基于Bootstrap-DEA-Gini模型的公交线路运行效率评价方法

严修; 鲁誉; 谢谦; 刘强; 解孝民

doi:10.3963/j.jssn.1674-4861.2023.01.017

基于Bootstrap-DEA-Gini模型的公交线路运行效率评价方法

doi: 10.3963/j.jssn.1674-4861.2023.01.017

严修^1,,
鲁誉^{1, 2},
谢谦¹,
刘强^{1, 3, ,},
解孝民⁴

1.
中山大学智能工程学院广东深圳 518107
2.
广东省海洋工程施工与水上应急救援工程技术中心广州 510006
3.
中山大学-广汽研究院智慧交通与人工智能联合实验室广州 510006
4.
广东玛西尔电动科技有限公司广东肇庆 523268

基金项目:

国家自然科学基金项目 51675540

广东省基础与应用基础研究基金项目 2022A1515010692

详细信息

作者简介:
严修（1998—），硕士研究生. 研究方向：城市公交管理与规划. E-mail：yanx29@mail2.sysu.edu.cn

通讯作者:
刘强（1981—），博士，教授. 研究方向：交通安全. E-mail：liuq32@mail.sysu.edu.cn

中图分类号: U491.1+7
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出版历程
- 收稿日期: 2022-10-18
- 网络出版日期: 2023-05-13

A Method for Evaluating Operation Efficiency of Bus Lines Based on a Bootstrap-DEA-Gini Model

YAN Xiu^1
,,
LU Yu^{1, 2},
XIE Qian¹,
LIU Qiang^{1, 3
, ,},
XIE Xiaomin⁴

1.
School of Intelligent Systems Engineering, Sun Yat-sen University, Shenzhen 518107, Guangdong, China
2.
Guangdong Provincial Marine Engineering Construction and Water Emergency Rescue Engineering Technology Center, Guangzhou 510006, China
3.
SYSU-GAC R&D Center Joint Laboratory of Intelligent Transportation and Artificial Intelligence, Guangzhou 510006, China
4.
Guangdong Marshell Electric Technology Co., Ltd, Zhaoqing 523268, Guangdong, China

摘要

摘要: 科学评价城市常规公交线路运行效率是优化公交线网、提升服务水平的前提。构建以线路配车数、线路长度、平均站距、非直线系数、发车间隔、运行速度和票价收入比为投入指标，客流服务居民数量比和每公里收益为产出指标的评价指标体系，采用数据包络分析（data envelopment analysis，DEA）模型对公交线路运行效率进行评价。为了修正小样本情况下随机因素带来的偏差，采用Bootstrap抽样法扩大样本数量使之接近总体分布；为了降低效率受指标维数影响的风险性，引入基尼不纯度（Gini impurity）系数赋予各指标子集权重并求出综合效率值，以此联合提升传统DEA模型的区分能力。同时，针对DEA模型难以确定评价指标的影响程度的问题，采用偏最小二乘回归方法量化各评价指标对公交线路运行效率的影响程度。基于构建的Bootstrap-DEA-Gini模型来联合改进DEA模型，并以广东省佛山市457条公交线路为例对其运行效率进行评价。结果表明：平均站距、线路长度和非直线系数对公交线路的运行效率具有显著影响，其中平均站距影响最大，影响程度高达0.98。平均发车间隔偏长、非直线系数偏大和线路配客座总数偏少是造成佛山市部分线路运行效率低的主要原因。提出的Bootstrap-DEA-Gini模型得到的效率值比传统DEA模型低，且能有效区分运行效率相近的公交线路，与实际运营情况更相符。
- 城市交通 /
- 公交线路 /
- 运行效率 /
- 数据包络分析 /
- Bootstrap /
- Gini
Abstract: Scientific evaluation of operation efficiency of urban bus lines is the premise of optimizing bus network and improving its level of service. An evaluation method is developed with the following indicators as the input: number of lines, line length, average station distance, non-linear coefficient, departure interval, operating speed, and ratio of the average fare to the average income. The outputs of the evaluation include the ratio of the daily average passenger flow to the number of residents served and the revenue per kilometer. Then, a data envelopment analysis (DEA) model is developed to evaluate the operation efficiency of bus lines. In order to correct the bias from the random factors in the case study with a small sample, the Bootstrap sampling method is used to expand the number of samples to in order to reproduce the overall distribution. In order to reduce the risk associated with the high dimensionality of the input indicators, Gini impurity is introduced to determine the weights of each subset of indicators and a combined value is calculated, in order to jointly improve the ability of the DEA model to differentiate the operation efficiency of different bus lines. At the same time, as it is difficult to determine the impact of different indicators by DEA, a partial least squares regression method is used to quantify the impact of each indicator on the operation efficiency of bus lines. Based on this, a Bootstrap-DEA-Gini model is proposed to evaluate the operation efficiency of 457 bus lines in the City of Foshan, Guangdong Province, China. Study results show that the average station distance, line length, and non-linear coefficients have a significant impact on the operation efficiency of bus lines, of which the average station distance has the highest impact ratio of up to 0.98. It is also found that the main reasons for the low operation efficiency of bus lines in the City of Foshan are long average departure interval, large non-linear coefficient, and small number of passenger seats. The operation efficiencies calculated based on the proposed Bootstrap-DEA-Gini model are lower than the traditional DEA model, and bus lines with similar operating efficiency can be effectively distinguished, which indicates that proposed method is effective for evaluating the efficiency of real-world bus operation.
- public transit /
- bus line /
- operation efficiency /
- DEA /
- Bootstrap /
- Gini

