# Model and Solution of Complex Emergency Dispatch by Multiple Rescue Centers with Limited Capacity to Different Disaster Areas

^{1}

^{2}

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## Abstract

**:**

## 1. Introduction

## 2. Task Allocation Model for Emergency Dispatch

#### 2.1. Proposed Model

#### 2.2. Model Construction

#### 2.3. Model Unfolding

## 3. Model Solving Based on Genetic Algorithm

#### 3.1. Coding Scheme and Individual Representation

#### 3.2. Fitness Function

#### 3.3. Crossover Operator

#### 3.4. Mutation

## 4. Case Analysis

_{i}is the i-th rescue center, and its rescue team capacity is 10. As is shown in Table 2, 2/9 indicates that the distance from rescue center C1 to the disaster area θ1 is 9km. The team under the command of C1 to perform task θ1 has a capability of level 2.

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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Rescue Teams Needed in the Disaster Area | ${\mathit{t}}_{\mathit{\theta}1}$ | … | ${\mathit{t}}_{\mathit{\theta}\mathit{j}}$ | … | ${\mathit{t}}_{\mathit{\theta}\mathit{m}}$ | ||
---|---|---|---|---|---|---|---|

Rescue team capacity | ${\theta}_{1}$ | … | ${\theta}_{j}$ | … | ${\theta}_{m}$ | Number of rescue teams to be dispatched by each rescue center | |

${t}_{c1}$ | ${C}_{1}$ | ${t}_{11}$ | … | ${t}_{1j}$ | … | ${t}_{1m}$ | $\sum _{j=1}^{m}{t}_{1j}$ |

… | … | … | … | … | … | ||

${t}_{ci}$ | ${C}_{i}$ | ${t}_{i1}$ | … | ${t}_{ij}$ | … | ${t}_{im}$ | $\sum _{j=1}^{m}{t}_{ij}$ |

… | … | … | … | … | … | ||

${t}_{cn}$ | ${C}_{n}$ | ${t}_{n1}$ | … | ${t}_{nj}$ | … | ${t}_{nm}$ | $\sum _{j=1}^{m}{t}_{nj}$ |

Number of rescue teams dispatched by each mission | $\sum _{i=1}^{n}{t}_{i1}$ | … | $\sum _{i=1}^{n}{t}_{ij}$ | … | $\sum _{i=1}^{n}{t}_{im}$ | $\sum _{i=1}^{n}{\displaystyle \sum _{j=1}^{m}{t}_{ij}}$ |

Rescue Team Rescue Capability/Rescue Distance | Rescue Team t θj Required in the Disaster Area | 7 | 8 | 5 | 6 |
---|---|---|---|---|---|

Rescue Team Capacity t ci | θ1 | θ2 | θ3 | θ4 | |

10 | C1 | 2/9 | 4/14 | 3/7 | 1/12 |

10 | C2 | 3/13 | 1/13 | 2/7 | 4/8 |

10 | C3 | 1/12 | 2/6 | 4/14 | 3/7 |

θ1 | θ2 | θ3 | θ4 | |

C1 | 3 | 3 | 3 | 0 |

C2 | 3 | 1 | 1 | 3 |

C3 | 1 | 4 | 1 | 3 |

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**MDPI and ACS Style**

Duan, Z.; Huang, Y.; Huang, P.; Guo, J.; Yang, F.; Fu, L.
Model and Solution of Complex Emergency Dispatch by Multiple Rescue Centers with Limited Capacity to Different Disaster Areas. *Symmetry* **2020**, *12*, 1138.
https://doi.org/10.3390/sym12071138

**AMA Style**

Duan Z, Huang Y, Huang P, Guo J, Yang F, Fu L.
Model and Solution of Complex Emergency Dispatch by Multiple Rescue Centers with Limited Capacity to Different Disaster Areas. *Symmetry*. 2020; 12(7):1138.
https://doi.org/10.3390/sym12071138

**Chicago/Turabian Style**

Duan, Zaipeng, Yueling Huang, Ping Huang, Jin Guo, Fuqiang Yang, and Libi Fu.
2020. "Model and Solution of Complex Emergency Dispatch by Multiple Rescue Centers with Limited Capacity to Different Disaster Areas" *Symmetry* 12, no. 7: 1138.
https://doi.org/10.3390/sym12071138