Detours in Shared Rides

Detours are considered key for the efficient operation of a shared rides service, but they are also a major pain point for consumers of such services. This paper studies the relationship between the value generated by shared rides and the detours they create for riders. We establish a limit on the sum of value and detour, and we prove that this leads to a tight bound on the Pareto frontier of values and detours in a general setting with an arbitrary number of requests. We explicitly compute the Pareto frontier for one family of city topologies and construct it via simulation for several more networks, including one based on ride-sharing data from commute hours in Manhattan. We find that average detours are usually small, even in low-demand-density settings. We also find that by carefully choosing the match objective, detours can be reduced with a relatively small impact on values and that the density of ride requests is far more important than detours for the effective operations of a shared rides service. In response, we propose that platforms implement a two-product version of shared rides and limit the worst-case detours of its users.