HTML全文

图 1 评价指标体系

Figure 1. Evaluation index system

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图 2 Bootstrap-DEA-Gini模型

Figure 2. Bootstrap-DEA-Gini model

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图 3 各投入指标对效率影响程度

Figure 3. Degree of impact of each input indicator on efficiency

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图 4 2种方法评价结果

Figure 4. Results of the evaluation of the two methods

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图 5 各低效线路差异明显指标

Figure 5. Obvious different indicators of each inefficient line

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表 1 部分线路各项指标值

Table 1. Values of various indicators for some lines

指标	线路名称
指标	100	101	102	103	05	106
A₁₁线路配客座总数/个	18	30	748	324	33	402
A₁₂线路长度/km	18.8	13.85	13.85	19.56	16.75	15.4
A₁₃平均站距/km	0.783 3	0.494 6	0.446 8	0.652 0	0.598 2	0.570 4
A₁₄非直线系数	1.60	2.20	1.31	1.68	2.46	2.16
A₂₁票价收入比	0.382 0	0.390 2	0.365 3	0.390 7	0.393 3	0.359 8
A₂₂运行速度（/ km/h）	16.35	11.54	11.38	14.31	13.58	17.9
A₂₃平均发车间隔/min	13.25	9.50	7.75	13.75	9.50	8.50
A₃₁每公里收益/元	2.071	3.138	4.155	1.500	3.409	2.326
A₃₂客流服务居民比	0.045 6	0.100 6	0.182 8	0.039 3	0.091 9	0.079 3

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表 2 2种模型评价结果对比

Table 2. Comparison of evaluation results between the two methods

方法	最大值	最小值	平均值	标准差	离散系数
DEA	1	0.026 95	0.376 6	0.183 4	0.487 1
Bootstrap-DEA-Gini	0.990 9	0.020 13	0.305 9	0.154 5	0.505 1

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表 3 企业评价结果对比

Table 3. Comparison of enterprise evaluation results

低效线路	效率值		排名
低效线路	DEA	Bootstrap-DEA-Gini	DEA	Bootstrap-DEA-Gini
江03B	0.113 4	0.081 52	15	9
398B	0.150 1	0.089 54	36	18
965	0.164 4	0.082 14	41	17
里06B	0.195 1	0.093 90	58	23
樵09（支线）	0.206 6	0.096 94	72	30
938	0.234 4	0.108 0	118	35
平均	0.177 3	0.092 01	56.67	22

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表 4 低效线路各指标平均值与所有线路平均值对比

Table 4. Comparison of the average of each index of inefficient lines and all lines

各项指标	低效线路	所有线路	差值	差率/%
线路配客座总数/个	139.1	228.9	-89.72	-39.20
线路长度/km	16.89	19.61	-2.729 -	13.91
平均站距/km	0.863 8	0.690 2	0.17 36 2	5.15
非直线系数	2.691	1.981	0.710 1 3	5.85
票价收入	0.420 8	0.446 5	-0.025 6 -	5.515
运行速度（/km/h）	20.90	19.10	2.645 1	3.85
平均发车间隔/min	43.22	23.28	19.95 8	5.73
每公里收益/元	0.732 0	2.141	-1.475 -	68.88
客流服务居民比	0.005 787	0.031 33	-0.025 54-	81.53

