IDEAS home Printed from https://ideas.repec.org/a/spr/jcomop/v36y2018i3d10.1007_s10878-018-0273-y.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10878-018-0273-y
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10878-018-0273-y?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Ogbe, Emmanuel & Li, Xiang, 2017. "A new cross decomposition method for stochastic mixed-integer linear programming," European Journal of Operational Research, Elsevier, vol. 256(2), pages 487-499.
    2. Alexis Tantet & Philippe Drobinski, 2021. "A Minimal System Cost Minimization Model for Variable Renewable Energy Integration: Application to France and Comparison to Mean-Variance Analysis," Energies, MDPI, vol. 14(16), pages 1-38, August.
    3. Ying-Yi Hong & Gerard Francesco DG. Apolinario, 2021. "Uncertainty in Unit Commitment in Power Systems: A Review of Models, Methods, and Applications," Energies, MDPI, vol. 14(20), pages 1-47, October.
    4. Philip J. Neame & Andrew B. Philpott & Geoffrey Pritchard, 2003. "Offer Stack Optimization in Electricity Pool Markets," Operations Research, INFORMS, vol. 51(3), pages 397-408, June.
    5. Nogata, Daisuke, 2022. "Determinants of household switching between natural gas suppliers: Evidence from Japan," Utilities Policy, Elsevier, vol. 76(C).
    6. Chyong, Chi Kong & Newbery, David, 2022. "A unit commitment and economic dispatch model of the GB electricity market – Formulation and application to hydro pumped storage," Energy Policy, Elsevier, vol. 170(C).
    7. Suvrajeet Sen & Lihua Yu & Talat Genc, 2006. "A Stochastic Programming Approach to Power Portfolio Optimization," Operations Research, INFORMS, vol. 54(1), pages 55-72, February.
    8. Matt Thompson, 2013. "Optimal Economic Dispatch and Risk Management of Thermal Power Plants in Deregulated Markets," Operations Research, INFORMS, vol. 61(4), pages 791-809, August.
    9. Kjetil Haugen & Stein Wallace, 2006. "Stochastic programming: Potential hazards when random variables reflect market interaction," Annals of Operations Research, Springer, vol. 142(1), pages 119-127, February.
    10. Claudio Gambella & Joe Naoum-Sawaya & Bissan Ghaddar, 2018. "The Vehicle Routing Problem with Floating Targets: Formulation and Solution Approaches," INFORMS Journal on Computing, INFORMS, vol. 30(3), pages 554-569, August.
    11. Tonbari, Mohamed El & Ahmed, Shabbir, 2023. "Consensus-based Dantzig-Wolfe decomposition," European Journal of Operational Research, Elsevier, vol. 307(3), pages 1441-1456.
    12. Jirutitijaroen, Panida & Kim, Sujin & Kittithreerapronchai, Oran & Prina, José, 2013. "An optimization model for natural gas supply portfolios of a power generation company," Applied Energy, Elsevier, vol. 107(C), pages 1-9.
    13. 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.
    14. Sanjay Dominik Jena & Jean-François Cordeau & Bernard Gendron, 2017. "Lagrangian Heuristics for Large-Scale Dynamic Facility Location with Generalized Modular Capacities," INFORMS Journal on Computing, INFORMS, vol. 29(3), pages 388-404, August.
    15. Wim Ackooij & Jérôme Malick, 2016. "Decomposition algorithm for large-scale two-stage unit-commitment," Annals of Operations Research, Springer, vol. 238(1), pages 587-613, March.
    16. Igor Litvinchev & Socorro Rangel & Jania Saucedo, 2010. "A Lagrangian bound for many-to-many assignment problems," Journal of Combinatorial Optimization, Springer, vol. 19(3), pages 241-257, April.
    17. Antonio Frangioni & Claudio Gentile & Enrico Grande & Andrea Pacifici, 2011. "Projected Perspective Reformulations with Applications in Design Problems," Operations Research, INFORMS, vol. 59(5), pages 1225-1232, October.
    18. Knudsen, Brage Rugstad & Whitson, Curtis H. & Foss, Bjarne, 2014. "Shale-gas scheduling for natural-gas supply in electric power production," Energy, Elsevier, vol. 78(C), pages 165-182.
    19. Lara, Cristiana L. & Mallapragada, Dharik S. & Papageorgiou, Dimitri J. & Venkatesh, Aranya & Grossmann, Ignacio E., 2018. "Deterministic electric power infrastructure planning: Mixed-integer programming model and nested decomposition algorithm," European Journal of Operational Research, Elsevier, vol. 271(3), pages 1037-1054.
    20. Kai Pan & Ming Zhao & Chung-Lun Li & Feng Qiu, 2022. "A Polyhedral Study on Fuel-Constrained Unit Commitment," INFORMS Journal on Computing, INFORMS, vol. 34(6), pages 3309-3324, November.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:jcomop:v:36:y:2018:i:3:d:10.1007_s10878-018-0273-y. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.