Advances in Environmental Biology in Iran

Advances in Environmental Biology, 8(1) January 2014, Pages: 221-226
AENSI Journals
Advances in Environmental Biology
Journal home page: http://www.aensiweb.com/aeb.html
Using Order Preference by Similarity to Ideal Solution (TOPSIS) for Seven Industries
in Iran
1
Esmaeil Khoshbakht, 2Zinat Ansari, 3Nasim Osouli, 4Mahdi Kazemi
1,2,4
Department of Accounting, Shiraz Branch, Islamic Azad University, Shiraz, Iran.
Hafez Institute of Higher Education, Shiraz, Iran.
3
ARTICLE INFO
Article history:
Received 12 October 2013
Received in revised form 18
December 2013
Accepted 29 December 2013
Available online 25 February 2014
Key words:
Topsis continues,
MCDM methods,
Tehran Stock Exchange,
ABSTRACT
Multi-Criteria Decision Making (MCDM) methods have received much attention from
researchers in evaluating, ranking alternatives across diverse industries. Among
numerous MCDM methods developed to solve real-world decision problems, the
Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) continues to
work satisfactorily across different application areas. The Technique for Order of
Preference by Similarity to Ideal Solution (TOPSIS) is a multi-criteria decision analysis
method. In this paper, we used TOPSIS methods for ranking seven companies (2012) in
Iran. This paper provides useful insights into the TOPSIS method and suggests a
framework for future attempts in this area for ranking and determination operation of
statement of companies listed in Tehran Stock Exchange.
© 2014 AENSI Publisher All rights reserved.
To Cite This Article: Esmaeil Khoshbakht, Zinat Ansari, Nasim Osouli, Mahdi Kazemi., Using Order Preference by Similarity to Ideal
Solution (Topsis) for Seven Industries in Iran. Adv. Environ. Biol., 8(1), 221-226, 2014
INTRODUCTION
The Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) is a multi-criteria decision
analysis method, which was originally developed by Hwang and Yoon in 1981 with further developments by
Yoon in 1987, and Hwang, Lai and Liu in 1993 [1]. TOPSIS is based on the concept that the chosen alternative
should have the shortest geometric distance from the positive ideal solution and the longest geometric distance
from the negative ideal solution [2]. It is a method of compensatory aggregation that compares a set of
alternatives by identifying weights for each criterion, normalizing scores for each criterion and calculating the
geometric distance between each alternative and the ideal alternative, which is the best score in each criterion.
An assumption of TOPSIS is that the criteria are monotonically increasing or decreasing. Normalization is
usually required as the parameters or criteria are often of incongruous dimensions in multi-criteria problems [3,
4]. Compensatory methods such as TOPSIS allow trade-offs between criteria, where a poor result in one
criterion can be negated by a good result in another criterion. This provides a more realistic form of modelling
than non-compensatory methods, which include or exclude alternative solutions based on hard cut-offs [5].
1980: development by Kwangsun Yoon and Hwang Ching-Lai – Yoon, K., “System Selection by Multiple
Attribute Decision Making,” Ph. D. Dissertation, Kansas State University, Manhattan, Kansas, 1980. – Yoon, K.
and C. L. Hwang, “TOPSIS (Technique for Order Preference by Similarity to Ideal Solution)- A Multiple
Attribute Decision Making,” a paper to be published, 1980.
Objective:
This paper provides useful insights into the TOPSIS method and suggests a framework for future attempts
in this area for ranking and determination operation of statement of companies listed in Tehran Stock Exchange.
MATERIAL AND METHOD
The TOPSIS process is carried out as follows:
Step 1:
Corresponding Author: Zinat Ansari, Department of Accounting, Shiraz Branch, Islamic Azad University, Shiraz, Iran.
Tel: +98-917-1048553; E-mail: [email protected]
222
Zinat Ansari et al, 2014
Advances in Environmental Biology, 8(1) January 2014, Pages: 221-226
Create an evaluation matrix consisting of m alternatives and n criteria, with the intersection of each
alternative and criteria given as , we therefore have a matrix
.
