The ridesharing problem without predetermined drivers and riders: formulation and heuristic

We consider a ridesharing service in which no driver and rider's roles are pre-determined, but left to decide by the system to further reduce costs compared to the typical version with preassigned roles. Travelers are motivated to participate in the service by saving individual transportation costs and accept its rules. We first formally define it as a generalized ridesharing optimization problem (RSP), propose its transformation into a single-depot multiple traveling salesman problem with pickup and delivery constraints (SDMTSP-PD) and provide its mixed-integer program (MIP) formulation. We then develop a polynomial-time solution method based on optimal pair matching among participants, improved by a construction insertion-based heuristic to obtain approximate solutions to the SDMTSP-PD. Experiments show that this approach could solve the problem very fast and provide near-optimal solutions and that the proposed RSP model provides substantial system-wide travel cost saving (25%+) and vehicle-trip saving (50%) compared to the non-ridesharing system and perform better than companion services with preassigned roles (P-RSP).