DESIGNING VENDOR SELECTION FRAMEWORK USING

FUZZY LOGIC

Sonu Verma1#, Dr Kavita Chauhan1, Greeshma P Rao2

1#SonuVerma, Research Scholar, Centre for Management Studies, Jamia Millia Islamia

University, New Delhi.

Mobile Number: +91-999-036-8829/852-745-4892. E-mail id: sonu.vd@gmail.com.

1Dr Kavita Chauhan, Associate Professor, Centre for Management Studies, Jamia Millia

Islamia University, New Delhi.

2Greeshma P Rao, 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.

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 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 manufacturers [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 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 termse) Quantity discountf) Competitive pricing

4. Service a) Reliabilityb) 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 featuresd) Product performance,

6. Technical capabilities a) Technical knowhow,b) Performance historyc) Offering technical support,d) Innovativeness,e) R&D capability,f) Future manufacturing capabilities,g) Processh) Manufacturing Capability,i) Design capabilities

7. Organizational andcultural factors

a) Globalization, procedural complianceb) Compatibility of organizational culturesc) Competitive pressured) Supplier strategic objectivee) 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

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

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 categorized

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.

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 few

cases, 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:

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 capabilitiesExisting 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

Delivery flexibility

Delivery responsiveness

After Sales Service responsiveness

Spare Parts Accessibility

Reputation/ professionalism

Communication & Information transparency

Collaborative development

Financial stability

Environment and social concernTable 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

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

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

Quality 218 0.21226874 Product rejection rate 267 0.412674

supplier ISO

Certifications

218 0.33694

Adherence to quality 162 0.250386

Table 6: share of weights for sub criterion

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 Weightsfor 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,

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.

ParametErs

Average score

Criterion

SubcriteriOn

normalisedweights

supplier 1

supplier 2

Supplier 3

supplier 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

qualitytools,

personal,

processes

0.053149

206

186 190 146 177 9.8857

52

10.098

35

7.7597

84

9.4074

1

TotalScore

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

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]

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]

Table 10: Defining membership function

Figure 3: Membership function definition for output

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.

Table 11: Calculations for TOPSIS

7. 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 MATLAB TOPSIS Supplier

A SUPPLIER

1

0.667 0.95514787 1B SUPPLIER

2

0.535 0.50017748 2

C SUPPLIER

3

0.5 0.30400511 4

D 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).

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.

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