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Asia Pacific Journal of Research ISSN (Print) : 2320-5504

ISSN (Online) : 2347-4793

www.apjor.com Vol: I. Issue XL, June 2016

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DESIGNING VENDOR SELECTION FRAMEWORK USING FUZZY LOGIC

Sonu Verma1#

, Dr Kavita Chauhan1, Greeshma P Rao

2

1#Research Scholar, Centre for Management Studies, Jamia Millia Islamia University, New Delhi.

1Associate Professor, Centre for Management Studies, Jamia Millia Islamia University, New Delhi.

2 Post Graduate Student, Indian Institute of Foreign Trade, New Delhi.

ABSTRACT

An industry’s success depends on product cost optimization and the above goal can be achieved only when the supplier

selection is error free and efficient. This problem of the supplier selection is multi-objective and involves both qualitative and

quantitative factors. The problem is made highly complex by these factors and their interdependencies. The issue of supplier

selection is found to be a fundamental operation in the supply chain.

A fuzzy expert decision support system has been developed, in this study, for the purpose of solving the multi-objective supplier

selection problem for automobile sector. To ensure relevance , considering only the sector specific factors and then simulating

these factors with the data derived from the field experts was adopted for the fuzzy based model. Furthermore, the validation of

the above developed model was done by TOPSIS and Industry’s perception of the suppliers.

Keywords: Supply chain Management; Fuzzy Logic; Automobile Sector; TOPSIS; Vendor Selection Framework.

Acknowledgement: This research work is a part of the thesis to be submitted by the corresponding author for Ph.D

degree awarded by the Centre for Management Studies, Jamia Millia Islamia University, New Delhi

1.Introduction:

In today‗s accelerating world economy, where the advancements in technology and Internet channels have not limited the

access of businesses local boundaries, manufacturing companies are facing the market realities like shrinking the product

lifecycles and steep price erosion more than ever before .The customers are expecting different product specifications,

higher product quality at a lower product price and faster response. In an effort to cope with the above demands, the firms try

and work with the suppliers who can assure the best product quality, at reasonable cost and desired flexibility. This condition

drives them to continually cut costs, focus on core competencies (outsource some or all of their production), increase efforts to

improve the supply chain execution and to leverage the supply base which has become more critical to achieve a competitive

advantage through robust supplier selection process. The overall objective of the supplier selection process is to maximize

overall value to the manufacturer.

The cost of purchasing raw materials and component parts is significant in most manufacturing companies. Purchased

products and services account for more than 60% of an average organization‗s total costs. Accordingly, improvement in the

procurement process can help organization to increase their profits as well as the relationship quality with their suppliers which

can be deemed as one of the significant criteria in the evaluation of organizations‘ economic performance. Selection of the

suppliers is considered a critical process, cumbersome and lengthy process. In fact, supplier selection is purchasing‘s most

important responsibility. Later, Weber et al. (1991) made the same point by stating, ―In today‗s competitive operating

environment it is impossible to successfully produce low cost, high quality products without satisfactory supplier. Thus one of

the important purchasing decisions is the selection of suppliers. More recently, with emergence of the concept of supply chain




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management, more and more scholars and practitioners have realized that supplier selection was a vehicle that can be used to

increase the competitiveness of the entire supply. The selections of suppliers are strategic decisions to be made by an

organization with long-term or short term implications. These decisions are highly complex and the most difficult

responsibility of the organization and depends on a wide range of criteria such as price, quality, reliability, service, track record,

adequate financial resources and ability to comply with the delivery requirements etc. How an organization weighs up the

importance of these different criteria will be based on business‘ priorities, strategy and characteristic of organization. In this

study the major focus will be on supplier selection for auto industry. The objectives are two fold enumerated as follows:

1. To understand the criterion for vendor selection for automobile manufactures in India and develop a validated framework

for the same using fuzzy logic decision making methodology for a single product category.

2. To cross validate the fuzzy logic methodology with another popular method known asTOPSIS, and check if the final

results were consistent with the industry perception of the suppliers for a particular product.

The remainder of the paper is organized as follows; Section 2 deals with a brief note on automotive industry in India, followed

by a summary of the literature on supplier selection issues and supplier selection criteria in Section 3. Session 4 sets the

theoretical framework for fuzzy logic. In the Section 5 methodology adopted is discussed. Section 6 deals with discussion of

results and section 7 concludes along with scope for future research.

