Min-up/Min-down Polytopes

In power generation and other production settings, technological constraints force restrictions on the number of time periods that a machine must stay up once activated, and stay down once deactivated. We characterize the polyhedral structure of a model representing these restrictions. We also describe a cutting-plane method for solving integer programs involving such min-up and min-down times for machines. Finally, we demonstrate how the polytope of our study generalizes the well-known cross polytope (i.e., generalized octahedron).