Plane Thermoelastic Waves in Infinite Half-Space Caused
Decision Making: Applications in Management and Engineering
Vol. 1, Number 1, 2018, pp. 82-96
ISSN: 2560-6018
DOI: https://doi.org/10.31181/dmame180182v
* Corresponding author.
E-mail addresses: zeljkostevic88@yahoo.com (Ž. Stević)
** An earlier version of this paper was presented at the 1st International Conference on
Management, Engineering and Environment – “ICMNEE 2017” (Fazlollahtabar et al., 2017).
A ROUGH MULTICRITERIA APPROACH FOR EVALUATION
OF THE SUPPLIER CRITERIA IN AUTOMOTIVE INDUSTRY
Marko Vasiljević1, Hamed Fazlollahtabar2, Željko Stević1*, Slavko
Vesković3
1 University of East Sarajevo, Faculty of Transport and Traffic Engineering Doboj,
Bosnia and Herzegovina
2 Department of Industrial Engineering, School of Engineering, Damghan Univeristy,
Damghan , Iran
3 University of Belgrade, Faculty of Transport and Traffic Engineering, Serbia
Received: 25 December 2018;
Accepted: 29 January 2018;
Published: 15 March 2018.
Original scientific paper
Abstract. Ensuring costs reduction and increasing competitiveness and
satisfaction of end users are the goals of each participant in the supply chain.
Taking into account these goals, the paper proposes methodology for
defining the most important criteria for suppliers’ evaluation. From a set of
twenty established criteria, i.e. four sets of criteria: finances, logistics, quality
and communication and business including its sub-criteria, we have allocated
the most important ones for supplier selection. Analytic Hierarchy Process
(AHP) based on rough numbers is presented to determine the weight of each
evaluation criterion. For the criteria evaluation we have used knowledge
from the expert in this field. The efficacy of the proposed evaluation
methodology is demonstrated through its application to the company
producing metal washers for the automotive industry. Next a sensitivity
analysis is carried out in order to show the stability of the model. For
checking stability the AHP method in conventional form is used in
combination with fuzzy logic.
Key words: Rough AHP, Supplier Criteria, Fuzzy AHP, Logistics, Quality.
1. Introduction
One of the most important strategic issues in logistics procurement according to
Stević, (2017c) is a correct and optimal supplier selection, which enables an increase
of market competitiveness. The importance of an adequate supplier selection was
recognized at the beginning of the last decade of the 20th century when Davis (1993)
emphasized that the failure of suppliers to fulfill the promises and expectations
regarding delivery is one of the three main sources of uncertainty plaguing the
mailto:veskolukovac@yahoo.com
A rough multicriteria approach for evaluation of the supplier criteria in automotive industry
83
supply chain. Kagnicioglu (2016) considers that the supplier selection is a critical
procurement activity in the supply chain management because of the crucial role that
the supplier characteristics play regarding price, quality, delivery and service in
achieving the objectives of the supply chain. Van Weele (2009) points out that a
healthy relationship with the suppliers can improve the financial position in a short
term and so can a competitive strategy over a long period of time.
Today the company must strive to enlarge the quality of product itself so that the
end user is satisfied with provided services, which would make him a loyal user. Due
to the above mentioned, it is necessary, during the first phase of logistics, i.e.
purchasing logistics, to commit good evaluation and choice of the supplier, which can
largely influence the forming of the product’s final price; thus, it can, in this way,
accomplish a significant effect in the complete supply chain. It is possible to
accomplish the above mentioned if the evaluation is done on the basis of a multi-
criteria decision-making that includes a large number of criteria as well as an
expert’s estimation of their relative significance (Stević et al. 2016).
This paper is structured as follows. Section 2 shows the fundamentals of a rough
set theory, operations with rough numbers and rough Analytic Hierarchy Process.
Section 3 makes up the body of the paper: it gives a practical example besides
showing results of the proposed model. Section 4 presents a sensitivity analysis. This
section also gives discussion and model stability. Section 5 presents conclusions
before the paper ends with a list of references.
