Split Cuts

Abstract Split cuts were introduced by Cook and his colleagues in the 1990s. Split cuts are based on the following simple Observation. Given an integer vector π ∈ ℤ n , and an integer π 0 ∈ ℤ, every integer point x ∈ ℤ n satisfies the split disjunction : either π T x ≤ π 0 or π T x ≥ π 0 + 1. Split cuts are a special case of the disjunctive cuts introduced by Balas . The set obtained by adding all split cuts to the linear program (LP) relaxation of a mixed integer program (MIP) is called the split closure . We show how split cuts can be obtained from a basis of the LP relaxation of a mixed integer program, and we describe the structure of the split closure. Furthermore, we give a summary of the computational results that have been obtained in the literature on the strength of the split closure as a relaxation of a MIP.