Study on Re-Evaluation of Technological Innovation Efficiency Based on
the C2r Improvement Model in Zhongguancun High-Tech Enterprises
Jing-wen An, Sen Zhang, Guang-lin Sui
School of Management,China University of Mining & Technology Beijing, Beijing, China
E-mail: zhangs_zs@163.com
Abstract - To begin with, this paper studied the relative
efficiency of the Innovation Efficiency of 10 major High-tech
industries in Zhongguancun. The study found that 7 of the
10 high-tech industries in Zhongguancun are relatively
effective in their Innovation Efficiency. They are industries
of electronic information, advanced manufacturing, new
energy, new materials, modern farming, ocean engineering
and nuclear application. Then this article introduced the
virtual optimization of DMU based on the C2R model, which
re-evaluated the relative effectiveness of the abovementioned 7 industries. Then this paper gave some
suggestions to improve the innovation efficiency of these
industries.
Key words - Zhongguancun; High-tech Industries; Data
envelopment analysis; DEA; Virtual decision making units
I.
INTRODUCTION
The innovation efficiency of the high-tech industries
in Zhongguancun demonstration industrial park is the
conversion efficiency of input-output of production
factors. It reflects the capacity of the industrial park to
utilize technological resources and develop high-tech
industries, as well as the quality and standard of the
Zhongguancun innovation system. The Zhongguancun
National Self-innovation Demonstration Park (hereafter
referred to as “Zhongguancun”) is China’s first selfinnovation park, a leading area of high-tech industries and
the hotbed of the strategic newly emerging industries. In
the new stages of the 21st century, a re-evaluation of the
innovation efficiency of the Zhongguancun high-tech
industries can help government better plan new industries,
utilize resources, raise efficiency and promote industrial
restructuring.
II.
DEA MODEL
C2R model
Data Envelopment Analysis is a nonparametric
comprehensive evaluation method to analyze the relative
effectiveness of the DMU featured by high input and
［ ］
output 1 . It has been widely used to assess the efficiency
of technology innovation within the same category of
［
］
DMU 2, 3 . Usually DEA can be divided into C2R model
2
and B C model, both of which conduct horizontal
comparison and analysis to different DMUs at the same
［ ］
time. The C2R model is as follows 4 :
A.
(1)
s

 m 
 
 min  -   S   S   vd   
i

1
r

1



 s.t.
 n
 X   S   X
0
 j j
( D )  j 1
 n
 Y j  j  S  Y0
 j 1
  0, j  1, 2
,n
 j
S  0,S  0

Within the (D) model, ϴ represents the effective value
of DMU0, which is the effective use of the input against
output. X j   x1 j , x 2 j ,
, xmj  , j  1, 2,
T
the input of DMU, Y j   y1 j , y 2 j ,
, n represents
, ysj  , j  1, 2,
T
,n
represents the output of DMU. S ，S stands for the
slack variable, which is supposedly bigger than zero. λj
stands for composition ratio of DMUj within the DMU
［ ］
composition 5 .
+
-
B. Improved DEA-C2R model
In actual DEA evaluation processes, most of the DMU
are relative effective, and only a few of the DMUs are
invalid. This is because there are too many indexes and
［
too few DMUs, making the analysis result less practical 6
］
. In this case, it should be made further analysis to the
relative effective DMUs to evaluate the efficiency. There
are many ways of sequencing in the DEA evaluation, and
［
］
this paper adopts the virtual unit method 6,7,8 .
Within the virtual unit method, a virtual decision
making unit DMUn+1 is introduced to replace the normal
DMU0 within the General model of constraint conditions
so as to distinguish the different degrees of different
DMUs. Suppose the input and output of DMU n+1 is
（ xi,n+1,yk,n+1 ） ,
xi , n 1  min xij (i  1,   , m)
1 j  n
yk ,n 1  max ykj (k  1,   , s) .
1 j  n
The
virtual
decision
making unit DMU n+1 is the best decision making unit
among the valid DMUs. It’s compared the efficiency
value of virtual DMU with the efficiency value of other
DMUs. If the DMU show a value that is approximate to
the virtual DMU, then the value is high. The evaluation
process can be achieved by inputting valid DMU, or by
introducing a virtual DMUn+1.. the result can be calculated
［ ］
through (Dε1) 8 .
a result, the paper selected 6 indicators as the evaluation
criteria of the innovation efficiency of Zhongguancun
high-tech industries. Among these 6 indicators, 3 are
［
］
input indicators and 3 are output indicators 9,10,11,12 .
min[   (eˆ T s   eT s  )]
 n +1
 s.t.  x  s    x , j  1, 2,   , n  1; j  j
j j
0
0
 