2.Supply chain of automobile industries:

Many industrial branches such as iron & steel, light metals, petro-chemicals, glass, tires, etc, see a principal customer in the

automobile industry.Consequently, with its suppliers as well as the auxiliary sectors of marketing, distribution, services,

fuel, finance and insurance which supply automotive products/services to customers, the automobile industry creates a vast

business volume and employment together. The above factors are mainly the reasons that contribute to why it can be

considered as the flagship of the economy in all industrialized nations. The overall success in this industry is extremely

important to flourish, especially for developing countries.

Automotive Sector quality management system standards requires the organization to assess and select suppliers in view of

their capacity to supply item as per the organization‘s prerequisites and to set up criteria for choice, evaluation and re-

evaluation. The supplier determination process varies based upon the type of the items and services to be purchased. The

supplier choice procedure, for the most part, comprises of various stages some of which don't have any significant bearing

to basic buys. At every stage, the number of potential suppliers is whittled down to end with the choice of what is

considered to be the most reasonable to meet the prerequisites. Every organization should initially meet the purchase

request qualifiers. After that, the selection process goes ahead with assessing the potential suppliers against request

winner‘s criteria. For unique case buys occasional re-evaluation would not be fundamental. Where a contract between both

players (buyer and supplier) are made to supply items and services constantly till expiry, some method for re-evaluation is

essential as a shield against degrading quality standards. The re-evaluation might be based on supplier compliance to

requirements, length of supply, volume supplied, risks or changes in requirements and can be directed not withstanding any

item check that might be done.

3.Review of Literature

Supplier selection has attained the highest significance for the companies because of the increasing competition. Improper

selection of suppliers will have a poor impact on the overall performance of the manufacturer. In the past many models have been

proposed. These could be: categorical methods, data envelopment analysis, cluster analysis, case based reasoning systems,

linear weighting methods, total cost of ownership based models, mathematical programming models, artificial intelligence (AI)

based systems. These essentially focused the complex and unstructured nature of present day decisions. However many factors

are not taken into account and are rather standardized instead being industry specific making room for errors. There can be both

qualitative and quantitative objectives however the problem aggravates when there could be room for conflicting metrics. Past

works have also indicated that there could be two kinds of selection models. Compensatory and non-compensatory or scoring

system. The present study mainly focusses on the scoring model for evaluation. As stated before there needs to be the

consideration of both qualitative and quantitative variables in evaluating performance of the supplier based on the efficiency

and effectiveness of car anufacturers [1]. The first stage is mostly qualitative stage by utilizing weights to determine the

criterion importance and the second stage is quantitative which gives the supplier score. Assigning weights is important for

various criteria and these ratings of qualitative criteria are considered as linguistic variables. Because linguistic evaluations

merely approximate the subjective judgment of decision-makers, linear trapezoidal functions are considered to be adequate for

capturing the vagueness of these linguistic evaluations. These linguistic variables can be expressed in positive trapezoidal

fuzzy numbers. Linguistic ratings are used by the decision makers to evaluate importance of criterion and ratings of

alternatives with respect to qualitative criterion [2].

The key point is that generally these problems are multi-objective in nature [3]. However, researchers have pointed out that these

methods cannot be directly applied to assess a large number of alternatives, since they tend to generate inconsistencies. In view of




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this, this work has mainly tried to restrict the number of alternative parameters, by considering the most crucial through expert

validation [4].

In the past many studies have been carried out with improved fuzzy models. For instance the

TOPSIS which took linear trapezoidal models to convert qualitative linguistic criterion to quantitative score and according

weights to each criterion [2] as stated before. Importance of weights in a multi objective linear fuzzy logic model is seen to be

of great significance [3]. Also it is helpful categorizing supplier performance according to the item category so as to indicate

strengths and weaknesses of current suppliers, thus helping decision makers review supplier development action plans [5]. Thus

supplier frameworks and supplier categorization change along with the change in the items supplied in the automobile industry

where multiple suppliers are pooled in for multiple items (A, B and C classes). For the definition of criterion for selection of

suppliers many past papers have listed various metrics. For instance Dickson first identified 23 criterions. In many studies price