2. Methods
2.1. A rough set theory
Due to the complexity and uncertainty of numerous real indicators in the process
of multi-criteria decision-making, as well as the occurrence of the ambiguity of
human thinking, there are difficulties in presenting information about the attributes
of decisions through accurate (precise) numerical values. These uncertainties and
ambiguities are commonly exploited through application of rough numbers (Song et
al., 2014; Zhu et al., 2015).
In addition to the fuzzy theory, a very suitable tool for the treatment of
uncertainty without any impact of subjectivism is a rough set theory, which was first
introduced in (Pawlak, 1982). From the beginning until today, the theory of rough
sets has evolved through solving many problems by using rough sets (Khoo & Chai,
2001; Chai & Liu, 2014; Nauman et al. 2016; Liang et al. 2017; Pamučar et al. 2017a)
and through the use of rough numbers as in (Tiwari et al., 2016; Shidpour et al.,
2016; Stević et al., 2017b; 2017d; 2017e).
In the theory of rough sets only the internal knowledge is used, i.e. operational
data, and there is no need to rely on the models of assumptions. In other words, in
the application of rough sets, instead of various additional/external parameters, we
use exclusively the structure of the data provided (Duntsch et al., 1997). In rough
sets the measurement of uncertainty is based on the uncertainty that is already
contained in the data (Khoo & Chai, 2001). This leads to objective indicators that are
contained in the data. In addition, the theory of rough sets is suitable for application
in the sets that are characterized by a small number of data, and for which statistical
methods are not suitable (Pawlak, 1991).
Vasiljević et al./Decis. Mak. Appl. Manag. Eng. 1 (1) (2018) 82-96
84
2.2. Operations with rough numbers
In the rough set theory, any vague concept can be represented as a pair of precise
concepts based on the lower and upper approximations (Pawlak, 1991) as shown in
Figure 1.
Figure 1. Basic notions of the rough set theory (Stević et al., 2017a)
Let’s U be a universe containing all objects and X be a random object from U .
Then we assume that there exists set build with k classes representing DMs
preferences, ( )
q
Apr J
1 2
( , ,..., )
k
R J J J with condition
1 2
,...,
k
J J J . Then,
, , 1
q
X U J R q k lower approximation , upper approximation ( )
q
Apr J and
boundary interval ( )
q
Bnd J are determined, respectively, as follows:
( ) / ( )q qApr J X U R X J (1)
( ) / ( )q qApr J X U R X J (2)
