Cutting Planes for Branch-and-Price Algorithms

Publication: Research - peer-reviewJournal article – Annual report year: 2011

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This article presents a general framework for formulating cutting planes in the context of column generation for integer programs. Valid inequalities can be derived using the variables of an equivalent compact formulation (i.e., the subproblem variables) or the master problem variables. In the first case, cuts are added to the compact formulation, either at the master level or the subproblem level, and the decomposition process is reapplied. In the second case, we show that it is possible to model inequalities defined on the master problem variables by adding new variables and constraints to the subproblem formulation. The augmented subproblem indirectly indicates that there exists an augmented compact formulation that includes these new variables and constraints. Three examples on how to apply this framework are presented: the vehicle routing problem with time windows, the edge coloring problem, and the cutting stock problem. © 2011 Wiley Periodicals, Inc. NETWORKS, Vol. 58(4), 301–310 2011
Original languageEnglish
JournalNetworks
Publication dateNov 2011
Volume58
Journal number4
Pages301-310
ISSN0028-3045
DOIs
StatePublished
CitationsWeb of Science® Times Cited: No match on DOI

Keywords

  • column generation, integer programming, cutting planes, Dantzig-Wolfe decomposition
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