Data envelopment analysis procedure with two non-homogeneous DMU groups

doi:10.21629/JSEE.2018.04.12

Journal of Systems Engineering and Electronics ›› 2018, Vol. 29 ›› Issue (4): 780-788.doi: 10.21629/JSEE.2018.04.12

收稿日期:2017-10-18 出版日期:2018-08-01 发布日期:2018-08-30

Data envelopment analysis procedure with two non-homogeneous DMU groups

Ye CHEN*(), Liangpeng WU(), Bo LU()

College of Economics and Management, Nanjing University of Aeronautics and Astronautics, Nanjing 211106, China

Received:2017-10-18 Online:2018-08-01 Published:2018-08-30
Contact: Ye CHEN E-mail:chenye@nuaa.edu.cn;1017379408@qq.com;lubo1991@163.com
About author:CHEN Ye was born in 1974. He received his Ph.D. degree from University of Waterloo, Canada. He is a professor with the College of Economics and Management, Nanjing University of Aeronautics and Astronautics, Nanjing, China. He has published papers in journals including European Journal of Operational Research, Computers and Operations Research, Decision Support Systems, IEEE Transactions on Systems, Man, and Cybernetics, Socio-Economic Planning Sciences, and Journal of Systems Science and Systems Engineering. His research interests include multiple criteria decision analysis, efficiency analysis, and conflict analysis. E-mail: chenye@nuaa.edu.cn|WU Liangpeng was born in 1991. He received his B.S. degree in Xuzhou University of Technology in 2013. He made research from 2013 to 2016 as a master candidate in University of South China. He is now pursuing his Ph.D. degree in the College of Economics and Management, Nanjing University of Aeronautics and Astronautics. His research interests include efficiency analysis, multiple criteria decision analysis and multiple objective optimization. E-mail: 1017379408@qq.com|LU Bo was born in 1991. He received his B.S. degree in Xidian University in 2014. He is currently pursuing his master's degree in the College of Economics and Management, Nanjing University of Aeronautics and Astronautics. His research interests include efficiency analysis and multiple criteria decision analysis with applications. E-mail: lubo1991@163.com
Supported by:
ccthe National Natural Science Foundation of Chinac(71471087);This work was supported by the National Natural Science Foundation of China (71471087)

摘要/Abstract

Abstract:

The classic data envelopment analysis (DEA) model is used to evaluate decision-making units' (DMUs) efficiency under the assumption that all DMUs are evaluated with the same criteria setting. Recently, new researches begin to focus on the efficiency analysis of non-homogeneous DMU arose by real practices such as the evaluation of departments in a university, where departments argue for the adoption of different criteria based on their disciplinary characteristics. A DEA procedure is proposed in this paper to address the efficiency analysis of two non-homogeneous DMU groups. Firstly, an analytical framework is established to compromise diversified input and output (IO) criteria from two nonhomogenous groups. Then, a criteria fusion operation is designed to obtain different DEA analysis strategies. Meanwhile, Friedman test is introduced to analyze the consistency of all efficiency results produced by different strategies. Next, ordered weighted averaging (OWA) operators are applied to integrate different information to reach final conclusions. Finally, a numerical example is used to illustrate the proposed method. The result indicates that the proposed method relaxes the restriction of the classical DEA model, and can provide more analytical flexibility to address different decision analysis scenarios arose from practical applications.

Key words: data envelopment analysis (DEA), non-homogeneous decision-making unit (DMU), criteria fusion, Friedman test, ordered weighted averaging (OWA) operator

. [J]. Journal of Systems Engineering and Electronics, 2018, 29(4): 780-788.

Ye CHEN, Liangpeng WU, Bo LU. Data envelopment analysis procedure with two non-homogeneous DMU groups[J]. Journal of Systems Engineering and Electronics, 2018, 29(4): 780-788.

