The Round-Trip Ridesharing Problem with Relay Stations

In this work, we investigate the potential benefits of introducing relay stations in the round-trip ridesharing problem. In the classical round-trip ridesharing system, the pick-up and drop-off locations for the rider don’t differ from his origin and destination, respectively, for both outgoing and return trips. This system is straightforward but inflexible and unbalanced as it puts the whole detour effort on the driver’s shoulders. In this paper, we propose to consider a meeting location as flexible and to determine its optimal position minimizing total travel cost for the round-trip. The meeting locations correspond to relay stations in which riders find ridesharing vehicles. The introduction of relay stations in the round-trip ridesharing problem creates dependency between the outgoing and return trips, in the sense that the relay stations must be chosen in such a way as to minimize the combined travel cost of the outgoing and return trips. In this setting, the rider is supposed to drive to the relay station with his private car and to park it there, so the return trip has to drop him there to get his car back. We present efficient algorithms to solve this problem and, finally, we perform a comparative evaluation using a real road network and real dataset provided by a local company. Our numerical results show the effectiveness of our system, which improves participants’ cost-savings and matching rate compared to the classical round-trip ridesharing system.