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Assessing policy quality in a multistage stochastic program for long-term hydrothermal scheduling

Author

Listed:
  • Vitor L. de Matos

    () (Plan4 Engenharia)

  • David P. Morton

    () (Northwestern University)

  • Erlon C. Finardi

    () (Universidade Federal de Santa Catarina)

Abstract

We consider a multistage stochastic linear program in which we aim to assess the quality of an operational policy computed by means of a stochastic dual dynamic programming algorithm. We perform policy assessment by considering two strategies to compute a confidence interval on the optimality gap: (i) using multiple scenario trees and (ii) using a single scenario tree. The first approach has already been considered in several applications, while the second approach has been discussed previously only in a two-stage framework. The second approach is useful in practical applications in order to more quickly assess the quality of a policy. We present these ideas in the context of a multistage stochastic program for Brazilian long-term hydrothermal scheduling, and use numerical instances to compare the confidence intervals on the optimality gap computed via both strategies. We further consider the relative merits of using naive Monte Carlo sampling, randomized quasi Monte Carlo sampling, and Latin hypercube sampling within our framework for assessing the quality of a policy.

Suggested Citation

  • Vitor L. de Matos & David P. Morton & Erlon C. Finardi, 2017. "Assessing policy quality in a multistage stochastic program for long-term hydrothermal scheduling," Annals of Operations Research, Springer, vol. 253(2), pages 713-731, June.
  • Handle: RePEc:spr:annopr:v:253:y:2017:i:2:d:10.1007_s10479-016-2107-6
    DOI: 10.1007/s10479-016-2107-6
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    References listed on IDEAS

    as
    1. Tanrisever, Fehmi & Morrice, Douglas & Morton, David, 2012. "Managing capacity flexibility in make-to-order production environments," European Journal of Operational Research, Elsevier, vol. 216(2), pages 334-345.
    2. Vincent Guigues, 2014. "SDDP for some interstage dependent risk-averse problems and application to hydro-thermal planning," Computational Optimization and Applications, Springer, vol. 57(1), pages 167-203, January.
    3. Shapiro, Alexander, 2011. "Analysis of stochastic dual dynamic programming method," European Journal of Operational Research, Elsevier, vol. 209(1), pages 63-72, February.
    4. Güzin Bayraksan & David P. Morton, 2011. "A Sequential Sampling Procedure for Stochastic Programming," Operations Research, INFORMS, vol. 59(4), pages 898-913, August.
    5. Kjetil Høyland & Stein W. Wallace, 2001. "Generating Scenario Trees for Multistage Decision Problems," Management Science, INFORMS, vol. 47(2), pages 295-307, February.
    6. David P. Morton, 1998. "Stopping Rules for a Class of Sampling-Based Stochastic Programming Algorithms," Operations Research, INFORMS, vol. 46(5), pages 710-718, October.
    7. Philpott, A.B. & de Matos, V.L., 2012. "Dynamic sampling algorithms for multi-stage stochastic programs with risk aversion," European Journal of Operational Research, Elsevier, vol. 218(2), pages 470-483.
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    Cited by:

    1. van Ackooij, Wim & De Boeck, Jérôme & Detienne, Boris & Pan, Stefania & Poss, Michael, 2018. "Optimizing power generation in the presence of micro-grids," European Journal of Operational Research, Elsevier, vol. 271(2), pages 450-461.
    2. W. Ackooij & X. Warin, 2020. "On conditional cuts for stochastic dual dynamic programming," EURO Journal on Computational Optimization, Springer;EURO - The Association of European Operational Research Societies, vol. 8(2), pages 173-199, June.
    3. 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.

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