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An integrated group decision making model and its evaluation
by DEA for automobile industry
Ali Yousefi
a
, Abdollah Hadi-Vencheh
b,*
a
Department of Industrial Management, Islamic Azad University, Najafabad Branch, Isfahan, Iran
b
Department of Mathematics, Islamic Azad University, Khorasgan Branch, Isfahan, Iran
article info
Keywords:
Group MCDM
AHP
TOPSIS
DEA
Automobile industry
Customer’s criteria
abstract
In this paper we propose an integrated model from the most important and usable Multi-Criteria Deci-
sion Making (MCDM) techniques, means Analytic Hierarchy Process (AHP) and Technique for Ordering
Preference by Similarity to Ideal Solution (TOPSIS), in order to examine the improvement fields of Iran
automobile industry. A new approach, AT method, has been suggested to combine the results of two tech-
niques to find the final ranking. Besides, we propose a developing Data Envelopment Analysis (DEA)
model as a basis for comparing the reliability of results of the MCDM techniques, which depicts AT is
more reliable than AHP and TOPSIS. Our results have certified that safety and then price are the custom-
ers’ most important criteria for automobile selection. After comparing the internal and external products,
and ranking them based on the criteria and sub-criteria, the necessity to improve internal automobiles on
various fields has been prioritized.
Ó2010 Elsevier Ltd. All rights reserved.
1. Introduction
By extending the cities and rushing the population to the large
centers availability to an instrument to transport became one of
the essentials of individual and family. There are too many choices
for transportation in each country depending on factors such as
government politics; transportation infra structures improvement
level and too many other factors that the most important one is
economic. In some countries governments have promoted and
developed the culture of using non-motorized vehicles and non-
contaminants and public transportation system, since years ago.
Expensiveness of gasoline and automobile, extra costs and govern-
ment politics in relation to environment protection are the other
obstacles to buy an automobile.
Automobile manufacturer companies try to improve their
products, follow environment protection rules, decrease remark-
able fuel consumption, create new techniques and improve their
products quality in the field of beauty, convenience and applicabil-
ity. Globalization and comparative markets accounts as another
important factors increasing manufacturers products quality. In
this market, the companies are successful which are able to
conform their products to world standard level and more impor-
tant with all over the world’s people criteria (Chen, Khoo, & Yan,
2003). Knowing the customer’s criteria open the success gates for
the producers (Han & Hong, 2003). In fact, without considering
mentioned point the company would not guarantee its products.
We would be able to devote the majority part of the market to
us by knowing customers different perspective and conforming
products within known domains.
Making decision to buy an automobile is important. The number
of this kind of decision making is rare in Iran. Actually people do not
buy an automobile each year, thus its decision making influences
are more dominant than daily shopping like detergent powder
(Korhonen, Moskowitz, & Wallenius, 1992). Thus, customers take
different steps to make this decision like: consulting the experts,
getting their ideas, grading personal criteria and also evaluating dif-
ferent alternatives due to criteria. Considerable criteria for custom-
ers are: economic, social, technical and also personal attitude
regarding to automobile design and beauty. Some governments
limit and forbid foreign automobile imports to support local indus-
try by heavy tariffs custom on automobile import. These politics
also cause lake of spare parts and reduction of foreign-made auto-
mobile after sale services. On the other hand, local manufacturers
possess majority share of the market by much advertisement, prod-
ucts guarantee and after sale services extending financial facilities
even if their products are on the lower level in accordance with
technical features and efficiency. Except economic, social and polit-
ical features, automobile evaluating criteria are as follow: technical
features, performance and beauty. In studying technical features,
safety, speed and power can be considered. Also beauty contains
trunk design and color variety, internal design, color variety and fit-
ness and quality of used materials in internal decoration.
Multi-criteria decision making techniques are used to make this
kind of decisions which take into account different criteria. Priority
based, outranking, distance-based and combined methods could be
0957-4174/$ - see front matter Ó2010 Elsevier Ltd. All rights reserved.
doi:10.1016/j.eswa.2010.05.021
*Corresponding author.
E-mail address: ahadi@khuisf.ac.ir (A. Hadi-Vencheh).
Expert Systems with Applications 37 (2010) 8543–8556
Contents lists available at ScienceDirect
Expert Systems with Applications
journal homepage: www.elsevier.com/locate/eswa
considered as the primary classes of the current methods (Pomerol
& Barba Romero, 2000). One of the most outstanding MCDM ap-
proaches is the Analytic Hierarchy Process (AHP) Saaty, 1980;
Saaty & Vargas, 2001 which has its roots on obtaining the relative
weights among the factors and the total values of each alternative
based on these weights. The AHP is an intuitively easy method for
formulating and analyzing decisions (Saaty, 1980; Saaty & Kearns,
1985). It was developed to solve a specific class of problems that
involves prioritization of potential alternate solutions. This is
achieved by evaluation of a set of criteria elements and sub-criteria
elements through a series of pairwise comparisons (Bhyun, 2001).
Also, group decision-making problems are easily formulated by the
Expert Choice software package (Bhyun & Suh, 1996; Forman,
Saaty, Selly, & Waldron, 1983; Lai, Trueblood, & Wong, 1999); this
allows the decision-maker to derive geometric means as weights
or priorities instead of using an eigenvector method. The geometric
mean is an appropriate rule for combining individual judgments to
obtain the group judgment for each pairwise comparison.
TOPSIS is a distance-based MCDM method (Hwang & Yoon,
1981). This technique is based on ideal and negative-ideal solu-
tions, which are determined in respect to the distance of each
alternative to the best and the worst performing alternative,
respectively. In this paper, problem solving by TOPSIS method
has been done using the Excel software. AHP has been utilized in
order to obtain criteria weight and TOPSIS to obtain the ranking.
DEA is a technique for deciding the relative efficiency of a Deci-
sion Making Unit (DMU) by comparing it with linear combinations
of other DMUs engaged in providing the same outputs from the
same inputs. The pioneering work of the economist Farrel (1957)
provided a non-parametric method of determining the relative effi-
ciency of a DMU. He gave a method of computing the facets of the
efficient production frontier from a set of observations from empir-
ically observed DMUs, rather than by estimating the parameters of
postulated production functions. The celebrated paper of Charnes,
Cooper, and Rhodes (1978) introduced DEA, a linear programming
based technique, to measure Farrell type efficiency. In recent dec-
ades, DEA has rapidly expanded into new application areas (see
Seiford (1996) for a survey). In this study we propose a DEA model
as a basis for comparing reliability of the obtained results.
The aim of this paper is to examine and also analytically evalu-
ate different automobile alternatives in respect to both qualitative
and quantitative criteria together. The main objective of this study
is proposing a mechanism to decide on the most suitable automo-
bile in the marketplace. Suggesting a new method to compare and
combine alternatives values extracted by AHP and TOPSIS, and
reaching to the final ranking according to both methods’ results,
are the other characteristics of this paper.
The rest of this paper is organized as follows. In the following
section we review the literature. In Section 3we take a look at
MCDM models. In Section 4we state our methodology. Section 5
determines criteria and makes the hierarchy. In Section 6we eval-
uate and calculate the criteria and alternative weights. In this sec-
tion we evaluate problem alternatives in relation with each sub-
criterion. Section 7devoted to computation of the final weights
of the alternatives. In section 8we investigate alternatives final
ranking, in this section we rank alternatives by AHP, TOPSIS and
the proposed model. Besides, Section 9discusses obtained results
using DEA. Finally conclusions are given in Section 10.
2. Literature review
Numerous applications of the MCDM methods have been made
since their development and have been applied to many types of
decision problems. Bhyun (2001) use AHP for deciding on car pur-
chase. In the context of shopping, it is important to include ele-
ments that provide attributes that make consumer decision-
making easier, comfortable and therefore, lead to a car purchase.
