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

Abstract

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

CLC Number:

F224

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.

Figures/Tables 5

References 32

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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)

A Robust Data Envelopment Analysis Model with Common Weights Considering Uncertainty and Its Application

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