Stability Analysis of Runway Schedules

By performing stability analysis on an optimal runway schedule, this paper derives a method to determine whether an optimized 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 with the objective of maximizing throughput under changing external conditions such as delays caused by 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 for all landing sequences yield the stability information. Furthermore, the properties of a first-come-first-serve policy are studied by giving sufficient conditions and a heuristic condition for the optimality of first-come-first-serve sequences. The given results are shown to be also applicable to landing sequences obtained through local neighborhood search, sequences that obey a position shift constraint, and subsequences of landing sequences as used in a rolling horizon approach.