A hybrid MCDM model encompassing AHP and COPRAS-G methods for selecting company supplier in Iran.
Zolfani, Sarfaraz Hashemkhani ; Chen, I-Shuo ; Rezaeiniya, Nahid 等
Reference to this paper should be made as follows: Hashemkhani
Zolfani, S.; Chen, I-S.; Rezaeiniya, N.; Tamosaitiene, J. 2012. A hybrid
MCDM model encompassing AHP and COPRAS-G methods for selecting company
supplier in Iran, Technological and Economic Development of Economy
18(3): 529-543.
JEL Classification: C44, C51.
1. Introduction
Due to global intensive competition, many companies prioritize
quick and precise responses to customers' various demands improving
their supply chain management (SCM). Many manufacturers seek to
collaborate with their suppliers in order to upgrade their management
performance and competitiveness. Thus, decisions on supplier selection
are an important component of production and logistics management for
plenty of firms in the process of SCM (Xia, Wu 2007). In addition,
selecting suitable suppliers significantly reduces material purchasing
cost, improves the competitiveness of businesses, increases flexibility
and product quality and helps with speeding up the process of material
purchasing. This is why many experts believe that supplier selection is
the most important activity in a purchasing department.
The term SCM was first used in the 1980s and as such is a
relatively new discipline within a management theory about tools and
concepts still being developed (Lummus, Vokurka 1999). Many definitions
have been used to explain SCM: an integrating philosophy to manage the
total flow of a distribution channel from supplier to ultimate customer
(Ellram, Cooper 1990), the management of upstream and downstream
relationships with suppliers and customers to deliver a superior
customer value at less cost to the supply chain as a whole (Christopher
1998), etc. The subject is multi-disciplinary and has its origins in a
number of fields, including purchasing, logistics and operations.
Given its multi-disciplinary nature, there is a requirement for
cross-boundary management (Lummus, Vokurka 1999). Whichever definition
is applied in today's dynamic business environments, cost-effective
SCM is a matter of survival as purchased goods and services account for
up to 80 percent of sales revenue (Quayle 2003). When building the idea
of SCM as a strategic shift in company's governing principles, SCM
must be seen as professional practice and the one that is at the heart
of a corporate strategy of the organization (Quayle 2003). The
importance of effective SCM can also be seen in the ability of an
organization to gain competitive advantage.
Owing to the fact that external pressure from consumers requires
organizations to focus on better quality, lower prices, shorter lead
times and greater cost efficiencies to achieve the above requirements,
there is growing recognition of the need to externalize SCM and take a
holistic view focusing on relationships in order to secure more
profitable outcomes for all parties in the chain (Christopher 1998).
Therefore, the selection of the best supplier for such relationships is
becoming a critical issue for most organizations in each industry alike.
Supplier selection is a multiple criteria decision-making (MCDM)
problem affected by several conflicting factors. Consequently, a
purchasing manager must analyze trade-off between several criteria. MCDM
techniques support decision-makers (DMs) in evaluating a set of
alternatives (Amid, Ghodsypour 2006). The problem of supplier selection
in a supply chain system is a group decision based on multiple criteria.
Besides, purchase managers should especially know the most appropriate
method and then use it for selecting the right supplier. It is because
the right supplier could work with companies closely and offer the
sustained company competitive advantages such as low purchase prices, on
time products, high product quality and customer satisfaction. Since
there is a lack of studies related to such topic in Iran, supplier
selection is therefore one of the most important problems encountered by
a number of companies in Iran due to the fact that most of those have
currently failed to benefit by selecting their suppliers.
Quite a few traditional MCDM methods such as COmplex PRoportional
Assessment--COPRAS (Zavadskas, Kaklauskas 1996), AHP (Saaty 1990), ARAS
(Zavadskas, Turskis 2010; Zavadskas et al. 2010b), etc. can be
introduced. Specifically, AHP is initially used for calculating the
weight of each criterion and the COPRAS-G method is employed for ranking
and selecting the target suppliers. AHP is a tool for complex problems
where both qualitative and quantitative aspects need to be considered.
