考虑不确定性的共同权重鲁棒DEA模型及其应用研究

doi:10.16381/j.cnki.issn1003-207x.2024.0206

摘要/Abstract

摘要：

数据包络分析（data envelopment analysis，DEA）是一种数据驱动的效率测度方法，已广泛应用于各种组织的绩效分析。传统DEA方法假设所使用的数据完全精确，并且为各决策单元分配不同的投入产出权重，导致效率评价结果缺乏稳健性和可比性。针对这些不足，本文基于鲁棒优化技术与多目标规划方法，构建了一种具有共同权重的鲁棒DEA模型。基于我国30个省份众创空间的数据，验证了本文所构建方法的可行性与有效性。此外，本文引入了鲁棒价格的概念来评估决策单元抵御数据不确定性的能力，并设计了一个蒙特卡罗仿真来分析不同保守水平下效率排名的一致性。

关键词: 数据包络分析, 效率评价, 共同权重, 不确定性

Abstract:

Data Envelopment Analysis （DEA） is a non-parametric technique for evaluating the relative efficiency of a group of homogeneous Decision-making units （DMUs）. Unlike other efficiency evaluation methods， DEA does not require pre-specification of production functions， making it widely applicable for performance analysis across various organizations. However， traditional DEA assigns different weights to each DMU， leading to a lack of consistent basis for comparison between different DMUs. Additionally， traditional DEA assumes input-output data are accurate， yet data uncertainty is an inevitable issue in the real world.To address the shortcomings of traditional DEA， a robust DEA model with common weights is developed using the robust optimization method. Specifically， a robust counterpart of the CCR-DEA model is first proposed. Then， the ideal efficiency values of each DMU are obtained from the robust CCR-DEA model. After that， a multi-objective programming model is developed to obtain a set of common weights. Finally， the efficiency scores of each DMU under the common weights are calculated.Based on the data of crowd innovation spaces in 30 provinces and cities in China， the feasibility and effectiveness of our method are verified. Empirical analysis reveals that under different levels of data perturbation， Beijing， Jiangxi， Hubei， Gansu， and Guizhou are always in the top 5 in terms of efficiency ranking， while Hainan， Guangxi and Shanxi are always in the last three. Furthermore， the concept of the price of robustness is used to evaluate the ability of regions to cope with data uncertainty. A Monte Carlo simulation is designed to analyze the consistency of efficiency rankings under different conservatism levels. Lastly， the constructed method with existing models is compared， and the results indicate that our method has a smaller computational burden and is more suitable for real-world performance evaluation problems.

Key words: data envelopment analysis, efficiency evaluation, common weights, uncertainty

中图分类号:

F224

李犟,吴和成,王励文. 考虑不确定性的共同权重鲁棒DEA模型及其应用研究[J]. 中国管理科学, 2026, 34(3): 333-344.

Jiang Li,Hecheng Wu,Liwen Wang. A Robust Data Envelopment Analysis Model with Common Weights Considering Uncertainty and Its Application[J]. Chinese Journal of Management Science, 2026, 34(3): 333-344.