图/表 8

参考文献 27

1	FARRELL M J. The measurement of productive efficiency. Journal of the Royal Statistical Society: Series A (General), 1957, 120 (3): 253- 290. doi: 10.2307/2343100
2	LERTXUNDI A. Transfer of HRM practices to subsidiaries: importance of the efficiency of the HRM system. Management Research, 2008, 6 (1): 63- 73.
3	ZUCKERMAN S, HADLEY J, IEZZONI L. Measuring hospital efficiency with frontier cost functions. Journal of Health Economics, 1994, 13 (3): 255- 280.
4	SONG F, GUAN Y, SONG M L. Environmental efficiency, advances in environmental technology and total factor of environmental productivity of China. Kybernetes, 2013, 42 (6): 943- 954. doi: 10.1108/K-02-2013-0025
5	SELLERS-RUBIO R, MAS-RUIZ F J, CASADO-DÍAZ A B. University efficiency: complementariness versus trade-off between teaching, research and administrative activities. Higher Education Quarterly, 2010, 64 (4): 373- 391.
6	CHARNES A, COOPER W W, RODES E. Measuring the efficiency of decision making units. European Journal of Operational Research, 1978, 2 (6): 429- 444.
7	BANKER R D, CHARNES A, COOPER W W. Some models for estimating technical and scale inefficiencies in data envelopment analysis. Management Science, 1984, 30 (9): 1078- 1092. doi: 10.1287/mnsc.30.9.1078
8	COOK W D, TONE K, ZHU J. Data envelopment analysis: prior to choosing a model. Omega, 2014, 44 (2): 1- 4.
9	YANG F, YANG C, LIANG L. New approach to determine common weights in DEA efficiency evaluation model. Journal of Systems Engineering and Electronics, 2010, 21 (4): 609- 615.
10	WANG K, WEI F. Robust data envelopment analysis based MCDM with the consideration of uncertain data. Journal of Systems Engineering and Electronics, 2010, 21 (6): 981- 989.
11	GHOLAMI K, BEIGI Z G, HADIVENCHEH A. The allocation of sub-decision making units to parallel fuzzy network systems. Kybernetes, 2014, 43 (7): 1079- 1097. doi: 10.1108/K-02-2013-0016
12	ZHA Y, WANG J, ZHAO L. Efficiency improvement based upon overall value judgment and weight restriction. Kybernetes, 2015, 44 (5): 721- 738.
13	SEIFORD L M, THRALL R M. Recent developments in DEA: the mathematical programming approach to frontier analysis. Journal of Econometrics, 2004, 46 (1): 7- 38.
14	KANG H, LEE A H I. A new supplier performance evaluation model: a case study of integrated circuit (IC) packaging companies. Kybernetes, 2010, 39 (1): 37- 54.
15	BI G B, WANG H L, DING J J. Integration of α-fairness with DEA based resource allocation model. Journal of Systems Engineering and Electronics, 2014, 25 (6): 1027- 1036.
16	SAEN R F, MEMARIANI A, LOTFI F H. Determining relative efficiency of slightly non-homogeneous decision making units by data envelopment analysis: a case study in IROST. Applied Mathematics & Computation, 2005, 165 (2): 313- 328.
17	BOUGNOL M L, DULA J H. Validating DEA as a ranking tool: an application of DEA to assess performance in higher education. Annals of Operations Research, 2006, 145 (1): 339- 365.
18	Maclean's magazine, Canadian university ranking, http://www.macleans.ca/education/university-rankings-2016C, accessed on June 1, 2017.
19	LI W H, LIANG L, COOK W D. DEA models for nonhomogeneous DMUs with different input configurations. European Journal of Operational Research, 2016, 254 (3): 946- 956.
20	COOK W D, HARRISON J, IMANIRAD R. Data envelopment analysis with non-homogeneous DMUs. Operations Research, 2013, 61 (3): 666- 676.
21	FRIEDMAN M. The use of ranks to avoid the assumption of normality implicit in the analysis of variance. Publications of the American Statistical Association, 1939, 32 (200): 675- 701.
22	YAGER R R. On ordered weighted averaging aggregation operators in multicriteria decisionmaking. Readings in Fuzzy Sets for Intelligent Systems, 1993, 18 (1): 80- 87.
23	TORRA V, NARUKAWA Y. Modeling decisions-information fusion and aggregation operators. Cognitive Technologies, 2007, 61 (12): 1090- 1093.
24	LIU X. On the methods of decision making under uncertainty with probability information. International Journal of Intelligent Systems, 2004, 19 (12): 1217- 1238.
25	BADELLO M R, MOSHIRI B, ARAABI B N. A novel detection and navigation approach based on OWA fusion method. Sensor Review, 2011, 31 (4): 328- 340.
26	YAGER R R. New modes of OWA information fusion. International Journal of Intelligent Systems, 2015, 13 (7): 661- 681.
27	GAO C L, LI C Q. Improvement of cross-efficiency ranking methods. Systems Engineering, 2003, 21 (3): 81- 86.

Division	Department	ESP	NFP	EHP	JP	AC	NAW	SCA
G₁	A	54 284	1 934	359	1 794	91	5	3
	B	48 879	454	1 250	744	26	0	0
	C	96 830	1 269	285	800	49	5	2
	D	54 595	790	765	470	22	2	2
	F	46 512	1 122	962	1 481	39	0	5
	G	53 834	1 798	743	865	90	1	3
	J	53 207	1 501	686	1 624	91	1	1
	H	90 563	487	628	585	50	4	3
	I	72 830	845	1 252	1 287	20	4	0
	J	53 207	1 501	686	1 624	91	1	1
	K	90 563	487	628	585	50	4	3
	L	53 271	641	366	1 475	85	3	2
	M	47 361	1 685	1 287	1 722	31	0	4
	N	70 816	861	1 056	1 201	77	2	4
G₂	a	51 629	872	4 283	902	25	3	5
	b	23 814	240	3 514	349	28	2	3
	c	21 179	609	2 658	536	22	0	9
	d	32 474	732	5 904	567	27	1	6
	e	47 789	974	5 744	720	52	4	7
	f	53 584	263	2 045	651	28	0	8
	g	49 254	223	5 775	624	33	2	10
	h	30 295	682	2 140	885	46	5	9
	i	34 424	259	2 283	339	58	2	3
	j	59 245	251	3 816	854	32	5	8
	k	37 524	463	3 156	596	38	4	3
	l	55 776	904	2 794	698	49	1	7
	m	27 032	282	4 515	793	31	0	5
	n	30 359	981	5 413	368	47	1	4

