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A hybrid MCDM approach to supplier selection
Article in International Journal of Engineering Management and Economics · January 2012
DOI: 10.1504/IJEME.2012.052403
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Mani Ilangkumaran
K. S. Rangasamy College of Technology
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3. 2 M. Ilangkumaran et al.
Biographical notes: M. Ilangkumaran is a Professor of the Mechatronics
Engineering, K.S. Rangasamy College of Technology, Tiruchengode, India. He
completed his BE (Mechanical) from K.S. Rangasamy College of Technology,
Tiruchengode in the year 1999, he completed his ME (Industrial Engineering)
from Kumaraguru College of Technology, Coimbatore in the year 2001. He
received his PhD in the area of maintenance management in the year 2010. He
has published more than six papers in national conferences and six papers in
international journal. He is a Life Member of ISTE. His research interest is
maintenance management.
M. Dinesh is a student of BE (Mechatronics Engineering) at K.S. Rangasamy
College of Technology, Trichengode, Tamil Nadu, India.
M.M. Jegan is a student of BE (Mechatronics Engineering) at K.S. Rangasamy
College of Technology, Trichengode, Tamil Nadu, India.
T. Loganathan is a student of BE (Mechatronics Engineering) at K.S.
Rangasamy College of Technology, Trichengode, Tamil Nadu, India.
K.M. Mouleeshwaran is a student of BE (Mechatronics Engineering) at K.S.
Rangasamy College of Technology, Trichengode, Tamil Nadu, India.
V. Sasirekha is an Assistant Professor at the Department of Computer
Applications, K.S. Rangasamy College of Engineering, Tiruchengode, India.
She completed her BSc (CSE) from K.S. Rangasamy College of Technology,
Tiruchengode in the year 2000. She completed her MCA from Bharathiyar
University, Coimbatore in the year 2003. She has published more than three
papers in national conferences. She has published one paper in international
journal. She is a life member of ISTE. Her research interest is fuzzy
applications.
Boopathi Raja is a student of BE (Mechatronics Engineering) at K.S.
Rangasamy College of Technology, Trichengode, Tamil Nadu, India.
Nizamuddin Pallikadath is a student of BE (Mechatronics Engineering) at K.S.
Rangasamy College of Technology, Trichengode, Tamil Nadu, India.
S. Praveen Kumar is a student of BE (Mechatronics Engineering) at K.S.
Rangasamy College of Technology, Trichengode, Tamil Nadu, India.
T. Ruban Sundara Raj is a student of BE (Mechatronics Engineering) at K.S.
Rangasamy College of Technology, Trichengode, Tamil Nadu, India.
C.N.S. Siddharatha is a student of BE (Mechatronics Engineering) at K.S.
Rangasamy College of Technology, Trichengode, Tamil Nadu, India.
1 Introduction
For an industry to survive today’s fierce competition prevailing in manufacturing sector,
it should pay more attention towards supply chain management (SCM). In SCM,
especially for a purchasing department, the most important activity and responsibility is
to evaluate and find the best supplier who can improve the competitive strategy of the
organisation. The some of the main objectives of supplier selection are minimising the
4. A hybrid MCDM approach to supplier selection 3
purchasing cost, maximising the quality, stabilising the supply of raw material, increasing
flexibility and improving the customer satisfaction. To achieve the aforementioned
advantages in SCM, optimum supplier must be selected. Dickson (1966) listed about
23 criteria for the evaluation of suppliers, out of which quality, delivery time,
performance history, production capability, price, technical capability, financial position,
geographical location and flexibility are more important. Thus, the supplier selection
problem is an MCDM problem involving both quantitative and qualitative criteria.
