In this paper, we introduce a new formulation of the multivehicle point-to-point network problem to be utilised in urban air mobility (UAM) vertiport-to-vertiport network operations. Vehicle routing problems (VRPs) and their variants have previously been studied and applied in real-world situations, but these problems require additional depot locations, and not all the vehicles can travel to all the locations. In UAM operations, additional depot locations may not be required, and all vehicles can travel to all locations, meaning that existing routing problems are not suitable for application to the management of UAMs. Therefore, we propose a new formulation for UAM vertiport-to-vertiport operation by introducing new constraints. In addition, we integrate dynamic scheduling with the flight mission by controlling cruise speed and waiting in each UAM at each vertiport location to generate an arrival and departure schedule for different vertiports that can avoid collisions and increase the number of vehicles. A computational experiment is conducted using an MILP model, and the results show that although our formulation satisfies the problem definition, the computation time increases exponentially with an increase in the problem size. A case study is conducted in the Seoul area involving five vertiports, with 10- and 15-vehicle scenarios studied. This case study shows that the cruise speed variable is active only for the lower and upper bounds under dynamic scheduling, whereas the waiting time variable can be controlled between user-defined limits that can be applied to the management of vertiport-to-vertiport UAM operations.