was determined to be the most important factor. Many authors identify multiple criterion. However four criterion have been

cited as the most popular for supplier selection criterion [6]. These further included many sub criterions. The four criterion

were supplier criteria, product performance criteria, service performance criteria, or cost criteria. Supplier criterion includes

aspects like financial, technical, quality systems and processes etc. product performance criterion includes aspects of usability

etc. service performance includes aspects of accessibility, timeliness, responsiveness, dependability, value add,

customer satisfaction etc. Of the many popular methods and approaches, this work choses to adapt a combination of criterion

and sub criterion and has also tried to incorporate normalized weighted multi criterion fuzzy logic approach to solve the vendor

selection problem [7]. A comprehensive list of selection factors has been stated in Table 1 after extensive literature survey.

1. Delivery a) Compliance with due date,

b) Fill rate,

c) Lead time,

d) Delivery Speed,

e) Delivery flexibility (change in delivery date,

special requests, meeting fluctuations in

demand),

f) Condition of product on arrival,

g) Accuracy in filling order,

h) Order cycle time,

i) Accuracy in billing and credit,

j) Reserve capacity,

k) Modes of transportation facility,

l) Delivery Personnel capabilities,

m) Safety and security components,

n) Packaging ability,

o) JIT

2. Quality a) Quality control rejection rate,

b) Customer rejection rate,

c) Product durability,

d) Product reliability,

e) Product performance,

3. Cost /price a) Purchase price,

b) Logistics cost,

c) Cost harness capability,

d) Payment terms

e) Quantity discount

f) Competitive pricing




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4. Service a) Reliability

b) Empathy(communication, access,

understanding)

c) Assurance (competence, courtesy, credibility

Responsiveness)

d) Ability and willingness to assist in design

process,

e) Post sales assistance and support,

f) After sales services (e.g., Warranties and

Claims policies), Training aids,

g) Payment procedures understanding,

h) Spare parts availability,

i) Handling of complaints,

j) Ability to maintain product/service

5. Product a) Product range,

b) New product availability,

c) Additional features

d) Product performance,

6. Technical capabilities a) Technical knowhow,

b) Performance history

c) Offering technical support,

d) Innovativeness,

e) R&D capability,

f) Future manufacturing capabilities,

g) Process

h) Manufacturing Capability,

i) Design capabilities

7. Organizational and

cultural factors

a) Globalization, procedural compliance

b) Compatibility of organizational cultures

c) Competitive pressure

d) Supplier strategic objective

e) Training and education Reputation and

position in the market,

f) Financial stability,

g) Geographic location and its political and

economic stability,

h) Quality performance accreditation,

i) Knowledge of the market,

j) Information systems,

k) Management capability,

l) Company assets,

m) Work safety and labor health,

n) Sustainability Environmental policies,

o) Top management support,

p) Supplier Integrity

8. Relationship factors

a) Trust and information sharing,

b) Ease of communication,

c) Long-term relationship,

d) Reciprocal arrangement,

e) Ability to identify needs,

f) Ability to maintain

g) Commercial relations,

h) Cooperation,

i) Supplier Willingness

Table 1: Selection factors for suppliers




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However all these factors are quite generic and are applicable to multiple industries. To make it rather specific this list is validated

by experts from the industry and specific factors are taken to make further analysis.

4.Theoretical Background

In this section we will discuss the fundamental frameworks underlying the two methodologies, called the fuzzy logic

method and the TOPSIS framework, which are used to score the suppliers.

Fuzzy logic

In a human body, the imprecise and incomplete sensory information provided by perceptive organs is interpreted by the

human brain. Pioneered by Lotfi A. Zadeh, the Fuzzy Set Theory is an appropriate tool to uncertainty, ambiguity, vagueness

and imprecision of the human cognitive processes. A systemic calculus is provided by this theory in order to linguistically

deal with such information and perform a numerical computation using the membership functions stipulated linguistic labels.

These are spcial rule-based systems which are using the fuzzy logic in their knowledge base to derive conclusions from user

inputs and fuzzy inference process. The knowledge base of the system is made up by the functions [8]. ―Fuzzy if-then‖ rule, in

other words, is an ―if-then‖ rule in which a few terms are given with continuous functions. When selected properly, Fuzzy

Logic System(FLS), can effectively model human expertise in a specific application.

