On the Rank of Disjunctive Cuts
Alberto Del Pia · Mathematics of Operations Research · 2012
Let ℒ be a family of lattice-free polyhedra in ℝ m containing the splits. Given a polyhedron P in ℝ m + n , we characterize when a valid inequality for P ∩ (ℤ m × ℝ n ) can be obtained with a finite number of disjunctive cuts corresponding to the polyhedra in ℒ. We also characterize the lattice-free polyhedra M such that all the disjunctive cuts corresponding to M can be obtained with a finite number of disjunctive cuts corresponding to the polyhedra in ℒ for every polyhedron P. Our results imply interesting consequences, related to split rank and to integral lattice-free polyhedra, that extend recent research findings.