The integrated on-demand bus routing problem: Combining on-demand buses with a high-frequency fixed line public transport network

In this work we analyze the performance of integrating a large-scale on-demand bus system with a high-frequency fixed line public transport network in an urban context. Given are a high-speed metro network, a set of real-time requests, a set of bus station locations and a fleet of fixed capacity minibuses. Requests have a set of possible departure/arrival bus stations within walking distance of the actual departure/arrival location and have to be served within a certain time window. The aim is to simultaneously (1) decide on the trip type for each passenger (only bus, only metro or mixed), (2) route the on-demand buses, (3) in the case of a bus-leg in the trip, assign each passenger to a departure and arrival bus station (bus station assignment), and (4) in the case of a metro-leg in the trip, decide the assigned transfer station(s) and used metro lines (transfer station assignment). We call this problem the integrated on-demand bus routing problem. After presenting a mathematical model, we propose a quick and scalable insertion-based heuristic to solve the problem. The results found by the heuristic are further used to compare the performance of an integrated system, to a system that only uses on-demand buses. It is concluded that the integrated system always performs better regarding the service rate or number of served requests. Depending on the speed and layout of the metro network, also the average user ride time per passenger improves by the integration.