Transcript S A Simulation-Based Optimization Model to Schedule ystems

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
S ystems
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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Analysis Laboratory
Helsinki University of Technology
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Aircraft usage and maintenance
Usage
Different forms of pilot and
tactical training
A number of aircraft chosen
each day to flight duty
Maintenance
Failure repairs
Unplanned
Periodic
maintenance
Based on
usage
Several missions during one
day
Different level
maintenance facilities
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Analysis Laboratory
Helsinki University of Technology
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Periodic maintenance of a Hawk Mk51
training aircraft
Type of PM task
Maintenance interval
Average duration
(flight hours)
(hours)
Maintenance level
Organizational level (O-level),
C
50
10
Squadron
Intermediate level (I-level),
D1, D2
125 to 250
75 to 200
Air command’s repair shop
Depot level (D-level),
E, F, G
500 to 2000
300 to 500
Industrial repair shop
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Analysis Laboratory
Helsinki University of Technology
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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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Analysis Laboratory
Helsinki University of Technology
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The maintenance scheduling problem
max f ( X )  EL( X , )
X
s.t. xi , k  0, i  1,..., N ; k  1, and
(nonnegativity)
xi , k  xi , k 1  0, i  1,..., N ; k  2...ni, (time precedence)
N
X=(x1,1,...,x1,n1,...,xN,1,...,xN,nN)
L

the total number of aircraft
the maintenance schedule of the fleet
simulated average aircraft availability
sample path
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Analysis Laboratory
Helsinki University of Technology
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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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Analysis Laboratory
Helsinki University of Technology
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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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Analysis Laboratory
Helsinki University of Technology
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The simulation model
No maintenance or repair need
Turnaround
or pre-flight
inspection
O-level
maintenance
Mission
Check for failures
and periodic
maintenance need
Need for periodic
maintenance or
failure repair
I-level
maintenance
D-level
maintenance
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Helsinki University of Technology
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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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Analysis Laboratory
Helsinki University of Technology
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An example case
Number of aircraft
Length of planning period
16
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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Analysis Laboratory
Helsinki University of Technology
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Average aircraft availability
Optimization results
0.73
0.72
0.71
0.7
0.69
0.68
0.67
0.66
0.65
0.64
0.63
0.62
0
200
400
600
800
1000
1200
Simulation model evaluations
Average
Individual Runs
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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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Analysis Laboratory
Helsinki University of Technology
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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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Analysis Laboratory
Helsinki University of Technology
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Scheduling vs. no scheduling in the
example case
1
Aircraft availability
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0
50
100
150
200
250
Time (days)
No Scheduling
With Scheduling
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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
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Analysis Laboratory
Helsinki University of Technology
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