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Journal of Applied Physics and Engineering Vol.1, No.3 (2016) 32–46
32
DEVELOPMENT OF A FRAMEWORK FOR
MANUFACTURING SUPPLY CHAIN PERFORMANCE
MANAGEMENT
K.Selvaraj1*
, P.Janarthanan1, P.Manuneethi Arasu
1, P.Krishnan
1, N.Senniangiri
2
1Department Of Mechanical Engineering, KSR College Of Engineering, Tiruchengode – 637 215.
2Department Of Mechanical Engineering, Nandha College Of Technology, Erode– 638052.
*Corresponding Author
Received: 13/11/2015, Revised: 11/01/2016 and Accepted: 10/03/2016
Abstract
In recent decades competitiveness is the major issue for all the manufacturing industries. The performance of the companies should be improved to withstand against stiff competitions. The overall performance of an industry can be improved by evaluating and analysing their current performance with the performance level of their counterparts. Supply chain management maintains a good relationship between the customers and manufacturers. In customer’s point of view, performance level is rated, based on product quality, time, cost, service, relationship and so on.
The aim of the paper is to collect feedbacks about the various parameters from the customers and sorting out the key parameters is ranked based on priority. The feedbacks recorded by the customers will be vague and uncertain. All the parameters are evaluated and the alternative solutions are collected for each parameter and recorded. The particular parameters with a very low rank as compared to other parameters will be given more priority and fuzzy tools like Delphi, AHP, TOPSIS and QFD can be utilized to study by these key parameters and alternative solutions can be obtained to wipe out the problems, thereby improving the performance index. In this project work, the above mentioned tools are being used
to study the problems faced by a forging industry and resolving it.
*Reviewed by ICETSET'16 organizing committee
Index Terms- Performance measurement, Manufacturing companies, Fuzzy Delphi, Analytical Hierarchy Process, TOPSIS.
I .Introduction
Now a days manufacturing industries are finding it really difficult to withstand the competitiveness the global
market. Various factors such as cost, quality and time to delivery of products, service and relationships with
customers are of major concern. The company is identified for this paper is a primary manufacturing industry
that produces metal castings and forged products. SCM organizes and manages the whole process of activities of
supply network from customers through manufacturers. The success of an industry can be clearly depicted based
on the length of their chain and it is possible by adopting an effective SCM achieve customer satisfaction. Fuzzy tools are used to evaluate and improve the performance criteria’s. Fuzzy tools such Delphi to shortlist the
performance criteria, AHP used to rank the criteria, TOPSIS used to rank the alternative solutions.
SCM is a strategy where business partners jointly commit to work closely together, to bring greater value to the consumer and/or their customers for the least possible overall supply cost. This coordination includes that of
order generation, order taking and order fulfilment/distribution of products, services or information. Effective
supply chain management enables business to make informed decisions along the entire supply chain, from
acquiring raw materials to manufacturing products to distributing finished goods to the consumers. At each link,
businesses need to make the best choices about what their customers need and how they can meet those
requirements at the lowest possible cost. The supply chain network demand problem consists of making the
above-mentioned decisions to satisfy customer demands while minimizing the sum of strategic, tactical, and
operational costs. The importance of the interactions between these decisions, important benefits can be
obtained by treating the network as a whole and considering its various components simultaneously.
Supplier Relationship Management (SRM) is the discipline of strategically planning for, and managing, all
interactions with third party organizations that supply goods and/or services to an organization in order to
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maximize the value of those interactions. In practice, SRM entails creating closer, more collaborative
relationships with key suppliers in order to uncover and realize new value, and reduce risk.
Customer Relationship Management (CRM) is a widely implemented model for managing a company’s
interactions with customers, clients, and sales prospects. It involves using technology to organize, automate, and
synchronize business processes principally sales activities, but also those for marketing, customer service, and
technical support. The overall goals are to find, attract, and win new clients, service and retain those the
company already has, entice former clients to return, and reduce the costs of marketing and client service.
Customer relationship management describes a company-wide business strategy including customer-interface departments as well as other departments. Measuring and valuing customer relationships is critical to
implementing this strategy.
