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浙江大学学报(工学版)
Journal of ZheJiang University (Engineering Science)  2021, Vol. 55 Issue (1): 20-30    DOI: 10.3785/j.issn.1008-973X.2021.01.003
    
Emergency allocation optimization model considering reliability of replaceable rescue
Xi-ran ZHANG1(),Shao-kuan CHEN1,*(),Bo WANG2,Shuang LIU1,Zhuo WANG1
1. MOT Key Laboratory of Transport Industry of Big Data Application Technologies for Comprehensive Transport, Beijing Jiaotong University, Beijing 100044, China
2. Beijing Transportation Information Center, Beijing 100161, China
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Abstract  

The impact of the rescue vehicle failure was analyzed in order to obtain a reasonable emergency facility location and vehicle allocation plan. A rescue reliability calculation method was proposed by constructing the hypothetical vehicle resource pool and fully considering the situation of using remaining available vehicles in the emergency system to replace the failed vehicles. A bi-level model for emergency allocation considering replaceable rescue was constructed by considering the facility classification and the matching of two types of rescue vehicles in order to minimize the total cost. The upper-level model aimed to optimize the plan of emergency facility location and vehicle allocation, and the lower-level model assigned the emergency supplies demand. A bi-level heuristic algorithm was designed to solve the model. The case study shows that the total cost tends to decrease firstly and then stabilize as the capacity multiple between vehicles increases within a reasonable range. A basis for the optimization of vehicle types matching can be provided by the model. The comparison with the traditional reliability calculation method shows that the total cost can be effectively reduced by using the proposed method, and the average optimization degree of the total cost in different vehicle types matching scenarios is 9.01%.

Key words： emergency facility location and vehicle allocation      set covering      vehicle resource pool      rescue coverage reliability      replaceable rescue     
Received: 06 April 2020      Published: 05 January 2021
CLC:  U 491  
Corresponding Authors: Shao-kuan CHEN     E-mail: 931669521@qq.com;shkchen@bjtu.edu.cn
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Xi-ran ZHANG
Shao-kuan CHEN
Bo WANG
Shuang LIU
Zhuo WANG
Cite this article:

Xi-ran ZHANG,Shao-kuan CHEN,Bo WANG,Shuang LIU,Zhuo WANG. Emergency allocation optimization model considering reliability of replaceable rescue. Journal of ZheJiang University (Engineering Science), 2021, 55(1): 20-30.

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http://www.zjujournals.com/eng/10.3785/j.issn.1008-973X.2021.01.003     OR     http://www.zjujournals.com/eng/Y2021/V55/I1/20


考虑替代救援可靠度的应急配置优化模型

为了合理规划应急设施选址与资源配置方案，分析救援车辆失效对系统覆盖可靠度的影响. 通过构建虚拟车辆资源池，考虑实际中存在使用系统内剩余可用车辆替代失效车辆的情景，提出救援覆盖可靠度的计算方法. 以系统总成本最小化为目标，考虑设施分级和2种救援车辆的匹配，建立考虑替代救援的应急配置双层规划模型. 上层模型优化设施选址与车辆配置方案，下层模型进行物资需求分配. 设计双层启发式算法进行求解. 案例分析表明：随着车辆间容量倍数在合理范围内增长，系统总成本呈现先降低后平稳的趋势，该模型可以为最优的车辆种类匹配方案选择提供依据. 通过与基于传统可靠度计算方法得到的结果对比表明，使用所提的可靠度计算方法，有助于减少系统总成本，在不同车辆类型匹配方案下的平均优化程度为9.01%.


