The Multi-Airport Ground-Holding Problem in Air Traffic Control

Abstract

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, we 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. We 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, we present extensive computational results with the goal of obtaining qualitative insights on the behavior of the problem under various combinations of the input parameters. We demonstrate that the problem can be solved in reasonable computation times for networks with at least as many as 6 airports and 3,000 flights. Congestion problems are becoming increasingly I ~~ acute in many major European and American airports. For European airlines, the total yearly delay cost due to congestion (including cost to passengers) was estimated to be $5 billion in 1989 (Terrab 1990). For U.S. airlines, the direct delay cost due to conges- tion is claimed to amount to approximately $2 billion per year. Given the fact that the total profits of the U.S. airline industry rarely exceed $1 billion, conges- tion problems are a phenomenon of undeniable significance.