Two-stage stochastic mixed-integer programming with chance constraints for extended aircraft arrival management

Ahmed Khassiba (1, 2, 3) , Fabian Bastin (3, 1) , Sonia Cafieri (2) , Bernard Gendron (1, 3) , Marcel Mongeau (2)

1 CIRRELT - Centre Interuniversitaire de Recherche sur les Réseaux d'Entreprise, la Logistique et le Transport
2 ENAC - Ecole Nationale de l'Aviation Civile
3 DIRO - Département d'Informatique et de Recherche Opérationnelle [Montreal]

The extended aircraft arrival management problem, as an extension of the classic Aircraft Landing Problem, seeks to pre-schedule 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.

Domaines: Mathématiques [math]; Optimisation et contrôle [math.OC]; Informatique [cs]; Recherche opérationnelle [cs.RO]

Ahmed Khassiba, Fabian Bastin, Sonia Cafieri, Bernard Gendron, Marcel Mongeau. Two-stage stochastic mixed-integer programming with chance constraints for extended aircraft arrival management. Transportation Science, 2020, 54 (4), pp. 897-919. ⟨10.1287/trsc.2020.0991⟩. ⟨hal-02921462⟩