IEOR%20E4405.001

1

• IEOR E4405.001
• Airline Crew
• Scheduling
• Presented by
• Fatima Khalid

2
Scope

• Goal of airline industry Maximization of
  Profits.
• Requirement for reaching the goal Planning at
  strategic, tactical and operational levels.
• Airline planning involves processes such as
  timetable, fleet assignment, crew pairing and
  crew assignment.
• Note Focus of presentation Crew pairing and
  Crew assignment.

3

• Research based on following papers
• A Stochastic Programming Approach to the Airline
  Crew Scheduling Problem
• Joyce W.Yen
• An Optimization Approach to Solving the Airline
  Crew Pairing Problem
• Amy Cohn and Shervin AhmadBeygi

4
Characteristics of Crew Scheduling Problem

• Comprises of two components
• Crew-Pairing Problem Assigning crew pairings
  (crew comprising pilot, co-pilot and flight
  attendants) to flights such that all flights are
  covered.
• Crew Assignment Crews are assigned to given
  pairings. Most airlines use a kind of bidding
  system to assign pairings to crews.

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Background on Aircraft Economics

• Two costs components

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IP Formulation Crew Pairing

• Min Sp cp xp
• st Sp dfp xp 1 for all f
• xp E 0, 1 for all p
• Terminology
• Xp -gt is the binary variable taking the value 1
  if pairing p is included in the solution else the
  solution is 0.
• dfp -gt is a binary variable with value 1 if
  flight is included in the pairing else 0.
• Cp -gt cost of pairing p.

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Solution to the problem formulated

• First Approach Branch and Bound (as explained in
  class)
• The Algorithm tries to find the optimal solution
  of the problem, that is root problem.
• In case the optimal solution could not be found,
  the feasible region is then subdivided into sub
  regions and the algorithm is then applied to each
  respective sub-region, resulting in sub problems.
• If an optimum solution is found to a sub problem
  it is feasible solution to the root problem but
  not necessarily globally optimal.
• The optimal solution to the sub problem can be
  used to prune the tree.

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Solution to the problem formulated

• Second Approach Carmin Algorithm
• This algorithm uses reduced costs and dual values
  to find the integer solutions.
• The IP is formulated as unconstrained non-linear
  problem
• The reduced cost is found by finding solutions to
  the equation ri c i yi where yi (ri- ri)
  / 2

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Analysis

• The advantage of using branch and bound over
  Carmins method is the confirmation of optimality
  that branch and bound solution has.
• In addition, model doesnt change with duals
• However, drawback is the lack in efficiency in
  finding the solution.