## 3 Integrated Disaster Resource Scheduling Modeling
### User Satisfaction-Oriented Dynamic Scheduling Model
#### 3.2.4 Constraints  
We impose the following constraints:  
\[T_{c}^{\text{resp}}\leq T_{\max}\quad\forall c, \tag{25}\] \[T_{c1}^{\text{resp}}\leq T_{c2}^{\text{resp}},\quad\text{where }P_{c1}>P_{c2},\] (26) \[SOC_{c}^{\text{new,min}}\leq SOC_{c}^{\text{new}}(t)\leq SOC_{c }^{\text{new,max}}\quad\forall c,t,\] (27) \[SOC_{c}^{\text{new}}(t+1)=SOC_{c}^{\text{new}}(t)+P_{\text{ charge}}-P_{\text{use}}\quad\forall c,t,\] (28) \[R_{m,n}(t)\leq A_{m,n}(t),\quad\forall m,n,t,\] (29) \[R_{c}^{\min}\leq R_{c}^{\text{alloc}},\quad\forall c,\] (30) \[V_{\text{available}}(t)\geq V_{\text{required}},\quad\forall t, \tag{31}\]  
where Equation (25) ensures that the response time \(T_{c}^{\text{resp}}\) of each mobile energy storage vehicle \(c\) does not exceed the maximum allowable time, guaranteeing that resources can reach each node within the specified time to meet emergency needs; Equation (26) ensures that the response time of high-priority vehicles is less than or equal to that of low-priority ones (\(P_{c1}>P_{c2}\)); Equation (27) ensures that the battery state of each mobile energy storage vehicle \(c\) at time \(t\) remains between the minimum allowable value \(SOC_{c}^{\text{new,min}}\) and that the maximum allowable value \(SOC_{c}^{\text{new,max}}\); Equation (28) represents the battery state variation of energy storage vehicle \(c\) between time \(t\) and \(t+1\), considering both charging power \(P_{\text{charge}}\) and consumption power \(P_{\text{use}}\); and Equation (29) determines whether the path from node \(m\) to node \(n\) is feasible at time \(t\). When the path feasibility parameter \(A_{m,n}(t)=1\), the path is accessible; otherwise, the path is inaccessible. This ensures that the selected route remains viable under disaster conditions. Equation (30) ensures that the resource amount \(R_{c}^{\text{alloc}}\) obtained by each energy storage vehicle \(c\) meets the minimum resource guarantee requirement \(R_{c}^{\text{min}}\). This prevents excessive resource concentration in a subset of vehicles during emergencies, ensuring that the basic needs of all task nodes are met. Finally, Equation (31) ensures that the number of available vehicles \(V_{\text{available}}(t)\) at time \(t\) is not less than the minimum number \(V_{\text{required}}\). Constraints of Mobile Energy Storage Vehicles  
When a mobile energy storage vehicle needs to move from node \(m\) to \(n\), it must first select the optimal route under disaster conditions in order to minimize the travel time \(T_{\text{ME},m,n}\). Prior to reaching node \(n\), the mobile energy storage vehicle maintains a valid connection status. The spatial state scheduling constraints are as follows:\[\sum_{c=1}^{C}\zeta_{t,c}^{\text{new}}+\zeta_{t,c}^{\text{new}}=1, \quad\forall t, \tag{32}\] \[\sum_{t=t_{0}}^{t_{0}+h-1}\zeta_{t,c}^{\text{new}}\geq h\left( \zeta_{t_{0}-1,c}^{\text{new}}-\zeta_{t_{0}-1,c}^{\text{new}}\right),\quad \forall t,c,\] (33) \[\sum_{t=t_{0}+1}^{t_{0}+h+1}\left(\zeta_{t,c}^{\text{new}}+\zeta_ {t,c}^{\text{new}}\right)\leq 1,\quad\forall t,c, \tag{34}\]  
where Equation (32) ensures the uniqueness of its location of mobile energy storage vehicle \(c\), Equation (33) stipulates that the transmission time must not be less than \(h\) to ensure that the switching process meets the minimum required time, and Equation (34) ensures that the vehicle does not appear at multiple nodes simultaneously during the transmission time, which prevents state overlap and scheduling conflicts.