j 1
 n 1

( D 1 )    j y j  s   y 0 , j  1, 2,   , n  1; j  j0
 j 1
   0, j  1, 2 , n  1
j

 s  (s1 ,s 2 , ,s s )  0,s  (s1 ,s 2 , ,s s )  0


(2)
The sequence of efficiency value from (D)ε is the
sequence of quality of the decision making unit DMUj0. If
the DMU value ≤1, the bigger the value is, the better the
quality of this DMUj0.
The DMU efficiency value (Dε2) can be calculated
after the introduction of the virtual DMUn+1.
max[   (eˆ T s   eT s  )]
 n +1
 s.t.  x  s    x , j  1, 2,   , n  1; j  j
j j
0
0
 
j 1
 n 1

( D 2 )    j y j  s   y 0 , j  1, 2,   , n  1; j  j0
 j 1
   0, j  1, 2 , n  1
j

 s  (s1 ,s 2 , ,s s )  0,s  (s1 ,s 2 , ,s s )  0


(3)
The sequence of efficiency value from (D)ε is the
sequence of quality of the decision making unit DMU j0.If
the value is 1, the smaller the value is, the smaller the
gap between it and the virtual DMU, thus the better the
quality of the DMUj0.
This paper firstly evaluates the DMU through C2R and
B C model within the DEA method. Then the paper
introduces the virtual processing unit DMUn+1.The
effectiveness of the DMU is calculated through the
efficiency evaluation of the valid DMU.
2
III. CASE STUDY OF THE EFFECTIVENESS OF THE
INNOVATION EFFICIENCY OF ZHONGGUANCUN HIGH-TECH
INDUSTRIES
A. establishment of the indicator system
This paper studied the innovation efficiency of the
Zhongguancun innovation system and the research results
of relative scholars, took into consideration the
representativeness and accessibility of these indicators. As
Among the input indicators are: proportion of
technology staff in the industry I1, total expenditure of the
technological innovation I2, proportion of technology
expenditure in the total revenue I3. I1 stands for the input
intensity of technology staff, which is the ratio of
technology staff against the total staff. I2 stands for the
activity of technological innovation of the industry. I3
stands for the level and intensity of the industry
［
］
independent innovation 13,14 .
Among the Output indicators are: quantity of the
patent accredit O1, proportion of new product sales
revenue accounted for product sales revenue O2,
proportion of new product sales revenue accounted for
gross value of industrial output O3. O1 stands for the
industry innovation important output value; O2 stands for
the rate of new product sales, the contribution degree of
industry enterprise technology innovation into new
products on enterprise value creating; O3 stands for the
transformation ability of the industry technology
［ ］
innovation 15 .
B. Selection of data
All of the evaluation indicators used in this article
in assessing the innovation efficiency of Zhongguancun
high-tech industries are objective. The data used here are
mainly from the Annual Book of Zhongguancun Hightech Industrial Park and the Annual Book of
Zhongguancun National Demonstration Park of Selfinnovation. Part of the data is from statistical data of the
website of Zhongguancun National Demonstration Park
of
Self-innovation
from
2006
to
2010(http://www.zgc.gov.cn/tjxx/). And part of the data is
through calculation of these existing data. Therefore,
these data are highly objective and credible.
This paper treats the high-tech industries of
Zhongguancun as a high-input and high-output system.
Decision variables （DMUj，j=1，2，…，10）are the
10 high-tech industries of Zhongguancun Demonstration
