考虑决策者偏好结构的交叉效率评价方法

doi:10.16381/j.cnki.issn1003-207x.2021.2359

Abstract

Abstract:

In practice， managers or decision-makers usually need to make strategic decisions among similar decision-making units， such as team performance， project performance， etc. Due to the same external environment， evaluation indicators， and other characteristics of similar decision-making units， it is difficult for decision-makers to make correct evaluations. Scholars have proposed and employed the cross-efficiency evaluation method to solve the above problems. However， the classic cross-efficiency of DEA pursues the absolute objectivity of the evaluation results and ignores the subjectivity of decision-makers in the evaluation process， which leads to the loss of decision-making information and weakens the validity of the evaluation results. In response to this problem， a cross-efficiency evaluation method is given considering the decision-maker preference structure， which combines with DEA and OWA operators.Specifically， the radical DEA model is used to obtain the initial cross-efficiency matrix of the decision-making units at first. Second， skewness and standard deviation are used to measure the preference structure of decision-makers， that is preference difference and priority， and to modify the initial cross-efficiency matrix. Subsequently， the weights of decision-making units are obtained based on maximizing the minimum preference difference. The final cross-efficiency values of the decision-making units are received by the OWA operator to aggregate the evaluation information.The statistical data of 27 industrial robots from the study of Wang and Chin are used to test the proposed method. Further， the proposed method is compared with the traditional DEA and Chen's method. The perspective of overall ranking， the changing trend of ranking obtained by the three methods is similar； the perspective of specific ranking， the cross-efficiency difference of the proposed method is bigger than that of the other two methods. In sum， the evaluation results of the proposed method have excellent consistency， and it is more conducive for decision-makers or managers to further understand and compare the differences between decision-making units.

Key words: cross efficiency, preference structure, DEA, OWA

CLC Number:

F272.3

Yinyun Yu,Congdong Li,Yelin Fu,Kinkeung Lai. A Cross-efficiency Evaluation Method Considering Decision Maker Preference Structure[J]. Chinese Journal of Management Science, 2024, 32(8): 117-126.

Figures/Tables 11

决策单元	DMU₁	DMU₂		DMU_n	交叉效率评价值
DMU₁	E₁₁	E₁₂	$?$	E₁_n	$1 n ∑ r = 1 n E 1 r$
DMU₂	E₂₁	E₂₂	$?$	E₂_n	$1 n ∑ r = 1 n E 2 r$
$?$	$?$	$?$	$?$	$?$	$?$
DMU_n	E_n₁	E_n₂	$?$	E_nn	$1 n ∑ r = 1 n E n r$

DMU	w₁	w₂		w_n	最终评价值
DMU₁	$E ? 11$	$E ? 12$	$?$	$E ? 1 n$	$∑ r = 1 n E ? 1 r ? w r$
DMU₂	$E ? 21$	$E ? 22$	$?$	$E ? 2 n$	$∑ r = 1 n E ? 2 r ? w r$
$?$	$?$	$?$	$?$	$?$	$?$
DMU_n	$E ? n 1$	$E ? n 2$	$?$	$E ? n n$	$∑ r = 1 n E ? n r ? w r$

