# Scenario-Based Allocation of Emergency Resources in Metro Emergencies: A Model Development and a Case Study of Nanjing Metro

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Literature Review

#### 2.1. Metro Emergency Management

#### 2.2. The Allocation of Emergency Resources

#### 2.3. Scenario Analysis Theories

#### 2.4. Review Summary

## 3. The Application of Scenario Analysis in Metro Emergencies

#### 3.1. Classification of Metro Emergencies

#### 3.2. Classification of Corresponding Emergency Resources

#### 3.3. Scenario Analysis of Metro Emergencies

#### 3.4. Logic Framework

## 4. Resource Allocation Model for Metro Emergencies

#### 4.1. Model Development

#### 4.1.1. Explanation of Hypothesis

#### 4.1.2. Modeling

#### 4.1.3. Model Analysis

_{i}, the allocation quantity of each emergency resource x

_{i}

^{k}, and the delayed time (t

_{i}− T), which can be represented by this expression:

_{i}was set according to an investigation to several experts implemented by another researcher [64]. The investigation evaluated different levels of the costs of property damage and casualties due to resource delays. There were totally five levels according to the length of the delay time. The value of β

_{i}varies according to different delay time of the resources. The coefficient increases sharply as the delay time is close to the bearing limit of the disaster point. The value of β

_{i}requires to be further defined during actual use.

_{i}is less than its inventory; article 3 indicates that at least a portion of each kind of resource should reach the disaster site within the emergency time limit; and the fourth factor is the non-negative constraint and integer constraint on decision variables.

_{1}(x) is the function used to represent objective (1), and F

_{2}(x) is used to represent objective (2). η

_{1}and η

_{2}are weight coefficients. Therefore, the transformed single-objective function F(x) is:

_{1}and η

_{2}. Subjective weighting methods include the analytic hierarchy process (AHP) method, and the Delphi method, and objective weighting methods chiefly include the dispersion method, principal component analysis method, and entropy method [68].

#### 4.2. Model Solving Algorithm

_{1}, the group-cognition coefficient c

_{2}, the maximum number of iterations T

_{max}, the maximum position coordinate value x

_{max}, the maximum velocity V

_{max}, the upper bound of inertia weight δ

_{max}, and the lower bound of inertia weight δ

_{min}.

_{id}(t) is the position vector. The function value of the position coordinate is used as the fitness value of the particle. The maximum position coordinate value x

_{max}represents the maximum distance over which a particle can search. V

_{id}(t) is the velocity vector, representing the velocity of the ith particle in the dth dimension of the solution space. The velocity determines the displacement of each iteration of each particle in the search space, namely step size [71]. The particle rate updating formula contains random variables, which may produce a large velocity value in the iteration process. Consequently, the particles may run out of the solution space and generate damped vibration. In order to avoid this phenomenon, the upper and lower limits of velocity can be defined [72]. V

_{max}is equivalent to the maximum value of each forward step. The settings of V

_{max}depend mainly on the optimization precision. If V

_{max}is too large, the particle may run unsteadily. The search process will be too fast to find the optimal solution. On the other hand, if V

_{max}is too small, the motion of the particle will be limited, and the optimal solution might not be obtained. Previous research suggested that it should ideally be less than 20% of the maximum search space [73].

_{i}and the global extreme value p

_{g}of the fitness values, the speed and position of each particle are constantly updated and the fitness values are compared until the optimal solution is finally found. The update formulas are shown below:

^{T}and V = (v [i,1], v [i,2], …, v [i,D])

^{T}can be used to represent the position and velocity of the ith particle. X, which represents the number of the emergency resources allocated, is the solution to this problem. The fitness function is,

## 5. Case Study

#### 5.1. Scenario Description

_{1}, S

_{2}, S

_{3}, S

_{4}, and S

_{5}, respectively. The disaster point was assumed to be Andemen station. The specific distribution is illustrated in Figure 3.

