Modelling either-or relations in integer programming

Abstract

Logical relations occur frequently in integer programming problems and are modelled by introducing binary variables in association with linear expressions. Applications requiring constraints involving precedence, exclusion, implication and other conditions give rise to the logical relations OR and IMPLIES in the models. These relations will be considered in this paper from a modelling point of view and formulations investigated for situations where the logical variables link sets of integer variables. Valid inequalities (cuts) that can be added to a model will be developed for a number of the formulations and the computational benefits of these cuts will be considered from an experimental point of view by considering the performance of sets of problem instances. New formulations and combinations of older established formulations will be considered. It will be contended that tight formulations may not always be the most successful.