| Abstract: | We consider mixed-integer sets of the form X = {(s, y) ∈ ?+ × ? n : s + a j y j ≥ b j , ?j ∈ N}. A polyhedral characterization for the case where X is defined by two inequalities is provided. From that characterization we give a compact formulation for the particular case where the coefficients of the integer variables can take only two possible integer values a 1, a 2 ∈ ?+ : X n,m = {(s, y) ∈ ?+ × ? n+m : s + a 1 y j ≥ b j , ?j ∈ N 1, s + a 2 y j ≥ b j , j ∈ N 2} where N 1 = {1, …, n}, N 2 = {n + 1, …, n + m}. In addition, we discuss families of facet-defining inequalities for the convex hull of X n,m . |
