An Evaluation Model for Green and Low-Carbon Suppliers
Amy H. I. Lee
1,2,3
, He-Yan Kang
4
, Chun Yu Lin
2
and Hsin Wei Wu
3
1
Department of Technology Management, Chung Hua University, Hsinchu, Taiwan, ROC
2
Ph. D. Program of Technology Management- Industrial Management, Chung Hua University, Hsinchu, Taiwan, ROC
3
Department of Industrial Management, Chung Hua University, Hsinchu, Taiwan, ROC
4
Department of Industrial Engineering and Management, National Chin-Yi University of Technology,
Taichung, Taiwan, ROC
Keywords: Suppliers, Low-Carbon, Fuzzy Analytic Network Process, Fuzzy Set.
Abstract: Under a conventional supplier evaluation, cost, on-time delivery and quality are treated as the most
important factors. However, in today’s increasingly environmental conscious market with growing
demands of green products, more and more firms are aiming to manufacture green products to reduce the
damage to the environment and to limit the use of energy and other resources at any stage of its life,
including raw materials, manufacture, use, and disposal. Thus, a firm needs to select the right suppliers that
not only can satisfy the basic requirements, such as cost and quality, but also can provide green and low-
carbon materials. The goal of this research is to construct a green and low-carbon supplier evaluation
model. The criteria to evaluate green and low-carbon suppliers are analyzed first, and the most important
ones are selected. Fuzzy analytic network process (FANP) model is constructed to evaluate various aspects
of suppliers. By applying the model, the manufacturer can find the most suitable suppliers for cooperation.
Goal programming (GP) is applied next to allocate the most appropriate amount of orders to each of the
selected suppliers.
1 INTRODUCTION
Firms today have entered a slim profit-margin era
due to global competition and fast-changing
technology. In order to lower costs, raise profit and
attain core technology and competitiveness in the
supply chain, firms often needs to switch from arm’s
length purchasing transactions into some kind of
buyer-supplier partnership, such as contractual
purchase and cooperative relationship. The selection
of suitable suppliers for partnership is one of the
most important steps in creating a successful supply
chain and in attaining reasonable profits for a firm
(Todeva and Knoke, 2005). In addition, to confront
the global warming problem and the increase in
environmental consciousness, many countries have
devised various environmental protection policies.
For instance, with the Energy-using Product
Directive (2005/32/EC), the European Commission
has been addressing energy-using and energy-related
products which have a considerable impact on the
energy consumption in the market (Friedman, 2008).
International environmental issues have also built up
some technical non-tariff barriers to trade.
Therefore, the communities are paying attention to
the environmental protection of the enterprises, and
international companies and original design
manufacturing (ODM) manufacturers need to start
promoting green products actively. The purpose of
this study aims to incorporate the concept of carbon
reduction and green environmental considerations in
designing a supplier selection model. The fuzzy
analytic network process (FANP) model is
constructed to calculate the weights of performance
criteria and to obtain the overall performance of
suppliers. By applying goal programming (GP), the
order allocation to the suppliers can be determined.
The model can generate a list of criteria which are
the most important for firms to assess the
performance of suppliers and to give directions for
suppliers to improve their performances.
The rest of the paper is organized as follows. In
the next section, the methodologies are introduced.
In section 3, a FANP/GP model is constructed. A
case study is presented next in section 4. In the last
section, some conclusion remarks and future
research directions are made.
604
Lee A., Kang H., Lin C. and Wu H..
An Evaluation Model for Green and Low-Carbon Suppliers.
DOI: 10.5220/0004030406040608
In Proceedings of the 9th International Conference on Informatics in Control, Automation and Robotics (OMDM-2012), pages 604-608
ISBN: 978-989-8565-22-8
Copyright
c
2012 SCITEPRESS (Science and Technology Publications, Lda.)
2 METHODOLOGIES
2.1 Fuzzy Analytic Network Process
(Fanp)
Because analytic network process (ANP) can
consider the interrelationships among elements in a
problem setting, the use of the ANP instead of
analytic hierarchy process (AHP) has increased
substantially in recent years. To consider the
fuzziness and vagueness in the decision making
process, fuzzy set theory can be incorporated into
the ANP, so called FANP. An example of the
procedures for the FANP is as follows (Kang, Lee
and Yang, 2010; Lee, Wang and Lin, 2010):
1. Decompose the problem into a network.
2. Prepare a questionnaire based on the constructed
network, and ask experts to fill out the
questionnaire. The questionnaire will be
prepared based on pairwise comparison with
Saaty’s nine point scales (Saaty, 1980). Experts
are asked to fill out the questionnaire.