( ) / ( ) / ( ) / ( )q q q qBnd J X U R X J X U R X J X U R X J (3)
The object can be presented with rough number (RN) defined with lower limit
( )
q
Lim J and upper limit ( )
q
Lim J , respectively:
1
( ) ( ) ( )
q q
L
Lim J R X X Apr J
M
(4)
1
( ) ( ) ( )
q q
U
Lim J R X X Apr J
M
(5)
where
L
M and
U
M represent the sum of objects contained in the lower and
upper object approximation of
q
J , respectively. Obviously, the lower limit and upper
limit denote the mean value of elements included in the lower approximation and
upper approximation, respectively. Their difference is defined as rough boundary
interval (𝐼𝑅𝐵𝑛𝑑(𝐺𝑞)):
𝐼𝑅𝐵𝑛𝑑(𝐺𝑞) = 𝐿𝑖𝑚(𝐺𝑞) − 𝐿𝑖𝑚(𝐺𝑞) (7)
Operation for two rough numbers 𝑅𝑁(𝛼) = [𝐿𝑖𝑚(𝛼), 𝐿𝑖𝑚(𝛼)] and 𝑅𝑁(𝛽) =
[𝐿𝑖𝑚(𝛽), 𝐿𝑖𝑚(𝛽)] according to (Zhai et al., 2009) are:
A rough multicriteria approach for evaluation of the supplier criteria in automotive industry
85
Addition (+) of two rough numbers (𝛼) and (𝛽)
𝑅𝑁(𝛼) + 𝑅𝑁(𝛽) = [𝐿𝑖𝑚(𝛼) + 𝐿𝑖𝑚(𝛽), 𝐿𝑖𝑚(𝛼) + 𝐿𝑖𝑚(𝛽)] (8)
Subtraction (-) of two rough numbers (𝛼) and (𝛽)
𝑅𝑁(𝛼) − 𝑅𝑁(𝛽) = [𝐿𝑖𝑚(𝛼) − 𝐿𝑖𝑚(𝛽), 𝐿𝑖𝑚(𝛼) − 𝐿𝑖𝑚(𝛽)] (9)
Multiplication (×) of two rough numbers (𝛼) and (𝛽)
𝑅𝑁(𝛼) × 𝑅𝑁(𝛽) = [𝐿𝑖𝑚(𝛼) × 𝐿𝑖𝑚(𝛽), 𝐿𝑖𝑚(𝛼) × 𝐿𝑖𝑚(𝛽)] (10)
Division (÷) of two rough numbers 𝑅𝑁(𝑎) and 𝑅𝑁(𝑏)
𝑅𝑁(𝛼) ÷ 𝑅𝑁(𝛽) = [𝐿𝑖𝑚(𝛼) ÷ 𝐿𝑖𝑚(𝛽), 𝐿𝑖𝑚(𝛼) ÷ 𝐿𝑖𝑚(𝛽)] (11)
Scalar multiplication of rough number 𝑅𝑁(𝛼), where 𝜇 is a nonzero constant
𝜇 × 𝑅𝑁(𝛼) = [𝜇 × 𝐿𝑖𝑚(𝛼), 𝜇 × 𝐿𝑖𝑚(𝛼)] (12)
2.3. Rough Analytic Hierarchy Process
The procedure of the rough AHP is described as follows (Zhu et al., 2015):
Step 1: Identify the evaluation objective, criteria and alternatives. Construct a
hierarchical structure with the evaluation objective at the top layer, criteria in the
middle and alternatives at the bottom.
Step 2: Conduct AHP survey and construct a group of pair-wise comparison
matrices. The pair-wise comparison matrix of the eth expert is described as:
𝐵𝑒 = [
1
𝑥21
𝑒
⋮
𝑥𝑚1
𝑒
𝑥12
𝑒
1
⋮
𝑥𝑚2
𝑒
⋯
⋯
⋱
⋯
𝑥1𝑚
𝑒
𝑥2𝑚
𝑒
⋮
1
] (13)
where 𝑥𝑔ℎ
𝑒 (1 ≤ 𝑔 ≤ 𝑚, 1 ≤ ℎ ≤ 𝑚, 1 ≤ 𝑒 ≤ 𝑠)is the relative importance of
criterion g on criterion h given by expert e, m is the number of criteria, s is the
number of experts.
Calculate maximum eigenvalue 𝜆𝑚𝑎𝑥
𝑒 of Be, then compute consistency index 𝐶𝐼 =
(𝜆𝑚𝑎𝑥
𝑒 − 𝑛)/(𝑛 − 1).
Determine random consistency index (RI) in Table 1 according to n. Compute
consistency ratio CR=CI/RI.
Table 1. Value of random index depending on the rank of matrix (Saaty &
Vargas, 2012)
n 1 2 3 4 5 6 7 8 9 10
RI 0.00 0.00 0.52 0.89 1.11 1.25 1.35 1.40 1.45 1.49
Conduct consistency test. If CR<0.1, the comparison matrix is acceptable.
