IDEAS home Printed from https://ideas.repec.org/a/spr/jcomop/v33y2017i1d10.1007_s10878-015-9935-1.html
   My bibliography  Save this article

Benders decomposition for set covering problems

Author

Listed:
  • S. Haddadi

    (8 Mai 1945 University)

Abstract

This paper describes Benders decomposition approaches to optimally solve set covering problems “ almost” satisfying the consecutive ones property. The decompositions are based on the fact that set covering problems with consecutive ones property have totally unimodular coefficient matrices. Given a binary matrix, a totally unimodular matrix is enforced by filling up every row with ones between its first and its last non-zero entries. The resulting mistake is handled by introducing additional integer variables whose number depends on the reordering of the columns of the given matrix. This leads us to consider the consecutive block minimization problem. Two cutting plane algorithms are proposed and run on a large set of benchmark instances. The results obtained show that the cutting plane algorithms outperform an existing tree search method designed exclusively for such instances.

Suggested Citation

  • S. Haddadi, 2017. "Benders decomposition for set covering problems," Journal of Combinatorial Optimization, Springer, vol. 33(1), pages 60-80, January.
    • Handle: RePEc:spr:jcomop:v:33:y:2017:i:1:d:10.1007_s10878-015-9935-1
    DOI: 10.1007/s10878-015-9935-1
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10878-015-9935-1
    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/s10878-015-9935-1?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. Jean-François Cordeau & François Soumis & Jacques Desrosiers, 2000. "A Benders Decomposition Approach for the Locomotive and Car Assignment Problem," Transportation Science, INFORMS, vol. 34(2), pages 133-149, May.
    2. Jean-François Cordeau & Goran Stojković & François Soumis & Jacques Desrosiers, 2001. "Benders Decomposition for Simultaneous Aircraft Routing and Crew Scheduling," Transportation Science, INFORMS, vol. 35(4), pages 375-388, November.
    3. A. M. Geoffrion & G. W. Graves, 1974. "Multicommodity Distribution System Design by Benders Decomposition," Management Science, INFORMS, vol. 20(5), pages 822-844, January.
    4. Anita Schöbel & Horst W. Hamacher & Annegret Liebers & Dorothea Wagner, 2009. "The Continuous Stop Location Problem In Public Transportation Networks," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 26(01), pages 13-30.
    5. Alberto Caprara & Paolo Toth & Matteo Fischetti, 2000. "Algorithms for the Set Covering Problem," Annals of Operations Research, Springer, vol. 98(1), pages 353-371, December.
    6. Marshall L. Fisher & Pradeep Kedia, 1990. "Optimal Solution of Set Covering/Partitioning Problems Using Dual Heuristics," Management Science, INFORMS, vol. 36(6), pages 674-688, June.
    7. Beasley, J. E. & Jornsten, K., 1992. "Enhancing an algorithm for set covering problems," European Journal of Operational Research, Elsevier, vol. 58(2), pages 293-300, April.
    Full references (including those not matched with items on IDEAS)

