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.

Urban air mobility path planning must account for objects that do not provide cooperative surveillance information, but their motion and avoidance responses vary by class, making a single extrapolated trajectory insufficient to inform every path decision. We propose PRISM to bring alternative futures and their uncertainty into path planning. Using current sensor tracks, PRISM predicts three 15 s trajectory branches with probabilities and time-varying positional uncertainty. Forecast positions are used to screen candidate paths for potential collisions, while a time-indexed risk field derived from the predictive distribution ranks the paths that remain. This allows different possible futures to inform path selection without being collapsed into one trajectory. While work to extend the method to three-dimensional motion continues, the present study evaluates this approach in a two-dimensional horizontal-plane simulation containing aircraft, birds, and drifting objects with different motion and avoidance rules, including classes absent from training. Prediction tests, repeated futures from saved simulator states, and paired closed-loop episodes assess forecast quality and planning outcomes against a constant-velocity forecast. In in-distribution (ID) tests, PRISM’s mixture-mean average displacement error was 72.54 m versus 122.53 m for constant velocity, about 41% lower without future-based branch selection; the closest of three branches gave a 62% reduction. With raw predictive scales, exploratory paired comparisons supported fewer screened severe union encounters (minimum separation below 45 m) and greater lower-tail separation in three of five settings. The nominal out-of-distribution (OOD) severe-encounter contrast was uncertain without screening, while both ID contrasts retained support. Nominal-OOD sampling was extended after initial outcomes were examined. Total encounter counts within 152.4 m showed no clear difference from constant velocity. In the recalibration control, improved predictive coverage did not yield a consistent planning gain. PRISM brings possible motion across object classes into a common planning interface without requiring the target’s class or intent in advance. Its contribution is to make those alternatives and their uncertainty usable for path selection without changing the planner’s structure, and to assess their value through closed-loop separation as well as trajectory accuracy.