Combining Column Generation and Lagrangian Relaxation

Dennis Huisman (), Raf Jans (), Marc Peeters () and Albert P.M. Wagelmans ()
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Dennis Huisman: Erasmus University Rotterdam
Raf Jans: Erasmus University Rotterdam
Albert P.M. Wagelmans: Erasmus University Rotterdam

Chapter Chapter 9 in Column Generation, 2005, pp 247-270 from Springer

Abstract: 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.

Keywords: Column Generation; Master Problem; Lagrangian Relaxation; Crew Schedule; Restricted Master Problem (search for similar items in EconPapers)
Date: 2005
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Citations: View citations in EconPapers (15)

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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-0-387-25486-9_9

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DOI: 10.1007/0-387-25486-2_9

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