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

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