The insufficient air routes combined with the adverse weather and congestion to air sectors lead to economic, environmental and safety problems to political aviation in Europe. This situation creates negative aspects to airlines and airports, as well. Furthermore, according to recent studies over 40,000 daily flights are predicted for 2020, and therefore the current ATM system will not be able to handle this volume of traffic in an efficient manner. A new promising approach of solving these problems in the future consists of transforming the ATM system from an 'airport-centered' to an 'airplane-centered' system so it can: (i) increase safety and energy efficiency, (ii) support the free flight concept, (iii) distribute fairly ground-holding and air delays among the flights, (iv) minimize the volume of work of ATCs as an observer, (v) relax the existing distance limits between airplane since the human factor has been annihilated, and therefore, (vi) increase the air sectors' capacity avoiding congestions and (vii) prioritize the airline preferences. Our attempt will be to develop a mathematical model for a support system for the free flight concept. We divide the problem into two sub-problems (upper and lower level) in order to decrease the computational efforts and the complexity of the air traffic flow management problem and to allow flexibility, supporting in the same time the free flight scenario.