Step 2:
The matrix is
method
then normalized to form the matrix
, using the normalization
where
is the maximum possible
.
value of the indicator
Step 3:
Calculate the weighted normalized decision matrix:
Step 4:
Determine the worst alternative
and the best alternative
:
Where,
associated with the criteria having a positive impact, and
associated with the criteria having a negative impact.
Step 5:
Calculate the L2-distance between the target alternative and the worst condition
And the distance between the alternative and the best condition
Where
and
respectively.
:
are L2-norm distances from the target alternative
Step 6:
Calculate the similarity to the worst condition:
if and only if the alternative solution has the worst condition;
to the worst and best conditions,
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Zinat Ansari et al, 2014
Advances in Environmental Biology, 8(1) January 2014, Pages: 221-226
if and only if the alternative solution has the best condition.
Step 7:
linear normalization can be calculated as in Step
Rank the alternatives according to
2 of the TOPSIS process above. Vector normalization was incorporated with the original development of the
TOPSIS method [6, 7] and is calculated using the following formula:
RESULT AND DISCUSSION
In this section, we used TOPSIS methods for ranking seven companies (2012) in Iran that shown in
following:
Table 1: Step 1 in TOPSIS method used for ranking seven companies
margin(M)
earnings growth(Eg)
Sales growth (Sg)
long term debt to equity
ratio(Ld to E)
debt to equity ratio
debt ratio(Dr)
inventory turnover(IT)
fixed assets
turnover(FaT)
receivable turnover(RT)
inventory turnover(IT)
momentary ratio
Current ratio
Companies
importance
0.23
0.23
0.15
0.15
0.15
0.15
0.08
0.08
0.001
0.31
0.31
0.38
Kharg
1
1
0
0.43
0.16
0.33
0
0
0
1
1
1
Sharnd
0
0
0.29
0
0.17
0.64
0.63
0.21
0.06
1.1
0.15
0.28
Shiraz
0.11
0.18
0.04
1
0
0
0.69
0.25
1
0.18
0.047
0.23
Farabi
0.06
0.13
1
0.29
1
1
1.01
1
0.28
0
0.001
0
Fanavaran
0.15
0.23
0.05
0.69
0.09
0.21
0.46
0.12
0.05
0.28
0.39
0.38
Abadan
0
0.07
0.54
0.2
0.1
0.37
0.75
0.32
0.21
0.02
0
0.008
Table 2: Step 2 in TOPSIS method used for ranking seven companies
0.15
0.04
0.01
0.65
0.91
0.879
Sharnd
0.18
0.12
0.33
0.07
0.18
0.49
0.40
0.21
0.06
0.71
0.156
0.253
Shiraz
0.26
0.26
0.18
0.71
0.02
0.11
0.43
0.25
0.93
0.15
0.055
0.214
Farabi
0.22
0.22
0.75
0.26
0.95
0.70
0.56
0.88
0.27
0.03
0.013
0.005
Fanavaran
0.28
0.29
0.19
0.51
0.11
0.23
0.33
0.14
0.05
0.21
0.36
0.34
Abadan
0.18
0.17
0.48
0.20
0.12
0.33
0.45
0.31
0.21
0.04
0.0129291
98
Weight
4.62
3.85
26.5
436.
22
17.46
2.61
1.57
8.08
1.34
59946
89.14
0.012145
726
4379894.
