IDEAS home Printed from https://ideas.repec.org/a/spr/annopr/v166y2009i1p203-22210.1007-s10479-008-0409-z.html
   My bibliography  Save this article

Modelling either-or relations in integer programming

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10479-008-0409-z
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10479-008-0409-z?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. 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.
    2. 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.
    3. 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.
    4. Monique Guignard & Ellis Johnson & Kurt Spielberg, 2005. "Logical Processing for Integer Programming," Annals of Operations Research, Springer, vol. 140(1), pages 263-304, November.
    5. 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).
    6. 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.
    7. 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.
    8. 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.
    9. Beaumont, Nicholas, 1990. "An algorithm for disjunctive programs," European Journal of Operational Research, Elsevier, vol. 48(3), pages 362-371, October.
    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. John N. Hooker, 2002. "Logic, Optimization, and Constraint Programming," INFORMS Journal on Computing, INFORMS, vol. 14(4), pages 295-321, November.
    2. Yannis Pavlis & Will Recker, 2009. "A Mathematical Logic Approach for the Transformation of the Linear Conditional Piecewise Functions of Dispersion-and-Store and Cell Transmission Traffic Flow Models into Linear Mixed-Integer Form," Transportation Science, INFORMS, vol. 43(1), pages 98-116, February.
    3. Maenhout, Broos & Vanhoucke, Mario, 2010. "A hybrid scatter search heuristic for personalized crew rostering in the airline industry," European Journal of Operational Research, Elsevier, vol. 206(1), pages 155-167, October.
    4. Tsoukias, Alexis, 2008. "From decision theory to decision aiding methodology," European Journal of Operational Research, Elsevier, vol. 187(1), pages 138-161, May.
    5. Tallys Yunes & Ionuţ D. Aron & J. N. Hooker, 2010. "An Integrated Solver for Optimization Problems," Operations Research, INFORMS, vol. 58(2), pages 342-356, April.
    6. Vipul Jain & Ignacio E. Grossmann, 2001. "Algorithms for Hybrid MILP/CP Models for a Class of Optimization Problems," INFORMS Journal on Computing, INFORMS, vol. 13(4), pages 258-276, November.
    7. Pascal Van Hentenryck, 2002. "Constraint and Integer Programming in OPL," INFORMS Journal on Computing, INFORMS, vol. 14(4), pages 345-372, November.
    8. Moeini, Asghar., 2017. "Identification of unidentified equality constraints for integer programming problems," European Journal of Operational Research, Elsevier, vol. 260(2), pages 460-467.
    9. Dan A. Iancu & Marek Petrik & Dharmashankar Subramanian, 2015. "Tight Approximations of Dynamic Risk Measures," Mathematics of Operations Research, INFORMS, vol. 40(3), pages 655-682, March.
    10. STEPHAN, Rüdiger, 2010. "An extension of disjunctive programming and its impact for compact tree formulations," LIDAM Discussion Papers CORE 2010045, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    11. I. R. De Farias & E. L. Johnson & G. L. Nemhauser, 2002. "Facets of the Complementarity Knapsack Polytope," Mathematics of Operations Research, INFORMS, vol. 27(1), pages 210-226, February.
    12. repec:ehu:biltok:5576 is not listed on IDEAS
    13. Plastria, Frank, 2002. "Formulating logical implications in combinatorial optimisation," European Journal of Operational Research, Elsevier, vol. 140(2), pages 338-353, July.
    14. Atoosa Kasirzadeh & Mohammed Saddoune & François Soumis, 2017. "Airline crew scheduling: models, algorithms, and data sets," EURO Journal on Transportation and Logistics, Springer;EURO - The Association of European Operational Research Societies, vol. 6(2), pages 111-137, June.
    15. Brailsford, Sally C. & Potts, Chris N. & Smith, Barbara M., 1999. "Constraint satisfaction problems: Algorithms and applications," European Journal of Operational Research, Elsevier, vol. 119(3), pages 557-581, December.
    16. Filipa D. Carvalho & Maria Teresa Almeida, 2017. "The triangle k-club problem," Journal of Combinatorial Optimization, Springer, vol. 33(3), pages 814-846, April.
    17. Peter Kirst & Fabian Rigterink & Oliver Stein, 2017. "Global optimization of disjunctive programs," Journal of Global Optimization, Springer, vol. 69(2), pages 283-307, October.
    18. Ioannis Mourtos, 2016. "Cardinality constraints and systems of restricted representatives," Journal of Combinatorial Optimization, Springer, vol. 31(3), pages 1061-1089, April.
    19. Nishi, Tatsushi & Sugiyama, Taichi & Inuiguchi, Masahiro, 2014. "Two-level decomposition algorithm for crew rostering problems with fair working condition," European Journal of Operational Research, Elsevier, vol. 237(2), pages 465-473.
    20. Taccari, Leonardo, 2016. "Integer programming formulations for the elementary shortest path problem," European Journal of Operational Research, Elsevier, vol. 252(1), pages 122-130.

    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:annopr:v:166:y:2009:i:1:p:203-222:10.1007/s10479-008-0409-z. 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.