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Risk-Averse Two-Stage Stochastic Linear Programming: Modeling and Decomposition

Author

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  • Naomi Miller

    (RUTCOR, Rutgers University, Piscataway, New Jersey 08854)

  • Andrzej Ruszczyński

    (Department of Management Science and Information Systems, Rutgers University, Piscataway, New Jersey 08854)

Abstract

We formulate a risk-averse two-stage stochastic linear programming problem in which unresolved uncertainty remains after the second stage. The objective function is formulated as a composition of conditional risk measures. We analyze properties of the problem and derive necessary and sufficient optimality conditions. Next, we construct a new decomposition method for solving the problem that exploits the composite structure of the objective function. We illustrate its performance on a portfolio optimization problem.

Suggested Citation

  • Naomi Miller & Andrzej Ruszczyński, 2011. "Risk-Averse Two-Stage Stochastic Linear Programming: Modeling and Decomposition," Operations Research, INFORMS, vol. 59(1), pages 125-132, February.
    • Handle: RePEc:inm:oropre:v:59:y:2011:i:1:p:125-132
    DOI: 10.1287/opre.1100.0847
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    References listed on IDEAS

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    1. Ogryczak, Wlodzimierz & Ruszczynski, Andrzej, 1999. "From stochastic dominance to mean-risk models: Semideviations as risk measures," European Journal of Operational Research, Elsevier, vol. 116(1), pages 33-50, July.
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    Cited by:

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    3. Sıtkı Gülten & Andrzej Ruszczyński, 2015. "Two-stage portfolio optimization with higher-order conditional measures of risk," Annals of Operations Research, Springer, vol. 229(1), pages 409-427, June.
    4. Bushaj, Sabah & Büyüktahtakın, İ. Esra & Haight, Robert G., 2022. "Risk-averse multi-stage stochastic optimization for surveillance and operations planning of a forest insect infestation," European Journal of Operational Research, Elsevier, vol. 299(3), pages 1094-1110.
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    6. R. Tyrrell Rockafellar & Johannes O. Royset, 2018. "Superquantile/CVaR risk measures: second-order theory," Annals of Operations Research, Springer, vol. 262(1), pages 3-28, March.
    7. Zhao, Shuaiqi & Yang, Hualong & Zheng, Jianfeng & Li, Dechang, 2024. "A two-step approach for deploying heterogeneous vessels and designing reliable schedule in liner shipping services," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 182(C).
    8. Bei, Xiaoqiang & Zhu, Xiaoyan & Coit, David W., 2019. "A risk-averse stochastic program for integrated system design and preventive maintenance planning," European Journal of Operational Research, Elsevier, vol. 276(2), pages 536-548.
    9. Fernández, Elena & Hinojosa, Yolanda & Puerto, Justo & Saldanha-da-Gama, Francisco, 2019. "New algorithmic framework for conditional value at risk: Application to stochastic fixed-charge transportation," European Journal of Operational Research, Elsevier, vol. 277(1), pages 215-226.
    10. Alois Pichler, 2017. "A quantitative comparison of risk measures," Annals of Operations Research, Springer, vol. 254(1), pages 251-275, July.
    11. Fei, Xin & Gülpınar, Nalân & Branke, Jürgen, 2019. "Efficient solution selection for two-stage stochastic programs," European Journal of Operational Research, Elsevier, vol. 277(3), pages 918-929.
    12. Ricardo Collado & Dávid Papp & Andrzej Ruszczyński, 2012. "Scenario decomposition of risk-averse multistage stochastic programming problems," Annals of Operations Research, Springer, vol. 200(1), pages 147-170, November.
    13. Escudero, Laureano F. & Garín, M. Araceli & Monge, Juan F. & Unzueta, Aitziber, 2020. "Some matheuristic algorithms for multistage stochastic optimization models with endogenous uncertainty and risk management," European Journal of Operational Research, Elsevier, vol. 285(3), pages 988-1001.
    14. Elçi, Özgün & Noyan, Nilay, 2018. "A chance-constrained two-stage stochastic programming model for humanitarian relief network design," Transportation Research Part B: Methodological, Elsevier, vol. 108(C), pages 55-83.

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