Mathematical Programming

, Volume 112, Issue 1, pp 3–44 | Cite as

Valid inequalities for mixed integer linear programs



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.


Mixed integer linear program Lift-and-project Split cut Gomory cut Mixed integer rounding Elementary closure Polyhedra Union of polyhedra 

Mathematics Subject Classification (2000)

90C10 90C11 90C57 


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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

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