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Two-stage stochastic linear programs with incomplete information on uncertainty

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  • Ang, James
  • Meng, Fanwen
  • Sun, Jie

Abstract

Two-stage stochastic linear programming is a classical model in operations research. The usual approach to this model requires detailed information on distribution of the random variables involved. In this paper, we only assume the availability of the first and second moments information of the random variables. By using duality of semi-infinite programming and adopting a linear decision rule, we show that a deterministic equivalence of the two-stage problem can be reformulated as a second-order cone optimization problem. Preliminary numerical experiments are presented to demonstrate the computational advantage of this approach.

Suggested Citation

  • Ang, James & Meng, Fanwen & Sun, Jie, 2014. "Two-stage stochastic linear programs with incomplete information on uncertainty," European Journal of Operational Research, Elsevier, vol. 233(1), pages 16-22.
    • Handle: RePEc:eee:ejores:v:233:y:2014:i:1:p:16-22
    DOI: 10.1016/j.ejor.2013.07.039
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    References listed on IDEAS

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    1. Wenqing Chen & Melvyn Sim & Jie Sun & Chung-Piaw Teo, 2010. "From CVaR to Uncertainty Set: Implications in Joint Chance-Constrained Optimization," Operations Research, INFORMS, vol. 58(2), pages 470-485, April.
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    6. Erick Delage & Yinyu Ye, 2010. "Distributionally Robust Optimization Under Moment Uncertainty with Application to Data-Driven Problems," Operations Research, INFORMS, vol. 58(3), pages 595-612, June.
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    Cited by:

    1. Gong, Hailei & Zhang, Zhi-Hai, 2022. "Benders decomposition for the distributionally robust optimization of pricing and reverse logistics network design in remanufacturing systems," European Journal of Operational Research, Elsevier, vol. 297(2), pages 496-510.
    2. Ling, Aifan & Sun, Jie & Xiu, Naihua & Yang, Xiaoguang, 2017. "Robust two-stage stochastic linear optimization with risk aversion," European Journal of Operational Research, Elsevier, vol. 256(1), pages 215-229.
    3. Jie Sun & Di Wu & Changjun Yu, 2024. "Risk-Averse Optimal Control Model Under Uncertainty and Its Modified Progressive Hedging Algorithm," Journal of Optimization Theory and Applications, Springer, vol. 203(1), pages 960-984, October.
    4. Haodong Yu & Jie Sun & Yanjun Wang, 2021. "A time-consistent Benders decomposition method for multistage distributionally robust stochastic optimization with a scenario tree structure," Computational Optimization and Applications, Springer, vol. 79(1), pages 67-99, May.
    5. Yining Gu & Yicheng Huang & Yanjun Wang, 2024. "Data-Driven Distributionally Robust Risk-Averse Two-Stage Stochastic Linear Programming over Wasserstein Ball," Journal of Optimization Theory and Applications, Springer, vol. 200(1), pages 242-279, January.

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