Consistency index and consistency ratio for each
comparison matrix are calculated to examine the
consistency of each expert’s judgment (Saaty,
1980). If the consistency test is not passed, the
original values in the pairwise comparison matrix
must be revised by the expert.
3. Aggregate the results of the experts’
questionnaires. The scores of pairwise
comparison are transformed into linguistic
variables by the transformation concept.
According to Buckley (1985) the fuzzy positive
reciprocal matrix can be defined as:
[
]
k
ij
k
a
~
~
=Α
(1)
k
Α
~
: a positive reciprocal matrix of decision
maker k;
ij
a
~
: relative importance between decision
elements i and j;
jia
ij
=∀= ,1
~
and nji
a
a
ji
ij
,,2,1,,
~
1
~
KK=∀=
If there are k experts P
1
, P
2
…., P
k
, every pairwise
comparison between two criteria has k positive
reciprocal triangular fuzzy numbers. Employ
geometric average approach to aggregate
multiple experts’ responses, and the aggregate
fuzzy positive reciprocal matrix is:
[
]
ij
a
~
~
*
*
=
Α
(2)
where
()
k
k
ijijijij
aaaa
/1
21
*
~
......
~
~
~
⊗⊗⊗=
4.
Defuzzy the synthetic triangular fuzzy numbers
(
)
*
,,
ij ij ij ij
axyz=
%
into crisp numbers. For
instance, the center of gravity (COG) method can
be applied.
(
)
nji
zyx
ij
a
ijijij
,,2,1,,
3
*
KK=∀
+
+
=
(3)
5.
Form pairwise comparison matrices using the
defuzzificated values, and apply software, such
as Super Decisions or Excel, to form an
unweighted supermatrix. Next, form a weighted
supermatrix to ensure column stochastic.
6.
Calculate the limit supermatrix by taking the
weighted supermatrix to 2q +1 powers so that the
supermatrix converges into a stable supermatrix.
Obtain the priority weights of the alternatives
from the limit supermatrix.
2.2 Goal Programming (GP)
Goal programming (GP) is useful in dealing with
multi-criteria decision problems where the goals
cannot simultaneously be optimized, and decision
makers can consider several objectives together in
finding a set of acceptable solutions and to obtain an
optimal compromise (Lee, Kang and Chang, 2009).
The purpose of GP is to minimize the deviations
between the achievement of goals and their
aspiration levels (Chang, 2007). GP has been
applied in various studies. For example, an
integrated AHP and preemptive goal programming
methodology is developed by Wang, Huang and
Dismukes (2004) to select the best set of multiple
suppliers to satisfy capacity constraint.
The achievement function of GP is (Chang,
2007; Lee et al., 2009):
Min
)(
1
−
=
+
+
∑
i
n
i
ii
ddw
(4)
s.t.
)(Xf
i
-
∑
=+
=
−+
m
j
ijijii
BSgdd
1
)( , ni ,...,2,1=
(5)
0, ≥
−+
ii
dd , ni ,...,2,1
=
(6)
),()( xUBS
iij
∈
ni ,...,2,1
=
(7)
F
X
∈
(F is a feasible set) (8)
where
i
d is the deviation from the target value
i
g ;
i
w represents the weight attached to the deviation;
))(,0max(
iii
gXfd −=
+
and
))(,0max( Xfgd
iii
−=
−
are, respectively, over- and
under-achievements of the ith goal; )(BS
ij
AnEvaluationModelforGreenandLow-CarbonSuppliers
605
represents a function of binary serial number; and
)(xU
i
is the function of resources limitations.
Based on the fuzzy theory, the highest possible
value of membership function is 1 for something
that is more/higher the better in the aspiration levels
(Charnes and Cooper, 1961). To achieve the
maximization of )(BSg
ijij
, the flexible membership
function goal with aspiration level 1 (i.e., the highest
possible value of membership function) is (Chang,
2007):
1
)(
minmax
min
=+−
−
−
−+
ii
ijij
dd
gg
gBSg
(9)
where
max
g and
min
g
are, respectively, the upper
and lower bound of the right-hand side (i.e.,
aspiration levels) of equation (5).
For a simpler calculation, the fractional form of
equation (9) is:
1
L
1
)(
L
1
min
=+−−
−+
ii
i
ijij
i
ddgBSg
(10)
where
minmax
L gg
i
−= .