AHP could reduce the risk of making the wrong decision through breaking
down the decision problem into a hierarchy of more easily comprehended
sub-problems. It utilizes the consistency index and the random index to
verify the consistency of the comparison matrix (Saaty 1990). Therefore,
AHP is a useful method for weighting and ranking alternatives. COPRAS-G
(Zavadskas et al. 2008a) and ARAS-G (Turskis, Zavadskas 2010) methods
are based on the Grey system theory and Grey relational analysis. The
advantages of that are as follows: involves simple calculations and
requires a smaller number of samples; a typical distribution of samples
is not required; quantified outcomes from grey relational grade do not
result in contradictory conclusions to qualitative analysis; the Grey
relational grade model is a transfer functional model effective in
dealing with discrete data (Deng 1982). Both methods, including AHP
(Liberatore, Nydick 2008; Sivilevicius 2011a, b) and COPRAS-G (Zavadskas
et al. 2008b; Datta et al. 2009; Hashemkhani Zolfani et al. 2011) have
been applied to many management decision-making situations. For supplier
selection, this research uses a hybrid MCDM model encompassing AHP and
the COmplex PRoportional ASsessment of alternatives to Grey relations
(COPRAS-G method).
2. The problem of selecting suppliers to construction
At present, the study of supplier selection has been a very popular
question for discussions on the worldwide basis. A number of evaluation
criteria that could significantly impact the successful selection of
suppliers have been proposed. The main factors to consider include time
(T), quality (Q), cost (C) and service (S) and are the key factors for
getting success in the process of choosing suppliers. The cost of the
construction project could be broadly divided into three major groups,
namely materials, labour and overhead. In addition, the cost of the
labour is generally governed by the availability of workers within
proximity; only construction materials can provide the greatest
flexibility in seeking lower cost for construction companies. The model
of supplier selection must include two general skills: effective and
efficient. The "best" suppliers take a proposal concerning the
right cost in the right quantity with the right quality and at the right
time has a significant effect on business success in property
developers.
Furthermore, Shuyong and Rongqiu (1998) maintained that supplier
evaluation should rely on the following attributes: quality, delivery
period, batch flexibility, the balance between the delivery period and
price, the balance between the price and batch, variety, etc. Shihua and
Xubin (2002) developed an integrated evaluating attribute system for
selecting co-partners under the circumstances of supply chain management
and generalized four main factors that could affect co-partner
selection: outstanding achievement of an enterprise, operation structure
and throughput, quality system and enterprise environment. Lijuan (2002)
proposed that criteria for supplier selection were composed of nine
evaluating attributes: product quality, product price, after service,
distance, technological level, supply capability, economic revenue,
delivery and market influence. In construction industry, suppliers offer
heavy equipment and machinery, labour, building materials, service
expertise, etc. (Florez-Lopez 2007; Ustun, Demirtas 2008; Lam et al.
2010). Due to the nature of construction industry, such specialization
of work and the fragmentation of the overall process taking into account
the coordination of the procurement process of supply chain members
becomes a challenging task. Therefore, an important point is the
selection of the right supplier in each life cycle of construction
building (see Figure 1).
[FIGURE 1 OMITTED]
The study has summarized the latest studies on supplier selection
and pointed out eight evaluation criteria: cost, quality, distance,
delivery reliability, reputation, technology level, compatibility and
development ability.
3. Model for selecting suppliers based on AHP and COPRAS-G methods
The problem of supporting supplier selection have been analyzed by
a number of authors.
