Please wait a minute...
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
Download: HTML     PDF(1194KB) HTML
Export: BibTeX | EndNote (RIS)      

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 wordsemergency 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
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.

URL:

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
[1]   冯凯, 徐志胜, 冯春莹, 等 小城镇突发公共事件应急决策系统的研究[J]. 灾害学, 2005, 20 (2): 6- 10
FENG Kai, XU Zhi-sheng, FENG Chun-ying, et al Study on decision-making system of unexpected public emergency events in small towns[J]. Journal of Catastrophology, 2005, 20 (2): 6- 10
doi: 10.3969/j.issn.1000-811X.2005.02.002
[2]   BOONMEE C, ARIMURA M, ASADA T Facility location optimization model for emergency humanitarian logistics[J]. International Journal of Disaster Risk Reduction, 2017, 24: 485- 498
doi: 10.1016/j.ijdrr.2017.01.017
[3]   郑斌, 马祖军 震后恢复期物资配送中的多周期选址—联运问题[J]. 交通运输系统工程与信息, 2014, 14 (4): 230- 238
ZHENG Bin, MA Zu-jun Multi-period joint location-transportation during post-earthquake restoration[J]. Journal of Transportation Systems Engineering and Information Technology, 2014, 14 (4): 230- 238
doi: 10.3969/j.issn.1009-6744.2014.04.033
[4]   龙京, 黄钢, 王孟钧, 等 铁路应急物资储备点选址[J]. 交通运输工程学报, 2011, 11 (1): 74- 78
LONG Jing, HUANG Gang, WANG Meng-jun, et al Reserve depot location of railway emergency material[J]. Journal of Traffic and Transportation Engineering, 2011, 11 (1): 74- 78
doi: 10.3969/j.issn.1671-1637.2011.01.013
[5]   吴艳华, 王富章, 李芳 铁路救援基地层级规划选址模型[J]. 交通运输工程学报, 2013, 13 (3): 86- 93
WU Yan-hua, WANG Fu-zhang, LI Fang Hierarchical planning location model of railway rescue center[J]. Journal of Traffic and Transportation Engineering, 2013, 13 (3): 86- 93
doi: 10.3969/j.issn.1671-1637.2013.03.012
[6]   YANG Z, CHEN H X, CHU F, et al An effective hybrid approach to the two-stage capacitated facility location problem[J]. European Journal of Operational Research, 2018, 275: 467- 480
[7]   KILCI F, KARA B Y, BOZKAYA B Locating temporary shelter areas after an earthquake: a case for Turkey[J]. European Journal of Operational Research, 2015, 243 (1): 323- 332
doi: 10.1016/j.ejor.2014.11.035
[8]   黄亚东, 张土乔, 王直民, 等 部分覆盖下供水管网水质监测点优化选址方法[J]. 浙江大学学报: 工学版, 2008, 42 (1): 8- 12
HUANG Ya-dong, ZHANG Tu-qiao, WANG Zhi-min, et al Optimizing water quality monitoring stations in water distribution network in presence of partial coverage[J]. Journal of Zhejiang University: Engineering Science, 2008, 42 (1): 8- 12
[9]   张燕, 张念卿 基于部分覆盖理论的供水管网二次加氯点选址[J]. 浙江大学学报: 工学版, 2011, 45 (4): 695- 698
ZHANG Yan, ZHANG Nian-qing Optimization of locations of booster chlorination stations in water distribution system based on theory of partial coverage[J]. Journal of Zhejiang University: Engineering Science, 2011, 45 (4): 695- 698
[10]   周向红, 成思婕, 成鹏飞 自营回收模式下再制造逆向物流网络多周期多目标选址规划[J]. 系统工程, 2018, 36 (9): 146- 153
ZHOU Xiang-hong, CHENG Si-jie, CHENG Peng-fei Multi cycle and multi objective location planning for remanufacturing reverse logistics network under self recovery mode[J]. Systems Engineering, 2018, 36 (9): 146- 153
[11]   王来军, CHIEN S I J, 赵建有, 等 货运站场选址分配问题的两阶段决策优化: 以中国延安为例(英文)[J]. 中国公路学报, 2015, 28 (7): 102- 114
WANG Lai-jun, CHIEN S I J, ZHAO Jian-you, et al Two-stage decision optimization of freight station location-allocation problem: a case study in Yan’an, China (English Edition)[J]. China Journal of Highway and Transport, 2015, 28 (7): 102- 114
doi: 10.3969/j.issn.1001-7372.2015.07.013
