Scheduling Periodic Maintenance of Aircraft through simulation-based optimization

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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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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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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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Scheduling vs. no scheduling

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0.1

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0.4

0.5

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0.9

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0 50 100 150 200 250

Time (days)

Air

cra

ft a

va

ilab

ility

No Scheduling With Scheduling

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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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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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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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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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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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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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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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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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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