References 36

1	Chen L， Huang Y， Li M J， et al. Meta-frontier analysis using cross-efficiency method for performance evaluation［J］. European Journal of Operational Research， 2020， 280（1）： 219-229.
2	Liu S T. A DEA ranking method based on cross-efficiency intervals and signal-to-noise ratio［J］. Annals of Operations Research， 2018， 261： 207-232.
3	Li J， Wang P， Tao X Y， et al. Productivity analysis for banks' merger and acquisition using two-stage dea： Evidence from china［J］. Journal of Systems Science and Information， 2021， 9（6）：627-659.
4	Charnes A， Cooper W W， Rhodes E. Measuring the efficiency of decision making units［J］. European Journal of Operational Research， 1978， 2（6）： 429-444.
5	Liu H H， Song Y Y， Yang G L. Cross-efficiency evaluation in data envelopment analysis based on prospect theory［J］. European Journal of Operational Research， 2019， 273： 364-375.
6	Ma H W， Geng B X， Fu Y X， et al. Efficiency analysis of industrial water treatment in China based on two-stage undesirable fixed-sum output DEA model［J］. Journal of Systems Science and Information， 2021，9（6）： 660-680.
7	Sun J S， Wu J， Wang Y M， et al. Cross-efficiency evaluation method based on the conservative point of view［J］. Expert Systems， 2020， 37（4）： e12336.
8	Sexton T R， Silkman R H， Hogan A J. Data envelopment analysis： Critique and extensions［J］. New Directions for Program Evaluation， 1986， 32： 73-105.
9	Doyle J， Green R. Efficiency and cross-efficiency in DEA： Derivations， meanings and uses［J］. Journal of The Operational Research Society， 1994， 45（5）： 567-578.
10	Wang Y M， Chin K S. A neutral DEA model for cross-efficiency evaluation and its extension［J］. Expert Systems with Applications， 2010， 37（5）： 3666-3675.
11	Alcaraz J， Ramón N， Ruiz J L， et al. Ranking ranges in cross-efficiency evaluations［J］. European Journal of Operational Research， 2013， 226（3）： 516-521.
12	Örkcü H H， Bal H. Goal programming approaches for data envelopment analysis cross efficiency evaluation［J］. Applied Mathematics and Computation， 2011， 218（2）： 346-356.
13	Lin R Y， Chen Z P， Xiong W T. An iterative method for determining weights in cross efficiency evaluation［J］. Computers & Industrial Engineering， 2016， 101： 91-102.
14	刘文丽，王应明，吕书龙. 基于交叉效率和合作博弈的决策单元排序方法［J］. 中国管理科学， 2018， 26（4）： 163-170.
	Liu W L， Wang Y M， Lv S L. Ranking decision making units based on cross-efficiency and cooperative game［J］. Chinese Journal of Management Science， 2018， 26（4）： 163-170.
15	Carrillo M， Jorge J M. An alternative neutral approach for cross-efficiency evaluation［J］. Computers & Industrial Engineering， 2018， 120： 137-145.
16	Wu J， Sun J S， Liang L. DEA cross-efficiency aggregation method based upon Shannon entropy［J］. International Journal of Production Research， 2012， 50（23）： 6726-6736.
17	王旭，王应明，王亮，等. 基于证据推理和前景理论的交叉效率排序方法研究［J］. 中国管理科学， 2022， 11（30）： 250-259.
	Wang X， Wang Y M， Wang L， et al. Study on cross-efficiency ranking based on evidential reasoning and prospect theory［J］. Chinese Journal of Management Science， 2022， 11（30）： 250-259.
18	Yang G L， Yang J B， Liu W B， et al. Cross-efficiency aggregation in DEA models using the evidential-reasoning approach［J］. European Journal of Operational Research， 2013， 231（2）： 393-404.
