Hybrid Scheduling and Routing for Rural Transit with Flexible and Fixed-Route Integration

Abstract

Rural public transit systems frequently face challenges in balancing operational efficiency and passenger convenience. Addressing the issue of transportation insecurity in rural areas, this study analyzes the total cost and effectiveness of public transit service in regions characterized by low demand density. Flexible-route services generally perform well in low-demand environments due to their adaptability, but they cannot accommodate long-distance trips required by passengers without access to personal vehicles. Conversely, traditional fixed-route buses are cost-effective along core corridors while suffering from limited coverage, forcing inconvenient transfers and extra travel times beyond the established network. Consequently, neither purely flexible nor purely fixed-route approaches effectively meet the transportation needs of low-density communities. To overcome these limitations, this paper proposes an integrated public transit framework formulated as a deterministic two-stage optimization model, combining flexible-route services with scheduled fixed-route operations to achieve seamless door-to-door connectivity. The framework explores controlled deviations of fixed-route buses with limited headway adjustments and coordinates flexible shuttles to effectively serve first- and last-mile segments. This integrated approach aims to minimize overall system operating costs while maintaining acceptable passenger waiting and in-vehicle travel times. Computational experiments and sensitivity analyses on synthetic rural networks demonstrate the scalability and effectiveness of the model in reducing combined vehicle-mileage and passenger-time costs.