Otherwise, experts’ judgments should be adjusted until CR < 0.1
Then, integrated comparison matrix �̃� is built as:
�̃� = [
1
�̃�21
𝑒
⋮
�̃�𝑚1
𝑒
�̃�12
𝑒
1
⋮
�̃�𝑚2
𝑒
⋯
⋯
⋱
⋯
�̃�1𝑚
𝑒
�̃�2𝑚
𝑒
⋮
1
] (14)
Vasiljević et al./Decis. Mak. Appl. Manag. Eng. 1 (1) (2018) 82-96
86
where �̃�𝑔ℎ{𝑥𝑔ℎ
1 , 𝑥𝑔ℎ
2 , … . , 𝑥𝑔ℎ
𝑠 }, �̃�𝑔ℎ is the sequence of relative importance of
criterion g on criterion h.
Step 3: Construct a rough comparison matrix.
Translate element 𝑥𝑔ℎ
𝑒 in �̃� into rough number 𝑅𝑁(𝑥𝑔ℎ
𝑒 ) using Eqs. (1) - (6):
𝑅𝑁(𝑥𝑔ℎ
𝑒 ) = [𝑥𝑔ℎ
𝑒𝐿 , 𝑥𝑔ℎ
𝑒𝑈] (15)
where 𝑥𝑔ℎ
𝑒𝐿 is the lower limit of 𝑅𝑁(𝑥𝑔ℎ
𝑒 ) while 𝑥𝑔ℎ
𝑒𝑈 is the upper limit.
Then rough sequence 𝑅𝑁(�̃�𝑔ℎ) is represented as:
𝑅𝑁(�̃�𝑔ℎ) = {[𝑥𝑔ℎ
1𝐿, 𝑥𝑔ℎ
1𝑈], [𝑥𝑔ℎ
2𝐿, 𝑥𝑔ℎ
2𝑈], … , [𝑥𝑔ℎ
𝑠𝐿 , 𝑥𝑔ℎ
𝑠𝑈]} (16)
It is further translated into an average rough number 𝑅𝑁(𝑥𝑔ℎ) by rough
arithmetic Eqs. (8) - (12):
𝑅𝑁(𝑥𝑔ℎ) = [𝑥𝑔ℎ
𝐿 , 𝑥𝑔ℎ
𝑈 ] (17)
𝑥𝑔ℎ
𝐿 =
𝑥𝑔ℎ
1𝐿 +𝑥𝑔ℎ
2𝐿 +⋯+𝑥𝑔ℎ
𝑠𝐿
𝑆
(18)
𝑥𝑔ℎ
𝑈 =
𝑥𝑔ℎ
1𝑈
+𝑥𝑔ℎ
2𝑈
+⋯+𝑥𝑔ℎ
𝑠𝑈
𝑆
(19)
where 𝑥𝑔ℎ
𝐿 is the lower limit of 𝑅𝑁(𝑥𝑔ℎ) and 𝑥𝑔ℎ
𝑈 is the upper limit.
Then rough comparison matrix M is formed as:
𝑀 =
[
[1,1]
[𝑥21
𝐿 , 𝑥21
𝑈 ]
⋮
[𝑥𝑚1
𝐿 , 𝑥𝑚1
𝑈 ]
[𝑥12
𝐿 , 𝑥12
𝑈 ]
[1,1]
⋮
[𝑥𝑚2
𝐿 , 𝑥𝑚2
𝑈 ]
⋯
⋯
⋱
⋯
[𝑥1𝑚
𝐿 , 𝑥1𝑚
𝑈 ]
[𝑥2𝑚
𝐿 , 𝑥2𝑚
𝑈 ]
⋮
[1,1] ]
(20)
Step 4: Calculate rough weight wg of each criterion:
𝑤𝑔 = [ √∏ 𝑥𝑔ℎ
𝐿 ,𝑚ℎ=1
𝑚
√∏ 𝑥𝑔ℎ
𝑈 ,𝑚ℎ=1
𝑚
] (21)
𝑤𝑔
′ = 𝑤𝑔/max (𝑤𝑔
𝑈) (22)
where 𝑤𝑔
′ is the normalization form.
Finally, the criteria weights are obtained.
