Open Journal of Social Sciences, 2014, 2, 161-166
Published Online September 2014 in SciRes.
How to cite this paper: Wang, X.J. (2014) An Integrated Fuzzy Approach for the Evaluation of Supply Chain Risk Mitigation
Strategies. Open Journal of Social Sciences, 2, 161-166.
An Integrated Fuzzy Approach for the
Evaluation of Supply Chain Risk Mitigation
Xiaojun Wang
School of Economics, Finance and Management, University of Bristol, Bristol, UK
Received June 2014
Competing in an increasingly uncertain business environment, organizations need to mitigate its
supply chain risks to enhance their resiliency. However, it is important to implement appropriate
strategies to meet business needs. This paper presents a novel approach that integrates fuzzy risk
assessment and fuzzy Delphi for the evaluation of strategies in order to mitigate supply chain risks.
The novelty of the model lies in the fact that an analytical tool enables the specific business prefe-
rences concerning supply chain risks to be taken into consideration in making the strategic deci-
sions. It provides a practical solution by which companies can systematically assess the risks in-
volved in the supply chain and select appropriate strategies to address them.
Supply Chain Risk, Strategy Evaluation, Fuzzy Risk Assessment, Delphi
1. Introduction
In a supply chain, uncertainty is a major factor that can influence the effectiveness of supply chain coordination.
With the increasing trend of collaboration with international supply partners and extended supply networks, it
also brings uncertainties that significantly threaten normal business operations of the organizations in the supply
chain. Supply chain risk or vulnerability has emerged as a key challenge to supply chain management (SCM).
Supply chain risk management (SCRM) is a field of escalating importance and is aimed at developing ap-
proaches to the identification, assessment, analysis and treatment of areas of vulnerability and risk in supply
chains [1]. When assessing supply chain risk, the causes, probability, and consequences for each potential risk
have to be collected and documented. There has emerged a growing body of research into risk from a number of
different perspectives such as economics, finance and international management [2].
In order to adapt quickly and effectively to the changing environment, supply chains need to be flexible and
work in a more collaborative manner. Businesses have recognized the potential competitive advantages of being
resilience in a volatile market condition, agility for coping with increased environmental uncertainty, and react-
ing within smaller windows of opportunity for decision-making [3]. However, implementing appropriate strate-
X. J. Wang
gies is important, because any strategic investments based on poorly considered competenciescould be detri-
mental [4] [5]. For instance, flexibility in delivery quantity and due date could lead to a reduction of production
cost and, at the same time, compromise service by increasing the risk of failing to meet customer demand. In
fact, the decision of adopting appropriate strategies for managing supply chain risks requires a trade-off between
the benefits of implementing such strategies and cost involved.
More specifically, Lee [6] expressed that alignment, adaptability, and agility are the basic ingredients for
managing supply chain risks. Essentially, alignment and adaptability connote long- and medium-term perspec-
tives respectively, supply chain agility enables a firm to reduce the impact of short-term changes in demand or
supply [7]. Faisal et al. [8] listed several enablers for supply chain risk mitigation including information sharing,
supply chain agility, trust, collaborative relationships etc. Yang et al. [9] had grouped the tools and strategies for
managing supply chain risk into four main themes: multi-sourcing, alternative supply sources and backup pro-
duction, flexibility, and supplier selection.
Organizations are facing unique challenges in managing supply chain risks. Selecting appropriate strategies
for supply chain risk mitigation is a difficult task due to the complexity of decision making. This paper provides
a new approach to model the decision on supply chain risk mitigation strategies using an integrated fuzzy ap-
proach. With the advantage of mathematically representing vagueness and uncertainty, fuzzy risk assessment
offers a more precise and accurate analysis by encountering the uncertainty in a fuzzy environment [10]. The
fuzzy Delphi method is used to extract appropriate risk mitigation strategies for evaluation by incorporating ex-
pertsopinion into consideration. Through integrating abovementioned fuzzy techniques, this research provides
an analytical tool that enables the specific uncertainty concerning the supply chain to be taken into consideration
in making the choice of risk mitigation strategies. It would help companies to identity appropriate strategies as
well as meet their specific business needs.
2. Proposed Fuzzy Approach
The approach proposed in this section focuses on prioritizing alternative strategies for mitigating supply chain
risks. Firstly, supply chain risk assessment matrix is proposed to identify relevant risks and conduct an initial
assessment. It is followed with quantifying the level of identified risks through the use of fuzzy set theory.
Fuzzy Delphi is then applied to extract relevant supply chain risk mitigation strategies for further evaluation.
