An exact algorithm for IP column generation

Authors:
François Vanderbeck;Laurence A. Wolsey
Affiliations:
Department of Engineering and Judge Institute of Management Studies, Cambridge University, Trumpington Street, Cambridge CB2 1AG, UK;CORE, Université Catholique de Louvain, Voie du Roman Pays 34, B-1348 Louvain-la-Neuve, Belgium
Venue:
Operations Research Letters
Year:
1996

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Abstract

An exact column generation algorithm for integer programs with a large (implicit) number of columns is presented. The family of problems that can be treated includes not only standard partitioning problems such as bin packing and certain vehicle routing problems in which the columns generated have 0-1 compenents and a right-hand side vector of 1's, but also the cutting stock problem in which the columns and right-hand side are nonnegative integer vectors. We develop a combined branching and subproblem modification scheme that generalizes existing approaches, and also describe the use of lower bounds to reduce tailing-off effects.