Park. Because of the different time-lag between input and
［ ］
output of the innovation 5 , the DEA efficiency analysis
only uses the average figure of the indicator data in the
Annual Book of the 11th five-year plan period.
TABLE 1 STATISTICAL INDICATORS OF THE 10 HIGH-TECH INDUSTRIES OF ZHONGGUANCUN IN THE 11TH TWELFTH FIVE-YEAR PLAN PERIOD.
Industries
electronic information
biomedicine
New material
Advanced manufacturing
aerospace
Modern agriculture
new energy
Environment protection
ocean engineering
Nuclear application
I1（%）
39%
25%
25%
25%
40%
24%
30%
34%
27%
45%
I2（billion Yuan）
36.159
1.945
2.493
4.133
1.751
0.427
2.643
1.029
0.075
0.275
I3（%）
13%
8%
7%
6%
37%
6%
4%
15%
14%
12%
O1（item）
2764.00
378.20
676.00
1022.00
51.80
71.00
439.80
227.60
11.60
67.20
O2（%）
61%
41%
66%
42%
53%
70%
77%
63%
20%
79%
O3（%）
83%
45%
88%
51%
62%
97%
103%
113%
24%
69%
TABLE 2 INNOVATION EFFICIENCY VALUE OF ZHONGGUANCUN HIGH-TECH INDUSTRIES
field of technology
Overall efficiency
Pure technical efficiency
Scale efficiency
Returns to scale
Electronic information
Biomedicine
New material
Advanced manufacturing
Aerospace
Modern agriculture
New energy
Environment protection
Ocean engineering
Nuclear application
Average value
1.000
0.718
1.000
1.000
0.454
1.000
1.000
0.957
1.000
1.000
0.913
1.000
0.973
1.000
1.000
0.600
1.000
1.000
1.000
1.000
1.000
0.957
1.000
0.738
1.000
1.000
0.757
1.000
1.000
0.957
1.000
1.000
0.945
crs
irs
crs
crs
irs
crs
crs
drs
crs
crs
TABLE 3 INDICATORS OF VIRTUAL DMUS
I1（%）
24%
DMU
DMU11
I2（million）
75
I3（%）
4%
C. Evaluation of DEA-B2C model
This paper utilizes the DEA input-output returns to
scale B2C model, puts the data of TABLE 1 into the
model and gets the result through DEAP 2.1. The
innovation efficiency value of the 10 key high-tech
industries is shown in TABLE 2. Since the DEA method
is a relative evaluation method, the DEA value in TABLE
［ ］
2 just stands for its degree of the relative effectiveness 16 .
It can be seen from TABLE 2 that the biggest overall
DEA value is 1, the smallest being 0.454 and the average
value being 0.913. Among the innovation efficiency
evaluation of Zhongguancun high-tech industries, 7
industries
(electronic
information,
advanced
manufacturing, new energy, new material, and modern
agriculture, ocean engineering and nuclear application)
have an innovation efficiency value of 1. This means that
70% of the DMUs are effective while 30% (environment
protection, biomedicine and aerospace) of these are not.
Generally speaking, most of the high-tech industries are
relative effective in terms of innovation efficiency.
D. Evaluation of the improved DEA-C2R model
It can be seen from the results of the C2R and B2C
model that industries with relative effective innovation
efficiency account for a bigger share. In order to
O1（item）
2764
O2（%）
79%
O3（%）
103%
distinguish the efficiency value of these industries, a
virtual unit DMU11 was introduced to re-evaluate the
innovation efficiency, as is shown in TABLE 3.
Suppose ε=10-6, a C2R model based on the input of
Archimedes infinitesimal C2R model is established. The
C2R model of DMU1 is as follows:
min[   (s1- +s2- +s3-  s1+  s2+  s3+ )]

 s.t.0.391 +0.252 +0.253 +0.244 +0.35 +0.276 +0.457  0.248  s1  0.24

361.591 +24.932 +41.333 +4.274 +26.435 +0.756 +2.757  0.758  s2  0.75
0.13 +0.07 +0.06 +0.06 +0.04 +0.14 +0.12  0.04  s  0.04

