A Fuzzy Multi-Criteria Group Decision Making Model for Measuring ...

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A Fuzzy Multi-Criteria Group Decision Making Model for Measuring Risks in a Supply Chain Using Extended VIKOR Method Muhammad Nazam, Jamil Ahmad, Muhammad Kashif Javed, Muhammad Hashim, Adnan Sarwar and Shahid Rasheed Abstract In this paper, we quantify risks in a supply chain process from an aviation’s perspective. Due to globalization, supply chains are getting more and more risky than before. As risk is inherent and uncertain activity, if it occurs then all of the supply chain partners will be impacted with a significant loss. To deal with this problem, a comprehensive risk evaluation index system has been proposed, which captures the level of risk faced by a supply chain in a given situation. For measuring risks in a supply chain we formulated a fuzzy multi-criteria group decision making model based on extended VIKOR method to determine the best feasible solution according to the selected risk parameters. A practical case study is conducted to test the applicability of the proposed methodology. Finally, we discuss the effectiveness of the proposed framework and rank the risk alternatives in descending order. Keywords Supply chain risk management · Multi-criteria group decision making · Fuzzy VIKOR · Risk index · Aviation sector

1 Introduction In todays scenario, supply chain risk management has become a significant issue for supply chain management [4]. An important factor of the rapidly evolving global business environment, spurred on by significant technology shifts, innovation, M. Nazam (B) · J. Ahmad · M.K. Javed · A. Sarwar Uncertainty Decision-Making Laboratory, Sichuan University, Chengdu 610064, People’s Republic of China e-mail: [email protected] M. Hashim Department of Business Administration, National Textile University, Faisalabad 37610, Pakistan S. Rasheed School of Economics and Management, Beijing University of Posts and Telecommunications, Beijing 100876, People’s Republic of China © Springer-Verlag Berlin Heidelberg 2015 J. Xu et al. (eds.), Proceedings of the Ninth International Conference on Management Science and Engineering Management, Advances in Intelligent Systems and Computing 362, DOI 10.1007/978-3-662-47241-5_122

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communication technologies and globalization, is the increasing prevalence of risk in almost every aspect of our lives. The companies face so many risks because they can never know exactly what will happen in the future. With the ever-increasing push for efficiency, supply chains environment recently are getting more and more risky [7]. An important element of the risk management procedure is the identification, evaluation and mitigation of risk. The procedure of risk assessment involves understanding the reasons that give rise to potential problems, and then evaluating the likelihood and severe impact of such kind of problems [11]. The major hurdles in evaluating risks comes from the fact that there is a lot of subjectivity involved [9, 10]. The observations and input of the experts on the subject mainly comes in the form of subjective assessments. Therefore, this necessitates the application of theories such as fuzzy or grey analysis which are useful tools of dealing with uncertainty and subjectivity. To deal with this kind of problem, most of the previous researchers used multi-criteria decision making techniques. Liou et al. [5] proposed a modified VIKOR multi-criteria decision method for improving domestic airlines service quality but did not consider the risk of whole supply chain. In this study, we applied the extended VIKOR method, which was developed for multi-criteria optimization for complex systems, to find a compromise priority ranking of supply chain risks according to the risk parameters in supply chain environment of aviation industry. Linguistic variables, expressed in trapezoidal or triangular fuzzy numbers, are used to assess the ratings and weights for each risk against three selected criteria, namely probability of occurrence, impact of the risk on supply chain if it occurred and how easily the mitigation would be for the impact of that risk. The extended VIKOR method is used to quantify risks in a supply chain and consolidate the values into a comprehensive risk index. Consequently, a new fuzzy multi-criteria group decision-making model based on fuzzy sets theory and VIKOR method is proposed to deal with the risk measuring problems in a supply chain system. The rest of this paper is structured as follows. Following the introduction, in Sect. 2, the key problem for the aviation industry with different kinds of risks in a supply chain under uncertain environment is described. The formulation of a fuzzy (MCGDM) model for measuring risks in a supply chain and its conversion into a crisp value can be explained in Sect. 3. In Sect. 4, a practical case study is presented to demonstrate the applicability of the proposed model. In the final section, the conclusions and directions for future research are discussed.

