SCHEDULING AIRCRAFT LANDING Mike Gerson Albina Shapiro.
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Transcript of SCHEDULING AIRCRAFT LANDING Mike Gerson Albina Shapiro.
SCHEDULINGAIRCRAFT LANDINGMike GersonAlbina 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 = machinesPlanes = jobsEarliest 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) 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.