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浙江大学学报(工学版)
浙江大学学报(工学版)  2021, Vol. 55 Issue (1): 20-30    DOI: 10.3785/j.issn.1008-973X.2021.01.003
土木工程、交通工程、水利工程     
考虑替代救援可靠度的应急配置优化模型
张翕然1(),陈绍宽1,*(),汪波2,刘爽1,王卓1
1. 北京交通大学 交通运输部综合交通运输大数据应用技术交通运输行业重点实验室，北京 100044
2. 北京市交通信息中心，北京 100161
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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摘要：

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    
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
收稿日期: 2020-04-06 出版日期: 2021-01-05
CLC:  U 491  
基金资助: 国家自然科学基金资助项目（71571015，71621001）；北京市自然科学基金资助项目（L191023）
通讯作者: 陈绍宽     E-mail: 931669521@qq.com;shkchen@bjtu.edu.cn
作者简介: 张翕然(1995—)，男，博士生，从事交通运输规划与管理的研究. orcid.org/0000-0002-2255-6865. E-mail： 931669521@qq.com
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引用本文:

张翕然,陈绍宽,汪波,刘爽,王卓. 考虑替代救援可靠度的应急配置优化模型[J]. 浙江大学学报(工学版), 2021, 55(1): 20-30.

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.

链接本文:

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

图 1  上层模型染色体编码
图 2  下层模型粒子编码
图 3  双层启发式算法流程图
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
表 1  应急设施候选点相关成本汇总表
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
表 2  应急设施选址与车辆配置结果（容量倍数=2）
图 4  算法稳定性随容量倍数的变化
图 5  总成本随容量倍数的变化
图 6  车辆数量随容量倍数的变化
图 7  设施数量随容量倍数的变化
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
表 3  不同容量倍数下的应急设施选址结果
图 8  分项成本随容量倍数的变化
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
表 4  不同容量倍数下的应急设施选址结果（对照组）
图 9  不同可靠度计算方法的总成本对比
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