Airline Optimization Problems

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Airline Optimization Problems
Constraint Technologies International www.contecin
t.com.au
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Airline Management Timeframes

• Strategic Planning
• Years to months.
• Scenario based / what if? / resource planning
  etc.
• Can use operational planning tools.

• Operational Planning
• Months to weeks.
• e.g. aircraft schedule development, crew
  scheduling, rostering, maintenance planning etc.

• Operations
• Days to real-time
• e.g. situation awareness, tracking, disruption
  management, maintenance etc.

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The Crew Scheduling Problem

• Given an aircraft schedule that specifies a
  couple of months worth of flying at some point in
  the future...
• Problem what is the most efficient way to crew
  all the planes?
• Must abide by statutory and union regulations.

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Crew Scheduling - Pairings

• An aircraft schedule is a list of plane legs to
  be crewed
• A crew schedule partitions these legs into
  pairings

AKL
AKL
FLT17
FLT13
BNE
BNE
FLT19
FLT714
SYD
SYD
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Set Covering Formulation

• How do we handle the often complicated and messy
  cost and legality rules for pairings?
• Choose a subset of all possible pairings that
  forms an optimal complete crew schedule.
• Translations for the pragmatist
• (some)
• (good)

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Set Covering Formulation
Cost of ith pairing
1 for all selected pairings, else 0
1 if leg i is in pairing j, else 0
i indexes plane legs, j indexes pairings
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Set Covering Formulation
x
Legs
Pairings
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Crew Scheduling Computational Challenges

• Tens of thousands of legs in a schedule.
• Number of possible pairings is almost unlimited.
• Two (related) problems
• 1 Too many legal pairings to even begin to solve
  LP, let alone MIP.
• 2 Even if we reduce number of pairings, still
  have to be able to solve large MIP problems
  efficiently (tens of thousands of constraints,
  hundreds of thousands of variables).

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Column Generation Techniques

• First solve a restricted crew scheduling problem
  that includes a small subset of the total
  possible pairings.
• Use dual LP solution to generate extra pairings
  to add to the LP in order to improve the cost
  function. Extra pairings are generated by solving
  column generation subproblem.
• Iterate.
• Integrality constraints require special
  techniques - branch and price etc.
• Column generation subproblem can use
  constrained shortest path / k-shortest path /
  stochastic methods / constraint programming etc.

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Pairing Recombination (k-opt)

• Start with a feasible crew schedule.
• Choose a limited subset of the pairings in this
  schedule, and re-optimize the mini aircraft
  schedule defined by the legs in these pairings.
• Gets around the scaling problem.
• Need to decide which pairings to re-optimize at
  each iteration.

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Systemic Challenges

• How do we handle the complicated legality and
  costing rules in a flexible yet efficient manner?
  -- e.g. CTI Common Rules system.
• Human factors make this all the more important.
• Solution should be robust and efficient within
  the wider airline context. e.g. robustness with
  respect to disruptions, rosterability problem,
  non-independence of separate pairings etc.
• How do we handle the data interface between
  various systems in an airline e.g. operations,
  crew tracking systems etc.?

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Other Airline Optimization Problems

• Rostering (given a crew schedule, assign actual
  crew members to the pairings so as to satisfy
  crew preferences and legality requirements)
• Aircraft scheduling (develop an aircraft schedule
  that efficiently matches the fleet with passenger
  demand, maintenance requirements, airport slot
  restrictions etc.)
• Other e.g. problems arising from warehousing,
  maintenance scheduling etc.

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Integration

• Can get into trouble viewing optimization
  problems as idealized problems in isolation.
• Improvements can come from moving to a more
  holistic approach.
• e.g. we would like to be able to do robust
  scheduling over the entire cycle from initial
  planning to flying.
• A very important area requiring a holistic
  approach is disruption management...

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Disruption Management

• Requires integration of several domains
• Aircraft routing problem.
• Crew disruptions.
• Passenger disruption problem (connections etc.).
• Slot management, aircraft maintenance, catering
  etc. etc.
• There is always a degree of incompleteness and
  uncertainty in the data and the model thus it
  is more important to be able to choose from a
  range of feasible solutions, rather than having
  one best solution.
• Need to be fast!
• Heuristic exploration of solution space.
• Optimization possibilities?

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Questions?
Constraint Technologies International www.contecin
t.com.au dan.gordon_at_contecint.com.au ian.evans_at_co
ntecint.com.au