## 2 Models
### Parcel-Receiving Station and Public Air-Route Planning  
The existing studies only focus on the problem of landing-point location or air-route planning. However, we believe that the location of parcel-receiving stations and the planning of public air routes are mutually influenced. In this section, the parcel-receiving station location problem and the public air-route planning problem are modeled as a bilayer optimization problem. The upper-layer model is the parcel-receiving station location \begin{table}
\begin{tabular}{c c} \hline \hline \multicolumn{2}{c}{**Notations**} \\ \hline \(AR_{\text{max}}\) & the maximum acceptable air range of the UAV air route \\ \(\theta_{\text{max}}\) & the maximum acceptable turning angle of the UAV air route \\ \hline \multicolumn{2}{c}{**Sets**} \\ \hline \(G\) & the set of grids through which the route passes \\ \hline \multicolumn{2}{c}{**Variables**} \\ \hline n & the number of grids through which the route passes \\ \(\left(x_{i},y_{i}\right)\) & the horizontal and vertical coordinates of grid \(i\) \\ \(D_{i}\) & collision-risk value of grid \(i\) \\ \(S_{i}\) & crash-risk value of grid \(i\) \\ \(L_{i}\) & noise-risk value of grid \(i\) \\ \(\theta_{i}\) & turning angle of the air route at grid \(i\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Related parameters for single-air-route planning formulation defined. model, and the lower-layer model is the public air-route planning model. The public air-route planning needs to be based on the parcel-receiving station location results of the upper-layer model, and the evaluation criteria of the station location results is also affected by the public air-route planning results of the lower-layer model. The upper-layer model is a multi-objective optimization model that is used to select a parcel-receiving stations set \(S=\{s_{i}|i=1,2,\ldots,n_{s}\}\) of \(n_{s}\) stations from alternative locations. The objective of the upper-layer model is to minimize the selected station count, average picking distance, and picking distance standard deviation of unit demand in the planning area, so as to reflect the economy, practicability, and fairness of the location results. In order to meet the pick-up needs of all customers, each demand point in the demand point set \(D=\{d_{i}|i=1,2,\ldots,n_{d}\}\) of \(n_{d}\) demand points should be assigned a parcel-receiving station. The customers of the demand point go to the assigned parcel-receiving station to receive and send parcels, which is called the matching relationship between demand point and parcel-receiving station. The lower-layer model is a single-objective optimization model that is used to determine the configuration of the public air route. The public air route is the set of connecting edges \(E=\{e_{i}|i=1,2,\ldots,n_{s}\}\) between the warehouse and the stations in a transport network diagram. The edge between two nodes is the output of the single air-route planning. The air route of parcel-receiving station \(s\) is a set \(R_{s}=\left\{e_{j}|j=1,2,\ldots,n_{r}\right\}\) of the passing edges between the warehouse and the station in the public air route, where \(n_{r}\) refers to the number of passing edges. As in Section 2.3, in order to quantify the operating cost of public air routes, the edge \(e_{i}\) of set \(E\) can also be split according to the grids-traversed set \(G^{i}=\left\{g_{j}^{i}|j=1,2,\ldots,n_{e}^{i}\right\}\) of \(n_{e}^{i}\) grids. The objective of the lower-layer model is to minimize the operating cost of the public air route, including the flight risk of the public air route and the air range of the air route between each warehouse and station, so as to reflect the safety and efficiency of the planning results. Compared with the result of single-air-route planning, the air route of stations in the public air route includes a direct route and transit route to reduce the operating cost. The direct route is the same as the result of the single-route planning.