Also, there are numerous evaluation methods for selecting the
required suppliers. Additionally, Xu et al. (2009) put forward the rough
data envelopment analysis model (DEA) to deal with the problem of
supplier selection. Furthermore, Shiromaru (2000) adopted the fuzzy
programming approach to dealing with the problems of fuzzy goals in the
process of supplier selection and used inheritance arithmetic to request
the solution. Moreover, Zhu (2004) simplified DEA through the game model
of swapper twain stages and conducted efficiency interior to evaluate
suppliers. Shihua and Xubin (2002) published a Grey relating model to
settle supplier evaluation on the weight of evaluation criteria.
Numerous researches concentrate on the problem of selecting supplier
using different methods (Balezentis, A., Balezentis, T. 2011).
Therefore, the aim of this study is to overcome this deficiency
referring to the oldest and most famous company producing disposable
containers in Iran as a case of a hybrid MCDM model encompassing AHP and
COPRAS-G methods.
AHP not only helps with the analysis of arriving at the best
decision but also provides a clear rational orientation to the made
choices, involves the principles of decomposition, pair-wise comparisons
and the generation and synthesis of priority vectors. COPRAS-G is a
distinct measure that combines qualitative and quantitative factors such
as trust and feature state (Madhuri, Chandulal 2010). It assumes the
direct and proportional dependence of the significance and utility
degree of investigated versions on a system of attributes adequately
describing the alternatives, values and weights of the attributes
(Zavadskas et al. 2008a, b, 2009, 2010a). Hence, AHP and COPRAS-G
combined are useful and flexible MCDM methods for discovering the aim of
this study.
Hybrid MCDM model
The proposed hybrid MCDM model for problem solving consists of AHP
and COPRAS-G methods. Saaty proposed AHP as a multiple criteria
decision-making method applied to overcoming problems under uncertain
conditions. The goal of COPRAS-G method finds the rational solution by
applying utility degree of each alternative using criterion values
expressed in intervals. Proposed hybrid MCDM model to pursue the
decision-maker find the rational solution. Hierarchy appraisal and
decomposition of the problem separation makes it possible to describe
the problem. The goal of the proposed model achieve a more accurate
solution. The elements of hierarchy can relate to any aspect of the
decision problem such as tangible or intangible, carefully measured or
roughly estimated, well or poorly understood, i.e. anything that applies
to the decision at hand. It has been well utilized in several fields
(Saaty 1990) that require choosing alternatives and weight exploration
of evaluation indices like business (Angelou, Economides 2009), industry
(Chen, Wang 2010) and healthcare (Liberatore, Nydick 2008).
Decision analysis is concerned with the situation when a
decision-maker has to choose among several alternatives considering a
particular set of evaluation criteria. For this reason, the COPRAS-G
method can be applied. In 1982, Deng developed the Grey system theory.
The idea of the COPRAS-G method, along with criterion values expressed
in the intervals, is based on real conditions for decision making and
applications for the Grey system theory that uses a stepwise ranking and
evaluating procedure of alternatives in terms of significance and
utility degree (Zavadskas et al. 2008b). Research on the selection model
of construction supplier is based on grey relevancy presented by Wang
and Guo (2007) and fuzzy multiple criteria introduced by Wang (2008). In
this case, the hybrid MCDM model encompassing AHP and COPRAS-G methods
for reaching a solution to the problem is presented in Figure 2.
In the past, 13 major conditions were discovered to be well suited
to the utilization of AHP and included setting priorities, generating a
set of alternatives, choosing the best alternatives for the policy,
determining requirements, allocating resources, predicting outcomes,
measuring performance, designing systems, ensuring system stability,
optimization, planning, resolving conflict and risk assessment (Saaty
1990). Construction environment is risky, and therefore the risk of
construction was analyzed by Zavadskas et al. (2010a). The calculation
of AHP is the adopted ratio scale for developing a pair-wise comparison
matrix. Ratio values from 1 to 9 are given to each sub-scale and
presented in Table 1, which can be typically categorized into five
sub-scales based on different levels of importance. There are still four
sub-scales above the five major sub-scales making a total of nine
sub-scales.
