The aircraft maintenance routing problem

Federal aviation regulations require that all aircraft undergo maintenance after flying a certain number of hours. To ensure high aircraft utilization, maintenance is done at night, and these regulations translate into requiring aircraft to overnight at a maintenance station every three to four days (depending on the fleet type), and to visit a balance-check station periodically. After the schedule is fleeted, the aircraft are routed to satisfy these maintenance requirements. We give fast and simple polynomial-time algorithms for finding a routing of aircraft in a graph whose routings during the day are fixed, that satisfies both the three-day maintenance as well as the balance-check visit requirements under two different models: a static infinite-horizon model and a dynamic finite-horizon model. We discuss an implementation where we embed the static infinite-horizon model into a three-stage procedure for finding a maintenance routing of aircraft.