Critical flights detected with time windows

Airlines need to pay special attention to flights that may be liable to produce undesired downstream effects if subjected to delay. A mathematical formulation is proposed to identify these critical flights by defining a set of temporal intervals, called time window, which must be met during the flight execution. The width of the time window is variable because it reflects all known constraints on runway capacities or on congested en route sectors that the flight will go through, or both. The set of optimal time window that maximizes their overall width was chosen, thus providing airline operators with the largest degree of flexibility to perform their flights. Three possible approaches are presented to compute the utilization of the system capacity. By means of a computational analysis, it is shown that the solution of the time window model is insensitive about the formulation used for the capacity constraints.