The multi-airport ground-holding problem in air traffic control

Motivated by the important problem of congestion costs (they were estimated to be $2 billion in 1991) in air transportation and observing that ground delays are more preferable than airborne delays, the authors have formulated and studied several integer programming models to assign ground-holding delays optimally in a general network of airports, so that the total (ground plus airborne) delay cost of all flights is minimized. All previous research on this problem has been restricted to the single-airport case, which neglects ‘down-the-road’ effects due to transmission of delays between successive flights performed by the same aircraft. The authors formulate several models, and then propose a heuristic algorithm which finds a feasible solution to the integer program by rounding the optimal solution of the LP relaxation. Finally, they present extensive computational results with the goal of obtaining qualitative insights on the behavior of the problem under various combinations of the input parameters. The authors demonstrate that the problem can be solved in reasonable computation times for networks with at least as many as 6 airports and 3000 flights.