As the car market becomes more competitive, there is a greater de-
mand for innovation that provides better customer service and
strategic competition in the business management. He presents a
methodological extension of the AHP by focusing on two issues.
One combines pairwise comparison with a spreadsheet method
using a 5-point rating scale. The other applies the group weight
to a reciprocal consistency ratio. Three newly formed car models
of midsize are used to show how the method allows choice to be
prioritized and analyzed statistically. Bhyun and Suh (1996) study
criteria of full-featured executive information systems packages in
the evaluation stage and consider the prioritization of these criteria
at the laboratory experiment using the process AHP method. Lai
et al. (1999) discuss the multimedia processing environment, the
applicability of AHP in problem solving, and how AHP can be ap-
plied to the selection of multimedia authorizing systems (MAS)
in a group decision environment. A MAS selection model is pro-
posed to facilitate the group’s decision making in the selection of
MAS. The results indicated that AHP offers chances for every partic-
ipant to fully understand, discuss, and objectively evaluate all MAS
products before identifying and selecting the most efficient MAS. In
2001, Tam and Tummala (2001) formulated an AHP-based model
and applied to a real case study to examine its feasibility in select-
ing a vendor for a telecommunications system. The use of the pro-
posed model indicates that it can be applied to improve the group
decision making in selecting a vendor that satisfies customer spec-
ifications. Also, it is found that the decision process is systematic
and that using the proposed AHP model can reduce the time taken
to select a vendor. Salmeron and Herrero (2005) propose the use of
the AHP to set critical success factors priorities. Results suggest
that technical elements are less critical than information and
human factors and that an adequate knowledge of the information
requirements of users is the most important critical success factors
related with executive information systems. Dyer and Forman
(1992) explain why AHP is so well-suited to group decision making
and show how AHP can be applied in a variety of group decision
contexts, and discuss four applications of AHP in group decisions.
Gibney and Shang (2007) describe the use of the AHP in the dean
selection process. The authors conclude that AHP is a valuable tool
and should be incorporated into personnel selection processes in
academia. Isßıklar and Büyüközkan (2007) propose a multi-criteria
decision making (MCDM) approach to evaluate the mobile phone
options in respect to the users’ preferences order. Firstly, the most
desirable features influencing the choice of a mobile phone are
identified. This is realized through a survey conducted among the
target group, the experiences of the telecommunication sector ex-
perts and the studies in the literature. Two MCDM methods are
then used in the evaluation procedure. More precisely, AHP is ap-
plied to determine the relative weights of evaluation criteria and
the extension of the TOPSIS is applied to rank the mobile phone
alternatives. Tsaur, Chang, and Yen (2002) apply the fuzzy set the-
ory to evaluate the service quality of airline. By applying AHP in
obtaining criteria weight and TOPSIS in ranking, they found the
most concerned aspects of service quality are tangible and the least
is empathy. The most concerned attribute is courtesy, safety and
comfort. Feng and Wang (2000) apply TOPSIS method for the out-
ranking of airlines when they evaluate performance of airlines.
Shanian and Savadogo (2006) shows an application of the TOPSIS
for solving the material selection problem of metallic bipolar plates
for polymer electrolyte fuel cell, which often involves multiple and
conflicting objectives. Recently Azadeh, Ghaderi, and Izadbakhsh
(2008) propose integration of DEA and AHP with computer simula-
tion for railway system improvement and optimization. Wang, Liu,
and Elhag (2008) in a very interesting paper propose an integrated
AHP–DEA methodology to evaluate bridge. The proposed AHP–DEA
8544 A. Yousefi, A. Hadi-Vencheh / Expert Systems with Applications 37 (2010) 8543–8556
methodology uses the AHP to determine the weights of criteria, lin-
guistic terms to assess bridge risks under each criterion, the DEA
method to determine the values of the linguistic terms, and the
simple additive weighting method to aggregate bridge risks under
different criteria into an overall risk score for each bridge structure.
On the other hand Lin, Wang, Chen, and Chang (2008) use AHP and
TOPSIS approaches in customer-driven product design process.
They present a framework that integrates the AHP and the TOPSIS
to assist designers in identifying customer requirements and de-
sign characteristics, and help achieve an effective evaluation of
the final design solution. The proposed approach starts with apply-
ing the AHP method to evaluate the relative overall importance of
customer requirements and design characteristics. The TOPSIS
method is then used to perform competitive benchmarking. Yang
and Kuo (2003) propose an AHP process and DEA approach to solve
a plant layout design problem. They used a computer-aided layout-
planning tool to generate a considerable numbers of layout alterna-
tives as well as to generate quantitative decision-making unit
(DMU) outputs. The qualitative performance measures were
weighted by AHP. DEA is then used to solve the multiple-objective
layout problem. Tseng, Chiu, and Chen (2008) measure business
performance in the high-tech manufacturing industry. To do so, a
DEA, an AHP, and a fuzzy multi-criteria decision-making approach
are used. Önüt and Soner (2008) apply a fuzzy TOPSIS based meth-
odology to solve the solid waste transshipment site selection prob-
lem in Istanbul, Turkey. The criteria weights are calculated by using
the AHP in their work.
The above literature shows that the study of the applications of
the MCDM techniques for automobile industry, until now is very
few. Therefore the results obtained in this paper are completely
new and very valuable.
3. Introduction to MCDM methods
3.1. Analytic hierarchy process (AHP)
AHP is developed by Saaty (1980), probably the best-known and
most widely used model in decision making. AHP is a powerful
decision making methodology in order to determine the priorities
among different criteria. The AHP encompasses six basic steps as
summarized as follows:
Step 1. AHP uses several small subproblems to present a com-
plex decision problem. Thus, the first act is to decompose the
decision problem into a hierarchy with a goal at the top, criteria
and sub-criteria at levels and sub-levels of and decision alterna-
tives at the bottom of the hierarchy (Fig. 1).
Step 2. The decision matrix, which is based on Saaty’s nine-point
scale, is constructed. The decision maker uses the fundamental
1–9 scale defined by Saaty to assess the priority score. In this
context, the assessment of 1 indicates equal importance, 3 mod-
erately more, 5 strongly more, 7 very strongly and 9 indicates
extremely more importance. The values of 2, 4, 6, and 8 are
allotted to indicate compromise values of importance. In this
paper this definition has been changed a little (Table 1).
The decision matrix involves the assessments of each alterna-
tive in respect to the decision criteria. If the decision making prob-
lem consists of ncriteria and malternatives; the decision matrix
takes the form:
D¼
d
11
d
12
d
1n
d
21
d
22
d
2n
.
.
..
.
..
.
..
.
.
d
m1
d
m2
d
mn
2
6
6
6
6
4
3
7
7
7
7
5
ð1Þ
The elements {d
ij
} signify the rating of the ith alternative in respect
to the jth criteria.
Step 3. The third step involves the comparison in pairs of the
elements of the constructed hierarchy. The aim is to set their
relative priorities with respect to each of the elements at the
next higher level. The pairwise comparison matrix, which is
based on the Saaty’s 1–9 scale, has the form:
a
11
a
12
a
1n
a
21
a
22
a
2n
.
.
..
.
..
.
..
.
.
a
n1
a
n2
a
nn
2
6
6
6
6
4
3
7
7
7
7
5
¼
w
1
=w
1
w
1
=w
2
w
1
=w
n
w
2
=w
1
w
2
=w
2
w
2
=w
n
.
.
..
.
..
.
..
.
.
w
n
=w
1
w
n
=w
2
w
n
=w
n
2
6
6
6
6
4
3
7
7
7
7
5
ð2Þ
If n(n1)/2 comparisons are consistent with nis the number of cri-
teria, then the elements {a
ij
} will satisfy the following conditions:
a
ij
=w
i
/w
j
=1/a
ji
and a
ii
= 1 with i,j,k=1,2,...,n.
