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Decomposition methods for monotone two-time-scale stochastic optimization problems

Author

Listed:
  • Tristan Rigaut

    (Schneider Electric)

  • Pierre Carpentier

    (ENSTA Paris)

  • Jean-Philippe Chancelier

    (École des Ponts ParisTech)

  • Michel Lara

    (École des Ponts ParisTech)

Abstract

It is common that strategic investment decisions are made at a slow time-scale, whereas operational decisions are made at a fast time-scale. Hence, the total number of decision stages may be huge. In this paper, we consider multistage stochastic optimization problems with two time-scales, and we propose a time block decomposition scheme to address them numerically. More precisely, (i) we write recursive Bellman-like equations at the slow time-scale and (ii), under a suitable monotonicity assumption, we propose computable upper and lower bounds—relying respectively on primal and dual decomposition—for the corresponding slow time-scale Bellman functions. With these functions, we are able to design policies. We assess the methods tractability and validate their efficiency by solving a battery management problem where the fast time-scale operational decisions have an impact on the storage current capacity, hence on the strategic decisions to renew the battery at the slow time-scale.

Suggested Citation

  • Tristan Rigaut & Pierre Carpentier & Jean-Philippe Chancelier & Michel Lara, 2024. "Decomposition methods for monotone two-time-scale stochastic optimization problems," Computational Management Science, Springer, vol. 21(1), pages 1-37, June.
    • Handle: RePEc:spr:comgts:v:21:y:2024:i:1:d:10.1007_s10287-024-00510-5
    DOI: 10.1007/s10287-024-00510-5
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    References listed on IDEAS

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    1. Benjamin Heymann & Pierre Martinon, 2018. "Optimal Battery Aging: An Adaptive Weights Dynamic Programming Algorithm," Journal of Optimization Theory and Applications, Springer, vol. 179(3), pages 1043-1053, December.
    2. Pierre Carpentier & Jean-Philippe Chancelier & Michel Lara & François Pacaud, 2020. "Mixed Spatial and Temporal Decompositions for Large-Scale Multistage Stochastic Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 186(3), pages 985-1005, September.
    3. Michal Kaut, 2021. "Scenario generation by selection from historical data," Computational Management Science, Springer, vol. 18(3), pages 411-429, July.
    4. Michal Kaut & Kjetil Midthun & Adrian Werner & Asgeir Tomasgard & Lars Hellemo & Marte Fodstad, 2014. "Multi-horizon stochastic programming," Computational Management Science, Springer, vol. 11(1), pages 179-193, January.
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