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A Robust Optimization Perspective on Stochastic Programming

Author

Listed:
  • Xin Chen

    (Department of Industrial and Enterprise Systems Engineering, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801)

  • Melvyn Sim

    (NUS Business School, National University of Singapore and Singapore MIT Alliance (SMA), Singapore)

  • Peng Sun

    (Fuqua School of Business, Duke University, Durham, North Carolina 27708)

Abstract

In this paper, we introduce an approach for constructing uncertainty sets for robust optimization using new deviation measures for random variables termed the forward and backward deviations . These deviation measures capture distributional asymmetry and lead to better approximations of chance constraints. Using a linear decision rule, we also propose a tractable approximation approach for solving a class of multistage chance-constrained stochastic linear optimization problems. An attractive feature of the framework is that we convert the original model into a second-order cone program, which is computationally tractable both in theory and in practice. We demonstrate the framework through an application of a project management problem with uncertain activity completion time.

Suggested Citation

  • Xin Chen & Melvyn Sim & Peng Sun, 2007. "A Robust Optimization Perspective on Stochastic Programming," Operations Research, INFORMS, vol. 55(6), pages 1058-1071, December.
    • Handle: RePEc:inm:oropre:v:55:y:2007:i:6:p:1058-1071
    DOI: 10.1287/opre.1070.0441
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    References listed on IDEAS

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    Keywords

    programming; stochastic;

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