Parametric integer linear programming: A synthesis of branch and bound with cutting planes

On Linear Programming, Integer Programming and Cutting Planes

Cutting Planes for Mixed Integer Programming

The purpose of this paper is to present an overview of families of cutting planes for mixed integer programming problems. We examine the families of disjunctive inequalities, split cuts, mixed integer rounding inequalities, mixed integer Gomory cuts, intersection cuts, lift-and-project cuts, and reduceand-split cuts. In practice, mixed integer Gomory cuts are very useful in obtaining solutions ...

Cutting planes in integer and mixed integer programming

This survey presents cutting planes that are useful or potentially useful in solving mixed integer programs. Valid inequalities for i) general integer programs, ii) problems with local structure such as knapsack constraints, and iii) problems with 0-1 coefficient matrices, such as set packing, are examined in turn. Finally the use of valid inequalities for classes of problems with structure, su...

Branch and bound, integer, and non-integer programming

In this note we review the development of the first commercial branch and bound codes at CEIR/Scicon, with particular emphasis on those features not commonly emphasized today that is the use of branch and bound to handle discrete constructs, which, while often formally representable in terms of zero-one integer variables, can be handled more elegantly and effectively by applying branch and boun...

Cutting planes in mixed integer programming: theory and algorithms