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 Chvatal-Gomory inequalities obtained by strengthening Chvatal-Gomory inequalities using the bounds on the variables. We prove that the closure of a rational polyhedron obtained after applying the generalized Chvatal-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 both upper or lower bounds or both while the rest of them are unbounded.
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