2 Key Problem Statement In this problem, we classified supply chain risks into ten major types. One simple classification can be external or internal risks but another classification can be of strategic, tactical or operational risks. Based on the literature review, supply chain risks can be categorized in many different ways with different perspectives [1, 2]. In this study, a comprehensive risk index has been proposed in manufacturing facility of

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Global risks (SCR2) Disruption risks (SCR3) Logistics risks (SCR4) Supply chain risks

Market risks (SCR5) Financial risks (SCR6) Process risks (SCR7) Technology risks (SCR8) Terrorism risks (SCR9) Environmental risks (SCR10)

Fig. 1 Classification of supply chain risks

an aviation industry. Major potential risks are identified by a group of supply chain risk management team in the manufacturing process of high-tech products. The experts categorized most important supply chain risks (SCR) such as: outsourcing risk (SCR1 ), global risk (SCR2 ), disruption risk (SCR3 ), logistics risk (SCR4 ), market risk (SCR5 ), financial risk (SCR6 ), process risk (SCR7 ), technology risk (SCR8 ), terrorism risk (SCR9 ), environmental risk (SCR10 ). The detailed classification of risks is structured in Fig. 1.

3 Formulating a Fuzzy MCGDM Model for Measuring Risks in a Supply Chain Multi-criteria decision making problems are mostly consider under fuzzy environment. In the fuzzy environment, the uncertain parameters are the decision maker (DM)s degree of optimism, which has a significant effect on the results. It has been extensively argued that supply chain risks are not easy to be precisely evaluated and traditional techniques take no account of relative importance of the risk parameters [8]. In this paper the risk parameters and their relative importance weights are taken as linguistic variables. A systematic approach to apply the VIKOR is proposed to determine risk priorities of supply chain risks under a fuzzy environment [6]. The general framework of our proposed model is shown in Fig. 2. The VIKOR method is started with the following form of Lp-metric.

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Group working

Apply VIKOR approach

Identify risk assessment objectives

Defuzzify

Determine best and worst values

Classification of supply chain risks

˜ ˜ D&W

f j* & f˜j

Compute the criteria weight

Evaluate risks and risk parameters weights

Compute S, R and Q values

Risks Ranking

Aggregation

Formation of risk index Assign experts inputs in linguistic form Rank risks indescending order Aggregate the expert’s subjective opinion

˜ ˜ D&W

Recommend corrective actions and modifications

Fig. 2 The general framework for the fuzzy MCGDM model of supply chain risk evaluation

L p,i

n  p = [w j ( f j∗ − f i j /( f j∗ − f j− )) ]1/ p , 1 ≤ p ≤∝, i = 1, 2, . . . , m. (1) j=1

In order to sum the risk priorities of supply chain risks, following are the steps which we determined: Step 1. Defining the problem importance and identifying the objectives of the decision making process. Firstly, our objective is to categorizing risks in a supply chain and then consolidating the the values into a comprehensive risk index. Step 2. Forming the group of decision-makers and state a finite set of relevant attributes. For our measuring risks in a supply chain problem we have three different risk criterion and ten different alternatives. Step 3. In this step, the appropriate linguistic variables for the importance weight of criteria, and the fuzzy rating for alternatives with respect to each criterion these linguistic variables can be expressed in positive trapezoidal fuzzy numbers, as in Figs. 3 and 4 must be defined. The decision makers use the linguistic variables shown in Figs. 3 and 4 to evaluate the importance of the criteria and the ratings of alternatives with respect to qualitative criteria. Step 4. To construct a fuzzy decision matrix, pull the decision makers? advices to get the aggregated fuzzy weight of selected criteria and rating of alternatives: Let the fuzzy rating and importance weight of the kth decision maker be x˜i jk = (xi jk1 , xi jk2 , xi jk3 , xi jk4 ) and w˜ jk = (w jk1 , w jk2 , w jk3 , w jk4 ); i = 1, 2, . . . , m and

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µ Ã(x) VL

L

ML

H

MH

M

VH

1.0

0

0.1

0.2

0.3

0.5

0.4

0.6

0.7

0.8

0.9

1

Fig. 3 Membership function for rating the weight of risk parameters

µ Ã(x) VL

ML

L

H

MH

M

VH

1.0

0

1

2

3

4

5

6

7

8

9

10

Fig. 4 Membership function for rating the supply chain risks

j = 1, 2, . . . , n respectively. Hence, the aggregated fuzzy ratings (x˜i j ) of alternatives with respect to each criterion can be computed as: x˜i jk = xi j1 , xi j2 , xi j3 , xi j4 , K K where xi j1 = min{xi jk1 }k , xi j2 = K1 k=1 xi jk2 , xi j3 = K1 k=1 xi jk3 , xi j4 = max{xi jk4 }k . The aggregated fuzzy weights (w˜ j ) of each criterion can be calculated as: w˜ j = (w j1 , w j2 , w j3 , w j4 ), where w j1 = min{w jk1 }k , w j2 = min{w jk4 }k . ⎡

x˜11 ⎢ x˜21 =⎢ D ⎢ .. ⎣.

x˜12 x˜22 .. .

