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.