    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. Vedat Bayram & Hande Yaman, 2018. "Shelter Location and Evacuation Route Assignment Under Uncertainty: A Benders Decomposition Approach," Transportation Science, INFORMS, vol. 52(2), pages 416-436, March.
    2. Zetina, Carlos Armando & Contreras, Ivan & Fernández, Elena & Luna-Mota, Carlos, 2019. "Solving the optimum communication spanning tree problem," European Journal of Operational Research, Elsevier, vol. 273(1), pages 108-117.
    3. Hanif Sherali & Ki-Hwan Bae & Mohamed Haouari, 2013. "A benders decomposition approach for an integrated airline schedule design and fleet assignment problem with flight retiming, schedule balance, and demand recapture," Annals of Operations Research, Springer, vol. 210(1), pages 213-244, November.
    4. Gao, Chao & Yao, Xin & Weise, Thomas & Li, Jinlong, 2015. "An efficient local search heuristic with row weighting for the unicost set covering problem," European Journal of Operational Research, Elsevier, vol. 246(3), pages 750-761.
    5. Özgün Elçi & John Hooker, 2022. "Stochastic Planning and Scheduling with Logic-Based Benders Decomposition," INFORMS Journal on Computing, INFORMS, vol. 34(5), pages 2428-2442, September.
    6. Roni, Md.S. & Eksioglu, Sandra D. & Searcy, Erin & Jha, Krishna, 2014. "A supply chain network design model for biomass co-firing in coal-fired power plants," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 61(C), pages 115-134.
    7. Ricardo Saraiva de Camargo & Gilberto de Miranda & Henrique Pacca L. Luna, 2009. "Benders Decomposition for Hub Location Problems with Economies of Scale," Transportation Science, INFORMS, vol. 43(1), pages 86-97, February.
    8. Beasley, J. E. & Chu, P. C., 1996. "A genetic algorithm for the set covering problem," European Journal of Operational Research, Elsevier, vol. 94(2), pages 392-404, October.
    9. Maher, Stephen J., 2021. "Implementing the branch-and-cut approach for a general purpose Benders’ decomposition framework," European Journal of Operational Research, Elsevier, vol. 290(2), pages 479-498.
    10. Lan, Guanghui & DePuy, Gail W. & Whitehouse, Gary E., 2007. "An effective and simple heuristic for the set covering problem," European Journal of Operational Research, Elsevier, vol. 176(3), pages 1387-1403, February.
    11. Masoud Yaghini & Mohammad Karimi & Mohadeseh Rahbar, 2015. "A set covering approach for multi-depot train driver scheduling," Journal of Combinatorial Optimization, Springer, vol. 29(3), pages 636-654, April.
    12. Camilo Ortiz-Astorquiza & Ivan Contreras & Gilbert Laporte, 2019. "An Exact Algorithm for Multilevel Uncapacitated Facility Location," Transportation Science, INFORMS, vol. 53(4), pages 1085-1106, July.
    13. Samir Elhedhli & Jean-Louis Goffin, 2005. "Efficient Production-Distribution System Design," Management Science, INFORMS, vol. 51(7), pages 1151-1164, July.
    14. Patrizia Beraldi & Andrzej Ruszczyński, 2002. "The Probabilistic Set-Covering Problem," Operations Research, INFORMS, vol. 50(6), pages 956-967, December.
    15. Wang, Yiyuan & Pan, Shiwei & Al-Shihabi, Sameh & Zhou, Junping & Yang, Nan & Yin, Minghao, 2021. "An improved configuration checking-based algorithm for the unicost set covering problem," European Journal of Operational Research, Elsevier, vol. 294(2), pages 476-491.
    16. Ivan Contreras & Jean-François Cordeau & Gilbert Laporte, 2011. "Benders Decomposition for Large-Scale Uncapacitated Hub Location," Operations Research, INFORMS, vol. 59(6), pages 1477-1490, December.
    17. Dimitris Bertsimas & Velibor V. Mišić, 2019. "Exact First-Choice Product Line Optimization," Operations Research, INFORMS, vol. 67(3), pages 651-670, May.
    18. Rahmaniani, Ragheb & Crainic, Teodor Gabriel & Gendreau, Michel & Rei, Walter, 2017. "The Benders decomposition algorithm: A literature review," European Journal of Operational Research, Elsevier, vol. 259(3), pages 801-817.
    19. Yu Zhou & Leishan Zhou & Yun Wang & Zhuo Yang & Jiawei Wu, 2017. "Application of Multiple-Population Genetic Algorithm in Optimizing the Train-Set Circulation Plan Problem," Complexity, Hindawi, vol. 2017, pages 1-14, July.
    20. Bernardes Real, Luiza & O'Kelly, Morton & de Miranda, Gilberto & Saraiva de Camargo, Ricardo, 2018. "The gateway hub location problem," Journal of Air Transport Management, Elsevier, vol. 73(C), pages 95-112.

    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:33:y:2017:i:1:d:10.1007_s10878-015-9935-1. 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.