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A model for dynamic chance constraints in hydro power reservoir management

Author

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  • Andrieu, L.
  • Henrion, R.
  • Römisch, W.

Abstract

In this paper, a model for (joint) dynamic chance constraints is proposed and applied to an optimization problem in water reservoir management. The model relies on discretization of the decision variables but keeps the probability distribution continuous. Our approach relies on calculating probabilities of rectangles which is particularly useful in the presence of independent random variables but works equally well in the case of correlated variables. Numerical results are provided for two and three stages.

Suggested Citation

  • Andrieu, L. & Henrion, R. & Römisch, W., 2010. "A model for dynamic chance constraints in hydro power reservoir management," European Journal of Operational Research, Elsevier, vol. 207(2), pages 579-589, December.
    • Handle: RePEc:eee:ejores:v:207:y:2010:i:2:p:579-589
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    References listed on IDEAS

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    1. N.C.P. Edirisinghe & E.I. Patterson & N. Saadouli, 2000. "Capacity Planning Model for a Multipurpose Water Reservoir with Target-Priority Operation," Annals of Operations Research, Springer, vol. 100(1), pages 273-303, December.
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    Cited by:

    1. Minjiao Zhang & Simge Küçükyavuz & Saumya Goel, 2014. "A Branch-and-Cut Method for Dynamic Decision Making Under Joint Chance Constraints," Management Science, INFORMS, vol. 60(5), pages 1317-1333, May.
    2. Holger Berthold & Holger Heitsch & René Henrion & Jan Schwientek, 2022. "On the algorithmic solution of optimization problems subject to probabilistic/robust (probust) constraints," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 96(1), pages 1-37, August.
    3. I. Bremer & R. Henrion & A. Möller, 2015. "Probabilistic constraints via SQP solver: application to a renewable energy management problem," Computational Management Science, Springer, vol. 12(3), pages 435-459, July.
    4. Guigues, Vincent & Sagastizábal, Claudia, 2012. "The value of rolling-horizon policies for risk-averse hydro-thermal planning," European Journal of Operational Research, Elsevier, vol. 217(1), pages 129-140.
    5. Andre Luiz Diniz & Maria Elvira P. Maceira & Cesar Luis V. Vasconcellos & Debora Dias J. Penna, 2020. "A combined SDDP/Benders decomposition approach with a risk-averse surface concept for reservoir operation in long term power generation planning," Annals of Operations Research, Springer, vol. 292(2), pages 649-681, September.
    6. Balata, Alessandro & Ludkovski, Michael & Maheshwari, Aditya & Palczewski, Jan, 2021. "Statistical learning for probability-constrained stochastic optimal control," European Journal of Operational Research, Elsevier, vol. 290(2), pages 640-656.
    7. Michel Minoux & Riadh Zorgati, 2019. "Sharp upper and lower bounds for maximum likelihood solutions to random Gaussian bilateral inequality systems," Journal of Global Optimization, Springer, vol. 75(3), pages 735-766, November.
    8. Ignacio Marín Cruz & Mohamed Badaoui & Ricardo Mota Palomino, 2023. "Medium-Term Hydrothermal Scheduling of the Infiernillo Reservoir Using Stochastic Dual Dynamic Programming (SDDP): A Case Study in Mexico," Energies, MDPI, vol. 16(17), pages 1-26, August.
    9. Alessandro Balata & Michael Ludkovski & Aditya Maheshwari & Jan Palczewski, 2019. "Statistical Learning for Probability-Constrained Stochastic Optimal Control," Papers 1905.00107, arXiv.org, revised Aug 2020.
    10. Peng, Shen & Maggioni, Francesca & Lisser, Abdel, 2022. "Bounds for probabilistic programming with application to a blend planning problem," European Journal of Operational Research, Elsevier, vol. 297(3), pages 964-976.
    11. Drew P. Kouri & Mathias Staudigl & Thomas M. Surowiec, 2023. "A relaxation-based probabilistic approach for PDE-constrained optimization under uncertainty with pointwise state constraints," Computational Optimization and Applications, Springer, vol. 85(2), pages 441-478, June.
    12. Chen, Zhen & Archibald, Thomas W., 2024. "Maximizing the survival probability in a cash flow inventory problem with a joint service level constraint," International Journal of Production Economics, Elsevier, vol. 270(C).

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