Yahya Fathi

The n-step mixed integer rounding (MIR) functions are used to generate n-step MIR inequalities for (mixed) integer programming problems (Kianfar and Fathi, 2006). We show that these functions are sources for generating extreme valid inequalities (facets) for group problems. We first prove the n-step MIR function, for any positive integer n, generates two-slope facets for … Read more

We present new families of valid inequalities for (mixed) integer programming (MIP) problems. These valid inequalities are based on a generalization of the 2-step mixed integer rounding (MIR), proposed by Dash and Günlük (2006). We prove that for any positive integer n, n facets of a certain (n+1)-dimensional mixed integer set can be obtained through … Read more