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

, Volume 1, Issue 3, pp 173-207

First online:

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

  • Quentin LouveauxAffiliated withCORE and INMA, Université Catholique de Louvain Email author 
  • , Laurence A. WolseyAffiliated withCORE and INMA, Université Catholique de Louvain

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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.


Lifting mixed integer rounding single node flow sets