[FIGURE 2 OMITTED]
A review of recent applications for AHP, COPRAS and COPRAS-G
methods is presented in Table 2.
The calculation steps of AHP are as follows (Saaty 1990):
The first step is structuring a problem as hierarchy.
The second step is the elicitation of a judgment on pair wise
comparison.
The third step is establishing the composite or global priorities
of alternatives.
The procedure of applying the COPRAS-G method consists of the
following steps (Zavadskas et al. 2009):
1. Selecting the set of the most important criteria describing
alternatives.
2. Constructing decision-making matrix [cross product] X:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1)
where [cross product][x.sub.ji] is determined by [[x.bar].sub.ji]
(lowest value, lower limit) and [[bar.x].sub.ji] (highest value, higher
limit).
3. Determining the significance of criteria [q.sub.i].
4. Normalized values of decision-making matrix [cross product] X
are calculated applying formula 2:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (2)
where [[x.bar].sub.ji] is a lower value of criterion i in
alternative j of the achieved solution; [[bar.x].sub.ji] is a higher
value of criterion i in alternative j of the achieved solution; m is the
number of criteria; n is the number of compared alternatives.
The decision-making matrix is normalized applying Formula 3:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (3)
5. When calculating the weighted normalized decision matrix [cross
product][??], the weighted normalized values [cross
product][[??].sub.ji] are calculated as follows:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (4)
where [q.sub.i] is the significance of the i-th criterion. Then,
the weighted normalized decision-making matrix [cross product][??] is
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (5)
6. When calculating the sums [P.sub.j] of criterion values, higher
values are more preferable:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (6)
where k is the number of attributes to be maximized.
7. Calculating the sums [R.sub.j] of attribute values, lower values
are more preferable:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (7)
where (m - k) is the number of attributes to be minimized.
8. Calculating the relative significance of each alternatively
[Q.sub.j], the expression is as follows:
[Q.sub.j] = [P.sub.j] + [[n.summation over (j=1)]
[R.sub.j]]/[[R.sub.j][n.summation over (j=1)] [1/[R.sub.j]]] (8)
9. The optimally criterion by K is calculated by applying the
formula:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (9)
10. For calculating the utility degree of each alternative, the
formula is as follows:
[N.sub.j] = [Q.sub.j]/[Q.sub.max] x 100% (10)
where [Q.sub.j] and [Q.sub.max] are the relative significance of
alternatives obtained from Equation (8).
11. When applying the calculation results of [N.sub.j] the order of
alternative priority is constructed.
4. A case study: selecting a supplier company
The aim of this case study is to utilize a new hybrid model of MCDM
methods for selecting a supplier. A case company for selecting a
supplier is Kalleh Company, the oldest and most famous company producing
disposable containers in Iran.
4.1. Selecting criteria and survey data
Kalleh Company tends to select one supplier among three partners.
As highlighted previously, eight evaluation criteria are used.
Criteria for selecting a supplier include:
[cross product][x.sub.1]--cost;
[cross product][x.sub.2]--quality;
[cross product][x.sub.3]--distance;
[cross product][x.sub.4]--delivery reliability;
[cross product][x.sub.5]--reputation;
[cross product][x.sub.6]--technology level;
[cross product][x.sub.7]--compatibility;
[cross product][x.sub.8]--development ability.
Based on the nature of eight criteria for evaluation, optimization
directions for each criterion are determined as follows:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
Then, a questionnaire was sent to a group of 10 senior experts the
majority of which have been working in the companies producing
disposable containers for at least six years. All of 10 questionnaires
have been finally determined to be utilized for this study with a total
response rate of 100%. Demographic information is provided in Table 3.
70 per cent of the respondents are males. More than a half (60%) of the
surveyed participants are between 31 and 40 years of age. 60% of the
respondents have served between 6 and 10 years and about 30%--under 5
years. 50% of the respondents are BA graduates and 100% of those have
industrial background. Their ratings adopted the ratio scale as given in
Table 1 with respect to the importance of evaluation criteria; ratings
used a range of 0-100 with regard to the initial decision-making matrix
[cross product]X.
