## 2 Motivation  
The nature of UAM operations is inherently different from that of ground-based transportation, and new concepts and procedures are currently being developed to ensure the safety and efficiency of such operations, which will take place alongside traditional aviation. New models of operations management are also needed to support strategic and tactical decision making by service providers, such as optimum route planning and fleet scheduling to maximise their preferred objectives. Although these models are critical for UAM operations, researchers are still searching for the best model for use in UAM operations management. Hence, we propose a new point-to-point network formulation by considering existing routing problems and the TSP. The VRP and TSP have been widely used in recent decades for aerial vehicle applications, robotics, transportation and networking [11]. The difference between them is that the TSP considers a single vehicle that visits multiple customer locations before returningto the depot, with the aim of minimising the total travel time and distance [12], whereas the VRP involves a single depot and can also be interpreted as a multiple TSP (mTSP). The mTSP represents a relaxation of the VRP, in which neither the vehicle capacity nor customer demand are considered, whereas the VRP does consider customer demand [11]. However, the mTSP does not allow for multiple visits and subtours, meaning that the solution to the mTSP can be applied to the VRP [11]. There are several variants of the TSP in real-world applications, such as the single-depot mTSP, the multidepot TSP [11] and the coloured TSP (CTSP) [13]. The VRP also has many variants, such as the single-depot VRP (SDVRP) and the multidepot VRP (MDVRP [11]); in addition, to consider customer satisfaction, time windows can be introduced to the routing problem, yielding the SDVRP with time window (SDVRPTW [14]) and MDVRP with time window (MDVRPTW [15]). These problems have been addressed by many researchers by adding constraints to real-world applications. The VSP and TSP are seen as NP-hard problems, as the solution space and search space expand exponentially [12]. Hence, many algorithms have been developed to solve these problems, including deterministic, metaheuristic and market-based approaches, with additional approaches, such as fuzzy logic and game theory, that have been studied by many researchers [11]. [PERSON] et al. solved the classical formulation of the mTSP using the NSGA-II framework [16]. [PERSON] et al. proposed a new variant of the MDVRPTW under shared depot resources by introducing new constraints and applied a hybrid genetic algorithm [17]. [PERSON] et al. developed a metaheuristic algorithm to solve the MDVRP with limited capacity and stochastic demand [18]. [PERSON] et al. also solved the VRP with particle swarm optimisation to achieve a satisfactory distribution [12]. However, all of the above formulations adopted an accurate formulation of the mTSP and multidepot routing problem with relaxed capacity and time windows. All vehicles need to start and end at the same depot, and not all vehicles can visit each customer location, as exactly one customer is visited by one vehicle. In addition, the depot locations are different from the customer locations, whereas in the case of UAM operations, the depot and customer are at the same location. For instance, an aircraft travels from A to B, where A is the depot and B is the customer location; however, location B also has an aeroplane that can travel to another location A, in which case B is the depot and A is the customer location. These networks form a point-to-point network model, whereas the classical formulation of the routing problem can be seen as a hub-and-spoke network model after optimisation which can be seen in Figure 1. Hence, a classical formulation of the mTSP or MDVRP is not suitable for UAM operations. A new formulation is therefore required for application to UAM operations. In addition, scheduling needs to be performed to achieve safe operation.