@inbook{f20d9011fb234a6a8d8a11edd3eaf7e9,

title = "Semi-continuous cuts for mixed-integer programming",

abstract = "We study the convex hull of the feasible set of the semi-continuous knapsack problem, in which the variables belong to the union of two intervals. Besides being important in its own right, the semi-continuous knapsack problem is a relaxation of general mixed-integer programming. We show how strong inequalities that are valid for the semi-continuous knapsack polyhedron can be derived and used as cuts in a branch-and-cut scheme for mixed-integer programming and problems with semi-continuous variables. We present computational results that demonstrate the effectiveness of these inequalities, which we call collectively semi-continuous cuts. Our computational experience also shows that dealing with semi-continuous constraints directly in the branch-and-cut algorithm through a specialized branching scheme and semi-continuous cuts is considerably more practical than the {"}textbook{"} approach of modeling semi-continuous constraints through the introduction of auxiliary binary variables in the model.",

keywords = "Branch-and-cut, Disjunctive programming, Mixed-integer programming, Polyhedral combinatorics, Semi-continuous variables",

author = "{De Farias}, {I. R.}",

year = "2004",

doi = "10.1007/978-3-540-25960-2_13",

language = "English",

isbn = "3540221131",

series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

publisher = "Springer-Verlag",

pages = "163--177",

editor = "Daniel Bienstock and George Nemhauser",

booktitle = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

}