2.1. Supply Chain Risk Assessment Matrix
The proposed approach starts with defining the problem under study which is the evaluation of strategies for mi-
tigating supply chain risk. A system analysis is required to identify all potential supply chain risks that the busi-
ness could be exposed to. In each risk category, potential risks are identified and listed, and information about
risks may be collected from survey, interview, best practice, brainstorming, etc. For example, risks associated
with supply cost, supply quality and supply commitment can be included in the supply risk category. The quality,
time, and capacity risks associated with in-bound and out-bound logistics, and in-house operations need to be
identified and listed in the process risk categories. Demand risks include risks associated with demand uncer-
tainty. Similarly, based on the specific supply chain environment, risks associated with intellectual property,
behavioral, and political/social risk categories need to be identified.
According to the Royal Society [11], “risk is the chance, in quantitative terms, of a defined hazard occurring.
It therefore combines a probabilistic measure of the occurrence of the primary event(s) with a measure of the
consequences of that/those event(s)”. Hence, risk reflects both the range of possible outcomes and the distribu-
tion of respective probabilities for each of the outcomes. This quantitative definition could be expresses as:
R PS= ×
where R is the risk associated with a hazardous event, P represents the probability (or likelihood) of the occur-
rence of the hazardous event, S represents the severity or consequence of the event. This definition can also be
illustrated in the supply chain risk assessment matrix shown in Figure 1. By positioning various supply chain
risks on the matrix, it gives an overall view upon all risks, and makes the most important risks requiring the
most attention visible. In addition, it indicates whether the risks can be mitigated by decreasing their probability
or the severity of their consequences.
X. J. Wang
Figure 1. Supply chain risk assessment matrix.
2.2. Fuzzy Risk Assessment
Since there may be a number of potential risks that have been identified and managing each risk will incur cer-
tain costs, it is necessary to assess the identified risks. In many cases, a full systematic and quantitative risk as-
sessment along the supply chain may not be allowed due to constraints in data quality, time, or expertise. More-
over, uncertainty problems cannot be expressed simply by using the concept of probability or crisp values [12].
Fuzzy set theory has been frequently used to solve problems of uncertain nature. A fuzzy number is a special
fuzzy set, such that N = {(x, μN(x), x F)}, where the value of x lies on the real line F[0, 1]. TFN is employed
to characterize the fuzzy values of quantitative data and linguistic terms are used in approximate reasoning. We
define a fuzzy number N on F to be a triangular fuzzy number and the membership function can be described as:
12 112
() / (),[,]
()() / (),[,]
0, otherwise
x nnnxnn
− −∈
=− −∈
where n1 n2 n3, n1and n3 stand for the lower and upper value of the support of N respectively, and n2 denotes
to the most promising value.
In practice, companies have difficulties in evaluating these factors due to uncertainty and lack of knowledge
and information [13]. Instead, risk assessors often rank these risk factors in terms of linguistic variables such as
high, moderate and low, etc. In this research, the qualitative scales are expressed by TFNs to capture the vague-
ness in the linguistic subjectivity of risk definitions. Table 1 describes this qualitative scaling system for severi-
ty of the risk, probability of an adverse effect consequential to the risk. Two fuzzy numbers Np and Ns with
membership functions Np(x) and Ns(x) the grades of the two factors respectively.
To determine the magnitude and intensity of the risk, the two risk factors are multiplied to produce the risk
evaluation. The product of two TFNs is also a fuzzy member, but not necessary a triangle. To simplify multipli-
cation calculations, a standard approximation is used. The standard approximation has been defined in the forms
described as:
12 3
12 3
Aaa a
Bbb b
Cab abab
= ⊗
(3 )
To ensure accuracy of the assessment, group risk assessment is incorporated in the model. First of all, a risk
assessment team or group is formed. With reference to Table 1, a set of integers (from 1 to 11) are assigned to
the two elements for each risk item in the supply chain risk assessment matrix by individual assessors. Using
fuzzy geometric mean, both fuzzy grading for the severity
and likelihood
of each item can be obtained
using Equation (4) and Equation (5) respectively:
Supply chain risks
X. J. Wang
Table 1. Linguistic classification of risk grades.
