# Scenario-Based Emergency Material Scheduling Using V2X Communications
## SEMS Method
### Calculate the SEMS Transportation Time  
The existing emergency material scheduling is mainly about road transportation, which ignores the preparation time of vehicles and the recovery time for damaged road repair. The SEMS takes into account both of the time and the automobile and airplane transportation in material scheduling as well. The SEMS transportation time includes preparation time, automobile traveling time, and road repair time as Equations (1) and (2). The preparation time consists of material loading and refueling time. The road transportation time is the sum of the preparation time, automobile traveling time and road repair time. The air transportation time is the sum of the airplane preparation time and airplane traveling time. The SEMS obtains the transportation time more accurately and results in a more precise schedule by collecting real-time vehicle speeds. \[t_{i\,j1}^{p}=t_{1}+\frac{l_{ij1}}{v_{1}}+\frac{l_{ij1}\,s_{ij}^{p}}{v_{3}} \tag{1}\]  
\[t_{i\,j2}^{p}=t_{2}+\frac{l_{ij2}}{v_{2}} \tag{2}\] \begin{table}
\begin{tabular}{c c c} \hline \hline  & **Maximum Eigenvalues** & **C. I.** & **C. R.** \\ \hline O & 2 & 0 & 0 \\ O1 & 3.0337 & 0.020 & 0.034 \\ O2 & 2 & 0 & 0 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Maximum eigenvalues, consistency index (C. I.) and consistency ratio (C. R.). \begin{table}
\begin{tabular}{c c} \hline \hline  & \(\omega\) \\ \hline O & (0.667, 0.333) \\ O1 & (0.637, 0.258, 0.105) \\ O2 & (0.750, 0.250) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Values of the weight vector. Figure 1: Evaluation indicators for the scenario-based approach for emergency material scheduling (SEMS) scenario coefficient. where  
\(l_{ijr}\): the distance from the supply depot \(i\) to disaster depot \(j\) with mode \(r\). \(r\)= 1 means road transportation, and \(r\)= 2 means air transportation;  
\(p\): the period stage of a disaster depot for a kind of emergency material;  
\(x_{ij}^{p}\): the road damage rate, a percentage of the damaged road between the supply depot \(i\) and disaster depot \(j\) in stage \(p\);  
\(v_{1}\): the vehicle speed;  
\(v_{2}\): the airplane speed;  
\(v_{3}\): the road repair speed, which refers to repaired road distance per hour;  
\(t_{1}\): the automobile preparation time, set to 0.5 h;  
\(t_{2}\): the airplane preparation time, set to 3 h;  
\(t_{ij1}^{p}\): the road transportation time from [PERSON]i\) to \(j\) in stage \(p\);  
\(t_{ij2}^{p}\): the air transportation time from \(i\) to \(j\) in stage \(p\). Equation (1) demonstrates that the road transportation time is the sum of the automobile preparation time, traveling time and road repair time. Road damage does not exist in air transportation, so Equation (2) shows that the air transportation time is the sum of airplane preparation time and airplane traveling time. The SEMS inputs real-time vehicle speeds into the model, which obtains the transportation time more accurately, resulting in a more precise schedule. [PERSON] SEMS Fairness  
Fairness should be considered in emergency material scheduling, especially when the supply is insufficient. [PERSON] first noted the possibility of using [PERSON]'s information theory to produce measures of income fairness. Later, many researchers used the Theil index to analyze the fairness and variance of fiscal expenditure, resource allocation, [PERSON] development, etc. [29]. The SEMS chooses the Theil L index to denote fairness, which is expressed in Equation (3):  
\[T_{L}=\sum\limits_{k=1}^{m}v_{k}\ln\frac{v_{k}}{u_{k}} \tag{3}\]  
where \(T_{L}\) is Theil \(L\) index, \(m\) is the number of groups, \(v_{k}\) is the proportion of the population of group \(k\), and \(u_{k}\) is the proportion of the income of group \(k\). The Theil \(L\) index is used to show the fairness of people income among different groups. Inspired by Equation (3), we improved it to indicate the fairness of emergency material scheduling.