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参考文献(21)

[1]	庞敏. 基于AHP-DEA模型的常规公交线路评价[D]. 北京: 北京交通大学, 2017. PANG M. Bus line evaluation based on AHP-DEA model[D]. Beijing: Beijing Jiaotong University, 2017. (in Chinese)
[2]	谭英嘉, 郭莉. 城市常规公交评价指标体系研究: 以深圳为例[J]. 公路与汽运, 2014(6): 72-76. (in Chinese) doi: 10.3969/j.issn.1671-2668.2014.06.020 TAN Y J, GUO L. Study on the evaluation index system of urban conventional public transport: Taking Shenzhen as an example[J]. Highway and Motor Transport, 2014(6): 72-76. doi: 10.3969/j.issn.1671-2668.2014.06.020
[3]	宋妙环. 基于DEA的北京市轨道交通运行效率评价研究[D]. 北京: 北京交通大学, 2017. SONG M H. Study on operation efficiency evaluation of Beijing rail transit based on DEA[D]. Beijing: Beijing Jiaotong University, 2017. (in Chinese)
[4]	孔宁, 翁剑成, 史清帅, 等. 基于数据包络分析的公交线路接驳效用评价方法[J]. 交通信息与安全, 2022, 40(1): 89-96. doi: 10.3963/j.jssn.1674-4861.2022.01.011 KONG N, WENG J C, SHI Q S, et al. A method for evaluating transfer efficiency between bus and subway based on data envelopment analysis[J]. Journal of Transport Information and Safety, 2022, 40(1): 89-96. (in Chinese) doi: 10.3963/j.jssn.1674-4861.2022.01.011
[5]	HAHN J S, KIM D K, KIM H C, et al. Efficiency analysis on bus companies in Seoul city using a network DEA model[J]. Ksce Journal of Civil Engineering, 2013, 17(6): 1480-1488. doi: 10.1007/s12205-013-0467-x
[6]	彭辉, 赵亚军. 基于DEA模型的城市公交交通效益对比评价[J]. 重庆交通大学学报(自然科学版), 2019, 38(12): 110-114. doi: 10.3969/j.issn.1674-0696.2019.12.17 PENG H, ZHAO Y J. Comparative evaluation of urban public traffic benefits based on DEA model[J]. Journal of Chongqing Jiaotong University(Natural Science), 2019, 38(12): 110-114. (in Chinese) doi: 10.3969/j.issn.1674-0696.2019.12.17
[7]	张春勤, 隽志才, 徐丽群. 基于SE-DEA模型与Malmquist指数的城市公交企业运营绩效评价[J]. 系统管理学报, 2017, 26(1): 134-141. https://www.cnki.com.cn/Article/CJFDTOTAL-XTGL201701017.htm ZHANG C Q, JUAN Z C, XU L Q. Evaluating the operations performance of urban public transit firms based on SE-DEA model and Malmquist index[J]. Journal of Systems & Management, 2017, 26(1): 134-141. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-XTGL201701017.htm
[8]	ADHIKARI A, BASU S, BISWAS I, et al. A route efficiency analysis using Shannon entropy-based modified DEA method and route characteristics investigation for urban bus transport in India[J]. INFOR: Information Systems and Operational Research, 2018, 56(3): 332-359. doi: 10.1080/03155986.2017.1393727
[9]	马嘉欣, 陈旭梅, 柯靖宇, 等. 公交线路资源配置与客流状况协调性综合评价方法[J]. 交通信息与安全, 2021, 39(3): 121-127, 135. doi: 10.3963/j.jssn.1674-4861.2021.03.015 MA J X, CHEN X M, KE J Y, et al. Comprehensive evaluation method for coordinating resource allocations and passenger flow of bus lines[J]. Journal of Transport Information and Safety, 2021, 39(3): 121-127, 135. (in Chinese) doi: 10.3963/j.jssn.1674-4861.2021.03.015
[10]	LI X, YU J, SHAW J, et al. Route-level transit operational-efficiency assessment with a bootstrap super-data envelopment analysis model[J]. Urban Planning and Development, 2017, 143(3): 04017007. doi: 10.1061/(ASCE)UP.1943-5444.0000388
