Valid inequalities for mixed integer linear programs

Authors:
Gérard Cornuéjols
Affiliations:
Carnegie Mellon University, Tepper School of Business, 15213, Pittsburgh, PA, USA and Université d’ Aix-Marseille, LIF, Faculté des Sciences de Luminy, 13288, Marseille, Franc ...
Venue:
Mathematical Programming: Series A and B
Year:
2007

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Abstract

This tutorial presents a theory of valid inequalities for mixed integer linear sets. It introduces the necessary tools from polyhedral theory and gives a geometric understanding of several classical families of valid inequalities such as lift-and-project cuts, Gomory mixed integer cuts, mixed integer rounding cuts, split cuts and intersection cuts, and it reveals the relationships between these families. The tutorial also discusses computational aspects of generating the cuts and their strength.