## 4 Case Study  
In order to further verify the correctness of the spatial mathematical model of WEEE return prediction of reverse logistics based on the Kriging method, the WEEE return prediction of J company is taken as an example for case study in this paper. J company is one of the key national eco city demonstration enterprises in Shanghai, China. With the goal of promoting the rational utilization of resources, J company is committed to becoming a comprehensive service provider of renewable resources industrial chain. Taking the recycling of electronic waste as the business starting point, it has established an e-waste recycling system with the Internet of Things technology as the core. The reverse logistics network is shown in Figure 5. There are 1416 secondary recycling sites, 51 primary recycling sites, seven recycling centers, one waste treatment center and five remanufacturing product suppliers, which are distributed in various administrative districts of Shanghai. This paper is focused on these 51 primary recycling sites, which have a large amount of return and spatial correlation. From 2017 to 2019, the statistics of return amount of large and small waste electronic products of J company are shown in Figure 6 and the total number in three years has reached 1,375,155. Large and small pieces are divided by product volume. For example, large waste electronic products include refrigerators and televisions, while small waste electronic products refer to mobile phones and batteries. All these waste electronic products are recycled through 51 primary recycling sites. Figure 5: Electronic waste remanufacturing systems recycling network. Case conclusion 1:As can be seen from Figure 7, the correlation length of WEEE return amount of \(J\) company from 2017 to 2019 is about 90 km, that is, if the distance exceeds 90 km, the correlation will decrease quickly. This phenomenon is consistent with the actual situation. The distance from Baoshan District in the north of Shanghai to Hangzhou Bay in the southernmost Jinshan District of Shanghai is about 90 km. If this distance is exceeded, the two recycling sites will be located in two different administrative areas (such as Shanghai and Kunshan City of Jiangsu Province). Due to the great differences in regional policies, the spatial correlation of the two recycling sites will decrease rapidly. Case conclusion 2:It can be seen from Figure 8 that for company \(J\) with 51 primary recycling sites, the structural variance ratio is 90.39% when using exponential variogram. Meanwhile, the structural variance ratio of the sample with 50 recycling sites using exponential variogram in the simulation example is 89.41%. The simulation results are basically consistent with the measured data. In order to further analyze and compare the fitting performance of the different variograms, the measured data are used for comparative analysis, and the results are shown in Figure 8.  
Case conclusion 3:According to the fitting results of the measured data, both exponential variogram and spherical variogram are better than the Gaussian variogram, which verifies the simulation results. The actual WEEE return of J company in 36 months is divided into two parts. The data of first 24 months are used as training samples, and the data of last 12 months are used as test samples. The Kriging model of exponential variogram is used to predict the return in the next 12 months. The final evaluation of the prediction results is shown in Table 6.  
Case conclusion 4:The prediction error percentage of the Kriging model using exponential variogram is 1.43%, and the standard deviation is 0.04578. The prediction error is close to the total error (1.21%) in the simulation example. Generally speaking, the prediction performance of this paper based on the Kriging model is acceptable. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**No. of Sites** & **Variogram** & **PEP** & **SDPE** \\ \hline
51 & Exponential & 1.43\% & 0.04578 \\ \hline \hline \end{tabular}
\end{table}