Cutting planes in integer and mixed integer programming

Authors:
Hugues Marchand;Alexander Martin;Robert Weismantel;Laurence Wolsey
Affiliations:
Electrabel, Boulevard du Regent 8, 1000 Brussels, Belgium;Fachbereich Mathematik, Technische Universität Darmstadt, Schlossgartenstr, 7, 64289 Darmstadt, Germany;Fakultät för Mathematik, IMO Otto-von-Guericke Universität Magdeburg Universitätsplatz 2 D-39106 Magdeburg, Germany;CORE and INMA, Universit́ Catholique de Louvain, 1348 Louvain-la-Neuve, Belgium
Venue:
Discrete Applied Mathematics
Year:
2002

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Abstract

This survey presents cutting planes that are useful or potentially useful in solving mixed integer programs. Valid inequalities for (i) general integer programs, (ii) problems with local structure such as knapsack constraints, and (iii) problems with 0-1 coefficient matrices, such as set packing, are examined in turn. Finally, the use of valid inequalities for classes of problems with structure, such as network design, is explored.