SCHEDULING AIRCRAFT LANDING

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SCHEDULINGAIRCRAFT LANDING

• Mike Gerson
• Albina Shapiro

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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)

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Potential Objectives

• Punctuality
• Minimize average lateness or number of late
  planes
• Efficiency
• Maximize airport capacity (similar to minimizing
  makespan)
• Costs
• Minimize costs

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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)
• Planes cruise speed
• A planes most economical speed. A cost is
  incurred if the plane is forced to deviate from
  this speed.

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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!

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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

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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

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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)
• ObjectiveMinimize total scaled cost

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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

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Local Search Heuristic

• Swap neighborhood

Shift neighborhood
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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

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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)

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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 RD Seminar (1998).
• J.E. Beasley, M. Krishnamoorthy, Y.M. Sharaiha,
  D. Abramson, Scheduling Aircraft Landings The
  Static Case, in Transportation Science 34 (2000)
  180197.
• 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) 483493.
• M.J. Soomer, G.J. Franx, Scheduling Aircraft
  Landings using Airlines Preferences, in
  European Journal of Operational Research 190
  (2008) 277-291.