Departure Runway Scheduling at London Heathrow Airport Extended Abstract

London Heathrow airport is one of the busiest airports in the world as it is very popular with both airlines and passengers. The capacity of the departure system at Heathrow is limited by the capacity of the runway. It is therefore imperative to maximise the throughput of the single available departure runway. Aircraft taxi from the stands to the ends of the runway where they queue in holding points, awaiting instructions to take off. We will present a model for scheduling aircraft awaiting take-off at the runways at London Heathrow and evaluate the effectiveness of our approach to solving it. In [11] and [12] Idris et al. analysed the departure flow at Logan airport and identified the runway as the key constraint. In [14], Newell provided a model for estimating the capacity of an airport in terms of number of arrivals and departures from the runways. The capacity of an airport was shown to be increased when all of the runways are used for alternating arrivals and departures. In both the departure and arrival systems, separations need to be enforced between aircraft for reasons of safety. The departure problem involves finding a take-off sequence for which either the throughput of the runway is maximised or the delay upon the aircraft awaiting take-off is minimised. The arrivals problem involves finding a landing order for arriving aircraft so that either the total deviation from ideal landing times for aircraft or the landing time for the last aircraft is minimised. There are obvious similarities between the arrivals and departures problem. Both of these problems can be seen to be similar to the machine job scheduling problem with release times and sequence dependent processing times. The objective is often to minimise the total completion time or to minimise earliness and tardiness. Bianco et al. showed in [8] that the single machine problem with sequence-dependent set-up times and release dates is equivalent to the cumulative asymmetric travelling salesman problem with release dates. A dynamic programming formulation was used to attain lower bounds for the problem and then heuristic algorithms were presented to find approximate solutions. This model and algorithms were then applied to the arrivals problem to sequence arriving aircraft. Abela et al. [1] presented a genetic algorithm and branch and bound approaches for solving the arrivals problem. Beasley et al. used mixed integer 0-1 formulations to solve the arrivals problem