The Air Traffic Flow Management Problem with Time Windows

This paper defines time windows of variable size through which flights execute their actions, e.g., enter an airspace sector, depart from or arrive at an airport. We propose a two-step approach based on a mixed integer programming formulation. The first step determines a set of time windows such that the overall cost of delay is minimized. As there might be different sets of time windows generating the same minimum delay, in the second step we choose the set of optimal time windows which also maximizes the overall time window size. In such a way, we provide to airlines, air navigation service providers and airports the largest degree of flexibility to perform their operations under the constraint that the minimum achievable delay is kept constant. We also gain information on the critical flights of the system: if the optimal width of a time window is equal to its minimum available value, any disruption that may cause the flight not to meet it may produce undesired downstream effects. Some computational experience for small-scale random instances is reported