In the comparison matrix, a
ij
can be interpreted as the degree of
preference of ith criteria over jth criteria. It appears that the weight
determination of criteria is more reliable when using pairwise
comparisons than obtaining them directly, because it is easier to
make a comparison between two attributes than make an overall
weight assignment.
Step 4. AHP also calculates an inconsistency index (or consis-
tency ratio) to reflect the consistency of decision maker’s judg-
ments during the evaluation phase. The inconsistency index in
both the decision matrix and in pairwise comparison matrices
could be calculated with the equation:
Objective
Criteria
Alternatives
Fig. 1. The hierarchical structure of the decision making problem.
A. Yousefi, A. Hadi-Vencheh / Expert Systems with Applications 37 (2010) 8543–8556 8545
CI ¼k
max
N
N1:ð3Þ
The closer the inconsistency index is to zero, the greater the consis-
tency. The consistency of the assessments is ensured if the equality
a
ij
a
jk
=a
ik
holds for all criteria. The relevant index should be lower
than 0.10 to accept the AHP results as consistent. If this is not the
case, the decision-maker should go back to Steps 2 and 3 and redo
the assessments and comparisons.
Step 5. Before all the calculations of vector of priorities, the com-
parison matrix has to be normalized. Therefore, each column
has to be divided by the sum of entries of the corresponding col-
umn. In that way, a normalized matrix is obtained in which the
sum of the elements of each column vector is 1.
Step 6. For the following part, the eigenvalues of this matrix are
needed to be calculated which would give the relative weights
of criteria. This procedure is common in mathematics; however
we have made use of the Expert Choice software, a multi-objec-
tive decision support tool. The relative weights obtained in the
third step should verify
AW¼k
max
W:ð4Þ
where Arepresents the pairwise comparison matrix, Wthe eigen-
vector and k
max
the highest eigenvalue. If there are elements at
the higher levels of the hierarchy, the obtained weight vector is
multiplied with the weight coefficients of the elements at the high-
er levels, until the top of the hierarchy is reached. The alternative
with the highest weight coefficient value should be taken as the
best alternative (Isßıklar & Büyüközkan, 2007).
3.2. Technique for order preference by similarity to ideal solution
(TOPSIS)
TOPSIS method, which is based on choosing the best alternative
having the shortest distance to the ideal solution and the farthest
distance from the negative-ideal solution (Hwang & Yoon, 1981).
The ideal solution is the solution that maximizes the benefit and
also minimizes the total cost. On the contrary, the negative-ideal
solution is the solution that minimizes the benefit and also maxi-
mizes the total cost.
For the first step of this methodology, the decision matrix, rep-
resenting the performance values of each alternative with respect
to each criterion, is computed. Next, these performance values
are multiplied with the criteria weights calculated with AHP. The
step of defining the ideal solution consists of taking the best values
of alternatives and with the similar principle, the negative-ideal
solution is obtained by taking the worst values of alternatives. Sub-
sequently, the alternatives are ranked with respect to their relative
closeness to the ideal solution.
The TOPSIS procedure consists of the following steps:
Step 1. The first step of the procedure involves the calculation of
the normalized decision matrix. The normalized value {r
ij
}is
calculated as
r
ij
¼f
ij
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
P
J
j¼1
f
2
ij
q;j¼1;...;J;i¼1;...;n:ð5Þ
Step 2. In the next step, the weighted normalized decision
matrix is calculated. The weighted normalized value
v
ij
is calcu-
lated as
v
ij
¼w
i
r
ij
;j¼1;...;J;ı¼1;...;n:ð6Þ
where w
i
is the weight of the ith criterion, and P
n
i¼1
w
i
¼1.
Step 3. In this step, the ideal and negative-ideal solutions are
determined.
A
þ
¼
v
þ
1
;...;
v
þ
n
¼max
j
v
ij
ji2I
0
;min
j
v
ij
ji2I
00
;ð7Þ
A
¼
v
1
;...;
v
n
¼min
j
v
ij
ji2I
0
;max
j
v
ij
ji2I
00
;ð8Þ
where I
0
is associated with benefit criteria, and I
00
is associated with
cost criteria.
Step 4. The separation measures are calculated using the n-
dimensional Euclidean distance. The separation of each alterna-
tive from the ideal solution is given as
d
þ
j
¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
X
n
i¼1
ð
v
ij
v
þ
i
Þ
2
v
u
u
t;j¼1;...;J:ð9Þ
Similarly, the separation from the negative-ideal solution is given
as
d
j
¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
X
n
i¼1
ð
v
ij
v
i
Þ
2
v
u
u
t;j¼1;...;J:ð10Þ
Step 5. The next step consists of the calculation of the relative
closeness to the ideal solution. The relative closeness of the
alternative a
j
with respect to A
+
is defined as
D
j
¼d
j
ðd
þ
j
þd
j
Þ;j¼1;...;J:ð11Þ
Step 6. At the final step, the preference order is ranked.
In TOPSIS method, the chosen alternative has the maximum va-
lue of D
j
with the intention to minimize the distance from the ideal
solution and to maximize the distance from the negative-ideal
solution (Isßıklar & Büyüközkan, 2007).
4. Methodology
In this paper two MCDM methods have been used to evaluate
improvement fields of Iran automobile manufacturing industry,
and then obtained results have been compared and combined.
At first, customers’ criteria based on the research literature, ex-
perts (10 professions with at least B.Sc. degree and 10 years expe-
rience), mechanics, sellers and customers ideas have been
selected. Having too many criteria and sub-criteria cause to in-
crease pairwise assessments and addressees’ tiredness and care-
lessness, thus inconsistency rate goes up as a result. Therefore,
a 9 scales ranking spread sheet model suggested to decrease
the volume of pairwise assessments. In spread sheet model,
same-level criteria compare in one stage, and take a score from
1 (with no importance) to 9 (extremely important). We have sug-
gested a spread sheet model, because the criteria of this case
Table 1
The numerical assessments and their linguistic meanings.
Numerical assessment Linguistic meaning
1 With no importance
3 Less importance
5 Moderately important
7 Strongly important
9 Extremely important
2, 4, 6, 8 Intermediate values of importance
8546 A. Yousefi, A. Hadi-Vencheh / Expert Systems with Applications 37 (2010) 8543–8556
study are completely tangible and perceptible for decision maker
and the decision maker would be able to compare them in one
stage. Table 2 shows the spread sheet model for criteria and
sub-criteria evaluation.
After evaluating the criteria and sub-criteria and specifying
their importance degree (weights), next stage is evaluating the
alternatives with regard to each sub-criterion, which has been
done by spread sheet method like the previous stage. In this
stage the alternatives are compared with regard to each sub-cri-
terion and take a score from 1 (extremely weak) to 9 (extremely
strong) (Table 4). As we know, some of the sub-criteria are
quantitative (like: price, speed and the fuel cost), which their
quantity have been placed in the model, directly. For instance,
when the alternatives are evaluated based on speed, the number
which is related to the maximum speed of each alternative is
placed in the spread sheet model, directly. Furthermore, the cri-
teria with negative effect (e.g. price and fuel cost) are inverted
after computing.
In this paper, group multi criteria decision making technique
(Group MCDM) has been used in order to be able to import dif-
ferent ideas like automobile industries experts, mechanics, sell-
ers and customers in the model. The volume of statistical
sample (the number of peoples who participated in decision
making) is 126. When criteria, sub-criteria and the alternatives
have been evaluated and compared by each decision maker
and their single importance degrees have been calculated, in
the next step their group importance degrees would be calcu-
lated. Group importance degree of each criterion equals geomet-
ric average of single importance degrees of that criterion.
