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Management & Engineering 03 (2011) 1838-5745
Contents lists available at SEI
Management & Engineering
journal homepage: www.seiofbluemountain.com
Applying DEA to
Performance
the
Construction
Safety Management
Jinxian Zhao , Yuanlu Qiao
School of Management, Qingdao Technological University 266520, China
KEYWORDS
ABSTRACT
Construction safety,
DEA,
Safety management
In order to solve the problem of the construction site safety evaluation performance, this
thesis come up with one method based on DEA to evaluate it. From this paper, you will
find the author try to explain the connotation of Data Envelopment Analysis (DEA) and
apply it to the construction management research. Through this way, we can widen the
applications area of DEA method. Meanwhile, a sample measuring the On-site safety
management is given.
© ST. PLUM-BLOSSOM PRESS PTY LTD
1 Introduction
Construction is one of pillar industries in china, while safety accidents happened frequently in this area. Therefore, many scholars
place a great value on this subject and take the research of construction safety management seriously. At present, China is in the
large-scale infrastructure construction. It goes without saying that safety management and construction site safety performance
evaluation obtain the same weight. So doing research on the construction site safety performance evaluation has an important
practical significance on improving the construction site safety and ensuring the smooth implementation of the construction project.
In order to judge construction site safety management effectiveness, we need to evaluate the construction site safety performance.
Nowadays, the method of safety checklist is widely used in Chinese construction. [1] However, this method has great limitations .For
instance, it can not reflect the overall construction site safety management effectively. And Chinese scholars do a lot research on the
construction safety performance, and they aimed at the index of security measure, which is proposed to based on AHP and other
methods ,such as analytic hierarchy process (AHP) and grey theory of fuzzy evaluation method [2-3] as combination method to
evaluate. These methods are only an assessment of safety performance, and lack of accurate information about weighting factor, and
more important is that it can not accurately response building safety management performance of the site.
TO evaluate the safety management performance of construction site, in practice, is to judge of the security management in the
construction site or is to evaluate whether the output could reach the maximum when the input of security management is kept
constant, or is to assess whether the input could stay minimal when the output is kept constant. This provides a similar solution
solved by models of Data Envelopment Analysis (DEA). DEA is a perfect method to evaluate the “efficient scale” and “efficient

Corresponding author .
Email: qiaoyuanlu2006@163.com
English edition copyright © ST. PLUM-BLOSSOM PRESS PTY LTD
DOI:10.5503/J.ME.2011.03.018
109
technology” of one program which is equipped with multiple input and output events. My paper started with the analyzing of DEA
model, and then we studied the established program of security input and loss in the construction with the cases of verification
research. In addition, I choose the effectiveness of security management to evaluate the performance of construction security.
2 DEA Model
The basic idea of DEA is to form the first decision unit to determine the input and output factors. If n departments involved in one
production activity, they can be schools, hospitals, courts, construction projects, and it also can be banks or enterprises. Each DMU
has m types of factor inputs and s types of outputs. xij is ith input amount for DMUj, x ij >0, yrj is rth output amount for DMUj, yrj>0,vi
is weight of ith input ,ur is weight of rth output ,i=1,2,…m,j=1,2,…n,r=1,2,…s. Recorded input vector as Xj and input vector Yj,v
and u is weight vector of m inputs and s outputs, we have
X j  x1 j , x2 j ,, xmj  ,
T
v  v1 , v2 ,, vm 
T
,
j  1,, n ;
Y j   y1 j , y 2 j ,, y sj  ,
T
j  1,, n
u  u1 , u2 ,, um 
T
The efficiency evaluation index can be showed
hj 
uTYj
vT X j
,
j  1,2,, n
We can choose weight coefficient v and u , let
h j  1,
j  1,2, , n
For the efficiency of DMUjo,we have the target
hj0 
u T Y0
vT X 0
So , we compose a fractional programming (C2R model)
u T Y0

max
 V PI

vT X 0

uTYj

2
I
(C R ) 
1
vT X j

 u  0, v  0


Let
t
1
, w  tv,   tu
v X0
T
(1)
, fractional programming (1) problem can be changed into linear programming (2)
 max  T Y0  VCI2 R

 T X j   T Y j  0
( PCI2 R )
T X0 1


   0,   0
(2)
DMU j0
is weak efficient if the optimal value of linear programming
VCI2 R  1
0
0
and   0,   0 , DMU j
0
( PCI2 R ) VCI2 R  1 ,if the model ( PCI2 R )
is efficient.
Following Charnes and Banker, we assume that the technology sets is estimated by
110
optimal solution
n
n



T  ( X , Y )   j X j  X ,  j Y j  Y ,  j  0
j 1
j 1



Correspond to the technology sets, we have the following linear programming problems which called C2R model
 min   VD
 n
  j X j  X 0
 j 1
( D) n
   j Y j  Y0
 j 1

