Standard Article

Lifting Techniques For Mixed Integer Programming

  1. Jean-Philippe P. Richard

Published Online: 15 FEB 2011

DOI: 10.1002/9780470400531.eorms0464

Wiley Encyclopedia of Operations Research and Management Science

Wiley Encyclopedia of Operations Research and Management Science

How to Cite

Richard, J.-P. P. 2011. Lifting Techniques For Mixed Integer Programming. Wiley Encyclopedia of Operations Research and Management Science. .

Author Information

  1. University of Florida, Department of Industrial and Systems Engineering, Gainesville, Florida

Publication History

  1. Published Online: 15 FEB 2011

Abstract

This article provides a review of lifting techniques for the generation of cutting planes in mixed integer programming. After motivating the notion of lifting graphically, four key steps in the derivation of lifted inequalities are described: (i) variables fixing, (ii) derivation of seed inequalities, (iii) (re-)computation of lifting functions, and (iv) derivation of lifting coefficients. Practical considerations that are relevant to each of these steps are discussed and is emphasized the importance of superadditivity in designing efficient lifting procedures. This concluded with a description of the strength of lifted cuts. Throughout, concepts on a simple example are illustrated.

Keywords:

  • mixed integer programs;
  • cutting planes;
  • facet;
  • lifting techniques;
  • superadditive lifting