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Combining Column Generation and Lagrangian Relaxation

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Column Generation

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 formulation. 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.

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Author information

Authors and Affiliations

  1. Erasmus University Rotterdam, The Netherlands

    Dennis Huisman, Raf Jans & Albert P.M. Wagelmans

  2. Place de L’Université 16, Belgium

    Marc Peeters

Authors
  1. Dennis Huisman
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  2. Raf Jans
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  3. Marc Peeters
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  4. Albert P.M. Wagelmans
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Editor information

Editors and Affiliations

  1. GERAD and École Polytechnique de Montréal, Canada

    Guy Desaulniers

  2. GERAD and HEC Montréal, Canada

    Jacques Desrosiers

  3. GERAD and Northeastern University, Boston

    Marius M. Solomon

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© 2005 Springer Science+Business Media, Inc.

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Huisman, D., Jans, R., Peeters, M., Wagelmans, A.P. (2005). Combining Column Generation and Lagrangian Relaxation. In: Desaulniers, G., Desrosiers, J., Solomon, M.M. (eds) Column Generation. Springer, Boston, MA. https://doi.org/10.1007/0-387-25486-2_9

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