Grade of risk A qualitative explanation of probability of
risk (p) A qualitative explanation of severity of
the consequence (s) Triangular fuzzy numbers
1 Definitely low Definitely no effect (0.0, 0.0, 0.1)
2 Extremely low Extremely minor (0.0, 0.1, 0.2)
3 Very low Very minor (0.1, 0.2, 0.3)
4 Low Minor (0.2, 0.3, 0.4)
5 Slightly low Slightly minor (0.3, 0.4, 0.5)
6 Middle Middle (0.4, 0.5, 0.6)
7 Slightly high Slightly severe (0.5, 0.6, 0.7)
8 High Severe (0.6, 0.7, 0.8)
9 Very high Very severe (0.7, 0.8, 0.9)
10 Extremely high Extremely severe (0.8, 0.9, 1.0)
( )
ii iin
=⊗ ⊗⊗
 
(5 )
With the fuzzy grading, the risk level of identified risk item can be calculated individually as:
, ,
i ii
= ⊗
MgLg , ,
represent the lower, middle and upper values of the fuzzy grade of the ith risk item. Since
the calculation so far involves fuzzy variables, the next step is to defuzzify the grades to form meaningful fig-
ures for analysis (e.g. ranking). Many methods exist in the literature but Centre of Area (COA) is by far the most
popular and easy to use one. Then, using the COA method, the non-fuzzy risk value of the ith risk item is given
() ()
i ii iii
gUg LgMg LgLg
=−+ −+
The higher value indicates a higher risk level of the assessed risk item.
2.3. Risk Mitigation Strategy Evaluation with Fuzzy Delphi
Many strategies that mitigate supply chain risks have been discussed in the literature. While it is good to have
choices of strategies for mitigating supply chain risks, how to tailor them with their various features and benefits
is still a big challenge. Here, fuzzy Delphi is applied to select relevant risk mitigation strategies for further eval-
uation. Following the references of [14]-[16], the steps for executing the fuzzy Delphi method are described as
Step 1: Conduct a questionnaire and organize an appropriate panel of expert to express their most conserva-
tive (minimum) value and the most optimistic (maximum) value of the importance of each strategy in the possi-
ble strategy set S in a range from 1 to 10. A score is then denoted as
( )
∈= ,,
, where
are the conservative index and the optimistic index of strategy i rated by expert k respectively.
Step 2: Organize expert opinions collected from questionnaires and determine the TFNs for the most con-
servative index
( )
and the most optimistic index
( )
for each strategy i.
Use the conservative index
( )
as an example,
indicates the minimum of all the experts’
most conservative value as:
( )
LLC min=
(8 )
is the geometric mean of all the experts’ most conservative value for strategy i. It is obtained
X. J. Wang
( )
indicates the maximum of all the experts’ most conservative value as:
( )
LUC max=
In the same way, the minimum (LOi), geometric mean (MOi), and the maximum (UOi) of the group’s most
optimistic values for strategy i can be obtained.
Step 3: Calculate the TFNs for the most conservative index Ci = (LCik, MCik, UCik) and the most optimistic
index Oi = (LOik, MOik, UOik) for the remaining strategies,
Step 4: Examine the consistency of experts’ opinions and calculate the consensus significance value, Gi for
each strategy. The gray zone ([15] [17]), the overlap section of Ci and Oi in Figu re 2, is used to examine the
consensus of experts in each strategy and calculate its consensus significance value, Gi,.
If the TFN pair does not overlap (i.e.
) and no gray zone exists, the expert options in strategy i
achieve consensus, the consensus significance value is calculated as:
If there is an overlap (i.e. UCi > LOi) and the gray zone interval value gi is equal to
, and gi is less
than the interval value of Ci and Oi
( )
, that is, gi < di, then the consensus significance value G is
determined in accordance with cross point
( )
of gray zone in Figure 2. The consensus significance
value Gi of each strategy can be calculated by Equation (12) and (13).
( )
( )
( )
{ }
max min,
Gpp dp
() ()
i ii i
ii iii
× −×
(13 )
If the gray zone exists and gi < di, then there are great discrepancies among the experts’ opinions. Repeat steps
1 to 4 until a convergence is attained.
Adapted from (Ishikawa et al. [18])
Step 5: Extract strategies from the candidate list. Compare consensus significance value with a threshold val-
ue, T, which is determined by experts subjectively based on the geometric mean of all consensus significance
value Gi [15] [17] [18]. If Gi > T, strategy i is then selected for further evaluation.
3. Conclusion
This paper presents a novel approach that enables to perform structured analysis of supply chain risks and eva-
luate different strategies for mitigating these risks. The novelty of the model lies in the fact that an analytical
tool enables the specific business preferences concerning supply chain risks to be taken into consideration in
making the strategic decisions. It is a systematic method which is capable of capturing a human’s appraisal of
ambiguity when complex multi-criteria decision making problems are considered. It offers a more precise and
Figure 2. Gray zone of Ci and Oi.
