SCHEDULING AIRCRAFT LANDING Mike Gerson Albina Shapiro
Background Air traffic has been on the rise for decades, but there has not been a corresponding increase in the number of airports and runways Airlines are forced to improve their efficiency High capital investments and operational costs Heightened security Increased competition due to low-cost airlines Little tactical planning is currently done – sequence is approximately FCFS Planning allows delays to be assigned before departure: delays on the ground are half as costly as in the air Allows for different objectives to be met (besides just getting all the planes on the ground)
Potential Objectives Punctuality Minimize average lateness or number of late planes Efficiency Maximize airport capacity (similar to minimizing makespan) Costs Minimize costs
The Decision Problem An airport's Air Traffic Control (ATC) is responsible for creating a schedule of plane landings Separation Times Mandatory inter-landing time between planes (wake vortex), determined by plane size and visibility Time window Bounded by earliest time a plane can land (flying at maximum speed) and by latest a plane can land (flying at most fuel-efficient speed while circling for maximum possible time) Plane’s cruise speed A plane’s most economical speed. A cost is incurred if the plane is forced to deviate from this speed.
Job Shop Model Early research (late 1970s) modeled problem as a job shop Runways = machines Planes = jobs Earliest feasible landing time = release date Sequence-dependent processing times Maintains separation time Typical objective function: minimize makespan And the problem becomes np-hard!
Prioritizing Flights Allows airlines to set their own preferences Size of plane or number of passengers Connecting flights (passengers and cargo) Fuel capacity considerations 1998 – Carr, et al Priority ranking system per airline Objective: minimize deviations from preferred order
Prioritizing Flights 1995 – Abela, et al, 2000 – Beasley, et al Simple cost function, linearly tied to deviation from a target arrival time Objective: Minimize weighted deviations from scheduled time
Prioritizing Flights 2008 – Soomer and Franx More complex linear cost function more accurately accounts for airline preferences Includes scaling procedure to normalize costs between airlines (prevents one airline from receiving priority for a higher cost structure) Objective: Minimize total scaled cost
Solution Methods Simulation Genetic algorithms Population heuristics Formulate mixed-integer programming model Branch and bound Use an upper bound heuristic, then LP-based tree search Local search heuristic
Local Search Heuristic Swap neighborhood Shift neighborhood
Results Soomer, et al: Local Search Heuristic Significant cost savings over FCFS Average savings per flight: 33% of FCFS costs Total savings: 81% of scaled costs
Advantages over FCFS Cost Savings Consistent Performance Automated system vs human judgment Allows active scheduling Computations run quickly enough to allow updated schedules to be calculated as circumstances change (departure delays, weather conditions, etc)
References J. Abela, D. Abramson, M. Krishnamoorthy, A. De Silva, and G. Mills, “Computing Optimal Schedules for Landing Aircraft,” in Proceedings of the 12th National ASOR Conference, Adelaide, Australia, (1993) G.C. Carr, H. Erzberger, F. Neuman. “Airline Arrival Prioritization in Sequencing and Scheduling,” in Proceedings of the 2nd USA/EUROPE Air Traffic Management R&D Seminar (1998). J.E. Beasley, M. Krishnamoorthy, Y.M. Sharaiha, D. Abramson, “Scheduling Aircraft Landings – The Static Case,” in Transportation Science 34 (2000) 180–197. J.E. Beasley, J. Sonander, P. Havelock, “Scheduling Aircraft Landings at London Heathrow using a Population Heuristic,” in Journal of the Operational Research Society 52 (2001) 483–493. M.J. Soomer, G.J. Franx, “Scheduling Aircraft Landings using Airlines’ Preferences,” in European Journal of Operational Research 190 (2008)