# Scenario-Based Emergency Material Scheduling Using V2X Communications
## 4 Experiment
### Parameters
#### 4.2.1 Fairness Analysis  
The proposed SEMS model includes two objectives, i.e., maximum fairness and minimum time, which are solved by a hierarchical sequence method. We took fairness as the main objective and transport time as the secondary objective. First, the fairness model was solved with MATLAB. Table 10 presents the used parameters. Figure 5 presents the iteration curve for optimizing the SEMS fairness. Table 11 presents the scheduling plan with the maximum fairness. In Figure 5, the x-axis represents the number of iterations, and the y-axis represents the optimized value of fairness. Thus, the unit for the x-axis is time. It is the same in Figures 6-9. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **Item** & **Chengdu** & **Shifang** & **Jiangyou** \\ \hline \multirow{2}{*}{Xi’an} & Road distance/km & 726 & 680 & 585 \\  & Flight distance/km & 545 & 510 & 439 \\ \multirow{2}{*}{Lanzhou} & Road distance/km & 950 & 900 & 823 \\  & Flight distance/km & 713 & 675 & 617 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Shortest transportation distance between depots. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Material** & **Chengdu** & **Shifang** & **Jiangyou** \\ \hline G/Packages & 5735 & 10,000 & 7750 \\ T/Tops & 10,993 & 4462 & 149 \\ W/Boxes & 18,487 & 54,196 & 12,260 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Relief demand for each disaster depot. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Fish** & **Maximum Number** & **Maximum Number** & **Perceived** & **Congestion** & **Step** \\
**Number** & **of Iterations** & **of Trials** & **Distance** & **Factor** & **Distance** \\ \hline
30 & 800 & 50 & 0.01 & 1 & 0.1 \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Parameters used in the SEMS algorithm. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Item** & **Chengdu** & **Shifang** & **Jiangyou** \\ \hline Xi’an & Road/h & 11.390 & 14.100 & 15.125 \\ Xi’an & Air/h & 5.725 & 5.550 & 5.195 \\  & Road/h & 24.250 & 18.500 & 12.845 \\  & Air/h & 6.565 & 6.375 & 6.085 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: The minimum transportation time between depots. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Material** & **Xi’an** & **Lanzhou** \\ \hline G/Packages & 10,000 & 10,000 \\ T/Tops & 6000 & 6000 \\ W/Boxes & 40,000 & 40,000 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Relief demand for amount for each supply depot. Figure 5: Iteration curve for SEMS fairness optimization. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline  & \multicolumn{2}{c}{**Chengdu**} & \multicolumn{4}{c}{**Shifang**} & \multicolumn{4}{c}{**Jiangyou**} \\ \cline{2-10}  & **G** & **T** & **W** & **G** & **T** & **W** & **G** & **T** & **W** \\ \hline Amt & 4165 & 7304 & 15,434 & 9165 & 4293 & 53,169 & 6672 & 122 & 10,873 \\ Sat Rate & 0.7262 & 0.6644 & 0.8348 & 0.9165 & 0.9620 & 0.9810 & 0.8608 & 0.8187 & 0.8869 \\ \hline \hline \end{tabular}
\end{table} 
Table 11: Scheduling plan with maximum fairness. Figure 6: Iterative curve for the Gini model optimization. Figure 7: Iterative curve for the enhanced Theil fairness optimization. The abbreviation Amt denotes the amount of relief demand, and Sat Rate denotes the demand satisfaction rate of the disaster depots. To prove the priority of the SEMS model, we compared it with the Gini index fairness model (Gini model) in [21] using the AFSA. The related results of the Gini model are given in Figure 6 and Table 12.  
Similarly, we also compared the SEMS with the enhanced Theil fairness model (enhanced Theil model) as Equation (12).