Comparing Valid Inequalities for Cyclic Group Polyhedra

We study the interpolation procedure of Gomory and Johnson (1972), which generates cutting planes for general integer programs from facets of cyclic group polyhedra, and has recently been re-considered by Gomory, Johnson and Evans (2003). We compare inequalities generated by this procedure with MIR inequalities and also with the two-step MIR inequalities discussed in Dash and Gunluk (2003). Our results generalize a result of Cornuéjols, Li and Vandenbussche (2003) on comparing the strength of the Gomory mixed-integer cut with related inequalities. We also show that in some cases, given an inequality generated by the interpolation procedure, one can generate stronger inequalities via the MIR principle, and a similar two-step MIR principle.

By: Sanjeeb Dash, Oktay Günlük

Published in: RC22989 in 2003


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