In this paper, we propose a novel, computational efficient, dynamic
ridesharing algorithm. The beneficial computational properties of the algorithm
arise from casting the ridesharing problem as a linear assignment problem
between fleet vehicles and customer trip requests within a federated
optimization architecture. The resulting algorithm is up to four times faster
than the state-of-the-art, even if it is implemented on a less dedicated
hardware, and achieves similar service quality. Current literature showcases
the ability of state-of-the-art ridesharing algorithms to tackle very large
fleets and customer requests in almost near real-time, but the benefits of
ridesharing seem limited to centralized systems. Our algorithm suggests that
this does not need to be the case. The algorithm that we propose is fully
distributable among multiple ridesharing companies. By leveraging two datasets,
the New York city taxi dataset and the Melbourne Metropolitan Area dataset, we
show that with our algorithm, real-time ridesharing offers clear benefits with
respect to more traditional taxi fleets in terms of level of service, even if
one considers partial adoption of the system. In fact, e.g., the quality of the
solutions obtained in the state-of-the-art works that tackle the whole customer
set of the New York city taxi dataset is achieved, even if one considers only a
proportion of the fleet size and customer requests. This could make real-time
urban-scale ridesharing very attractive to small enterprises and city
authorities alike. However, in some cases, e.g., in multi-company scenarios
where companies have predefined market shares, we show that the number of
vehicles needed to achieve a comparable performance to the monopolistic setting
increases, and this raises concerns on the possible negative effects of
multi-company ridesharing.