4.2. Selection of the best supplier
After summarizing the opinions of senior experts and following the
steps of AHP, the weights of evaluation criteria are provided in Table
4. The table also indicates the initial decision-making matrix [cross
product]X and the values of evaluation criteria are described in
intervals. The initial decision-making matrix [cross product]X has been
normalized and weighted initially and the obtained result [cross
product][??] is provided in Table 5. In accordance with the steps of
COPRAS-G, the evaluation of three suppliers is computed and ranking
suppliers for Kalleh Company is finally discovered (Table 6).
The weights of the criteria were determined applying the AHP
method. The assessment results of alternatives are presented in Table 6.
Ranking alternatives applying AHP and COPRAS-G methods are presented in
Tables 5 and 6. Specifically, according to [N.sub.j], ranking obtained
in the procedure of supplier selection is as follows: [Supplier.sub.3]
[??] [Supplier.sub.2] [??] [Supplier.sub.1] It is advised that the
supplier corresponding to the highest utility degree should be selected
as the best one (e.g. [Supplier.sub.3]). The overall results of the
COPRAS-G method and ranking are summarized in Table 6.
5. Generalization
Dynamic business environments lead to selecting the best suppliers
that are very important for companies. The model of supplier selection
is the foundation of supply chain cooperation that seems to be a MCDM
problem involving numerous tasks (evaluation criteria).
The paper has developed a hybrid model of the MCDM method. The
proposed model consists of AHP for weighing eight evaluation criteria
and the COPRAS-G method for evaluating performance. Research focuses on
the problem of selecting a supply company at the national and
international level. The proposed SCM model can also be a guide to other
foreign companies efficiently selecting their suppliers for the
decision-making process.
On the basis of calculated results of AHP and COPRAS-G methods, the
best supplier for Kalleh Company has been verified. By applying
calculation results, ranking obtained in the procedure of supplier
selection is as follows: [Supplier.sub.3] [??] [Supplier.sub.2] [??]
[Supplier.sub.1].
doi: 10.3846/20294913.2012.709472
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of Buildings. Vilnius: Technika.
Zhu, J. 2004. A buyer-seller game model for selection and
negotiation of purchasing bids: extension and new models, European
Journal of Operational Research 154: 150-156.
http://dx.doi.org/10.1016/S0377-2217(02)00697-5
Sarfaraz HASHEMKHANI ZOLFANI. B.Sc. in Industrial Management from
Shomal University of Amol, Iran. M.Sc. in Industrial Engineering-System
Management and Productivity from Shomal University. Works at the
Research Institute of the Internet and Intelligent Technologies, Vilnius
Gediminas Technical University. The member of EURO Working Group OR in
Sustainable Development and Civil Engineering. The author of more than
40 scientific papers presented, published or reviewed at/for
International Conferences and Journals (including ISI-cited
publications). Research interests: performance evaluation, strategic
management, decision-making theory, supply chain management, (fuzzy)
multi-criteria decision making and marketing.
I-Shuo CHEN. Perusing PhD in Business at Trinity College Dublin,
Ireland. Tutor of organizational behaviour at Trinity College Dublin,
Ireland. A reviewer of journals, including Journal of Operational
Research Society, International Journal of Information Technology &
Decision Making, Knowledge-Based Systems, Applied Soft Computing, Annals
of Operations Research, African Journal of Business Management, Social
Behaviour and Personality, etc. Research interests: creativity,
organizational innovation, organizational behaviour, vision, performance
systems and evaluation, TQM and (Fuzzy) MCDM. The articles have been
published in several high level peer reviewed journals (including
ISI-cited publications).