Decision matrix is obtained as a result of this stage. AHP and
TOPSIS have been used to rank and prioritize the alternatives.
AHP method has been used for ranking in respect to assessment
of criteria and sub-criteria, and TOPSIS in order to ranking the
alternatives in respect to their distance from ideal and negative
ideal solutions.
Since in the both methods, the decision matrix and the weight
vector of the sub-criteria are the same, we expect that the
obtained results of the both methods be also the same. But after
comparing the results, some differences are considered between
them, which may make the final decision maker hesitant for
making the final decision. Therefore, a new equation has been
suggested in order to obtain a unique result which contains spec-
ifications and advantages of the both MCDM methods. This equa-
tion is as follow
Table 2
The spread sheet model for criteria and sub-criteria assessment and evaluation.
Table 3
Scores of main criteria and sub-criteria.
Main criteria Sub-criteria Score
Technical features (8.89695) Engine features 2.10407
Safety 8.91556
Speed 1.04501
Comfortableness and relaxation 6.61233
Beauty (5.96692) Internal design 8.75498
External design 6.41184
Color beauty and variety 1.91129
Manufacturer (3.66692) Country 8.72539
Company 5.71982
Brand 2.16801
Tools availability (7.18075) Spare parts 7.82939
Consumption tools 5.95694
Economical aspects (7.99747) Price 8.84057
Fuel consumption (cost) 4.44567
Payment flexibility 3.59531
Social aspects (1.77917) Advertisement 8.36580
Social atmosphere 2.33131
Owners’ satisfaction 5.96159
A. Yousefi, A. Hadi-Vencheh / Expert Systems with Applications 37 (2010) 8543–8556 8547
AT
j
¼W
j
d
j
d
þ
j
;j¼1;...;J:ð12Þ
W
j
is the normalized weight of jth alternative which obtained by
AHP, d
þ
j
is the normalized distance of jth alternative from ideal solu-
tion (by TOPSIS), d
j
is the normalized distance of jth alternative from
negative ideal solution (by TOPSIS). Here AT
j
is the final weight of jth
alternative (which obtained by integrated AHP–TOPSIS model).
The results of Eq. (12) are affected by assessment of criteria and
sub-criteria, in addition, considered the distance of alternatives
from ideal solution and negative ideal solution. Therefore this tech-
nique contains the specifications and advantages of the both AHP
and TOPSIS methods, and is more reliable for decision making.
In order to compare the results of two MCDM methods (AHP and
TOPSIS) with suggested model above (AT), DEA is applied in this pa-
per. An input-oriented model with non-decreasing return to scale
(NDRS), considering environmental variables, is define as follow:
Min Z
0
¼hX
2
i¼1
e
Sn
i
X
3
r¼1
e
Sp
r
;
s:t:X
9
j¼1
y
rj
k
j
Sp
r
¼y
r
0
;r¼1;...;5;
X
9
j¼1
x
ij
k
j
þSn
i
hx
i
0
¼0;i¼1;2;3;ð13Þ
X
9
j¼1
E
lj
k
j
hE
l
0
60;l¼1;...;10;
X
9
j¼1
k
j
P1;
k
j
;Sp
r
;Sn
i
0;h:Free:
The inputs of this model are: engine specifications, fuel consump-
tion, and price. And outputs are: speed, safety, comfort and conve-
nience, owners’ satisfaction, and social atmosphere. The remained
sub-criteria are neither input nor output, but they effect on the units’
efficiency, they are thus considered as environmental factors (E
l
).
Based on a experimental relation in DEA, the number of decision
making units (DMUs), must be at least three times of sum of the
numbers of inputs, outputs and environmental variables. Note that
this relation causes lots of units place on the efficiency frontier, in
the other word their efficiency scores equal one. Therefore separabil-
ity of the model decreases. Since, in the present paper the number of
DMUs equals 9, and sum of the numbers of inputs, outputs, and envi-
ronmental variables equals 18, so the relation above has not ob-
served and we see all units placed on the efficiency frontier and
their efficiency scores equaled one. In order to rank these units, rank-
ing the efficient units techniques are applied. Obtained scores of the
units, after normalization using Euclidean norm, are basis for com-
paring the results of the MCDM techniques. Mean Absolute Percent
Error (MAPE) of the results of AHP, TOPSIS and AT is calculated in re-
spect to the result of DEA, each of three techniques above which has
less amount of MAPE, is more reliable than the other two techniques.
5. Determining automobile evaluation criteria and making the
hierarchy
Following cases have used to determine evaluation criteria in
addition to personal opinions:
(1) Knowing experts’ suggestions: consists of automobile manu-
facturing industries experts (10 professions with at least
B.Sc. degree and 10 years experience) in designing, manufac-
turing and selling, automobile dealers in private section and
automobile mechanics mentioned above.
(2) Research literature.
(3) Manufacturer companies: studying of announced specifica-
tion by manufacturer companies by automobile manuals,
internet websites and statistics results in the other websites
(http://chryslercorp.com,www.toyota.com,www.gm.com,
www.SAIPAcorp.com,www.ikco.com).
After specifying a set of criteria, some criteria were omitted
from the model. Because our alternatives include internal and
external automobiles and statistical information about some crite-
ria (e.g. average of repairing time, and the number of service sta-
tions) is not available for several alternatives. On the other hand,
some criteria (e.g. salespersons personality and behavior) have lit-
tle importance among Iranian customers. Some criteria like insur-
ance were forced by law for all automobiles, thus all alternatives
based on these criteria are equal, and these criteria were also omit-
ted from the model. Finally, 6 main criteria which consist of 18
sub-criteria were considered.
We can extract some features which characterize main criteria.
(1) Technical features
(2) Beauty
Table 4
The spread sheet model for alternatives evaluating and assessment in relation to each sub-criterion.
Sub-criteria Alternatives (Automobiles)
Xantia Pride Pars Samand Peugeot 206 Camry Sonata Benz E240 Maxima
Engine features
Safety
Speed
Comfortableness and relaxation
Internal design
External design
Color beauty and variety
Country
Company
Brand
Spare parts
Consumption tools
Price
Fuel consumption
Payment flexibility
Advertisement
Social atmosphere
Owners’ satisfaction
8548 A. Yousefi, A. Hadi-Vencheh / Expert Systems with Applications 37 (2010) 8543–8556
(3) Manufacturer
(4) Tools availability
(5) Economical aspects
(6) Social aspects
Every main criterion includes some sub-criteria, which can be
defined as below:
5.1. Technical features (TECHNICA)
(1) Engine specification (ENGINE): Including maximum power,
maximum torque, emission level, cubic capacity, number
of valves and number of cylinders. Furthermore, capacity
of petrol tank has considered in this sub-criteria.
(2) Safety (SAFETY): Number of air bags, back and fore passen-
gers seat belt, braking system quality, anti lock braking sys-
tem (ABS), Measure of stability in the turns, trunk
consistence and resistance, external light system, central
locking and burglar alarm.
(3) Speed (SPEED): Maximum speed considered by Manufac-
turer Company.
(4) Comfortableness and relaxation (RELAX): Including conve-
nience and seats regulating system, air conditioning and
temperature setting system, automobile inside noise, inter-
nal light, audio system and other facilities.
5.2. Beauty (BEAUTY)
(1) Internal design (INTERNAL): Beauty and variety in decora-
tion, color and automobile internal space.
(2) External design (EXTERNAL): Trunk evaluation for beauty,
size proportion and trunk aerodynamic coefficient.
(3) Color beauty and variety (COLOR): number and quality of
existent color.
5.3. Manufacturer (MANUFACT)
(1) Manufacturer country (COUNTRY): Evaluation and ranking
of manufacturer country in automobile manufacturing
industry.
(2) Manufacturer company (COMPANY): Evaluation and ranking
of manufacturer company in automobile manufacturing
industry.
