FUZZY ANALYTIC HIERARCHY PROCESS AND AN APPLICATION …akademikpersonel.kocaeli.edu.tr/kbaynal/bildiri/kbaynal16.10.2014... · FUZZY ANALYTIC HIERARCHY PROCESS AND AN APPLICATION

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

[email protected]

İlksen COŞAR


Türkiye

[email protected]

Öznur ERGÜL


Türkiye

[email protected]

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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