Multi Hierarchy Fuzzy Synthetic Evaluation for Vendor Selection

Multi Hierarchy Fuzzy Synthetic Evaluation for Vendor Selection
YU Peimin
Tianjin University of finance and economics, P.R.China, 300022
Purchases from vendors involve significant cost for many firms. In this paper we review
current criteria and methods for vendor selection. We further propose a multi hierarchy
fuzzy synthetic approach for vendor evaluation and selection. The paper also gives an
average score as the final evaluation result. The result indicates that although managers say
that quality is the most important attribute for a vendor, they actually choose vendors based
largely on their synthetic performance.
Key words SCM, Multi-criteria decision making, Vendor selection, Fuzzy synthetic evaluation
Abstract
1
Introduction
During recent years vendor (supplier) selection process has received considerable attention in the
supply chain management (SCM). External purchases are a substantial expenditure for most companies.
They represent an important part of the value of products. The cost of components and parts purchased
from external source by automotive manufacturers may total more than 50% in US. For high technology
firms, purchased material and services represent up to 80% of total product costs. Some famous
enterprises, such as IBM Company, GE Company, NIKE Company, DELL Computer Company and HP
Company have gotten great success through the vendor selection in their supply chain.
Selecting the right vendor is always a difficult task for buyers and purchasing managers. Suppliers
have varied strengths and weaknesses that require careful assessment by the purchasers before orders
could be given to them. The vendor selection process would be simple if only one criterion were used in
the decision making process. However in many situations, purchasers have to take account of a range of
criteria in making their decisions. If several criteria are used then it is necessary to determine how far
each criterion influences the decision making process, whether all are to be equally weighted or whether
the influence varies accordingly to the type of criteria. Dickson (1966) identified 23 criteria that have
been considered by purchasing managers in various vendor selection problems. Since the Dickson study,
vendor selection and performance evaluation concepts and techniques have been the topic of much
discussion. More recently, a review of vendor selection criteria and methods by Weber et al. (1991)
found that 47 of the 76 articles reviewed addressed more than one criterion. Many papers have also
suggested different mathematical techniques to weigh the different criteria that influence the purchasing
decision process.
In this paper we propose a fuzzy synthetic evaluation approach for selecting and evaluating
suppliers. The paper is organized as follows. Following this introduction, section 2 reviews the supplier
selection criteria and methods. In section 3 we present mathematical formulations of the vendor
evaluation and selection. The case study is described in section 4. A summary and conclusions are
presented in the final section.
2
Review
Vendor selection decisions are complicated by the fact that various criteria and purchasing
environment must be considered in the decision making process. The approaches of vendor selection are
also different in many cases.
2.1 Criteria review
The first step in any vendor rating procedure is to establish the criteria to be used for assessing the
vendors. The pioneering effort in this regard was the work of Dickson. The Dickson study was based on
the responses of 170 purchasing agents and managers from the United State and Canada. Table 1
summarizes the findings of Dickson’s study regarding the importance of the 23 criteria for vendor
