Efficiency Evaluation of the Listed Corporations of Automobile

Efficiency Evaluation of the Listed Corporations of Automobile
Industry Based on DEA
Li Yaosheng1, Wang Xiping2
1, Normal College of Dingzhou, P. R. China, 073000
2, School of Business Administration, North China Electric Power University, P. R. China, 071003
：
Abstract
Data Envelopment Analysis (DEA) is becoming an increasingly popular tool for assessing
the relative efficiency. Compared to conventional methods, DEA shows several advantages and the
evaluating results are more objective and systematic. So, by applying DEA theory to automobile
industry, this paper analyzes the relative efficiency of twelve listed corporations. The results indicate
that the performance of several listed corporations is sub-optimal, suggesting the potential for significant
cost reductions. So, measures for improving the efficiency also discussed.
Key words
Automobile industry, Listed corporations, Data Envelopment Analysis, Efficiency
：
1 Introduction
Automobile industry, as one major part of national economy, has becoming rapid growth with the
economic development and the improvement of people’s life. And the listed corporation of automobile
industry therefore becomes a focus attaching much attention. So it is a meaningful work to evaluate the
performance of listed corporations, which can help a corporation to identify performance targets and to
acquire a strong competitive edge using the least possible resources.
In the literature there has not been much discussion about the efficiency of the automobile listed
corporations. The traditional method focused on financial ratio analysis, usually in the form of a single
index to analyze the corporations’ capability of payment and profitability, however, the results cannot
reflect the overall efficiency of the companies. More recently, principal components analysis (PCA) was
introduced to analyze this problem, but it cannot provide indirection for improving efficiency because of
without analyzing the structure transformation. Data Envelopment Analysis (DEA), originally proposed
by Charnes, Cooper and Rhodes [1978 and 1979], is a methodology for analyzing the relative efficiency
and managerial performance of decision-making units (DMUs), having the same multiple inputs and
multiple outputs. It allows us to compare the relative efficiency of corporations by determining the
efficient DMUs as benchmarks and by measuring the inefficiencies input combinations (slack variables)
to the benchmark. Compared to conventional methods, DEA shows several advantages. First, DEA
allows handling multiple inputs and outputs (with different units) in a noncomplex way. Second, DEA
does not require any initial assumption about a specific functional form linking inputs and outputs.
Accordingly, this study applies DEA to analyze the relative efficiency of twelve automobile listed
companies and further discusses the method for improving the management efficiency.
The rest of this paper is organized as follows. Section 2 gives a brief review of DEA method.
Section 3 gives the DEA results and further discussion. Finally, our conclusions are presented in section
4.
2 Data Envelopment Analysis
DEA is a multi-factor productivity analysis model for measuring the relative efficiencies of a
homogenous set of decision making units (DMUs). The efficiency score in the presence of multiple
input and output factors is defined as:
Efficiency =weighted sum of outputs/weighted sum of inputs
(1)
Assuming that there are n decision-making units (DMUs) to be evaluated, each DMU uses m inputs to
produce s outputs, the relative efficiency score of a test DMU0 can be calculated by solving the
following mathematical programming problem:
*The Project Sponsored by North China Electric Power University Scientific Research Fund for Doctoral Teachers
418
s
∑u y
r
r0
r =1
m
max
∑v x
i i0
i =1
subject to:
s
∑u y
r rj
≤ 1, j = 1,2,..., j0 ,..., n
r =1
m
∑v x
(2)
i ij
i =1
ur , vi ≥ 0, r = 1,2,..., s; i = 1,2,..., m
where xij = the observed amount of input of the ith type of the jth DMU
y rj =
the observed amount of input of the rth type of the jth DMU
ur = weight given to output r
vi = weight given to input i
The fractional programming problem shown as (2) can be converted to a linear program as shown
in (3). For more details on model development see Charnes et al. (1978).
