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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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    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. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.

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