For something that is less/lower the better in the
aspiration levels, the similar idea of maximization of
)(BSg
ijij
can be used to achieve the minimization of
)(BSg
ijij
. The flexible membership function goal
with the aspiration level 1 (i.e., the lowest possible
value of membership function) is (Chang, 2007):
1
)(
minmax
max
=+−
−
−
−+
ii
ijij
dd
gg
BSgg
(11)
where
max
g and
min
g are, respectively, the upper and
lower bound of the right-hand side (i.e., aspiration
levels) of equation (5).
The fractional form of equation (11) can be
converted into a polynomial form:
1)(
L
1
L
1
max
=+−−
−+
iiijij
ii
ddBSgg
(12)
3 AN INTEGRATED MODEL FOR
FANP AND GP MODEL
The steps of the proposed FANP and GP model are
summarized as follows:
Step 1.
Define the green and low-carbon supplier
evaluation problem, and construct an
evaluation network with criteria, detailed
criteria and alternatives.
Step 2.
Prepare and distribute a questionnaire. A
questionnaire with five linguistic terms, as
shown in Table 1, is prepared based on the
constructed network.
Table 1: Triangular fuzzy numbers.
Linguistic
variable
Fuzzy number
Membership
function of fuzzy
number
Extremely
strong
9
~
(9,9,9)
Intermediate
8
~
(7,8,9)
Very strong
7
~
(6,7,8)
Intermediate
6
~
(5,6,7)
Strong
5
~
(4,5,6)
Intermediate
4
~
(3,4,5)
Moderately
strong
3
~
(2,3,4)
Intermediate
2
~
(1,2,3)
Equally strong
1
~
(1,1,1)
Step 3. Prepare pairwise comparison matrix. With
pairwise comparison of criteria with respect
to the overall objective, we can obtain a
matrix (
1k
Α
~
) for expert k:
12
1
12 1
2
2
12
1
12
C C C C C
C
1
C
1
1
1
1
C
1
1
C
1
11
1
C
ij m
kmk
mk
k
k
ijk
i
j
ijk
mk mk
m
aa
a
a
a
a
aa
⎡
⎤
⎢
⎥
⎢
⎥
⎢
⎥
⎢
⎥
⎢
⎥
=
⎢
⎥
⎢
⎥
⎢
⎥
⎢
⎥
⎢
⎥
⎢
⎥
⎢
⎥
⎣
⎦
A
LL
%%
LL LL
%
LL LL
%
MM LLLL
M
%
%
MMM LL
MMM LL
%
M
LLLLL L
LL LL
%%
(13)
where m is the number of criteria (C).
Step 4.
Aggregate experts’ opinions and build an
aggregated fuzzy pairwise comparison
matrix. Geometric average approach is
employed to aggregate experts’ responses and
to obtain a synthetic triangular fuzzy number
(Lee, 2009; Lee et al., 2009):
(
)
k
ijkijijij
aaaa
1
21
~
~
~
~
⊗⊗⊗= KK
(14)
where
(
)
ijkijkijkijk
utla ,,
~
=
The fuzzy aggregated pairwise comparison
matrix is:
ICINCO2012-9thInternationalConferenceonInformaticsinControl,AutomationandRobotics
606
12 1
2
12
1
12
1
1
1
1
1
1
1
1
11
1
⎡⎤
⎢⎥
⎢⎥
⎢⎥
⎢⎥
⎢⎥
=
⎢⎥
⎢⎥
⎢⎥
⎢⎥
⎢⎥
⎢⎥
⎢⎥
⎣⎦
%%
LLLL
%
LLLL
%
MM LLLL
%
MMM LL
%
MMM LL
%
LLLLL L
LLLL
%%
j
j
ij
ij
jj
aa
a
a
a
a
aa
A
(15)
where
(
)
ijijijij
utla ,,
~
=
Step 5.
Calculate crisp relative importance weights
(priority vectors) for factors by adopting the
center of gravity.
Step 6.
The consistency test (Saaty, 1980) is
performed by calculating the consistency
index (CI) and consistency ratio (CR). If the
consistency test is not passed, the expert will
be asked to re-do the part of the
questionnaire.
max
1
−
=
−
n
CI
n
λ
(16)
RI
CI
CR =
(17)
where
max
λ
is the largest eigenvalue of
1
A
, n
is the number of items being compared in the
matrix, and RI is random index defined by
Saaty (1980). If CR is less than 0.1, the
threshold for consistency, the expert’s
judgment is consistent. If the consistency test
is not passed, the expert will be asked to re-
do the part of the questionnaire.
Step 7.
Calculate the weights of sub-criteria, the
interdependence among sub-criteria with
respect to the same upper-level criterion, and
the performance of suppliers with respect to
each sub-criterion using a similar procedure
from Step 3 to Step 6.