s
∑u y
Max
r
r0
r =1
subject to:
s
∑u
m
r
yrj − ∑ vi xij ≤ 0, j = 1, 2,..., n;
r =1
i =1
m
∑v x
i i0
(3)
= 1, vi ≥ 0; u r ≥ 0
i =1
For the above linear programming problem, the dual can be written (for the given DMU0) as:
m
s


m in θ − ε ( ∑ S i− + ∑ S r+ 
i =1
r =1


Subject to
n
∑λ
j
x ij + S i− = θ x i 0 , i = 1, 2, ..., m
j =1
n
∑λ
j
(4)
y rj − S r+ = y r 0 , r = 1, 2 , ...s
j =1
λ j , S i− , S r+ ≥ , j = 1, 2, ..., n
where Si− and Sr+ are the slacks in the system, and ε is a small non-Archimedean value
( ε = 10−6 )
The above problem is run n times in identifying the relative efficiency scores of all the DMUs, and
values of θ (efficiency score), and λj (weights for the inputs and outputs) are computed. The optimal
value of the variable θ indicates the proportional reduction of all inputs for DMU0 that will move it
onto the frontier, which is the envelopment surface defined by the efficient DMUs in the sample. A
*
DMU is termed efficient if and only if the optimal value θ is equal to 1 and all the slack variables are
zero.
In the case of inefficient DMUs, data envelopment analysis models also identify target input-output
levels, which would render them efficient and efficient peers; they could emulate to improve their
*
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performance. For inefficient DMUs the optimal inputs and output values are calculated as follows:
x *ij =θ * x ij -s*-i
(5)
y*rj =yrj +s*+
r
(6)
3. Empirical Research
3.1 Specification of the data
Twelve listed corporations of automobile industry were chosen from Shanghai and Shenzhen Stock
Exchanges as our decision-making units (DMUs). As a statistical basis for evaluation, the end-of-year
2005 annual reports were used.
Table 1
DMUs
Input and Output variables for CCR Model
Input factors
X1
X2
Output factors
Y1
Y2
Y3
Jiangling Auto
466327.0
490041.1
628063.6
49543.1
0.574
Ankai Auto
127419.9
91765.36
105454.2
1564.11
0.071
ST Zhongqi
538682.8
595583.5
650632.2
15064
0.59
Xiamen Auto
384321.3
670316.7
0.68
1865149.8
154235.4
771714.8
1916854.9
10310.2
Changan Auto
23675
0.15
Yutong Auto
278749.6
373037.4
45764.36
18567.8
0.7
Zhongtong Auto
122427.6
74044.87
85567.9
961.02
0.04
Shanghai Auto
1459484.9
520974.8
638868.91
110462.2
0.337
Jianghuai Auto
481772.04
771910.9
939465.88
49775.3
0.55
Dongfeng Auto
974612.5
748153.9
880105.8
39388.5
0.197
Yiqi Auto
795797.9
795665.09
1032711.9
33762.5
0.207
Anhui heli
146823.04
131544.5
174703.2
1447.98
0.47
Source: data taken from http:// hexun.news.com
After the units of assessment are identified, we need to define potential input and output variables.
Selection of input and output variables is one of the important tasks of performance analysis and the
choice of variables depends on not just the choice of methodology and technical requirements of the
chosen model, but also on data availability and its quality. No universally applicable rational template is
available for selection of variables. However, in general, the inputs should capture resources, which are
required to be minimized. The outputs should reflect all useful outcomes on which is wished to assess
the decision-making units.
This study uses two input and three output measures for evaluating these companies’ performance. Two
inputs selected for the DEA analysis are: Total Assets (X1), Operating Costs (X2). Three outputs include
Prime operating revenue (Y1), Net Profit (Y2) and Earnings per share of common stock (Y3). Total
Assets, Operating Costs, Prime operating revenue, and Net Profit are measured in billions of RMB. All
input and output data of these variables are listed in table 1.
3.2 Mathematical Solutions
Using the data listed in Table 1, a CCR input oriented DEA model was used to analyze the relative
efficiency of the 12 listed automobile corporations. The results are presented in table 2. According to the
results, the twelve auto corporations can be divided into two groups: the efficient and the inefficient.
And for the inefficient corporations, the new input and output values are calculated by using (5) and (6),
and the results of the calculation are presented in Table 3.