关键词： 应急设施选址与车辆配置,  集合覆盖,  车辆资源池,  救援覆盖可靠度,  替代救援 
Fig.1 Chromosome coding for upper-level model
Fig.2 Particle coding for lower-level model
Fig.3 Flowchart of bi-level heuristic algorithm
万元
$j $ ${g_j}$ ${f_{j1}}$ ${f_{j2}}$
1 0.50 0 130.00
2 1.00 234.00 421.20
3 0.60 234.00 421.20
4 0.75 182.00 327.60
5 1.15 234.00 421.20
6 0.80 182.00 327.60
7 0.85 175.50 315.90
8 1.00 247.00 444.60
9 1.05 182.00 327.60
10 1.25 169.00 304.20
11 0.75 169.00 304.20
12 0.65 175.50 315.90
13 1.15 182.00 327.60
14 1.25 221.00 397.60
15 0.95 227.50 409.50
16 0.83 0 117.00
Tab.1 Summary of costs associated with emergency facilities candidates
j a xj1 xj2 j a xj1 xj2
1 2 4 2 9 0 0 0
2 0 0 0 10 1 2 1
3 0 0 0 11 0 0 0
4 1 2 0 12 0 0 0
5 0 0 0 13 1 1 1
6 1 2 1 14 0 0 0
7 0 0 0 15 1 1 1
8 0 0 0 16 1 1 1
Tab.2 Emergency facility location and vehicle allocation results（capacity multiple is 2）
Fig.4 Change of computational stability with capacity multiple
Fig.5 Change of total cost with capacity multiple
Fig.6 Change of vehicle quantity with capacity multiple
Fig.7 Change of facility quantity with capacity multiple
n 设施等级选择结果
j=1 j=2 j=3 j=4 j=5 j=6 j=7 j=8 j=9 j=10 j=11 j=12 j=13 j=14 j=15 j=16
1.2 2 0 0 1 0 2 1 0 0 0 0 0 2 0 1 2
1.3 2 0 0 1 0 2 0 0 0 1 0 0 2 0 1 1
1.4~1.6 2 0 0 1 0 2 1 0 0 0 0 0 2 0 1 1
1.7 2 0 0 1 0 2 0 0 0 1 0 0 1 0 1 1
1.80~1.90 2 0 0 1 0 2 1 0 0 0 0 0 1 0 1 1
2.0 2 0 0 1 0 1 0 0 0 1 0 0 1 0 1 1
2.1 2 0 0 1 0 1 1 0 0 0 0 0 1 0 1 1
2.2 2 0 0 1 0 1 0 0 1 0 0 0 1 0 1 1
2.3 2 0 0 1 0 1 0 0 0 1 0 1 0 0 1 1
2.4 2 0 0 1 0 1 1 0 0 0 0 1 0 0 2 1
2.5 2 0 0 1 0 1 0 0 0 1 0 1 0 0 1 1
2.6 2 0 0 1 0 2 0 0 0 1 0 0 0 0 1 1
2.7~3.0 2 0 0 1 0 1 0 0 0 1 0 0 0 0 1 1
Tab.3 Emergency facility location results under different capacity multiples
Fig.8 Change of subentry cost with capacity multiple
n 设施等级选择结果
j=1 j=2 j=3 j=4 j=5 j=6 j=7 j=8 j=9 j=10 j=11 j=12 j=13 j=14 j=15 j=16
1.2 2 0 0 2 0 1 2 0 0 0 0 0 2 1 1 1
1.3 2 0 0 1 0 1 0 0 0 2 0 0 1 2 1 1
1.4 2 0 0 2 0 1 0 0 0 2 0 0 2 0 1 1
1.50~1.60 2 0 0 0 2 1 1 0 0 0 0 0 2 0 1 1
1.7 2 0 0 1 0 2 1 0 0 0 0 0 2 0 1 1
1.8 2 0 1 0 0 2 1 0 0 0 0 0 2 0 1 1
1.9 2 0 0 1 0 2 1 0 0 0 0 0 1 0 1 1
2.0 2 0 1 0 0 2 0 0 1 1 0 0 1 0 1 1
2.1 2 0 1 0 0 2 0 0 0 1 0 0 0 0 2 1
2.20~2.30 2 0 0 1 0 1 1 0 0 0 0 0 1 0 1 1
2.4 2 0 0 0 1 1 1 0 0 0 0 0 1 0 1 1
2.5 2 0 0 1 0 1 0 0 0 2 0 0 0 0 1 1
2.6 2 0 0 1 0 1 1 0 0 0 0 0 1 0 1 1
2.70~2.80 2 0 0 1 0 2 0 0 0 1 0 0 0 0 1 1
2.90~3.00 2 0 0 1 0 1 0 0 0 1 0 0 0 0 1 1
Tab.4 Emergency facility location results under different capacity multiples (control group)
Fig.9 Comparison of total cost between different reliability calculation methods
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