期刊名称：CORE Discussion Papers / Center for Operations Research and Econometrics (UCL), Louvain
出版年度：2008
卷号：1
出版社：Center for Operations Research and Econometrics (UCL), Louvain
摘要：In this note, we present a simple geometric argument to determine a lower bound on the split
rank of intersection cuts. As a first step of this argument, a polyhedral subset of the latticefree
convex set that is used to generate the intersection cut is constructed. We call this subset
the restricted lattice-free set. It is then shown that
!
"log2(l)# is a lower bound on the split rank
of the intersection cut, where l is the number of integer points lying on the boundary of the
restricted lattice-free set satisfying the condition that no two points lie on the same facet of the
restricted lattice-free set. The use of this result is illustrated to obtain a lower bound of
!
log2" (n +1)# on the split rank of n-row mixing inequalities.
