Flight Scheduling

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Flight Scheduling

• Resolving Conflicts to Reach Optimality
• Advisor Wanpracha Art Chaovalitwongse

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Jessica McCoy
NC STATE UNIVERSITY

• Senior at NC State University
• Majors Industrial Engineering
• Applied Mathematics
• Minors Spanish and Italian
• DIMACS REU Participant

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Motivation
NC STATE UNIVERSITY

• 400 flights every day on just one track system
  (PACOTS)
• On average, 26 of these flights are delayed
• The majority of the delays are between 10-15
  minutes

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Track Advisory System
NC STATE UNIVERSITY

• Three requests are made for each flight
• Departure Time
• Track
• Level

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What does all of this mean?
NC STATE UNIVERSITY

• Think of a road trip.
• Tracks Routes
• Levels Lanes
• Times Times
• Safety first!
• Each car must be separated by route, lane, time,
  or some combination.

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What constitutes a conflict?
NC STATE UNIVERSITY

• If two flights are on the same track and at the
  same level, they must be at least 20 minutes
  apart.

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Approaching the problem
NC STATE UNIVERSITY

• Resolve conflicts while minimizing
• Number of track changes
• Number of level changes
• Combined delay of all flights
• Levels and departure times must remain within
  bounds
• Flights must be separated appropriately

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IP Formulation 1
NC STATE UNIVERSITY

• min c1y1(f) c2y2(f) c3y3(f)
• s.t. r2(f) 4 Þ 1 x2(f) 4 for all fÎFLIGHTS
• r2(f) 5 Þ 5 x2(f) 8 for all fÎFLIGHTS
• r3(f) x3(f) r3(f) 20 for all fÎFLIGHTS
• where ci(f) are cost coefficients, ri(f) are
  requested
• parameters, xi(f) are actual values, and yi(f)
  are the changes
• in values 1 track, 2 level, and 3 time

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IP Formulation 2
NC STATE UNIVERSITY

• min c1y1(f) c2y2(f) c3y3(f)
• s.t. y1(f) x1(f) r1(f) for all fÎFLIGHTS
• y2(f) x2(f) r2(f) for all fÎFLIGHTS
• y3(f) x3(f) r3(f) for all fÎFLIGHTS
• 20x2(f) x2(ff) x3(f) x3(ff) 20
• for all f,ffÎFLIGHTS, f?ff
• xi(f), yi(f) Î Z 0 for all fÎFLIGHTS
• for i 1,2,3

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Challenges
NC STATE UNIVERSITY

• Develop familiarity with code and software
• Reformulate the problem
• Resolve modeling issues
• Address dimensional complexity
• Improve model capacity

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Any questions?
NC STATE UNIVERSITY
For more information, check out my webpage
at http//dimax.rutgers.edu/jhmccoy/