  In this paper, we study the polyhedral structure of an integrated
minimum-up/-down time and ramping polytope, which has broad applications in
variant industries. The polytope we studied includes minimum-up/-down time,
generation ramp-up/-down rate, logical, and generation upper/lower bound
constraints. By exploring its specialized structures, we derive strong valid
inequalities and explore a new proof technique to prove these inequalities are
sufficient to provide convex hull descriptions for variant two-period and
three-period polytopes, under different parameter settings. For multi-period
cases, we derive generalized strong valid inequalities (including one, two, and
three continuous variables, respectively) and further prove that these
inequalities are facet-defining under mild conditions. Moreover, we discover
efficient polynomial time separation algorithms for these inequalities to
improve the computational efficiency. Finally, extensive computational
experiments are conducted to verify the effectiveness of our proposed strong
valid inequalities by testing the applications of these inequalities to solve
both self-scheduling and network-constrained unit commitment problems, for
which our derived approach outperforms the default CPLEX significantly.
