@MISC{Bonami_usa., author = {Pierre Bonami and Gérard Cornuéjols and Pierre Bonami}, title = {USA.}, year = {} }

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Abstract

In 1988, Nemhauser and Wolsey introduced the concept of MIR inequality for mixed integer linear programs. In 1998, Wolsey defined MIR inequalities differently. In some sense these definitions are equivalent. However, this note points out that the natural concepts of MIR closures derived from these two definitions are distinct. Dash, Günlük and Lodi made the same observation independently. Let S: = {(x, y) ∈ Zn+ × Rp+: Ax + Gy ≤ b} be a mixed integer set. Here A ∈ Rm×n and G ∈ Rm×p are matrices and b ∈ Rm is a vector. Let P:= {(x, y) ∈ Rn+ × Rp+: Ax + Gy ≤ b} be the polyhedron that arises as the natural linear relaxation of S. We assume P 6 = ∅. Nemhauser and Wolsey [6,7] define MIRNW inequalities by the following pro-cedure. If c1x+ hy ≤ c10 and c2x+ hy ≤ c20