## 2 The Proposed Approach
### Variogram of WEEE Return Amount  
The return variogram reveals the spatial variation degree and correlation structure of the WEEE return amount in different spatial locations of the recycling network in the whole area D, indicating the randomness as well as the structure characteristics at the same time. Taking the variogram value as the \(Y\)-axis and the distance between two different recycling sites h as the \(x\)-axis, the spatial variogram of WEEE return amount in recycling sites is shown as Figure 3.  
There are several concepts that need to be illustrated in Figure 3. Firstly, when the distance \(h=0\), the variogram value \(\gamma(0)\) is termed as the nugget and denoted by \(C_{0}\), reflecting the variation caused by sampling scale and other factors. Secondly, the return variogram \(\gamma(h)\) continuously increases from non-zero value and finally reaches a relatively stable constant as the distance between two different recycling sites \(h\) grows. Moreover, this constant value is termed as sill and denoted by \(C_{0}+C_{1}\), indicating the maximum variation range or total variation degree of the WEEE return amount of each recycling site. Thirdly, when the return variogram value reaches sill, the distance is termed as the correlation length and denoted by \(a\), which means \(\gamma(a)=C_{0}+C_{1}\). If and only if the distance between two recycling sites is less than the correlation length, i.e., \(h<a\), the detected values is deemed as spatially correlated. Otherwise, the spatial correlation is too weak to worth consideration and thus can be negligible in this study.  
In spatial statistics, the commonly used spatial variograms include spherical, exponential, and Gaussian variogram, which have been proved to be effective for analysis of spatial variation structure. Three kinds of return variogram employed in this paper are given as follows.  
(1) The spherical variogram is formulated as  
\[\gamma(h)=\left\{\begin{array}{c}C_{0}+C_{1}\big{[}1.5(h/a)-0.5(h/a)^{3}\big{]},\ 0\leq h\leq a\\ C_{0}+C_{1},h>\ \text{a}\end{array}\right. \tag{10}\]  
The corresponding covariance function is given by  
\[C(h)=\left\{\begin{array}{c}C_{0}+C_{1},h=0\\ C_{1}[1-1.5(h/a)+0.5(h/a)^{3}\big{]},0<h\leq a\\ 0,h>a\end{array}\right. \tag{11}\]  
(2) The exponential variogram is formulated as  
\[\gamma(h)=C_{0}+C_{1}\Big{(}1-e^{-3h/a}\Big{)} \tag{12}\]  
And its corresponding covariance function is given by  
\[C(h)=C_{0}+C_{1}e^{-3h/a} \tag{13}\]  
(3) The Gaussian variogram is formulated as  
\[\gamma(h)=C_{0}+C_{1}\Big{(}1-e^{-3(h/a)^{2}}\Big{)} \tag{14}\]  
The corresponding covariance function is given by  
\[C(h)=C_{0}+C_{1}e^{-3(h/a)^{2}} \tag{15}\]  
Note that the degree of spatial variability can be expressed by dividing the variation range between nodes \(C_{1}\) by the total variation degree of the system \(C_{0}+C_{1}\), that is, the structural variance ratio \(\frac{C_{1}}{C_{0}+C_{1}}\). This ratio indicates the proportion of the spatial variation caused by the autocorrelation part of the return amount in the total variation of the system, and can reflect the spatial correlation degree of the return variable. In reverse logistics, if the structural variance ratio is less than 25%, it means that there is a weak  
Figure 3: Spatial variogram of WEEE return amount.  
spatial correlation between the return variables of different recycling sites; when this ratio is within the range of 25-75%, the return variables have a moderate spatial correlation; when this ratio is more than 75%, the spatial correlation between return variables is deemed to be strong.