A tighter mathematical programming formulation for an air traffic flow management problem with dynamic selection of the airspace configuration

The aim of this thesis is to find a tighter mathematical programming formulation for an air traffic flow management problem with dynamic selection of the airspace configuration. In particular, we start from an Integer Linear Programming model proposed in literature, we improve some of its constraints and we devise some valid inequalities. We thus obtain a tighter formulation that allows us to better approximate the region of the feasible solutions of the problem. The importance of finding a tight formulation lies in the fact that the methods for solving an integer linear programming problem are, in principle, more efficient if the formulation is tight. The ideal would be to find the tightest possible formulation, i.e. the convex hull of the solutions of the problem, but in practice this is very difficult to obtain. The formulation that we propose is not at all close to the ideal one, but it is significantly tighter than the starting one as shown by the computational experiments we carried out.