Research on Risk Evaluation in Supply Chain ... - ResearchGate
Research on Risk Evaluation in Supply Chain ... - ResearchGate Research on Risk Evaluation in Supply Chain ... - ResearchGate
28 JOURNAL OF COMPUTERS, VOL. 3, NO. 10, OCTOBER 2008
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28 JOURNAL OF COMPUTERS, VOL. 3, NO. 10, OCTOBER 2008<br />
<str<strong>on</strong>g>Research</str<strong>on</strong>g> <strong>on</strong> <strong>Risk</strong> Evaluati<strong>on</strong> <strong>in</strong> <strong>Supply</strong> Cha<strong>in</strong><br />
Based <strong>on</strong> Grey Relati<strong>on</strong>al Method<br />
Peide Liu<br />
Informati<strong>on</strong> Management School, Shand<strong>on</strong>g Ec<strong>on</strong>omic University, Ji’nan, Ch<strong>in</strong>a<br />
Email: Peide.liu@gmail.com<br />
T<strong>on</strong>gjuan Wang<br />
Informati<strong>on</strong> Management School, Shand<strong>on</strong>g Ec<strong>on</strong>omic University, Ji’nan, Ch<strong>in</strong>a<br />
Email: wangt<strong>on</strong>g002003@yahoo.com.cn<br />
Abstract—<strong>Supply</strong> cha<strong>in</strong> risk evaluati<strong>on</strong> is a multi-criteria<br />
decisi<strong>on</strong> mak<strong>in</strong>g problem under fuzzy envir<strong>on</strong>ments. To<br />
tackle the problem, this paper firstly identifies and discusses<br />
some of the important and critical decisi<strong>on</strong> criteria and<br />
c<strong>on</strong>structs the evaluati<strong>on</strong> <strong>in</strong>dicator framework. Then this<br />
paper presents a modified grey relati<strong>on</strong>al analysis method<br />
based <strong>on</strong> the c<strong>on</strong>cepts of ideal and anti-ideal po<strong>in</strong>ts. In the<br />
method, the weight <strong>in</strong>formati<strong>on</strong> is partially known and the<br />
vagueness and subjectivity are handled with l<strong>in</strong>guistic terms<br />
parameterized by triangular fuzzy numbers. Besides, a<br />
s<strong>in</strong>gle objective programm<strong>in</strong>g model is developed to<br />
determ<strong>in</strong>e the relati<strong>on</strong> degree between every alternative and<br />
positive ideal po<strong>in</strong>t or negative ideal po<strong>in</strong>t. By solv<strong>in</strong>g the<br />
programm<strong>in</strong>g model, the weight vector of criteria is<br />
calculated. The alternatives are ranked by the relative<br />
relati<strong>on</strong> degree. F<strong>in</strong>ally, a case study is given to dem<strong>on</strong>strate<br />
the proposed method’s effectiveness.<br />
Index Terms—supply cha<strong>in</strong>, risk evaluati<strong>on</strong>, multi-criteria<br />
decisi<strong>on</strong> mak<strong>in</strong>g, grey relati<strong>on</strong>al analysis<br />
I. INTRODUCTION<br />
Any organizati<strong>on</strong> <strong>in</strong> bus<strong>in</strong>ess today is under pressure to<br />
stay competitive and make profit. Over the last 10 to 15<br />
years, many companies urged to focus their energy <strong>on</strong><br />
core value-add<strong>in</strong>g activities by employ<strong>in</strong>g new supply<br />
cha<strong>in</strong> strategies for this reas<strong>on</strong>. Apparently, this will help<br />
companies to reduce the cost of goods, develop new<br />
markets and free-up resources. However, these benefits<br />
are often accompanied by greater supply cha<strong>in</strong><br />
complexity and exposure to new risks. Terrorist strikes,<br />
natural disasters, <strong>in</strong>dustrial acti<strong>on</strong>s and political<br />
<strong>in</strong>stability <strong>in</strong> Third World countries have awakened<br />
managers as never before to supply cha<strong>in</strong> risks. The fact<br />
is that supply cha<strong>in</strong> are not <strong>on</strong>ly more efficient but also<br />
riskier. Although it’s impossible to elim<strong>in</strong>ate risk entirely,<br />
companies still try to learn about and mitigate risk by<br />
evaluat<strong>in</strong>g the supply cha<strong>in</strong> risk. Up to date, supply cha<strong>in</strong><br />
risk evaluati<strong>on</strong> has become a key l<strong>in</strong>k of supply cha<strong>in</strong><br />
management.<br />
This work is supported by Nati<strong>on</strong>al Science Foundati<strong>on</strong> of Shand<strong>on</strong>g<br />
Prov<strong>in</strong>ce(No.Y2007H23); Corresp<strong>on</strong>d<strong>in</strong>g author: Peide Liu.<br />
The objective of supply cha<strong>in</strong> risk evaluati<strong>on</strong> is to<br />
alert the manage team to potential harm posed by <strong>in</strong>ternal<br />
and external sources. Meanwhile, systematic supply cha<strong>in</strong><br />
risk evaluati<strong>on</strong> provide a basel<strong>in</strong>e for risk c<strong>on</strong>trol<br />
plann<strong>in</strong>g. It goes without say<strong>in</strong>g that risk evaluati<strong>on</strong> is<br />
vital for effective risk c<strong>on</strong>trol. The big disasters, such as<br />
supply cha<strong>in</strong> disrupti<strong>on</strong> or break, always result from<br />
undervalu<strong>in</strong>g the element and complexity of risk. So<br />
be<strong>in</strong>g aware of the importance of supply cha<strong>in</strong> risk<br />
evaluati<strong>on</strong> is important for supply cha<strong>in</strong> risk<br />
management.<br />
<strong>Risk</strong> is the possibility of suffer<strong>in</strong>g harm or loss and<br />
born of uncerta<strong>in</strong>ty. <strong>Supply</strong> cha<strong>in</strong> risk refers to<br />
uncerta<strong>in</strong>ty or unpredictable event affect<strong>in</strong>g <strong>on</strong>e or more<br />
of the parties with<strong>in</strong> the supply cha<strong>in</strong> or its bus<strong>in</strong>ess<br />
sett<strong>in</strong>g, which can <strong>in</strong>fluence the achievement of your own<br />