Memb ership
Gray zone
Cognition Value (p)
X. J. Wang
accurate analysis by incorporating the uncertainty that is encountered in a fuzzy environment. It is considered to
be supportive for managers in planning and making significant strategic decisions on supply chain risk man-
Nevertheless, the presented approach also has its own limitations, which imply fruitful directions for future
research. For instance, users have to make subjective decisions when conducting fuzzy risk assessment and ob-
tain priority ratings for alternative strategies. In fact the functionality of the model is highly dependent on the
knowledge, expertise and communication skills of the decision makers. Therefore, one future research is to con-
sider a more objective assessment technique such as entropy method. Moreover, there may be some mutual in-
teractions between assessment items, which may have consequent effect on the level of supply chain risk.
Another possible future research direction would be to use the network approach to incorporate inner and outer
dependencies that occur between identified risk items.
[1] Neiger, D., Botaru, K. and Churilov, L. (2009) Supply Chain Risk Identification with Va lue -Focused Process Engi-
neering. Journal of Operations Management, 27, 154-168.
[2] Jüttner, U., Peck, H. and Christopher, M. (2003) Supply Chain Risk Management, Outlining an Agenda for Future Re-
search. International Journal of Logistics, 6(4), 197-219.
[3] Giachetti, R.E., Martinez, L.D., Saenz, O.A. and Chen, C.S. (2003) Analysis of the Structural Measures of Flexibility
and Agility Using a Measurement Theoretical Framework. International Journal of Production Economics, 86, 47-62.
[4] Narasimhan, R., Talluri, S. and Das, A. (2004) Exploring Flexibility and Execution Competencies of Manufacturing
Firms. Journal of Operations Management, 22, 91-106.
[5] Sawhney, R. (2006) Interplay between Uncertainty and Flexibility across the Val ue -Chain: Towards a Transformation
Model of Manufacturing Flexibility. Journal of Operations Management, 24, 476-493.
[6] Lee, H. (2004) The Triple—A Supply Chain. Harvard Business Review, 102-112.
[7] Tang, C. and Tomlin, B. (2008) The Power of Flexibility for Mitigating Supply Chain Risks. International Journal of
production Economics, 116, 12-27.
[8] Faisal, M.N., Banwet, D.K. and Shankar, R. (2006) Supply Chain Risk Mitigation: Modeling the Enablers. Business
Process Management Journal, 12, 535-552.
[9] Yang, Z.B., Aydin, G., Babich, V. and Beil, D.R. (2009) Supply Disruptions, Asymmetric Information, and a Backup
Production Option. Management Science, 55, 192-209.
[10] Chan, H.K. and Wang, X. (2013) Fuzzy Hierarchical Model for Risk Assessment: Principles, Concepts, and Practical
Applications. Springer, London.
[11] The Royal Society (1992), Analysis, Perception and Management, The Royal Society, London.
[12] Wang, X., Li, D. and Shi, X. (2012) A fuzzy Enabled Model for Aggregative Food Safety Risk Assessment in Food
Supply Chains. Production Planning and Control, 23, 377-395.
[13] Wang, X., Chan, H.K., Yee, W.Y. and Diaz-Rainey, I. (2012) A Two-Stage Fuzzy-AHP Model for Risk Assessment of
Implementing Green Initiatives in the Fashion supply Chain. International Journal of Production Economics, 135,
[14] Kuo, Y.F. and Chen, P.C. (2008) Constructing Performance Appraisal Indicators for Mobility of the Service Industries
Using Fuzzy Delphi Method. Expert Systems with Applications, 35, 1930-1939.
[15] Lee, A.H.I., Wang, W. and Lin, T. (2010) An Evaluation Framework for Technology Transfer of New Equipment in
High Technology Industry. Technological Forecasting & Social Change, 77, 135-150.
[16] Wang, X. and Durugbo, C. (2013) Analysing Network Uncertainty for Industrial Product-Service Delivery: A Hybrid
Fuzzy Approach. Expert Systems with Applications, 40, 4621-4636.
[17] Hsiao, T.Y. (2006) Establish Standards of Standard Costing with the Application of Convergent Gray Zone Test.
European Journal of Operational Research, 168, 593-611.
[18] Ishikawa, A., Amagasa, T., Shiga, T., Tomizawa, G., Tatsuta, R. and Mieno, H. (1993) The Max-Min Delphi Method
and Fuzzy Delphi Method via Fuzzy Integration. Fuzzy Sets Systems, 55, 241-253.