To improve the efficiency in power generation and to reduce the greenhouse gas emission, both Demand Response (DR) strategy and intermittent renewable energy have been proposed or applied in electric power systems. However, the uncertainty and the generation pattern in wind farms and the complexity of demand side management pose huge challenges in power system operations. In this paper, we analytically investigate how to integrate DR and wind energy with fossil fuel generators to (i) minimize power generation cost; (2) fully take advantage wind energy with managed demand to reduce greenhouse emission. We first build a two-stage robust unit commitment model to obtain day-ahead generator schedules where wind uncertainty is captured by a polyhedron. Then, we extend our model to include DR strategy such that both price levels and generator schedule will be derived for the next day. For these two NP-hard problems, we derive their mathematical properties and develop a novel and analytical solution method. Our computational study on a IEEE 118 system with 36 units shows that (i) the robust unit commitment model can significantly reduce total cost and fully make use of wind energy; (ii) the cutting plane method is computationally superior to known algorithms.