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A stochastic optimization model for planning capacity expansion in a service industry under uncertain demand

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  • Oded Berman
  • Zvi Ganz
  • Janet M. Wagner

Abstract

A stochastic optimization model for capacity expansion for a service industry that incorporates uncertainty in future demand is developed. Based on a weighted set of possible demand scenarios, the model generates a recommended schedule of capacity expressions, and calculates the resulting sales under each scenario. The capacity schedule specifies the size, location, and timing of these expansions that will maximize the company's expected profit. The model includes a budget constraint on available resources. By using Lagrangian relaxation and exploiting the special nested knapsack structure in the sub‐problems, an algorithm was developed for its solution. Based on the initial computational results, this algorithm appears to be more efficient than linear programming for this special problem. © 1994 John Wiley & Sons, Inc.

Suggested Citation

  • Oded Berman & Zvi Ganz & Janet M. Wagner, 1994. "A stochastic optimization model for planning capacity expansion in a service industry under uncertain demand," Naval Research Logistics (NRL), John Wiley & Sons, vol. 41(4), pages 545-564, June.
    • Handle: RePEc:wly:navres:v:41:y:1994:i:4:p:545-564
    DOI: 10.1002/1520-6750(199406)41:43.0.CO;2-Z
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    References listed on IDEAS

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    1. Dudzinski, Krzysztof & Walukiewicz, Stanislaw, 1987. "Exact methods for the knapsack problem and its generalizations," European Journal of Operational Research, Elsevier, vol. 28(1), pages 3-21, January.
    2. Marshall L. Fisher, 1981. "The Lagrangian Relaxation Method for Solving Integer Programming Problems," Management Science, INFORMS, vol. 27(1), pages 1-18, January.
    3. Dimitris Paraskevopoulos & Elias Karakitsos & Berc Rustem, 1991. "Robust Capacity Planning Under Uncertainty," Management Science, INFORMS, vol. 37(7), pages 787-800, July.
    4. 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.
    5. Ganz, Zvi & Berman, Oded, 1992. "The capacity expansion problem in the service industry with multiple resource constraints," Socio-Economic Planning Sciences, Elsevier, vol. 26(1), pages 1-14, January.
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    Cited by:

    1. 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.
    2. Van-Anh Truong & Robin O. Roundy, 2011. "Multidimensional Approximation Algorithms for Capacity-Expansion Problems," Operations Research, INFORMS, vol. 59(2), pages 313-327, April.
    3. 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).
    4. Suleyman Karabuk & S. David Wu, 2003. "Coordinating Strategic Capacity Planning in the Semiconductor Industry," Operations Research, INFORMS, vol. 51(6), pages 839-849, December.
    5. 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.
    6. A. Marín & J. Salmerón, 2001. "A risk function for the stochastic modeling of electric capacity expansion," Naval Research Logistics (NRL), John Wiley & Sons, vol. 48(8), pages 662-683, December.
    7. 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.
    8. Woonghee Tim Huh & Robin O. Roundy, 2005. "A continuous‐time strategic capacity planning model," Naval Research Logistics (NRL), John Wiley & Sons, vol. 52(4), pages 329-343, June.
    9. 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.

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