j  0

(3)
3 Construction Safety Management Performance Evaluation
Construction safety management investment and benefits not only include construction companies or construction projects for the
security of investment, but also the direct and indirect casualty losses. How to apply DEA model to evaluate the effectiveness of
building safety, the answer is that we need to do the statistical analysis of their input. According to the survey conducted by Fang
Dongping, [5] who divide the safety input into four aspects, individual labor protection, civil construction, safety education and on-site
safety. The proportion as the Figure 1:
Safety investment proportion
1% 3%
29%
67%
Personal labor
protection
The on-site safety
measures
Civilization
construction
Safety education
Figure 1 Safety input and proportion
As the Figure 1 conclude, on-site safety facility and civil construction takes the largest proportion, and personal protection and safety
education work very little. So we select three of them as the DMU units—evaluation index, on-site safety, civil construction,
protection of individual labor. At least as safe investment in education, the indicators will not be considered again. Security
investment income is received from the accident rate of the resulting casualties and economic losses (including direct economic
losses and indirect economic losses). Nevertheless, it is because the DEA evaluation is the evaluation of its effectiveness, and output
indicators must be direct benefits.
Traditional safe accidents are recorded as losses. Construction accidents and injuries are divided into economic losses, and casualties
can be counted as general economic losses. In this paper, we divide the loss of construction into two areas, the direct losses and
indirect losses. Through statistical analysis, the more serious casualties, the greater the loss the company did not record, and it can be
say the greater the indirect losses that is accidents.
Safety management brought about by the accident rate of casualties and economic losses are not suitable for DEA. Here we
transforming economic losses into two aspects, one is economic benefits of enterprise bring about by the direct economic loss. The
greater the economic losses, the lower the economic benefits of enterprise are. The other is the indirect losses, the greater the indirect
loss of business, the greater the impact on the company's social benefits, social benefits and thus lower the corporate. According to
DEA model, the output units include social and economic benefits.
111
4 Case Study
The effectiveness evaluation of construction safety management should be measured from the logical relationship between safety
investment and income from the security (social and economic benefits). Firstly do DEA effective analysis of all executation parts
which are deemed as different appraisal unit, and then representative investment items are determined as follows: on-site safety x1,
civilized construction x2, x3 personal labor protection as three input x, their income factors: social and economic y2 y1 as two output
y. (In dollars / year)
Here selecting Qingdao 10 major construction projects to evaluate, by statistical analysis of each item, its index data see table 1
below:
DMU Serial
Input indicators
Output indicators
numbers
X1
X2
X3
Y1
Y2
1
2000
3355
42
5000
30000
2
1300
2211
57
3562
38000
3
1020
1400
38
2191
20000
4
330
800
39
1643
12000
5
450
750
50
2329
11000
6
960
2110
42
4000
20000
7
2800
1850
49
3562
30000
8
849
1208
56
1233
19000
9
680
1000
61
1370
17000
10
113
2749
46
2749
29000
Table 1 Evaluation of the effectiveness of construction safety management information
Since the order of data in the table is very large, to facilitate the solution of linear programming problems, standardization of the
evaluation indicators, set up
Zj
=
1
10
10
10
 Z ij , S j
i 1
=
1
10
 (Z
i 1
ij
 Z j )2
; Standardized indicators is
Z
Z ij' = Sijj
The standard input and output indicators of table 1 is displayed in table 2
DMU Serial
X1
X2
X3
Y1
Y2
1
2.8296
4.0664
5.5339
4.2466
3.6053
2
1.8392
2.6798
7.5104
3.0253
4.5667
3
1.4431
1.6968
5.0069
1.8608
2.4035
4
0.4668
0.9696
5.1387
1.3954
1.4421
5
0.6366
0.9090
6.5880
1.9780
1.3219
6
1.3582
2.5574
5.5339
3.3973
2.4035
7
3.9614
2.2423
6.4563
3.0253
3.6053
8
1.2011
1.4641
7.3786
1.0472
2.2833
9
0.9620
1.2120
8.0374
1.1635
2.0430
10
1.5746
3.3310
6.0610
2.3348
3.4851
numbers
Table 2 Evaluation index of the standard value
Applying DEA (C2R) model on standardized data ,the evaluation of the validity of the results obtained DEA in Table 3.
112
DMU Serial
RMS
Slack variable
numbers

1
s1
s2
s3
s1
1
0
0
0
0
2
1
0
0
0
0
3
0.8881
0
0
0
0
4
1
0
0
0
0
5
1
0
0
0
0
6
1
0
0
0
0
7
1
0
0
0
0
8
0.9151
0.1796
0
2.9974
0.4654
9
0.9891
0.1288
0
4.5902
0.1898
10
0.9419
0
0.9805
0
0.0813
Table 3 DEA efficiency evaluation results
From
Table 2 we can know  value of project 1,2,4,5,6,7 is 1, so at least they are weak DEA efficient, then its slack variable s ,
s  are also 0, that prove DEA effective unit, indicating that the 6 safety management of construction projects is relatively effective.
The 3,8,9,10 project DEA RMS are less than 1, and it is neither for the weak effective and not effective for the DEA. This number
can indicate that the security management of these companies is ineffective, and accidents are occurring frequently in this way.
Therefore, more attention should be paid to renovation. The smaller the  Value is, the smaller the project safety management
performance is, and the worse the management is.

5 Conclusion
In this paper, a new method C2R DEA model is applied to evaluate the construction safety management performance evaluation .
Through the example, the method is feasible and reliable. But the treatment of the two output variables is needed to deepen the study,
to make it more objective and accurate.
References
[1]. Construction safety inspection standards JGJ 59-99(in Chinese)
[2]. SHUANG Liang, ZHANG Shoujian. Construction Safety Fuzzy Comprehensive Evaluation [J]. Journal of Harbin Institute of
Technology (Natural Science), 2003, (11):1357-1362 (in Chinese)
[3]. SUN Shoupeng, YU ZHijun. Study on Construction Safety Evaluation [J]. Journal of Qingdao Technological University, 2009,
30(6): 45-52(in Chinese)
[4]. WEI Songling .The Data Envelopment Analysis[M].Science Press, 2004: 1-20(in Chinese)
[5]. FANG Dongping, HUANG Xinyu, Jimmie Hinze. Construction Safety Management [M]. Beijing: China WaterPower Press,
2003:73-124(in Chinese)
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