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

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 Usage 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

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

10. The genetic algorithm (GA) • Real-coded GA • Binary tournament selection for reproduction of solutions • Simulatedbinarycrossover 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

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