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A Branch & Cut algorithm for a four-index assignment problem

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  • G Appa

    (London School of Economics)

  • D Magos

    (Technological Educational Institute of Athens)

  • I Mourtos

    (London School of Economics)

Abstract

In this paper, we examine the orthogonal Latin squares (OLS) problem from an integer programming perspective. The OLS problem has a long history and its significance arises from both theoretical aspects and practical applications. The problem is formulated as a four-index assignment problem whose solutions correspond to OLS. This relationship is exploited by various routines (preliminary variable fixing, branching, etc) of the Branch & Cut algorithm we present. Clique, odd-hole and antiweb inequalities implement the ‘Cut’ component of the algorithm. For each cut type a polynomial-time separation algorithm is implemented. Extensive computational analysis examines multiple aspects concerning the design of our algorithm. The results illustrate clearly the improvement achieved over simple Branch & Bound.

Suggested Citation

  • G Appa & D Magos & I Mourtos, 2004. "A Branch & Cut algorithm for a four-index assignment problem," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 55(3), pages 298-307, March.
    • Handle: RePEc:pal:jorsoc:v:55:y:2004:i:3:d:10.1057_palgrave.jors.2601655
    DOI: 10.1057/palgrave.jors.2601655
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    References listed on IDEAS

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    1. Egon Balas & Matthew J. Saltzman, 1991. "An Algorithm for the Three-Index Assignment Problem," Operations Research, INFORMS, vol. 39(1), pages 150-161, February.
    2. Karla L. Hoffman & Manfred Padberg, 1993. "Solving Airline Crew Scheduling Problems by Branch-and-Cut," Management Science, INFORMS, vol. 39(6), pages 657-682, June.
    3. Magos, D. & Miliotis, P., 1994. "An algorithm for the planar three-index assignment problem," European Journal of Operational Research, Elsevier, vol. 77(1), pages 141-153, August.
    4. Atamturk, Alper & Nemhauser, George L. & Savelsbergh, Martin W. P., 2000. "Conflict graphs in solving integer programming problems," European Journal of Operational Research, Elsevier, vol. 121(1), pages 40-55, February.
    5. Egon Balas & Sebastián Ceria & Gérard Cornuéjols, 1996. "Mixed 0-1 Programming by Lift-and-Project in a Branch-and-Cut Framework," Management Science, INFORMS, vol. 42(9), pages 1229-1246, September.
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    Cited by:

    1. Appa, G. & Magos, D. & Mourtos, I., 2006. "Searching for Mutually Orthogonal Latin Squares via integer and constraint programming," European Journal of Operational Research, Elsevier, vol. 173(2), pages 519-530, September.
    2. Zhang, Abraham & Luo, Hao & Huang, George Q., 2013. "A bi-objective model for supply chain design of dispersed manufacturing in China," International Journal of Production Economics, Elsevier, vol. 146(1), pages 48-58.

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