# Optimizing a Reverse Supply Chain Network for Electronic Waste under Risk and Uncertain Factors
## 5 An Illustrative Example
These results are shown in columns 3-4 of Table 16.  
According to the results in Table 16, a satisfactory solution of the fuzzy problem is found at \(\alpha=0.7\), which is the highest degree balance. With \(\alpha=0.7\), the result shows that the total cost of the RSC model is in the possibility distributions ($170,505; 187,369; 210,821). These figures can assist DM in terms of the overall cost when designing an RSC network. In the optimistic case, the total cost can be $ 170,505 USD, whereas the figure can increase to $ 210,821 USD in the pessimistic situation. The overall cost in the most likely case is $187,369 USD. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & \multicolumn{5}{c}{**Probability**} \\ \hline  & \multicolumn{2}{c}{**Dismantling Centers**} & \multicolumn{2}{c}{**Repairing Centers**} \\ \hline  & \(\overline{\mathbb{P}}\hat{1}_{1d}\) & \(\overline{\mathbb{P}}\hat{2}_{2d}\) & & \(\overline{\mathbb{P}}\hat{1}_{1e}\) & \(\overline{\mathbb{P}}\hat{2}_{2e}\) \\ \(d=1\) & (2.7,3,3,3) & (3.6,4,4.4) & \(e=1\) & (3.6,4,4.4) & (3.6,4,4.4) \\ \(d=2\) & (1.8,2,2.2) & (1.8,2,2.2) & \(e=2\ \begin{table}
\begin{tabular}{c c c c} \hline \hline \multicolumn{1}{c}{**Feasibility Degree**} & \multicolumn{1}{c}{**Possibility Distributions of Objective Value**} & \multicolumn{1}{c}{**Compatibility Index**} & \multicolumn{1}{c}{**Degree of Balance of of Each Solution**} \\ \hline
0.4 & (167,544; 182,128; 204,809) & 0.720 & 0.4 \\
0.5 & (169,254; 183,972; 207888) & 0.684 & 0.5 \\
0.6 & (169,864; 185,644; 208,663) & 0.652 & 0.6 \\
0.7 & (170,505; 187,369; 210,821) & 0.619 & 0.619 \\
0.8 & (173,029; 189,103; 211,795) & 0.586 & 0.586 \\
0.9 & (175,816; 191,104; 214,036) & 0.547 & 0.547 \\
1 & (176,262; 192,636; 219,605) & 0.518 & 0.518 \\ \hline \hline \end{tabular}
\end{table} 
Table 16: \(\alpha\)-acceptable optimal solutions. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multicolumn{5}{c}{**Probability**} & \multicolumn{2}{c}{**Impact**} \\ \hline route c-\(d\) & \(\widetilde{P4}_{1d}\) & \(\widetilde{P4}_{2d}\) & \(\widetilde{I4}_{1d}\) & \(\widetilde{I4}_{2d}\) \\ \(d=1\) & (2.7,3,3.3) & (1.8,2,2.2) & (1.8,2,2.2) & (2.7,3,3.3) \\ \(d=2\) & (2.7,3,3.3) & (2.7,3,3.3) & (1.8,2,2.2) & (2.7,3,3.3) \\ route d-\(s\) & \(There are three scenarios to be considered in this study. The first scenario is that risk and uncertain factors are not considered in the proposed model while keeping the rest of the parameters as constant. The second scenario addresses the costs without incorporating uncertain parameters. The last scenario (the proposed model) is that risk costs and uncertain parameters are simultaneously incorporated in the model. The first scenario can be considered as the optimistic case where every factor works perfectly as expected and no risk occurs. The second case is less optimistic than the first case, but its consideration is still limited due to lack of uncertainty. The last scenario is the most comprehensive. Investigating all three cases will give us an overall insight of how strategy decisions, i.e., opening centers, will vary with different points of view. This insight is important since strategy decisions are not easy to change during an RSC operation planning horizon. After solving these models with CPLEX software, the results show that the total cost of the first scenario is $ 171,906 USD, while that of the second case is $192,508 USD. The flow of materials and components of the 1 st and 2 nd scenarios are presented in Tables 18 and 19, respectively. The figure of the third scenario is the possibility distributions (170,505; 187,369; 210,821). As can be seen, the total cost of the second scenario is slightly higher than the most likely case in the third scenario ($ 192,508 vs. $ 187,369). The likely explanation is that there is no interactive fuzzy solution approach considered to determine the optimal value to balance between the two conflicting issues: to enhance the objective value as well as to strengthen the degree of satisfaction of constraints.