FUZZY ANALYTIC HIERARCHY PROCESS AND AN APPLICATION...
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CIE44 & IMSS’14 Proceedings, 14-16 October 2014, Istanbul / Turkey, Pages: 2210-2226
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FUZZY ANALYTIC HIERARCHY PROCESS AND AN APPLICATION OF
SUPPLIER SELECTION IN A FOOD COMPANY
Kasım BAYNAL
Endüstri Mühendisliği Bölümü Mühendislik Fakültesi Kocaeli Üniversitesi, Kocaeli,
Türkiye
İlksen COŞAR
Endüstri Mühendisliği Bölümü Mühendislik Fakültesi Kocaeli Üniversitesi, Kocaeli,
Türkiye
Öznur ERGÜL
Endüstri Mühendisliği Bölümü Mühendislik Fakültesi Kocaeli Üniversitesi, Kocaeli,
Türkiye
ABSTRACT
In today’s world, supply chain management became one of the most important
matters of companies. Thus, any smallest change in the supply chain affects all the
rings of the chain. Suppliers are the most crucial ring of that chain. Supplier
companies are not only responsible to their own management in their inside
organization but also carry a responsibility to their customers. Nowadays especially
food industry supplier number is increased. In order to make a decision among all
these suppliers, a number of criteria exist such as price, quality, production for food,
on-time delivery and etc. Decision making with these varieties of criteria is very
difficult. In this study, a food industry company’s supplier performance evaluation
and decision making in the supplier selection problem was examined and fuzzy AHP
method was applied.
Keywords; Supply Chain Management, Supplier Performance, Fuzzy AHP
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1. INTRODUCTION
Purchasing, or in a wider term, supply process of the sub-products (raw materials) in
the production BOM tree of the end- products, carry a more important role in today’s
world where the competition is increasing and the marketing of the products are
taking over regarding to the sales of the products. As supplier companies of these
products increase, the selection of the right supplier is becoming more vital every
day.
Suppliers stand for a critical source that supply direct and indirect materials and
services, which are the inputs for the production process of a company. The quality
and the cost of the product or service that is served into the market are not only
dependent to the abilities of the producer but also to the suppliers [1].
Criteria and importance levels for supplier selection are changed enormously
according to the past. Supply chain includes all the demand and supply management,
raw material supply, production and montage, inventory management, order
management and distribution of the product to the end-customers activities and the
information systems needed to maintain these activities [2].
In this study, the supplier selection among 3 competitors is aimed, in daily
consumption products for food industry producing company. The package material
suppliers produce is selected over a number of criteria, such as material’s mass, odor
test (not quantitative), price, compliance with the quality standards, color according
to the witness sample, supplier’s delivery performance and supplier’s production
capacity are only some of them. As some of the evaluation criteria of the suppliers
are not possible to interpret as quantitative metrics in this study, fuzzy logic approach
is used.
The targets of this study are choosing the most reasonable supplier and fulfilling the
needs of the company working in daily consumption products industry, using fuzzy
logic AHP method.
2. LITERATURE RESEARCH
2.1. FUZZY LOGIC STUDIES
The first information on fuzzy logic is submitted into the literature by Lotfi Zadeh in
1965. The principles of fuzzy logic take over with their ability to explain uncertainty.
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The theory is also available for applying the mathematical operations and
programming into practical use. A fuzzy cluster is defined by a function with the
members changing the membership degree from 0 to 1. These membership degrees
show consistency for a fuzzy cluster [3].
Many studies are performed on fuzzy logic area after Zadeh. Thus, methods are
developed using AHP with fuzzy numbers. [5] The method with the widest usage
among all is Chang’s Degree Analysis Technique (1996) [4].
Leung and Cao (2000) take tolerance deviation for fuzzy AHP alternatives and find a
solution for fuzzy stability condition [6]. Rong et al. (2003) used AHP via fuzzy
clusters in order to eliminate waste and recycle [7]. Shamsuzzaman et al. (2003)
evaluated the alternatives for flexible production systems and used AHP method [8].
Kahraman et al. made a decision among 3 catering companies by survey studies
using AHP method [9]. Gu and Zhu solved a fuzzy multi-attribute decision problem
using AHP [10].
Ertuğrul and Karakaşoğlu used Chang’s widened degree analysis technique for the
selection between suppliers [11]. Durdudiller used classical and fuzzy AHP methods to
choose the most advantageous supplier in retail business [12].