Realising the importance of supplier selection, many researchers and academicians have
published numerous research papers and solutions for innovative MCDM techniques for
supplier evaluation. Tahriri et al. (2008) have stated that the supplier selection problem
has been gaining momentum for the recent years, in which the analytical hierarchy
process (AHP), developed by Saaty (1980), play a significant role. The quality is a major
factor that determines the level of customer satisfaction (Tam and Tummala, 2001). An
MCDM approach such as AHP is needed to take both qualitative and quantitative factors
into account (Chan and Chan, 2010). The AHP method is an effective and practical
approach for solving complex and unstructured decision making problems. Although the
AHP has its own advantages and has produced ideal results in various fields (Table 1),
researchers have found certain deficiencies in it. In the conventional AHP, a decision
maker determines his or her weights by conducting pair-wise comparisons between
criteria but it cannot fully reflect the human thinking style. In classical AHP, the
numerical values are exact numbers which are useful only for crisp decision making
applications. So, ranking of the AHP is not precise enough. In AHP, the deterministic
scale may produce some misleading consequences. For example, some pessimistic people
may not give more than four points but very optimistic people may readily give five
points even if it does not deserve to it. These limitations of AHP are to be addressed
(Deng, 1999; Mikhailov, 2003; Chang et al., 1999; Chan, 2003). The human preference
model used in this technique is uncertain and decision makers might be reluctant or
unable to assign exact numerical values to the comparison judgements (Bellman and
Zadeh, 1970). To resolve this problem, the fuzzy set theory (FST) has been integrated
with the MCDM techniques to improve the consistency of decision making. Apart from
AHP, many tools have been used for supplier selection problem. Gencer and Gürpinar
(2007) have proposed a model based on analytical network process (ANP), a more
sophisticated version of AHP, for supplier selection problem and it has been explained
with a case study from an electronic firm. Teeravaraprug (2008) has proposed a model
for vendor selection, in which Taguchi loss function is applied to measure the non-cash
impacts that cause an expected value of loss. In addition to it, many hybrid approaches
have been proposed to overcome the disadvantages of one another. Haq and Kannan
(2006) have used AHP and fuzzy AHP for evaluating and selecting a vendor. Yang et al.
(2008) have proposed a hybrid MCDM technique using interpretive structural modelling
(ISM) and FAHP to determine the best vendor. Jadidi et al. (2008) have established
a model for supplier selection problem based on integrated TOPSIS and fuzzy
multi-objective model. Ti et al. (2010) have proposed an ANP-based hybrid MCDM for
outsourcing vendor selection and demonstrated with a case study for a semiconductor
manufacturing industry. Shahanaghi and Yazdian (2009) have proposed fuzzy group
decision making using technique for order preference by similarity to ideal solution
(TOPSIS) method for evaluating and selecting an appropriate vendor. Mohammady and
Amid (2010) have contributed an integrated fuzzy VlseKriterijumska Optimizacija I
Kompromisno Resenje (VIKOR) and fuzzy AHP method to supplier selection problem
5. 4 M. Ilangkumaran et al.
with a case study on outsourcing process. Shemshadi et al. (2011) have proposed a hybrid
MCDM based on ANP and fuzzy TOPSIS approach to select the best supplier from
potential alternatives. Cheng et al. (2009) have proposed a model applying fuzzy Delphi
method (FDM) and fuzzy AHP for evaluating supplier for semiconductor manufacturing
industry. According to Boer et al. (1998), AHP, SMART and other linear weighing
models are fully compensatory and these techniques may be sometimes against reality.
They had mentioned that outranking methods like ELECTRE, PROMETHEE and
ORESTE are only partially compensatory and these techniques can handle imprecise
situation. Almeida (2007) has proposed an MCDM model using ELECTRE method for
outsourcing vendor selection. Sevkli (2010) has applied fuzzy ELECTRE method for
supplier selection.
It is clear from the literature that the implementation of outranking methods in
supplier selection problem is less. Realising the importance of the AHP method and the
outranking method, this paper proposes a combined FAHP and PROMETHEE technique
for selecting the best supplier. This hybrid MCDM method overcomes the drawbacks of
traditional AHP method by incorporating the FST and PROMETHEE.
Table 1 Review on applications of AHP procedure
Year Authors Application areas
1986 Brad Manufacturing
1987 Libertore Social
1994 Ceha and Ohta Political
1995 Ahire and Rana Social
1999 Rezqallah et al Maintenance management
1999 Raju and Pillai Government
2001 Al Harbi Personal
2002 Al Khalil Social
2002 Lai et al. Engineering
2003 Nordggrd et al. Maintenance management
2003 Bahurmoz Education
2004 Yurdakul Manufacturing
2009 Socorro and Teresa Maintenance management
2009 Parthiban et al. Network management
2011 Zhang et al. Management Science and Industrial Engineering
2012 Rouyendegh and Erkan Business management
2 Proposed model
The proposed methodology for the supplier selection problem combines AHP, FAHP and
PROMETHEE methods and consists of three distinct stages:
1 identification of criteria for evaluating the suppliers
2 formation of decision hierarchy
6. A hybrid MCDM approach to supplier selection 5
3 AHP and FAHP computations
4 ranking of suppliers using PROMETHEE with AHP and FAHP weights.