5
margin(M)
Sales growth (Sg)
earnings growth(Eg)
0.31
long term debt to equity
ratio(Ld to E)
0.17
debt to equity ratio
receivable turnover(RT)
0.35
debt ratio(Dr)
inventory turnover(IT)
0.16
inventory turnover(IT)
momentary ratio
0.87
fixed assets
turnover(FaT)
Current ratio
0.86
Companies
Kharg
7107633.6
224
Zinat Ansari et al, 2014
Advances in Environmental Biology, 8(1) January 2014, Pages: 221-226
Table 3: Step 3 in TOPSIS method used for ranking seven companies
momentary ratio
receivable turnover(RT)
fixed assets turnover(FaT)
inventory turnover(IT)
debt ratio(Dr)
debt to equity ratio
long term debt to equity
ratio(Ld to E)
Sales growth (Sg)
earnings growth(Eg)
margin(M)
0.2001
0.024
0.0525
0.0255
0.0465
0.012
0.0032
0.00001
0.2015
0.28
0.33
Sharnd
0.041
0.0276
0.0495
0.0105
0.027
0.0735
0.032
0.0168
0.00006
0.2201
0.05
0.09
Shiraz
0.059
0.0598
0.027
0.1065
0.003
0.0165
0.034
0.02
0.00093
0.0465
0.02
0.08
Farabi
0.050
0.0506
0.1125
0.039
0.1425
0.105
0.044
0.0704
0.00027
0.0093
0.00
0
Fanavaran
0.064
0.0667
0.0285
0.0765
0.0165
0.0345
0.026
0.0112
0.00005
0.0651
0.11
0.12
Abadan
0.041
0.0391
0.072
0.03
0.018
0.0495
0.036
0.0248
0.00021
0.0124
0.00
0
importance
0.23
0.23
0.15
0.15
0.15
0.15
0.08
0.08
0.001
0.31
0.31
0.38
inventory turnover(IT)
Current ratio
0.197
Companies
Kharg
Table 4: Step 4 in TOPSIS method used for ranking seven companies
receivable
turnover(RT)
fixed assets
turnover(FaT)
inventory turnover(IT)
debt ratio(Dr)
debt to equity ratio
Sales growth (Sg)
earnings growth(Eg)
0.0078
0.0029
0.0137
0.0034
0.0000
0.0000
0
0.0003
0.0000
0
0.024
0.0298
0.0040
0.0092
0.0133
0.0010
0.0004
0.0002
0
0.0000
0.0529
0.05
Shiraz
0.019
0.0197
0.0073
0.0000
0.0195
0.0078
0.0005
0.0003
0
0.0301
0.0676
0.06
Farabi
0.021
0.0224
0.0000
0.0046
0.0000
0.0000
0.0011
0.0045
0
0.0444
0.0784
0.11
0.017
0.0178
0.0071
0.0009
0.0159
0.0050
0.0002
0.0001
0
0.0240
0.0289
0.04
0.024
0.0259
0.0016
0.0059
0.0155
0.0031
0
0.0005
0
0.0431
0.0784
0.10
0.197
0.2001
0.1125
0.1065
0.1425
0.1050
0.012
0.0032
0
0.2201
0.2800
0.33
Companies
Fanavara
n
Abadan
A+
margin(M)
inventory turnover(IT)
0.0000
long term debt to
equity ratio(Ld to E)
momentary ratio
0
Sharnd
Current ratio
Kharg
Table 5: Step 5 in TOPSIS method used for ranking seven companies
0.0000
0.0007
0.0000
0.0006
0.0003
0.0010
0.0000
0.0092
0.0000
0.0001
0.0005
0.0078
0.0008
0.0195
0.0005
0.0015
0.0000
0.0044
0.0002
0.0000
0.0001
0.0023
0.0004
0.0002
0.0414
0.0276
0.0240
0.0105
0.0030
0.0011
0.0045
0
0.0369
0
0.110
0.0002
0.0029
0
0.0444
0
0.008
0.0001
0.0025
0
0.0014
0
0.006
0.0000
0.0000
0
0.0000
0
0
0.0003
0.0035
0
0.0031
0
0.016
0.0001
0.0021
0
0.0000
0
0
0.0448
0.0704
0
0.0093
0
0.002
margin(M)
0
0.000
9
0.003
2
0.000
0
0.007
8
0.000
3
0.001
1
0.016
5
earnings growth(Eg)
0.0005
Sales growth (Sg)
0.0018
long term debt to equity
ratio (Ld to E)
0.0000
debt to equity ratio
0.0298
debt ratio(Dr)
0.024
inventory turnover (IT)
A-
fixed assets turnover
(FaT)
Fanavara
n
Abadan
receivable turnover
(RT)