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selection. Dickson asked the respondents to assess the importance of each criterion on a five-point scale:
of Extreme, Considerable, Average, Slight and No importance. The five points were given scores of 4
down to 0 and the average values over all the respondents then computed. The resulting values are also
given in Table 1.
One of the authors was involved with a repetition of this exercise in a major engineering company
in 1991. The study had the eight senior buyers in the company making the assessments. It found very
similar results to Dickson's study, as shown by comparing the ranks and mean scores given in the final
two columns of Table 1 with those of Dickson.
Weber, Current and Benton (1991) reviewed 74 papers on vendor selection in the academic
literature in terms of the criteria they used. They found that 47 of 74 articles or 64% discussed more than
one criterion. Table 1 also lists the number of articles in which each criterion was addressed. The rank
was also the same as the Dickson’s result.
Therefore, it can be concluded, that even though it is 30 years since the Dickson paper was
published, the basic criteria for vendor selection are little changed. Industrial purchasers can still regard
the Dickson criteria as a starting benchmark for assessing vendor selection. Of course there are
variations in terms of the ranking of these criteria.
Criteria
Quality
Delivery
Performance
Warranties & claim policies
Production facilities/capacity
Price
Technical capability
Financial position
Procedural compliance
Communication system
Industry reputation & position
Desire for business
Management & organization
Operating controls
Repair service
Attitude
Impression
Packaging ability
Labor relations record
Geographical location
Amount of past business
Training aids
Reciprocal arrangement
Table 1 Dickson’s criteria for assessing vendors
Mean
Rank
Evaluation
Mean
Rank
Dickson (1966)
Yahya (1991)
3.508
1
E (Extreme)
3.6
1
3.417
2
C (Considerable)
2.9
4
2.998
3
C
3.4
2
2.849
4
C
2.9
4
2.775
5
C
2.8
6
2.758
6
C
3.1
3
2.545
7
C
2.4
10
2.514
8
C
2.5
8
2.488
9
A (Average)
2.5
8
2.426
10
A
2.412
11
A
2.4
10
2.256
12
A
2.6
7
2.216
13
A
2.3
12
2.211
14
A
1.9
14
2.187
15
A
1.6
15
2.12
16
A
2.054
17
A
1.4
17
2.009
18
A
2.003
19
A
1.1
18
1.872
20
A
1.5
16
1.597
21
A
2.1
13
1.537
22
A
0.61
23
S (Slight)
Number of articles
Weber (1999)
40
44
7
0
23
61
15
7
2
2
8
1
10
3
7
6
2
3
2
16
1
2
2
Purchasing environments also decide the criteria selection. Possible purchasing environments
include JIT or MRP, global purchase, a special industry, large project purchase, etc.
2.2 Method review
A number of approaches, such as Categorical method, weighted point plan, liner programming
model and mixed integer optimization model have been suggested to make decision for vendor
evaluation and selection. Following are some common used methods recently.
Multi-objective programming (MOP) techniques would allow purchasers to systematically
examine the tradeoffs among the various criteria when selecting specific vendors. Such analysis would
enable purchasers to select the vendors who best satisfy the requirements necessary to implement
management strategy.
Analytic Hierarchy Process (AHP) is a theory of measurement to determine the relative importance
of a set of criteria. It provides a possible new approach similar to the linear weighted average idea,
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which has the ability to generate weights from subjective assessments. It is a more systematic process
for determining the weights, which still relies on subjective judgment to determine them. It does this by
a series of pairwise comparisons of all the criteria. It is the use of these pairwise comparisons that is at
