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

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

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

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

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

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

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

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

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

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

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

Optimization results

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

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

Scheduling vs. no scheduling in the example case

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