Stability analysis of optimal runway schedules

By performing stability analysis on an optimal runway schedule, this paper derives a method to determine whether the landing sequence of aircraft remains optimal after an arbitrary number of aircraft in that sequence are delayed by an arbitrary amount of time. We consider the problem of scheduling aircraft landing on a single runway such that the runway throughput is maximized under changing external conditions such as delays caused by for example weather. Instead of optimizing the schedule every time delays occur, stability criteria allow for fast evaluation of whether schedules remain optimal. This paper develops a method to compute stability regions for a set of schedules. Sensitivity analysis of the linear programming relaxation and a nonlinear relationship between the delay of individual aircraft and the incurred cost change of any potential landing sequence yield the desired stability information. Furthermore, the properties of a greedy first come first serve policy are studied by giving sufficient conditions to determine whether first come first serve is optimal.