A Hierarchical Grouping Algorithm for the Multi-Vehicle Dial-a-Ride Problem

Ride-sharing is an essential aspect of modern urban mobility. In this paper, we consider a classical problem in ride-sharing - the Multi-Vehicle Dial-a-Ride Problem (Multi-Vehicle DaRP). Given a fleet of vehicles with a fixed capacity stationed at various locations and a set of ride requests specified by origins and destinations, the goal is to serve all requests such that no vehicle is assigned more passengers than its capacity at any point in its trip. We give an algorithm HGR, which is the first non-trivial approximation algorithm for the Multi-Vehicle DaRP. The main technical contribution is to reduce Multi-Vehicle DaRP to a certain capacitated partitioning problem, which we solve using a novel hierarchical grouping algorithm. Experimental results show that the vehicle routes produced by our algorithm not only exhibit less total travel distance compared to state-of-the-art baselines, but also enjoy a small in-transit latency, which crucially relates to each individual rider's traveling time. This suggests that HGR enhances rider experience while being energy-efficient.