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The min-up/min-down unit commitment polytope

Author

Listed:
  • Pascale Bendotti

    (Sorbonne Universités, Université Pierre et Marie Curie
    EDF R&D)

  • Pierre Fouilhoux

    (Sorbonne Universités, Université Pierre et Marie Curie)

  • Cécile Rottner

    (Sorbonne Universités, Université Pierre et Marie Curie
    EDF R&D)

Abstract

The min-up/min-down unit commitment problem (MUCP) is to find a minimum-cost production plan on a discrete time horizon for a set of fossil-fuel units for electricity production. At each time period, the total production has to meet a forecast demand. Each unit must satisfy minimum up-time and down-time constraints besides featuring production and start-up costs. A full polyhedral characterization of the MUCP with only one production unit is provided by Rajan and Takriti (Minimum up/down polytopes of the unit commitment problem with start-up costs. IBM Research Report, 2005). In this article, we analyze polyhedral aspects of the MUCP with n production units. We first translate the classical extended cover inequalities of the knapsack polytope to obtain the so-called up-set inequalities for the MUCP polytope. We introduce the interval up-set inequalities as a new class of valid inequalities, which generalizes both up-set inequalities and minimum up-time inequalities. We provide a characterization of the cases when interval up-set inequalities are valid and not dominated by other inequalities. We devise an efficient Branch and Cut algorithm, using up-set and interval up-set inequalities.

Suggested Citation

  • Pascale Bendotti & Pierre Fouilhoux & Cécile Rottner, 2018. "The min-up/min-down unit commitment polytope," Journal of Combinatorial Optimization, Springer, vol. 36(3), pages 1024-1058, October.
    • Handle: RePEc:spr:jcomop:v:36:y:2018:i:3:d:10.1007_s10878-018-0273-y
    DOI: 10.1007/s10878-018-0273-y
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    References listed on IDEAS

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    1. Samer Takriti & Benedikt Krasenbrink & Lilian S.-Y. Wu, 2000. "Incorporating Fuel Constraints and Electricity Spot Prices into the Stochastic Unit Commitment Problem," Operations Research, INFORMS, vol. 48(2), pages 268-280, April.
    2. Antonio Frangioni, 2005. "About Lagrangian Methods in Integer Optimization," Annals of Operations Research, Springer, vol. 139(1), pages 163-193, October.
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    Cited by:

    1. Jianqiu Huang & Kai Pan & Yongpei Guan, 2021. "Multistage Stochastic Power Generation Scheduling Co-Optimizing Energy and Ancillary Services," INFORMS Journal on Computing, INFORMS, vol. 33(1), pages 352-369, January.

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