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Modelling either-or relations in integer programming

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  • L. Foulds
  • B. Toklu
  • J. Wilson

Abstract

Logical relations occur frequently in integer programming problems and are modelled by introducing binary variables in association with linear expressions. Applications requiring constraints involving precedence, exclusion, implication and other conditions give rise to the logical relations OR and IMPLIES in the models. These relations will be considered in this paper from a modelling point of view and formulations investigated for situations where the logical variables link sets of integer variables. Valid inequalities (cuts) that can be added to a model will be developed for a number of the formulations and the computational benefits of these cuts will be considered from an experimental point of view by considering the performance of sets of problem instances. New formulations and combinations of older established formulations will be considered. It will be contended that tight formulations may not always be the most successful. Copyright Springer Science+Business Media, LLC 2009

Suggested Citation

  • L. Foulds & B. Toklu & J. Wilson, 2009. "Modelling either-or relations in integer programming," Annals of Operations Research, Springer, vol. 166(1), pages 203-222, February.
    • Handle: RePEc:spr:annopr:v:166:y:2009:i:1:p:203-222:10.1007/s10479-008-0409-z
    DOI: 10.1007/s10479-008-0409-z
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    References listed on IDEAS

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    1. Williams, H. P. & Brailsford, S. C., 1997. "The splitting of variables and constraints in the formulation of integer programming models," European Journal of Operational Research, Elsevier, vol. 100(3), pages 623-628, August.
    2. Egon Balas, 2005. "Projection, Lifting and Extended Formulation in Integer and Combinatorial Optimization," Annals of Operations Research, Springer, vol. 140(1), pages 125-161, November.
    3. Mitra, G. & Lucas, C. & Moody, S. & Hadjiconstantinou, E., 1994. "Tools for reformulating logical forms into zero-one mixed integer programs," European Journal of Operational Research, Elsevier, vol. 72(2), pages 262-276, January.
    4. A Volgenant & A de Waal, 2006. "A heuristic for multiple-feeder PCB manufacturing," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 57(9), pages 1134-1141, September.
    5. Alexander Bockmayr & Thomas Kasper, 1998. "Branch and Infer: A Unifying Framework for Integer and Finite Domain Constraint Programming," INFORMS Journal on Computing, INFORMS, vol. 10(3), pages 287-300, August.
    6. Beaumont, Nicholas, 1990. "An algorithm for disjunctive programs," European Journal of Operational Research, Elsevier, vol. 48(3), pages 362-371, October.
    7. BALAS, Egon & BOCKMAYR, Alexander & PISARUK, Nicolai & WOLSEY, Laurence, 2002. "On unions and dominants of polytopes," LIDAM Discussion Papers CORE 2002008, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    8. Meinolf Sellmann & Kyriakos Zervoudakis & Panagiotis Stamatopoulos & Torsten Fahle, 2002. "Crew Assignment via Constraint Programming: Integrating Column Generation and Heuristic Tree Search," Annals of Operations Research, Springer, vol. 115(1), pages 207-225, September.
    9. Monique Guignard & Ellis Johnson & Kurt Spielberg, 2005. "Logical Processing for Integer Programming," Annals of Operations Research, Springer, vol. 140(1), pages 263-304, November.
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