1
2
3
4
5
6
7
8
3
( D 1 ) 
+
27641 +6762 +10223 +714 +439.85 +11.66 +67.27  27648  s1  2764
0.61 +0.66 +0.42 +0.7 +0.77 +0.2 +0.79  0.79  s +  0.79
1
2
3
4
5
6
7
8
2

0.831 +0.882 +0.513 +0.974 +1.035 +0.246 +0.697  1.038  s3+  1.03

  j  0, j  1,2 ,8，s (s1 ,s2 ,s3 )  0,s  (s1 ,s 2 ,s3 )  0
(4)
After calculation by Matlab, the following results are
innovation efficiency of Zhongguancun high-tech
industries. See TABLE 4.
TABLE 4 EVALUATION OF DEA EFFICIENCY C2R WHEN COMBINED WITH VIRTUAL DMUS
DMU
ϴ(Initial)
ϴ（after improvement）
1~4
5
6~7
8
9
1
n


j 1
Electronic information
1
0.615
0.000
1.000
1.000
1.626
New material
1
0.820
0.000
0.854
0.854
1.042
Advanced manufacturing
1
0.510
0.000
0.532
0.532
1.042
Modern agriculture
1
0.942
0.000
0.942
0.942
1.000
New energy
1
0.999
0.187
0.813
1.000
1.000
Ocean engineering
1
0.253
0.000
0.253
0.253
1.000
j
Nuclear application
1
0.533
TABLE 5 VALUE OF INPUT-OUTPUT SLACK VARIABLES
S1-
S2-
S3-
Electronic information
0.61
0.31
New material
0.05
0.18
0.61
Advanced manufacturing
0.06
0.07
0.16
Modern farming
0.01
0.15
0.92
0.07
0.00
0.68
0.03
0.00
DMU
New energy
0.13
Ocean engineering
0.02
Nuclear application
0.06
S1+
S2+
S3+
0.30
0.24
0.02
0.00
0.05
0.19
0.25
0.03
0.18
0.98
0.41
It’s known that virtual evaluation unit is the best
decision making unit. Therefore, we can rank the
innovation efficiency of Zhongguancun high-tech
industries in the following sequence: new energy >
modern agriculture > new material> electronic
information > nuclear application > advanced
manufacturing > ocean engineering. In terms of
economies of scale, industries of new energy, modern
agriculture and ocean engineering are in the best
condition, while all other industries have witnessed an
increasing trend of returns to scale.
Based on the DEA-C2R, it can get the invalid input
indicator slack variable value and output indicator slack
variable value of the 7 high-tech industries in
Zhongguancun Demonstration Park. See TABLE 5(the
input residual value and insufficient output value is zero,
which is nothing in the TABLE).
According to the projection analysis theory, it got
the input residual value and the insufficient output value
of the 7 high-tech industries of Zhongguancun
Demonstration Park, which is relatively invalid. See
TABLE 6 (the input residual value and insufficient
output value is zero, which is nothing in the TABLE).
IV.
CONCLUSION
Through the DEA analysis of innovation efficiency
of the high-tech industries in the Zhongguancun
industrial park, It can be seen that:
A. Electronic information
The efficiency value of the electronic information
industry is 0.615 as evaluated through the DEA, ranking
the 4th in the seven high-tech industries, with an
economy of scale of 1.626 and an increasing trend. In
0.000
1.000
1.000
1.876
2010, electronic information industry accounted for
46.29% of the Demonstration Park. It also accounted
for the largest proportion of technological expenditure
in the 11th five-year plan period, almost 2.5 times as the
other 9 fields. This shows that electronic information
industry is No.1 pillar industry of Zhongguancun
Industrial Park, with the most active innovation but
relatively low innovation efficiency. According to
TABLE 6, on condition that the input does not change,
it should reduce the technological expenditure by
22.1767 billion Yuan, and the input intensity be reduced
by 40%. And while maintaining a constant input, it
should raise the proportion of sales revenue of new
products in total sales revenue and total industrial
output by 18% and 20% respectively, an effective