··· ··· .. .

1 K

K

x˜1n x˜2n .. .

k=1 w jk2 ,

w j3 =

(2) 1 K

K

k=1 w jk3 ,

w j4 =

⎤ ⎥ ⎥  ⎥ , W = [w˜ 1 , w˜ 2 , . . . , w˜ n ], ⎦

(3)

x˜m1 x˜m2 · · · x˜mn

where x˜i j the rating of alternative Ai with respect to C j , (w˜ j ) the importance weight of the j th criterion holds, x˜i j xi j1 ; xi j2 ; xi j3 ; xi j4 and (w˜ j ) w j1 ; w j2 ; w j3 ; w j4 ; i = 1, 2, . . . , m and j = 1, 2, . . . , n are linguistic variables can be approximated by positive trapezoidal fuzzy numbers.

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Step 5. Defuzzify the fuzzy decision matrix and fuzzy weight of each criterion into crisp values: This calculation is done by using center of area defuzzification method. The centroid defuzzification method can be expressed by following relation:  = x¯0 ( A)

xµ A(x)d  x µ A(x)d  x

,

(4)

 is the defuzzified value. For trapezoidal fuzzy number (a1 , a2 , a3 , a4 ), where x¯0 ( A) the centroid-based defuzzified value turns out to be [3].  = x¯0 ( A)



1 a4 a3 − a1 a2 a1 + a2 + a3 + a4 − . 3 (a4 + a3 ) − (a1 + a2 )

(5)

Step 6. Determine the best f j∗ and the worst f j− values of all criterion ratings, j = 1, 2, . . . , n and i = 1, 2, 3, . . . , m f j∗ = {max xi j , for benefit criteria, min xi j , for cost criteria},

(6)

f j−

(7)

= {min xi j , for benefit criteria, max xi j for cost criteria}.

Step 7. Compute the values Si and Ri , i = 1, 2, . . . , m, by the relations: Si =

n 

w j ( f j∗ − xi j )/( f j∗ − f j− ),

(8)

j=1

Ri = max w j ( f j∗ − xi j )/( f j∗ − f j− ),

(9)

where w j are the weights of criteria, expressing their relative importance. Step 8. Compute the values Q i , i = 1, 2, . . . , m, by the relation Q i = v(Si − S ∗ )/(S − − S ∗ ) + (1 − v)(Ri − R ∗ )/(R − − R ∗ ),

(10)

where S ∗ = mini Si , S − = maxi Si , R ∗ = mini Ri , R − = maxi Ri and v is introduced as a weight for the strategy of maximum group utility, whereas 1 v is the weight of the individual regret. The value of v is set to 0.5 in this study. Step 9. Rank the alternatives, sorting by the values S, R and Q in descending order. The results are three ranking lists. Step 10. Propose a compromise solution, the alternative (A(1) ), which is the best ranked by the measure Q (minimum) if the following two conditions are satisfied: QA(2) − QA(1) ≥ DQ

(11)

where A(2) is the alternative with second position in the ranking list by Q; DQ = 1/(m1). C2 (Table 1).

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Table 1 Linguistic variables for rating the supply chain risks and weight of risk parameters respectively Linguistic variables Trapezoidal FNs Trapezoidal FNs Very low (VL) Low (L) Medium low (ML) Medium (M) Medium High (MH) High (H) Very high (VH)

(0, 0, 1, 2) (1, 2, 2, 3) (2, 3, 4, 5) (4, 5, 5, 6) (5, 6, 7, 8) (7, 8, 8, 9) (8, 9, 10, 10)

(0.0, 0.0, 0.1, 0.2) (0.1, 0.2, 0.2, 0.3) (0.2, 0.3, 0.4, 0.5) (0.4, 0.5, 0.5, 0.6) (0.5, 0.6, 0.7, 0.8) (0.7, 0.8, 0.8, 0.9) (0.8, 0.9, 1.0, 1.0)

• C2 . Acceptable stability in decision making: The alternative A(1) must also be the best ranked by S or/and R. This compromise solution is stable within a decision making process, which could be: voting by majority rule when v > 0.5 is needed, or by consensus v is 0.5, or with veto v < 0.5. Here, v is the weight of decision making strategy of the maximum group utility. If one of the conditions is not satisfied, then a set of compromise solutions is proposed, which consists of: • alternatives A(1) and A(2) if only the condition C2 is not satisfied. • alternatives A(1) , A(2) , . . . , A(M) if the condition C1 is not satisfied; A(M) is determined by the relation Q(A(M) ) Q(A(1) ) < DQ for maximum M (the positions of these alternatives are in closeness).