3. Numerical example
The main activity of the company which is the subject of research is the
production of metal washers for the automotive industry. Its product range covers
up over 3000 types of metal washers, and the largest part of it is used for mechanical
transmissions in heavy machinery, cranes, trucks, and the like. The company is
focused on the production and sale of flat and elastic washers. The ability of
production is over 3500 tons of finished products.
The aim of this paper is to determine the most important criteria for suppliers’
evaluation in the mentioned company. Figure 2 presents criteria finance, logistics,
quality and communications and business, and each of these criteria contains five
subcriteria which are also shown in the figure below each criterion. A review of the
given criteria for suppliers’ evaluation through literature is presented in the paper
(Stević, 2017c).
A rough multicriteria approach for evaluation of the supplier criteria in automotive industry
87
Figure 2. Criteria for supplier selection (Stević, 2017b)
Collect individual judgments and construct a group of pairwise comparison
matrices. Take the consistency examination until all the comparison matrices can
pass through. Integrate individual comparison matrices to generate an integrated
comparison matrix. The individual pair-wise comparison matrices are as follows:
𝐵1 = [
1 1/4 1/3
4 1 3
3 1/3 1
1/3 1/5 1/4
3
5
4
1
] , 𝐶𝑅 = 0,068 < 0,10
𝐵2 = [
1/
1 4 1
4 1 1/4
1 4 1
1/3 3 1/3
3
1/3
4
1
] , 𝐶𝑅 = 0,047 < 0,10
𝐵3 = [
1 4
1/4 1
1 4
1/4 3
1 4
1/4 1/3
1 5
1/5 1
] , 𝐶𝑅 = 0,049 < 0,10
Obviously CRe < 0.1 (e= 1, 2, 3), all the comparison matrices are acceptable. Then
integrated comparison matrix �̃� is generated by combining with the above three
individual comparison matrices.
�̃� = [
1,1,1 1/4,4,4
4,1/4, 1/4 1,1,1
1/3,1,1 3,3,4
3,1/4,1/4 5,1/3,3
3,1,1 1/3,4,4
1/3,1/4,1/4 1/5,3,1/3
1,1,1 4,4,5
1/4,1/3,1/5 1,1,1
]
Translate the elements in �̃� into rough numbers and correspondingly original
integrated comparison matrix �̃� is converted into a rough comparison matrix.
Vasiljević et al./Decis. Mak. Appl. Manag. Eng. 1 (1) (2018) 82-96
88
Take as an example x̃24 = {5,1/3,3}
𝐿𝑖𝑚 (
1
3
) =
1
3
, 𝐿𝑖𝑚 (
1
3
) =
1
3
(5 +
1
3
+ 3) = 2,78
𝐿𝑖𝑚(3) =
1
2
(
1
3
+ 3) = 1,67, 𝐿𝑖𝑚(3) =
1
2
(3 + 5) = 4
𝐿𝑖𝑚(5) =
1
3
(5 +
1
3
+ 3) = 2,78, 𝐿𝑖𝑚(5) = 5
Thus, 𝑥24
𝑒 can be expressed in rough number:
𝑅𝑁(𝑥24
1 ) = 𝑅𝑁(5) = [2,78; 5]
𝑅𝑁(𝑥24
2 ) = 𝑅𝑁 (
1
3
) = [0,33; 2,78]
𝑅𝑁(𝑥24
3 ) = 𝑅𝑁(3) = [1,67; 4]
According to Eqs. (17) - (19)
𝑥24
𝐿 =
𝑥24
1 + 𝑥24
2 + 𝑥24
𝑠
𝑆
=
2,78 + 0,33 + 1,67
3
= 1,59
𝑥24
𝑈 =
𝑥24
1 + 𝑥24
2 + 𝑥24
𝑠
𝑆
=
5 + 2,78 + 4
3
= 3,93
Thus rough sequence �̃�24 in �̃� is transformed into rough number
𝑅𝑁(𝑥24) = [1,59; 3,93]. The transformation of other elements in �̃� is implemented in
the same way.
