1. 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

2. 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

3. Aircraft usage and maintenance
Different forms of pilot and tactical training
A number of aircraft chosen each day to flight duty
Several missions during one day
Failure repairs
Unplanned
Periodic maintenance
Based on usage
Different level maintenance facilities

4. 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 command’s repair shop
E, F, G
500 to 2000
300 to 500
Depot level (D-level),
Industrial repair shop

5. 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

6. 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

7. 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

8. 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

9. The simulation model No maintenance or repair need
Check for failures and periodic maintenance need
Turnaround or pre-flight inspection
Mission
O-level maintenance
I-level maintenance
D-level maintenance
Need for periodic maintenance or failure repair
No maintenance or repair need

10. 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

11. 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
Number of daily flights per aircraft
O-level maintenance capacity
1 aircraft
I-level maintenance capacity
3 aircraft
D-level maintenance capacity
2 aircraft

12. Optimization results

13. 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

14. 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

15. Scheduling vs. no scheduling in the example case

16. 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