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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
Abstract
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.
1 Introduction
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 [5]. 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.
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