Mathematical Programming

, Volume 98, Issue 1–3, pp 89–113 | Cite as

Lifted inequalities for 0-1 mixed integer programming: Basic theory and algorithms

  • J.-P.P. Richard
  • I.R. de Farias Jr
  • G.L. Nemhauser
Article

Abstract.

We study the mixed 0-1 knapsack polytope, which is defined by a single knapsack constraint that contains 0-1 and bounded continuous variables. We develop a lifting theory for the continuous variables. In particular, we present a pseudo-polynomial algorithm for the sequential lifting of the continuous variables and we discuss its practical use.

Keywords

0-1 mixed integer programming polyhedral theory lifting 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • J.-P.P. Richard
    • 1
  • I.R. de Farias Jr
    • 2
  • G.L. Nemhauser
    • 3
  1. 1.School of Industrial and Systems EngineeringGeorgia Institute of TechnologyAtlantaUSA
  2. 2.Center for Operations Research and EconometricsLouvain-La-NeuveBelgium
  3. 3.School of Industrial and Systems EngineeringGeorgia Institute of TechnologyAtlantaUSA

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