Abstract We describe a new two-level hierarchical architecture for air traffic management problems with corresponding mathematical models. The first level represents the air route network, and its solutions provide the air traffic flows on each arc of the network. This level interacts with the second one, which represents the single airway and its own air traffic flows. This latter model allows us to assign the optimal air traffic route to each aircraft and to optimise the airway's capacity. Furthermore, for the airway optimisation model we have also carried out a computational analysis, providing both exact and heuristic solutions, for problem instances based on real data. These are obtained with the Cplex solver exploiting the mixed integer mathematical formulation and with a proposed heuristic algorithm for problems of larger size, respectively. The heuristic solutions obtained are within a maximum gap of 13% from the LP relaxation.