A mathematical programming model for air traffic flow management with horizontal and vertical separation constraints

This thesis presents a new integer linear programming (ILP) model for the air traffic flow management (ATFM) problem. The model objective is to minimize the cost of flight delays. This issue is of primary concern in the air traffic system. The introduction provides some insight on ATFM. The problem is then addressed through a combination of flow management actions, including ground-holding, airborne-holding and distribution by levels of air traffic. Exploiting the fact that actual airspace sectors observed capacities are often higher than the nominal capacities, two types of flights separation constraints are proposed in order to increase the use of airspace without compromising safety requirements. Furthermore, in order to avoid complex trajectories, an additional class of constraints is discussed. Two classes of valid inequalities are also presented with the purpose of strengthening the underlying relaxation. The thesis subsequently reports computational experiments on small instances. The model with separation constraints is then compared to the model where no separation constraints are imposed and nominal capacities restriction are maintained. These comparisons show that the model can improve the solution for small instances. Improvements are correlated to low nominal capacities and high maximum flight level variation. Finally, implementation details are provided.