development of a framework for manufacturing supply chain … · 2016. 5. 4. · south asian...

South Asian Journal of Engineering and Technology Vol.2, No.23 (2016) 32 – 46

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Development of A Framework For Manufacturing Supply Chain

Performance Management

K.Selvaraja, P.Janarthanan

a, P.Manuneethi Arasu

a, P.Krishnan

a, N.Senniangiri

b

b Department Of Mechanical Engineering, KSR College Of Engineering, Tiruchengode – 637 215.

b Department Of Mechanical Engineering, Nandha College Of Technology, Erode– 638052.

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.

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

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.


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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:

(4)


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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)

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:


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(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:

(14)


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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


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=(1×4.949×5.233)1/3,(1×5.958×6.236)1/3, (1×6.964×7.238)1/3

= (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


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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

Technical support 6 7.25 9 7.08

Quick responsiveness 6 7.11 9 7.04

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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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.

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


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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

TABLE 7

Relationship

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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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