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On the complexity of the Unit Commitment Problem

Author

Listed:
  • Pascale Bendotti

    (Sorbonne Université, LIP6-CNRS (Laboratoire d’Informatique de Paris 6)
    EDF R&D)

  • Pierre Fouilhoux

    (Sorbonne Université, LIP6-CNRS (Laboratoire d’Informatique de Paris 6))

  • Cécile Rottner

    (Sorbonne Université, LIP6-CNRS (Laboratoire d’Informatique de Paris 6)
    EDF R&D)

Abstract

This article analyzes how the Unit Commitment Problem (UCP) complexity evolves with respect to the number n of units and T of time periods. A classical reduction from the knapsack problem shows that the UCP is NP-hard in the ordinary sense even for $$T=1$$ T = 1 . The main result of this article is that the UCP is strongly NP-hard. When the constraints are restricted to minimum up and down times, the UCP is shown to be polynomial for a fixed n. When either a unitary cost or amount of power is considered, the UCP is polynomial for $$T=1$$ T = 1 and strongly NP-hard for arbitrary T. The pricing subproblem commonly used in a UCP decomposition scheme is also shown to be strongly NP-hard for a subset of units.

Suggested Citation

  • Pascale Bendotti & Pierre Fouilhoux & Cécile Rottner, 2019. "On the complexity of the Unit Commitment Problem," Annals of Operations Research, Springer, vol. 274(1), pages 119-130, March.
    • Handle: RePEc:spr:annopr:v:274:y:2019:i:1:d:10.1007_s10479-018-2827-x
    DOI: 10.1007/s10479-018-2827-x
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    References listed on IDEAS

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    1. Antonio Frangioni & Claudio Gentile, 2006. "Solving Nonlinear Single-Unit Commitment Problems with Ramping Constraints," Operations Research, INFORMS, vol. 54(4), pages 767-775, August.
    2. Jonathan F. Bard, 1988. "Short-Term Scheduling of Thermal-Electric Generators Using Lagrangian Relaxation," Operations Research, INFORMS, vol. 36(5), pages 756-766, October.
    3. 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. Luis Montero & Antonio Bello & Javier Reneses, 2022. "A Review on the Unit Commitment Problem: Approaches, Techniques, and Resolution Methods," Energies, MDPI, vol. 15(4), pages 1-40, February.
    2. Layon Mescolin de Oliveira & Ivo Chaves da Silva Junior & Ramon Abritta, 2022. "Search Space Reduction for the Thermal Unit Commitment Problem through a Relevance Matrix," Energies, MDPI, vol. 15(19), pages 1-16, September.
    3. L. Alvarado-Barrios & A. Rodríguez del Nozal & A. Tapia & J. L. Martínez-Ramos & D. G. Reina, 2019. "An Evolutionary Computational Approach for the Problem of Unit Commitment and Economic Dispatch in Microgrids under Several Operation Modes," Energies, MDPI, vol. 12(11), pages 1-23, June.

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