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Optimal Sizing and Timing of Modular Capacity Expansions

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  • Porteus, Evan L.

    (Stanford U)

  • Angelus, Alexandar

    (Strategic Decision Group)

  • Wood, Samuel C.

    (Stanford U)

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    Abstract

    We build a discrete time, serially correlated stochastic demand, nonstationary, finite horizon, capacity expansion model that includes (1) economies of scale in capacity costs, (2) positive expansion leadtimes, and (3) a fixed maximum cumulative capacity, called the shell size. When the shell size is finite, we have what is called the modular approach to capacity expansion, in which a shell is built along with the first module, and additional modules (of varying sizes) can be added at less cost than entire new plants of their respective sizes. (When the shell size is infinite, we have the traditional approach in which every expansion is a new plant.) We show that an (s, S) expansion point, expansion level, policy is optimal: Capacity is expanded to S if and only if the initial level is below s. These parameters depend on the period, the last observed demand, and the shell size. We also show that the optimal value of the enterprise is a convex decreasing function of the lump-sum cost incurred at the time of each expansion. We illustrate the model with a numerical example taken from semiconductor manufacturing.

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    Bibliographic Info

    Paper provided by Stanford University, Graduate School of Business in its series Research Papers with number 1479r2.

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    Date of creation: Jun 2000
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    Handle: RePEc:ecl:stabus:1479r2

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    1. Buzacott, J. A. & Chaouch, A. B., 1988. "Capacity expansion with interrupted demand growth," European Journal of Operational Research, Elsevier, vol. 34(1), pages 19-26, February.
    2. Higle, Julia L. & Corrado, Charles J., 1992. "Economic investment times for capacity expansion problems," European Journal of Operational Research, Elsevier, vol. 59(2), pages 288-293, June.
    3. Jan A. Van Mieghem, 1998. "Investment Strategies for Flexible Resources," Management Science, INFORMS, vol. 44(8), pages 1071-1078, August.
    4. Avinash Dixit, 1992. "Irreversible Investment with Uncertainty and Scale Economies," STICERD - Theoretical Economics Paper Series 240, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    5. Sampath Rajagopalan & Medini R. Singh & Thomas E. Morton, 1998. "Capacity Expansion and Replacement in Growing Markets with Uncertain Technological Breakthroughs," Management Science, INFORMS, vol. 44(1), pages 12-30, January.
    6. Pindyck, Robert S, 1988. "Irreversible Investment, Capacity Choice, and the Value of the Firm," American Economic Review, American Economic Association, vol. 78(5), pages 969-85, December.
    7. Gupta, Diwakar & Gerchak, Yigal & Buzacott, John A., 1992. "The optimal mix of flexible and dedicated manufacturing capacities: Hedging against demand uncertainty," International Journal of Production Economics, Elsevier, vol. 28(3), pages 309-319, December.
    8. Joseph Hall & Evan Porteus, 2000. "Customer Service Competition in Capacitated Systems," Manufacturing & Service Operations Management, INFORMS, vol. 2(2), pages 144-165, November.
    9. Harrison, J. Michael & Van Mieghem, Jan A., 1999. "Multi-resource investment strategies: Operational hedging under demand uncertainty," European Journal of Operational Research, Elsevier, vol. 113(1), pages 17-29, February.
    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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