[12]   XIE S Y, OUYANG Y F Reliable service systems design under the risk of network access failures[J]. Transportation Research Part E, 2019, 122: 1- 13
[13]   白雪洁 模糊环境下应急物资预置的优化方法[J]. 系统工程理论与实践, 2015, 35 (6): 1465- 1473
BAI Xue-jie Optimization for pre-positioning emergency supplies problem under fuzzy environment[J]. Systems Engineering: Theory and Practice, 2015, 35 (6): 1465- 1473
doi: 10.12011/1000-6788(2015)6-1465
[14]   MOHAMMADI M, JULA P, TAVAKKOLI-MOGHADDAM R Reliable single-allocation hub location problem with disruptions[J]. Transportation Research Part E, 2019, 123: 90- 120
doi: 10.1016/j.tre.2019.01.008
[15]   于冬梅, 高雷阜, 赵世杰 不确定与损毁情景下可靠性设施选址鲁棒优化模型与算法研究[J]. 系统工程理论与实践, 2019, 39 (2): 498- 508
YU Dong-mei, GAO Lei-fu, ZHAO Shi-jie Robust optimization model and algorithm for reliability facility location under uncertainty and failure scenarios[J]. Systems Engineering: Theory and Practice, 2019, 39 (2): 498- 508
doi: 10.12011/1000-6788-2017-1365-11
[16]   RAWLS C G, TURNQUIST M A Pre-positioning of emergency supplies for disaster response[J]. Transportation Research Part B, 2010, 44 (4): 521- 534
doi: 10.1016/j.trb.2009.08.003
[17]   CAUNHYE A M, ZHANG Y D, LI M Z, et al A location-routing model for prepositioning and distributing emergency supplies[J]. Transportation Research Part E, 2016, 90 (43): 161- 176
[18]   JIN J G, LU L J, SUN L J, et al. Optimal allocation of protective resources in urban rail transit networks against intentional attacks [J]. Transportation Research Part E, 2015, 84: 73-87.
[19]   BAHARMAND H, COMES T, LAURAS M Bi-objective multi-layer location-allocation model for the immediate aftermath of sudden-onset disasters[J]. Transportation Research Part E, 2019, 127: 86- 110
doi: 10.1016/j.tre.2019.05.002
[20]   CHAUHAN D, UNNIKRISHNAN A, FIGLIOZZI M Maximum coverage capacitated facility location problem with range constrained drones[J]. Transportation Research Part C, 2019, 99: 1- 18
doi: 10.1016/j.trc.2018.12.001
[21]   AI Y F, LU J, ZHANG L L The optimization model for the location of maritime emergency supplies reserve bases and the configuration of salvage vessels[J]. Transportation Research Part E, 2015, 83: 170- 188
doi: 10.1016/j.tre.2015.09.006
[22]   艾云飞, 曹德胜, 沈兵, 等 VTS中心布局及雷达站选址-配置双层规划模型[J]. 大连海事大学学报, 2017, 43 (3): 107- 111
AI Yun-fei, CAO De-sheng, SHEN Bing, et al Bi-level optimization model of VTS center layout and radar station location-configuration[J]. Journal of Dalian Maritime University, 2017, 43 (3): 107- 111
[23]   秦进, 叶勇, 申纯燕, 等 考虑可靠性的交通网络应急资源布局优化[J]. 铁道科学与工程学报, 2018, 15 (2): 506- 514
QIN Jin, YE Yong, SHEN Chun-yan, et al Optimization method for emergency resource layout for transportation network considering service reliability[J]. Journal of Railway Science and Engineering, 2018, 15 (2): 506- 514
doi: 10.3969/j.issn.1672-7029.2018.02.031
[24]   郭咏梅, 胡大伟, 珠兰, 等 考虑可靠性要素的应急物流设施选址分配问题的建模研究[J]. 中国安全生产科学技术, 2017, 13 (2): 85- 89
GUO Yong-mei, HU Da-wei, ZHU Lan, et al Study on modeling for location-allocation problem of emergency logistics facility considering reliability element[J]. Journal of Safety Science and Technology, 2017, 13 (2): 85- 89
[25]   刘晗, 王健, 安实, 等 超立方体排队均衡的卫星消防站选址调度优化[J]. 交通运输系统工程与信息, 2018, 18 (2): 201- 207
LIU Han, WANG Jian, AN Shi, et al Satellite fire stations location and allocation model under the hypercube queuing equilibrium[J]. Journal of Transportation Systems Engineering and Information Technology, 2018, 18 (2): 201- 207
[26]   王炜. 公路交通流车速-流量实用关系模型[J]. 东南大学学报: 自然科学版, 2003, 33(4): 109-113.