4 Practical Application The proposed model has been applied in aviation industry to the understand the status of supply chain risk management. A supply chain management or logistics team of five decision makers, DM1 , DM2 , DM3 , DM4 , and DM5 , has been formed to provide the desired information on supply chain risk management. We analyze the internal or process risk of aviation industry because its higher level of risks. The steps of the risk measuring process can be defined as follows: Step 1. The manufacturer desires to identify several most serious supply chain risks during production process to take appropriate measures. After preliminary screening, ten supply chain risks (SCR1 , SCR2 , SCR3 , SCR4 , SCR5 , SCR6 , SCR7 , SCR8 , SCR9 , and SCR10 ) remain for further evaluation. Step 2. Each risk is measured against three parameters, namely probability of occurrence, impact of the risk on the supply chain if it occurred and how easily the mitigation would be for the impact of that risk. Step 3. A team of five decision-makers use the linguistic weighting variables shown in Fig. 3 to assess the relative importance of the risk parameters. The importance weights of the risk parameters determined by these five decision makers are shown

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Table 2 Importance weight of risk parameters from five supply chain team members Risk parameters Decision maker DM1 DM2 DM3 DM4 DM5 Probability Impact Mitigation

M MH H

VH H M

H MH MH

MH VH MH

MH H M

in Table 2. The experts also use the linguistic rating variables shown in Fig. 4 to evaluate the ratings of supply chain risks with respect to each risk parameter. The ratings of the ten supply chain risks by the decision makers under the three risk parameters are shown in Table 3. Step 4. The linguistic evaluations shown in Tables 2 and 3 are converted into trapezoidal fuzzy numbers. Then the aggregated weight of risk parameters and aggregated fuzzy rating of supply chain risks are calculated to determine the fuzzy weight of each risk factor and construct the fuzzy decision matrix, as in Table 4. Step 5. The crisp values for decision matrix and weight of each risk parameters are computed as shown in Table 5. Step 6. The best and the worst values of all risk parameters ratings are determined as follows: ∗ = 2.600, f − = 6.778, f − = 6.900, f − = f P∗ = 4.000, f I∗ = 4.889, f M P I M 4.933.

Step 7. The value of S is calculated by Eq. (8) for all risks as shown in Table 6. Step 8.The value of R is calculated by Eq. (9) for all risks as shown in Table 6. Step 9. The value of Q is calculated by Eq. (10) for all risks as shown in Table 6. Step 10. The ranking of the alternative supply chain risks by S, R and Q in decreasing order is shown in Table 7. From the Table 7, it can be seen that the supply chain risk SCR3 is apparently the most serious supply chain risk according to Q values and should be given the top risk priority by the the company, this will be followed by supply chain risks SCR6 , SCR9 , SCR10 , SCR2 , SCR7 , SCR8 , SCR1 , SCR4 and SCR5 .

5 Conclusions and Future Research In this study, we proposed a new comprehensive risk index under uncertain environment and can be applied in any industry situation. To formulate this risk index we take experts opinion as its input and delivers a crisp number as the risk score. In the proposed model, we first categorize the risk status for the said environment, secondly identification of the weights of the supply chain risks, then computation

a Risk parameters. b Decision-makers

M ML MH ML M M ML L H H

ML M VH M M MH H VH MH M

M H H L M MH VH L M MH

M MH ML L ML H MH L VH MH

Supply chain risks

SCR1 SCR2 SCR3 SCR4 SCR5 SCR6 SCR7 SCR8 SCR9 SCR10

Probability Impact Mitigation DM1 DM2 DM3 DM4

Ra Db ML M H MH M ML ML L M MH

DM5 M ML MH ML MH H M H H M

DM1 ML MH MH M M H ML MH MH MH

DM2 MH H MH MH ML MH ML H ML M

DM3

Table 3 Judgment on ten supply chain risks by supply chain team members under risk parameters

MH MH MH MH M MH H L M MH

DM4 MH M MH M M H M L M H

DM5 ML MH M VL M L M ML MH VL

DM1

ML M ML L ML L L L M VL

DM2

M ML MH ML VL ML M L L M

DM3

M M MH MH ML L L MH L L

DM4

ML ML M M L ML L MH VL L

DM5

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Table 4 Aggregated fuzzy rating of ten supply chain risks and aggregated fuzzy weight of risk parameters Supply chain Riks Probability Impact Mitigation SCR1 SCR2 SCR3 SCR4 SCR5 SCR6 SCR7 SCR8 SCR9 SCR10 Weight