the heart of the method. The method consists of three steps, structuring the problem hierarchy, the
evaluation process, and calculating the weights and the consistency index of the judgments made.
Multi-period Multi-supplier optimization (MMO) techniques use total cost of ownership
information to simultaneously select suppliers and determine order quantities over a multi-period time
horizon. The total cost ownership quantifies all costs associated with the purchasing process and is
based on the activities and cost driver determined by an activity based costing system.
Data Envelopment Analysis (DEA) would determine the points of vendor efficiency on multi
criteria and construct an index of relative vendor efficiency (RVE) to operationalize the concept of
vendor performance.
Activity based costing approach (ABC) is systematic method to compute a total cost caused by a
supplier in a production process improves the objectivity to judge a vendor’s performance.
This paper proposals a multi hierarchy fuzzy synthetic evaluation in that many vendor’s
performance have fuzzy character. Multi hierarchy fuzzy synthetic evaluation approach (MFSE) is one
of the most common evaluation methods and is widely used in many fields. It can help purchasing
manager to make a better decision for vendor evaluation and selection.
3
Formulation
3.1 single hierarchy fuzzy synthetic evaluation
We believe that one important application of fuzzy sets is in multiple criteria decisions making.
That is, as a decision problem gets large, the number of alternatives, number of objectives increases; it is
impossible for a decision maker to do all the manipulations in his head. Our goal is to create a repertoire
of forms that the decision maker can use in these cases.
When u = {u1 , u 2 ,⋅ ⋅ ⋅, u n }, the fuzzy subset A expressed in Zadeh’s form.
A = u A (u1 ) u1 + ⋅ ⋅ ⋅ + u A (u n ) u n
The symbol + and / are not the real mathematic calculation. It express the membership degree of an
individual element u i in relation to the fuzzy set A.
≤u
where 0
A
(u i )
≤1
When u A (u i )=1 then u i ∈ A
When u A (u i )=0 then u i ∉ A
Fuzzy set can be defined by membership function and expressed as fuzzy vector.
A(u i ) = [ u A (u1 ) , u A (u 2 ) , ····, u A (u n ) ]
The two most common operations on fuzzy sets are union and intersection. They are defined as
follows.
Thus
Thus
A ∪ B = C ⇔ u C ( x) = u A ( x) ∨ u B ( x)
u C (x) =Max [ u A (x) , u B (x) ]
A ∩ B = D ⇔ u D ( x) = u A ( x) ∧ u B ( x)
u D (x) =Min [ u A (x) , u B (x) ]
∨
∧
The operation label
and
represent the operation of getting maximum or minimum number.
Effect grades universe are good, general, and worse.
V = { A1 , A2 , A3 }
We define the universe of evaluation factors u , select eight criteria as factor: quality, delivery,
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geographical location, packaging ability, production facilities, price, technical capability and financial
position. The individual label is B1 , B 2 , B3 , B4 , B5 , B6 , B7 , B8 . The purchasing environment is JIT.
Let u = {B1 , B2 , B3 , B4 , B5 , B6 , B7 , B8 }
Assume fuzzy set of evaluation factor on u :
B=
0
b1 b2 b3 b4 b5 b6 b7 b8
+
+
+
+
+
+
+
B1 B2 B3 B4 B5 B6 B7 B8
≤ b ≤1
I=1,2, ···,8
i
b1, b 2, b 3, b 4, b 5, b 6, b 7, b 8 Is a set of membership degree of a specific evaluation in relation to
the factors B1 , B 2 , B3 , B4 , B5 , B6 , B7 , B8 . They are the weight of different criteria and can be
getting from table 1.
Assume fuzzy subset of effect grades universe:
A=
0
a1 a 2 a3
+
+
A1 A2 A3
≤ a ≤1
i=1,2, 3
i
a1, a 2, a 3 is a set of membership degree of evaluation grade A1 , A2 , A3 . It is also the result we
need. Obviously, effect grades universe and evaluation grade universe have a fuzzy relationship which
can be expressed by 3 × 8 fuzzy matrix R.
 r11
r
 21
 r31

