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Decision rule approximations for the risk averse reservoir management problem

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  • Gauvin, Charles
  • Delage, Erick
  • Gendreau, Michel

Abstract

This paper presents a new formulation for the risk averse stochastic reservoir management problem. Using recent advances in robust optimization and stochastic programming, we propose a multi-stage model based on minimization of a risk measure associated with floods and droughts for a hydro-electrical complex. We present our model and then identify approximate solutions using standard affine decision rules commonly found in the literature as well as lifted decision rules. Finally, we conduct thorough numerical experiments based on a real river system in Western Québec and conclude on the relative performance of families of decision rules.

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  • Gauvin, Charles & Delage, Erick & Gendreau, Michel, 2017. "Decision rule approximations for the risk averse reservoir management problem," European Journal of Operational Research, Elsevier, vol. 261(1), pages 317-336.
    • Handle: RePEc:eee:ejores:v:261:y:2017:i:1:p:317-336
    DOI: 10.1016/j.ejor.2017.01.044
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    Cited by:

    1. Feng, Wei & Feng, Yiping & Zhang, Qi, 2021. "Multistage robust mixed-integer optimization under endogenous uncertainty," European Journal of Operational Research, Elsevier, vol. 294(2), pages 460-475.
    2. Rahal, Said & Papageorgiou, Dimitri J. & Li, Zukui, 2021. "Hybrid strategies using linear and piecewise-linear decision rules for multistage adaptive linear optimization," European Journal of Operational Research, Elsevier, vol. 290(3), pages 1014-1030.
    3. Gauvin, Charles & Delage, Erick & Gendreau, Michel, 2018. "A stochastic program with time series and affine decision rules for the reservoir management problem," European Journal of Operational Research, Elsevier, vol. 267(2), pages 716-732.
    4. Felipe Nazare & Alexandre Street, 2021. "Solving Multistage Stochastic Linear Programming via Regularized Linear Decision Rules: An Application to Hydrothermal Dispatch Planning," Papers 2110.03146, arXiv.org, revised Jan 2023.
    5. Amir Ardestani-Jaafari & Erick Delage, 2021. "Linearized Robust Counterparts of Two-Stage Robust Optimization Problems with Applications in Operations Management," INFORMS Journal on Computing, INFORMS, vol. 33(3), pages 1138-1161, July.
    6. Rodríguez, Jesús A. & Anjos, Miguel F. & Côté, Pascal & Desaulniers, Guy, 2021. "Accelerating Benders decomposition for short-term hydropower maintenance scheduling," European Journal of Operational Research, Elsevier, vol. 289(1), pages 240-253.
    7. Charles Gauvin & Erick Delage & Michel Gendreau, 2018. "A successive linear programming algorithm with non-linear time series for the reservoir management problem," Computational Management Science, Springer, vol. 15(1), pages 55-86, January.
    8. Nazare, Felipe & Street, Alexandre, 2023. "Solving multistage stochastic linear programming via regularized linear decision rules: An application to hydrothermal dispatch planning," European Journal of Operational Research, Elsevier, vol. 309(1), pages 345-358.

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