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.

The extended aircraft arrival management problem, as an extension of the classic aircraft landing problem, seeks to preschedule aircraft on a destination airport a few hours before their planned landing times. A two-stage stochastic mixed-integer programming model enriched by chance constraints is proposed in this paper. The first-stage optimization problem determines an aircraft sequence and target times over a reference point in the terminal area, called initial approach fix (IAF), so as to minimize the landing sequence length. Actual times over the IAF are assumed to deviate randomly from target times following known probability distributions. In the second stage, actual times over the IAF are assumed to be revealed, and landing times are to be determined in view of minimizing a time-deviation impact cost function. A Benders reformulation is proposed, and acceleration techniques to Benders decomposition are sketched. Extensive results on realistic instances from Paris Charles-de-Gaulle airport show the benefit of two-stage stochastic and chance-constrained programming over a deterministic policy.

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