Power systems are on the cusp of a rapid technological, economic, and environmental evolution. Classical problems considered by the power community must naturally adapt to new requirements. Physical and computational constraints within a new landscape must be revisited. In this paper, we focus on the generator scheduling problem, which is also known as the unit commitment problem, in which we incorporate the new constraints of transmission line capacity limits and policy to give a more comprehensive view for planning in a smart grid. Moreover, we consider implications of our formulation to solution complexity. We introduce the concept of matroid theory to model unit commitment as a combinatorial problem and propose distributed solutions to facilitate optimal and correct generator scheduling. We account for communications and computational complexity and demonstrate how although the constrained generator scheduling problem is NP-hard, simpler versions of the problem lead to polynomial-time solutions.