In this paper, we present a new Integer Program (IP) for the Air Traffic Flow Management (ATFM) problem. The model we propose provides a complete representation of all the phases of each flights, i.e., the phase of taking-off, of cruising and of landing; suggesting all the actions to be implemented to achieve the goal of safe, efficient, and expeditious aircraft movement. The distinctive feature of the model is that it allows rerouting decisions. These decisions are formulated by means of "local" conditions, which allow us to represent such decisions in a very compact way by only introducing new constraints. Moreover, to strengthen the polyhedral structure of the underlying relaxation, we also present three classes of valid inequalities. We report short computational times (less than 15 minutes) on instances of the size of the US air traffic control system that make it realistic that our approach can be used as the main engine of managing air traffic in the US.