2. Proposed Hybrid Fuzzy Methodology
The proposed methodology consists of four stages to select network uncertainty metrics and to apply the
fuzzy Delphi method, fuzzy AHP and Fuzzy Hierarchical TOPSIS techniques. These stages are shown in Fig. 1.
2.1 Network Uncertainty Metrics
Grounded on management, production and operations literature, the metrics of network uncertainty
applied in this research originate from manufacturing product, service and relationship sources, as summarised
in Table 1. These widely studied sources of uncertainty plague supply chains, business environments and
industrial networks, and their use in the framework is to serve as a baseline for firms to evaluate uncertainty of
industrial performances. Manufacturing product uncertainty refers to volatility in product performances caused
by unreliable manufacturing and production processes. Relationship uncertainty is reflected in the adaptability
of customer to specification changes at short notice and predictability of customer performance for next business
cycles.
2.2 Fuzzy Delphi method
Following and steps for executing the fuzzy Delphi method were conceptualised as follow:
Step 1: Organize an appropriate panel of experts and administer a questionnaire to allow the experts express
their options regarding the significance of each criterion in the possible criteria set S in a range from 1 to 10. A
score is then denoted as where the index of criteria i is rated by expert k.
Step 2: Organize expert opinions collected from questionnaires and determine the triangular fuzzy numbers
(TFNs) for index for each criterion i. Li indicates the minimum of all the experts’ rating
value as:
(1)
is the geometric mean of all the criteria ratings for criterion i. It is obtained through Eq. (2).
(2)
indicates the maximum value of experts’ rating and is determined as follows:
(3)
A fuzzy number is a special fuzzy set, such that
, where the value of x lies on the real line
. We define a fuzzy number Ầ on R to be a triangular fuzzy number and the membership function
can be described as:
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(4)
Where , L and U stand for the lower and upper value of the support for Ầ respectively, and M
denotes the most promising value.
Step 3: Once the triangular fuzzy numbers are determined for all the criteria, the Centre of Area approach is
used to defuzzify the triangular fuzzy number of each evaluation criterion to definite value as:
(5)
Step 4: Screen out the evaluation criteria by setting the threshold α. The principle of screening is as follow:
If then No. i criterion is selected for the evaluation criteria:
If then delete I criterion (6)
C. Fuzzy AHP
Next, the importance of a main criteria in relation to sub criteria was evaluated using Fuzzy AHP as follows:
Step 1: Construct pairwise comparison matrices from the panel of experts. Linguistic variables are then used to
construct a matrix per expert as shown in Eq. (7). For simplicity, reference to different experts is omitted (see
Step 2):
(7)
Where
Step 2: Since the evaluation of different experts would lead to different matrices, the opinions of different
experts are integrated to form one synthetic pairwise comparison matrix. Obviously, this step can be skipped if
there is only one expert in Step 1. The elements of the synthetic pairwise comparison matrix are calculated by using the geometric mean method proposed by specifically for Fuzzy AHP: if criterion i is
relatively less important to criterion j.
(8)
The superscript in Eq. (8) refers to different experts where there is a total of E experts.
Step 3: Make use of the synthetic pairwise comparison matrix from Step 2 to define the fuzzy geometric
mean and fuzzy weights of each criterion ) using Eqs. (9) and (10) respectively:
(9)
(10)
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Step 4: Since the calculation so far involves linguistic variables, the next step involves defuzzifying the
different weights from Step 3 to form meaningful values for analysis (e.g., ranking).
Again, the COA method is used for defuzzification. Assume the fuzzy weights of each criterion can be
expressed in the following form:
(11)
Where represent the lower, middle and upper values of the fuzzy weight of the ith criterion.
Then, the non-fuzzy (i.e., defuzzified) is given as:
(12)
D. The fuzzy TOPSIS methodology
To evaluate the criteria’s of a set of alternative solutions, a fuzzy decision matrix , is constructed based on a given set of categories and criteria. This requires l alternatives
and n main categories.