WANG Wei. Practical speed-flow relationship model of highway traffic-flow [J]. Journal of Southeast University: Natural Science Edition, 2003, 33(4): 109-113.
[1] Qi ZHANG,Hong CHEN,Ji-biao ZHOU,Min ZHANG,Lin GUO,Ren-fa YANG. Effect of roadway access on traffic safety at adjacent intersection[J]. Journal of ZheJiang University (Engineering Science), 2021, 55(4): 720-726.
[2] Chen-xin ZHAO,Hong-zhao DONG,Wei-na HAO. Setting condition and traffic critical model of bus lane with time-division multiplexing[J]. Journal of ZheJiang University (Engineering Science), 2021, 55(4): 704-712.
[3] Zhong-yu WANG,Ling WANG,Yan-li WANG,Bing WU. Traffic congestion prevention method during large-scale special events based on variable network topology optimization[J]. Journal of ZheJiang University (Engineering Science), 2021, 55(2): 358-366.
[4] Jia-qi ZENG,Dian-hai WANG. Improved numerical method for two-way arterial signal coordinate control[J]. Journal of ZheJiang University (Engineering Science), 2020, 54(12): 2386-2394.
[5] Xin-wei MA,Yan-jie JI,Xue JIN,Yang XU,Rui-ming CAO. Analysis on travel characteristics of bike-sharing users and influence factors on way to travel[J]. Journal of ZheJiang University (Engineering Science), 2020, 54(6): 1202-1209.
[6] Kai LU,Xin TIAN,Guan-rong LIN,Xing-dong DENG. Simultaneous optimization model of signal phase design and timing at intersection[J]. Journal of ZheJiang University (Engineering Science), 2020, 54(5): 921-930.
[7] Wen-tao ZHU,Guo-min QIAN,Dong-fang MA,Dian-hai WANG. Bus delay model considering influence of stop at upstream of intersection[J]. Journal of ZheJiang University (Engineering Science), 2020, 54(4): 796-803.
[8] Chao SUN,Meng-hui LI,Fei HAN. Traffic evolution model with multi-source data of intelligent highway[J]. Journal of ZheJiang University (Engineering Science), 2020, 54(3): 546-556.
[9] Xiu-juan TIAN,De-xin YU,Hu-xing ZHOU,Xue XING,Shi-guang WANG. Dynamic control subdivision based on improved Newman algorithm[J]. Journal of ZheJiang University (Engineering Science), 2019, 53(5): 950-956.
[10] Si-jia ZHANG,Shun-ping JIA,Bao-hua MAO,Cun-rui MA,Tong ZHANG. Influence of passenger trip distance distribution on competitiveness of bus lines in urban rail transit network[J]. Journal of ZheJiang University (Engineering Science), 2019, 53(2): 292-298.
[11] NI Ling-lin, ZHANG Shuai-chao, CHEN Xi-qun. Spatial effects of urban travel using cellular signaling data[J]. Journal of ZheJiang University (Engineering Science), 2017, 51(5): 887-895.
[12] QU Zhao-wei, CAO Ning-bo, CHEN Yong-heng, BAI Qiao-wen, KANG Meng, CHEN Ming-tao. Leading pedestrian intervals modeling at signalized intersections[J]. Journal of ZheJiang University (Engineering Science), 2017, 51(3): 538-544.
[13] WANG Han qi, CHEN Hong, FENG Wei, LIU Wei wei. Multi-dimensional travel decision model of heterogeneous commuters based on Cumulative Prospect Theory[J]. Journal of ZheJiang University (Engineering Science), 2017, 51(2): 297-303.
[14] WANG Fu jian, GONG Cheng yu, MA Dong fang, Guo Wei wei, WANG Dian hai. Signal coordination control for traffic bottleneck using OD data[J]. Journal of ZheJiang University (Engineering Science), 2017, 51(2): 273-278.
[15] YU Qian, LI Tie zhu, REN Yan ming. Influence of passenger load on diesel bus emission[J]. Journal of ZheJiang University (Engineering Science), 2016, 50(10): 2009-2017.