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All-integer column generation for set partitioning: Basic principles and extensions

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  • Rönnberg, Elina
  • Larsson, Torbjörn

Abstract

Column generation, combined with an appropriate integer programming technique, has shown to be a powerful tool for solving huge integer programmes arising in various applications. In these column generation approaches, the master problem is often of a set partitioning type.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:ejores:v:233:y:2014:i:3:p:529-538
    DOI: 10.1016/j.ejor.2013.08.036
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    References listed on IDEAS

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    1. Dennis J. Sweeney & Richard A. Murphy, 1979. "A Method of Decomposition for Integer Programs," Operations Research, INFORMS, vol. 27(6), pages 1128-1141, December.
    2. 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.
    3. Michel Gamache & François Soumis & Gérald Marquis & Jacques Desrosiers, 1999. "A Column Generation Approach for Large-Scale Aircrew Rostering Problems," Operations Research, INFORMS, vol. 47(2), pages 247-263, April.
    4. Marco E. Lübbecke & Jacques Desrosiers, 2005. "Selected Topics in Column Generation," Operations Research, INFORMS, vol. 53(6), pages 1007-1023, December.
    5. 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.
    6. H.A. Eiselt & C.‐L. Sandblom, 1985. "External Pivoting In The Simplex Algorithm," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 39(4), pages 327-341, December.
    7. Egon Balas & Manfred W. Padberg, 1972. "On the Set-Covering Problem," Operations Research, INFORMS, vol. 20(6), pages 1152-1161, December.
    8. Torbjörn Larsson & Michael Patriksson, 2006. "Global Optimality Conditions for Discrete and Nonconvex Optimization---With Applications to Lagrangian Heuristics and Column Generation," Operations Research, INFORMS, vol. 54(3), pages 436-453, 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. Siqi Guo & Fan Xiao & Zhe Liang, 2025. "Nested Set-Covering/Packing Problem: Degeneracy Alleviation and Dual Stabilization," Operations Research, INFORMS, vol. 73(6), pages 2886-2913, November.
    3. Wang, Dian & D’Ariano, Andrea & Zhao, Jun & Zhan, Shuguang & Peng, Qiyuan, 2024. "Joint rolling stock rotation planning and depot deadhead scheduling in complicated urban rail transit lines," European Journal of Operational Research, Elsevier, vol. 314(2), pages 665-684.
    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.

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