Each main category has criteria where the total number of criteria is equal to . In addition,
represents the value of the criterion within main category of the alternative, which can be
crisp data or appropriate linguistic variables which can be further represented by fuzzy numbers
(e.g., ). A hierarchical MCDM problem can be concisely expressed in a fuzzy
decision matrix as:
Where is the fuzzy evaluation score of alternative with respect to criterion
evaluated by expert from a total of S experts and
In general, the criteria can be classified into two categories: benefit and cost. The benefit criterion means
that a higher value is better while the cost criterion is valid for the opposite. The data of the decision matrix
comes from different sources and it is necessary to normalize in order to transform it into a dimensionless matrix, which allows for the comparison of various criteria. In this research, the normalized fuzzy decision
matrix is denoted by shown as:
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(14)
The normalization process can then be performed by the following fuzzy operations:
(15)
Where and represent the largest and the lowest value of each criterion respectively. The weighted
fuzzy normalized decision matrix is shown as:
Where (16)
is the final weight score for each criterion which is the product of the main category weight score and the
criterion weight score with respect to the corresponding main category as follows:
(17)
Where and denote the ith main category weight score and the criterion weight score respectively. Both
and are obtained through the Fuzzy AHP analysis method fuzzy addition principle is used to aggregate
the values within each main criterion as follows: discussed in section
Fig.1
Main criteria Sub criteria Performance measurement
Product performance Quality Consistent product properties and processibility
Packing Quality of packing: type & quality meets your
requirements
New product Timely commitment on new and improved products
Product appearancence Aesthetically good
Complaint Promptness in handling & providing timely response
Utilization Percentage of excess or lack of that particular
resource within a period
Efficiency Percentage of actual production time to the planed
time
Accuracy Percentage of accurate goods delivered to clients
Manufacturing cost Labour, maintenance, cutting tools, scrapes, and
rework costs
Manufacturing type The ability to deal with different production process
Flexibility The ability to meet customer requests for different
product types in a variety of volumes
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Labour Performance of workers
Service Order processing Timely response
Delivery On time, as requested and in satisfactory condition
Technical service Accessibilities, responsiveness and effectiveness
Supply flexibility Response to urgent and special delivery requirements
Documentation Documents are received on time
Price Value for money
Technical support Improve product characteristics and process
Quick responsiveness Activeness
Supply capacity Fulfill your orders
Relationship Supplier integrity Credibility and integrity
Personal relationships People to people relationships with your supplier
Listening Listening and responding to your needs
Customer visits Value of visit to our plant
Supply constraint Overcome up struggles
Buyer supplier constraint Economic flexibility
Supplier profile Obey industrial ethics
TABLE-1
(18)
The results of Eq. (16) can be summarized as: Subsequently, the fuzzy addition principle is used to aggregate
the values within each main criterion as follows:
(19)
The matrix is thus converted into the final weighted normalized fuzzy decision matrix
,
(20)
This addition operation is important as the final weighted normalized fuzzy decision matrix becomes a one
layer fuzzy TOPSIS model after the calculation of the final weight score for each criterion. Therefore, the
hierarchical structure can be reflected only when aggregation of the weighted values within each main category
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is conducted. Now, let and denote the fuzzy positive ideal solution (FPIS) and fuzzy negative
ideal solution (FNIS) respectively. According to the weighted normalized fuzzy-decision matrix, we have:
(21)
Where and are the fuzzy numbers with the largest and the smallest generalized mean respectively. The
generalized mean for the fuzzy number , i is defined as:
(22)
For each column i, the greatest generalized mean of and the lowest generalized mean of can then be
used to derive values for FPIS ) and the FNIS ) respectively. Then, the distances of each
alternative from
and can be calculated by the area compensation method as
(23)
(24)
By combining the difference distances and , the relative closeness index is calculated as follows:
(25)
Using the index value, the set of alternatives can be ranked from the most preferred to the least preferred
feasible solutions.
III. Case study
This section presents a case study of Foundry division, to illustrate how the proposed framework can be
applied to evaluate the performance activities.
A. Case Background
The company is identified for this paper is a primary manufacturing industry that produces metal
castings and forged products. A foundry is a factory that produces metal castings. Metals are cast into shapes by
melting them into a liquid, pouring the metal in a mold, and removing the mold material or casting after the
metal has solidified as it cools. The most common metals processed are aluminium and cast iron. However,
other metals, such as bronze, brass, steel, magnesium, and zinc, are also used to produce castings in foundries.
In this process, parts of desired shapes and sizes can be formed.
