MODELING AND IMPLEMENTING FUZZY LINGUISTIC
QUANTIFIER TO SELECT SUPPLY CHAIN PARTNERS AT
DIFFERENT PHASES OF PRODUCT LIFE CYCLE
Advisor: Prof. Chu, Ta Chung 朱大中
Student: Dao, Xuan Tung 桃春松 (M977Z202)
INTRODUCTION
• Owing to rapidly growing global competition, enterprises are increasingly
focusing on their core competencies. The focal company faces the
challenge of creating alliances with more suppliers to create outsourcing
synergy and provide heterogeneous products for customers.
• An effective supplier assessment and selection process is essential for
improving the performance of a focal company and its supply chains
• The weights not only represented the importance of attributes or criteria
that decisively influenced the evaluation result, but also correlated with
product life cycle and even more with enterprise product development
strategy.
• Cycle time also influenced supplier selection and even performance
representation, and the future development of long-term relationships and
commitments
• The competitive criteria generally differ during different phases of
product life cycle (e.g. availability and technology are needed at the
‘‘introduction’’ phase, and cost, quality and speed are needed at the
‘‘maturity’’ phase).
• This investigation aims to develop a supplier selection procedure by
considering different fuzzy linguistic environments and different product
life cycle phases.
• This study uses the fuzzy linguistic quantifier guided order-weighted
aggregation (FLQG-OWA) operator.
MATHEMATICAL MODEL
1. Constructing a multiple attribute matrix for supply chain performance
and Developing into fuzzy preference relation
• Supplier performance is related to two factors:
 Feature Attribute (FA; inter-attribute) of a contract
 Behavior Characteristic (BC; intra-attribute) of a supplier
• For subsequent trade-off computing purposes, a multiple attribute matrix is
defined to represent the fuzzy preference relation of supplier BC factors.
•
The multiple attribute matrix
attribute matrix
is converted into the fuzzy multiple
using the fuzzy membership function, where:
suppliers i = 1,…,m; FA k = 1,…,5 and BC j = 1,…,n
Table 1. The core of factors on supply chain performance (FA and BC)
Table 2. Linguistic interval scale
Fig.1 Linguistic rating on membership function corresponding to fuzzy number
•
On converting into fuzzy preference relation:
 For positive BC:
 For negative BC:
where
2. Fitting supply chain strategy with fuzzy linguistic quantifier
• A FLQG-OWA operator of dimension n is a mapping to generation
function
where
guided a monotonically non-decreasing fuzzy linguistic
quantifier Q with an associated n vector
such that
.
where
denotes the jth largest of
.
• The aggregation weighted vector W is a mapping to membership function
Q(r)
Fig.2 Monotonically non-decreasing fuzzy linguistic quantifier.
Table 3. Product attributes and supply chain strategy on product life cycle.
3. Optimizing FLQG-OWA operator
• Optimizing the FLQG-OWA operator requires calculating the degree of
‘‘orness’’ and ‘‘entropy’’ (dispersion). The calculation is based on the
aggregation weighted vector W, displayed in Eqs. (5) and (6).
• Orness is a good measurement for characterizing the degree to which the
aggregation is an or-like (max-like) or and-like (min-like) operation.
• Entropy represents the measurement for characterizing the degree to which
information on the individual objectives in the aggregation process is used.
• The concept and purpose of optimization is based on the premise that the
current orness should be kept constant to implement an amendment
process for maximizing the entropy.
Maximize
subject to
• The Lagrange multiplier method can be used to obtain the maximal
entropy aggregation weighted vector W* , which can aggregate the
maximum information from objectives.
• Eq.(7) can be simplified as Eq.(8) and (9)
• The initial value of W thus is replaced by the new W* thus optimizing the
FLQG-OWA operator.
4. Aggregating on optimal FLQG-OWA operator
• Eq. (10) illustrates aggregating BCs within FA.
• Eq. (11) illustrates aggregating whole FAs.
is the jth largest of the
is the jth largest of the
ALGORITHM
NUMERICAL EXAMPLE
• Consider the case of a focal company specialized in manufacturing
notebook computers, which must select a supplier from three possible
candidates to form a local supply chain.
 Supplier A has an advantage in R&D,
 Supplier B in manufacturing,
 Supplier C in distribution.
• It is agreed that the product life cycle of notebook computers has entered the
‘‘maturity’’ phase, and the multiple attribute matrix for supply performance
and fuzzy conversion for all candidates is listed in the table 4.
Table 4. Multiple attribute matrix on supply performance and fuzzy converting
•
An example of the conversion process of the ‘‘design’’ of BC
into
:
• The aggregation weighted vector W and maximal entropy aggregation
weighted vector W* are calculated based on the number of BCs within FA.
• The computing process dealing with the fuzzy linguistic quantifier ‘‘most’’
and involving four items, j = 1,…, 4 , is displayed below:
•
Tables 5 and 6 list vector W and W* based on the number of BCs within FA
under the determined strategy.
Table 5. Vector W and W* on fitting supply chain strategy with four items
Table 6. Vector W and W* on fitting supply chain strategy with five items
•
Since the industry of notebook computer has reached the ‘‘maturity’’ phase
of its product life cycle, the ‘‘cost’’ of FA is assigned to the ‘‘critical’’
factor and ‘‘quality’’, ‘‘service’’ and ‘‘response’’ of FA are considered the
‘‘major’’ factor. Because the mass production system is generally adopted
for a mature industry, R&D advantage is no longer the focus of attention,
and thus ‘‘R&D’’ of FA is considered a ‘‘fundamental’’ factor.
•
Table 7 lists the results of aggregating BCs within FA on the optimal
FLQG-OWA operator using fuzzy linguistic quantifier considering the
supply chain strategies at the ‘‘maturity’’ phase of the product life cycle.
Table 7. Optimal aggregating BCs within FA and whole FAs (maturity)
•
•
Finally, Table 7 also shows the aggregation of whole FAs on the optimal
FLQG-OWA operator which regards as fuzzy majority rule ‘‘most’’. From
the aggregation results, Supplier B has the highest priority, followed by
Supplier A and finally Supplier C.
The optimal aggregating whole FAs for all candidates are presented as
follows:
SENSITIVITY ANALYSIS
• Different supply chain strategies could be adopted at different phases of the
product life cycle, significantly influencing supplier selection decisions.
Using the same focal company, Table 8 gives an example of aggregating
BCs within FA, and compares between the ‘‘maturity’’ and ‘‘introduction’’
phases.
Table 8. Optimal aggregating BCs within FA and whole FAs (introduction versus maturity)
• From the results of R&D FA in the ‘‘maturity’’ phase, the algorithm shows
and
for Suppliers A and B. The
model demonstrates that this approach cannot only adopt the supply chain
strategy according to the degree of concern at different phases, but also
consider the trade-off effect to avoid selecting an alternative with only one
attribute with a powerful advantage while the remainders re weak. Even
alternatives with slight power advantages are considered.
• Table 8 also lists the optimal aggregating whole FAs related to the
appropriate supply chain strategy using the data in section numerical
example for different phases of the product life cycle.
• From the results listed in Table 8 for the ‘‘maturity’’ phase, Supplier B has
the highest priority. Meanwhile, for the ‘‘introduction’’ phase, Supplier A
has the highest priority. This fact demonstrates that this approach can adopt
different supply chain strategies related to the product strategies of a focal
company.