(3) Brand (BRAND): Evaluation and ranking of automobile brand
in market.
5.4. Tools availability (TOOLS)
(1) Availability of spare parts (SPARE): How much and how fast
automobile spare parts are supplied?
(2) Availability of consumption tools (CONSUMPT): How much
and how fast automobile consumption tools are supplied?
5.5. Economical aspects (ECONOMIC)
(1) Automobile price (PRICE)
(2) Fuel consumption (cost) (FUEL): The average consumption,
inside and outside of city according to ECE R 101 standard.
(3) Payment flexibility (how to pay) (PAYMENT): Facilities and
duration of installment payment plan.
5.6. Social aspects (SOCIAL)
(1) Advertisement (ADVERTIS): Media and society advertise-
ment.
(2) Society atmosphere (ATMOSPHE): Is there a positive attitude
toward product, in society?
(3) Owners’ satisfaction (SATISFAC): The degree of present auto-
mobile owners’ satisfaction.
Automobile
selection
Social aspects
Economical
aspects
Tools
availability
Manufacturer
Beauty
Technical
features
Comfort and
relaxation
Speed
Safety
Engine
specification
Color beauty
and variety
External
design
Internal
design
Brand
Manufacturer
company
Manufacturer
country
Consumption
tools
Spare parts
Payment
flexibility
Fuel
consumption
Owners’
satisfaction
Society
atmosphere
Nissan
Maxima
Mercedes Benz
E240
Hyundai
Sonata
Toyota
Camry
Peugeot
206Typ6
Samand LX
Peugeot
Pars
Pride
Citroen
Xantia
Advertisement
Price
Fig. 2. The problem hierarchical structure.
A. Yousefi, A. Hadi-Vencheh / Expert Systems with Applications 37 (2010) 8543–8556 8549
We have made hierarchy model according to main criteria and
sub-criteria (Fig. 2). This model includes 4 levels: goal, main crite-
ria, sub-criteria, and alternatives.
Some of these criteria are not unique and it might be a limita-
tion for using AHP. We should consider to all dependent parts at
the same time. For example, we can reduce automobile height to
maximize speed, or to design seats in a way to reduce noise and in-
crease safety. It is clear that price and fuel consumption are negative
criteria and have the opposite effect on the alternatives. Three fol-
lowing ways have used for exertion of the price in the model:
(1) Selecting all alternatives with the same price, and eliminat-
ing the price as a criterion.
(2) Adding a linear programming model for exertion of price in
the main model.
(3) Considering the price as a decision making criterion, beside
the other criteria of the model. The level of criterion impor-
tance from customers’ point of view, and effect of price on
the alternatives, could be inspected just by third way, that’s
why we have used it, here. In this paper 9 most common
automobiles have been evaluated as alternatives. At the
end they will be graded and studied in accordance with
mentioned criteria.
6. Evaluating and calculating criteria and alternatives weights
6.1. Evaluating and calculating criteria’s weights
After recognition of acceptable criteria, the next step is extract-
ing criteria and sub-criteria’s preferences and priorities from sam-
ple group. The main purpose is ranking alternatives regarding to
the customers preferences. Plurality of criteria and sub-criteria
causes pairwise assessment volume increasing and as result tired-
ness and less accuracy of addressees. Thus, increasing the inconsis-
tency index of pairwise assessment matrixes call data validity into
question. A 9 scale ranking spread sheet was applied to solve this
problem and decrease assessment volume, because the criteria
are so clear and sensible for decision makers (Table 2). The sample
group was asked to grade each criterion with regard to same-level
criteria from 1 (with no importance) to 9 (extremely important).
Fig. 3. Main criteria ranking and their normalized weight.
Fig. 4. Sub-criteria ranking and their normalized weight.
8550 A. Yousefi, A. Hadi-Vencheh / Expert Systems with Applications 37 (2010) 8543–8556
After collecting questionnaires and considering results and
omitting imperfect ones, for obtaining total score of each crite-
rion, geometrical mean of that criterion scores are calculated in
all valid questionnaires. So, we will obtain a score from 1 to 9
for each criterion, and same-level criteria will be compared with
each other in this way. To compare and rank all the sub-criteria,
the sub-criteria score and its main criteria score are multiplied
by each other. Table 3 shows obtained main and sub-criteria
scores.
Total inconsistency index is always zero, as the pairwise
assessment is not done in this method and same-level criteria’s
weight is calculated directly. The problem solving steps are done
by Expert Choice software. Fig. 3 shows ranking of main criteria
with their weight after normalization. As we see, technical fea-
tures and economical aspects have the most weights, 0.251 and
0.225, respectively. Thus account as the most important main
criteria.
Fig. 4 shows ranking of sub-criteria with their weight after nor-
malization. Safety, price, availability of spare parts, comfortable-
ness and relaxation, and availability of consumption tools are the
most important sub-criteria. Also as we mentioned and observed,
total inconsistency index in main and sub-criteria assessment is
considered zero.
6.2. Evaluating and calculating alternatives weight in relation with
sub-criteria
We specified main and sub-criteria then calculated their
weights and ranked, by turning the face toward preferences of
sample group members, in the previous steps. In this step we will
evaluate problem alternatives in relation with each sub-criterion.
So we have tried to evaluate some of the most common
automobiles.
Several criteria have been considered in automobile selection
such as local products, the products which assembled in Iran,
and foreign-made products which are welcomed by the society
and also the wide-variety of prices, remarkable automobile differ-
ences with each other in accordance with sub-criteria. According to
what we mentioned above, 9 alternatives were selected as follow:
Xantia (Citroen, assembled by Saipa), Pride (Saipa), Peugeot Pars,
Samand LX (Iran Khodro), Peugeot 206 (type 6, assembled by Iran
Khodro), Sonata (Hyundai), Camry (Toyota), Mercedes Benz (E240),
Maxima (Nissan, assembled by Pars Khodro).
To evaluate alternatives we have done these three, simulta-
neously. We have used companies’ published information in regard
to quantitative criteria like speed, fuel consumption, engine fea-
tures, variety and number of colors. We have evaluated alternatives
Table 5
Normalized decision matrix.
Sub-criteria Alternatives
Xantia Pride Pars Samand Peugeot 206 Camry Sonata Benz E 240 Maxima
Engine features 0.117 0.021 0.064 0.064 0.085 0.149 0.149 0.191 0.160
Safety 0.124 0.021 0.062 0.072 0.062 0.165 0.165 0.186 0.144
Speed 0.114 0.083 0.098 0.960 0.098 0.124 0.124 0.134 0.129
Comfortableness and relaxation 0.148 0.019 0.074 0.093 0.065 0.167 0.148 0.157 0.130
Internal design 0.111 0.022 0.089 0.044 0.067 0.178 0.156 0.200 0.133
External design 0.120 0.022 0.101 0.067 0.084 0.156 0.145 0.169 0.137
Color beauty and variety 0.037 0.130 0.056 0.093 0.111 0.167 0.167 0.167 0.074
Country 0.048 0.048 0.048 0.048 0.048 0.240 0.171 0.301 0.048
Company 0.043 0.043 0.092 0.092 0.092 0.194 0.160 0.228 0.056
Brand 0.141 0.027 0.117 0.041 0.117 0.155 0.123 0.175 0.104
Spare parts 0.117 0.191 0.160 0.138 0.160 0.053 0.064 0.021 0.096
Consumption tools 0.124 0.159 0.150 0.150 0.150 0.053 0.062 0.035 0.115
Price 0.088 0.294 0.134 0.152 0.141 0.048 0.060 0.026 0.056
Fuel cost 0.108 0.146 0.093 0.097 0.114 0.128 0.120 0.093 0.102
Payment flexibility 0.143 0.184 0.163 0.163 0.163 0.020 0.020 0.041 0.102
Advertisement 0.141 0.193 0.163 0.187 0.159 0.027 0.027 0.029 0.074
Social atmosphere 0.121 0.024 0.100 0.078 0.088 0.151 0.141 0.166 0.131
Owners’ satisfaction 0.133 0.038 0.095 0.076 0.057 0.152 0.171 0.152 0.124
Fig. 5. Alternatives final weight and ranking by AHP method.