In a literature study on the usage of multi criteria decision making methods in
supplier evaluation and selection applications, Ho et al. examined 78 papers
published in international magazines between 2000 and 2008 [13]. In this study, the
most used criteria for supplier selection were determined as quality (68), delivery
(64), price/cost (63), production capacity (39), service (35), management (25),
technology (25), research and development (24), finance (23), flexibility (18),
reputation (15), relations (3), risk (3), security and environment (3). In another
literature study on the same area covering years between 1966 and 1990, the 23
criteria used in supplier selection were determined as quality, delivery, performance
history, warranty and complaint policy, production abilities and capacity, price,
technical capacity, financial position, compliance to procedures, communication
system, reputation and position in the industry, commitment for work, management
and organization, operational control, maintenance services, attitude, influence,
packaging ability, industrial relations records, geographical location, past business
volume, training supports and corresponding regulations (Weber et al., 1991). [14]
Wang et al. used a modified fuzzy logarithmic smallest squares technique, [15]; Xu
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used a fuzzy smallest squares priority technique [16]; Mikhailo used a fuzzy
preference programming technique which also takes out net weights from fuzzy
comparison matrix [17], [18].
2.2. DEGREE ANALYSIS TECHNIQUE APPLICATIONS
This is one of the most used techniques for the solution of fuzzy logic analytic
hierarchical problems. A short literature scanning for the ones using this method
shows these; Tang and Beynon [19], used fuzzy AHP in order to add the uncertainty
that the problem naturally includes in the automobile purchasing selection for a car
rental company [18].
Alkan and Akman made a fuzzy logic AHP method study for the most suitable
supplier selection for an OEM supplier in Kocaeli [3]. Bozdağ as well made an
evaluation to process the non-quantitative data for choosing the best CAM system
[20]. Bozbura and Beskese, used fuzzy AHP and degree analysis technique in order to
solve the most effective indicator selection problem [21]. Yurdakul used this method for
machinery device part selection [22].
3. CRITERIA DETERMINATION IN SUPPLIER SELECTION
Many criteria, which are unique for the company and its product, develop in a
supplier evaluation process. For example, for a plant in heavy industry, the hygiene
of a technical material may not be a problem where in a food processing plant the
hygiene of the technical material may be an important problem, similarly in one of
the two food processing plants, Halal Certificate of the raw materials may be
considerable and counted as a criteria where for the other plant it is not. Thus,
companies shape some of the criteria uniquely for them while preparing their quality
standards.
The effects of the criteria may be equal or unequal to each other. So the effect of
each criteria implying to the decision must be determined [23]. The number of
criteria for supplier selection increased during industrialization. While in the early
years of industrialization development there were only 3 basic criteria (delivery,
price, quality) involved, nowadays the number of criteria increased and as mentioned
in the beginning they became specialized for companies. In this study, 4 basic criteria
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of a food industry company which must be considered and 2 or 3 sub-criteria for
these criteria have been based for a selection (Table 1).
Table 1: Criteria for supplier selection
Target Main criteria Sub-criteria
Su
pp
lier
Sel
ecti
on
wit
h
Fu
zzy
AH
P M
eth
od
Delivery On-time delivery
Ability to fulfill urgent orders
Quality
Rejected product ratio
Visual smoothness of the material
Production compliance for food
Service
Customer Satisfaction
Supplier’s capacity
Fast responses to e-mails etc.
Costing Proper price
Price update due to raw material prices updates
Figure 1: Hierarchical Display of Supplier Selection Criteria
Supplier Selection Criterias
Delivery
On-time delivery
Ability to fulfill urgent orders
Quality
Rejected product ratio
Visual smoothness of the
material
Production compliance for
food
Service
Customer satisfaction
Supplier’s capacity
Fast responses to e-mails etc.
Pricing
Proper price
Price update due to raw material prices
updates
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3.1. Delivery
Today’s world’s competition between companies forces them to work with almost
zero stock. Thus, the shortness of delivery and time-window compliance of the
supplier became extremely important due to the risk of line stoppages. Because of
this, delivery-on-time is an important sub-criterion of delivery criteria for supplier
selection. The other important branch of delivery is the supplier’s flexibility to fulfill
urgent orders.