B. Criteria Selection with Fuzzy Delphi Method
To begin the evaluation, the fuzzy Delphi method was applied to derive evaluation criteria for foundry
from the network uncertainty metrics listed in Table 2. The objective was to establish an appropriate list of
evaluation criteria representing a consensus of experts’ opinion on sources of network uncertainty. A
questionnaire was prepared to evaluate the importance of each criteria and distributed to the seven members of
foundry management team. Table 2 shows the minimum, geometric mean, and maximum values of each item
with respect to the network uncertainty metrics. These values were then converted to TFNs.
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Fuzzy
Numbers
Linguistic
Variables
Triangular
Fuzzy
Numbers
9
8
7
6
5
4
3
2
1
Extremely High
Very High
High
Medium High
Medium
Medium Low
Low Very Low
Extreme Low
(8, 9, 10)
(7, 8, 9)
(6, 7, 8)
(5, 6, 7)
(4, 5, 6)
(3, 4, 5)
(2, 3,4)
(1, 2, 3)
(1, 1, 1)
was then calculated by defuzzifying the TFNs through the COA method outlined in Section 2.2 and the results are displayed in Table 2. In order to develop a comprehensive evaluation hierarchical model that reflects
the complexity of evaluating the uncertainty of criteria’s that deliver an industrial performances, the geometric mean was set as the threshold to select an appropriate number of criteria. Through this process, 28 evaluation
items were removed and 14 items were used as the eventual assessment criteria.
C. Weights Estimation with Fuzzy AHP
After selecting the evaluation criteria, it was essential to know how important one evaluation category was
over other criteria. In other words, decision makers have to determine the weights between the main evaluation
categories and the associated criteria. The different weights of evaluation categories and their associated criteria
were calculated using the fuzzy AHP method discussed in Section II.C. Using the demand uncertainty category
as an example, the fuzzy evaluation matrix was constructed by the pairwise comparison of three criteria using
TFNs, as shown in Table 3.
Fuzzy
Numbers
Linguistic
Variables
Triangular
Fuzzy
Numbers
9
8
7
6
5
4
3
2
1
Perfect
Absolute
Very good
Fairly good
Good
Preferable
Not bad
Weak advantage
Equal
(8, 9, 10)
(7, 8, 9)
(6, 7, 8)
(5, 6, 7)
(4, 5, 6)
(3, 4, 5)
(2, 3,4)
(1, 2, 3)
(1, 1, 1)
Using the table, the fuzzy geometric mean and fuzzy weights of three evaluation criteria were then calculated. Eq. (9) was then used to obtain the fuzzy weights of criteria for participants from foundry
management team, i.e.
r1 = (a11 × a12 × a13)1/3
=(1×4.949×5.233)1/3,(1×5.958×6.236)1/3, (1×6.964×7.238)1/3
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= (2.959, 3.337, 3.694)
Similarly, other values for ri can be obtained as follows:
r2 = (0.524, 0.552, 0.587)
r3 = (0.264, 0.291, 0.327)
The weight of each criterion was then calculated using Eq. (10) as follow,
w1 = r1 × (r1 + r2 + r3) -1
= (2.959, 3.337, 3.694) × (1/ (3.694 + 0.587 + 0.327), 1/ (3.337 + 0.552 + 0.291), 1/ (2.959 +
0.524 + 0.264))
= (0.642, 0.798, 0.986)
Likewise, the remaining fuzzy weights (w2 and w3) of the demand category were then obtained.
w2 = (0.114, 0.132, 0.157)
w3 = (0.057, 0.070, 0.087)
Using the COA method (Eq. (12)), the non-fuzzy weight value for each uncertainty metric was then
calculated. Using criterion C11 as an example, the calculation process was performed as follows:
BNPW1 = (0.986–0.642) + (0.798–0.642) + 0.642
3
= 0.809
The fuzzy weights of the remaining evaluation criteria and their normalised non-fuzzy values are displayed in
Table 4.
Using the same approach, the relative importance weights with respect to the main values propositions of
the industrial performance evaluation approach and their associated criteria were computed and the results are
summarized in Table 5.
