A note on the split rank of intersection cuts

作者：Dey Santanu S^*

来源：Mathematical Programming, 2011, 130(1): 107-124.

DOI：10.1007/s10107-009-0329-y

• Mixed integer programming
• Split rank
• Intersection cuts

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 lattice-free 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 [log(2)(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 by obtaining a lower bound of [log2(n + 1)] on the split rank of n-row mixing inequalities.

• 出版日期2011-11