A Mixed Integer Linear Programming Approach for Computing the Optimal Chance-Constrained Push Back Time Windows

Abstract

Due to the stochastic uncertainties in ramp area aircraft trajectories, the optimization of push back time windows has to account for randomness associated with the trajectories. This paper formulates a mixed integer linear program for computing the optimal chanceconstrained aircraft push back time windows. The solutions are chance-constrained because they allow for a non-zero but bounded probability of conflicts among the sampled aircraft trajectories. Solutions of the mixed integer linear program are shown to be significantly impacted by the presence of even a few rare conflict points within an otherwise empty domain. By allowing for some conflict points inside the time windows, the solutions become much more attractive. The runtime of the mixed integer linear program is shown to be most influenced by a parameter within the objective function, the distribution of conflict points, and the number of conflict points that are allowed inside the time window. In order to reduce the runtime we introduce various cutting methods applied to the mixed integer linear program domain. Overall, the analysis shows that the cutting methods reduce both the runtime and standard deviation of the runtime for the mixed integer linear program.