Following the advent of drones for surveillance and cargo delivery purposes, advancements in recent years have also been made towards the development of larger drones for passenger transport. The concept of Urban Air Mobility (UAM) prospects to offer ride-sharing services within and between cities. While trip scheduling and vehicle routing algorithms exist for various forms of road-based transportation services, UAM operations pose specific constraints and requirements that, to the best of our knowledge, have not been addressed comprehensively in academic literature. The purpose of this research is to develop a Mixed-Integer Linear Programming (MILP) model that optimally matches the available VTOL (Vertical Take-off and Landing) vehicle fleet with customer trip requests, subject to (UAM-specific) constraints, and which subsequently provides a vehicle’s routing. The model, in particular, addresses the constraint of limited ground infrastructure capacity. A case study is performed where multiple demand distribution scenarios, resembling different use cases, are applied to the model. Results show that wider time windows do not have a clear beneficial effect on the profit and that customer demand distribution has an impact on the efficiency of the operation. Additionally, the results enable the identification of various key input parameters for infrastructure, fleet size and vehicle technology that can improve the overall operation.