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S ystemsAnalysis LaboratoryHelsinki University of Technology
Scheduling Periodic Maintenance of Aircraft through simulation-based optimization
Ville Mattila and Kai Virtanen
Systems Analysis Laboratory, Helsinki University of Technology
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S ystemsAnalysis LaboratoryHelsinki University of Technology
Contents
• The need for periodic maintenance (PM) scheduling
• Scheduling of PM tasks in the Finnish Air Force (FiAF)
• A simulation-based optimization model for the scheduling task
• Results from an example scheduling case
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S ystemsAnalysis LaboratoryHelsinki University of Technology
Aircraft usage and maintenance
Usage
Pilot and tactical training, air surveillance
A number of aircraft chosen each day to flight duty
Several missions during one day
Maintenance
Different level maintenance facilities
Periodic maintenance
Based on usage
Failure repairs
Unplanned
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S ystemsAnalysis LaboratoryHelsinki University of Technology
Periodic maintenance of a Hawk Mk51 training aircraft
Type of PM task Maintenance interval
(flight hours)
Average duration
(hours)
Maintenance level
C 50 10Organizational level (O-level),
Squadron
D1, D2 125 to 250 75 to 200Intermediate level (I-level),
Air command’s repair shop
E, F, G 500 to 2000 300 to 500Depot level (D-level),
Industrial repair shop
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S ystemsAnalysis LaboratoryHelsinki University of Technology
The need for PM scheduling
• Scheduling is done for two primary reasons
1 Avoid degradation of aircraft availability
2 Allow maintenance facilities to plan for supply of resources
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S ystemsAnalysis LaboratoryHelsinki University of Technology
Scheduling vs. no scheduling
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0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 50 100 150 200 250
Time (days)
Air
cra
ft a
va
ilab
ility
No Scheduling With Scheduling
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S ystemsAnalysis LaboratoryHelsinki University of Technology
Difficulty of scheduling
• Starting times of PM tasks can not be assigned with certainty
– Timing depends on the maintenance interval and on the usage
of the aircraft
– Usage is affected by unexpected failures and subsequent repairs
– Intervals are not adjusted during normal conditions
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S ystemsAnalysis LaboratoryHelsinki University of Technology
Maintenance schedule
• A maintenance schedule consists of targeted starting times of PM tasks
• The schedule is used to allocate flight time among aircraft by
prioritizing aircraft with the highest ratio of
• The allocation governs the accumulation of flight hours and the actual
timing of PM tasks
emaintenanc to time
emaintenanc to time flight
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S ystemsAnalysis LaboratoryHelsinki University of Technology
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
),()(max XLEXfX
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S ystemsAnalysis LaboratoryHelsinki University of Technology
The simulation optimization model
• A discrete-event simulation model
– Describes aircraft usage and maintenance under a given
maintenance schedule
– Returns aircraft availability as output
• A search method
– Produces new schedules based on the simulated availabilities
– A genetic algorithm (GA) or simulated annealing (SA)
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S ystemsAnalysis LaboratoryHelsinki University of Technology
A case example
• The scheduling case
– A fleet of 16 aircraft
– A time period of 1 year
– 4 of the aircraft each perform 4 daily flight missions
– 4 PM tasks scheduled per each aircraft in the fleet
• The performance of different configurations of GA and SA in the
case are compared
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S ystemsAnalysis LaboratoryHelsinki University of Technology
Design of experiment
• 300 evaluations of the simulation for each combination of parameters
GA
Population size 10 20 30
Probability of crossover 0.6 0.8 1.0
Amplitude of crossover 1arge medium small
SA
Number of rescheduled
tasks per iteration3 6 9
Amplitude of
reschedulingsmall medium large
Probability of accepting
a degrading schedulesmall medium large
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S ystemsAnalysis LaboratoryHelsinki University of Technology
Results
• Highest average availability obtained in the optimization
GA
Population size 0.636 0.657 0.647
Probability of crossover 0.638 0.646 0.654
Amplitude of crossover 0.668 0.638 0.633
SA
Number of rescheduled
tasks per iteration0.682 0.697 0.726
Amplitude of
rescheduling0.658 0.713 0.733
Probability of accepting
a degrading schedule0.702 0.705 0.698
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S ystemsAnalysis LaboratoryHelsinki University of Technology
Analysis of the obtained schedule
• The simulation can be used to further assess the schedule obtained in
the optimization
– The queuing times in the maintenance facilities indicate whether
the schedule can still be improved
– The simulation also provides information on the distribution of
times, when the PM tasks are actually materialized
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S ystemsAnalysis LaboratoryHelsinki University of Technology
Concluding remarks
• The presented model has been implemented as a design tool
for FiAF
• Final validation can be conducted by comparing actual flight
operations and maintenance with the simulation
• Future work includes the consideration of task priorities in the
optimization problem