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.

中文翻译：

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具有变量边界的整数程序的广义 Chvátal-Gomory 闭包

实践中出现的整数规划问题通常涉及具有一侧或两侧边界的决策变量。在本文中，我们考虑通过使用变量的边界加强 Chvátal-Gomory 不等式而获得的 Chvátal-Gomory 不等式的推广。我们证明应用广义Chvátal-Gomory不等式后得到的有理多面体的闭包也是有理多面体。这将 Dunkel 和 Schulz 在 0-1 问题上的结果推广到某些变量具有上限或下限或两者都有而其余变量无界的情况。