Analyzing valid inequalities of the generation unit commitment problem

The use of Mixed Integer Programming (MIP) within the electric industry is increasing. Many US ISOs are testing and planning to use MIP in the near future or they are already using MIP. There are various MIP formulations published for generation unit commitment with little consensus as to which formulation is preferred. In particular, various valid inequalities are used to model the minimum up and down time constraints for generation unit commitment. In this paper, we first discuss valid inequalities and facet defining valid inequalities. We then present and compare these previously published valid inequalities and we demonstrate why certain valid inequalities dominate other valid inequalities. We also present previously published facet defining valid inequalities.