(2, 4.2, 4.6, 6) (2, 5.4, 5.8, 8) (2, 6.2, 6.8, 10) (1, 3.6, 4, 8) (2, 4.6, 4.8, 6) (2, 5.6, 6.2, 9) (2, 5.8, 6.6, 10) (1, 3.4, 3.6, 10) (4, 6.6, 7, 10) (4, 6.2, 6.8, 9) (0.58, 0.68, 0.74, 0.82)

(2, 5.2, 6, 8) (2, 5.6, 6.2, 9) (5, 6, 7, 8) (2, 5, 5.6, 8) (2, 4.8, 5.2, 8) (5, 7.2, 7.6, 9) (2, 4.8, 5.2, 9) (1, 5.2, 5.4, 9) (2, 5.4, 5.8, 9) (4, 6, 6.4, 9) (0.64, 0.74, 0.80, 0.88)

(2, 3.8, 4.4, 6) (2, 4.4, 5, 8) (2, 5, 5.6, 8) (0, 3.2, 3.8, 8) (0, 2.6, 3.2, 6) (1, 2.4, 2.8, 5) (1, 3.2, 3.2, 6) (1, 3.8, 4.4, 8) (0, 3, 3.4, 8) (0, 1.8, 2.2, 6) (0.50, 0.60, 0.64, 0.74)

Table 5 Crisp values for decision matrix and weight of each risk parameter Risk Supply chain risks parameters SCR1 SCR2 SCR3 SCR4 SCR5 SCR6 SCR7 SCR8 SCR9 SCR10 Weight Probability 4.000 5.089 6.017 4.181 4.167 5.476 5.867 4.793 6.778 6.240 Impact 4.978 5.476 5.778 4.933 4.899 6.900 5.229 5.058 5.429 6.227 Mitigation 3.833 4.733 4.933 3.733 2.867 2.767 3.400 4.238 3.667 2.600

0.705 0.765 0.621

Table 6 The values of S, R and Q for all supply chain risks Compromise Supply chain risks value SCR1 SCR2 SCR3 SCR4 SCR5 SCR6 SCR7 SCR8 SCR9 SCR10 By S By R By Q

0.362 0.328 0.277

1.067 0.568 0.709

1.471 0.621 0.896

0.364 0.113 1.184 0.816 0.702 1.194 1.077 0.302 0.071 0.765 0.474 0.436 0.705 0.568 0.259 0.000 0.894 0.549 0.480 0.855 0.713

of the scores of the supply chain risk and finally consolidation of the weights and scores into one single crisp value, which is the risk index. The addition of a main supplier is a major change in the supply chain, therefore the determination of the risk index should be carried out at regular intervals. Being notified of the risk status of the chain, the companies can decide on when risk management in supply chain needs more attention. This will allow them to free up available resources for the risk management team and thus can reduce the redundancy being built into the system.

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Table 7 The ranking of the supply chain risks by S, R and Q values Ranking Supply chain risks SCR1 SCR2 SCR3 SCR4 SCR5 SCR6 SCR7 By S By R By Q

9 8 8

5 4 5

1 3 1

8 9 9

10 10 10

3 1 2

6 6 6

SCR8

SCR9

SCR10

7 7 7

2 2 3

4 4 4

In this article, the integration of fuzzy linguistic VIKOR with the support of trapezoidal fuzzy set theory is proposed for the prioritization of measuring risks in a supply chain of aviation industry. Some steps of the extended fuzzy VIKOR method are discussed to show there are other possible extensions. It is an effective and simple tool to solve the imprecise, vague, intangible information for MCGDM problem. The verified example concerning the aviation supply chain risk shows that the proposed method is very useful for measuring of risks and also applicable to other management decision problem. In the future, our research plans to develop new risk indexes by incorporating the new frameworks incorporating the various artificial intelligence modeling techniques, multi-agent, petri net, graph theory, gray theory, game theory and so on, and then comparing the performances of these risk indexes with the propose one. Acknowledgments The authors wish to thank the anonymous referees for their helpful and constructive comments and suggestions. The work is supported by the National Natural Science Foundation of China (Grant No. 71301109, 71401114), the Western and Frontier Region Project of Humanity and Social Sciences Research, Ministry of Education of China (Grant No. 13XJC630018), the Philosophy and Social Sciences Planning Project of Sichuan province (Grant No. SC12BJ05).

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