3.2. Quality
Quality is a common issue for supply chain because the supplier’s product quality
directly affects the producer’s quality. Defect ratio of a supplier’s products is one of
the most important quality indicators. Another one is the supplier’s compliance with
the food producer company’s regulations for adequate food processing. This
compliance is a criteria which is traced by both certifications and routine audits.
3.3. Service
Service quality is one of the criteria which are very difficult to define quantitatively
and can be spread into many sub-criteria according to the customer’s expectations.
Customer satisfaction, immediate responses to e-mails and, supplier’s fast action
ability are connected to service quality main criteria.
3.4. Costing
Price is a main factor that affects supplier selection. Existence of alternative suppliers
for the material to be purchased makes the decision very complicated. The buyer
pursuits and, the firm giving the minimum offer considering are also the other
criteria. The following process after proposal which is the supplier’s updating the
price according to the raw material prices and other indirect costs are a sub-criteria of
price.
4. FUZZY AHP TECHNIQUE and DEGREE ANALYSIS METHOD
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Fuzzy AHP is a method which enables the use of non-quantitative relative concepts.
Fuzzy AHP emerged by the combination of fuzzy relationship and binary
comparison concepts.
First information regarding to fuzzy logic was submitted into the literature by Lotfi
Zadeh in 1965. Fuzzy logic principles take out with their ability to explain
uncertainty. The theory is also available for applying the mathematical operations
and programming into practical use. A fuzzy cluster is defined by a function with the
members changing the membership degree from 0 to 1. These membership degrees
show consistency for a fuzzy cluster [3].
Fuzzy linguistic approach is recommended instead of conventional AHP technique
because it can take into account the optimistic/pessimistic attitude of the decision
maker. In fuzzy AHP technique, generally verbal expressions used which are
characterized with fuzzy numbers in order to show all the alternatives’ evaluation
values according to the subjective and objective criteria. For the blurry qualitative
criteria values evaluations expressions, also fuzzy numbers are used. When decision
makers’ judgments based on sensations are subjected, fuzzy approach can identify a
more accurate decision making process. Fuzzy binary comparisons express the
decision makers’ undefined judgments more rationally [18].
4.1. Triangular Fuzzy Numbers
Triangular fuzzy numbers can be considered as ordered trilogy in real numbers. But
what differs fuzzy numbers is the elements are written from smallest to largest.
Every number consists of 3 components. The first component shows the minimum
value, the second component which is the middle one shows the optimum value and
the third component shows the maximum value [24]. According to Chang’s (1996)
Degree Analysis Technique, the triple numbers are shown as (l, m, u) [4]. In this
study Degree Analysis Technique (MAT) will be mentioned and an application of
supplier selection will be shown.
A fuzzy cluster’s simulated symbol is . The display of a triangular number is as
Fig 2.
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Figure 2: Triangular fuzzy numbers display
4.2. Fuzzy AHP Degree Analysis Technique
According to Chang’s (1996) MAT the steps are as follows [3];
Step 1: According to Metric i, fuzzy synthetic degree value is defined as:
(1)
Here in order to obtain
value, fuzzy addition operation is directed to m
degree analysis value.
(2)
(3)
Then the vector is reversed and the following is obtained;
(4)
Step 2:
M₂= (l₂, m₂, u₂) ≥M₁ = (l₁, m₁, u₁) possibility degree is defined as;
(5)
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This definition can be expressed with the equation (6).
(6)
Step 3: It can be identified a convex fuzzy number’s being major likelihood ratio
from k pcs of fuzz numbers , i=1,2,...,k like below;
(7)
If it assumes true below expression for k = 1, 2, n; k ≠ i;
(8)
Weight vector is;
(9)
Here Ai ( i=1,2,...,n) is n pcs member.
Step 4: Every member of weight vector is being normalized as division to total like
below and so total value will be 1 and the value is between (0,1).
The weight vector that is normalized is like below and here W is not a fuzzy number.
5. SUPPLIER SELECTION WITH FUZZY AHP
The problem’s subject Company ABC is a firm in food industry. The number of
selection competitors is 3. The suppliers working in food package producers are
named as T1, T2 and T3. In order to digitize the non-numeric data in the problems
which are being tried to solve with fuzzy logic approach, binary comparison matrix
is used. The target here is to show qualitative data as quantitative data. As relative
concepts are included in this qualitative data, criteria weights are determined for the
results of interviews, surveys etc. performed with many people.
