A stochastic 0–1 program based approach for the air traffic flow management problem

We present a model and a robust algorithmic framework for the Air Traffic Flow Management Problem under uncertainty in airport arrival and departure and airspace capacity due to weather conditions. For this purpose we use the state-of-the-art 0–1 deterministic model due to Bertsimas and Stock. We present two 0–1 versions of the stochastic model, depending upon the type of recourse policy to use. A multistage scenario analysis approach based on a simple and full recourse scheme is used. The air traffic scheduling can be implemented for a given set of initial time periods in the full recourse environment and the solution for the other periods does not need to be anticipated and, then, it depends on the scenario to occur. We present a Fix-and-Relax approach to solve the very large-scale 0–1 deterministic equivalent model. Computational results are presented by comparing the deterministic approach (where the stochasticity of the uncertain parameters is reduced to their average) with the recourse based schemes; the optimality gap is within 0.25% of the LP optimal solution for most of the cases with tens of thousands of constraints and variables.