Extended Aircraft Arrival Management Under Uncertainty: A Computational Study

Abstract

Arrival Manager operational horizon, in Europe, is foreseen to be extended up to 500 nautical miles around destination airports. In this context, arrivals need to be sequenced and scheduled a few hours before landing, when uncertainty is still significant. A computational study, based on a two-stage stochastic program, is presented and discussed to address the arrival sequencing and scheduling problem under uncertainty. This preliminary study focuses on a single Initial Approach Fix and a single runway. Different problem characteristics, optimization parameters as well as fast solution methods for real-time implementation are analyzed in order to evaluate the viability of our approach. Paris Charles-De-Gaulle airport is taken as a case study. A simulation-based validation experiment shows that our approach can decrease the number of expected conflicts near the terminal area by up to 70%. Moreover, in a high-density traffic situation, the total time-to-lose inside the terminal area can be decreased by more than 71%, while the expected landing rate can be increased by 7.7%, compared to the first-come first-served policy. This computational study demonstrates that sequencing and scheduling arrivals under uncertainty, a few hours before landing, can successfully diminish the need for holding stacks by relying more on upstream linear holding.

Two-Stage Stochastic Mixed-Integer Programming with Chance Constraints for Extended Aircraft Arrival Management

“…Moreover, stochastic schedules exhibit fewer position shifts among aircraft from the same turbulence category than their deterministic counterparts, which ensures fairness among aircraft. As a drawback, we remark that stochastic schedules span over longer time frames than deterministic schedules, which may decrease the arrival/landing rate in low-to-moderate density traffic situations, as observed in Khassiba et al 29.…”

“…For this assumption to hold, we have to ensure that the set of considered aircraft will arrive at the IAF during a reasonably short time frame, so that when the uncertainty of the last aircraft is revealed, second-stage decisions can still be implemented. Moreover, in more operational terms, as suggested in [29], the beginning of the second stage can be set to the entry time of the last considered aircraft to the en-route sector neighboring the terminal area.…”

“…The results of these n c scenario subproblems are aggregated to compute the results of the Benders subproblem associated to cluster c (objective-function value, dualvariables values, etc). Let R c and T c be respectively the set of extreme rays and the set of extreme points of the Benders-dual-subproblem polyhedron corresponding to cluster c. Benders feasibility and optimality cuts for the partially-aggregated-cut version of our SAA model are given by constraints (28) and (29)…”

“…In the wide instances, the IAF time window is given by E I i = P I i − 1 min and L I i = P I i + 15 min. These IAF time window widths are motivated as in [29]. A one-minute advance can be achieved by speeding up the aircraft, while 5 minutes of delay can be absorbed by speed reduction, both over 300 nautical miles, according to the concept of E-AMAN.…”

Aircraft sequencing and scheduling in TMAs under wind direction uncertainties

“…The first stage obtains the aircraft weight class sequence, then the second stage assigns the individual flight to the aircraft sequence. Similarly, Khassiba et al (28) proposed a two-stage stochastic programming model for a single-runway airport. Their findings indicated that their stochastic model reduced the need for a holding stack by a few hours by offering more upstream linear holding.…”