An optimization model for assigning 4D-trajectories to flights under the TBO concept

The objective of this paper is to present a mathematical model that will contribute to the optimization and optimum configuration of the TBO concept. We develop a binary integer programming model whose aim is to assign a 4D-trajectory to each flight in order to optimize the efficiency of the ATM system. The model considers the preferred 4D-trajectory of all the flights in the pre-tactical planning phase and outputs an optimal pre-departure 4D-trajectory for each flight to be shared or negotiated with other stakeholders and subsequently managed throughout the flight. These output trajectories are obtained by minimising the deviation (in terms of time delay, lateral and vertical deviation) from the original preferred trajectories. The particularities of this model are that it considers the complete 4D-trajectory for each flight as well as it incorporates the preferences and priorities of the ATM stakeholders. Some computational results are presented, which show that our optimization model has the ability to identify some trade-offs between the objectives of the stakeholders of the ATM system under the TBO concept. It can also provide the network manager with useful decision tools to choose a trajectory for each flight.