## 3 Integrated Disaster Resource Scheduling Modeling
### User Satisfaction-Oriented Dynamic Scheduling Model
#### 3.2.2 Path Optimization for Mobile Energy Storage and Water Vehicles  
Because transportation networks are highly susceptible to disaster impacts [31], unexpected events during an ice disaster can cause significant variations in the actual travel time of mobile energy storage vehicles along the same road at different time intervals and environmental conditions. To ensure reliability, this study incorporates factors such as road congestion and snow accumulation into traffic condition assessments [32]. A traffic congestion parameter is introduced to model the spatial relationship between the actual speed of mobile energy storage vehicles and the equivalent travel time.  
The driving speeds of mobile energy storage and water vehicles are affected under disaster conditions; therefore, it is necessary to estimate their speed based on the congestion level \(A\) of the transportation network under disaster scenarios and the actual traffic conditions. The relationship between the travel time \(T_{\text{new},m,n}\) and the equivalent travel distance \(L_{m,n}(t)\) between node \(m\) and node \(n\) with the actual vehicle speed \(v_{\text{new}}(t)\) can be expressed as  
\[v_{\text{new}}(t)=v_{0}e^{-1.7\alpha}, \tag{18}\]  
where \(v_{0}\) represents the ideal vehicle speed and \(\alpha\) denotes the congestion level of the transportation network under disaster conditions, which is related to the severity of the disaster and traffic flow. In practical applications, \(\alpha\) can be estimated by assessing the impact of the disaster. Under disaster scenarios, the actual travel distance is influenced not only by geographical distance but also by road condition deterioration. To account for this, we introduce the equivalent travel distance \(L_{m,n}(t)\) to represent the travel distance under disaster conditions:  
\[L_{m,n}(t)=L_{m,n,0}\bigg{(}1+\frac{1}{v_{\text{new}}(t)}\bigg{)} \tag{19}\]  
Figure 4: Locations of mobile resource vehicles, charging stations, and reservoirs based on disaster scheduling.  
where \(L_{m,n,0}\) represents the geographical distance between node \(m\) and node \(n\) under normal conditions. Considering the impact of the disaster on road conditions, the travel time can then be expressed as  
\[T_{\text{new},j,m,n}(t)=\frac{L_{m,n}(t)}{v_{\text{new}}(t)}. \tag{20}\]  
For each possible route, the travel times of all possible paths are calculated and the optimal path is selected to minimize travel time, as follows:  
\[T_{\text{travel},\text{min}}=\min_{r\in R_{i}}T_{\text{travel},r}. \tag{21}\]  
Therefore, the transportation network between communities \(j\) and \(k\) can be simplified into a single optimal mobility route, as illustrated in Figure 5.  
Specifically, Figure 5a depicts the original transportation network, where each mobile energy storage vehicle may traverse multiple potential paths connecting various community nodes and resource depots (charging stations/reservoirs). After path optimization, as shown in Figure 5b, redundant and suboptimal routes are eliminated, resulting in a streamlined network in which each vehicle follows the most efficient route between resource depots and community nodes. This approach not only reduces overall travel distance and time but also improves scheduling efficiency and system resilience during disaster response.