303, GREEN.
    10. Sarah M. Ryan, 2003. "Capacity expansion with lead times and autocorrelated random demand," Naval Research Logistics (NRL), John Wiley & Sons, vol. 50(2), pages 167-183, March.
    11. Gkochari, Christiana C., 2015. "Optimal investment timing in the dry bulk shipping sector," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 79(C), pages 102-109.
    12. Thijssen, Jacco J.J., 2015. "A model for irreversible investment with construction and revenue uncertainty," Journal of Economic Dynamics and Control, Elsevier, vol. 57(C), pages 250-266.
    13. Guerra, Manuel & Kort, Peter & Nunes, Cláudia & Oliveira, Carlos, 2018. "Hysteresis due to irreversible exit: Addressing the option to mothball," Journal of Economic Dynamics and Control, Elsevier, vol. 92(C), pages 69-83.
    14. Poretus, Evan L. & Angelus, Alexander, 2000. "Simultaneous Production and Capacity Management under Stochastic Demand for Perishable Goods," Research Papers 1419r, Stanford University, Graduate School of Business.
    15. Akamatsu, Takashi & Nagae, Takeshi, 2011. "A network of options: Evaluating complex interdependent decisions under uncertainty," Journal of Economic Dynamics and Control, Elsevier, vol. 35(5), pages 714-729, May.
    16. Milne, Alistair & Whalley, A. Elizabeth, 2001. "Time to build and aggregate work-in-progress," International Journal of Production Economics, Elsevier, vol. 71(1-3), pages 165-175, May.
    17. El-Shazly Alaa, 2004. "Investment Under Uncertainty in Egypt: A Real-Options Approach," Review of Middle East Economics and Finance, De Gruyter, vol. 2(2), pages 51-60, August.
    18. Bulan, Laarni T., 2005. "Real options, irreversible investment and firm uncertainty: New evidence from U.S. firms," Review of Financial Economics, Elsevier, vol. 14(3-4), pages 255-279.
    19. Gryglewicz, Sebastian & Huisman, Kuno J.M. & Kort, Peter M., 2008. "Finite project life and uncertainty effects on investment," Journal of Economic Dynamics and Control, Elsevier, vol. 32(7), pages 2191-2213, July.
    20. Bardia Kamrad & Akhtar Siddique & Ricardo Ernst, 2012. "Partial equilibrium in risk‐based production decisions," Naval Research Logistics (NRL), John Wiley & Sons, vol. 59(1), pages 1-17, February.

    Corrections

    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.

    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 bibliographic 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.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.html .

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

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.