On the binary formulation of air traffic flow management problems

We discuss a widely used air traffic flow management formulation. We show that this formulation can lead to a solution where air delays are assigned to flights during their take-off which is prohibited in practice. Although air delay is more expensive than ground delay, the model may assign air delay to a few flights during their take-off to save more on not having as much ground delay. We present a modified formulation and verify its functionality in avoiding incorrect solutions.