bus<strong>in</strong>ess objectives [1,2]. Generally, there are two steps<br />
to take to evaluate the supply cha<strong>in</strong> risk.<br />
The first step of supply cha<strong>in</strong> risk evaluati<strong>on</strong> is to<br />
identify the risks <strong>in</strong> supply cha<strong>in</strong>, namely risk<br />
identificati<strong>on</strong>. <strong>Risk</strong> identificati<strong>on</strong> means discover<strong>in</strong>g,<br />
def<strong>in</strong><strong>in</strong>g, describ<strong>in</strong>g, document<strong>in</strong>g and communicat<strong>in</strong>g<br />
risks before they become problems and adversely affect<br />
the supply cha<strong>in</strong>. In order to manage supply cha<strong>in</strong> risks<br />
effectively and mitigate them to the most degree, the<br />
important th<strong>in</strong>g is to know what they are. This seems<br />
simple, but actually to capture all the possible risks is<br />
rather difficult, even impossible. Ow<strong>in</strong>g to the complexity<br />
of the envir<strong>on</strong>ment and limitati<strong>on</strong> of the human’s<br />
knowledge, what can be d<strong>on</strong>e is to capture as many risks<br />
as possible and make sure that as less risks as possible<br />
will be missed out. Besides, risk identificati<strong>on</strong> is a very<br />
subjective process, and to avoid the subjectivity, it is<br />
usually best to <strong>in</strong>volve outsiders as well as people who<br />
are familiar with the bus<strong>in</strong>ess and know it well. In this<br />
case, people’s expertise could be made good use of and<br />
fresh viewpo<strong>in</strong>t’s benefits will be reaped.<br />
In regard to risk identificati<strong>on</strong>, there have been a lot of<br />
research. Sunil Chopra and Sodhi surveyed a variety of<br />
risks threaten<strong>in</strong>g supply cha<strong>in</strong>s and expla<strong>in</strong>ed each of<br />
n<strong>in</strong>e categories of risk, al<strong>on</strong>g with their specific drivers:<br />
disrupti<strong>on</strong>, procurement, <strong>in</strong>tellectual property, delay,<br />
systems, forecast, receivables, <strong>in</strong>ventory, and capacity<br />
© 2008 ACADEMY PUBLISHER
JOURNAL OF COMPUTERS, VOL. 3, NO. 10, OCTOBER 2008 29<br />
[3]. Sim<strong>on</strong>s regarded that the supply cha<strong>in</strong> risk can be<br />
classified four categories: strategy risk, operati<strong>on</strong> risk,<br />
asset damage risk and competiti<strong>on</strong> risk [4]. Meulbrook<br />
stated five k<strong>in</strong>ds of supply cha<strong>in</strong> risk: customer risk,<br />
f<strong>in</strong>ancial risk, account<strong>in</strong>g risk and legal risk [5].<br />
Smallman illustrated two k<strong>in</strong>ds of risk: reputati<strong>on</strong> risk<br />
and legal risk [6]. Zhang B<strong>in</strong>gxuan studied and analyzed<br />
the risk factors of supply cha<strong>in</strong>: market risk and<br />
cooperati<strong>on</strong> risk, profit distributi<strong>on</strong> risk, profit fluctuati<strong>on</strong><br />
risk, technique risk, <strong>in</strong>formati<strong>on</strong> resource risk and moral<br />
risk [7]. Dang Xian<strong>in</strong>g classified supply cha<strong>in</strong> risk <strong>in</strong>to<br />
four categories: efficient risk, <strong>in</strong>formati<strong>on</strong> risk, capital<br />
risk and external risk [8].<br />
In brief, majority of these researches classify supply<br />
cha<strong>in</strong> risk from two perspectives: the first perspective<br />
with natural envir<strong>on</strong>ment and social envir<strong>on</strong>ment<br />
dimensi<strong>on</strong>s, Zhang B<strong>in</strong>gxuan [7], Han D<strong>on</strong>gd<strong>on</strong>g [9], L<strong>in</strong><br />
Zhaoyang [10] illustrated their views respectively from<br />
this perspective; and the other with <strong>in</strong>ternal and external<br />
dimensi<strong>on</strong>s, D<strong>in</strong>g Weid<strong>on</strong>g et. al., George A. Zsidis<strong>in</strong><br />
[11] expressed their po<strong>in</strong>ts from this perspective.<br />
The sec<strong>on</strong>d step of supply cha<strong>in</strong> risk evaluati<strong>on</strong> is<br />
determ<strong>in</strong><strong>in</strong>g which method should be used to measure the<br />
risk level. Harland et al. po<strong>in</strong>ted out the possibility of risk<br />
event relied <strong>on</strong> the risk exposure degree and occurrence<br />
possibility of trigger factors [12]. Crockford thought the<br />
result of risk event can be measured by the possibility of<br />
risk occurrence and severe degree [13]. Mitchell agreed<br />
that it was a comm<strong>on</strong> way to measure the risk from<br />
possibility and <strong>in</strong>fluence two aspects [14]. Stan smith<br />
classified the risk <strong>in</strong>to five rank from the possibility of<br />
risk occurrence and severe level two aspects and<br />
c<strong>on</strong>structed a risk evaluati<strong>on</strong> matrix with 25 panes. So<br />
accord<strong>in</strong>g to the evaluati<strong>on</strong> matrix, the identificati<strong>on</strong><br />
results of the risk <strong>in</strong> supply cha<strong>in</strong> can be classified, and<br />
different methods can be used to handle different degrees<br />
of risk [15]. Fu Yu et al. applied case-based reas<strong>on</strong><strong>in</strong>g<br />
technology <strong>in</strong> supply cha<strong>in</strong> risk evaluati<strong>on</strong>, and designed<br />
an <strong>in</strong>cidental risk estimati<strong>on</strong> system [16]. D<strong>in</strong>g Weid<strong>on</strong>g<br />
proposed a fuzzy comprehensive evaluati<strong>on</strong> method and<br />
measured the risk of supply cha<strong>in</strong> system by the<br />
reliability of supply cha<strong>in</strong> system [17]. Jiang Youl<strong>in</strong>g<br />
