View
1
Download
0
Category
Preview:
Citation preview
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.
References1. 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.
Recommended