Mathematical Programming

, Volume 112, Issue 1, pp 3–44

Valid inequalities for mixed integer linear programs

FULL LENGTH PAPER

DOI: 10.1007/s10107-006-0086-0

Cite this article as:
Cornuéjols, G. Math. Program. (2008) 112: 3. doi:10.1007/s10107-006-0086-0

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.

Keywords

Mixed integer linear programLift-and-projectSplit cutGomory cutMixed integer roundingElementary closurePolyhedraUnion of polyhedra

Mathematics Subject Classification (2000)

90C1090C1190C57

Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  1. 1.Tepper School of BusinessCarnegie Mellon UniversityPittsburghUSA
  2. 2.LIF, Faculté des Sciences de LuminyUniversité d’ Aix-MarseilleMarseilleFrance