A. Yousefi, A. Hadi-Vencheh / Expert Systems with Applications 37 (2010) 8543–8556 8551
in accordance with availability of tools, safety, comfortableness and
relaxation using information by manufacturer companies, dealers
and mechanics. We have evaluated alternatives in accordance
with other criteria such as trunk design, color beauty, advertise-
ment and society atmosphere by a combination of the manufac-
turer companies’ information, expert ideas and statistical sample
group ideas.
The spread sheet model for simultaneous evaluation and
assessment of alternatives in relation to each sub-criterion is
shown in Table 4. Addresses are asked to score alternatives from
1 (Extremely weak) to 9 (Extremely strong) regarding each sub-cri-
terion. Data sources have been weighed according to their validity.
To evaluate automobiles the latest model features (last three
months of 1385 in Iranian calendar, three first months of 2007)
was considered. As same as criteria, alternatives evaluation is done
by the spread sheet model and simultaneous comparison of alter-
natives due to each criterion. The weight in data sources was also
considered in geometrical mean calculating process. It is inevitable
that, in alternative evaluating in accordance with negative
specifications (price and fuel consumption) obtained values will
be inverted. Decision matrix obtains by comparing the alternatives
with respect to sub-criteria. Table 5 shows normalized decision
matrix.
7. Calculating alternatives final weight
7.1. Calculating alternatives final weight by AHP
To compute the final weight of the alternatives, the weights of
different levels of hierarchy should be synthesized. Here, Expert
Choice software is used to combine hierarchy different levels
weight. The result of this combination is shown in Fig. 5, which
is consisting of alternatives final weight and their rankings.
As we see inconsistency index is 0.0, Benz and Samand with
0.122 and 0.103 obtained scores placed on the first and the eighth
position, respectively. By having a renewed glance on the decision
matrix we consider Benz E240 duo to many sub-criteria such as
safety, comfortableness and relaxation, engine features, speed,
internal and external design, brand, producer country and com-
pany, stands on the first step. Remarkable point in Fig. 5 is the
closeness of the alternatives together which has decreased the sep-
arability of the model. This problem is due to the numerous crite-
ria, sub-criteria and the alternatives.
7.2. Sensitivity analysis of the AHP results
The sensitivity analysis lets us to review the results of decision,
and could also illustrate sensitivity level of the alternatives in rela-
tion to changing the importance of criteria. Expert Choice software
provides following four graphical modes for the sensitivity analy-
sis: Dynamic, Gradient, Performance, and 2D Plot. The Gradient
and 2D Plot modes have applied in this paper. The Gradient mode
of sensitivity analysis illustrates behavior of each alternative, while
the importance degree of each criterion varies from 0 to 1. The dia-
grams of the Gradient mode depict, when importance degree of
Technical features varied, then the score of Benz and Pride varies
with the highest positive gradient and the highest negative gradi-
ent, respectively. Such that if the importance degree of that crite-
rion becomes less than 0.166, then Pride will place on the first
position and if it becomes more than 0.332 then Pride will place
on the last position, in addition, if it decreases from 0.166 to zero,
then the rank of Benz will increase from first to sixth (Fig. 6). The
behavior of Benz and Pride under variation of the importance de-
gree of Economic Factors, are completely opposite of Technical fea-
tures (Fig. 7). In the other words, Benz and Pride varies with the
highest negative gradient and the highest positive gradient respec-
tively, by increasing the importance degree of Economic Factors,
which if be less than 0.160 or more than 0.275 then Pride will be
the last alternative or the first alternative, respectively. Further-
more, if the importance degree of Economic Factors be less than
0.275 or more than 0.50, then Benz will be the first or the last alter-
native, respectively.
Therefore, Benz is the most technical alternative and Pride is the
most economical one. After inspection the other criteria by the
same way, it is observed that Benz is the best alternative based
on beauty criteria and manufacturer’s specifications, and Pride is
the best alternative with regard to tools availability.Xantia is
the best alternative in relation to social aspects criteria, and if the
importance degree of that criterion becomes more than 0.68, then
Xantia will place on the first rank. Fig. 8 depicts 2D Plot sensitivity
analysis of alternatives with regard to Technical features and
Economical Aspects. Negative correlation of these two criteria is
observable clearly.
Fig. 6. Analyzing the alternatives’ sensitivity with regard to technical features.
Fig. 7. Analyzing the alternatives’ sensitivity with regard to economical aspects.
8552 A. Yousefi, A. Hadi-Vencheh / Expert Systems with Applications 37 (2010) 8543–8556
7.3. Calculating alternatives final weight by TOPSIS
In this section alternative final weight will calculate by TOPSIS
according to mentioned steps in 3–2.
Step 1. First of all, obtained decision matrix in Table 5 will nor-
malize with Euclidean norm according to Eq. (5) Normalized
matrix is shown in Table 6.
Step 2. Now by having above normalized matrix and sub-criteria
weight vector (W) which is computed by AHP (Fig. 4), weighted
normalized matrix will evaluate by Eq. (6). Weighted normal-
ized matrix is shown in Table 7.
Step 3. In this step ideal solution and negative ideal solution will
determine according to Eqs. (7) and (8). Weight vector of sub-
criteria (W) ideal solution (A
+
) and negative ideal solution (A
)
is shown in Table 8.
Steps 4, 5, 6. In this stage, every alternative distance with ideal
solution and negative ideal solution will calculate by Eqs. (9)
and (10), then closeness to ideal solution for each alternative
will obtain. Relative closeness to ideal solution will calculate
by Eq. (11). The more alternative relative closeness to ideal
solution be the larger number, the more the alternative (would
be). In the final step alternatives will rank duo to (D
i
). Alterna-
tives distances from the ideal solution (d
þ
i
), negative ideal solu-
tion (d
i
), and relative closeness to ideal solution (D
i
) and
obtained ranking by TOPSIS method are shown in Table 9,
respectively.
The last row of table above shows the alternatives ranking,
using TOPSIS method in which Pride and Maxima have became
the first and the last; Benz and Samand are also third and eighth,
respectively. Same process is considered by comparing results of
AHP and TOPSIS which are different in some aspects, however. In
both methods alternatives with second and fourth grade are the
same (Toyota and Xantia), five alternatives have partial differences
(Pars, Samand, Peugeot 206, Benz E240 and Maxima), but in two
other alternatives, differences are remarkable (Pride and Hyundai).
7.4. The ranking of improvement fields of internal products
The ranking of criteria and sub-criteria was considered in Figs. 3
and 4, now it is turn of inspecting strengths and weaknesses of
internal products and ranking their improvement fields. This point
should be noticed that an automobile is called an internal product,
if all stages of its designing and manufacturing have done by the
internal experts. As a result, many products which are manufactur-
ing in Iran now, could not be called as an internal product, because
those are external products originally, which just are assembled
and manufactured in Iran. According to definition above, Samand
is the only internal product of Iran automobile industry, which
all stages of its designing and manufacturing have done by internal
experts, using domestic technology, and is known as national auto-
mobile. Therefore, to rank the improvement fields of internal auto-
mobile industry, we compare the score of Samand in the weighted
normalized decision matrix (Table 7) and positive ideal solution
(A
+
in Table 8). As much as difference between score of Samand
and positive ideal solution, with relation to a criterion is bigger,
that criterion is needier to improvement.