efficiency.
B. Advanced manufacturing
As the second largest industry in Demonstration
Park, the advanced manufacturing industry has an
evaluation efficiency of 0.51 after DEA evaluation,
ranking the 6th with a scale efficiency value of 1.042
and a growing scale. Its revenue accounts for 11.89% of
the Zhongguancun Demonstration Park. Therefore, it
should, in accordance with the plan of upgrading
manufacturing industrial clusters, with the output
unchanged, cut technological expenditure by 269.5
million Yuan, or reduce 90% of its input intensity. And
while maintaining a constant input, it should increase
447.468 items of patents and raise the proportion of
new products sales revenue in total sales revenue by
38%.
C. New energy
As a growth point of the industries in the
Demonstration Park, the new energy industry has an
efficiency value of 0.999 after DEA evaluation, ranking
the first, with a scale efficiency of 1 and a constant
return to scale. In 2010, the revenue of the new energy
industry accounts for 10.93% of the industrial park.
Therefore, in accordance with the plan of developing
new energy, with the output unchanged, it should
reduce the proportion of technological staff by 60%, cut
the technological budget by 2.568 billion Yuan. While
remaining a constant input, it should increase the patent
authorization by 2324.2 pieces and the proportion of
new products sales revenue by 20%.
TABLE 6 INPUT RESIDUAL VALUE AND INSUFFICIENT OUTPUT VALUE
S2-(billion Yuan)
S3-（%）
Electronic information
22.1767
40%
New material
1.987
23%
1685.476
Advanced manufacturing
0.2695
90%
447.468
Modern agriculture
0.3315
19%
2531.99
44%
2324.2
20%
DMU
S1-（%）
New energy
60%
Ocean engineering
80%
2.568
25%
S1+（item）
688.147
S2+（%）
S3+（%）
18%
20%
15%
38%
21%
Nuclear application
0.0717
D. New material
As a fast growing industry, the new material
industry gets an efficiency evaluation value by 0.820%
after DEA evaluation, ranking the third, with a scale
efficiency of 1.042 and increasing trend. In 2010, the new
material industry accounted for 6.73% of the total revenue
in the industrial park. So, while maintaining a constant
output, it should cut the technological budget by 1.987
billion Yuan; reduce the budget input intensity by 23%.
And while maintaining a constant input, it should increase
patent authorization by 1685.476 items and the proportion
of new products sales revenue by 15%.
E. The modern agriculture industry
The modern agriculture industry gets an efficiency
evaluation value by 0.942, ranking the second, with a
scale efficiency of 1 and a constant return to scale. In
2010, modern agriculture industry accounted for 0.76% of
the total revenue in the Demonstration Park. Though the
proportion is small, this industry is essential to the
people’s wellbeing. So, while maintaining a constant
output, it should cut the technological budget by 331.5
million Yuan; reduce the budget input intensity by 19%.
And while maintaining a constant input, it should increase
patent authorization by 2531.99 items and the proportion
of new products sales revenue by 44%.
F. Nuclear application
The nuclear application industry gets an efficiency
evaluation value by 0.533, ranking the 7th, with a scale
efficiency of 1 and an increasing return to scale. In 2010,
modern agriculture industry accounted for 0.17% of the
total revenue in the Demonstration Park. Despite a tiny
proportion, this industry is strategically important to the
national economy. So enough attention should be paid to
this industry. While maintaining a constant output, it
