Two-stage Stochastic Programming Models for the Extended Aircraft Arrival Management Problem with Multiple Pre-Scheduling Points

Extended aircraft arrival management under uncertainty has been previously studied in the literature using two-stage stochastic optimization in the case of a single initial approach fix (IAF) and a single runway. In this paper, we propose an extension taking into account: (i) multiple IAFs feeding the landing runway, (ii) aircraft having different initial flight status (at-departure-gate or airborne) when making first-stage decisions, and (iii) a time-deviation cost function to minimize that is based on reference values depending on aircraft type and flight phase. Two problem variants are modeled according to the degree of freedom on IAF assignment to aircraft. In the first variant, IAFs are to be assigned to aircraft, as a first-stage decision. In the second variant, IAF assignment is fixed and considered as a problem input. Numerical results on realistic instances from Paris Charles-de-Gaulle airport confirm the benefit of taking into account uncertainty through two-stage stochastic programming, and through re-assignment of IAFs.