Selected Topics in Column Generation

Marco E. Luebbecke (m.luebbeckemath.tu-berlin.de)
Jacques Desrosiers (jacques.desrosiershec.ca)

Abstract: Dantzig-Wolfe decomposition and column generation, devised for linear programs, is a success story in large scale integer programming. We outline and relate the approaches, and survey mainly recent contributions, not found in textbooks, yet. We emphasize on the growing understanding of the dual point of view, which brought considerable progress to the column generation theory and practice. It stimulated careful initializations, sophisticated solution techniques for restricted master problem and subproblem, as well as better overall performance. Thus, the dual perspective is an ever recurring concept in our selected topics.

Keywords: Linear programming; integer programming; Dantzig-Wolfe decomposition; column generation; Lagrangian relaxation; branch-and-bound

Category 1: Integer Programming ((Mixed) Integer Linear Programming )

Citation: Les Cahiers de GERAD G-2002-64, Group for Research in Decision Analysis, Montreal, Canada, December 2002, revised 2004. To appear in Operations Research

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Entry Submitted: 12/09/2002
Entry Accepted: 12/09/2002
Entry Last Modified: 04/12/2005

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