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Combining Column Generation and Lagrangian Relaxation

29 Pages Posted: 26 Aug 2006  

Dennis Huisman

Erasmus University Rotterdam (EUR) - Department of Econometrics; Erasmus University Rotterdam (EUR) - Erasmus Center for Optimization in Public Transport (ECOPT)

Raf Jans

Erasmus University Rotterdam (EUR) - Rotterdam School of Management (RSM); HEC Montreal

Marc Peeters

Electrabel

Albert P. M. Wagelmans

Erasmus University Rotterdam (EUR) - Erasmus Center for Optimization in Public Transport (ECOPT); Erasmus University Rotterdam (EUR) - Department of Econometrics

Date Written: January 2003 1,

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.

Keywords: column generation, Lagrangean relaxation, lotsizing, vehicle and crew scheduling, cutting stock problem

JEL Classification: M, M11, C61, R4

Suggested Citation

Huisman, Dennis and Jans, Raf and Peeters, Marc and Wagelmans, Albert P. M., Combining Column Generation and Lagrangian Relaxation (January 2003 1,). ERIM Report Series Reference No. ERS-2003-092-LIS. Available at SSRN: https://ssrn.com/abstract=496704

Dennis Huisman (Contact Author)

Erasmus University Rotterdam (EUR) - Department of Econometrics ( email )

P.O. Box 1738
3000 DR Rotterdam
Netherlands
+31 10 408 1523 (Phone)
+31 10 408 9162 (Fax)

HOME PAGE: http://www.few.eur.nl/few/people/huisman/

Erasmus University Rotterdam (EUR) - Erasmus Center for Optimization in Public Transport (ECOPT)

3000 DR Rotterdam
Netherlands

Raf Jans

Erasmus University Rotterdam (EUR) - Rotterdam School of Management (RSM) ( email )

P.O. Box 1738
Room T08-21
3000 DR Rotterdam, 3000 DR
Netherlands

HEC Montreal ( email )

3000, Chemin de la Côte-Sainte-Catherine
Montreal, Quebec H2X 2L3
Canada
+1 514 340 6834 (Phone)

Marc Peeters

Electrabel ( email )

Place de L'Universite 16
1348 Louvain-La-Neuve
Belgium

Albert P. M. Wagelmans

Erasmus University Rotterdam (EUR) - Erasmus Center for Optimization in Public Transport (ECOPT) ( email )

3000 DR Rotterdam
Netherlands
+31 10 408 2576 (Phone)
+31 10 408 9162 (Fax)

Erasmus University Rotterdam (EUR) - Department of Econometrics

P.O. Box 1738
3000 DR Rotterdam
Netherlands

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