_{1}, emergency searchlight w

_{2}, and fume extractor w

_{3}. The number of gas masks required by the disaster site is presented as d

_{1}. We assumed that sufficient emergency supplies had been pre-positioned in the corresponding rescue points at an earlier stage. The number of gas masks, emergency searchlights and fume extractors stored in rescue point S

_{1}are denoted as p

_{1}

^{1}, p

_{1}

^{2}, and p

_{1}

^{3}, respectively. The rest can also be expressed in this way. Moreover, the estimated value of transport time from each rescue point to the disaster point and the unit costs of all kinds of emergency resources stored at each rescue point are also provided in Figure 4.

#### 5.2. Computational Results

_{1}of the first target was set as 0.70, and the weight coefficient η

_{2}of the second target was set as 0.30. To ensure global optimal search and convergence of the PSO algorithm, concrete setting values of the parameters are shown in Table 4. The maximum position coordinate value x

_{max}was set to 250. According to the description in Section 4.2, the maximum velocity V

_{max}was set to 10 accordingly. The upper and lower boundary values of the inertia coefficient were set to 0.9 and 0.4, respectively. The self-cognition coefficient c

_{1}and the group-cognition coefficient c

_{2}were both set to 1.424 [76]. After running the program, the optimal solution was obtained.

_{1}, S

_{3}, and S

_{4}. One hundred gas masks, 25 search lights, and three fume extractors are allocated from the rescue point S

_{1}to the disaster point E. Two hundred gas masks, 50 search lights, and nine fume extractors are allocated from the rescue point S

_{3}to the disaster point E. Sixty-eight gas masks and 11 search lights are allocated from the rescue point S

_{4}to the disaster point E. Under this allocation scheme, not only the demands of all the three types of emergency resources are met, but all the resources are also transported to the disaster point E as soon as possible. The penalty cost due to delays is 0 and the sum of the allocation costs is also the lowest. The optimal value of the fitness function F(x) is 6269.

#### 5.3. Sensitivity Analysis

## 6. Discussion

## 7. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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Metro Emergency Types | Site Management and Support Resources | Life Rescue Resources | Engineering Rescue and Professional Disposal Resources |
---|---|---|---|

Natural disasters | Meteorological monitoring equipment, aftershock monitoring equipment, emergency searchlight, gunny bag, cordon, intercom, fluorescent indicator rod. | Ventilator, life detector, stretcher, guide rope, first-aid kit, safety helmet, bandage, raincoat, life jacket, toothless saw, chain saw, glare flashlight, lifeboat. | Electric equipment inspection car, emergency pump, high-power drainage equipment, emergency tool kit. |

Production safety emergencies | Cordon, fume extractor, intercom, poisonous gas detector, emergency searchlight, emergency evacuation sign, bus, infrared detector, fire engine. | Fireproof suit, fireproof gloves, emergency medicine, stretcher, wet towel, gas mask, oxygen ventilator, oxygen bomb. | Hydraulic lifting equipment, cable tester, screw support frame, gear box oil, air compressor filter core, spare cable conductor, emergency tool kit. |

Social security emergencies | Emergency searchlight, cordon, emergency evacuation sign, intercom, poisonous gas detector, fume extractor, sprinkler system, explosive detector. | Protective glasses, oxygen ventilator, fireproof suit, fireproof gloves, anti-erode gloves, gas mask, first-aid kit, first-aid equipment, safety helmet. | Blast pipe, emergency tool kit. |

Public health emergencies | Microbiological detector, disinfectant, interphone, loudspeaker. | Vaccine, oxygen ventilator, medical protective mask, forehead temperature gun, defibrillation pacemaker. | Epidemic prevention vehicle. |

