# Optimizing a Reverse Supply Chain Network for Electronic Waste under Risk and Uncertain Factors
## 5 An Illustrative Example
Furthermore, the total cost of the first scenario ($ 171,906 USD) is lower than the figure of the most likely case in the third scenario ($187,369 USD), since risk costs are not incorporated in the model. Although the total costs of the first and second scenarios can be lower and higher than that of the proposed model (third scenario), the first and second scenarios cannot represent real situations in designing an RSC network for e-waste. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**No** & \(Q^{1}\)\({}_{cdp}\) & \(Q2\)\({}_{dsu}\) & \(Q3\)\({}_{dew}\) & \(Q4\)\({}_{dri}\) & \(Q5\)\({}_{dll}\) & \(Q6\) \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**No** & \(Q1_{cdp}\) & \(Q2_{dsu}\) & \(Q3_{dew}\) & \(Q4_{dri}\) & \(Q5_{dhh}\) & \(Q6_{esaw}\) & \(Q7_{mi}\) & \(Q8_{rhh}\) \\ \hline  
& & & \\ \hline \hline \end{tabular}
\end{table} 
Table 19: The flow of materials and components (2 nd scenario). \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**No** & \(Q1_{cdp}\) & \(Q2_{dsu}\) & \(Q3_{dew}\) & \(Q4_{dri}\) & \(Q5_{dhh}\) & \(Q6_{esaw}\) & \(Q7_{mi}\) & \(Q8_{rhh}\) \\ \hline  
& & & & & \\ \hline \hline \end{tabular} Note: No shows the number of center, material, or part.  
\end{table} 
Table 18: The flow of materials and components (1 st scenario). i.e., three cases which have the highest satisfaction degree. These decisions are classified as strategic decisions. In reality, strategy decisions are the most important decisions since they are very difficult to be changed. In contrast to strategy decisions are tactical planning decisions, i.e., the flow quantity between each pair of facilities. These decisions can be revised and corrected based on the realization of uncertain parameters. In this case, the values of strategy decisions are stable enough to apply. Furthermore, three scenarios with different configurations are also considered. Three scenarios also have three different configurations for opening repairing centers. The third and second scenarios require one repairing center each but at different locations, while the first scenario needs to open two repairing centers. The first scenario is an optimistic case, where there is no risk and the decision-maker overestimates the demands of the markets. The difference in strategy decisions between the second and the third scenarios can be explained as the results of not integrating the satisfaction of decision-makers into making the model. Unlike forward supply chains, uncertainties and risks are challenging issues in RSC systems, which significantly affect the performance of RSC network design in real-world applications. To deal with the uncertainty of input data, an FMILP is proposed to find a satisfactory solution. The result of this research provides a practical solution. There are some vital contributions to the study. Firstly, the research simultaneously considered risk and uncertain factors for an e-waste RSC problem. Secondly, the fuzziness in most of the parameters including all related costs, capacity, risk, and the quantity of returned products was addressed in our model. Thirdly, three different scenarios were analyzed to provide useful insights for decision-makers to design an e-waste RSC network effectively. Lastly, the proposed method can provide a satisfactory solution, balancing two conflicting factors: the level of satisfaction of constraints and the objective value. In other words, if the level of satisfaction of constraints is high, the objective value would be worse. Although FMILP is a very effective tool to handle the uncertain parameters, the stability of the solutions is one of the most challenging issues in this approach. Unlike traditional linear programming, it is extremely difficult to conduct sensitivity analyses in FMILP due to the script transformation process. For future research, the simulation-based optimization approach should be considered to obtain a more stable solution. In this approach, the problem can be separated into two stages.