Farabi
inventory turnover (IT)
Shiraz
momentary ratio
Sharnd
Current ratio
Companies
Kharg
225
Zinat Ansari et al, 2014
Advances in Environmental Biology, 8(1) January 2014, Pages: 221-226
Table 6: Step 6 in TOPSIS method used for ranking seven companies
0.0000
0.0007
0.0000
0.0006
Farabi
0.0003
0.0010
0.0000
0.0092
0.0000
0.0001
0.0005
0.0078
0.0008
0.0195
Fanavara
n
Abadan
0.0005
0.0015
0.0000
0.0044
0.0002
A-
0.0000
0.0001
0.0023
0.0004
0.0002
0.0414
0.0276
0.0240
0.0105
0.0030
margin(M)
0
earnings growth(Eg)
Shiraz
Sales growth (Sg)
Sharnd
0.000
9
0.003
2
0.000
0
0.007
8
0.000
3
0.001
1
0.016
5
long term debt to equity
ratio (Ld to E)
fixed assets turnover
(FaT)
0.0005
debt to equity ratio
receivable turnover (RT)
0.0018
debt ratio(Dr)
inventory turnover (IT)
0.0000
inventory turnover (IT)
momentary ratio
0.0298
Current ratio
0.024
Companies
Kharg
A-
0.0011
0.0045
0
0.0369
0
0.1103
0.0002
0.0029
0
0.0444
0
0.0088
0.0001
0.0025
0
0.0014
0
0.0063
0.0000
0.0000
0
0.0000
0
0.0000
0.0003
0.0035
0
0.0031
0
0.01
0.0001
0.0021
0
0.0000
0
0
0.0704
0.00
09
0.0093
0
0.0022
0.0448
0.02
45
0.00
00
0.00
03
0.00
01
0.00
05
0.00
00
0.04
14
Table 7: Step 7 in TOPSIS method used for ranking seven companies
0.0133
0.0197
0.0073
0.0000
0.0195
0.0224
0.0000
0.0046
0.0000
0.0178
0.0071
0.0009
0.0159
0.0259
0.0016
0.0059
0.0155
0.2001
0.1125
0.1065
0.1425
Table 8: Step 8 in TOPSIS method used for ranking seven companies
A+
A_
0.168
0.459
0.438
0.247
0.486
0.145
0.536
0.191
0.399
0.173
0.555
0.079
1.309
0.501
0
0.0003
0.0000
0.0004
0.0002
0
0.0000
0.0529
0.0005
0.0003
0
0.0301
0.0676
0.0011
0.0045
0
0.0444
0.0784
0.0002
0.0001
0
0.0240
0.0289
0.0006
0.0005
0
0.0431
0.0784
0.0120
0.0032
0
0.2201
0.2800
margin(M)
0.0092
0.0000
earnings growth(Eg)
0.0040
0
Sales growth (Sg)
0.0298
0.003
4
0.001
0
0.007
8
0.000
0
0.005
0
0.003
1
0.105
0
long term debt to equity
ratio (Ld to E)
0.0137
debt to equity ratio
0.0029
debt ratio(Dr)
0.0078
inventory turnover (IT)
A
0.0000
turnover
+
fixed assets
(FaT)
Fanavara
n
Abadan
receivable turnover (RT)
Farabi
inventory turnover (IT)
Shiraz
0.000
0
0.024
5
0.019
0
0.021
7
0.017
8
0.024
5
0.197
8
momentary ratio
Sharnd
Current ratio
Companies
Kharg
A+
0
0
0.05
67
0.06
39
0.11
03
0.04
20
0.10
85
0.33
43
0.02
45
0.01
90
0.02
17
0.01
78
0.02
45
0.19
78
Weight
0.268
0.640
0.771
0.737
0.697
0.875
0.723
Conclusion:
TOPSIS is a multiple-criteria method to evaluate alternatives based upon the minimization of the distance
from the positive ideal solution and maximization of distance from the negative ideal solution. This paper
provides useful insights into the TOPSIS method and suggests a framework for future attempts in this area for
ranking and determination operation of statement of companies listed in Tehran Stock Exchange. TOPSIS can
solve the problems such as rank for different problems.
226
Zinat Ansari et al, 2014
Advances in Environmental Biology, 8(1) January 2014, Pages: 221-226
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