1. SCHEDULING AIRCRAFT LANDING Mike Gerson Albina Shapiro

2. 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)

3. Potential Objectives  Punctuality  Minimize average lateness or number of late planes  Efficiency  Maximize airport capacity (similar to minimizing makespan)  Costs  Minimize costs

4. 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.

5. 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!

6. 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

7. 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

8. 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

9. 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

10. Local Search Heuristic Swap neighborhood Shift neighborhood

11. 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

12. 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)

13. 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) 71-90.  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) 277-291.