J. Serv. Sci. & Management, 2008, 1: 255-258
Published Online December 2008 in SciRes (www.SciRP.org/journal/jssm)
1
The Evaluation of Enterprises’ Sustainable Superiority
Degree of Technical Innovation Based on DEA Method
Bing Jiang, Lu Yang & Jun Fang
School of Management, Hefei University of Technology, 230009, China
Received August 31
st
, 2008; received November 20
th
, 2008; accepted December 5
th
, 2008.
ABSTRACT
The paper at first expounds two new concepts of sustainability degree and superiority degree, and founds a method of
DEA of relative efficiency index to rank all decision-making-units having been identified efficient. On the basis of them,
the definition and arithmetic are given to analyze them. Then seven input and output techno-innovation indexes which
belong to six automobile listed companies from 2002 to 2005 are used to evaluate enterprises’ sustainability degree and
superiority degree by vertical and horizontal calculation based on DEA method. At last, we get general conclusions
about enterprises’ sustainable superiority degree by weighting calculation.
Keywords: technical innovation, DEA, relative efficiency, sustainable superiority evaluation
1. Introduction
DEA model (Data Envelopment Analysis) is one of ma-
thematical programming approaches to analyze decision-
making-units’ (DMUs) relative efficiency. To some
enterprises’ inputs and outputs which are observed in a
period of time, we apply DEA model and acquire not only
vertical evaluation of enterprises’ sustainable innovation
based on time as DMU, but also horizontal relative
evaluation of enterprises’ innovation performance based on
enterprises as DMU.
However, in traditional DEA model, DMU can only be
examined as “effective” or “ineffective” but can not be
ranged by their weights. Furthermore, each DMU’ weight
is computed from the most beneficial angle, which,
obviously, will give birth to that most of DMU even all
will be described as effective. Consequently, the traditional
DEA model will affect the further comparable analysis. The
purpose of this paper is to calculate degree of technical
innovation sustainability and superiority according to the
definition of relative efficiency index and to present a
concept of sustainable superiority degree. In this paper, we
apply the ideal DMU and obtain a standard weights vector as
referenced ones, on the basis of these, the values of relative
efficiency index are available. We select six listed companies
in automobile industry as our research objects, and the
analysis data are based on seven indexes, which reflect the
innovations and originate from the 2002-2005 years’ reports
of relating companies.
2. DEA Model Based On Relative Efficiency
Indexes
2.1. The Basic Principle of Traditional DEA Model
Technical innovation in a specific enterprise can be
described by a group of innovation indexes of input-
output. We use vector A
j
to stand for input of decision-
making-unit j (DMUj) and vector B
j
for its output, i.e.:
A
j
=(a
1j
, a
2j
, ..., a
mj
)
T
，B
j
=(b
1j
, b
2j
, ..., b
sj
)
T
. The dual
programming model of DMUj can be constructed as
below: D: min V
D
=y
s.t. miyasxa
ijij
n
jij
,,2,1,
0
1
L==+
∑
=
skbtxb
kjkj
n
jkj
,,2,1,
0
1
L==−
∑
=
(1)
x
jnj ,,2,1,0 L
=
≥
; s
i
mi ,,2,1,0 L
=
≥
; t
k sk ,,2,1,0 L
=
≥
Where x
j
stands for the jth DMU’ decision-making
variable; s
i
for the slack variable of the ith input index; t
k
for the surplus variable of the kth output index; and y for
the input proportional variable.
If non-Archimedes infinitesimal quantity is applied,
then the equation will appear to:
:
ε
D
min V
D )()(
11
∑∑
==
+−=
s
kk
m
ii
tsy εε
s.t. miyasxa
ijij
n
jij
,,2,1,
0
1
L==+
∑
=
skbtxb
kjkj
n
jkj
,,2,1,
0
1
L==−
∑
=
(2)

256 Bing Jiang, Lu Yang & Jun Fang
x
j nj,,2,1,0 L
=
≥
;
s
i
mi ,,2,1,0L
=
≥
; t
k sk ,,2,1,0L=≥
On the assumption that optimum solutions of equation
(2) are x
j*
(j=1,2,…, n), s
i*
(i=1,2,…, m), t
k*
(k=1,2,…, s),
y
*
, some effective judgment rules will go like this:
(1) y
*
=1，and s
i*
=0(i=1,2,…, m)﹑t
k*
=0(k=1,2,…, s),
then DMUj
0
is DEA effective, and its economic
significance means the optimal innovative efficiency and
constant return to scale simultaneously.
