## 3 Problem Statement and Model Construction
### Model Construction  
The primary objective of EV scheduling in CER situations is to minimize the transportation time, considering socio-economic benefits and humanitarian concerns. In this paper, an optimization model is developed with the objectives of minimizing the transportation costs, dispatch costs, and risk of casualties. Here, transportation costs represent the transportation time, while dispatch costs represent the economic benefits. Together, they constitute the comprehensive cost of dispatch. The casualty risk function is designed to harmonize the competition between different priority disaster sites. The joint EVs scheduling model is as follows:  
\[\begin{split} minZ_{1}&=T_{transit}=\sum\limits_{i=0 }^{M}\sum\limits_{j=0}^{N}\sum\limits_{k=0}^{K}w_{ijk}\cdot T_{ij}\\ minZ_{2}&=C_{dispatch}=\sum\limits_{i=0}^{M}\sum \limits_{j=0}^{N}\sum\limits_{k=0}^{K}w_{ijk}\cdot C_{ik}\\ minZ_{3}&=f_{risk}\end{split} \tag{1}\]  
\(s.t.\)  
\[\sum\limits_{j\in N}w_{ijk}\leq S_{ik},\ \ \forall i\in M,\forall k\in K \tag{2}\]  
\[\sum\limits_{i\in M}w_{ijk}\geq D_{jk},\ \ \forall j\in M,\forall k\in K \tag{3}\]  
\[w_{ijk}\geq 0,\ \ \forall i\in M,\ \forall j\in N,\ \forall k\in K \tag{4}\]  
\[T_{ij}\geq 0,\ \ \forall i\in M,\ \forall j\in N \tag{5}\]  
\[S_{ik}\geq 0,\ \ \forall i\in M,\ \forall k\in K \tag{6}\]  
The above model is a MILP model. Here, \(w_{ijk}\) is an integer decision variable representing the total scheduling scheme, which consists of the sub-scheduling scheme \(w_{i}\) for a  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Type** & **Symbols** & **Definition** \\ \hline \multirow{6}{*}{_Parameter_} & \(\mathcal{C}_{dispatch}\) & Vehicle dispatch cost \\  & \(T_{transit}\) & Transportation cost, i.e., transportation time \\  & \(f_{risk}\) & Casualty risk \\  & \(L_{0}\sim L_{4}\) & Equilibrium coefficients \\  & \(t_{H}\) & Psychological threshold time \\  & \(\tau\) & Surge risk \\ \hline \multirow{6}{*}{_Condition matrix_} & \(C_{ik}\) & EVs dispatch cost matrix \\  & & \(C_{ik}=\begin{bmatrix}c_{11}&\cdots&c_{1K}\\ \vdots&\ddots&\vdots\\ c_{\text{M1}}&\cdots&c_{MK}\end{bmatrix}_{M\times K}\) \\  & & EVs transportation time cost matrix \\ \multirow{6}{*}{_Condition matrix_} & \(T_{ij}\) & \(T_{ij}=\begin{bmatrix}t_{11}&\cdots&t_{1N}\\ \vdots&\ddots&\vdots\\ t_{\text{M1}}&\cdots&t_{MN}\end{bmatrix}_{M\times N}\) \\  & & Demand matrix for disaster sites \\ \multirow{6}{*}{_Sik_} & \(D_{jk}=\begin{bmatrix}d_{11}&\cdots&d_{1K}\\ \vdots&\ddots&\vdots\\ d_{N1}&\cdots&d_{NK}\end{bmatrix}_{N\times K}\) \\  & & Reserve Matrix for resource sites \\ \multirow{6}{*}{_Sik_} & \(S_{ik}=\begin{bmatrix}s_{11}&\cdots&s_{1K}\\ \vdots&\ddots&\vdots\\ s_{\text{M1}}&\cdots&s_{MK}\end{bmatrix}_{M\times K}\) \\ \hline \hline \end{tabular}
\end{table}
Table 2: _Cont._single resource site, as shown in Figure 3. Equation (1) is the model's objective function, comprising transportation time, vehicle dispatch cost, and casualty risk function. The casualty risk function \(f_{risk}\) is introduced in Section 3.3.1. The constraint term (2) ensures that the allocation scheme of the resource site does not exceed its reserve and constraint term, and (3) ensures that the receipts at the disaster site meet or exceed its demand. Equations (4)-(6) indicate that the scheduling scheme, transportation time, and resource site storage all satisfy the non-negativity constraints.