Lets‘ try and understand fuzzy logic with the help of an example:A question how the temperature is sensed by people can be

demonstrated. The indoor temperature at around 20°C is perceived comfortable by majority of people. The result obtained for 19

°C

and 21°C would be the same. But, the temperatures 0

°C or 30

°C would be sensed differently and noted to be cold or hot. Whereas,

determination of 25°C as comfortable or rather warm temperature, is not as simple. Similar would be the condition for 15

°C to be

noted as cold or comfortable. The conclusion would be that, though the categorization is rather intuitive, the boundary between

them is not because the interface is without clear threshold.

A similar situation occurs during any other decision-making process. So, fuzzy logic could be effective in order to facilitate

it. The ease to comprehend is the biggest advantage about fuzzy logic. Due to its flexibility, it can be tailor made to the situation.

It is easy to understand and practice as it is similar to the thinking and decision making capacity of a human.

The MATLAB uses rules about variable names, a function similar to all the computer languages. It is a must for them to start with

a letter which could then be followed by other letters, numbers or underscores. Case Sensitivity is profound, for example Supplier

and SUPPLIER are read as two different names. A variable name can only be upto 63 characters long, beyond which the

characters stand ignored. There also are words which cannot be used for variable names. They are: if, for, end, while, else-if,

function, case, return, classdef, otherwise, continue, switch, try, else, persistent, global, catch, parfor, spmd, break. An error is

seen if any of the above listed names are entered for a variable.

There are four parts of fuzzy logic system as shown in Figure 1: 1.Fuzzifier; 2.Knowledge base; 3.Inference engine; and

4.Defuzzifier.

Figure 1: Fuzzy logic system




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Fuzzification

The measurements of the input variables (input signals, real variables), scale mapping and fuzzification (transformation)are

performed by fuzzifier. Fuzzification means that the measured signals or the crisp input quantities which have numerical

values are transformed into fuzzy quantities. Thus, all the monitored signals are scaled and a transformation of this sort is

performed using membership functions. The number of membership functions and their shapes are initially determined

by the user, in a conventional fuzzy logic. A value between 0 and 1 is given to a membership function, so as to indicate

a quantity‘s degree of belongingness to a fuzzy set. With 1 indicate the absolute belonging of the quantity to the fuzzy

set and 0 otherwise.

To summarize, the process of shifting a real scalar value into a fuzzy value is called fuzzification and this can be attained through

a variety of fuzzifiers or membership functions.

In Matlab, There are 11 membership functions, based on: Linear functions; Gaussian functions; Sigmoid curves; Polynomial

curves – Cubic and Quadratic.

A triangular membership function, is the simplest fuzzifier and it is also known as Trimf in MATLAB. Trapmf is the Matlab

nomenclature for the trapezoidal membership function. They are both simple and straightforward in terms of usage. Based

on Gaussian distribution curve are two membership functions, gaussmf and gauss2mf, apart from a bell membership called

gbellmf. The above functions have gained popularity for their smoothness. Sigmoidal fuzzifiers called sigmf, dsigmf and

psigmf (a combination of both sigmf and dsigmf), and polynomial based curves called zmf, smf and pimf are categori zed as

other fuzzifiers.

Finding appropriate linguistic variables and linguisticterms include the first step of problem solving. Linguistic variables could be

words or sentences written in natural or artificial language. Linguistic terms are what the values of linguistic variables are

called and they are not mathematically operable. An association of each term with a fuzzy number describing its meaning is a

mandate. These linguistic terms might be either importance weights or rating terms,like Very low (VL), Low (L), Medium low

(ML), Medium (M), Medium high (MH), High (H), Very high (VH) or Very poor (VP), Poor (P), Medium poor (MP), Fair

(F), Medium good (MG), Good (G) or Very good (VG), respectively.

Fuzzy inference process

The behavior of the system through rules like<when>, <After>, <then> etc, are defined by the second step. There are all

variables evaluating conditional sentences, on a linguistic level.

For example, a possible inputs like Food (which can be rancid, good and delicious) and Service (poor, good, excellent) can be

chosen during the decision-making process how much tip to leave at a restaurant. Then, being cheap, average or generous might

be the matching output. Eventually, the rules applied could be as follows:

The tip is cheap, if the food is rancid or service poor.