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Table 2: Importance degrees used in binary comparison (Akman G, Alkan A,
2006) [3]
ORAL IMPORTANCE FUZZY SCALE PROVISION SCALE
Equal (1,1,1) (1/1, 1/1, 1/1)
(1,2,3) (1/3, 1/2, 1)
Some more Strong (2,3,4) (1/4, 1/3, 1/2)
(3,4,5) (1/5, 1/4, 1/3)
Fairly Strong (4,5,6) (1/6, 1/5, 1/4)
(5,6,7) (1/7, 1/6, 1/5)
Very Strong (6,7,8) (1/8, 1/7, 1/6)
(7,8,9) (1/9,1/8, 1/7)
Absolute Strong (8,9,9) (1/9, 1/9, 1/8)
In this study firstly; the criteria will be identified by paired wise comparison method
and second the steps will be followed in the higher-order analytical method and the
matter will be solved by these steps. It will be used fuzzy criteria in Table 2 when
scaling the suppliers.
Table 3: The Pair Wise Comparison for Basic Criteria
DELIVERY COSTING SERVICE QUALITY
l m u l m u l m u l m u
DELIVERY 1 1 1 4.00 5.00 6.00 0.33 0.50 1.00 1.00 2.00 3.00
COSTING 0.17 0.20 0.25 1 1 1 0.25 0.33 0.50 0.33 0.50 1.00
SERVICE 1 2 3 2 3 4 1 1 1 0.20 0.25 0.33
QUALITY 0.3 0.5 1.0 1 2 3 3.00 4.00 5.00 1 1 1
In these step basic criteria compressed and the values are ready for the other step,
table 4.
Table 4: Synthetic Extent Value for Basic Criteria
l m u
D 0.20 0.35 0.62
Q 0.05 0.08 0.09
S 0.13 0.26 0.47
C 0.17 0.31 0.57
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For the all the pair extent values possibility of M2 =(l2,m2,u2) ≥ M1=(l1,m1,u1) is
like below. In table 5, it is calculated possibilities for all criteria and after the values
is normalized.
Table 5: Possibility
V(SJ≥Sİ) D C S Q minV(SJ≥Sİ)
D
1.00 1 1.00 1
C 0
0 0 0
S 0.20 1.00
0.86 0.2
Q 0.90 1.00 1.00
0.9
As the up values weight vector is W' = (1, 0, 0.2 0.9) and the normalized weight
vector is W = (0.47, 0, 0.09, 0.42).
The comparison for sub-criteria will be the same steps.
Table 6: Pair Comparison for Delivery Sub-Criteria
D1 D2
l m u l m u
D1 1 1 1 0.2 0.17 0.14
D2 5 6 7 1 1 1
In table 6 sub criteria of delivery is calculated and this values are ready for next step
like Table 7.
Table 7: Synthetic Extent Value for Delivery Sub-Criteria
l m u
D1 0.13 0.14 0.16
D2 0.65 0.85 1.11
For the all the pair extent values possibility of M2 = (l2,m2,u2)≥ M1=(l1,m1,u1) is like
below.
Table 8: Possibility for Delivery Sub-Criteria
V(SJ≥Sİ) D1 D2 minV(SJ≥Sİ)
D1 1.00 0
D2 0.00 1.00
W' = ( 0, 1 ) and W = ( 0, 1 )
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Table 9: Pair Comparison for Sub-Quality Criteria
Q1 Q2 Q3
l m u l m u l m u
Q1 1 1 1 0.333 0.500 1.000 0.143 0.167 0.200
Q2 1 2 3 1 1 1 0.111 0.125 0.143
Q3 5 6 7 7 8.00 9 1 1 1
In table 9, sub-quality criteria are compared.
Table 10: Synthetic Extent Value for Sub-Quality Criteria
l m u
Q1 0.06 0.08 0.13
Q2 0.09 0.16 0.18
Q3 0.56 0.76 1.02
For the all the pair extent values possibility of M2 = (l2,m2,u2)≥ M1=(l1,m1,u1) is like
below.
Table 11: Possibility for Sub-Quality Criteria
V(SJ≥Sİ) Q1 Q2 Q3 minV(SJ≥Sİ)
Q1
0.80 1 0.8
Q2 1
1 1
Q3 1.00 1.00
1
As the up values weight vector is W' = (0.8, 1, 1) and the normalized weight vector is
W = (0.28, 0.35, 0.35).