Then, the rough comparison matrix is obtained:
𝑀 = [
[1; 1]
[0,67; 2,33]
[1,22; 2,11]
[0,28; 0,32]
[1,92; 3,58]
[1; 1]
[1,96; 3,59]
[0,57; 1,95]
[0,63; 0,93]
[0,56; 1,78]
[1; 1]
[0,22; 0,24]
[3,11; 3,55]
[1,59; 3,93]
[4,11; 4,55]
[1; 1]
]
Calculate rough weights of the criteria using Eqs. (21) and (22).
𝑤 = {[1,39; 1,85]; [0,88; 2,01]; [1,77; 2,42]; [0,43; 0,62]}
𝑤′ = {[0,57; 0,76]; [0,36; 0,83]; [0,73; 1]; [0,18; 0,26]}
According to the obtained results, the third criterion quality is the most important
in the target company. Observing the obtained values of the upper and lower limits
of the rough number in all, except for the second criterion, shows that they have
relatively approximate values. The cause of a large difference between the lower and
the upper limit of logistics criteria are the different attitudes of decision-makers
when this criterion is concerned. That is why the decision-makers gave different
assessments of their preferences, for example, 1/3 and 5, etc.
A rough multicriteria approach for evaluation of the supplier criteria in automotive industry
89
Figure 3. Comparison of rough numbers (Zhai et al., 2008)
Figure 3 shows a comparison of rough numbers on the basis of which the criteria
or alternatives are ranked. A comparison of the two rough numbers is clearly
defined, depending on the lower and upper limits.
After obtaining the values that mark the weight of the criteria in the same way it
is necessary to make calculation for sub-criterion; so, the following is an example of
the calculation for the subcriteria that belong to the logistics.
The individual pair-wise comparison matrices are as follows:
𝐵1 =
[
1
1/4
1/4
4
4
4
1
1/3
5
5
4
3
1
5
5
1/4
1/5
1/5
1
1
1/4
1/5
1/5
1
1 ]
, 𝐶𝑅 = 0,088 < 0,10
𝐵2 =
[
1
1/4
3
1
3
4
1
5
4
5
1/3
1/5
1
1/3
1
1
1/4
3
1
3
1/3
1/5
1
1/3
1 ]
, 𝐶𝑅 = 0,028 < 0,10
𝐵3 =
[
1
3
1/4
1/5
1/7
1/3
1
1/5
1/7
1/9
4
5
1
1/3
1/4
5
7
3
1
1/3
7
9
4
3
1 ]
, 𝐶𝑅 = 0,062 < 0,10
Obviously CRe < 0.1 (e= 1, 2, 3), all the comparison matrices are acceptable. Then
integrated comparison matrix �̃� is generated by combining with the above three
individual comparison matrices.
�̃� =
[
1,1,1 4,4,1/3
1/4,1/4, 3 1,1,1
4,1/3,4 1/4,1,5 1/4,1/3,7
3,1/5,5 1/5,1/4,7 1/5,1/5, 9
1/4,3,1/4 1/3,5,1/5
4,1,1/5 5,4,1/7
4,3,1/7 5,5,1/9
1,1,1 1/5,3,3 1/5,1,4,
5,1/3,1/3 1,1,1 1,1/3,3
5,1,1/4 1,3,1/3 1,1,1 ]
Translate the elements in �̃� into rough numbers and correspondingly original
integrated comparison matrix �̃� is converted into a rough comparison matrix.
