Analyzing the benefits of an integrated mobility system using a matheuristic routing algorithm

•Dial-a-ride services are often invoked to replace unprofitable public transport in rural areas.•This work presents a routing algorithm to integrate dial-a-ride services into the remaining public transport network.•An integrated scheduling procedure synchronizes the dial-a-ride schedules to public transport timetables.•The efficiency of integration depends on operational characteristics of the system and geographical demand distribution.•The algorithm also solves related synchronization problems in passenger and freight transport.