Table 12: Pair Comparison for Sub-Service Criteria
In table 12, the sub service criteria calculated.
S1 S2 S3
l m u l m u l m u
S1 1 1 1 0.111 0.111 0.125 0.250 0.333 0.500
S2 8 9 9 1 1 1 0.111 0.125 0.143
S3 2 3 4 7 8.00 9 1 1 1
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Table 13: Synthetic Extent Value for Sub-Service Criteria
l m u
S1 0.05 0.06 0.08
S2 0.35 0.43 0.39
S3 0.39 0.51 0.68
For the all the pair extent values possibility of M2 =(l2,m2,u2)≥ M1=(l1,m1,u1) is
like below.
Table 14: Possibility for Sub-Service Criteria
V(SJ≥Sİ) S1 S2 S3 minV(SJ≥Sİ)
S1
0 0 0
S2 1
0 0
S3 3.60 1.00
1
As the up values weight vector is W' = (0, 0, 1) and the normalized weight vector is
(0, 0, 1)
Table 15: Pair Comparison for Sub-Costing
C1 C2
l m u l m u
C1 1 1 1 1 1 1
C2 1 1 1 1 1 1
In table 15 sub-costing criteria is calculated
Table 16: Synthetic Extent Value for Sub- Costing
W = (0.5, 0.5)
l m u
C1 0.50 0.50 0.50
C2 0.50 0.50 0.50
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Table 17: Delivery Associated Importance Weight
Delivery D1 D2
Weight 0 1 Sub-Criteria Weight
Suppliers
T1 0.33 0 0
T2 0.22 0.56 0.56
T3 0.44 0.33 0.33
In this step, delivery associated importance weight is calculated for all suppliers and
sub-criteria weight is founded. In tables 18, 19, 20 this step implemented for quality,
service and costing.
Table 18: Quality Associated Importance Weight
Quality Q1 Q2 Q3
Weight 0.28 0.35 0.35 Sub-Criteria Weight
Suppliers
T1 0.41 0.56 0 0.3108
T2 0.33 0.56 0.56 0.4844
T3 1 0 0.18 0.343
Table 19: Service Associated Importance Weight
Service S1 S2 S3
Weight 0 0 1 Sub-Criteria Weight
Suppliers
T1 0.18 0.22 0.41 0.41
T2 0.41 0.56 0.33 0.33
T3 0 1 0 0
Table 20: Costing Associated Importance Weight
Costing C1 C2
Weight 0 1 Sub-Criteria Weight
Suppliers
T1 0.18 0.33 0.33
T2 0.5 0.5 0.5
T3 0.44 0.33 0.33
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Table 21: Basic Criteria Weight
Basic Criteria
Weight Delivery Costing Service Quality Sub-priority
Weight Costing 0.47 0.1 0.09 0.42
Suppliers
T1 0 0.31 0.41 0.33 0.176
T2 0.56 0.48 0.33 0.5 0.503
T3 0.33 0.34 0 0.33 0.294
In table 21, it can be seemed basic criteria weight for all suppliers and this table
shows which supplier can be preferred. As up values, sup-priority weight is higher
than the other suppliers for T2 supplier. So T2 supplier can be choosed for this food
company.
6. RESULT AND DISCUSSIONS
In this study, most adequate semi-product supplier selection method is subjected.
When a selection is being made among suppliers, qualitative data consideration as
well as quantitative data is extremely important. In this study, fuzzy expressions
which are very difficult to digitize with high degree analysis technique are digitized
to help the selection. Digitization of these qualitative data during selection is very
complicated. Thus, linguistic variables were used to digitize data which are difficult
to digitize with fuzzy AHP method. Using fuzzy AHP method, supplier selection,
plant location selection, investment machinery selection etc. can be performed.
As can be seen in Table 21, the best performing supplier between T1, T2 and T3
suppliers upon the predetermined criteria is T2. That’s because the sub-criteria
weight value of the supplier T2 is highest and when the most advantageous supplier
is to be selected T2 is chosen. Purchasing is correct to be made from T2 supplier
which comparatively gives better conditions than others for this study’s supplier
selection criteria. T3 and T1 follow this situation.
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