Quarterly Journal of the Belgian, French and Italian Operations Research Societies

, Volume 1, Issue 3, pp 173–207

Lifting, superadditivity, mixed integer rounding and single node flow sets revisited


DOI: 10.1007/s10288-003-0016-4

Cite this article as:
Louveaux, Q. & Wolsey, L.A. 4OR (2003) 1: 173. doi:10.1007/s10288-003-0016-4


In this survey we attempt to give a unified presentation of a variety of results on the lifting of valid inequalities, as well as a standard procedure combining mixed integer rounding with lifting for the development of strong valid inequalities for knapsack and single node flow sets. Our hope is that the latter can be used in practice to generate cutting planes for mixed integer programs. The survey contains essentially two parts. In the first we present lifting in a very general way, emphasizing superadditive lifting which allows one to lift simultaneously different sets of variables. In the second, our procedure for generating strong valid inequalities consists of reduction to a knapsack set with a single continuous variable, construction of a mixed integer rounding inequality, and superadditive lifting. It is applied to several generalizations of the 0-1 single node flow set.


Liftingmixed integer roundingsingle node flow sets

Copyright information

© Springer-Verlag Berlin/Heidelberg 2003

Authors and Affiliations

  1. 1.CORE and INMA, Université Catholique de LouvainLouvain-la-NeuveBelgium