The tip is average, if the food and service are good.

The tip is generous, if the food is delicious or service excellent

The relation of fuzzy rule construction to supplier evaluation is another example. The Linguistic variables here are comprised

of price (linguistic terms: less, medium, high), quality (poor, acceptable, good) and service (bad, optimal, good). With the

choice of supplier selection outputs: reject, under consideration and accept, which provides the information about overall

rating to purchasing managers.

There is an example of possible rules:

With the choice of outputs of supplier selection:

Reject: If service is cheap and price less and quality poor.

Under consideration: If service is optimum and quality accepTable and price medium.

Accept: If service is good and price medium and quality good.

Defuzzification

Obtaining a linguistic output, which most appropriately represents the result of fuzzy computation, is the main aim of

defuzzification. In the previous example of tipping at arestaurant, the appropriate linguistic outputs are identified as cheap,

average and generous.

The linguistic outputs of reject, under consideration and accept, in the second case, simultaneously. The appropriateness of

fuzzy logic and supplier evaluation as found in many researches must be highlighted in the conclusion. For a decision

making process, fuzzy logic is considered a powerful tool.

The conceptual ease to understand is the one of the important features of fuzzy logic. The mathematical concepts behind

fuzzy reasoning are not complex and the ―naturalness‖ of its approach are what makes the fuzzy nice. The logic stands

flexible enough to provide, within an ongoing process/system, for a layering at any level (any variable/vendor). All the

variable parameters, like vendor potential, are initially imprecise and increases with increase in degree of inspection.




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TOPSIS (Technique for Order Performance by Similarity to Ideal Solution)

Introduced by Yoon and Hwang, the TOPSIS method was appraised by surveyors and different operators. A full ANP decision

process becomes impractical in a fewcases, due to the presence of a large number of potential available vendors in the current

marketing scenario.To avoid an unreasonably large number of pair-wise comparisons, the TOPSIS method is chosen as the

ranking technique due to its concepts ease of use. Also, for the acquisition of the weights of criteria the ANP is also adopted.

A general TOPSIS process with six activities is first listed below:

Activities

1) Decision matrix establishment for the ranking. The structure of the matrix could be expressed as follows:

Where,

Bi are the alternatives i, i = 1...,m;

Fj stands for the jth

attribute or criterion, j = 1...,n, related to ith

alternative;

Pij would be a crisp value indicating the performance rating of each alternative Bi with respect to each criterion Fj.

2) Normalized decision matrix Q= [Sij] calculation. The normalized value Sij can be calculated as follows:

3) Weighted normalized decision matrix calculation by multiplying it by its associated weights. The weighted normalized value vij

can be calculated as follows

Where,

Wj represents the weight of the jth attribute or criterion.

4) Determination of the PIS and NIS, respectively:

Where,

J – Has a positive criteria association

J' – Has a negative criteria association

5) Separation measures calculation with the help of m-dimensional Euclidean distance.

a) Separation measure + of each alternative from the PIS can be mentioned as follows:




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b) Separation measure − of each alternative from the NIS can be mentioned as follows:

6) Relative closeness to the idea solution calculation, and alternatives ranking in

descending order. The relative closeness of the alternative Ai with respect to PIS V+ can be given as follows:

Where,

Index value of Hi* lies between 0 and 1. (Larger the index value, better the performance of alternatives).

5.Research Methodology

Exploratory research was carried out to understand the various deciding factors for vendor selection for the automobile supply

chain. A mixed method approach was chosen, comprising: a focused literature review, to identify key issues, following which a

framework was prepared. This framework was validated by personal interviews study approach through opinion from experts

from the automobile industries, leading to the development of a concrete vendor selection Model.

