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Solving market split problems with heuristical lattice reduction

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  • Heiko Vogel

Abstract

The market sharing problem was proposed by M. Dawande and G. Cornuéjols (INFORMS J. Comput. 11, 1999 ) to compare the performance of linear integer programming algorithms. Haibo Wang (Manuscript No. 251, Annuals of Operations Research, 2008 ) examined some hard instances of these problems and reported the results he obtained with the commercially available program CPLEX. This paper first describes a model, which allows to embed integer programs with inequalities into a lattice and then reports the progress with Wang’s instances, by using a lattice based algorithm which employs a new heuristical sieving procedure. These results are compared to recent CPLEX 12.0 benchmarks. Copyright Springer Science+Business Media, LLC 2012

Suggested Citation

  • Heiko Vogel, 2012. "Solving market split problems with heuristical lattice reduction," Annals of Operations Research, Springer, vol. 196(1), pages 581-590, July.
    • Handle: RePEc:spr:annopr:v:196:y:2012:i:1:p:581-590:10.1007/s10479-012-1143-0
    DOI: 10.1007/s10479-012-1143-0
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    References listed on IDEAS

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    1. Alfred Wassermann, 2002. "Attacking the Market Split Problem with Lattice Point Enumeration," Journal of Combinatorial Optimization, Springer, vol. 6(1), pages 5-16, March.
    2. Gérard Cornuéjols & Milind Dawande, 1999. "A Class of Hard Small 0-1 Programs," INFORMS Journal on Computing, INFORMS, vol. 11(2), pages 205-210, May.
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