An optimization model of on-demand mobility services with spatial heterogeneity in travel demand

•We model on-demand mobility services at various service levels and demand patterns.•We investigate the effect of spatial demand heterogeneity on the required fleet size.•Demand–supply imbalance problem is solved through vehicle relocation.•Agent-based simulation is used to verify the proposed model.•Model can serve as the basis for the practical implementation of planned services. We propose an optimization model that predicts the required fleet size of on-demand mobility (ODM) services at various service levels for a range of demand patterns. Both customer waiting time and spatial heterogeneity in demand are considered when formulating the flow conservation equation for the system’s steady state. The demand–supply imbalance problem is solved through vehicle relocation. Vehicle relocation is reformulated into a simple linear programming problem, and the objective function is set to minimize the number of relocation vehicles. Furthermore, indicators were defined to more effectively explain the effects of spatial heterogeneity of travel demand on the required fleet size. The analysis results show that even among regions with the same average demand rate, the required fleet size may vary depending on the spatial demand pattern of origins and destinations. The higher the ratio of long-distance travel and the greater the need for vehicle relocation, the larger the fleet size required. Furthermore, the user travel time reduction effect is maximized at the minimum fleet size and then steadily decreases as fleet size increases. Cost minimization requires more vehicles than fleet size minimization. Cost minimization may be an advantageous goal for operation of an ODM service as a driverless vehicle service. The simultaneous consideration of both fleet size minimization and cost minimization provides a required fleet size range. Although the proposed model is simple and includes approximations, it helps provide insight into ODM service design and investment decision-making. Thus, the proposed model can be used by governments or agencies to design policy or operationally optimized services. Moreover, the model can serve as the basis for the practical implementation of planned services.