Main criteria Sub criteria Min Geometri
c mean
Max Gi Ave
Product
performance
Quality 7 8.41 10 8.47 7.84
Packing 7 8.41 10 8.47
New product 6 7.98 10 7.99
Product appearancence 6 8.26 10 8.09
Complaint 6 8.12 10 8.04
Utilization 6 8.12 10 8.04
Efficiency 5 7.21 10 7.40
Accuracy 6 7.56 9 7.52
Manufacturing cost 6 8.26 10 8.09
Manufacturing type 5 6.96 9 6.99
Flexibility 5 7.11 9 7.04
Labour 5 7.11 9 7.04
Service Order processing 7 8.41 10
8.47 7.69
Delivery 7 8.70 10 8.57
Technical service 7 7.83 10 7.94
Supply flexibility 6 7.11 9 7.04
Documentation 6 7.70 9 7.57
Price 6 7.52 10 7.51
Technical support 6 7.25 9 7.08
Quick responsiveness 6 7.11 9 7.04
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C11 C12 C13
C11 1 1 1 4.949 5.958 6.964 5.233 6.236 7.238
C12 0.144 0.168 0.202 1 1 1 5.477 6.481 7.483
C13 0.138 0.160 0.191 0.134 0.154 0.183 1 1 1
TABLE 3
Performance factors Lwi Mwi Uwi BNP
W1
Rank
Product 0.642 0.798 0.986 0.809 1
Service 0.114 0.132 0.157 0.134 2
Relationship 0.057 0.070 0.087 0.071 3
TABLE 4
Main criteria Weights Sub criteria BNPW1 Rank
C1 Product performance
factor
0.809 C11Quality 0.385 7
C12 Packing 0.389 6
C13 New product 0.403 5
C14 Product appearance 0.417 4
C15 Complaint 0.511 3
C16 Accuracy 0.585 2
C17 Manufacturing cost 1.029 1
C2 Service performance
factor
0.134 C21 Order processing 0.713 8
C22 Delivery 0.126 10
C23 Supply flexibility 0.128 9
C24 Supply capacity 0.053 11
C3 Relationship performance
factor
0.071 C31 Supplier integrity 0.734 12
C32 Personal relationships 0.216 13
C33 Listening 0.066 14
TABLE 5
The final weight scores for the evaluation criteria were obtained by calculating the performance of criteria
weight scores with respect to the corresponding evaluation category and the weight scores of its associated
evaluation category. The final weight scores give an indication of the important factors that influence the
industrial performance evaluation adoption decision.
Supply capacity 6 7.96 10 7.99
Relationship Supplier integrity 6 7.96 10 7.99 7.39
Personal relationships 6 7.96 10 7.99
Listening 6 7.54 10 7.85
Customer visits 5 7.11 9 7.04
Supply constraint 5 6.81 9 6.94
Buyer supplier
constraint 5 6.83 9
6.94
Supplier profile 5 6.96 9 6.99
TABLE-2
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D.Fuzzy TOPSIS
Next, questionnaires were given to four foundry customers for the evaluation of the alternative foundry
performance value propositions. Participants were asked to give ratings to the alternative value propositions
with respect to all the evaluation criteria. The qualitative explanation of rating levels and their corresponding
TFNs are described below.
Fuzzy
Numbers
Linguistic
Variables
Triangular
Fuzzy
Numbers
9
8
7
6 5
4
3
2
1
Extremely High
Very High
High
Medium High Medium
Medium Low
Low
Very Low
Extreme Low
(8, 9, 10)
(7, 8, 9)
(6, 7, 8)
(5, 6, 7) (4, 5, 6)
(3, 4, 5)
(2, 3,4)
(1, 2, 3)
(1, 1, 1)
Value
proposition d
+ d
- CC Ranking
Product
A1 4.367 2.666 0.379 4
A2 4.145 2.897 0.411 3
A3 4.093 2.942 0.418 2
A4 4.098 2.943 0.418 1
Service
A1 3.277 0.731 0.182 12
A2 3.259 0.749 0.187 11
A3 3.170 0.838 0.209 9
A4 3.175 0.833 0.208 10
Relationship
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Values from the responses were averaged to integrate the fuzzy judgement values of the different decision
makers regarding the same evaluation criteria. The results were then used to construct a hierarchical decision
making matrix D as illustrated in the appendix (Table A1). The hierarchical decision-making matrix was then
normalized using Eq. (15). The result is displayed in the appendix (Table A2).