[11]	孔雪, 任传祥, 高歌, 等. 考虑轨道交通规划的城市公交线路运行效率评价[J]. 科学技术与工程, 2020, 20(13): 5390-5395. doi: 10.3969/j.issn.1671-1815.2020.13.057 KONG X, REN C X, GAO G, et al. Evaluation on operation efficiency of urban public transport system considering rail transit planning[J]. Science Technology and Engineering, 2020, 20(13): 5390-5395. (in Chinese) doi: 10.3969/j.issn.1671-1815.2020.13.057
[12]	冯树民, 申翔浩. 公交线路资源配置与高峰客流协调评价研究[J]. 交通运输系统工程与信息, 2015, 15(4): 129-133. doi: 10.3969/j.issn.1009-6744.2015.04.020 FENG S M, SHEN X H. Evaluation of coordination between bus lines resource allocation and peak passenger flow[J]. Journal of Transportation Systems Engineering and Information Technology, 2015, 15(4): 129-133. doi: 10.3969/j.issn.1009-6744.2015.04.020
[13]	LIU Z C, WU N Q, QIAO Y, et al. Performance evaluation of public bus transportation by using DEA models and Shannon's entropy: An example from a company in a large city of China[J]. IEEE-CAA Journal of Automatica Sinica, 2021, 8(4): 779-795. doi: 10.1109/JAS.2020.1003405
[14]	季珏, 高晓路, 刘星辰. 城市交通效率的多目标评价方法研究: 以北京市城六区为例[J]. 地理科学进展, 2016, 35 (1): 118-125. JI J, GAO X L, LIU X C. Study on multi-objective evaluation method of urban traffic efficiency: Taking Beijing six districts as an example[J]. Progress in Geography, 2016, 35 (1): 118-125. (in Chinese)
[15]	高志方, 覃朝春, 彭定洪. 基于回归分析与网络DEA的城市公交企业运营效率分析[J]. 昆明理工大学学报(社会科学版), 2015, 15(4): 68-75. GAO Z F, QIN C C, PENG D H. Evaluating the operation efficiency of city bus enterprises based on regression analysis and network data envelopment analysis[J]. Journal of Kunming University of Science and Technology, 2015, 15(4): 68-75. (in Chinese)
[16]	王火根, 杨甜甜. 生物质发电企业绿色技术创新效率及其影响因素研究: 基于Bootstrap-DEA方法检验[J]. 科技管理研究, 2021, 41(17): 191-198. https://www.cnki.com.cn/Article/CJFDTOTAL-KJGL202117024.htm WANG H G, YANG T T. Research on green technology innovation efficiency and its influencing factors of biomass power generation enterprises: test based on Bootstrap-DEA method[J]. Science and Technology Management Research, 2021, 41(17): 191-198. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-KJGL202117024.htm
[17]	李学文, 徐丽群. 超效率Gini方法在城市交通行业面板数据中的研究[J]. 中国管理科学, 2014(增刊1): 1-7. https://www.cnki.com.cn/Article/CJFDTOTAL-ZGGK2014S1001.htm LI X W, XU L Q. A study on panel data of urban public transport based on super efficiency Gini approach[J]. Chinese Journal of Management Science, 2014(S1): 1-7. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-ZGGK2014S1001.htm
[18]	李学文, 徐丽群. 超效率Gini方法在城市交通行业面板数据中的研究[C]. 第十六届中国管理科学学术年会, 太原: 中国优选法统筹法与经济数学研究会, 2014. LI X W, XU L Q. A study on panel data of urban public transport based on super efficiency Gini approach[C]. 16th China Annual Conference on Management Science, Taiyuan: Chinese Society of Optimization & Overall Planning and Economic Mathematics, 2014. (in Chinese)
[19]	UPLIU Y F, CHIEN S, HU D W, et al. Developing an extenics-based model for evaluating bus transit system[J]. Advanced Transportation, 2020(1): 1-13.
[20]	UP彭春艳, 李文华, 陈国福. 基于文本分析和PLS模型的项目经理岗位胜任力研究[J]. 铁道科学与工程学报, 2021, 18(7): 1928-1934. https://www.cnki.com.cn/Article/CJFDTOTAL-CSTD202107031.htm
[35]	PENG C Y, LI W H, CHEN G F. Research on competency of project manager post based on text analysis and PLS model[J]. Journal of Railway Science and Engineering, 2021, 18 (7): 1928-1934.