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The Value of Multistage Stochastic Programming in Capacity Planning Under Uncertainty

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  • Kai Huang

    (School of Management, Binghamton University, State University of New York, Binghamton, New York 13902)

  • Shabbir Ahmed

    (School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332)

Abstract

This paper addresses a general class of capacity planning problems under uncertainty, which arises, for example, in semiconductor tool purchase planning. Using a scenario tree to model the evolution of the uncertainties, we develop a multistage stochastic integer programming formulation for the problem. In contrast to earlier two-stage approaches, the multistage model allows for revision of the capacity expansion plan as more information regarding the uncertainties is revealed. We provide analytical bounds for the value of multistage stochastic programming (VMS) afforded over the two-stage approach. By exploiting a special substructure inherent in the problem, we develop an efficient approximation scheme for the difficult multistage stochastic integer program and prove that the proposed scheme is asymptotically optimal. Computational experiments with realistic-scale problem instances suggest that the VMS for this class of problems is quite high; moreover, the quality and performance of the approximation scheme is very satisfactory. Fortunately, this is more so for instances for which the VMS is high.

Suggested Citation

  • 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.
    • Handle: RePEc:inm:oropre:v:57:y:2009:i:4:p:893-904
    DOI: 10.1287/opre.1080.0623
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    References listed on IDEAS

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