The list of validated factors identified and used for further research are shown in Table2

Criterion Sub criterion

Quality Product rejection rate

supplier ISO Certifications

Adherence to quality tools, personal, processes

Price/Cost Low initial cost

cost reduction activities (may be economies of scale)

Company capabilities Existing production technology support

R&D/ innovativeness (A)

Technology capacity expansion for future

Management information system

production capacity

production variety

Delivery Delivery-on time every time

Delivery quality

Delivery lead time




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Delivery flexibility

Delivery responsiveness

After Sales Service responsiveness

Spare Parts Accessibility

Reputation/ professionalism

Communication & Information transparency

Collaborative development

Financial stability

Environment and social concern

Table 2: Validated selection factors for suppliers

Descriptive Research

In second phase, descriptive research was carried out to get linguistic ratings on the determined factors of the vendor selection

considering agility of the supply chain. These ratings were used to develop the fuzzy rank and score. The first set of ratings is

done to indicate how important or significant the parameter is for vendor selection. These are needed to derive the weights for the

criterion and sub criterion. Following this scores of performance are taken for four suppliers of headlamp systems for Cars of

two auto companies under study.

Twenty one respondents from two Indian auto companies and from department of purchase and supply chain rated these suppliers

on 9 point Likert scale. Structured questionnaire with multiple items on Likert scale validated by some key experts as shown in

Table 2 were circulated .Out of 40 questionnaires send to the company 21 responses were found to be complete and valid for

further data analysis.

6. Discussion

The scores by the previous steps are converted to numerical values with the help of standard conversion Table as shown in Tables

3 and 4. Crisp scores are derived from the fuzzy number equivalents.

Phrase Numerical on Likert scale Actual value

Not important at all 1 11

Not important 2 36

Somewhat important 3 76

Slightly important 4 86

Moderately important 5 100

Important 6 140

Considerably important 7 162

Very important

8 218

Extremely important 9 267




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Table 3: Conversion for importance (weights)[9]

Phrase Numerical on Likert scale Actual value

Inferior 1 28

Poor 2 54

So-So 3 100

Fair 4 113

Satisfactory 5 119

Good 6 177

Very good 7 237

Excellent 8 321

Perfect 9 355

Table 4: Conversion for performance [9]

Rating given by experts (on a scale of 1-9) are converted into the numerical value given by the weightage or importance Table

3 and the average is taken.

Similarly each rating given by different respondents (on a scale of 1-9) are also converted into numeric values using Table 4,

i.e. the conversion for performance and then the average is taken.

These scores are finally used in further analysis in MATLAB and in TOPSIS validation. The sequence of steps to be followed

is indicated in the following sections.

MATLAB

Step A:

Find out the share of weights (obtained from the previous step). By dividing each weight by the sum of all weights. For example

for quality it will be:

218/ (218+267+140+162+140+100)= 0.21226474

Criterion Weights Share of weights

Quality 218 0.21226874

Price/Cost 267 0.25998053

Company capabilities 140 0.13631938

Delivery 162 0.15774099

Service 140 0.13631938

Company structure 100 0.09737098

Table 5: share of weights for criterion




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Step B:

Similarly calculate the share of weights for subcriterion. An example is shown for quality in Table 6.

Criterion Weights Share of

weights

Sub Criterion Weights Share of

weights for

sub criterion

Quality 218 0.21226874 Product rejection rate 267 0.412674

supplier ISO Certifications 218 0.33694

Adherence to quality

tools, personal, processes

162 0.250386

Table 6: share of weights for sub criterio

Step C:

Multiply the two share of weights to obtain the normalised score for each subcriterion. An example is shown in Table 7

Criterion Weights Share of

Weights

Sub Criterion Weights

Share of

Weights

for sub

criterion

Normalized

Weights

Quality 218 0.21226874 Product rejection

Rate

267 0.412674 0.087597766

supplier ISO

Certifications

218 0.33694 0.071521772

Adherence to

quality tools,

personal, processes

162 0.250386 0.053149206

Table 7: Normalized Weights.

Step D:

Multiply the supplier performance score as obtained from conversion and averaging by the normalized scores. Then obtain

the total for each supplier. Supplier 1, 2, 3 and 4 have the score of 63.72, 54.89, 34.101, 42.198. for the parameter of quality.

Similarly find out score for other parameters like delivery, service, company structure, capabilities, price. These will be the

input scores.




