Water Resources Management

, Volume 32, Issue 5, pp 1599–1614 | Cite as

Comparison Between Robust and Stochastic Optimisation for Long-term Reservoir Management Under Uncertainty

  • Thibaut CuvelierEmail author
  • Pierre Archambeau
  • Benjamin Dewals
  • Quentin Louveaux


Long-term reservoir management often uses bounds on the reservoir level, between which the operator can work. However, these bounds are not always kept up-to-date with the latest knowledge about the reservoir drainage area, and thus become obsolete. The main difficulty with bounds computation is to correctly take into account the high uncertainty about the inflows to the reservoir. In this article, we propose a methodology to derive minimum bounds while providing formal guarantees about the quality of the obtained solutions. The uncertainty is embedded using either stochastic or robust programming in a model-predictive-control framework. We compare the two paradigms to the existing solution for a case study and find that the obtained solutions vary substantially. By combining the stochastic and the robust approaches, we also assign a confidence level to the solutions obtained by stochastic programming. The proposed methodology is found to be both efficient and easy to implement. It relies on sound mathematical principles, ensuring that a global optimum is reached in all cases.


Long-term reservoir management Rule curve Stochastic optimisation Robust optimisation 



The authors gratefully acknowledge the Service Public de Wallonie (SPW) for providing data on the case study. They also thank Sébastien Erpicum for his help with the revision of the manuscript.

Compliance with Ethical Standards

Conflict of interests

The authors declare that they have no conflict of interest.

Supplementary material

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Copyright information

© Springer Science+Business Media B.V., part of Springer Nature 2018

Authors and Affiliations

  • Thibaut Cuvelier
    • 1
    Email author
  • Pierre Archambeau
    • 1
  • Benjamin Dewals
    • 1
  • Quentin Louveaux
    • 1
  1. 1.Université de LiègeLiègeBelgium

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