# Location Selection Methods for Urban Terminal Co-Distribution Centers with Air-Land Collaboration
## 5 Analysis  
### Preselected Set Construction  
To verify the feasibility of the proposed algorithm, we considered the Wangsheren area of Jinan City, China, as an example. Using the public control plan data on the Jinan Natural Resources and Planning Bureau website, as well as an electronic network map and the actual logistics and distribution demand, 492 customer demand points were identified. According to the land use nature of the different parcels and planning indicators, such as the plot ratio, the distribution of each demand point was calculated. The demand corresponding to the first 100 points is listed in Table 3. The distribution of demand points is illustrated in Figure 4.  
According to Table 3, Total Demand = 303,752 and Average Demand = 617.38. Before starting the clustering operation, a Cartesian coordinate transformation was applied to the latitude and longitude coordinates of the original data using the Mercator projection method. Let the radius of the earth be \(r\), the longitude be \(l_{o}\), and the latitude be \(la\). Therefore, the Cartesian \(XY\) coordinates can be expressed as  
\[\begin{cases}X=l_{o}\cdot R\\ Y=R\cdot\ln\Bigl{[}\tan\Bigl{(}\frac{\pi}{4}+\frac{la}{2}\Bigr{)}\Bigr{]}\end{cases} \tag{32}\]  
The service radius of the co-distribution center, \(R\), took the value [0.7, 0.8, 0.9, 1.0, 1.1, 1.2, 1.3] km. The values of \(K\) considered here were [14; 16; 19; 23; 29; 36; 47]. K-means clustering analysis using Matlab was performed, and compactness (CP), separation (SP), the Davies-Bouldin index (DBI), and the Dunn validity index (DVI) were calculated for each value of K [27]. The K-means clustering results are presented in Table 4.  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**Point** & **Demand** & **Point** & **Demand** & **Point** & **Demand** & **Point** & **Demand** & **Point** & **Demand** \\ \hline
1 & 278 & 21 & 584 & 41 & 1218 & 61 & 1529 & 81 & 1047 \\
2 & 541 & 22 & 152 & 42 & 324 & 62 & 445 & 82 & 1044 \\
3 & 358 & 23 & 229 & 43 & 404  
The CP and DVI values were optimized when the number of clusters was 47. From the perspective of the solution space, a higher number of co-distribution centers in the preselected set gave a higher-dimensional solution space, making it easier to explore better solutions using the optimization algorithm. Thus, it was reasonable to set the number of co-distribution centers to 47. The relationship between the co-distribution centers and demand points is shown in Figure 5.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**K** & **CP** & **SP** & **DB** & **DVI** \\ \hline
14 & 27.4086 & 1.1806 & 0.7883 & 0.0631 \\
16 & 24.2683 & 1.1166 & 0.8294 & 0.0647 \\
19 & 7.2490 & 1.0756 & 0.8364 & 0.0545 \\
23 & 9.6046 & 0.8206 & 0.8656 & 0.0701 \\
29 & 12.6379 & 0.7496 & 0.8308 & 0.0772 \\
36 & 6.0788 & 0.5983 & 0.8823 & 0.0711 \\
47 & 1.2362 & 0.4249 & 0.8446 & 0.1018 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Comparison of metrics for clustering results.  
Figure 4: Distribution of demand points.  
From Figure 5, it is clear that the alternative set of distribution centers is uniformly distributed inside the demand points. The distribution trend indicates that the preselected set is largely within the region with dense demand points and away from the region with sparse demand points, which is in line with expectations. In the next section, the distribution center location problem was solved based on this preselected set.