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Paramet

Ers

Average score

Criterion Subcriteri

On

normalis

ed

weights

suppli

er 1

suppli

er 2

Suppli

er 3

suppli

er 4

Quality Product

rejection

rate

0.087597

766

337 237 117 177 29.520

45

20.760

67

10.248

94

15.504

8

Supplier

ISO

Certificati

Ons

0.071521

772

340 336 225 241 24.317

4

24.031

32

16.092

4

17.236

75

Adheranc

e to

quality

tools,

personal,

processes

0.053149

206

186 190 146 177 9.8857

52

10.098

35

7.7597

84

9.4074

1

Total

Score

63.723

6

54.890

33

34.101

12

42.148

96

Table 8: Input Scores

Step E:

Range for functions:

Range in defined roughly as 1/3 the weights for the criterion. They are listed in Table 6.8. These will be useful in defining the

membership functions for fuzzy logic.

Parameter Range

Quality [0 73]

Price [0 89]

Company caapbilities [0 47]

Delivery [0 54]

Service [0 47]

Company structure [0 33]

Table 9: Range of membership function




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Step F:

Open the fuzzy logic tool box. Using the edit function add the six parameters: price, quality, delivery, company structure,

capabilities and service.

Figure 2: Defining the parameters

Step G:

Define the membership functions of each of the parameters and the output. Define the following;

1) And Method='min'

2) Or Method='max'

3) Imp Method='min'

4) Agg Method='max'

5) Defuzz Method='centroid'

The range is specified as given in Table 9. Further the range for output is defined as [0 1]. There may be a name defined for each

membership function. For instance Price_score, Quality_score etc. any number of membership function can be chosen.

Here, three membership functions namely high, medium and low are chosen for the input parameters or input membership

functions and five membership functions namely very high, high, medium, low and very low are chosen for the output. The

trapezoidal function is chosen for inputs and the triangular functions are chosen for the output. Sample functions are shown in

Figure7 and 8. Table10 enumerated the different functions.

Parameter

Quality_score MF1='Low':'trapmf',[0 0 8.9 40.05]

MF2='medium':'trapmf',[8.9 40.05 48.95 80.1]

MF3='High':'trapmf',[48.95 80.1 89 89] Price_score MF1='Low':'trapmf',[0 0 7.3 32.85]

MF2='medium':'trapmf',[7.3 32.85 40.15 65.7]

MF3='High':'trapmf',[40.15 65.7 73 73]

Company capabilities_score MF1='mf1Low':'trapmf',[0 0 4.7 21.15]

MF2='Medium':'trapmf',[4.7 21.15 25.85 42.3]

MF3='High':'trapmf',[25.97 42.3 47 68.27]




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Delivery_score MF1='Low':'trapmf',[0 0 5.4 24.3]

MF2='Medium':'trapmf',[5.4 24.3 29.7 48.6]

MF3='High':'trapmf',[29.84 48.6 54 54

Service_score MF1='Low':'trapmf',[0 0 4.7 21.15]

MF2='Medium':'trapmf',[4.7 21.15 25.85 42.3]

MF3='High':'trapmf',[25.85 42.3 47 47]

Company structure_score MF1='Low':'trapmf',[0 0 3.3 14.85]

MF2='Medium':'trapmf',[3.3 14.85 18.15 29.7]

MF3='High':'trapmf',[18.15 29.7 33 33]

Supplier_score MF1='Very_Low':'trimf',[-0.25 6.939e-018 0.25]

MF2='Low':'trimf',[0.15 0.25 0.5]

MF3='Medium':'trimf',[0.3 0.5 0.7]

MF4='High':'trimf',[0.5 0.75 0.85]

MF5='Very_HIgh':'trimf',[0.75 1 1.25] Figure 3: Membership function definition for output

Table 10: Defining membership function




27

Figure 4: Membership function definition for parameter Quality Score

Step H:

Through the edit menu, we can define new rules. A total of 178 if then rules were defined.

Step I:

After defining the rules, the final step involves viewing the results. The results can be seen in view> rules. In the dialog box that

opens the total score that was calculated as indicated in Table 8 is entered. i.e., total score for supplier 1 for each of the six

parameters in the defined order is entered. This is shown in Figure 9 for supplier 1. The six input numbers can be seen in Input

box.

Figure 5: Viewing rules

TOPSIS validation

TOPSIS is a validation step to the fuzzy logic method. First the normalized weights of each sub criterion are calculated as

stated earlier. The calculations done as per the discussion under the theoretical background section are as follows:

Sij is the supplier score divided by the square root of the sum of squares of the scores of all four suppliers.

