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Controlled approximation of the value function in stochastic dynamic programming for multi-reservoir systems

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  • Luckny Zéphyr
  • Pascal Lang
  • Bernard Lamond

Abstract

We present a new approach for adaptive approximation of the value function in stochastic dynamic programming. Under convexity assumptions, our method is based on a simplicial partition of the state space. Bounds on the value function provide guidance as to where refinement should be done, if at all. Thus, the method allows for a trade-off between solution time and accuracy. The proposed scheme is experimented in the particular context of hydroelectric production across multiple reservoirs. Copyright Springer-Verlag Berlin Heidelberg 2015

Suggested Citation

  • Luckny Zéphyr & Pascal Lang & Bernard Lamond, 2015. "Controlled approximation of the value function in stochastic dynamic programming for multi-reservoir systems," Computational Management Science, Springer, vol. 12(4), pages 539-557, October.
    • Handle: RePEc:spr:comgts:v:12:y:2015:i:4:p:539-557
    DOI: 10.1007/s10287-015-0242-1
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    References listed on IDEAS

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    1. Shmuel Gal, 1989. "The Parameter Iteration Method in Dynamic Programming," Management Science, INFORMS, vol. 35(6), pages 675-684, June.
    2. Deepti Rani & Maria Moreira, 2010. "Simulation–Optimization Modeling: A Survey and Potential Application in Reservoir Systems Operation," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 24(6), pages 1107-1138, April.
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    Cited by:

    1. Luckny Zephyr & Bernard F. Lamond & Pascal Lang, 2024. "Hybrid simplicial-randomized approximate stochastic dynamic programming for multireservoir optimization," Computational Management Science, Springer, vol. 21(1), pages 1-44, June.
    2. Wim Ackooij & Debora Daniela Escobar & Martin Glanzer & Georg Ch. Pflug, 2020. "Distributionally robust optimization with multiple time scales: valuation of a thermal power plant," Computational Management Science, Springer, vol. 17(3), pages 357-385, October.
    3. Luckny Zéphyr & C. Lindsay Anderson, 2018. "Stochastic dynamic programming approach to managing power system uncertainty with distributed storage," Computational Management Science, Springer, vol. 15(1), pages 87-110, January.

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