presented Ann-based comprehensive evaluati<strong>on</strong> model to<br />
assess supply cha<strong>in</strong> risk and studied its applicati<strong>on</strong> [18].<br />
Jiang Xiaogan, Chen Fengl<strong>in</strong>, Wang feng <strong>in</strong>vestigated<br />
from three aspects: the <strong>in</strong>ner risk of the enterprise <strong>in</strong><br />
supply cha<strong>in</strong> network, the cooperative risk between<br />
enterprises, the external envir<strong>on</strong>ment of supply cha<strong>in</strong><br />
network. Besides, they adopted fuzzy evaluati<strong>on</strong> method<br />
to def<strong>in</strong>e the probability and the <strong>in</strong>fluence degree so that<br />
risk can be evaluated by the product of these two factors<br />
[19]. Xiao Meidan, Li C<strong>on</strong>gd<strong>on</strong>g and Zhang Yugeng used<br />
the uncerta<strong>in</strong>ty and fuzzy method to calculate risk<br />
possibility and risk loss, then applied a comprehensive<br />
evaluati<strong>on</strong> model to evaluate the risk level [20].<br />
C<strong>on</strong>sider<strong>in</strong>g the advantages and disadvantages of<br />
above methods, this paper will employ a modified grey<br />
relati<strong>on</strong>al analysis method to evaluate the supply cha<strong>in</strong><br />
risk. In the method, the weight <strong>in</strong>formati<strong>on</strong> is partially<br />
known, and a s<strong>in</strong>gle objective programm<strong>in</strong>g model is<br />
developed to determ<strong>in</strong>e the weight vector. Then the<br />
relative relati<strong>on</strong> degree can be calculated, and the<br />
alternatives will be ranked by it.<br />
II. CRITERIA SELECTION FOR SUPPLY CHAIN RISK<br />
EVALUATION<br />
This paper analysis the <strong>in</strong>fluence factors to supply<br />
cha<strong>in</strong> risk from the s<strong>in</strong>gle corporati<strong>on</strong> perspective. And it<br />
divides the factors <strong>in</strong>to two k<strong>in</strong>ds: external risk and<br />
<strong>in</strong>ternal risk. External risk depends <strong>on</strong> the envir<strong>on</strong>ment<br />
outside the corporati<strong>on</strong> and the corporati<strong>on</strong> have little<br />
<strong>in</strong>fluence <strong>on</strong> such factors. What the corporati<strong>on</strong> could do<br />
is to prepare enough for such risks. Internal risk caused<br />
by the corporati<strong>on</strong> itself and could be mitigated by<br />
<strong>in</strong>vestigati<strong>on</strong> and improvement. And the corporati<strong>on</strong><br />
could do a lot <strong>in</strong> this scope. This paper studies the<br />
important characteristics of the two k<strong>in</strong>ds risks, and<br />
summarizes them as below:<br />
Political risk(C 1 ): Political risk is a type of risk faced<br />
by <strong>in</strong>vestors, corporati<strong>on</strong>s, and governments. It refers to<br />
the risk of loss when the supply cha<strong>in</strong> is disrupted by the<br />
changes <strong>in</strong> a country’s political structure or policies, such<br />
as tax laws, tariffs, expropriati<strong>on</strong> of assets. With the<br />
globalizati<strong>on</strong> become the trend of bus<strong>in</strong>ess, political<br />
change may result <strong>in</strong> disrupti<strong>on</strong> of supply cha<strong>in</strong>s around<br />
the world and br<strong>in</strong>g catastrophic results, especially for<br />
those corporati<strong>on</strong>s which have no preparati<strong>on</strong> to resp<strong>on</strong>d<br />
quickly to problems with overseas suppliers. And this<br />
<strong>in</strong>fluence is not limited to <strong>on</strong>e country, sometimes, it<br />
<strong>in</strong>volves the world.<br />
Ec<strong>on</strong>omic risk(C 2 ): Ec<strong>on</strong>omic risk is the danger that<br />
the ec<strong>on</strong>omy could br<strong>in</strong>g the loss to your supply cha<strong>in</strong>.<br />
And the risk associated with changes <strong>in</strong> exchange rates or<br />
local regulati<strong>on</strong>s, which may <strong>in</strong> your favour or favour<br />
your competitors. But th<strong>in</strong>k<strong>in</strong>g <strong>on</strong>ly about the advantages<br />
can have a downside, the companies should focus <strong>on</strong><br />
prepar<strong>in</strong>g for the probable catastrophic c<strong>on</strong>sequences<br />
caused by such risk.<br />
Technology risk(C 3 ): Technology risk is the danger<br />
caused by the development of science and technology as<br />
well as the changes of producti<strong>on</strong> mode. Technology<br />
effectively permeates the operati<strong>on</strong>s of the entire supply<br />
cha<strong>in</strong> and therefore defies compartmentalizati<strong>on</strong>. And it<br />
help to develop the key process of the supply cha<strong>in</strong>, and<br />
make it more efficient, secure. However, technology<br />
improvement also br<strong>in</strong>g risk. By understand<strong>in</strong>g the role<br />
that technology plays <strong>in</strong> supply cha<strong>in</strong>, company will be<br />
<strong>in</strong> a better positi<strong>on</strong> to handle it.<br />
Market risk(C 4 ): Market risk is exposure to uncerta<strong>in</strong>ty<br />
<strong>in</strong> loss caused by market changes. A supply cha<strong>in</strong> can not<br />
resp<strong>on</strong>sive to chang<strong>in</strong>g market trends and customer<br />
preferences without the right market signals. And it’s<br />
<strong>in</strong>evitable to lose the bus<strong>in</strong>ess opportunities <strong>in</strong> such case.<br />
Due to the new demands or the demands changes, it’s<br />
hard for a company to grasp the trend of market.<br />
Natural hazard(C 5 ): Natural hazard <strong>in</strong>cludes volcano,<br />