Scenario Elements | Literature Sources | |
---|---|---|

Event | Emergency type | [54] |

Event cause | [54] | |

Influence range | [55] | |

Event stage | [55] | |

Passenger | Passenger flow volume | [16,56] |

Passenger flow density | [16,56] | |

Number of stranded people | [16,56] | |

Time | The occurrence time | [57] |

Current time | [57] | |

Passenger flow period | [56] | |

Special date | [57] | |

Location | Line | [58] |

Station | [6] | |

Station type | [59] | |

Specific spot | [58] | |

Environment | Weather | [60,61] |

Demand | Resource demand location | [33,34,62] |

Resource type | [33,34,62] | |

Demanded resource quantity | [33,34,62] | |

Supply | Resource storage location | [52,62] |

Resource inventory quantity | [52,62] |

Notation | Description |
---|---|

S_{1}, S_{2}, … S_{n} | Rescue points. |

E | Disaster point. |

w | The number of emergency resource types. |

${x}_{i}^{k}$ | Decision variable which represents the number of type k resources allocated from rescue point S_{i} to disaster point E. |

${p}_{i}^{k}$ | The type k emergency resource inventory owned by rescue point S_{i}. |

${c}_{i}^{k}$ | The unit cost of type k emergency resource allocated from rescue point S_{i}, including use cost and deployment cost. |

${d}_{k}$ | Type k emergency resource demanded by disaster point E. |

${t}_{i}$ | Emergency resource transport time from rescue point S_{i} to disaster point E. |

T | Maximum time spent in delivering resource from an emergency rescue point to a disaster point, as set forth in the contingency plan of the metro management department. |

${\lambda}_{i}$ | $=\{\begin{array}{l}1,{t}_{i}\le T\\ 0,{t}_{i}>T\end{array}$ It is used to measure whether the transport time from rescue point Si and disaster point E has exceeded the maximal limit time. |

${\beta}_{i}$ | $=\{\begin{array}{l}0,{t}_{i}-T\le 0\\ 1,0<{t}_{i}-T\le 5\\ 2,5<{t}_{i}-T\le 10\\ 10,10<{t}_{i}-T\le 20\\ 100,{t}_{i}-T>20\end{array}$, [64] It is the penalty cost coefficient of losses caused by the delay of emergency resources per unit of time and quantity, which is calculated according to different delay time. In order to facilitate calculation, it is assumed that the coefficients of various resources are the same in the same time interval. Usually, the coefficient increases sharply when the delay time is close to the bearing limit of the disaster point. |

Parameters | Value |
---|---|

Initial population size N | 200 |

Search space dimensions D | 15 |

Maximum number of iterations T_{max} | 1000 |

Maximum position coordinate value x_{max} | 250 |

Maximum velocity V_{max} | 10 |

Upper bound of inertia weight δ_{max} | 0.9 |

Lower bound of inertia weight δ_{min} | 0.4 |

Self-cognition coefficient c_{1} | 1.424 |

Group-cognition coefficient c_{2} | 1.424 |

Rescue Point | S_{1} | S_{2} | S_{3} | S_{4} | S_{5} |
---|---|---|---|---|---|

w_{1} | 100 | 0 | 200 | 68 | 0 |

w_{2} | 25 | 0 | 50 | 11 | 0 |

w_{3} | 3 | 0 | 9 | 0 | 0 |

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**MDPI and ACS Style**

Lu, Y.; Sun, S. Scenario-Based Allocation of Emergency Resources in Metro Emergencies: A Model Development and a Case Study of Nanjing Metro. *Sustainability* **2020**, *12*, 6380.
https://doi.org/10.3390/su12166380

**AMA Style**

Lu Y, Sun S. Scenario-Based Allocation of Emergency Resources in Metro Emergencies: A Model Development and a Case Study of Nanjing Metro. *Sustainability*. 2020; 12(16):6380.
https://doi.org/10.3390/su12166380

**Chicago/Turabian Style**

Lu, Ying, and Shuqi Sun. 2020. "Scenario-Based Allocation of Emergency Resources in Metro Emergencies: A Model Development and a Case Study of Nanjing Metro" *Sustainability* 12, no. 16: 6380.
https://doi.org/10.3390/su12166380