Through computing the product, service, relationship of the normalized hierarchical decision matrix and
the final weight scores for each evaluation criterion, the weighted normalized fuzzy decision matrix is
obtained as presented in the appendix (Table A3). Since each element in is a fuzzy number, its generalized
mean was then calculated according to Eq. (22). The largest generalized mean and the smallest
generalized mean of each main criterion were then selected as FPIS and FNIS respectively. Next,
the difference distances of each of the alternatives was calculated using Eqs. (23) and (24). Finally, combining the difference distances, the relative closeness index for each alternative solution was
obtained. The results are presented in Table 6, together with the corresponding rankings based on the index
values. Then sum of three main criteria closeness coefficient values and customers ranking are presented in
Table 7.
Closeness Coefficient
Produ
ct
Servi
ce
Relations
hip
Sum Rank
ing
A
1
0.379 0.182 0.272 0.833 4
A
2
0.411 0.187 0.240 0.838 3
A
3
0.418 0.209 0.267 0.894 2
A
4 0.418 0.208 0.286 0.912 1
A1 2.192 0.817 0.272 6
A2 2.286 0.723 0.240 8
A3 2.207 0.802 0.267 7
A4 2.147 0.862 0.286 5
TABLE 6
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TABLE 7
3. Conclusion
A framework of performance measurement system, with an example of its application in a
manufacturing company has been presented. The application of the model to evaluate the performance shows
that the effects of different quantitative and qualitative factors on performance can be aggregated into a single
indicator. The proposed system uses the fuzzy Delphi and the Analytical Hierarchy Process (AHP) to identify
the performance and to evaluate alternative solutions / options using the fuzzy Technique for Order of
Preference by Similarity to Ideal Solution (fuzzy TOPSIS) technique. Based on the model output, the proposed
method provided an evaluation of performance of the different departments of the company. The measures were
performed for each department to diagnose the strengths and weakness of the performance indicator. By
addressing the individual weakness and finding complementary needs, the firms will increase the competitive
advantage. The approach has been successfully applied in the manufacturing environment.
4. References
[1] M. Adel El-Baz (2011) “Fuzzy performance measurement of a supply chain in manufacturing companies” Expert Systems with Applications Vol.38 pp.6681–6688.
[2] Xiaojun Wang and Christopher Durugbo (2013) “Analysing network uncertainty for industrial product-
service delivery: A hybrid fuzzy approach” Expert Systems with Applications Vol.40 pp.4621–4636.
[3] Metin Celik, Selcuk Cebi, Cengiz Kahraman and I.Deha Er (2009) “Application of axiomatic design and
TOPSIS methodologies under fuzzy environment for proposing competitive strategies on Turkish container
ports in maritime transportation network” Expert Systems with Applications Vol.36 pp.4541–4557.
[4] Chen-Tung Chen (2000) “Extensions of the TOPSIS for group decision-making under fuzzy environment”
Fuzzy Sets and Systems Vol.114 pp.1-9.
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Table A1
The normalised fuzzy decision matrix
Performance
criteria’s
CUSTOME
R A
CUSTOMER
B
CUSTOME
R C
CUSTOME
R D
Product C11 7 8 9 8 9 10 6 7 8 6 7 8
C12 6 7 8 7 8 9 7 8 9 7 8 9
C13 6 7 8 6 7 8 7 8 9 7 8 9
C14 6 7 8 6 7 8 8 9 10 8 9 10
C15 7 8 9 6 7 8 8 9 10 6 7 8
C16 7 8 9 7 8 9 7 8 9 7 8 9
C17 5 6 7 7 8 9 6 7 8 7 8 9
Service C21 6 7 8 6 7 8 7 8 9 7 8 9
C22 7 8 9 8 9 10 8 9 10 8 9 10
C23 6 7 8 6 7 8 7 8 9 7 8 9
C24 6 7 8 7 8 9 8 9 10 7 8 9
Relationshi
p C31 7 8 9 6 7 8 7 8 9 8 9 10
C32 7 8 9 6 7 8 6 7 8 6 7 8
C33 7 8 9 7 8 9 8 9 10 6 7 8
Table A2
The weighted normalised fuzzy decision matrix
Performance
criteria’s CUSTOMER A CUSTOMER B CUSTOMER C CUSTOMER D Wt.
