## 3 Monte Carlo simulation
### Prediction Results of WEEE Return Kriging Model  
The prediction accuracy of the Kriging method is evaluated by prediction error percentage (PEP) and standard deviation of prediction error (SDPE). The prediction error percentage is the difference between the real value and the predicted value divided by the real value, and the standard deviation of prediction error is the standard deviation of Kriging prediction error of multiple samples. The prediction results of the WEEE return Kriging spatial model proposed in this paper are shown in Table 4.  
_Simulation conclusion 3:_ The total prediction error percentage is 1.21%, and the standard deviation is 0.001532 which demonstrates that the proposed model can accurately predict the return of WEEE in reverse logistics. Moreover, the correctness of the method is also verified. The calculation result here refers to the average value of each sample repeated several times in all recycling sites in the whole area.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**No. of Sites** & **Variogram** & **PEP** & **SDPE** \\ \hline \multirow{3}{*}{100} & Spherical & 1.08\% & 0.015657 \\  & Exponential & 0.87\% & 0.016062 \\  & Gaussian & 1.71\% & 0.012183 \\ \hline \multirow{3}{*}{50} & Spherical & 1.04\% & 0.014249 \\  & Exponential & 0.84\% & 0.012343 \\  & Gaussian & 1.76\% & 0.014894 \\ \hline \multirow{3}{*}{20} & Spherical & 0.84\% & 0.014158 \\  & Exponential & 0.48\% & 0.018421 \\  & Gaussian & 1.42\% & 0.019510 \\ \hline \multirow{3}{*}{10} & Spherical & 1.07\% & 0.016518 \\  & Exponential & 0.87\% & 0.014328 \\ \cline{1-1}  & Gaussian & 2.49\% & 0.015571 \\ \hline \multicolumn{2}{c}{Total} & 1.21\% & 0.001532 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Evaluation of prediction results of WEEE Kriging model for simulation.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**No. of Sites** & **Variogram** & **Sill (\(C_{0}\)+\(C_{1}\))** & **Nugget (\(C_{0}\))** & **Structural Variance Ratio** \\ \hline \multirow{3}{*}{100} & Spherical & 0.80778 & 0.14828 & 81.64\% \\  & Exponential & 0.80664 & 0.10263 & 87.28\% \\  & Gaussian & 0.81273 & 0.24242 & 70.17\% \\ \hline \multirow{3}{*}{50} & Spherical & 0.82451 & 0.14717 & 82.15\% \\  & Exponential & 0.84158 & 0.08912 & 89.41\% \\  & Gaussian & 0.82170 & 0.18225 & 77.82\% \\ \hline \multirow{3}{*}{20} & Spherical & 0.90012 & 0.14104 & 84.33\% \\  & Exponential & 0.92157 & 0.09086 & 90.14\% \\  & Gaussian & 0.92108 & 0.16422 & 82.17\% \\ \hline \multirow{3}{*}{10} & Spherical & 0.94212 & 0.11194 & 88.12\% \\  & Exponential & 0.94852 & 0.55578 & 94.15\% \\ \cline{1-1}  & Gaussian & 0.92349 & 0.21733 & 76.47\% \\ \hline \hline \end{tabular}
\end{table}
Table 3: Quantitative analysis results of three different variograms.  
Simulation conclusion 4: From the perspective of variogram, the prediction error percentage of exponential variogram is 0.77%, which is lower than that of spherical variogram (1.01%) and Gaussian variogram (1.85%). The main reason for the low accuracy of Gaussian variogram is that the slope of Gaussian variogram at the origin is 0, which leads to the instability and abnormal phenomenon of Kriging prediction.  
Simulation conclusion 5: According to the influence of the number of recycling sites on the performance of the prediction model, the prediction error percentages of 100, 50, 20 and 10 are 1.22%, 1.21%, 0.91% and 1.48%, respectively. There is no significant fluctuation of prediction error. This also shows that the return Kriging model is applicable to a WEEE reverse logistics return system with different number of recycling sites, and the proposed model is universal.