Air traffic flow management with layered workload constraints

•Path&Cycle allows exact modelling of Air Traffic Flow Management problems.•Realistic modelling of Air Traffic Controller workload restrictions.•The Hotspot Problem is well suited to delayed variable and constraint generation. Many regions of the world are currently struggling with congested airspace, and Europe is no exception. Motivated by our collaboration with relevant European authorities and companies in the Single European Sky ATM Research (SESAR) initiative, we investigate novel mathematical models and algorithms for supporting the Air Traffic Flow Management in Europe. In particular, we consider the problem of optimally choosing new (delayed) departure times for a set of scheduled flights to prevent en-route congestion and high workload for air traffic controllers while minimizing the total delay. This congestion is a function of the number of flights in a certain sector of the airspace, which in turn determines the workload of the air traffic controller(s) assigned to that sector. We present a MIP model that accurately captures the current definition of workload, and extend it to overcome some of the drawbacks of the current definition. The resulting scheduling problem makes use of a novel formulation, Path&Cycle, which is alternative to the classic big-M or time-indexed formulations. We describe a solution algorithm based on delayed variable and constraint generation to substantially speed up the computation. We conclude by showing the great potential of this approach on randomly generated, realistic instances.