Incremental bus service design: combining limited-stop and local bus services

Long in-vehicle travel times resulting from frequent stops make bus service an unattractive choice for many commuters. Limited-stop bus services however have the advantage of shorter in-vehicle times experienced by passengers. In this work, we seek to modify a given bus service by optimally reassigning some number of bus trips, as opposed to providing additional trips, to operate a limited-stop service. We propose an optimization model to determine a limited-stop service route to be operated in parallel with the local service and its associated frequency to maximize total user welfare. A few theoretical properties of the model are established and used to develop a solution approach. As a proof of concept, we present numerical results obtained using real-world data together with comprehensive discussions of solution quality, computational times and the model's sensitivity to different parameters. Finally, we solve the optimization model for 178 real-world bus routes with different characteristics in order to demonstrate the impacts of some key attributes on potential benefits of limited-stop services.