Integer and combinatorial optimization
Integer and combinatorial optimization
Computational study of a family of mixed-integer quadratic programming problems
Mathematical Programming: Series A and B
Mixed logical-linear programming
Discrete Applied Mathematics - Special issue on the satisfiability problem and Boolean functions
A polyhedral approach to combinatorial complementarity programming problems
A polyhedral approach to combinatorial complementarity programming problems
A family of facets for the uncapacitated p-median polytope
Operations Research Letters
A Polyhedral Study of the Cardinality Constrained Knapsack Problem
Proceedings of the 9th International IPCO Conference on Integer Programming and Combinatorial Optimization
CP '01 Proceedings of the 7th International Conference on Principles and Practice of Constraint Programming
On the intersection of AI and OR
The Knowledge Engineering Review
A family of inequalities valid for the robust single machine scheduling polyhedron
Computers and Operations Research
Modeling disjunctive constraints with a logarithmic number of binary variables and constraints
IPCO'08 Proceedings of the 13th international conference on Integer programming and combinatorial optimization
A special ordered set approach for optimizing a discontinuous separable piecewise linear function
Operations Research Letters
Models for representing piecewise linear cost functions
Operations Research Letters
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Many optimisation problems involve combinatorial constraints on continuous variables. An example of a combinatorial constraint is that at most one variable in a group of nonnegative variables may be positive. Traditionally, in the mathematical programming community, such problems have been modeled as mixed-integer programs by introducing auxiliary binary variables and additional constraints. Because the number of variables and constraints becomes larger and the combinatorial structure is not used to advantage, these mixed-integer programming models may not be solved satisfactorily, except for small instances. Traditionally, constraint programming approaches to such problems keep and use the combinatorial structure, but do not use linear programming bounds in the search for an optimal solution. Here we present a branch-and-cut approach that considers the combinatorial constraints without the introduction of binary variables. We review the development of this approach and show how strong constraints can be derived using ideas from polyhedral combinatorics. To illustrate the ideas, we present a production scheduling model that arises in the manufacture of fibre optic cables.