tsunami, tornado, flood, earthquake, bushfire etc. It is<br />
usually bey<strong>on</strong>d the power of humans to c<strong>on</strong>ta<strong>in</strong> or<br />
c<strong>on</strong>trol. A natural disaster <strong>in</strong> a country <strong>in</strong> which a factory<br />
located that is the l<strong>in</strong>k of a supply cha<strong>in</strong> may resulted <strong>in</strong> a<br />
© 2008 ACADEMY PUBLISHER
30 JOURNAL OF COMPUTERS, VOL. 3, NO. 10, OCTOBER 2008<br />
disrupti<strong>on</strong> of the whole supply cha<strong>in</strong>. In a geographical<br />
area where natural disasters are comm<strong>on</strong>, most of<br />
companies c<strong>on</strong>fessed that if a natural disaster occurred<br />
they probably can not ma<strong>in</strong>ta<strong>in</strong> bus<strong>in</strong>ess operati<strong>on</strong>s and<br />
supply obligati<strong>on</strong>s.<br />
Cooperative risk(C 6 ): Cooperative risk means the loss<br />
result from the cooperati<strong>on</strong> breakdown or changes am<strong>on</strong>g<br />
the participants <strong>in</strong> the supply cha<strong>in</strong>. This may lead to bad<br />
results, such as supply cha<strong>in</strong> disrupti<strong>on</strong> or failure. And<br />
the distrust between the copartners <strong>in</strong> the supply cha<strong>in</strong> is<br />
supported to be the most important factor to br<strong>in</strong>g about<br />
such results.<br />
Management decisi<strong>on</strong> risk(C 7 ): As the bus<strong>in</strong>ess world<br />
becomes more complex, the decisi<strong>on</strong> envir<strong>on</strong>ment turn to<br />
be vague and uncerta<strong>in</strong>. So to make a right decisi<strong>on</strong> more<br />
depend <strong>on</strong> the understand<strong>in</strong>g of decisi<strong>on</strong> <strong>in</strong>formati<strong>on</strong> and<br />
the decisi<strong>on</strong> experience <strong>in</strong> the same circumstance. And<br />
for those who have a bad sense and are <strong>in</strong>experienced,<br />
this would be a missi<strong>on</strong> impossible.<br />
Informati<strong>on</strong> shar<strong>in</strong>g risk(C 8 ): The central purpose of<br />
<strong>in</strong>formati<strong>on</strong> shar<strong>in</strong>g is to assist <strong>in</strong> m<strong>in</strong>imiz<strong>in</strong>g the risk of<br />
harm to supply cha<strong>in</strong>. But the fact is <strong>in</strong>formati<strong>on</strong> shar<strong>in</strong>g<br />
accompanies greater risk. Sensitive <strong>in</strong>formati<strong>on</strong> revealed<br />
might result <strong>in</strong> loss of an advantage or level of security<br />
and may lead to the disrupti<strong>on</strong> of supply cha<strong>in</strong>. So to be<br />
clear with what <strong>in</strong>formati<strong>on</strong> can be shared and what can<br />
not will help the companies ma<strong>in</strong>ta<strong>in</strong> an efficient but<br />
secure supply cha<strong>in</strong>.<br />
Operati<strong>on</strong> schedule risk(C 9 ): Operati<strong>on</strong> schedule risk<br />
is the danger of loss <strong>in</strong> fail<strong>in</strong>g to meet schedule plans.<br />
S<strong>in</strong>ce uncerta<strong>in</strong>ly exists <strong>in</strong> every schedule. So it is<br />
impossible to predict, with complete c<strong>on</strong>fidence, the<br />
length of time necessary to produce the product, to<br />
deliver the product etc. And Schedule delay often results<br />
<strong>in</strong> loss of revenue, costs <strong>in</strong>creas<strong>in</strong>g and reputati<strong>on</strong><br />
damage.<br />
F<strong>in</strong>ancial risk(C 10 ): F<strong>in</strong>ancial risk is normally any risk<br />
associated with any form of f<strong>in</strong>anc<strong>in</strong>g. Fac<strong>in</strong>g f<strong>in</strong>ancial<br />
risk, the company <strong>in</strong> today’s bus<strong>in</strong>ess world need take<br />
TABLE I.<br />
INDICATOR SYSTEM FOR SUPPLY CHAIN RISK EVALUATION<br />
<strong>Risk</strong> category<br />
External risk<br />
Internal risk<br />
Political risk(C 1 )<br />
Ec<strong>on</strong>omic risk(C 2 )<br />
Technology risk(C 3 )<br />
Market risk(C 4 )<br />
Nature hazard(C 5 )<br />
Cooperative risk(C 6 )<br />
Criteria<br />
Management decisi<strong>on</strong> risk(C 7 )<br />
Informati<strong>on</strong> shar<strong>in</strong>g risk(C 8 )<br />
Operati<strong>on</strong> schedule risk(C 9 )<br />
F<strong>in</strong>ancial risk(C 10 )<br />
Human resource risk(C 11 )<br />
acti<strong>on</strong>s to mitigate the risk and create ec<strong>on</strong>omic value by<br />
us<strong>in</strong>g f<strong>in</strong>ancial <strong>in</strong>struments to manage exposure to risk.<br />
Human resource risk(C 11 ): Human resource risks are<br />
events that prevent employees from fulfill<strong>in</strong>g their<br />
resp<strong>on</strong>sibilities and thus keep the supply cha<strong>in</strong> from<br />
operat<strong>in</strong>g at full efficiency. Human resource risks<br />
<strong>in</strong>cludes death, disability, divorce, employee turnover etc.<br />
The ideal way to deal with human resource risk is to keep<br />
a c<strong>on</strong>t<strong>in</strong>gency plan <strong>in</strong> case of the available of key<br />
pers<strong>on</strong>nel.<br />
III. THE PROPOSED MODEL<br />
Suppose D is the decisi<strong>on</strong> matrix, A 1 , A 2 , … , A m are<br />
the alternatives to be chosen, C 1 , C 2 , …, C n denote the<br />
evaluati<strong>on</strong> criteria, x ij represents the rat<strong>in</strong>g of alternative<br />
A i with respect to criteri<strong>on</strong> C j .<br />
So a typical fuzzy multi-criteria decisi<strong>on</strong>-mak<strong>in</strong>g<br />
problem can be expressed <strong>in</strong> matrix format as<br />
C1<br />
C2<br />
L Cn<br />
A1<br />
⎡ x11<br />
x12<br />
L x1n<br />
⎤<br />
⎢<br />