Colum Vj gives SJ*the normalized weights

V+ and V- are the maximum and the minimum values among the four suppliers.

E+ and E- are the square root of the total of squares of deviations each suppliers Vj from V= and V- respectively.

Finally supplier scores are obtained by the formula

These scores help in giving the rank of the suppliers. Supplier with the highest score has the maximum rank and

that with the lowest score has the lowest rank

Sum of E+ and E-, Square roots of the sums (E+ and E-)

The relative closeness to ideal solution is calculated for alternative suppliers with index value Hi* showing higher

performance if the value is closer to 1 and low performing suppliers if value is near 0.

Performance evaluation and categorization of suppliers is done using above scores. Detailed calculations for TOPSIS

methodology of supplier evaluation is shown in Table 11.




28

Conclusion and scope

The results from both MATLAB and TOPSIS are tabulated in Table 12. Here we see that the scores are in perfect

synchronization with each other. Further these scores also tally with the overall perception of the supplier in the automobile

industry.

Name of

supplier

MATLAB

Score

TOPSIS

Score

Supplier

Rank

A SUPPLIER 1 0.667 0.95514787 1

B

lighting

SUPPLIER 2 0.535 0.50017748 2

C

lighting

SUPPLIER 3 0.5 0.30400511 4

D

lighting

SUPPLIER 4 0.519 0.37197204 3

Table 12: supplier Scores

Hence it can be safely assumed that fuzzy logic takes into consideration the ambiguities and uncertainties in human decisions

and provides a structured way of expert decision making with consistency in the approach. However there are some serious

shortcomings in the method developed. The method can only be used for a limited number of factors and merely accounts for a

total score. It fails to see the fuzziness in the sub criteria, as the conditions have been written merely for the 6 important factors

(and not the sub factors).

Table 11: Calculations for TOPSIS




29

Hence in future a new method can be developed to include many more parameters. Further

a two-step mechanism can be devised to calculate the fuzzy scores for each criterion with input as the respective sub criteria. This

will ensure that the fuzziness at sub-step level is also included. These resulting criterions can be fed to output function to get final

score as usual.

Further this study can be replicated to various other industries where supplier selectionplays a very important role, like

electronics, consumer durables etc.

References

1. P. Parthiban, Dr , H. Abdul Zubar, Chintamani P. Garge. (2012) ‗A multi criteria decision making approach for suppliers

selection‘ International conference on modelling optimisation and computing, Procedia Engineering, vol. 38,

September,pp. 2312-2328

2. Chen Tung Chen, ChingTorng Lin, Sue Fn Huang. (2006) ‗A Fuzzy approach for supplier evaluation and selection in

supply chain management‘, International Journal of Production Economics, Vol. 102 Iss: 2, August,pp. 289-301

3. A Amid, S.H Ghodsypour, C O Brien. (2008) ‗Fuzzy multi-objective liner model for supplier selection in supply chain‘,

International Journal of Industrial Engineering &

Production Research, Vol. 19No: 4, pp. 1-8

4. EleonoraBottani, Antonio Rizzi. (2008) ‗An adapted multi-criteria approach to suppliers and products selection—An

application oriented to lead-time reduction‘, International journal of production economics, Vol. 111, pp. 763- 781

5. LauroOsiro, Francisco R. Lima-Junior, Luiz Cesar R. Carpinetti. (2014) ‗A fuzzy logic approach to supplier evaluation

for development‘, International journal of

Production economics, Vol. 153 Iss: C, pp. 95-112

6. CengizKahraman, UfukCebeci, ZiyaUlukan. (2003) ‗Multi-criteria supplier selection using fuzzy AHP‘, Logistics

Information Management, Vol. 16No: 6, pp. 382-394

7. Sharon M. Ordoobadi, (2009) "Development of a supplier selection model using fuzzy logic", Supply Chain

Management: An International Journal, Vol. 14 Iss: 4, pp.314 – 327

8. LX Wang. (1997) A course in fuzzy systems and control, New Jersey:Prentice-Hall, Englewood Cliffs,ISBN 0 13

(540882), 2

9. DebashisPati, (2002)Marketing research, Universities Press.

http://www.google.co.in/search?tbo=p&tbm=bks&q=inauthor:%22Debashis+Pati%22

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