## 3 Optimization Model
### Multi-Objective Optimization Modeling  
Once an accident occurs, the timely arrival of rescue materials can effectively curb the secondary occurrence of injury. The total time for dispatching emergency resources defined in this paper is as follows: Based on the emergency weighting, the amount of rescue materials contained in the rescue point and the command staff are allocated. The dispatching of rescue resources after an accident is not uncontrolled and often requires a consideration of costs. In this paper, the total cost of dispatching is defined as the cost of transporting the materials needed to transport trapped personnel, the cost of transporting the materials needed to clean up hazardous material leaks, and the cost of transporting the materials needed to resume interval operation.  
\[minF1=T_{k}+T_{s}+T_{c}=\sum_{i=1}^{3}\left(\sum_{j=1}^{m}t_{ij}+\sum_{k=1}^{ b}t_{ik}\right). \tag{1}\]  
\[minF2=C_{k}+C_{s}+C_{c}=\sum_{i=1}^{3}\begin{pmatrix}\sum_{j=1}^{m}C_{cij}number (C_{cij})\\ +\sum_{k=1}^{b}C_{cik}number(CC_{cik})\end{pmatrix} \tag{2}\]  
\[\text{s.t.}\left\{\begin{array}{l}number(c_{cij})<f_{i},i=1,2,\ldots,m\\ number(C_{cik})<K_{i},i=1,2,\ldots,b\\ number(C_{kI_{n}})=w_{n}(P)\cdot M_{k}\\ number(C_{sI_{n}})=w_{n}(C)\cdot M_{s}\\ number(C_{cI_{n}})=w_{n}(R)\cdot M_{c}\end{array}\right. \tag{3}\]  
where \(F1\) denotes the total time for dispatching emergency resources, \(T_{k}\) denotes the time for transporting the supplies required for trapped personnel, \(T_{s}\) denotes the time to transport the materials required to handle hazardous material leaks, \(T_{c}\) denotes the time to deliver the materials needed to resume interval operation, \(t_{ij}\) is the time cost required to transport supplies from \(J\) to \(I\), and \(t_{ik}\) is the time cost of transporting the material from \(K\) to \(I\). \(F2\) denotes the total cost of dispatching emergency resources, \(C_{k}\) denotes the cost of transporting the supplies required to transport trapped personnel, \(C_{s}\) denotes the cost of transporting the materials required to clean up a hazardous material spill, \(C_{cj}\) denotes the cost of transporting the materials needed to resume interval operation, \(C_{cij}\) is the unit cost of transporting \(c\) from \(J\) to \(I\), \(number(c_{cij})\) is the quantity required of \(c\) material from \(J\) to \(I\), \(C_{cik}\) is the unit cost of \(c\) from \(K\) to \(I\), \(number(c_{cik})\) is the required quantity of \(c\) material from \(K\) to \(I\), and \(number(C_{kI_{n}})\) denotes the number of supplies needed to rescue the trapped people in \(I_{n}\). \(M_{k}\) denotes the collection of supplies contained in each rescue team, and \(number(C_{sI_{n}})\) denotes the quantity of hazardous materials needed to handle the incident point in \(I_{n}\). \(M_{k}\) denotes the collection of materials contained in each hazardous material handling team, \(number(C_{cI_{n}})\) denotes the amount of line repair materials required at the incident point in \(I_{n}\), and \(M_{k}\) denotes the collection of materials for each line repair team.  
In this paper, the dual objective function is solved under the constraints of weights and resource ceilings, with the objective of achieving the shortest arrival time of rescue supplies and the lowest cost of delivering rescue supplies.