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Table 2
DMU
θ
Jiangling Auto
Ankai Auto
ST Zhongqi
Xiamen Auto
Changan Auto
Yutong Auto
Zhongtong Auto
Shanghai Auto
Jianghuai Auto
Dongfeng Auto
Yiqi Auto
Anhui heli
1
0.8653
0.8532
1
0.9358
0.7845
0.8701
1
1
0.8858
0.9969
1
*
the Results of CCR Model
−
1
S 2−
S
S1+
2163.4
13442.6
9671.6
3462.05
12362
21443.6
S 2+
S3+
717.58
3090.6
0.2127
0.6003
13519.8
299.77
613.04
5.007
3355.62
4502.65
2.1707
2.0922
∑λ
*
i
0.1902
1
0.6036
2.4841
1
1.9720
1.4890
0.4897
1
1
5.0377
4.8486
1
3.3 Result Analysis
3.3.1 Efficiency Analysis
It is evident from table 2 that DMU1, DMU4, DMU8, DMU9, DMU12 are efficient. Since the
optimal value θ * is equal to 1 and all the slack variables are zero. This means that 5 corporations,
namely Jiangling Auto, Xiamen Auto, Shanghai Auto, Jianghuai Auto and Anhui heli are operating on
the CRS frontier, While the remaining 7 DMUs exhibited varying degrees of inefficiencies, which
implies that some latent and enterprise special resources are still not being penetrated and not being fully
utilized. This indicates its competitiveness cannot be taped effectively. So they need to rearrange input
to improve their performance.
3.3.2 Scale returns analysis
By solving CCR model, the value of λ j also can be calculated. According to the value of
*
we can judge the scale returns of DMUj. If
∑λ
*
i
∑λ
*
i
∑λ
*
i
=1 means the DMUj CRS (constant returns scale), if
<1 in CCR model indicates IRS (increasing returns scale), while
∑λ
*
i
>1 indicates DRS
(decreasing returns scale).
It is observed from Table 2 that the 5 efficient corporations also have constant returns-to-scale
(CRS), which means that at present output level, the inputs have reached the optimal value.
While the inefficient corporations, only two corporations, namely, Zhongtong and Ankai, exhibit
IRS, the remaining of the inefficient corporations exhibited decreasing returns to scale, indicating that
further expansion of services may not be productive.
3.3.3 Process improvement
The analysis of the previous section indicated which automobile corporations are efficient and
which are inefficient. Those inefficient corporations are able to improve their performance and the DEA
projections provide a prescription for improvement. For example, DMU2 (Ankai Auto) is inefficient,
however, it can move its performance to best practice by either decreasing its inputs or increasing its
outputs. Concretely, the input values should be decreased to: X1=0.8653*127419.9-2163.4=108093
X2=0.8653*91765.36=79404.57. Or the output values of Y2 and Y3 should be increased to 2281.69,
0.2837 respectively.
，
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Table 3
Adjusted Inputs and Outputs
Adjusted inputs
DMU
Adjusted outputs
X1
X2
Y1
Y2
Y3
Ankai Auto
108093
79404.57
105454.2
2281.69
0.2837
ST Zhongqi
459604
508151
650632.2
18154.6
1.1903
1731964.4
144333
1916854.9
37194.8
5.157
218679
282976
67207.96
18867.6
0.7
Changan Auto
Yutong Auto
Zhongtong Auto
103062
64426.4
85567.9
1574.06
0.2302
Dongfeng Auto
850949.8
662714.7
880105.8
42744
2.3677
Yiqi Auto
793330.9
793198.5
1032711.9
38265.15
2.2992
It is noted that reducing input or increasing output is usually used to improve inefficient DMUs.
But in fact, not every kind of inputs and outputs can be varied freely. For instance, when labor force is
taken as input, we cannot downsize the work force freely in order to achieve efficiency in a country like
China, which has an abundant supply of labor force. Likewise, the area of workshops and factories
cannot be reduced arbitrarily when they are taken as input variables.
4 Conclusions
This paper uses DEA to evaluate the performance of 12 listed corporations of the automobile
industry. The estimated results show that only 5 corporations, namely Jiangling Auto, Xiamen Auto,
Shanghai Auto, Jianghuai Auto and Anhui heli are efficient, while the remaining 7 corporations
exhibited varying degrees of inefficiencies. And further study indicates that the majority of the
inefficient corporations except two corporations, exhibited decreasing returns to scale. Therefore we
should strengthen the internal management and decrease the capital cost to improve the performance.
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