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Combining Column Generation and Lagrangian Relaxation

Author

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  • Huisman, D.
  • Jans, R.F.
  • Peeters, M.
  • Wagelmans, A.P.M.

Abstract

Although the possibility to combine column generation and Lagrangian relaxation has been known for quite some time, it has only recently been exploited in algorithms. In this paper, we discuss ways of combining these techniques. We focus on solving the LP relaxation of the Dantzig-Wolfe master problem. In a first approach we apply Lagrangian relaxation directly to this extended formulation, i.e. no simplex method is used. In a second one, we use Lagrangian relaxation to generate new columns, that is Lagrangian relaxation is applied to the compact for-mulation. We will illustrate the ideas behind these algorithms with an application in Lot-sizing. To show the wide applicability of these techniques, we also discuss applications in integrated vehicle and crew scheduling, plant location and cutting stock problems.

Suggested Citation

  • Huisman, D. & Jans, R.F. & Peeters, M. & Wagelmans, A.P.M., 2003. "Combining Column Generation and Lagrangian Relaxation," ERIM Report Series Research in Management ERS-2003-092-LIS, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam.
    • Handle: RePEc:ems:eureri:1098
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    References listed on IDEAS

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    Cited by:

    1. Silvio Alexandre de Araujo & Bert De Reyck & Zeger Degraeve & Ioannis Fragkos & Raf Jans, 2015. "Period Decompositions for the Capacitated Lot Sizing Problem with Setup Times," INFORMS Journal on Computing, INFORMS, vol. 27(3), pages 431-448, August.
    2. Huisman, D., 2005. "A column generation approach to solve the crew re-scheduling problem," Econometric Institute Research Papers EI 2005-54, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    3. Zeger Degraeve & Raf Jans, 2007. "A New Dantzig-Wolfe Reformulation and Branch-and-Price Algorithm for the Capacitated Lot-Sizing Problem with Setup Times," Operations Research, INFORMS, vol. 55(5), pages 909-920, October.
    4. Lucas P. Veelenturf & Daniel Potthoff & Dennis Huisman & Leo G. Kroon & Gábor Maróti & Albert P. M. Wagelmans, 2016. "A Quasi-Robust Optimization Approach for Crew Rescheduling," Transportation Science, INFORMS, vol. 50(1), pages 204-215, February.
    5. Annette Chmielewski & Boris Naujoks & Michael Janas & Uwe Clausen, 2009. "Optimizing the Door Assignment in LTL-Terminals," Transportation Science, INFORMS, vol. 43(2), pages 198-210, May.
    6. Veelenturf, L.P. & Potthoff, D. & Huisman, D. & Kroon, L.G. & Maróti, G. & Wagelmans, A.P.M., 2013. "A Quasi-Robust Optimization Approach for Resource Rescheduling," Econometric Institute Research Papers 50110, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    7. Ingmar Steinzen & Vitali Gintner & Leena Suhl & Natalia Kliewer, 2010. "A Time-Space Network Approach for the Integrated Vehicle- and Crew-Scheduling Problem with Multiple Depots," Transportation Science, INFORMS, vol. 44(3), pages 367-382, August.
    8. Eliashberg, J. & Hegie, Q. & Ho, J. & Huisman, D. & Miller, S.J. & Swami, S. & Weinberg, C.B. & Wierenga, B., 2007. "Demand-driven scheduling of movies in a multiplex," Econometric Institute Research Papers EI 2007-17, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.

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    More about this item

    Keywords

    Lagrangean relaxation; column generation; cutting stock problem; lotsizing; vehicle and crew scheduling;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • M - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics
    • M11 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Business Administration - - - Production Management
    • R4 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - Transportation Economics

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