r41
R= 
 r51

 r61
r
 71
 r81
r12
r22
r32
r42
r52
r62
r72
r82
r13 
r23 

r33 

r43 
r53 

r63 
r73 

r83 
≤ ≤1) is the degree of
rij ( 0 rij
the relationship and express probability of the i th evaluation
factor belong to the j th effect grade. It can be get from customers investigate and expert marking
With the fuzzy weight set B and fuzzy relation matrix R, the fuzzy conclusion can reach.
A=B×R
The add is (maximum) and the multiply is
(minimum) in calculation. And the result is the
fuzzy synthetic evaluation conclusion to a vendor. When a vendor has a number above 0.5 or more in
good grade, he will be a supplier of purchaser.
3.2 Multi hierarchy fuzzy synthetic evaluation (MFSE)
Some problems will appear when the evaluation factors are too many. (1) The membership degrees
are difficult to distribute. (2) Some evaluation factors have a no useful results where they are too small.
Multi hierarchy fuzzy synthetic evaluation will solve the problems well.
Divide evaluation element set U = {u1 , u 2 ,⋅ ⋅ ⋅, u n } to s subset U 1 , U 2 ,⋅ ⋅ ⋅U s as the
∨
∧
two-hierarchy universe, U i = {xi1 , xi 2 ,⋅ ⋅ ⋅, xini }, i = 1,2,3,⋅ ⋅ ⋅, s .
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① n + n + ⋅ ⋅ ⋅ + n = n;
②U ∪ U ∪ ⋅ ⋅ ⋅ ∪ U = U ;
③ U ∩ U = 0 when i≠j
1
2
s
1
2
i
j
s
V = {v1 , v 2 ,⋅ ⋅ ⋅, v m } is effect grades universe.
SBi = (bi1 , bi 2 ,⋅ ⋅ ⋅, bin ) is the weight subset of the second hierarchy evaluation factors. SRi is their
Evaluate
the
subset
Ui
separately.
relationship matrix to effect grades universe.
Then SAi = SBi × SRi = ( ai1 , ai 2 ,⋅ ⋅ ⋅, aim ), i = 1, 2,⋅ ⋅ ⋅, s. m = 1, 2,3 ⋅ ⋅ ⋅
Take U i as the first hierarchy evaluation factor K = {U 1 , U 2 ,⋅ ⋅ ⋅, U S } . The weight factor set
is K = {k1 , k 2 ,⋅ ⋅ ⋅, k s ) . The relationship matrix is SA = {a im }, i = 1,2,⋅ ⋅ ⋅, s. m = 1, 2,3 ⋅ ⋅ ⋅
Then A = K × SA = ( a1 , a 2 ,⋅ ⋅ ⋅, a m ), m = 1,2,3,⋅ ⋅ ⋅
When the effect grades universe has the value of (c1 , c 2 ,⋅ ⋅ ⋅, c m ).m = 1, 2,3,⋅ ⋅ ⋅
Then the final evaluation result will be S = a1 × c1 + a 2 × c 2 + ⋅ ⋅ ⋅ + a m × c m
4
Case study
4.1 Set up hierarchy structure
The case to be considered is Dickson’s 23 criteria. It is divided to two-hierarchy evaluation
structure as follow.
1st hierarchy
2nd hierarchy
Quality (u1 = 3.51)
Quality & technology( U 1 =3.5)
Technical capability (u 2 = 2.55)
Procedural compliance (u 3 = 2.49)
Production facilities & capacity (u 4 = 2.78)
Net price (u5 = 2.76)
Cost( U 2 =3.1)
Geographical location (u 6 = 1.87)
Packaging ability (u7 = 2.01)
Communication system (u 8 = 2.43)
Delivery (u 9 = 3.42)
Delivery( U 3 =2.7)
Performance (u10 = 3.0)
Warranties & claim policies (u11 = 2.84)
Repair service (u12 = 2.19)
Service( U 4 =2.3 )
Training aids (u13 = 1.54)
Reciprocal arrangement (u14 = 0.61)
Attitude (u15 = 2.12)
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Amount of past business (u16 = 1.6)
Impression( U 5 =1.5)
Desire for business (u17 = 2.26)
Impression (u18 = 2.05)
Industry reputation & position (u19 =
Financial position (u 20 = 2.51)
Management( U 6 =1.2)
Management & organization (u 21 = 2.22)
Operating controls (u 22 = 2.21)
Labor relations record (u 23 = 2.0)
4.2 Calculations
From the second hierarchy evaluation factors
SB1=(3.51,2.55,2.49,2.78)
SB2=(2.76,1.87,2.01,2.43)
……..
SB6=(3.51,2.22,2.21,2.0)
Effect grades universe are good, general, and worse. The experts or investigation give the
relationship matrix SRi . Make the numbers in the set of SBi normalization.
Then SAi = SBi × SRi = ( a i1 , ai 2 , a i 3 ), i = 1,2,⋅ ⋅ ⋅,6. m = 1, 2,3
From the first hierarchy evaluation factors
K=(3.5,3.1,2.7,2.3,1.5,1.2)
Then A = K 1×6 × SA6×3 = ( a1 , a 2 , a3 )
The result demonstrated that the vendor has a1 membership degree related to good effect grade
and a 2 membership degree related to general effect grade. So the result gave the purchasing manager
a synthetic performance.
Define effect grades universe set {good, general, worse} as c1=0.8, c2=0.5 and c3=0.2
Then S = 0.8a1 + 0.5a 2 + 0.2a 3 is the vendor’s synthetic score.
5
Conclusions
This paper developed a multi-criteria fuzzy synthetic evaluation approach to assist the purchasing
manager in making decisions. We can also evaluate several vendors and get their synthetic performance.
From the list of their rank, the first can be the selected vendor and the second will be the reserve one.
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