Even the most sophisticated methods currently available to solve pure integer and mixed integer programming problems require noticeably more computation than the methods for similarly sized pure linear programs. Many relatively small integer programming models, in fact, still take enormous amounts of computing time to solve. Indeed, some such models have never yet been solved. In the face of these practical obstacles to a solution, proper formulation of the model is crucial to successful solution of pure integer or mixed integer programs.

For help in formulating a model of your own integer or mixed integer problem, you may want to consult H.P. Williams's textbook about practical model building (referenced in Further Reading).

Also you may want to develop a better understanding of branch & cut, a feature of the ILOG CPLEX MIP Optimizer. For that purpose, Williams's book offers a good introduction, and Nemhauser and Wolsey's book (also referenced in Further Reading) goes into greater depth about branch & cut as well as other techniques implemented in the ILOG CPLEX MIP Optimizer.

While we have found that the default MIP parameters settings work well for most problems, runtimes can sometime be improved by modifying these settings. This section proposes alternate parameter settings that can help when you are solving difficult MIPs.