As it considers in Table 10, necessity to improvement of internal
automobiles in various fields, has ranked. To reduce the price, to
promote the safety, and internal designing are the three first fields
for improvement, respectively. To strengthen the position of Iran in
Fig. 8. Technical features and economical aspects 2D Plot sensitivity analysis.
Table 6
Normalized decision matrix with Euclidean norm.
Sub-criteria Alternatives
Xantia Pride Pars Samand Peugeot 206 Camry Sonata Benz E 240 Maxima
Engine features 0.3172 0.0569 0.1735 0.1735 0.2305 0.4040 0.4040 0.5179 0.4338
Safety 0.3332 0.0564 0.1935 0.1935 0.1666 0.4434 0.4434 0.4998 0.3870
Speed 0.3381 0.2462 0.2848 0.2848 0.2907 0.3678 0.3678 0.3975 0.3826
Comfortableness and relaxation 0.4074 0.0523 0.2560 0.2560 0.1789 0.4597 0.4074 0.4322 0.3579
Internal design 0.2958 0.0586 0.1172 0.1172 0.1785 0.4743 0.4157 0.5329 0.3544
External design 0.3337 0.0612 0.1863 0.1863 0.2336 0.4338 0.4032 0.4700 0.3810
Color beauty and variety 0.1020 0.3585 0.2564 0.2564 0.3061 0.4605 0.4605 0.4605 0.2041
Country 0.1098 0.1098 0.1098 0.1098 0.1098 0.5488 0.3910 0.6883 0.1098
Company 0.1120 0.1120 0.2396 0.2396 0.2396 0.5052 0.4167 0.5938 0.1458
Brand 0.3907 0.0748 0.1136 0.1136 0.3242 0.4295 0.3408 0.4849 0.2882
Spare parts 0.3161 0.5161 0.3729 0.3729 0.4323 0.1432 0.1729 0.0567 0.2594
Consumption tools 0.3449 0.4422 0.4172 0.4172 0.4172 0.1474 0.1724 0.0974 0.3199
Price 0.2167 0.7241 0.3744 0.3744 0.3473 0.1182 0.1478 0.0640 0.1379
Fuel cost 0.3200 0.4327 0.2875 0.2875 0.3378 0.3793 0.3556 0.2756 0.3023
Payment flexibility 0.3731 0.4801 0.4253 0.4253 0.4253 0.0522 0.0522 0.1070 0.2661
Advertisement 0.3620 0.4955 0.4801 0.4801 0.4082 0.0693 0.0693 0.0745 0.1900
Social atmosphere 0.3403 0.0675 0.2194 0.2194 0.2475 0.4246 0.3965 0.4668 0.3684
Owners’ satisfaction 0.3717 0.1062 0.2124 0.2124 0.1593 0.4248 0.4779 0.4248 0.3466
A. Yousefi, A. Hadi-Vencheh / Expert Systems with Applications 37 (2010) 8543–8556 8553
the global automobile industryand also improvement of comfort and
convenience factors of the automobile, are placed in the next ranks.
8. Alternatives final ranking
We have combined obtained results of AHP and TOPSIS to have
the final grading. As noticed in the methodology section, firstly, ob-
tained alternatives final weight by AHP (W
j
) and also obtained rel-
ative closeness to positive and negative ideal solutions by TOPSIS
(d
þ
j
;d
j
) will normalize; next, we compute the final score of jth
alternative (AT
j
), according to Eq. (12). Now its turn to rank alter-
natives based on final values. With that foundation Pride and Sa-
mand place on the first and eighth ranks, it means that with
contemplating the importance of criteria and sub-criteria and also
distance from positive and negative ideal solutions, Pride is the
best among the alternatives, totally. This conclusion is caused by
absolute superiority of Pride in the following sub-criteria: price,
tools availability, fuel consumption, payment flexibility, and adver-
tisement. As pointed in the methodology section, the final ranking
based on the AT results, includes the specifications and advantages
of the both MCDM methods (AHP and TOPSIS). Normalized relative
values, ranking of each method, with alternatives final values and
their final ranking are shown in Table 11.
9. Data envelopment analysis (DEA)
9.1. Evaluating the efficiency of DMUs (alternatives)
For selecting an appropriate DEA model to evaluate the effi-
ciency of DMUs, following points are noticed:
(1) In this paper environmental factors exist in addition to
inputs and outputs, which must be considered by the model.
(2) Since, the input-oriented and output-oriented models
provide similar results, so input-oriented model is used here.
(3) Non-decreasing return to scale (NDRS) is applied in order to
select the improving DMUs. Therefore, a NDRS input-ori-
ented model considering environmental variables (13) is
used. Input variables, output variables and environmental
variables were stated in the methodology section. Due to
the number of the DMUs and number of the inputs and out-
puts all units place on the efficiency frontier and techniques
for ranking the efficient units are used in order to rank the
units (Anderson & Peterson, 1993).
Table 12 shows the scores and ranking of DMUs using DEA. In
evaluating the efficiency of DMUs, Pride and Peugeot 206 were
Table 7
Weighted normalized matrix.
Sub-criteria Alternatives
Xantia Pride Pars Samand Peugeot 206 Camry Sonata Benz E 240 Maxima
Engine features 0.0089 0.0016 0.0049 0.0049 0.0065 0.0113 0.0113 0.0145 0.0121
Safety 0.0400 0.0068 0.0200 0.0232 0.0200 0.0532 0.0532 0.0600 0.0464
Speed 0.0047 0.0034 0.0041 0.0040 0.0041 0.0051 0.0051 0.0056 0.0054
Comfortableness and relaxation 0.0363 0.0047 0.0181 0.0228 0.0159 0.0409 0.0363 0.0385 0.0319
Internal design 0.0254 0.0050 0.0204 0.0101 0.0154 0.0408 0.0357 0.0458 0.0305
External design 0.0210 0.0039 0.0177 0.0117 0.0147 0.0273 0.0254 0.0296 0.0240
Color beauty and variety 0.0019 0.0068 0.0029 0.0049 0.0058 0.0087 0.0087 0.0087 0.0039
Country 0.0059 0.0059 0.0059 0.0059 0.0059 0.0296 0.0211 0.0372 0.0059
Company 0.0040 0.0040 0.0086 0.0086 0.0086 0.0182 0.0150 0.0214 0.0053
Brand 0.0051 0.0010 0.0042 0.0015 0.0042 0.0056 0.0044 0.0063 0.0037
Spare parts 0.0364 0.0593 0.0497 0.0429 0.0497 0.0165 0.0199 0.0065 0.0298
Consumption tools 0.0300 0.0385 0.0363 0.0363 0.0363 0.0128 0.0150 0.0085 0.0278
Price 0.0256 0.0854 0.0389 0.0442 0.0410 0.0140 0.0174 0.0076 0.0163
Fuel cost 0.0189 0.0255 0.0163 0.0170 0.0199 0.0224 0.0210 0.0163 0.0178
Payment flexibility 0.0179 0.0230 0.0204 0.0204 0.0204 0.0025 0.0025 0.0051 0.0128
Advertisement 0.0090 0.0124 0.0105 0.0120 0.0102 0.0017 0.0017 0.0019 0.0047
Social atmosphere 0.0024 0.0005 0.0020 0.0015 0.0017 0.0030 0.0028 0.0033 0.0026
Owners’ satisfaction 0.0067 0.0019 0.0048 0.0038 0.0029 0.0076 0.0086 0.0076 0.0062
Table 8
Sub-criteria weight (W), ideal solution (A
+
) and negative-ideal solution (A
) vectors.
