Optimizing a vehicle’s route in an on-demand ridesharing system in which users might walk

Within the context of a shared on-demand transport system, we study the problem of selecting the stopping points from which passengers should walk to their exact destinations (or from their exact origins). We focus on the single-vehicle case that must follow a predefined order of requests, posing the mathematical program, showing that it can be solved in polynomial time and proposing a heuristic that runs faster. We compare the optimal algorithm, the heuristic, and the routes that visit the exact request points, and we show that avoiding detours can reduce total costs by almost one fifth and vehicle costs by more than one third. The heuristic yields competitive results. Simulations over the real street network from Manhattan show that the time reduction achieved by the heuristic might be crucial to enable the system to operate in real-time.