On the facets of the mixed-integer knapsack polyhedron (Q1424283)

The author studies the mixed-integer knapsack polyhedron, which is the convex hull of the mixed-integer set defined by an arbitrary linear inequality and the bounds of the variables. The faces of the mixed-integer knapsack polyhedron are described through superadditive function and are closely related to the mixed-integer programming (MIP) inequalities. These new inequalities strengthen and/or generalize known inequalities for special cases of mixed-integer knapsack set studied earlier. In the last section the author presents a summary of computational experiments, which suggest that the new inequalities can be useful in a branch-and-cut algorithm for mixed-integer programming.