Optimal zone sizes and headways for flexible-route bus services

•Inter-relations between headways and service areas are explored for flexibly routed bus services.•Analytical relations and local search methods are used to jointly optimize headways and zone sizes with vehicle capacity constraints.•Effects of various factors on optimized system design are explored.•The modular many-to-one service analyzed here is useful as a building block for multi-zone many-to-many service. Flexible-route bus systems serving passengers at their doorsteps may be preferable to fixed-route bus systems in areas with low demand densities or whose roads cannot accommodate relatively large fixed-route buses. Flexible-route systems may also be preferable for elderly or handicapped riders for whom accessing the pre-determined stops on fixed routes is difficult. Since bus systems with flexible demand-responsive routes retain the economic and environmental advantages of public transportation, it is important to analyze them and optimize their characteristics to match their operating environments. This study shows how the total cost can be minimized for a flexible-route bus system with a many-to-one demand pattern by jointly optimizing its headway and service zone size. Numerical results demonstrate the model's applicability and indicate how such flexible-route systems should be adapted to demand characteristics and planning constraints.