Step 8.
Form an unweighted supermatrix. The local
priority vectors calculated from Step 5 and 7
are entered in the appropriate columns of a
matrix, known as an unweighted supermatrix,
as follows.
21 22
32 33
43
Goal Criteria Sub-criteria Alternatives
I
Goal
W
Criteria
WW
Sub-criteria
WI
Alternatives
w
⎡⎤
⎢⎥
=
⎢⎥
⎢⎥
⎢⎥
⎢⎥
⎣⎦
S
(18)
where
21
w is a vector that represents the
impact of the goal on the criteria,
32
W is a
matrix that represents the impact of criteria
on sub-criteria,
22
W indicates the
interdependency of the criteria,
43
W is a
matrix that represents the impact of criteria
on each of the alternatives,
33
W indicates the
interdependency of the sub-criteria, and
I is
the identity matrix (Saaty 1996).
Step 9.
Transform the unweighted supermatrix into a
weighted supermatrix (Saaty, 1996; Lee,
Chen and Tong, 2008).
Step 10.
Calculate the limit supermatrix. The
weighted supermatrix is raised to powers to
obtain the limit supermatrix.
Step 11.
Rank the suppliers. The priority weights of
the suppliers can be found in the
alternative-to-goal block, i.e. block (4,1), in
the limit supermatrix.
Step 12.
Construct a GP model for the green and
low-carbon supplier selection and order
allocation problem. Set the GP model
based on the results from Step 11 to
maximize satisfaction:
Max ....
0 1122 nn
Z
gGgG gG
=
×+×++×
(19)
Step 13.
Formulate the GP model by adopting
equations (21) to (27) to minimize the
aspiration level of i
th
objective. It is as
follows:
11 2 2
1
Min ( ( ))
n
i
iiiii
i
i
g
ZddLdd
L
+− +−
=
=+++
∑
(20)
s.t.
)(Xf
i
-
∑
=
−+
=+
m
j
ijijii
BSgdd
1
)(
n,...,2,1=
(21)
)( Xf
i
-
)1(
minmax
11 iiiiii
zgzgdd −+=+
−+
ni ,...,2,1=
(22)
=+−−+
−+
22
minmax
))1((
1
iiiiii
i
ddzgzg
L
)(
1
minmax
ii
i
gorg
L
ni ,...,2,1=
(23)
0,,,,,
2211
≥
−+−+−+
iiiiii
dddddd
ni ,...,2,1=
(24)
BX
∈
(B is a feasible set)
(25)
{
}
1,0
∈
i
z
(26)
4 A CASE STUDY
A case study is used to examine the practicality of
AnEvaluationModelforGreenandLow-CarbonSuppliers
607
the proposed FANP with GP model. A committee
of experts in the IC industry is formed to define the
problem of supplier selection. A questionnaire is
constructed and is targeted on the experts in the IC
design company. Based on the collected opinions of
the experts and the proposed model, the performance
results of the suppliers can be generated. The five
criteria and their respective sub-criteria are listed in
Table 2.
Table 2: Criteria and sub-criteria of FANP.
Criteria Sub-criteria
C1
Purchasing
management
C
11
Low pollution
C
12
Material label
C
13
Recycling
C
2
Process
management
C
21
Modularization
C
22
Process control
C
23
Technology level
C
24
Process improvement capability
C
3
Quality control
C
31
Environmental regulation fulfilment
C
32
Product quality control
C
33
Capability of handling abnormal
products
C
34
Delivery quality and date
C
35
Quality certification
C
4
Business
management
C
41
Internal education and training
C
42
Green R&D design capability
C
43
Pollution control
C
44
Regulation of harmful material control
C
5
Cost control
C
51
Production cost
C
52
Business
cost
C
53
Purchase cost
5 CONCLUSIONS
Green and low carbon supplier evaluation selection
and selection is a very complicated process
involving interrelationship among two or more firms
in a supply chain, and the process is multi-objective
in nature. This research thus develops a model for
fulfilling the task. Based on the selected criteria and
sub-criteria, fuzzy analytic network process (FANP)
is used to evaluate various aspects of suppliers, and
the most suitable suppliers for cooperation can be
obtained. Goal programming (GP) is applied next to
allocate the most appropriate amount of orders to
each of the selected suppliers. In the future, a case
study will be carried out to examine the practicality
of the proposed model. The results shall be a
reference for selecting and allocating orders to the
best green and low carbon suppliers.
ACKNOWLEDGMENTS
This work was supported in part by the National
Science Council in Taiwan under Grant NSC 99-
2632-H-216-001-MY2-2-4.
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