⎥<br />
D = A2<br />
⎢<br />
x21<br />
x22<br />
L x2n<br />
⎥ ,<br />
M ⎢ M M M M ⎥<br />
⎢<br />
⎥<br />
Am<br />
⎣xm1<br />
xm2<br />
L xmn<br />
⎦<br />
where, i =1, 2, …, m, j=1, 2, …, n, x ij is denoted by<br />
l<strong>in</strong>guistic term.<br />
T<br />
Let ϖ = w , w , ) be weight vector, w j be<br />
(<br />
1 2<br />
Lw n<br />
n<br />
∑ i = 1<br />
the weight of criteri<strong>on</strong> C j , and w = 1 .<br />
Ow<strong>in</strong>g to the complexity of evaluati<strong>on</strong> object, the<br />
evaluators usually just give partial weight <strong>in</strong>formati<strong>on</strong>.<br />
And there are 6 forms of partial weight <strong>in</strong>formati<strong>on</strong><br />
usually given by evaluators:<br />
wi ≥ w j<br />
,<br />
wi<br />
≥ ∂ijw<br />
j<br />
,<br />
wi − w j<br />
≥ βij<br />
,<br />
γ<br />
j<br />
≤ w<br />
j<br />
≤ η<br />
j<br />
,<br />
σ<br />
ij<br />
≤ wi<br />
/ w<br />
j<br />
≤ ζ<br />
ij<br />
,<br />
w + w ≤ 2w<br />
( i ≠ j ≠ k)<br />
,<br />
where<br />
ij<br />
i<br />
j<br />
j<br />
j<br />
∂ β , γ , η , σ , ζ are n<strong>on</strong>negative<br />
,<br />
ij<br />
c<strong>on</strong>stant numbers. For dem<strong>on</strong>strat<strong>in</strong>g the steps of the<br />
method, let Q be the set of above 6 forms.<br />
A. Normalize the Decisi<strong>on</strong> Matrix<br />
x ij is represented by l<strong>in</strong>guistic term, and x<br />
ij<br />
∈ S , S =<br />
{S1=EL, S2=VL, S3=L, S4=M, S5=H, S6=VH, S7=EH}.<br />
The exact mean<strong>in</strong>g of the elements <strong>in</strong> S is given <strong>in</strong><br />
Table II.<br />
Generally criteria can be classified <strong>in</strong>to two types:<br />
benefit criteria and cost criteria.<br />
For benefit criteria, the normalized formula is:<br />
ij<br />
ij<br />
k<br />
j<br />
© 2008 ACADEMY PUBLISHER
JOURNAL OF COMPUTERS, VOL. 3, NO. 10, OCTOBER 2008 31<br />
If x<br />
ij<br />
= S , x~ = S , j ∈ I'<br />
, (1)<br />
i<br />
For cost criteria, the normalized formula is:<br />
If x = = S<br />
n i<br />
j ∈ I ′<br />
ij<br />
Si<br />
, x~<br />
ij + 1−<br />
, , (2)<br />
where, n is the number of elements <strong>in</strong> S, here n=7,<br />
x~<br />
ij is the normalized form of x ij<br />
, I′ is associated with<br />
benefit criteria and I ′ is associated with cost criteria.<br />
B. C<strong>on</strong>vert the L<strong>in</strong>guistic Term <strong>in</strong>to Triangular Fuzzy<br />
Number<br />
S<strong>in</strong>ce the subjective judgment or predicti<strong>on</strong> of an<br />
expert may be ill expressed, it is reas<strong>on</strong>able to represent<br />
x ij as l<strong>in</strong>guistic variables and then c<strong>on</strong>verted it <strong>in</strong>to<br />
triangular fuzzy number. Table II shows the l<strong>in</strong>guistic<br />
values and their corresp<strong>on</strong>d<strong>in</strong>g triangular fuzzy numbers.<br />
So the l<strong>in</strong>guistic term x ij can be c<strong>on</strong>verted to triangular<br />
fuzzy number as<br />
L M U<br />
v = ( v , v , v ) .<br />
ij<br />
ij<br />
C. Determ<strong>in</strong>e the Ideal and Negative Ideal Soluti<strong>on</strong>s<br />
The fuzzy positive-ideal soluti<strong>on</strong> (FPIS,A * ) and the<br />
fuzzy negative-ideal soluti<strong>on</strong> (FNIS,A - ) are shown <strong>in</strong> the<br />
follow<strong>in</strong>g equati<strong>on</strong>s:<br />
A<br />
*<br />
* *<br />
= { v ,... v } = {max v | i = 1,2, K m,<br />
j = 1,2, K,<br />
n}<br />
, (3)<br />
1<br />
j<br />
i<br />
ij<br />
− − −<br />
A = { v 1<br />
,... v } = {m<strong>in</strong> v | i = 1,2 K m,<br />
j = 1,2, K,<br />
n}<br />
. (4)<br />
j<br />
i<br />
ij<br />
D. Calculate the Grey Relati<strong>on</strong> Coefficient<br />
The relati<strong>on</strong> coefficient between alternative i and FPIS<br />
with respect to criteri<strong>on</strong> C j (namely V ) is as follows:<br />
d<br />
=<br />
ij<br />
V<br />
ij<br />
= d(<br />
v<br />
1<br />
[( v<br />
3<br />
ij<br />
ij<br />
ij<br />
m<strong>in</strong> m<strong>in</strong> dij<br />
+ ρ max max dij<br />
i j<br />
i j<br />
= . (5)<br />
d + ρ max max d<br />
*<br />
j<br />
L*<br />
j<br />
,v )<br />
ij<br />
− v<br />
L<br />
ij<br />
2<br />
) + ( v<br />
M *<br />
j<br />
i<br />
− v<br />
i<br />
M<br />
ij<br />
ij<br />
ij<br />
j<br />
2<br />
) + ( v<br />
ij<br />
U *<br />
j<br />
− v<br />
U<br />
ij<br />
2<br />
) ]<br />
. (6)<br />
The relati<strong>on</strong> coefficient between alternative A i and<br />
FNIS with respect to criteri<strong>on</strong> C j (namely W<br />
ij<br />
) is as<br />
follows:<br />
ij<br />
W<br />
ij<br />
1<br />
[( v<br />
3<br />
m<strong>in</strong> m<strong>in</strong> s<br />
i<br />
s<br />
ij<br />
j<br />
ij<br />
+ ρ max max s<br />
= . (7)<br />
−<br />
j<br />
s = d(<br />
v<br />
=<br />
L−<br />
j<br />
, v )<br />
ij<br />
− v<br />
+ ρ max max s<br />
i<br />
L 2 M − M 2 U − U<br />
ij<br />
) + ( v<br />
j<br />
− vij<br />
) + ( v<br />
j<br />
− vij<br />
i<br />
j<br />
j<br />
ij<br />
ij<br />
2<br />
) ]<br />
. (8)<br />
TABLE II.<br />
LINGUISTIC TERMS AND THEIR CORRESPONDING TRIANGULAR FUZZY<br />
NUMBERS<br />
L<strong>in</strong>guistic values<br />
Extremely high(EH) (0.95,1,1)<br />
Very high(VH) (0.7,0.85,1)<br />
High(H) (0.55,0.7,0.85)<br />
Medium(M) (0.35,0.5,0.65)<br />
Low(L) (0.15,0.3,0.45)<br />
Very low(VL) (0,0.15,0.3)<br />
Extremely low(EL) (0,0,0.05)<br />
Where, i=1,2,…m, j=1,2,…n, d ij is the distance<br />
between triangular fuzzy numbers v * j and v ij , s ij is the<br />
-<br />
distance between triangular fuzzy numbers v j and v ij .<br />
ρ is the discrim<strong>in</strong>ati<strong>on</strong> coefficient, ρ ∈[0,1]<br />
and<br />
generally ρ =0.5. The relati<strong>on</strong> coefficient vector between<br />
alternative A i and FPIS(A * ) is<br />
(<br />
i<br />