Nahid REZAEINIYA. B.Sc. in Industrial Engineering from Shomal
University of Amol, Iran. M.Sc in Industrial Engineering--planning
program of economic and social systems from Alghadir Institute of higher
education, Tabriz, Iran (2009-2011). The author of 15 scientific papers.
Research interests: performance evaluation, (fuzzy) multi criteria
decision making, decision-making theory and quality management. Part
time teacher at Islamic Azad University.
Jolanta TAMOSAITIENE. PhD, Assoc. Prof. and Vice-Dean of the
Department of Construction Technology and Management at the Faculty of
Civil Engineering, Vilnius Gediminas Technical University, Lithuania.
The member of EURO Working Group OR in Sustainable Development and Civil
Engineering. The author of more than 50 scientific papers presented,
published or reviewed at/for International Conferences and Journals
(including ISI-cited publications). Research interests: construction
technology and organization, strategic management, supply chain
management, administration of construction projects, decision-making and
grey theory.
Sarfaraz Hashemkhani Zolfani (1,2), I-Shuo Chen (3), Nahid
Rezaeiniya (4), Jolanta Tamosaitiene (5)
(1) Research Institute of Internet and Intelligent Technologies,
Vilnius Gediminas Technical University, Sauletekio al. 11, LT-10223
Vilnius, Lithuania
(2) Shomal University, P.O. Box 731, Amol, Mazandaran, Iran
(3) School of Business (Research) Trinity College Dublin, College
Green, Dublin 2, Ireland
(4) Alghadir Institute of Higher Education P. O. Box 5166898691,
Tabriz, Azarbaijan Sharghi, Iran
(5) Department of Construction Technology and Management, Vilnius
Gediminas Technical University, Sauletekio al. 11, LT-10223 Vilnius,
Lithuania
E-mails: (1,2)
[email protected]; (3)
[email protected]; (4)
[email protected]; (5)
[email protected]
(corresponding author)
Received 12 February 2012; accepted 03 July 2012
Table 1. The ratio scale and definition
of AHP (Saaty 1990)
Intensity of Definition
importance
1 Equal importance
3 Somewhat more important
5 Much more important
7 Very much more important
9 Absolutely more important
2, 4, 6, 8 Intermediate values
Table 2. Recent applications for AHP, COPRAS and COPRAS-G
MCDM method Reference Considered problem
AHP Medineckiene et al. Sustainable construction
(2010)
Podvezko et al. (2010) Evaluation of contracts
Sivilevicius (2011a) Modelling transport system
Sivilevicius (2011b) Quality of technology
Fouladgar et al. (2011) Prioritizing strategies
Zavadskas et al. Enterprises management
(2011a)
Zavadskas et al. (2012) Selecting a project manager
COPRAS Chatterjee et al. Material selection based on
(2011) COPRAS and EVAMIX methods
Podvezko (2011) Comparative analysis of MCDM
methods (SAW and COPRAS)
COPRAS-G Zavadskas et al. Assessment of the indoor
(2011b) environment
Hashemkhani Zolfani Locating forest roads
et al. (2011)
Chatterjee and Using COPRAS-G method
Chakraborty (2012)
Table 3. Demographic information
Variable Items N Percentage
