A Polyhedral Study of the Integrated Minimum-Up/-Down Time and Ramping Polytope∗

In this paper, we consider the polyhedral structure of the integrated minimum-up/-downtime and ramping polytope, which has broad applications in power generation scheduling prob-lems. The generalized polytope we studied includes minimum-up/-down time, generation ramp-up/-down rate, logical, and generation upper/lower bound constraints. We derive strong validinequalities for this polytope by utilizing its specialized structures. These inequalities, plustrivial inequalities described in the original formulation, are sufficient to provide the convexhull descriptions for variant two-period and three-period polytopes corresponding to differentminimum-up/-down time limits. In addition, we derive more generalized strong valid inequal-ities (including one, two, and three continuous variable cases respectively) in polynomial sizeto strengthen the multi-period polytopes, and further prove that these inequalities are facet-defining under certain mild conditions. Finally, extensive computational experiments are con-ducted to verify the effectiveness of our proposed strong valid inequalities by testing the ap-plications of these inequalities to solve both the network-constrained and self-scheduling unitcommitment problems, for which our derived approach outperforms the default CPLEX signif-icantly.