Generalized Chvátal-Gomory closures for integer programs with bounds on variables

Integer programming problems that arise in practice often involve decision variables with one or two sided bounds. In this paper, we consider a generalization of Chvátal-Gomory inequalities obtained by strengthening Chvátal-Gomory inequalities using the bounds on the variables. We prove that the closure of a rational polyhedron obtained after applying the generalized Chvátal-Gomory inequalities is also a rational polyhedron. This generalizes a result of Dunkel and Schulz on 0–1 problems to the case when some of the variables have upper or lower bounds or both while the rest of them are unbounded.