1. Sex (1) Male 7 70%
(2) Female 3 30%
2. Age (1) Under 30 2 20%
(2) 31-40 6 60%
(3) 41-50 2 20%
(4) Above 51 0 0%
3. Service (1) Under 5 3 30%
tenure (2) 6-10 6 60%
(3) 11-20 1 10%
(4) Above 21 0 0%
4. Education (1) Vocational 0 0%
background (2) Bachelor 5 50%
(3) Master 4 40%
(4) Doctoral 1 10%
5. Occupational (1) Academic 0 0%
background (2) Industrial 10 100%
(3) Governmental 0 0%
Table 4. The initial decision-making matrix and the
values of evaluation criteria described in intervals
Criterion Optimal Weights
direction
[cross product] min 0.160
[x.sub.1]
[cross product] max 0.158
[x.sub.2]
[cross product] min 0.060
[x.sub.3]
[cross product] max 0.150
[x.sub.4]
[cross product] max 0.135
[x.sub.5]
[cross product] max 0.178
[x.sub.6]
[cross product] max 0.045
[x.sub.7]
[cross product] max 0.114
[x.sub.8]
[q.sub.i] = l
Criterion Initial decision making matrix
Supplier
[S.sub.1] [S.sub.2] [S.sub.3]
[cross product] [60; 70] [80; 90] [40; 60]
[x.sub.1]
[cross product] [70; 80] [90; 95] [60; 70]
[x.sub.2]
[cross product] [80; 90] [70; 80] [40; 60]
[x.sub.3]
[cross product] [90; 95] [80; 90] [70; 80]
[x.sub.4]
[cross product] [40; 60] [60; 70] [70; 80]
[x.sub.5]
[cross product] [60; 70] [80; 90] [70; 80]
[x.sub.6]
[cross product] [80; 90] [70; 80] [60; 70]
[x.sub.7]
[cross product] [70; 80] [90; 95] [80; 90]
[x.sub.8]
Table 5. Normalized and weighted-normalized
decision-making matrix and the values of evaluation
criteria described in intervals
Normalized decision
Criterion making matrix
Supplier
[S.sub.1] [S.sub.2] [S.sub.3]
[[??].sub.1n];[[??].sub.1n] [0.300; [0.400; [0,200;
0.350] 0.450] 0,300]
[[??].sub.2n];[[??].sub.2n] [0.297; [0.386; [0,253;
0.342] 0.405] 0,297]
[[??].sub.3n];[[??].sub.3n] [0.367; [0.333; [0,183;
0.417] 0.367] 0,283]
[[??].sub.5n];[[??].sub.4n] [0.353; [0.313; [0,273;
0.373] 0.353] 0,313]
[[??].sub.5n];[[??].sub.5n] [0.207; [0.311; [0,363;
0.311] 0.363] 0,415]
[[??].sub.6n];[[??].sub.6n] [0.264; [0.354; [0,309;
0.309] 0.399] 0,354]
[[??].sub.7n];[[??].sub.7n] [0.356; [0.311; [0,267;
0.400] 0.356] 0,311]
[[??].sub.8n];[[??].sub.8n] [0.272; [0.351; [0,316;
0.316] 0.368] 0,351]
Criterion Weighted-normalized decision
making matrix
Supplier
[S.sub.1] [S.sub.2] [S.sub.3]
[[??].sub.1n];[[??].sub.1n] [0.048; [0.064; [0.032;
0.056] 0.072] 0.048]
[[??].sub.2n];[[??].sub.2n] [0.047; [0.061; [0.040;
0.054] 0.064] 0.047]
[[??].sub.3n];[[??].sub.3n] [0.022; [0.020; [0.011;
0.025] 0.022] 0.017]
[[??].sub.5n];[[??].sub.4n] [0.053; [0.047; [0.041;
0.056] 0.053] 0.047]
[[??].sub.5n];[[??].sub.5n] [0.028; [0.042; [0.049;
0.042] 0.049] 0.056]
[[??].sub.6n];[[??].sub.6n] [0.047; [0.063; [0.055;
0.055] 0.071] 0.063]
[[??].sub.7n];[[??].sub.7n] [0.016; [0.014; [0.012;
0.018] 0.016] 0.014]
[[??].sub.8n];[[??].sub.8n] [0.031; [0.040; [0.036;
0.036] 0.042] 0.040]
Table 6. Evaluation of utility degree
Supplier [S.sub.1] [S.sub.3] [S.sub.3]
[P.sub.j] 0.249 0.281 0.25
[R.sub.j] 0.075 0.094 0.054
[Q.sub.j] 0.318 0.336 0.347
[N.sub.j] 91.64% 96.82% 100%
