Valid inequalities based on simple mixed-integer sets

Authors:
Sanjeeb Dash;Oktay Günlük
Affiliations:
Mathematical Sciences Department, IBM T. J. Watson Research Center, 10598, Yorktown Heights, NY, USA;Mathematical Sciences Department, IBM T. J. Watson Research Center, 10598, Yorktown Heights, NY, USA
Venue:
Mathematical Programming: Series A and B
Year:
2006

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Abstract

In this paper we use facets of simple mixed-integer sets with three variables to derive a parametric family of valid inequalities for general mixed-integer sets. We call these inequalities two-step MIR inequalities as they can be derived by applying the simple mixed-integer rounding (MIR) principle of Wolsey (1998) twice. The two-step MIR inequalities define facets of the master cyclic group polyhedron of Gomory (1969). In addition, they dominate the strong fractional cuts of Letchford and Lodi (2002).