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地区	CCR-RDEA				CW-RDEA
地区	e=0	e=1%	e=5%	e=10%	e=0	e=1%	e=5%	e=10%
北京	1.000(1)	0.962(1)	0.856(3)	0.762(3)	1.000 (1)	0.961(1)	0.822(2)	0.678(2)
天津	0.884(15)	0.849(15)	0.723(15)	0.592(15)	0.578(17)	0.538(18)	0.424(21)	0.320(24)
河北	0.892(14)	0.857(14)	0.730(14)	0.608(14)	0.465(27)	0.446(26)	0.380(25)	0.311(25)
山西	0.862(18)	0.828(18)	0.705(18)	0.579(18)	0.494(24)	0.462(25)	0.365(27)	0.276(28)
内蒙古	0.693(27)	0.665(27)	0.567(27)	0.464(28)	0.424(29)	0.406(29)	0.344(29)	0.288(27)
辽宁	0.732(26)	0.704(26)	0.599(26)	0.49(26)	0.463(28)	0.444(27)	0.377(26)	0.307(26)
吉林	1.000 (1)	0.962(1)	0.857(2)	0.767(2)	0.520(21)	0.499(21)	0.427(20)	0.352(15)
黑龙江	1.000 (1)	0.962(1)	0.844(5)	0.733(5)	0.565(19)	0.529(19)	0.466(14)	0.385(13)
上海	1.000 (1)	0.962(1)	0.845(4)	0.750(4)	0.875(6)	0.838(6)	0.727(6)	0.607(6)
江苏	0.843(20)	0.810(20)	0.690(20)	0.566(21)	0.706(8)	0.676(8)	0.519(9)	0.396(12)
浙江	0.854(19)	0.820(19)	0.699(19)	0.572(19)	0.607(16)	0.580(16)	0.503(10)	0.418(9)
安徽	1.000 (1)	0.961(7)	0.836(7)	0.724(7)	0.863(7)	0.801(7)	0.628(7)	0.510(7)
福建	0.741(25)	0.712(25)	0.607(25)	0.496(25)	0.609(15)	0.584(14)	0.496(12)	0.405(11)
江西	1.000 (1)	0.962(1)	0.861(1)	0.779(1)	1.000 (1)	0.961(1)	0.823(1)	0.680(1)
山东	0.672(29)	0.645(29)	0.550(29)	0.450(29)	0.618(13)	0.593(12)	0.450(18)	0.338(22)
河南	0.827(21)	0.794(21)	0.677(21)	0.571(20)	0.514(22)	0.480(23)	0.382(24)	0.344(19)
湖北	1.000 (1)	0.961(7)	0.827(10)	0.693(11)	0.985(3)	0.946(3)	0.808(3)	0.673(3)
湖南	0.911(13)	0.875(13)	0.746(13)	0.623(13)	0.546(20)	0.525(20)	0.452(17)	0.374(14)
广东	0.656(30)	0.630(30)	0.537(30)	0.439(30)	0.623(12)	0.598(11)	0.453(16)	0.340(21)
广西	0.870(17)	0.836(17)	0.712(17)	0.583(16)	0.469(26)	0.439(28)	0.351(28)	0.267(29)
海南	1.000 (1)	0.961(7)	0.837(6)	0.731(6)	0.278(30)	0.264(30)	0.219(30)	0.174(30)
重庆	0.871(16)	0.837(16)	0.713(16)	0.583(16)	0.640(10)	0.614(10)	0.467(13)	0.352(15)
四川	0.776(23)	0.746(23)	0.635(23)	0.519(23)	0.628(11)	0.584(14)	0.460(15)	0.348(18)
贵州	0.988(12)	0.950(12)	0.809(12)	0.662(12)	0.929(5)	0.861(5)	0.768(5)	0.638(5)
云南	1.000 (1)	0.962(1)	0.836(7)	0.718(8)	0.641(9)	0.615(9)	0.529(8)	0.438(8)
陕西	0.823(22)	0.790(22)	0.673(22)	0.551(22)	0.615(14)	0.590(13)	0.503(10)	0.412(10)
甘肃	1.000 (1)	0.961(7)	0.827(10)	0.697(10)	0.968(4)	0.928(4)	0.792(4)	0.652(4)
青海	0.750(24)	0.721(24)	0.614(24)	0.502(24)	0.510(23)	0.490(22)	0.419(22)	0.350(17)
宁夏	0.689(28)	0.662(28)	0.566(28)	0.486(27)	0.482(25)	0.463(24)	0.398(23)	0.334(23)
新疆	1.000 (1)	0.961(7)	0.836(7)	0.714(9)	0.576(18)	0.541(17)	0.439(19)	0.343(20)