should cut the technological budget by 71.7 million Yuan;
reduce the budget input intensity by 25%. And while
maintaining a constant input, it should increase patent
authorization by 2696.8 items and the proportion of new
products sales revenue by 34%.
G. Ocean engineering
The ocean engineering industry gets an efficiency
evaluation value by 0.253, ranking the 8th (the last place)
with a scale efficiency of 1 and a constant returns to scale.
In 2010, modern agriculture industry accounted for 0.17%
of the total revenue in the Demonstration Park. Given its
strategic importance, enough attention should be paid to
this industry. While maintaining a constant output, it
should cut the proportion of the technological staff by
80%; reduce the budget input intensity by 24%. And
while maintaining a constant input, we should increase
patent authorization by 2696.8 items and the proportion of
new products sales revenue by 34%.
24%
2696.8
34%
REFERENCES
[1]
[2]
[3]
[4]
[5]
[6]
[7]
[8]
[9]
[10]
[11]
[12]
[13]
[14]
[15]
[16]
Wei Quanling. Data envelopment analysis [ M ]. Beijing:
Science Press,2004.
Che Weihan, Zhang Lin. Shanghai City cooperative
efficiency evaluation -- Based on industry data DEA
analysis ( J ). Science technology progress and policy,2010,
(03).
Cheng Hongxing, Chen Yongli. DEA based in Hubei
Province high-tech industrial innovation efficiency analysis
[J ]. Science and technology journal,2009, (12).
Xu Juan, Sun Linyan, He Zhe. DEA based on China's interprovincial mode of high technology industrialization
development and relative advantage industry choose [ J ].
Science & technology progress and policy,2009(02).
Wang Xiuli, king sword. Cooperative innovation efficiency
evaluation of DEA ( J ). Statistics and decision
making,2009(3) : 54- 56
Duan Yongrui. Data envelopment analysis: Theory and
application [ M]. Shanghai science and Technology
Press,2007
Zhang Hua, Lv Tao. Safety efficiency evaluation of China's
coal enterprises based on DEA model and its improved
model [J ]. Coal economic research,2011(5):49-53.
Liu world, Song Mei. Coal listed company performance
evaluation -- based on DEA-C ~2R model perspective [J ].
Management engineer,2010(1):1-4.
He Ming, Shane king, Liu Yiwen. Innovation ability
evaluation analysis of Zhongguancun science and
technology garden based on DEA [J ]. Science &
technology progress and policy,2010(9):106-109.
Wang Dan. Technology innovation performance evaluation
of the East Lake High-tech Zone based on DEA [ J].
Journal of Chongqing Academy of Arts and Sciences (
NATURAL SCIENCE EDITION ),2008(2):84-87.
Xie Ziyuan. Study on the National High-tech Zone
technology innovation efficiency influence factors [J ].
Management of scientific research,2011(11):52-58.
Quan Jinmin, Yao Lan,Shi Benshan. National high-tech
zone sustainable development capacity evaluation based on
DEA [ J]. Soft science,2008(1):75-77.
Zhang Genming, Liu Tao. New and high area dominant
industry selection analysis based on DEA [J ]. Technology
economics and management research,2008(02):19-21.
Li Nan, Xie Zhongqiu. China regional innovation system
innovation efficiency evaluation -- Positive Analysis based
on DEA [J ]. Industrial technology economy,2010(8):122126.
Zhang Guowang, Li Baizhou. Regional innovation system
efficiency evaluation based on DEA [J ]. Management
science,2009(5):47-48.
Wang Peng, Wang Liangjian, Wang Lijuan. The
manufacturing industry in Hunan Province based on DEA
innovation efficiency analysis [J ]. Science and technology
management research,2009, (06).