Classification of Dantzig–Wolfe reformulations for binary mixed integer programming problems

In this note, we provide a classification of Dantzig–Wolfe reformulations for Binary Mixed Integer Programming Problems. We specifically focus on modeling the binary conditions in the convexification approach to the Dantzig–Wolfe decomposition. For a general Binary Mixed Integer Programming problem,...

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Bibliographic Details
Published in:European journal of operational research Vol. 204; no. 2; pp. 251 - 254
Main Author: Jans, Raf
Format: Journal Article
Language:English
Published: Amsterdam Elsevier B.V 16.07.2010
Elsevier
Elsevier Sequoia S.A
Series:European Journal of Operational Research
Subjects:
Applied sciences
Classification
Dantzig–Wolfe decomposition
Exact sciences and technology
Feasibility
Integer programming
Mathematical programming
Mixed integer programming
Mixed integer programming Dantzig-Wolfe decomposition Reformulation
Operational research and scientific management
Operational research. Management science
Reformulation
Studies
Dantzig–Wolfe decomposition
Mixed integer programming
Reformulation
Column generation
Zero one programming
Extremum
Classification
Linear programming
Dantzig-Wolfe decomposition
Modeling
ISSN:0377-2217, 1872-6860
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Summary:In this note, we provide a classification of Dantzig–Wolfe reformulations for Binary Mixed Integer Programming Problems. We specifically focus on modeling the binary conditions in the convexification approach to the Dantzig–Wolfe decomposition. For a general Binary Mixed Integer Programming problem, an extreme point of the overall problem does not necessarily correspond to an extreme point of the subproblem. Therefore, the binary conditions cannot in general be imposed on the new master problem variables but must be imposed on the original binary variables. In some cases, however, it is possible to impose the binary restrictions directly on the new master problem variables. The issue of imposing binary conditions on the original variables versus the master problem variables has not been discussed systematically for MIP problems in general in the literature and most of the research has been focused on the pure binary case. The classification indicates in which cases you can, and cannot, impose binary conditions on the new master problem variables.
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ISSN:0377-2217
1872-6860
DOI:10.1016/j.ejor.2009.11.014