, Vi2<br />
V , V )<br />
1<br />
L<br />
<strong>in</strong><br />
,<br />
and the relati<strong>on</strong> coefficient vector of alternative A i and<br />
FNIS(A - ) is<br />
(<br />
i<br />
, Wi2<br />
<strong>in</strong><br />
T<br />
W , W )<br />
T<br />
1<br />
L .<br />
E. C<strong>on</strong>struct the S<strong>in</strong>gle Objective Programm<strong>in</strong>g Problem<br />
to Determ<strong>in</strong>e the Weight Vector<br />
Suppose<br />
V<br />
i<br />
=<br />
n<br />
∑<br />
j=<br />
1<br />
V<br />
ij<br />
w<br />
j<br />
∑<br />
, W = W w ,<br />
i<br />
n<br />
j=<br />
1<br />
Where, i=1,2…,m. For get V i and W i , the vector<br />
T<br />
ϖ = ( w<br />
1,<br />
w2,<br />
Lw n<br />
) is need to be determ<strong>in</strong>ed first. So<br />
the multi-objective optimizati<strong>on</strong> model is developed to<br />
T<br />
get ϖ .<br />
=<br />
(<br />
1,<br />
w2,<br />
Lw n<br />
w )<br />
maxV<br />
m<strong>in</strong>W<br />
i<br />
i<br />
s.<br />
t.<br />
w<br />
w<br />
=<br />
=<br />
j<br />
j<br />
n<br />
∑<br />
j=<br />
1<br />
n<br />
∑<br />
j=<br />
1<br />
W w , i = 1,2,..., m,<br />
∈ Q,<br />
j = 1,2,... n,<br />
n<br />
∑<br />
j=<br />
1<br />
V w , i = 1,2,..., m,<br />
ij<br />
ij<br />
w<br />
j<br />
Triangular fuzzy numbers<br />
j<br />
= 1,<br />
ij<br />
≥ 0, j = 1,2,... n.<br />
S<strong>in</strong>ce every alternative is fair competiti<strong>on</strong> and there is<br />
no preference relati<strong>on</strong>, the above multi-objective<br />
optimizati<strong>on</strong> model can c<strong>on</strong>verted <strong>in</strong>to s<strong>in</strong>gle objective<br />
programm<strong>in</strong>g problem.<br />
j<br />
j<br />
(9)<br />
© 2008 ACADEMY PUBLISHER
32 JOURNAL OF COMPUTERS, VOL. 3, NO. 10, OCTOBER 2008<br />
TABLE III.<br />
TRIANGULAR FUZZY NUMBER DECISION MATRIX<br />
C 1 C 2 C 3 C 4 C 5 C 6<br />
A 1 (0,0,0.05) (0.95,1,1) (0.15,0.3,0.45) (0.35,0.5,0.65) (0.35,0.5,0.65) (0.35,0.5,0.65)<br />
A 2 (0,0.15,0.3) (0.95,1,1) (0.15,0.3,0.45) (0,0,0.05) (0.7,0.85,1) (0.35,0.5,0.65)<br />
A 3 (0,0.15,0.3) (0.35,0.5,0.65) (0.35,0.5,0.65) (0.55,0.7,0.85) (0.7,0.85,1) (0,0,0.05)<br />
A 4 (0,0.15,0.3) (0.35,0.5,0.65) (0.35,0.5,0.65) (0.55,0.7,0.85) (0,0.15,0.3) (0.15,0.3,0.45)<br />
C 7 C 8 C 9 C 10 C 11<br />
A 1 (0.55,0.7,0.85) (0.7,0.85,1) (0.95,1,1) (0.35,0.5,0.65) (0.35,0.5,0.65)<br />
A 2 (0.55,0.7,0.85) (0.35,0.5,0.65) (0.35,0.5,0.65) (0.7,0.85,1) (0.95,1,1)<br />
A 3 (0.7,0.85,1) (0.35,0.5,0.65) (0.35,0.5,0.65) (0.7,0.85,1) (0.95,1,1)<br />
A 4 (0.35,0.5,0.65) (0.95,1,1) (0.55,0.7,0.85) (0.7,0.85,1) (0.35,0.5,0.65)<br />
m<strong>in</strong>D<br />
=<br />
s.<br />
t.<br />
w<br />
w<br />
j<br />
j<br />
m<br />
i= 1 j=<br />
1<br />
( W<br />
∈ Q,<br />
j = 1,2,... n,<br />
n<br />
∑<br />
j=<br />
1<br />
n<br />
∑∑<br />
w<br />
j<br />
ij<br />
= 1,<br />
−V<br />
) w ,<br />
ij<br />
≥ 0, j = 1,2,... n.<br />
And with the s<strong>in</strong>gle objective programm<strong>in</strong>g problem,<br />
the weight vector ϖ can be determ<strong>in</strong>ed.<br />
j<br />
(10)<br />
F. Calculate the Relative Relati<strong>on</strong> Degree of Alternatives<br />
C<br />
V<br />
i<br />
i<br />
= . (11)<br />
Vi<br />
+ Wi<br />
Choose an alternative with maximum C i or rank<br />
alternatives accord<strong>in</strong>g to C i <strong>in</strong> ascend<strong>in</strong>g order.<br />
IV. EMPIRICAL STUDY OF SUPPLY CHAIN RISK<br />
ASSESSMENT<br />
<strong>Supply</strong> cha<strong>in</strong> risk evaluati<strong>on</strong> is generally complex <strong>in</strong><br />
operati<strong>on</strong> and it <strong>in</strong>volves a variety of factors aris<strong>in</strong>g from<br />
envir<strong>on</strong>ment, social, and even political c<strong>on</strong>cerns. Ow<strong>in</strong>g<br />
to the uncerta<strong>in</strong>ty <strong>in</strong> human judgment, decisi<strong>on</strong> mak<strong>in</strong>g <strong>in</strong><br />
supply cha<strong>in</strong> risk evaluati<strong>on</strong> is actually a multi-criteria<br />
decisi<strong>on</strong> mak<strong>in</strong>g problem under fuzzy envir<strong>on</strong>ment. Here<br />
we use the proposed method to evaluate the supply cha<strong>in</strong><br />
risk of 4 enterprises <strong>in</strong> Shand<strong>on</strong>g prov<strong>in</strong>ce of Ch<strong>in</strong>a.<br />
The partial weight <strong>in</strong>formati<strong>on</strong> is given as follows:<br />
w<br />
1<br />
/ w2<br />
= 0.07 ;<br />
w<br />
8<br />
>= 0.03 .<br />
w<br />
3<br />
>= 0.09<br />
And the l<strong>in</strong>guistic decisi<strong>on</strong> matrix is as follows:<br />
⎡EH<br />
EL H M M M L VL EL M M⎤<br />
⎢<br />
⎥<br />
= ⎢<br />
VH EL H EH VL M L M M VL EL .<br />
D<br />
⎥<br />
⎢VH<br />
M M L VL EH VL M M VL EL⎥<br />
⎢<br />
⎥<br />
⎣VH<br />
M M L VH H M EL L VL M ⎦<br />
Step1 normalized the decisi<strong>on</strong> matrix<br />
S<strong>in</strong>ce these criteria are all cost criteria, with (2), the<br />
normalized decisi<strong>on</strong> matrix is:<br />
⎡EL<br />
EH L M M M H VH EH M M ⎤<br />
⎢<br />
⎥<br />
= ⎢<br />
VL EH L EL VH M H M M VH EH<br />
D ~ .<br />
⎥<br />
⎢VL<br />
M M H VH EL VH M M VH EH⎥<br />
⎢<br />
⎥<br />
⎣VL<br />
M M H VL L M EH H VH M ⎦<br />
Step 2 c<strong>on</strong>vert the l<strong>in</strong>guistic term <strong>in</strong>to triangular fuzzy<br />
number<br />
Accord<strong>in</strong>g to Table II, c<strong>on</strong>vert the l<strong>in</strong>guistic decisi<strong>on</strong><br />
matrix <strong>in</strong>to triangular fuzzy number decisi<strong>on</strong> matrix, and<br />
get the matrix shown <strong>in</strong> Table III.<br />
Step 3 Determ<strong>in</strong>e the ideal and negative ideal soluti<strong>on</strong>s<br />
With (3) and (4), we get<br />
*<br />
A =<br />
((0.00,0.15,0.30), (0.95,1.00,1.00), (0.35,0.50,0.65),<br />
