Modelling and strong linear programs for mixed integer programming

Mixed integer programming modeling is considered from two points of view: getting the model correctly generated in an understandable form, and formulating or reformulating the model so that the problem can be solved. For the former considerations, a relational approach is presented. For the latter, three techniques are discussed: preprocessing, constraint generation, and column generation. For all three techniques, mixed integer problems are considered. For column generation, two problem classes (cutting stock and crew scheduling) for which column generation techniques are classical, are presented in a unified framework and then clustering problems are discussed in the same framework. In the constraint generation section, some constraints based on mixed 0–1 implication graphs are presented.