1 S ystems Analysis Laboratory Helsinki University of Technology Scheduling Periodic Maintenance of Aircraft through simulation-based optimization Ville Mattila and Kai Virtanen Systems Analysis Laboratory, Helsinki University of Technology

2 S ystems Analysis Laboratory Helsinki 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

3 S ystems Analysis Laboratory Helsinki 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

4 S ystems Analysis Laboratory Helsinki University of Technology Periodic maintenance of a Hawk Mk51 training aircraft Type of PM task Maintenance interval (flight hours) Average duration (hours) Maintenance level C5010 Organizational level (O-level), Squadron D1, D2125 to to 200 Intermediate level (I-level), Air command’s repair shop E, F, G500 to to 500 Depot level (D-level), Industrial repair shop

5 S ystems Analysis Laboratory Helsinki University of Technology The need for PM scheduling Scheduling is done for two primary reasons 1Avoid degradation of aircraft availability 2Allow maintenance facilities to plan for supply of resources

6 S ystems Analysis Laboratory Helsinki University of Technology Scheduling vs. no scheduling

7 S ystems Analysis Laboratory Helsinki 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

8 S ystems Analysis Laboratory Helsinki 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

9 S ystems Analysis Laboratory Helsinki University of Technology The maintenance scheduling problem Nthe total number of aircraft X=(x 1,1,...,x 1,n1,...,x N,1,...,x N,nN ) the maintenance schedule of the fleet Lsimulated average aircraft availability  sample path

10 S ystems Analysis Laboratory Helsinki 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)

11 S ystems Analysis Laboratory Helsinki 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

12 S ystems Analysis Laboratory Helsinki University of Technology Design of experiment 300 evaluations of the simulation for each combination of parameters GA Population size Probability of crossover Amplitude of crossover 1argemediumsmall SA Number of rescheduled tasks per iteration 369 Amplitude of rescheduling smallmediumlarge Probability of accepting a degrading schedule smallmediumlarge

13 S ystems Analysis Laboratory Helsinki University of Technology Results Highest average availability obtained in the optimization GA Population size Probability of crossover Amplitude of crossover SA Number of rescheduled tasks per iteration Amplitude of rescheduling Probability of accepting a degrading schedule

14 S ystems Analysis Laboratory Helsinki 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

15 S ystems Analysis Laboratory Helsinki 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