Summary: Sequential pairing of mixed integer inequalities
Yongpei Guan, Shabbir Ahmed, George L. Nemhauser
School of Industrial & Systems Engineering,
Georgia Institute of Technology, 765 Ferst Drive, Atlanta, GA 30332.
December 22, 2004
We present a scheme for generating new valid inequalities for mixed integer programs by taking pair-
wise combinations of existing valid inequalities. Our scheme is related to mixed integer rounding and
mixing. The scheme is in general sequence-dependent and therefore leads to an exponential number of
inequalities. For some important cases, we identify combination sequences that lead to a manageable set
of non-dominated inequalities. We illustrate the framework for some deterministic and stochastic integer
programs and we present computational results which show the efficiency of adding the new generated
inequalities as cuts.
We develop a scheme for generating new valid inequalities for mixed integer programs by taking pair-wise
combinations of existing valid inequalities. Our scheme is related to the mixed integer rounding (MIR)
procedure of Nemhauser and Wolsey [7, 8] and the mixing procedure of GĻunluk and Pochet . We derive
new inequalities iteratively by a very simple combination of two inequalities at a time, which we call pairing.
As will be seen, the order in which the inequalities are paired is important since the resulting new inequalities
depend on the order.