###### Abstract  
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. multivehicle point-to-point network; dynamic scheduling; problem formulation; UAM operation +
Footnote †: journal: Medical  
cloverleaf exchanges on freeways. The operation of UAMs has been divided into three categories: city taxi (on-demand flights between any available landing stations) airport shuttle (scheduled flights along defined routes between airports and landing stations) and intercity (scheduled flights along defined routes) [5]. To solve the problem of airspace use, route optimisation between vertiport locations and scheduling plans for each UAM are required. Commercial airlines operate based on a fixed, predetermined timetable of scheduled and assigned flights. To create this timetable, routes are first developed between cities depending on demand. Depending on these routes, a schedule is generated based on the specific operating restrictions of each airport, such as the fixed schedules available for a given airline. Fleets are then assigned, and a decision is made as to which aircraft will perform each scheduled flight; the best type of aircraft is assigned to each flight to maximise profitability [3]. In contrast, UAM flight operation services have been envisaged as an on-demand aerial travel service but may also be operated based on a fixed, predetermined timetable in the same way as airlines operate scheduled flights [4]. To provide an on-demand aerial travel service, it would be preferrable to consider each UAM flight mission, from takeoff to landing, as a series of flight segments before developing flight schedules. However, these vehicles may be operated in a city with many UAMs, so an optimum route for each UAM and preset schedules are required for flight safety. The increasing complexity of UAMs, as well as the intensification of competition between airlines, has led to a need to create models that include large numbers of routes and restrictions, which can be considered NP-hard integer programming problems [6]. Numerous routing problems have been proposed, such as the travelling salesman problem (TSP) and the vehicle routing problem (VRP), and their variants can be solved to find the optimum route for each vehicle. However, these solutions require additional depot locations, and not all of vehicles can travel to all locations.