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A Primer in Column Generation

In: Column Generation

Author

Listed:
  • Jacques Desrosiers

    (HEC Montréal and GERAD)

  • Marco E. Lübbecke

    (Technische Universität Berlin)

Abstract

We give a didactic introduction to the use of the column generation technique in linear and in particular in integer programming. We touch on both, the relevant basic theory and more advanced ideas which help in solving large scale practical problems. Our discussion includes embedding Dantzig-Wolfe decomposition and Lagrangian relaxation within a branch-and-bound framework, deriving natural branching and cutting rules by means of a so-called compact formulation, and understanding and influencing the behavior of the dual variables during column generation. Most concepts are illustrated via a small example. We close with a discussion of the classical cutting stock problem and some suggestions for further reading.

Suggested Citation

  • Jacques Desrosiers & Marco E. Lübbecke, 2005. "A Primer in Column Generation," Springer Books, in: Guy Desaulniers & Jacques Desrosiers & Marius M. Solomon (ed.), Column Generation, chapter 0, pages 1-32, Springer.
    • Handle: RePEc:spr:sprchp:978-0-387-25486-9_1
    DOI: 10.1007/0-387-25486-2_1
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    Cited by:

    1. Flores-Quiroz, Angela & Strunz, Kai, 2021. "A distributed computing framework for multi-stage stochastic planning of renewable power systems with energy storage as flexibility option," Applied Energy, Elsevier, vol. 291(C).
    2. Beraudy, Sébastien & Absi, Nabil & Dauzère-Pérès, Stéphane, 2022. "Timed route approaches for large multi-product multi-step capacitated production planning problems," European Journal of Operational Research, Elsevier, vol. 300(2), pages 602-614.
    3. Feng, Tao & Lusby, Richard M. & Zhang, Yongxiang & Peng, Qiyuan, 2024. "Integrating train service route design with passenger flow allocation for an urban rail transit line," European Journal of Operational Research, Elsevier, vol. 313(1), pages 146-170.
    4. Fowler, John W. & Mönch, Lars, 2022. "A survey of scheduling with parallel batch (p-batch) processing," European Journal of Operational Research, Elsevier, vol. 298(1), pages 1-24.
    5. Pan, Hanchuan & Liu, Zhigang & Yang, Lixing & Liang, Zhe & Wu, Qiang & Li, Sijie, 2021. "A column generation-based approach for integrated vehicle and crew scheduling on a single metro line with the fully automatic operation system by partial supervision," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 152(C).
    6. Blanco, Víctor & Gázquez, Ricardo & Ponce, Diego & Puerto, Justo, 2023. "A branch-and-price approach for the continuous multifacility monotone ordered median problem," European Journal of Operational Research, Elsevier, vol. 306(1), pages 105-126.
    7. F M Zeghal & M Haouari & H D Sherali & N Aissaoui, 2011. "Flexible aircraft fleeting and routing at TunisAir," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 62(2), pages 368-380, February.
    8. Justkowiak, Jan-Erik & Pesch, Erwin, 2023. "A column generation driven heuristic for order-scheduling and rack-sequencing in robotic mobile fulfillment systems," Omega, Elsevier, vol. 120(C).
    9. Christiane B. Haubitz & Ulrich W. Thonemann, 2021. "How to Change a Running System—Controlling the Transition to Optimized Spare Parts Inventory Policies," Production and Operations Management, Production and Operations Management Society, vol. 30(5), pages 1386-1405, May.
    10. Hagspihl, Thomas & Kolisch, Rainer & Ruf, Christian & Schiffels, Sebastian, 2022. "Dynamic gate configurations at airports: A network optimization approach," European Journal of Operational Research, Elsevier, vol. 301(3), pages 1133-1148.
    11. Benati, Stefano & Ponce, Diego & Puerto, Justo & Rodríguez-Chía, Antonio M., 2022. "A branch-and-price procedure for clustering data that are graph connected," European Journal of Operational Research, Elsevier, vol. 297(3), pages 817-830.
    12. Denissa Sari Darmawi Purba & Eleftheria Kontou & Chrysafis Vogiatzis, 2021. "Evacuation Route Planning for Alternative Fuel Vehicles," Papers 2109.01578, arXiv.org, revised May 2022.
    13. Wang, Tingsong & Meng, Qiang & Tian, Xuecheng, 2024. "Dynamic container slot allocation for a liner shipping service," Transportation Research Part B: Methodological, Elsevier, vol. 179(C).
    14. Mariana Escallón-Barrios & Daniel Castillo-Gomez & Jorge Leal & Carlos Montenegro & Andrés L. Medaglia, 2022. "Improving harvesting operations in an oil palm plantation," Annals of Operations Research, Springer, vol. 314(2), pages 411-449, July.
    15. Wang, Julong & Liu, Zhixue & Li, Feng, 2024. "Integrated production and transportation scheduling problem under nonlinear cost structures," European Journal of Operational Research, Elsevier, vol. 313(3), pages 883-904.
    16. Potthoff, D. & Huisman, D. & Desaulniers, G., 2008. "Column generation with dynamic duty selection for railway crew rescheduling," Econometric Institute Research Papers EI 2008-28, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    17. Haouari, Mohamed & Mhiri, Mariem, 2024. "Lower and upper bounding procedures for the bin packing problem with concave loading cost," European Journal of Operational Research, Elsevier, vol. 312(1), pages 56-69.
    18. Pan, Hanchuan & Yang, Lixing & Liang, Zhe, 2023. "Demand-oriented integration optimization of train timetabling and rolling stock circulation planning with flexible train compositions: A column-generation-based approach," European Journal of Operational Research, Elsevier, vol. 305(1), pages 184-206.
    19. Harwin de Vries & Joris van de Klundert & Albert Wagelmans, 2021. "Toward Elimination of Infectious Diseases with Mobile Screening Teams: HAT in the DRC," Production and Operations Management, Production and Operations Management Society, vol. 30(10), pages 3408-3428, October.
    20. Barbato, Michele & Ceselli, Alberto & Premoli, Marco, 2023. "On the impact of resource relocation in facing health emergencies," European Journal of Operational Research, Elsevier, vol. 308(1), pages 422-435.
    21. Thomas W.M. Vossen & Fan You & Dan Zhang, 2022. "Finite‐horizon approximate linear programs for capacity allocation over a rolling horizon," Production and Operations Management, Production and Operations Management Society, vol. 31(5), pages 2127-2142, May.
    22. Delle Donne, Diego & Alfandari, Laurent & Archetti, Claudia & Ljubić, Ivana, 2023. "Freight-on-Transit for urban last-mile deliveries: A strategic planning approach," Transportation Research Part B: Methodological, Elsevier, vol. 169(C), pages 53-81.
    23. Alessandro Druetto & Erica Pastore & Elena Rener, 2023. "Parallel batching with multi-size jobs and incompatible job families," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(2), pages 440-458, July.
    24. Veelenturf, L.P. & Potthoff, D. & Huisman, D. & Kroon, L.G., 2009. "Railway Crew Rescheduling with Retiming," Econometric Institute Research Papers EI 2009-24, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    25. Thomas, Anu & Venkateswaran, Jayendran & Singh, Gaurav & Krishnamoorthy, Mohan, 2014. "A resource constrained scheduling problem with multiple independent producers and a single linking constraint: A coal supply chain example," European Journal of Operational Research, Elsevier, vol. 236(3), pages 946-956.

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