## 3 Integrated Disaster Resource Scheduling Modeling
### Pre-Disaster Resource and Facility Optimization
#### 3.1.2 Pre-Deployment of Charging Stations and Reservoirs  
In this section, an optimal pre-disaster deployment strategy for charging stations and reservoirs is proposed with the aim of enhancing the timeliness of post-disaster resource dispatch and improving overall system resilience. While regional partitioning plays a crucial role in optimizing resource allocation and ensuring resource balance within communities, the placement of charging stations and reservoirs should be further refined for effective emergency dispatch after a disaster. Specifically, charging station locations should be selected to minimize travel time from high-priority nodes to lower-priority nodes, ensuring that energy storage vehicles can supply power efficiently and promptly to critical load areas during a disaster. The corresponding objective function is  
\[\min G_{i}=\sum_{i\in N}b_{i}(1-u_{i}^{s})\gamma_{i}T_{i}^{D}, \tag{5}\]where \(N\) denotes the set of all faulty load nodes. Here, \(b_{i}\in\{0,1\}\), \(u_{i}^{s}\in\{0,1\}\); if a charging station is deployed at load node \(i\), then \(b_{i}=1\), otherwise \(b_{i}=0\). If a mobile energy storage vehicle can restore power supply to node \(i\), then \(u_{i}^{s}=1\); otherwise, \(u_{i}^{s}=0\). In addition, \(\gamma_{i}\) represents the weight coefficient of load node \(i\), reflecting the importance of the node, while \(T_{i}^{D}\) denotes the shortest travel time from charging station \(m\) to node \(i\). To ensure that mobile water supply vehicles can rapidly replenish water sources and prioritize restoring water supply to critical load nodes, the pre-disaster placement of reservoirs must also be strategically planned. The reservoir locations should be selected to minimize the total travel time from high-priority nodes to lower-priority ones. The corresponding objective function is  
\[\min G_{w}=\sum_{i\in N}b_{i}(1-u_{i}^{s})\gamma_{i}T_{i}^{D,n}, \tag{6}\]  
where \(b_{i}\in\{0,1\}\), \(u_{i}^{s}\in\{0,1\}\), \(T_{i}^{D,n}\) denotes the shortest travel time from reservoir \(n\) to node \(i\). These two models address the positioning problems  
describe the conditions for meeting the electricity and water demands in each region, where \(D_{r}^{\text{dec shortage}}\) and \(D_{r}^{\text{water shortage}}\) respectively denote the shortage of electricity and water resources in region \(r\) and \(W\) represents the fixed resource capacity that each vehicle can carry. Equation (13) establishes the constraints on transportation distance and time, ensuring that the travel time \(T_{\text{travel},r}\) does not exceed \(T_{\text{max}}\). Equation (14) represents the resource priority constraints, taking into account the prioritization of resource demand across different regions. Here, \(p_{r}\) denotes the priority weight of region \(r\) and \(D_{\text{avail}}^{r}\) represents the allocated resource amount to meet regional demand, which must not be lower than \(p_{\text{min}}\). Equation (15) imposes vehicle capacity constraints, ensuring that the power supply capability \(F_{b}\) of energy storage vehicles does not exceed \(C_{\text{vehicle}}\), which guarantees safety and rationality in resource dispatching. Equation (16) specifies the path accessibility constraint, requiring that the path accessibility \(L_{\text{access},r}\) for each target region \(r\) must be equal to \(1\), which ensures that all planned routes remain feasible under the impact of the ice disaster. Equation (17) defines the energy consumption constraint, which requires that the remaining energy \(E_{\text{remain},r}\) of each vehicle after completing its assigned task must not be lower than the minimum energy requirement \(E_{\text{min}}\). Building upon the aforementioned model formulation and constraint conditions, the resource deployment and infrastructure siting problem is formulated as a mixed-integer linear programming (MILP) model. To balance computational efficiency and solution accuracy, the model is implemented in MATLAB using the YALMIP toolbox and solved with the Gurobi optimizer [30].