Lifting, Superadditivity, Mixed Integer Rounding and Single Node Flow Sets Revisited

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, empha-
sizing 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, construc-
tion of a mixed integer rounding inequality, and superadditive lifting. It is applied
to several generalizations of the 0-1 single node flow set.