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Column generation in the integral simplex method

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  • Rönnberg, Elina
  • Larsson, Torbjörn

Abstract

The integral simplex method for set partitioning problems allows only pivots-on-one to be made, which results in a primal all-integer method. In this technical note we outline how to tailor the column generation principle to this method. Because of the restriction to pivots-on-one, only local optimality can be guaranteed, and to ensure global optimality we consider the use of implicit enumeration.

Suggested Citation

  • Rönnberg, Elina & Larsson, Torbjörn, 2009. "Column generation in the integral simplex method," European Journal of Operational Research, Elsevier, vol. 192(1), pages 333-342, January.
    • Handle: RePEc:eee:ejores:v:192:y:2009:i:1:p:333-342
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    References listed on IDEAS

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    1. Egon Balas & Manfred W. Padberg, 1972. "On the Set-Covering Problem," Operations Research, INFORMS, vol. 20(6), pages 1152-1161, December.
    2. Martin Savelsbergh, 1997. "A Branch-and-Price Algorithm for the Generalized Assignment Problem," Operations Research, INFORMS, vol. 45(6), pages 831-841, December.
    3. Marco E. Lübbecke & Jacques Desrosiers, 2005. "Selected Topics in Column Generation," Operations Research, INFORMS, vol. 53(6), pages 1007-1023, December.
    4. Sastry Trilochan, 1998. "One and Two Facility Network Design Revisited," IIMA Working Papers WP1998-08-05, Indian Institute of Management Ahmedabad, Research and Publication Department.
    5. Trilochan Sastry, 2001. "One and Two Facility Network Design Revisited," Annals of Operations Research, Springer, vol. 108(1), pages 19-31, November.
    6. Egon Balas & Manfred Padberg, 1975. "On the Set-Covering Problem: II. An Algorithm for Set Partitioning," Operations Research, INFORMS, vol. 23(1), pages 74-90, February.
    7. 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.
    8. Cynthia Barnhart & Ellis L. Johnson & George L. Nemhauser & Martin W. P. Savelsbergh & Pamela H. Vance, 1998. "Branch-and-Price: Column Generation for Solving Huge Integer Programs," Operations Research, INFORMS, vol. 46(3), pages 316-329, June.
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    Cited by:

    1. Adil Tahir & Guy Desaulniers & Issmail El Hallaoui, 2022. "Integral Column Generation for Set Partitioning Problems with Side Constraints," INFORMS Journal on Computing, INFORMS, vol. 34(4), pages 2313-2331, July.
    2. Rosat, Samuel & Quesnel, Frédéric & Elhallaoui, Issmail & Soumis, François, 2017. "Dynamic penalization of fractional directions in the integral simplex using decomposition: Application to aircrew scheduling," European Journal of Operational Research, Elsevier, vol. 263(3), pages 1007-1018.
    3. Rönnberg, Elina & Larsson, Torbjörn, 2014. "All-integer column generation for set partitioning: Basic principles and extensions," European Journal of Operational Research, Elsevier, vol. 233(3), pages 529-538.
    4. Adil Tahir & Guy Desaulniers & Issmail El Hallaoui, 2019. "Integral column generation for the set partitioning problem," EURO Journal on Transportation and Logistics, Springer;EURO - The Association of European Operational Research Societies, vol. 8(5), pages 713-744, December.
    5. Abdelouahab Zaghrouti & François Soumis & Issmail El Hallaoui, 2014. "Integral Simplex Using Decomposition for the Set Partitioning Problem," Operations Research, INFORMS, vol. 62(2), pages 435-449, April.
    6. Abdelouahab Zaghrouti & Issmail El Hallaoui & François Soumis, 2018. "Improved integral simplex using decomposition for the set partitioning problem," EURO Journal on Computational Optimization, Springer;EURO - The Association of European Operational Research Societies, vol. 6(2), pages 185-206, June.

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