## 4 Numerical Analysis
### Decision Evaluation  
#### 4.3.1 Risk Appetite Analysis for Decision Makers  
The security parameter \(\Omega\) represents the decision maker's sentiment preference for the risk of demand volatility.  
The experimental result data in Table 3 above draw a topological overlay of the emergency facility that is not concise enough to visualize. For the sake of illustration, we use a small calculation example to make another diagram. Taking the maximum number of overcoverages = 2, as an example, 28 emergency facility points are randomly selected from the solved results, and the location optimization results under different robustness levels are shown in Table 5. The network topology of the siting results corresponding to the safety parameter \(\Omega\) for the shortest and longest emergency response mileage under the maximum number of overcoverages of two is shown in Figure 5.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Maximum Overcoverage** & **Downtrend Range** & **Uptrend Range** & **Global Optimal Solution** & **Minimum Rescue Mileage** \\ \hline
2 & \(\Omega\in\) [1,7] & \(\Omega\in\) (7,20] & \(\Omega=7\) & 682.89 km \\ \hline
3 & \(\Omega\in\) [1,7] & \(\Omega\in\) [7,20] & \(\Omega=3\) & 625.10 km \\ \hline
4 & \(\Omega\in\) [1,7] & \(\Omega\in\) (7,20] & \(\Omega=2\) & 672.83 km \\ \hline \hline \end{tabular}
\end{table}
Table 4: Comparison of the results of solving elliptic robust models with different maximum overcoverages.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Safety Parameter \(\Omega\)** & **Maximum Overcoverage** & **Total Emergency Rescue Mileage/km** \\ \hline  
\hline \end{tabular}
\end{table}
Table 5: Location optimization results under different robustness levels (overcoverages = 2).  
As seen in Figure 5, the red dotted line represents the demand point service relationship. (a) \(\Omega=6\); (b) \(\Omega=16\). When the safety parameter \(\Omega=6\), the optimal solution of the elliptical robust model appears at this time, and the total emergency rescue mileage of the whole system is 66.68 km. When the safety parameter \(\Omega=16\), which indicates that the decision makers are more pessimistic about the risk of demand fluctuation, the elliptical robust model at this time yields the longest total emergency relief mileage for the whole system, which is 133.13 km, and the obtained emergency siting road network topology is more resistant to the risk of demand fluctuation. When decision makers consider that the risk of demand fluctuation tends to be pessimistic, the corresponding safety parameter \(\Omega\) is larger; when the emergency facilities are more conservatively sited, the ability to resist the risk of demand fluctuation is stronger, but the total emergency rescue mileage of the system is relatively larger; and when decision makers tend to be optimistic considering the risk of demand fluctuations, the corresponding safety parameter \(\Omega\) is small, and the total system emergency rescue mileage is relatively small. Therefore, our model uses the safety parameter \(\Omega\) to measure the risk appetite of decision makers, and the appropriate safety parameter can be selected according to the degree of risk appetite and specific reality in the model application to achieve a systematic balance of risk resilience and rescue mileage optimization.