19	Li F， Zhu Q Y， Chen Z， et al. A balanced data envelopment analysis cross-efficiency evaluation approach［J］. Expert Systems with Applications， 2018， 106： 154-168.
20	Song M L， Zhu Q Y， Peng J， et al. Improving the evaluation of cross efficiencies： A method based on Shannon entropy weight［J］. Computers & Industrial Engineering， 2017， 112： 99-106.
21	Wang Y M， Chin K S. The use of OWA operator weights for cross-efficiency aggregation［J］. Omega， 2011， 39（5）： 493-503.
22	Oukil A. Embedding OWA under preference ranking for DEA cross-efficiency aggregation： Issues and procedures［J］. International Journal of Intelligent Systems， 2019， 34（5）： 947-965.
23	Li F， Wu H， Zhu Q Y， et al. Data envelopment analysis cross efficiency evaluation with reciprocal behaviors［J］. Annals of Operations Research， 2021， 302： 173-210.
24	杨国梁，刘文斌，郑海军. 数据包络分析方法综述［J］. 系统工程学报， 2013， 28（6）： 840-860.
	Yang G L， Liu W B， Zheng H J. Review of data envelopment analysis［J］. Journal of Systems Engineering， 2013， 28（6）： 840-860.
25	Angiz M Z， Mustafa A， Kamali M J. Cross-ranking of decision making units in data envelopment analysis［J］. Applied Mathematical Modelling， 2013， 37（1-2）： 398-405.
26	Chen L， Wang Y M， Huang Y. Cross-efficiency aggregation method based on prospect consensus process［J］. Annals of Operations Research， 2020， 288： 115-135.
27	Oukil A. Exploiting value system multiplicity and preference voting for robust ranking［J］. Omega， 2020， 94： e102048.
28	Fu Y L， Lai K K， Yu L A. Multi-nation comparisons of energy architecture performance： A group decision-making method with preference structure and acceptability analysis［J］. Energy Economics， 2021， 96： e105139.
29	Huang Y S， Chang W C， Li W H， et al. Aggregation of utility-based individual preferences for group decision-making［J］. European Journal of Operational Research， 2013， 229（2）： 462-469.
30	吴桂明. 基于改进区间交叉效率的云计算模型研究［J］. 控制工程， 2019， 26（12）： 2246-2251.
	Wu G M. Research on the cloud computing models based on the improved interval cross efficiency［J］. Control Engineering of China， 2019， 26（12）： 2246-2251.
31	Gholam R A， Mohaddeseh H. Application of optimistic and pessimistic OWA and DEA methods in stock selection［J］. International Journal of Intelligent Systems， 2016， 31： 1220-1233.
32	陈磊，王应明. 基于前景理论的交叉效率集结方法［J］. 系统科学与数学， 2018， 38（11）： 1307-1316.
	Chen L， Wang Y M. Cross-eficiency aggregate method based on prospect theory［J］. Systems Science and Mathematical Sciences， 2018，38（11）：1307-1316.
33	Yager R R. On ordered weighted averaging aggregation operators in multi-criteria decision making［J］. IEEE Transactions on Systems， Man and Cybernetics， 1988， 18（1）： 183-190.
34	张晓慧，冯源，曹月静. 最大最小偏差的多属性群决策方法［J］. 计算机与数字工程， 2020， 48（6）： 1360-1366.
	Zhang X H， Feng Y， Cao Y J. Method of max-min deviation in multiple-attribute group decision-making［J］. Computer & Digital Engineering， 2020， 48（6）： 1360-1366.
35	万树平. 对方案有偏好的最小最大偏差多属性决策方法［J］. 计算机工程与应用， 2009， 45（19）： 195-197.
	Wan S P. Min-max deviation method for multi-attribute decision-making with preference information on alternatives［J］. Computer Engineering & Applications， 2009， 45（19）： 195-197.
36	Sung J K， Myoungjae L. Q-convergence with inter-quartile ranges［J］. Journal of Economic Dynamics & Control， 2005， 29： 1785-1806.