(0.55,0.70,0.85), (0.70,0.85,1.00), (0.35,0.50,0.65), .<br />
(0.70,0.85,1.00), (0.95,1.00,1.00), (0.95,1.00,1.00),<br />
(0.70,0.85,1.00), (0.95,1.00,1.00))<br />
A − = ((0.00,0.00,0.05), (0.35,0.50,0.65), (0.15,0.30,0.45),<br />
(0.00,0.00,0.05), (0.00,0.15,0.30), (0.00,0.00,0.05), .<br />
(0.35,0.50,0.65), (0.35,0.50,0.65), (0.35,0.50,0.65),<br />
(0.35,0.50,0.65), (0.35,0.50,0.65))<br />
Step 4 calculate the grey relati<strong>on</strong> coefficient<br />
Use (6) and (8) to get V ij and W ij as follows:<br />
© 2008 ACADEMY PUBLISHER
JOURNAL OF COMPUTERS, VOL. 3, NO. 10, OCTOBER 2008 33<br />
V ij<br />
⎡0.675<br />
⎢<br />
⎢<br />
1.000<br />
=<br />
⎢1.000<br />
⎢<br />
⎣1.000<br />
1.000<br />
1.000<br />
0.415<br />
0.415<br />
0.636<br />
0.636<br />
1.000<br />
1.000<br />
0.636<br />
0.336<br />
1.000<br />
1.000<br />
0.500<br />
1.000<br />
1.000<br />
0.333<br />
1.000<br />
1.000<br />
0.415<br />
0.636<br />
0.700<br />
0.700<br />
1.000<br />
0.500<br />
0.675<br />
0.415<br />
0.415<br />
1.000<br />
1.000<br />
0.415<br />
0.415<br />
0.537<br />
0.500<br />
1.000<br />
1.000<br />
1.000<br />
0.415 ⎤<br />
1.000<br />
⎥ .<br />
⎥<br />
1.000 ⎥<br />
⎥<br />
0.415 ⎦<br />
W ij<br />
⎡1.000<br />
⎢<br />
⎢<br />
0.675<br />
=<br />
⎢0.675<br />
⎢<br />
⎣0.675<br />
0.415<br />
0.415<br />
1.000<br />
1.000<br />
1.000<br />
1.000<br />
0.636<br />
0.636<br />
0.415<br />
1.000<br />
0.336<br />
0.336<br />
0.500<br />
0.333<br />
0.333<br />
1.000<br />
0.415<br />
0.415<br />
1.000<br />
0.537<br />
0.636<br />
0.636<br />
0.500<br />
1.000<br />
0.500<br />
1.000<br />
1.000<br />
0.415<br />
0.415<br />
1.000<br />
1.000<br />
0.636<br />
1.000<br />
0.500<br />
0.500<br />
0.500<br />
1.000 ⎤<br />
0.415<br />
⎥ .<br />
⎥<br />
0.415 ⎥<br />
⎥<br />
1.000 ⎦<br />
Step 5 Calculate the weight vector<br />
⎧<br />
⎪<br />
⎪m<strong>in</strong>D<br />
= −0.649w1<br />
− 0.886w4<br />
− 0.667w<br />
⎨s.t.w<br />
j<br />
∈ Q,<br />
j = 1,2,....,11,<br />
⎪ 11<br />
⎪ =<br />
⎪∑<br />
w j<br />
1<br />
⎩ j=<br />
1<br />
5<br />
− 0.684w<br />
6<br />
− 0.127w<br />
7<br />
+ 0.410w<br />
8<br />
+ 0.684w<br />
9<br />
− w<br />
10<br />
Then, the weight vector<br />
ϖ = (0.172, 0.143, 0.090, 0.060,<br />
0.112,<br />
T<br />
0.080, 0.030, 0.163, 0.040, 0.070)<br />
And<br />
V 1 = 0.739 V 2 = 0.790<br />
V 3 = 0.780 V 4 = 0.671<br />
W 1 = 0.662 W 2 = 0.672<br />
W 3 = 0.696 W 4 = 0.756<br />
Step 6 Rank the alternatives<br />
Accord<strong>in</strong>g to (11),<br />
C 1 = 0.527 C 2 = 0.540<br />
C 3 = 0.528 C 4 = 0.470<br />
So,<br />
f f f ,<br />
A<br />
2<br />
A3<br />
A1<br />
A4<br />
Namely, alternative A 2 has least risk.<br />
0.040,<br />
V. RESULTS OF COMPARISION<br />
In order to validate the advantages and <strong>in</strong>troduce the<br />
applicati<strong>on</strong> field, this secti<strong>on</strong> compare the results of the<br />
proposed method and the TOPSIS method based <strong>on</strong> the<br />
data <strong>in</strong> Table III.<br />
And the TOPSIS method used <strong>in</strong> this paper <strong>in</strong>cludes<br />
such steps:<br />
1) Normalize the Decisi<strong>on</strong> Matrix<br />
Use (2) to get normalized decisi<strong>on</strong> matrix.<br />
2) C<strong>on</strong>vert the L<strong>in</strong>guistic Term <strong>in</strong>to Triangular Fuzzy<br />
Number<br />
Accord<strong>in</strong>g to the corresp<strong>on</strong>d<strong>in</strong>g relati<strong>on</strong>ship between<br />
l<strong>in</strong>guistic term and triangular fuzzy number listed <strong>in</strong> the<br />
Table II, the triangular fuzzy number-valued decisi<strong>on</strong><br />
matrix can be got.<br />
ρ = 0.1<br />
TABLE IV.<br />
CALCULATION RESULTS OF PROPOSED METHOD AND TOPSIS<br />
The proposed method with ρ equal to different values<br />
ρ = 0.3 ρ = 0.5 ρ = 0.7<br />
TOPSIS<br />
ρ = 0.9 TOPSIS<br />
Alternative C i CC i<br />
A1 0.519 0.529 0.527 0.525 0.522 0.381<br />
A2 0.586 0.554 0.540 0.532 0.527 0.389<br />
A3 0.576 0.542 0.528 0.522 0.518 0.433<br />
A4 0.470 0.467 0.470 0.474 0.477 0.624<br />
A2 A2 A2 A2 A2 A1<br />
Rank Results<br />
A3 A3 A3 A1 A1 A2<br />
A1 A1 A1 A3 A3 A3<br />
A4 A4 A4 A4 A4 A4<br />
© 2008 ACADEMY PUBLISHER
34 JOURNAL OF COMPUTERS, VOL. 3, NO. 10, OCTOBER 2008<br />
3) Determ<strong>in</strong>e the Ideal and Negative Ideal Soluti<strong>on</strong>s<br />
Use (3) and (4) to determ<strong>in</strong>e ideal and negative ideal<br />
soluti<strong>on</strong>s.<br />
4) Calculate the Grey Relati<strong>on</strong> Coefficient<br />
Use (5), (6), (7) and (8) to calculate the grey relati<strong>on</strong><br />
coefficient.<br />
5) C<strong>on</strong>struct the S<strong>in</strong>gle Objective Programm<strong>in</strong>g<br />
Problem to Determ<strong>in</strong>e the Weight Vector<br />
Use (10) to figure out the weight vector.<br />
6) Calculate the Distance between alternative A i and<br />
FPIS / FNIS<br />
Let d i + be the distance between alternative A i and FPIS ,<br />
d i<br />
-<br />
be the distance between alternative A i and FNIS. And<br />
the formula of d i + and d i - are:<br />
+ n<br />
i<br />
= ∑<br />
j=<br />
1<br />
j<br />
( v ,<br />
* ij<br />
v<br />
j<br />
)<br />
d w d . (12)<br />
d<br />
− n<br />
i<br />
= ∑<br />
j=<br />
1<br />
Where, i = 1 ,2L m,<br />
j = 1,2,<br />
Ln<br />
.<br />
7) Calculate the Closeness coefficient<br />
−<br />
di<br />
CCi<br />
=<br />
d + d<br />
j<br />
ij<br />
−<br />
j<br />
w d( v , v ) . (13)<br />
+ −<br />
i i<br />
. (14)<br />
Rank the alternatives with the value of CC i . The bigger<br />
the value of CC i , the alternative has the less risk.<br />
From the calculati<strong>on</strong> results of proposed methods and<br />
TOPSIS listed <strong>in</strong> Table IV, it is clear that the rank results<br />
of proposed method and TOPSIS are different. The<br />
alternative 4 has the same positi<strong>on</strong>, but the rank order of<br />