WA
+
A
Engine features 0.028 0.0145 0.0016
Safety 0.12 0.0600 0.0068
Speed 0.014 0.0056 0.0034
Comfortableness and relaxation 0.089 0.0409 0.0047
Internal design 0.086 0.0458 0.0050
External design 0.063 0.0296 0.0039
Color beauty and variety 0.019 0.0087 0.0019
Country 0.054 0.0372 0.0059
Company 0.036 0.0214 0.0040
Brand 0.013 0.0063 0.0010
Spare parts 0.115 0.0593 0.0065
Consumption tools 0.087 0.0385 0.0085
Price 0.118 0.0854 0.0076
Fuel cost 0.059 0.0255 0.0163
Payment flexibility 0.048 0.0230 0.0025
Advertisement 0.025 0.0124 0.0017
Social atmosphere 0.007 0.0033 0.0005
Owners’ satisfaction 0.018 0.0086 0.0019
Table 9
dþ
i,d
iand D
i
vectors and alternatives ranking by TOPSIS.
Xantia Pride Pars Samand Peugeot 206 Camry Sonata Benz E 240 Maxima
d
þ
i
0.0809 0.0895 0.0809 0.0815 0.0821 0.0912 0.0883 0.1014 0.0883
d
i
0.0699 0.1020 0.0697 0.0678 0.0690 0.0804 0.0739 0.0887 0.0680
D
i
0.4637 0.5327 0.4627 0.4542 0.4566 0.4686 0.4557 0.4667 0.4351
TOPSIS ranking 4158 6 273 9
8554 A. Yousefi, A. Hadi-Vencheh / Expert Systems with Applications 37 (2010) 8543–8556
ranked as the first and the last alternatives with scores 3.0476 and
1.000, respectively. Samand also ranked as fourth alternative with
score 2.0182.
9.2. Sensitivity analysis of DEA results
We know, if the DMUs do not be sensitive with relation
to variation of each criterion of the model (Input variables,
output variables or environmental variables), it will be better
to eliminate the criterion from the model. After analyzing the
sensitivity of the model, further clarifies that four criteria have
no influence on the DEA model, and omitting them doesn’t
change the results. Those four criteria are: consumption tools’
availability, manufacturer company, fuel consumption, and
external design. However, four criteria above are omitted from
the DEA model.
9.3. Evaluating the MCDM techniques by DEA
For evaluating the reliability of three MCDM methods AHP,
TOPSIS and AT, we compare their results with the result of DEA.
In this manner we calculate the mean absolute percent error
(MAPE) for each one of three MCDM methods regarding to DEA re-
sults. Each method which has lower percent of error will be more
reliable. The MAPE for ith MCDM method is calculated according to
the following formula:
MAPE
i
¼P
N
j¼1
ja
j
b
ij
j
a
j
N100;i¼1;2;3:ð14Þ
MAPE
i
is the mean absolute percent error for ith MCDM method, a
j
is the score of jth DMU computing by DEA, b
ij
is the score of jth DMU
computing by ith MCDM method (i= 1,2,3), N is the number of
DMUs (here is 9). Table 13 shows the results of each MCDM meth-
ods and their MAPE. It is considered that the last percent of error
equals 30.779 and is belonged to AT method. As a result, AT (sug-
gested method) is more reliable than AHP and TOPSIS for decision
making.
10. Conclusions
In this paper we proposed a decision making model in automo-
bile industry by integration of AHP and TOPSIS. Related criteria and
sub-criteria for evaluating the automobiles are determined consid-
ering several references. In order to decrease the volume of pair-
wise assessments, a spread sheet model is suggested. Obtained
results show that the most important criteria are: Technical features
and Economical Factors, furthermore, the most important sub-crite-
ria are: safety,price,spare parts availability,comfortableness and
relaxation in the automobile, respectively. The sensitivity analysis
of criteria and sub-criteria depicts that all of them are sensitive,
thus all remained in the model. Criteria and their details have been
defined in the Section 4. For instance, some details for improving
the automobile safety are: increasing the number of airbags, mak-
ing the brake system strong, increasing the stability on high speed
and turns, consistence and resistance of the trunk, external light
system, central lock and burglar alarm. Firstly, the automobile
ranking problem is solved by AHP and TOPSIS techniques sepa-
rately, and then AT index (Eq. (12)) is suggested in order to obtain
a unique ranking which include advantages and specifications of
these MCDM methods. The obtained result of AT are between the
results of AHP and TOPSIS. We use DEA to evaluate efficiency of
the alternatives as a basis for comparing three MCDM techniques.
The results show that AT is more reliable than both AHP and
TOPSIS.
Table 10
The difference between Samand and the ideal solution (A
+
) and ranking of improvement fields.
Sub-criteria Engine
features
Safety Speed Comfortableness
and relaxation
Internal
design
External
design
Color
beauty
and
variety
Country Company Brand Spare
parts
Consumption
tools
Price Fuel
cost
Payment
flexibility
Advertisement Social
atmosphere
Owners’
satisfaction
A
+
0.0145 0.0600 0.0056 0.0409 0.0458 0.0296 0.0087 0.0372 0.0214 0.0063 0.0593 0.0385 0.0854 0.0255 0.0230 0.0124 0.0033 0.0086
Samand score 0.0049 0.0232 0.0040 0.0228 0.0101 0.0117 0.0049 0.0059 0.0086 0.0015 0.0429 0.0363 0.0442 0.0170 0.0204 0.0120 0.0015 0.0038
Difference between
Samand and A
+
0.0096 0.0368 0.0016 0.0181 0.0357 0.0179 0.0039 0.0312 0.0128 0.0048 0.0165 0.0022 0.0413 0.0086 0.0026 0.0004 0.0017 0.0048
Differences’
ranking
9 2 17 5 3 6 13 4 8 11 7 15 1 10 14 18 16 12
A. Yousefi, A. Hadi-Vencheh / Expert Systems with Applications 37 (2010) 8543–8556 8555
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Table 11
Alternatives final value and ranking.
Xantia Pride Pars Samand Peugeot 206 Camry Sonata Benz E 240 Maxima
Alternatives normalized relative values obtained by AHP (W
j
) 0.1111 0.1101 0.1071 0.1031 0.1061 0.1201 0.1141 0.1221 0.1062
Normalized d
j
0.1014 0.1479 0.1011 0.0983 0.1001 0.1166 0.1072 0.1287 0.0987
Normalized d
þ
j
0.1031 0.1141 0.1032 0.1039 0.1048 0.1163 0.1126 0.1293 0.1127
AT
j
¼d
j
W
j
=d
þ
j
0.1092 0.1427 0.1049 0.0976 0.1014 0.1204 0.1086 0.1215 0.0930
AHP ranking 4569 8 231 7
TOPSIS ranking 4158 6 273 9
Final ranking by AT 4168 7 352 9
Table 12
The scores and ranking of DMUs obtained by DEA.
Xantia Pride Pars Samand Peugeot 206 Camry Sonata Benz E 240 Maxima
Efficiency of DMUs 2.2769 3.0476 1.3890 2.0182 1.0000 1.2857 1.5027 2.8450 1.7378
Normalized efficiency of DMUs 0.1331 0.1782 0.0812 0.1180 0.0585 0.0752 0.0879 0.1663 0.1016
DEA ranking 3 1 7 4 9 8 6 2 5
Table 13
The results of MCDM methods and their MAPE.
Xantia Pride Pars Samand Peugeot 206 Camry Sonata Benz E 240 Maxima MAPE
i
Normalized value in AHP 0.1111 0.1101 0.1071 0.1031 0.1061 0.1201 0.1141 0.1221 0.1062 33.496
Normalized value in TOPSIS 0.1105 0.1270 0.1103 0.1083 0.1088 0.1117 0.1086 0.1112 0.1037 31.475
Normalized value in AT 0.1092 0.1427 0.1049 0.0976 0.1014 0.1204 0.1086 0.1215 0.0930 30.779
8556 A. Yousefi, A. Hadi-Vencheh / Expert Systems with Applications 37 (2010) 8543–8556
