On t-branch split cuts for mixed-integer programs

In this paper we study the t-branch split cuts introduced by Li and Richard (Discret Optim 5, 2008). They presented a family of mixed-integer programs with n integer variables and a single continuous variable and conjectured that the convex hull of integer solutions for any n has unbounded rank with respect to (n-1)-branch split cuts. It was shown earlier by Cook et al. (Math Program 47, 1990) that this conjecture is true when n = 2, and Li and Richard proved the conjecture when n = 3. In this paper we show that this conjecture is also true for all n > 3. © 2012 Springer and Mathematical Optimization Society.