DMU	投入指标		产出指标
DMU	成本	可重复性	装载能力	运行速度
1	7.2	0.15	60	1.35
2	4.8	0.05	6	1.1
3	5	1.27	45	1.27
4	7.2	0.025	1.5	0.66
5	9.6	0.25	50	0.05
6	1.07	0.1	1	0.3
7	1.76	0.1	5	1
8	3.2	0.1	15	1
9	6.72	0.2	10	1.11
10	2.4	0.05	6	1
11	2.88	0.5	30	0.9
12	6.9	1	13.6	0.15
13	3.2	0.05	10	1.2
14	4	0.05	30	1.2
15	3.68	1	47	1
16	6.88	1	80	1
17	8	2	15	2
18	6.3	0.2	10	1
19	0.94	0.05	10	0.3
20	0.16	2	1.5	0.8
21	2.81	2	27	1.7
22	3.8	0.05	0.9	1
23	1.25	0.1	2.5	0.5
24	1.37	0.1	2.5	0.5
25	3.63	0.2	10	1
26	5.3	1.27	70	1.25
27	4	2.03	205	0.75

DMU	1	2	3	4	5
1	1.000	0.378	0.479	0.341	1.000
2	0.169	0.904	0.417	0.833	0.169
3	0.284	0.043	0.529	0.038	0.312
4	0.031	1.000	0.162	1.000	0.031
5	0.582	0.008	0.108	0.008	0.592
6	0.060	0.128	0.474	0.114	0.063
7	0.238	0.426	1.000	0.379	0.247
8	0.500	0.423	0.618	0.379	0.507
9	0.161	0.234	0.308	0.210	0.163
10	0.300	0.839	0.758	0.758	0.300
11	0.441	0.077	0.669	0.068	0.478
12	0.095	0.006	0.069	0.006	0.102
13	0.397	1.000	0.701	0.909	0.397
14	0.987	0.993	0.658	0.909	0.987
15	0.382	0.043	0.613	0.038	0.419
16	0.559	0.043	0.437	0.038	0.602
17	0.060	0.043	0.405	0.038	0.066
18	0.168	0.211	0.299	0.189	0.171
19	0.920	0.255	0.733	0.227	0.951
20	0.008	0.017	1.000	0.015	0.009
21	0.124	0.036	0.852	0.032	0.139
22	0.031	0.829	0.455	0.753	0.031
23	0.140	0.213	0.694	0.189	0.148
24	0.135	0.213	0.636	0.189	0.141
25	0.234	0.213	0.511	0.189	0.243
26	0.437	0.042	0.577	0.037	0.478
27	0.899	0.016	1.000	0.014	1.000

DMU	1	2	3	4	5
1	1.000	0.534	0.001	0.487	1.000
2	0.000	0.937	0.001	0.885	0.000
3	0.001	0.000	0.001	0.000	0.001
4	0.000	1.000	0.000	1.000	0.000
5	0.687	0.000	0.000	0.000	0.699
6	0.000	0.000	0.001	0.000	0.000
7	0.000	0.576	1.000	0.523	0.000
8	0.618	0.574	0.697	0.522	0.628
9	0.000	0.000	0.000	0.000	0.000
10	0.001	0.893	0.812	0.831	0.001
11	0.566	0.000	0.740	0.000	0.603
12	0.000	0.000	0.000	0.000	0.000
13	0.526	1.000	0.766	0.938	0.532
14	0.991	0.995	0.731	0.938	0.991
15	0.513	0.000	0.692	0.000	0.552
16	0.668	0.000	0.001	0.000	0.707
17	0.000	0.000	0.001	0.000	0.000
18	0.000	0.000	0.000	0.000	0.000
19	0.943	0.000	0.792	0.000	0.966
20	0.000	0.000	1.000	0.000	0.000
21	0.000	0.000	0.886	0.000	0.000
22	0.000	0.886	0.001	0.827	0.000
23	0.000	0.000	0.761	0.000	0.000
24	0.000	0.000	0.712	0.000	0.000
25	0.000	0.000	0.001	0.000	0.000
26	0.563	0.000	0.662	0.000	0.604
27	0.929	0.000	1.000	0.000	1.000

DMU	传统方法		Chen等的方法		本文方法
DMU	效率值	排名	效率值	排名	效率值	排名
1	0.571	7	0.754	7	0.488	8
2	0.438	9	0.554	14	0.238	17
3	0.306	20	0.436	20	0.010	23
4	0.238	24	0.355	22	0.127	19
5	0.184	26	0.300	26	0.103	21
6	0.280	21	0.413	21	0.041	22
7	0.686	3	0.967	1	0.673	3
8	0.552	8	0.703	8	0.632	6
9	0.260	22	0.334	23	0.001	24
10	0.673	4	0.847	6	0.658	5
11	0.430	11	0.601	11	0.423	9
12	0.057	27	0.082	27	0.000	27
13	0.692	2	0.854	5	0.740	2
14	0.802	1	0.959	2	0.833	1
15	0.365	16	0.518	17	0.271	14
16	0.349	17	0.498	19	0.191	18
17	0.195	25	0.307	25	0.000	26
18	0.251	23	0.325	24	0.001	25
19	0.665	5	0.880	4	0.664	4
20	0.339	19	0.692	9	0.299	13
21	0.346	18	0.573	13	0.245	16
22	0.417	12	0.548	15	0.249	15
23	0.436	10	0.636	10	0.406	10
24	0.409	13	0.591	12	0.386	11
25	0.377	14	0.516	18	0.111	20
26	0.368	15	0.522	16	0.324	12
27	0.626	6	0.929	3	0.587	7

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A Cross-efficiency Evaluation Method Considering Decision Maker Preference Structure

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