Product C1
1 0.7 0.8
0.
9 0.8 0.9 1 0.6 0.7 0.8 0.6 0.7 0.8 0.385
C1
2 0.6 0.7
0.
8 0.7 0.8
0.
9 0.7 0.8 0.9 0.7 0.8 0.9 0.389
C1
3 0.6 07
0.
8 0.6 0.7
0.
8 0.7 0.8 0.9 0.7 0.8 0.9 0.403
C1
4 0.6 0.7
0.
8 0.6 0.7
0.
8 0.8 0.9 1 0.8 0.9 1 0.417
C1
5 0.7 0.8
0.
9 0.6 0.7
0.
8 0.8 0.9 1 0.6 0.7 0.8 0.511
C1
6 0.7 0.8
0.
9 0.7 0.8
0.
9 0.7 0.8 0.9 0.7 0.8 0.9 0.585
C1
7 0.5 0.6
0.
7 0.7 0.8
0.
9 0.6 0.7 0.8 0.7 0.8 0.9 1.029
Service C2
1 0.6 0.7
0.
8 0.6 0.7
0.
8 0.7 0.8 0.9 0.7 0.8 0.9 0.713
C2
2 0.7 0.8
0.
9 0.8 0.9 1 0.8 0.9 1 0.8 0.9 1 0.126
C2
3 0.6 0.7
0.
8 0.6 0.7
0.
8 0.7 0.8 0.9 0.7 0.8 0.9 0.128
C2
4 0.6 0.7
0.
8 0.7 0.8
0.
9 0.8 0.9 1 0.7 0.8 0.9 0.053
Relationship C3
1 0.7 0.8
0.
9 0.6 0.7
0.
8 0.7 0.8 0.9 0.8 0.9 1 0.734
C3
2 0.7 0.8
0.
9 0.6 0.7
0.
8 0.6 0.7 0.8 0.6 0.7 0.8 0.216
C3
3 0.7 0.8
0.
9 0.7 0.8
0.
9 0.8 0.9 1 0.6 0.7 0.8 0.066
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Table A3
The weighted normalised fuzzy decision matrix
Performance
criteria’s CUSTOMER A CUSTOMER B CUSTOMER C CUSTOMER D
Product C11 0.27
0 0.308
0.34
7 0.308 0.347 0.385 0.231 0.270 0.308 0.231 0.270 0.308
C12 0.23
3 0.272
0.31
1 0.272 0.311 0.350 0.272 0.311 0.350 0.272 0.311 0.350
C13 0.24
2 0.282
0.32
2 0.242 0.282 0.322 0.282 0.322 0.363 0.282 0.322 0.363
C14 0.25
0 0.292
0.33
4 0.250 0.292 0.334 0.334 0.375 0.417 0.334 0.375 0.417
C15 0.35
8 0.409
0.46
0 0.307 0.358 0.409 0.409 0.460 0.511 0.307 0.358 0.409
C16 0.41
0 0.468
0.52
7 0.410 0.468 0.527 0.410 0.468 0.527 0.410 0.468 0.527
C17 0.51
5 0.617
0.72
0 0.720 0.823 0.926 0.617 0.720 0.823 0.720 0.823 0.926
Service C21 0.42
8 0.499
0.57
0 0.428 0.499 0.570 0.251 0.185 0.128 0.251 0.185 0.128
C22 0.83
1 0.809
0.78
6 0.809 0.786 0.764 0.809 0.786 0.764 0.809 0.786 0.764
C23 0.85
2 0.829
0.80
6 0.852 0.829 0.806 0.829 0.806 0.783 0.829 0.806 0.783
C24 0.93
7 0.927
0.91
7 0.927 0.917 0.907 0.917 0.907 0.897 0.927 0.917 0.907
Relationshi
p C31
0.51
4 0.587
0.66
1 0.440 0.514 0.587 0.514 0.587 0.661 0.587 0.661 0.734
C32 0.72
0 0.684
0.64
9 0.758 0.720 0.684 0.758 0.720 0.684 0.758 0.720 0.684
C33 0.91
0 0.897
0.88
5 0.910 0.897 0.885 0.897 0.885 0.872 0.922 0.910 0.897
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