Valid inequalities based on simple mixed-integer sets

Sanjeeb Dash, Oktay Günlük
2005 Mathematical programming  
In this paper we use facets of mixed-integer sets with two and three variables to derive valid inequalities for integer sets defined by a single equation. These inequalities also define facets of the master cyclic group polyhedron of Gomory. Facets of this polyhedron give strong valid inequalities for general mixed-integer sets, such as the well-known Gomory mixed-integer cut. In particular, our inequalities generalize the 2slope facets of Araoz, Gomory, Johnson and Evans (In this paper we
more » ... facets of P (n, r) (and valid inequalities for Y ) that can be derived from the following simple polyhedral sets: and their relaxations obtained by allowing the integral variables in these models to be (1/t)-integral for t ∈ Z. Our work is partly motivated by the work of Marchand and Wolsey [17] , who derive the GMIC using Q 1 .
doi:10.1007/s10107-005-0599-y fatcat:4rtsqasdafhqbi7vqq3smgbc7i