(2) y
*
=1, we can conclude that DMUj
0
is DEA
ineffective. Its economic significance means it is not
simultaneous to reach optimal innovative efficiency and
constant return to scale.
2.2. DEA Model Based on Relative Efficiency Index
To overcome the deficiency of traditional model which is
unable to discriminate the differences among different
efficient units, we apply ideal DMU. To each input index,
if minimum input vectors are made of minimums of all
DMU on the assumption, then A
min
=(a
1min
, a
2min
,…, a
mmin
);
likewise, if maximum output vectors are made of
maximum of all DMU, we mark B
max
=(b
1max
, b
2max
,…,
b
smax
), then we can say (A
min
, B
max
) stand for innovation
activity related to ideal DMU. We add the ideal DMU to
DEA model, and under the thought of using DEA method
to calculate weight, an efficient index model can be
constructed as below:
miv
sku
Av
Bu
nj
Av
Bu
ts
Av
Bu
h
i
k
T
T
j
T
j
T
T
T
，
，
，
…=≥
…=≥
≤
…=≤
=
,10
,10
1
,1,1..
max
min
max
min
max
max
(3)
The model is used to obtain a series of weights v
1
,
v
2
,…, v
m
; u
1
, u
2
,…, u
m
, which can optimize the efficiency
indexes of ideal DMU if all observed DMU’ indexes
meet the inequality: h
j
≤1. We take these weights as
referenced weights to calculate the relative efficiency
indexes of other units. Because of their inferior
efficiencies to the ideal DMU, we can tell the difference
between excellent DMU and bad ones easily.
Charnes-Cooper transformation is used, ordered: t=1/
(v
T
A
min
), ω
T
=tv
T
, µ
T
=tu
T
, There were: h
max
= (u
T
B
max
)
/(v
T
A
min
)=t(u
T
B
max
)=µ
T
B
max
But: h
j
=(u
T
B
j
)/(v
T
A
j
)= t(u
T
B
j
)/t(v
T
A
j
)= µ
T
B
j
/ω
T
A
j
≤1,
j=1,2,…, n
After transforming, it becomes an equal model of
linear programming:
max µ
T
B
max
s.t. µ
T
B
j
≤ω
T
A
j
j =1,2,…, n
µ
T
B
max
≤ω
T
A
min
(4)
ω
T
A
min
=1
ω
k
≥0，k=1,2,…, m；µ
i
≥0，i=1,2,…, s
We call h
*max
(h
*max
=µ
*T
B
max
) as efficient index of
ideal DMU and h
*j
(h
*j
=(µ
*T
B
j
)/(ω
*T
A
j
))as relative
efficient index of ideal DMU. Consequently, all DMU
can be ranked based on its relative efficiency index.
3. Sustainable Superiority Degree of Technical
Innovation in Enterprises
Sustainability degree of technical innovation is a new
concept that is mainly used to describe stability and
durative of technical innovation process in an enterprise
when it is considered as the main unit of technical
innovation activities. It isn’t only a matter of time, but
also refers to development of the technical innovation
activities in enterprise and furtherance of the innovative
spirit in corporate culture.
Technical innovation, which plays a role of encouraging
and promoting innovations in other departments, is the
inexhaustible motive force for sustainable development of
enterprises. The relation between techno-innovation and
techno-innovation sustainability just likes the relation
between qualitative change and quantitative change,
techno-innovation is the unity of gradual change and
abrupt change. On one hand, techno-innovation can lay a
solid foundation and offer technical supports for
innovations in other areas gradually and also the
guidance for future development. On the other hand,
when technical innovation is promoted to a certain phase,
it will break through the outdated formation and captures
the new technology primacy, which is the demonstration
of techno-innovation sustainability. Continuous technical
innovation presents a premise to techno-innovation
sustainability, and in turn, techno-innovation sustainability
provides assurance for techno-innovation.
Superiority degree is used to describe the degree of
primacy for a techno-innovation performance in a certain
domain. To an enterprise, higher sustainable superiority
means larger market share and more powerful
competitive advantage. Technical innovation is the only
access for the enterprise to be the leader in a market, and
then, the innovation performance depends on its
superiority.
According to the description above, sustainable
superiority degree of technical innovation could be
defined as bellow:
Sustainability degree of technical innovation describes
how techno-innovation performance keeps going with the
time changing, measured by the slope of linear regression
model which uses enterprises’ vertical efficiency indexes
as the vertical axis and years as the horizontal axis. The least

The Evaluation of Enterprises’ Sustainable Superiority Degree of Technical Innovation Based on DEA Method 257
square estimator is applied to calculate the parameter of
linear regression model, the formula appears to be:
mjxxyyxxb
n
ijijjij
n
i
j
ijj
，…=−−−=
∑∑
==
,2,1)(/))((1
1
2
1
(5)
Where, y
ij
stands for vertical efficiency index of the j
enterprise in year x
i
, n means how many years.