Take as an example �̃�45 = {1,1/3,3}
Vasiljević et al./Decis. Mak. Appl. Manag. Eng. 1 (1) (2018) 82-96
90
𝐿𝑖𝑚 (
1
3
) =
1
3
, 𝐿𝑖𝑚 (
1
3
) =
1
3
(1 +
1
3
+ 3) = 1,44
𝐿𝑖𝑚(1) =
1
2
(1 +
1
3
) = 0,66, 𝐿𝑖𝑚(1) =
1
2
(1 + 3) = 2
𝐿𝑖𝑚(3) =
1
3
(1 +
1
3
+ 3) = 1,44, 𝐿𝑖𝑚(3) = 3
Thus, 𝑥45
𝑒 can be expressed in rough number:
𝑅𝑁(𝑥45
1 ) = 𝑅𝑁(1) = [0,66; 2]
𝑅𝑁(𝑥45
2 ) = 𝑅𝑁 (
1
3
) = [0,33; 1,44]
𝑅𝑁(𝑥45
3 ) = 𝑅𝑁(3) = [1,44; 3]
According to Eqs. (17) - (19)
𝑥45
𝐿 =
𝑥45
1 + 𝑥45
2 + 𝑥45
𝑠
𝑆
=
0,66 + 0,33 + 1,44
3
= 0,81
𝑥45
𝑈 =
𝑥45
1 + 𝑥45
2 + 𝑥45
𝑠
𝑆
=
2 + 1,44 + 3
3
= 2,15
Thus rough sequence �̃�245 in �̃� is transformed into rough number
𝑅𝑁(𝑥45) = [0,81; 2,15]. The transformation of other elements in �̃� is implemented in
the same way.
Then, the rough comparison matrix is obtained:
𝑀 =
[
[1; 1]
[0,56; 1,78]
[0,56; 1,78]
[0,84; 2,74]
[1,36; 3,29]
[1,96; 3,59]
[1; 1]
[0,77; 3,17]
[1,75; 4,18]
[2,28; 4,46]
[1,96; 3,59]
[1,51; 3,91]
[1; 1]
[0,85; 2,93]
[0,98; 3,36]
[0,98; 3,36]
[0,97; 4,37]
[1,45; 2,69]
[1; 1]
[0,81; 2,15]
[1,02; 4,40]
[1,18; 5,09]
[0,84; 2,74]
[0,81; 2,15]
[1; 1] ]
Calculate rough weights of the criteria using Eqs. (21) and (22).
𝑤 = {[1,31; 2,86]; [0,99; 2,74]; [0,88; 2,11]; [1,00; 2,35]; [1,20; 2,54]}
𝑤′ = {[0,46; 1,00]; [0,35; 0,96]; [0,31; 0,74]; [0,35; 0,82]; [0,42; 0,89]}
In order to obtain the final values of the subcriteria belonging to the logistics
group, the following values are needed:
𝑤′ = {[0,46; 1,00]; [0,35; 0,96]; [0,31; 0,74]; [0,35; 0,82]; [0,42; 0,89]}
Multiplying with the values of the main criterion-logistics [0,36; 0,83] gives the
following values:
𝑤′′ = {[0,17; 0,83]; [0,13; 0,80]; [0,11; 0,61]; [0,13; 0,68]; [0,15; 0,74]}
The most important logistics sub-criteria are delivery and reliability, which in the
overall ranking occupy high positions, which can be seen in Table 2.
Following the above described methodology, the values for all the twenty criteria
are obtained and shown in Figure 4.
A rough multicriteria approach for evaluation of the supplier criteria in automotive industry
91
Figure 4 Values of all criteria in rough numbers
Figure 4 shows that the certification of products which is used in (Birgün Barla,
2003; Jamil et al., 2013; Ting & Cho, 2008; Uygun et al., 2013) and quality (Fallahpour
et al., 2017; Kilic, 2013; Özbek, 2015; Stević et al., 2016; Wang et al., 2017) are of
utmost importance in the company which is the subject of our research. These two
criteria are very important because the company exports its products to the
international market. The third place is taken by the criterion of volume discounts
(Jamil et al., 2013; Wang, 2010) because the company is located on the territory of
Bosnia and Herzegovina which is a very poor country; thus, additional discounts in
business are very popular. The next most important criterion is that of delivery time
(Chan & Kumar, 2007; Sawik, 2010; Yücenur et al., 2011; Rezaei et al., 2014) and
reliability (Gencer & Gürpinar, 2007; Muralidharan et al., 2002; Büyüközkan & Göçer,
2017).
