Event-based models for the electric autonomous dial-a-ride problem

On-demand transportation systems can serve to complement standard scheduled public transport in areas with low population density or to address the mobility needs of handicapped and elderly people. In this paper, we address the electric autonomous dial-a-ride problem (e-ADARP). In the e-ADARP, vehicle routes for serving user requests consisting of pickup and drop-off locations are determined. The objective is to minimize a weighted combination of travel distances and excess user ride time. Since it is assumed that an electric and autonomous vehicle fleet is used for the ride-sharing service, in addition to vehicle capacity, time windows, and maximum user ride times, also battery capacity constraints have to respected. We develop a mixed-integer linear programming (MILP) model for the e-ADARP that relies on an event-based graph. By using an event-based graph, capacity, pairing, and precedence constraints are implicitly applied. Several valid inequalities from the literature as well as newly developed ones are used to strengthen the model. In comparison to existing exact methods for the e-ADARP, we obtain competitive results on a set of available benchmark instances: we provide several improved upper and lower bounds and provide optimal solutions to previously unsolved instances. Furthermore, we analyze the impact of the capacity setting as well as different weight combinations on solution time and demonstrate the effect of battery start and end levels over several periods.