alternative 1,2,3 are different. This is because TOPSIS<br />
method c<strong>on</strong>centrate <strong>on</strong> how to balance the attribute<br />
values of alternatives, it take little c<strong>on</strong>siderati<strong>on</strong> of the<br />
positi<strong>on</strong> <strong>in</strong> the rank order of attribute values. This means<br />
when an alternative with 8 attributes has 7 attributes<br />
values be<strong>in</strong>g <strong>in</strong> good positi<strong>on</strong> of the rank order, but has<br />
an attribute which values is extreme small, it is possible<br />
that this alternative can be rank last.<br />
But the proposed method try to balance not <strong>on</strong>ly the<br />
attribute values but also the positi<strong>on</strong>s <strong>in</strong> rank orders of<br />
attribute values. So, for alternatives, like alternative 4,<br />
which have too much difference with others, the two<br />
methods will give the same rank orders, but for those<br />
which gap is not small, they will give different ranks<br />
ow<strong>in</strong>g to the characteristics of two methods, like the<br />
alternatives 1, 2, 3.<br />
So the result is when the decisi<strong>on</strong> situati<strong>on</strong> need to<br />
<strong>on</strong>ly c<strong>on</strong>sider the attribute values , the TOPSIS method is<br />
suitable, while when it is necessary to c<strong>on</strong>sider not <strong>on</strong>ly<br />
the attribute value but its rank positi<strong>on</strong>, the proposed<br />
method <strong>in</strong> this paper is suitable.<br />
Moreover, Table IV also lists the results of the<br />
proposed method with ρ is equal to different values. It<br />
shows the calculati<strong>on</strong> results may be different when ρ is<br />
set to be different values. When ρ =0.1, 0.3, 0.5, the<br />
rank results are same. And when ρ =0.5, 0.9, the rank<br />
results are same. It is clear that when ρ is bigger, the<br />
alternatives will take more c<strong>on</strong>siderati<strong>on</strong> from the<br />
perspective of the rank positi<strong>on</strong>.<br />
In brief, the proposed method <strong>in</strong> this paper not <strong>on</strong>ly<br />
balance the attribute values but also balance the positi<strong>on</strong><br />
<strong>in</strong> rank orders. And ρ goes to bigger when the<br />
alternatives need to be taken more c<strong>on</strong>siderati<strong>on</strong> of the<br />
positi<strong>on</strong> factors.<br />
VI. CONCLUSIONS<br />
<strong>Supply</strong> cha<strong>in</strong> risk evaluati<strong>on</strong> is an important part of<br />
supply cha<strong>in</strong> risk management. To date, there have been a<br />
number of evaluati<strong>on</strong> method. This paper develops a<br />
novel method based <strong>on</strong> grey relati<strong>on</strong>al analysis. And this<br />
method c<strong>on</strong>siders the overall risk level of criteria, takes<br />
the risk evaluati<strong>on</strong> problem as the multi-criteria decisi<strong>on</strong>mak<strong>in</strong>g<br />
problem. Besides, to address the effectiveness of<br />
the proposed methodology, this paper compared the<br />
results of TOPSIS method and the proposed<br />
methodology. The result shows the advantages and<br />
applicati<strong>on</strong> scope of the proposed method.<br />
ACKNOWLEDGMENT<br />
The authors gratefully acknowledge the f<strong>in</strong>ancial<br />
support from Nature Science Foundati<strong>on</strong> of Shand<strong>on</strong>g<br />
Prov<strong>in</strong>ce(No.Y2007H23). The authors also would like<br />
to express appreciati<strong>on</strong> to the an<strong>on</strong>ymous reviewers for<br />
their very helpful comments <strong>on</strong> improv<strong>in</strong>g the paper.<br />
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Peide Liu (Ch<strong>in</strong>a, 1966) graduated from the Southeast<br />
University and obta<strong>in</strong>ed the bachelor degree <strong>in</strong> electr<strong>on</strong>ic<br />
technology. And then he obta<strong>in</strong>ed his master degree <strong>in</strong><br />
<strong>in</strong>formati<strong>on</strong> process<strong>in</strong>g <strong>in</strong> the Southeast University. At present,<br />
he is study<strong>in</strong>g his <strong>in</strong>-service doctor of <strong>in</strong>formati<strong>on</strong> management<br />
<strong>in</strong> Beij<strong>in</strong>g Jiaot<strong>on</strong>g University. His ma<strong>in</strong> research fields are<br />
technology and <strong>in</strong>formati<strong>on</strong> management, decisi<strong>on</strong> support and<br />
electr<strong>on</strong>ic-commerce.<br />
He was engaged <strong>in</strong> the technology development and the<br />
technical management <strong>in</strong> the Inspur company a few years ago.<br />
Now he is a full-time professor <strong>in</strong> Shand<strong>on</strong>g Ec<strong>on</strong>omic<br />
University and assistant director of the Enterprise’s Electr<strong>on</strong>iccommerce<br />
Eng<strong>in</strong>eer<strong>in</strong>g <str<strong>on</strong>g>Research</str<strong>on</strong>g> Center of Shand<strong>on</strong>g.<br />
T<strong>on</strong>gjuan Wang (Ch<strong>in</strong>a, 1985) graduated from Qufu<br />
Normal University and ga<strong>in</strong>ed the bachelor degree <strong>in</strong><br />
<strong>in</strong>formati<strong>on</strong> management and <strong>in</strong>formati<strong>on</strong> system. At present,<br />
she is study<strong>in</strong>g her master degree of <strong>in</strong>formati<strong>on</strong> management <strong>in</strong><br />
Shand<strong>on</strong>g Ec<strong>on</strong>omic University. Her ma<strong>in</strong> research fields are<br />
<strong>in</strong>formati<strong>on</strong> management and decisi<strong>on</strong> support.<br />
© 2008 ACADEMY PUBLISHER