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Capacity Expansion when Demand Is a Birth-Death Random Process

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  • John Freidenfelds

    (AT & T Company, Basking Ridge, New Jersey)

Abstract

When demand is assumed to be a birth-death process, and capacity expansion costs are assumed to occur instantaneously at the time of expansion, it is shown that an “equivalent” deterministic-demand problem can readily be generated. The derived problem is equivalent in the sense that its solution by ordinary deterministic capacity expansion methods would also yield the solution of the stochastic problem. It is shown that the “equivalent deterministic demand” is always greater than the “expected demand,” where the latter is defined by the expected time to first reach various levels of demand, and is not the expected number of customers. In addition to general formulas for the discrete-customer case, equations are also derived for the “equivalent deterministic demand” when demand is based on a diffusion process.

Suggested Citation

  • John Freidenfelds, 1980. "Capacity Expansion when Demand Is a Birth-Death Random Process," Operations Research, INFORMS, vol. 28(3-part-ii), pages 712-721, June.
    • Handle: RePEc:inm:oropre:v:28:y:1980:i:3-part-ii:p:712-721
    DOI: 10.1287/opre.28.3.712
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    Cited by:

    1. Kavinesh J. Singh & Andy B. Philpott & R. Kevin Wood, 2009. "Dantzig-Wolfe Decomposition for Solving Multistage Stochastic Capacity-Planning Problems," Operations Research, INFORMS, vol. 57(5), pages 1271-1286, October.
    2. Shabbir Ahmed & Nikolaos V. Sahinidis, 2003. "An Approximation Scheme for Stochastic Integer Programs Arising in Capacity Expansion," Operations Research, INFORMS, vol. 51(3), pages 461-471, June.
    3. Jikai Zou & Shabbir Ahmed & Xu Andy Sun, 2018. "Partially Adaptive Stochastic Optimization for Electric Power Generation Expansion Planning," INFORMS Journal on Computing, INFORMS, vol. 30(2), pages 388-401, May.
    4. 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.
    5. Kogan, Konstantin & Chernonog, Tatyana, 2019. "Competition under industry-stock-driven prevailing market price: Environmental consequences and the effect of uncertainty," European Journal of Operational Research, Elsevier, vol. 276(3), pages 929-946.
    6. Avi Herbon & Konstantin Kogan, 2014. "Time-dependent and independent control rules for coordinated production and pricing under demand uncertainty and finite planning horizons," Annals of Operations Research, Springer, vol. 223(1), pages 195-216, December.
    7. Kai Huang & Shabbir Ahmed, 2009. "The Value of Multistage Stochastic Programming in Capacity Planning Under Uncertainty," Operations Research, INFORMS, vol. 57(4), pages 893-904, August.
    8. Yang, Qing & Zhang, Lei & Zou, Shaohui & Zhang, Jinsuo, 2020. "Intertemporal optimization of the coal production capacity in China in terms of uncertain demand, economy, environment, and energy security," Energy Policy, Elsevier, vol. 139(C).

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