Polyhedral Study of Stochastic Switching Polytopes

Abstract

In this chapter, we investigate the solution set of the minimum runtime and downtime conditions of a power plant, introduced in Section 3.1.3. When a plant is switched on, these restrictions ensure that the plant keeps running for a certain number of time steps and when it is turned off, it must remain off for a certain number of time steps, too. In our problem these restrictions have to be considered for the coal power plant in order to avoid increased thermal stress. In this chapter, we study the underlying 0/1 polytope for the stochastic formulation where uncertainty is modeled by a set of scenarios, as described in Section 3.2. Thus, we will call it stochastic switching polytope. For our studies, we used the software packages PORTA and POLYMAKE, see [CL] and [GJ00], in order to obtain a complete linear description of small instances.