Superiority degree of technical innovation represents
relative level of technical innovation performance among
all observed enterprises. If I we use the sum of
differences between horizontal efficiency indexes of each
year and average relative efficient index as the
measurement. The formula is as follows:
mjHHb
n
i
i
ijj
,,2,1)(2
1
…=−=
∑
=
−
(6)
Where, H
ij
stands for horizontal efficiency indexes of
the j enterprise in year i.
Sustainable superiority degree of technical innovation
represents comprehensive performance of an enterprise
considering both the time and its counterparts. We use
the method of normalized weighted average of
sustainability and superiority degree of technical
innovation to calculate them:
b=w
1
b1+w
2
b2，weight w
1
and w
2
can be evaluated
based on your preference. If you pay more importance to
growing character, weight w
1
should be higher; or
smaller.
4. Empirical Study
We select six automobile listed companies as our
research objects, and apply DEA model as mentioned
above to analyze the indicator of innovation input-output
during 2002 to 2005 from vertical and horizontal two
aspects. On the vertical aspect, we take each year as
DMU and then learn how is technical innovation
performance and returns to scale changing with time,
which, in fact, reflects the superiority characteristic of
techno-innovation; in contrast, On the horizontal aspect,
we use individual enterprise as DMU and relatively rank
each enterprise with their techno-innovation efficiency
and returns to the scale, which, correspondently reflects
the primacy of innovative enterprise among its
counterparts. To the convenience of building the model,
we categorize the data to two typies: data of each year for
all companies (vertical section) as in table 1, and data
of each company for all years( transect).
Table 1. The values of techno-innovation indexes of each enterprise in four years (vertical section)
DFAC JAC
indexes\years 2002 2003 2004 2005 2002 2003 2004 2005
ratio of technical staffs (%) 22.8 21 20.1 20.84 10.58 11.57 8.2 9.24
ratio of expenditure in technical development in the
main business income (%) 0.09 5.71 0.07 0.01 0.12 0.28 0.55 0.53
net profits of fixed assets (10million) 179.48 207.95 110.82 132.83 22.99 68.21 117.16 140.88
main business income (10million) 443.08 700.06 585.14 610.01 198.94 344.3 545.01 806.89
income taxes (10million) 9.23 10.39 5.5 8.1 1.53 2.97 8.09 12.99
return on total assets (%) 10.86 9.32 9.66 6.55 6.49 7.28 8.28 8.54
rate of net profit (%) 12.13 8.81 10.76 7.64 4.47 3.85 3.8 3.98
CHANGHE YXMC
indexes\years 2002 2003 2004 2005 2002 2003 2004 2005
ratio of technical staffs (%) 10.69 12.62 12.62 13.6 7.78 6.4 6.2 7.33
ratio of expenditure in technical development in the
main business income (%) 0.44 1.56 0.67 1.53 0.24 0.35 1.1 0.16
net profits of fixed assets (10million) 88.87 86.35 95.37 96.34 29.6 29.36 32.12 31.34
main business income (10million) 332.85 437.3 415.05 313.87 101.98 87.65 79.87 79.53
income taxes (10million) 1.96 2.79 1.49 1.4 0.38 0.63 0 0.02
return on total assets (%) 2.64 2.19 1.31 -1.32 4.14 1.93 -11.84 -5.68
rate of net profit (%) 2.61 1.94 1.22 -1.53 5.22 2.54 -18.47 -8.71
ANKAI JMC
indexes\years 2002 2003 2004 2005 2002 2003 2004 2005
ratio of technical staffs (%) 12.16 14.14 12.2 9.46 11.98 11.53 11.54 11.97
ratio of expenditure in technical development in the
main business income (%) 0.23 0.57 0.92 0.26 1.32 1.56 1.6 1.11
net profits of fixed assets (10million) 30.41 32.87 28.07 31.13 166.82 155.47 145.42 130.55
main business income (10million) 44.59 48.8 73.25 91.53 337.91 427.09 509.49 577.07
income taxes (10million) 0.11 0.07 0 0 0.48 2.33 4.84 6.79
return on total assets (%) 1.01 -4.09 1.82 0.87 2.75 8.01 11.8 9.36
rate of net profit (%) 2.3 -8.14 2.71 1.11 2.98 6.71 8.81 6.7
The origin of the data: Shanghai stock exchange; Shenzhen stock exchange; China finance online and so on

