A Simulation-Based Optimization Model to Schedule Periodic Maintenance of a Fleet of Aircraft

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A Simulation-Based Optimization Model to Schedule
Periodic Maintenance of a Fleet of Aircraft

• Ville Mattila and Kai Virtanen
• Systems Analysis Laboratory,
• Helsinki University of Technology

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Contents

• Scheduling the periodic maintenance (PM) of
  the aircraft fleet of the Finnish Air Force
  (FiAF)
• Objective of scheduling Improve aircraft
  availability
• A simulation-based optimization model for the
  scheduling task
• A discrete-event simulation model
• A genetic algorithm

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Aircraft usage and maintenance
Usage
Maintenance
Different forms of pilot and tactical training A
number of aircraft chosen each day to flight
duty Several missions during one day
Periodic maintenance Based on usage
Failure repairs Unplanned
Different level maintenance facilities
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Periodic maintenance of a Hawk Mk51 training
aircraft
Type of PM task Maintenance interval (flight hours) Average duration (hours) Maintenance level
C 50 10 Organizational level (O-level), Squadron
D1, D2 125 to 250 75 to 200 Intermediate level (I-level), Air commands repair shop
E, F, G 500 to 2000 300 to 500 Depot level (D-level), Industrial repair shop
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Periodic maintenance scheduling

• Difficulty starting times of PM can not be
  assigned with certainty
• Aircraft usage is affected by failures and
  subsequent repairs
• Working principle PM schedule governs the
  selection of aircraft to flight duty
• Each aircraft is assigned an index value based on
  the ratio flight hours to maintenance / time
  to maintenance
• The aircraft with the highest indices get
  selected to flight duty
• The schedule represents targeted starting times
  of PM tasks

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The maintenance scheduling problem

• N the total number of aircraft
• X(x1,1,...,x1,n1,...,xN,1,...,xN,nN) the
  maintenance schedule of the fleet
• L simulated average aircraft availability
• ? sample path

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Further assumptions

• Aircraft usage is limited by the flight
  operations plan
• PM may be conducted within the window of usage
  time defined in the PM program of the
  aircraft
• Failures can preclude aircraft from flight duty,
  a failed aircraft may not be flown until
  it has been repaired
• Maintenance facilities have a limited capacity

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The simulation optimization model

• A discrete-event simulation model
• Describes aircraft usage and maintenance
• Evaluates aircraft availability related to a
  given candidate solution,
  i.e., a maintenance schedule
• A genetic algorithm
• Produces new candidate solutions utilizing the
  simulated availabilities

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The simulation model
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The genetic algorithm (GA)

• Real-coded GA
• Binary tournament selection for reproduction of
  solutions
• Simulated binary crossover in crossover operation
• Mutation based on normal distribution
• Constraints handled by biasing infeasible
  solutions relative to the amount of constraint
  violation

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An example case
Number of aircraft 16
Length of planning period 260 days
Scheduled maintenance tasks per aircraft 4
Number of aircraft in daily flight duty 4
Number of daily flights per aircraft 4
O-level maintenance capacity 1 aircraft
I-level maintenance capacity 3 aircraft
D-level maintenance capacity 2 aircraft
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Optimization results
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The performance of the model

• The simulation-optimization model produces viable
  maintenence schedules
• The best example solution has an average aircraft
  availability of 0.72
• This level of availability is obtained with 1200
  simulation model evaluations using
  random initial solutions

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How good is the solution?

• Simulation output for evaluating the quality of
  the solution
• Queing times at maintenance facilities
• Indicate the maximum amount of improvement
  obtainable by means
  of scheduling
• In the example case, queuing is almost entirely
  eliminated
• The timely development of aircraft availability
  illustrates the impact of an
  efficient solution

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Scheduling vs. no scheduling in the example case
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Future work

• Ranking and selection procedures in comparison of
  candidate solutions to enhance the efficiency of
  optimization
• Extensions to the example case
• Different patterns of flight activity
• Time varying resource availability
• Larger fleet sizes
• Implementation of the model as a design-tool for
  maintenance designers