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.

In this paper, we develop and analyze a model to generate an equitable set of routes for hazardous material shipments. The objective is to determine a set of routes that will minimize the total risk of travel and spread the risk equitably among the zones of the geographical region in which the transportation network is embedded, when several trips are necessary from origin to destination. An integer programming formulation for the problem is proposed. We develop and test a heuristic that repeatedly solves single-trip problems: a Lagrangian dual approach with a gap-closing procedure is used to optimally solve single-trip problems. We report a sampling of our computational experience, based on a real-life routing scenario in the Albany district of New York State. Our findings indicate that one can achieve a high degree of equity by modestly increasing the total risk and by embarking on different routes to evenly spread the risk among the zones. Furthermore, it appears that our heuristic procedure is excellent in terms of computational requirements as well as solution quality. We also suggest some directions for future research.

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In many countries, freight trains have to share a rail network with passenger trains. In this paper, we consider a situation where passenger trains must adhere to a strict published schedule, whereas freight train movements can be inserted at any convenient time, without disrupting scheduled passenger trains. We propose an algorithm for the problem of routing and scheduling of a single freight train in a passenger rail network. However, the multiple freight train routing and scheduling problem is shown to be NP-complete, even for simplified instances. Specifically, we show that both routing and scheduling of freight trains are difficult, even when only two freight trains are considered. It is also difficult when freight train movements are restricted to reach their destinations with no idling permitted at intermediate stations. We have developed a Stepwise Dispatching Heuristic for routing and scheduling multiple freight trains in a passenger rail network. Computational results confirm the efficacy of our algorithm for single freight train routing and of the proposed Stepwise Dispatching Heuristic.