258 Bing Jiang, Lu Yang & Jun Fang
Table 2. The results of traditional DEA model
vertical section↓ transect→
years DFAC JAC CHANGHE YXMC ANKAI JMC DFAC JAC CHANGHE YXMC ANKAI JMC
02 1 1 1 1 1 0.585
1 1 1 1 0.4 0.933
03 1 0．895 1 1 0.893 0.819 1 1 1 0.591 0.293 1
04 1 1 1 0.94 1 1 1 1 0.869 0.47 0.494 1
05 1 1 0.671 1 1 1 1 1 0.568 0.443 0.513 1
Table 3. The results of relative efficiency index based on DEA model
vertical section↓ transect→
years DFAC JAC CHANGHE YXMC ANKAI JMC DFAC JAC CHANGHE YXMC ANKAI JMC
02 0.783 0.589 0.761 0.992 0.613 0.564 0.341 0.271 0.157 0.430 0.121 0.160
03 0.957 0.604 0.847 0.802 0.00002 0.740 0.305 0.272 0.317 0.125 0.032 0.339
04 0.529 0.970 0.804 0.185 0.998 0.882 0.308 0.377 0.189 0.054 0.227 0.442
05 0.752 0.887 0.564 0.351 0.182 0.963 0.352 0.550 0.215 0.195 0.403 0.557
Table 4. The evaluation of sustainability and superiority degree of enterprises’ techno-innovation
DFAC JAC CHANGHE YXMC ANKAI JMC
sustainability degree b1(0.6) -0.05228 0.12607 -0.0634 -0.25396 -0.02936 0.13411
superiority degree b2(0.4) 0.18289 0.34687 -0.24523 -0.31902 -0.33991 0.3744
sustainable superiority degree b 0.60459 0.97217 0.34765 0.01349 0.34726 1
the order 3 2 4 6 5 1
According to formula (2), we obtain the whole DEA
validity of each enterprise in four years and their validity
in each year, as displayed in table 2. From it, we can see
that , regarding of the enterprise itself, DFAC is the only
one which has been simultaneously on the state of
optimal innovation efficiency and constant returns to
scale simultaneously for four years, while JAC,
CHANGHE, ANKAI and YXMC each have one year in
DEA inefficiency, and JMC has two years in DEA
inefficiency. Compared these enterprises with each other,
we can find that in year 2002 and 2005 there were four
enterprises DEA efficiency, and in year 2003 and 2005
there were three. Among them, DFAC and JAC share the
leadership for four years. However, no matter from
vertical or horizontal section, traditional DEA analysis
will only result in many efficient DMU but can not tell
the differences between them, so here model (4) is used
to further discriminate degree in efficiency of those DMU.
The results are listed on Table 3.
According to the arithmetic of sustainability and
superiority degree mentioned above, we order their
correspondent weights equal to 0.6 and 0.4, then the
evaluation of all enterprises’ sustainability and
superiority can be acquired as in Table 3. The rank can be
seen in Table 4.
As in Table 4, JMC wins the No.1 in sustainability and
superiority, closely followed by JAC, and DFAC ranks
the third. Comparably, CHANGHE, ANKAI, YXMC
are lagged far behind them. And the conclusion is also
consistent with what really has happened. The new
concept, this paper aims to present, sustainability and
superiority, can not only evaluate enterprises’
innovation performances among counterparts and also
on the order of time in this paper. Because of the
constraint of observed samples and certain historical
period, the conclusion can only be used as reference.
Considering of the pertinence and practicability, you
can select specific sample for observation according to
your own needs.
REFERENCES
[1] Q. L. Wei, “Data envelopment analysis,” [M], Beijing:
Science Press, 2005.
[2] J. Y. Yan and B. J. Sun,” “System analysis and evaluation
of enterprises’ technical innovation,” [M], Beijing: China
Financial & Economical Publishing House, 2002.
[3] G. Li, X. Y. Shen, and Y. M. Wang, “A new method for
ranking DMUS,” [J], Forecasting, 2000(4): pp. 51-53.
[4] D. Du, “The evaluation of enterprises technical innovation with
Data Envelopment Analysis,” [J], Systems Engineering-
Theory Methodology Applications, 2002, 10(1): pp. 82-84.
[5] B. Jiang and C. Q. Zhang, “DEA on enterprise’s
technological progress and example research,” [J],Systems
Engineering-Theory & Practice, 7(7): pp. 65-70, 2002.