Department	$e_{{{{\rm{or}}}}}^{{{{\rm{or}}}}} $	$e_{{{{\rm{and}}}}}^{{{{\rm{or}}}}} $	$e_{{{{\rm{or}}}}}^{{{{\rm{and}}}}} $	$e_{{{{\rm{and}}}}}^{{{{\rm{and}}}}} $	$e_{{{{\rm{1}}}}}^{{{{\rm{1}}}}} $	$e_{{{{\rm{2}}}}}^{{{{\rm{2}}}}} $
A	1.000	1.000	1.000	1.000	1.000	1.000
B	0.665	0.665	0.573	0.573	0.573	0.665
C	1.000	1.000	0.439	0.439	0.418	1.000
D	0.538	0.520	0.342	0.342	0.342	0.538
F	1.000	0.989	0.960	0.960	0.960	1.000
G	0.995	0.477	0.986	0.463	0.978	0.677
H	1.000	0.995	0.556	0.556	0.556	1.000
I	0.796	0.796	0.712	0.712	0.712	0.796
J	1.000	0.943	1.000	0.901	1.000	0.943
K	1.000	1.000	0.588	0.494	0.588	1.000
L	1.000	1.000	1.000	1.000	1.000	1.000
M	1.000	1.000	1.000	1.000	1.000	1.000
N	0.811	0.609	0.689	0.601	0.673	0.805
a	0.605	0.605	0.605	0.605	0.605	0.605
b	0.915	0.764	0.915	0.764	0.915	0.764
c	1.000	0.735	1.000	0.735	0.775	1.000
d	0.606	0.554	0.606	0.554	0.567	0.606
e	0.687	0.544	0.687	0.544	0.683	0.544
f	1.000	0.871	0.833	0.758	0.796	1.000
g	1.000	0.838	1.000	0.838	0.974	1.000
h	1.000	1.000	1.000	1.000	1.000	1.000
i	1.000	0.587	1.000	0.587	1.000	0.587
j	1.000	1.000	1.000	1.000	1.000	1.000
k	0.926	0.887	0.926	0.887	0.926	0.887
l	0.633	0.423	0.576	0.417	0.529	0.595
m	1.000	1.000	1.000	1.000	1.000	1.000
n	0.942	0.369	0.942	0.369	0.909	0.421

Statistical parameter	Value
Number of departments	28
The value of c	54.543
Degree of freedom	5
P-value	0.000
The value of α	0.01

Statistical parameter	Value
Number of departments	28
The value of c	8.592
Degree of freedom	3
P-value	0.035
The value of α	0.01

Department	$A$	$B$	$C$	$D$	$E$	$F$	$G$	$H$	$I$	$J$	$K$	$L$	$M$	$N$	$a$	$b$	$c$	$d$	$e$	$f$	$g$	$h$	$i$	$j$	$k$	$l$	$m$	$n$
$OWA_{{{{\mathit{\boldsymbol{Q}}}}}_1}^j $	1	0.665	1	0.538	0.540	1	0.986	1	0.796	1	1	1	1	0.805	0.605	0.915	1	0.606	0.687	1	1	1	1	1	0.926	0.595	1	0.942
$OWA_{{{{\mathit{\boldsymbol{Q}}}}}_2}^j $	1	0.573	0.439	0.342	0.498	0.96	0.477	0.556	0.712	0.943	0.588	1	1	0.609	0.605	0.764	0.735	0.554	0.544	0.796	0.838	1	0.587	1	0.887	0.423	1	0.369
$OWA_{{{{\mathit{\boldsymbol{Q}}}}}_3}^j $	1	0.619	0.720	0.435	0.519	0.977	0.780	0.777	0.754	0.971	0.794	1	1	0.694	0.605	0.840	0.878	0.583	0.615	0.875	0.953	1	0.794	1	0.907	0.531	1	0.660

Data envelopment analysis procedure with two non-homogeneous DMU groups

RichHTML

PDF (PC)

可视化

摘要/Abstract

引用本文

使用本文

图/表 8

参考文献 27

相关文章 0

编辑推荐

Metrics

本文评价