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Benders decomposition for set covering problems

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  • 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
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    References listed on IDEAS

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    1. 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.
    2. A. M. Geoffrion & G. W. Graves, 1974. "Multicommodity Distribution System Design by Benders Decomposition," Management Science, INFORMS, vol. 20(5), pages 822-844, January.
    3. 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.
    4. 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.
    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.
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