4. Comparison and discussion
Once the results are obtained, a sensitivity analysis including comparison of the
values of the criteria using three different forms of the AHP method is carried out.
Figure 5 presents the values of the main criteria obtained using conventional
AHP, Fuzzy AHP and Rough AHP, while in Table 2 presented are all the results of the
sensitivity analysis including all the twenty criteria. The sensitivity analysis is very
important for all types of research; a very studious example of the sensitivity
analysis in the multicriteria decision-making can found in the paper (Pamučar et al.,
2017b) in which the authors use different methods for ranking solution.
Vasiljević et al./Decis. Mak. Appl. Manag. Eng. 1 (1) (2018) 82-96
92
Figure 5. Values of main criteria using AHP, FAHP and RAHP
Certification of products is the most important criterion using AHP and rough
AHP, while quality is the most important one using fuzzy AHP. Of equal rank by all
the methods is volume discount which thus occupies the third position. The results
show that the rough AHP has more similarity with the conventional AHP for this
research.
Table 2. Results of sensitivity analysis
Criteria
AHP FAHP RAHP
Values Rank Values Rank Values Rank
Price of material 0,084 4 0,068 4 (0,28;0,53) 7
Financial stability 0,047 5 0,052 6 (0,16;0,58) 8
Method of payment 0,025 14 0,039 13 (0,08;0,19) 14
Price of transport 0,025 14 0,026 18 (0,08;0,17) 15
Volume discounts 0,122 3 0,074 3 (0,42;0,76) 3
Delivery time 0,047 5 0,056 5 (0,17;0,83) 4
Reliability 0,033 10 0,043 11 (0,13;0,80) 5
Flexibility 0,034 9 0,042 12 (0,11;0,61) 9
Logistics capacity 0,039 7 0,050 7 (0,13;0,68) 10
The percentage of correct
realization of delivery
0,043 6 0,047 10 (0,15;0,74) 6
Quality of material 0,149 2 0,114 1 (0,46;0,90) 2
Warranty period 0,032 11 0,037 14 (0,09;0,20) 13
Certification of products 0,164 1 0,102 2 (0,50;1,00) 1
Reputation 0,037 8 0,033 15 (0,10;0,21) 12
Awards and honors 0,017 16 0,021 19 (0,04;0,09) 18
Communication system 0,012 17 0,032 16 (0,04;0,10) 17
Speed of response to
requirements
0,029 12 0,048 8 (0,10;0,26) 11
Reactions to reclamation 0,027 13 0,044 9 (0,08;0,24) 11
Information Technology 0,021 15 0,043 11 (0,08;0,24) 11
Clean of business 0,011 18 0,031 17 (0,04;0,14) 16
Ranking all criteria from the first to the twentieth place is also shown in Figure 6.
A rough multicriteria approach for evaluation of the supplier criteria in automotive industry
93
Figure 6. Ranking criteria by the three forms of the AHP method
The consequence of different results using different methods is reflected in
different scales for evaluating criteria, which according to Mukhametzyanov &
Pamučar (2017) is one of the five main reasons that influence the obtaining of results
and their ranking.
Rough AHP according to (Roy et al., 2016) enables us to measure consistency of
preferences, manipulate multiple decision-makers and calculate relative importance
for each criterion. The rough AHP according to (Song et al., 2013) combines the
strength of rough sets in handling subjectivity and the advantage of AHP in hierarchy
evaluation.
5. Conclusion
This study proposes a rough group AHP approach to the evaluation supplier
criteria in the company for producing metal washers for the automotive industry.
According to the methodology applied in this paper the conclusion is that decision-
making based on the rough AHP can be very helpful in production companies. The
proposed models allow the evaluation of alternatives despite the imprecision and
lack of quantitative information in the decision-making process. Future research
related to this work based on the most important criteria represents the application
of some of the multicriteria methods based on the rough theory, for example the
rough TOPSIS for suppliers evaluation and their ranking.
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