The schematic diagram of proposed model is shown in Figure 1. In the first stage,
alternative suppliers are determined and evaluating criteria are identified according to the
literature survey. A decision hierarchy is framed based on the identified evaluation
criteria and alternatives with consent of decision makers. The AHP and FAHP are
structured such that the objective is placed at top level of hierarchy; criteria are at the
second level and alternative suppliers at the third level. After the construction of the
decision hierarchy, the AHP and FAHP are used to compute the criteria weights. The
decision making team members are given a task to carry out individual pair-wise
comparison matrix using Saaty scale tabulated in Tables 2 and 3. After computing the
criteria weights, the decision making team should give consent and approve the weights.
The supplier ranks are determined using PROMETHEE method in the last stage with the
AHP and FAHP computation criteria weights.
Figure 1 The hybrid MCDM approach for supplier selection problem (see online version
for colours)
7. 6 M. Ilangkumaran et al.
Table 2 Pair-wise comparison scale
Scale of importance Crisp score Reciprocal of crisp score
Equal importance 1 1.00
Moderate 3 0.33
Strong importance 5 0.20
Very strong importance 7 0.14
Extremely preferred 9 0.11
Table 3 Membership function of fuzzy numbers
Scale of importance
Triangular fuzzy number (TFN)
(L, M, U)
Reciprocal of TFN
(1/L, 1/M, 1/U)
Just equal (1, 1, 1) (1, 1, 1)
Equal importance (1, 1, 3) (0.33, 1, 1)
Moderate (1, 3, 5) (0.20, 0.33, 1)
Strong importance (3, 5, 7) (0.14, 0.20, 0.33)
Very strong importance (5, 7, 9) (0.11, 0.14, 0.20)
Extremely preferred (7, 9, 9) (0.11, 0.11, 0.14)
3 Overview of the analytic hierarchy process
The analytic hierarchy process (AHP) was developed by Saaty (1980). It is a decision
making approach for evaluating complex multiple criteria alternatives involving
subjective judgement. This method is an effective and practical approach for solving
complex and unstructured decision making problems. The procedural steps of AHP are as
follow.
3.1 Hierarchical structure development
A complex decision making problem is structured using a hierarchy. The AHP initially
breaks down a complex MCDM problem into a hierarchy of inter-related decision
elements (criteria). With the AHP, the criteria are arranged in a hierarchical structure
similar to a family tree. A hierarchy has at least three levels: overall goal of the problem
at the top, multi criteria that define criteria at the middle, and decision criteria at the
bottom (Albayrak and Erensal, 2004).
8. A hybrid MCDM approach to supplier selection 7
3.2 Computation of weights
After the formation of the hierarchy, the next step is to determine pair-wise comparison
matrix using the suitable crisp score in Saaty scale listed in Table 2.
Let { }
1,2, ,
j
C C j n
= = … be a set of criteria. The result of the pair-wise comparison
on ‘n’ criteria can be summarised in an (n × n) evaluation matrix A in which every
element ( , 1,2, , )
ij
a i j n
= … is the quotient of weights of the criteria, as shown:
11 12 1
21 22 2
1 2
, 1, 1 , 0.
n
n
ii ij ij ij
n n nn
a a a
a a a
A a a a a
a a a
⎡ ⎤
⎢ ⎥
⎢ ⎥
= = = ≠
⎢ ⎥
⎢ ⎥
⎣ ⎦
…
…
…
(1)
At the last step, the mathematical process is commenced to normalise and find the
relative weights of each matrix. The relative weights are given by the right eigen vector
(W) corresponding to the largest eigen value (λmax), as:
max
W
A λ W
= (2)
It should be noted that the quality of output of FAHP is strictly related to the consistency
of the pair-wise comparison judgements. The consistency is defined by relation between
the entries of A: aij × ajk = aik. The consistency index (CI) is:
( ) ( )
max 1
CI λ n n
= − − (3)
The pair-wise comparison is normalised and priority vector is computed to weigh the
elements of the matrix. The values in this vector are summed to 1. The consistency of the
subjective input in the pair-wise comparison matrix can be determined by calculating a
consistency ratio (CR). In general, a CR having the value less than 0.1 is good (Saaty
1980). The CR for each square matrix is obtained from dividing CI values by random
consistency index (RCI) values.
/
CR CI RCI
= (4)
The RCI, which is obtained from a large number of simulations, runs and varies
depending upon the order of matrix. Table 4 lists the value of the RCI for matrices of
order 1 to 10 obtained by approximating random indices using a sample size of 500. The
acceptable CR range varies according to the size of matrix. In contrast, if CR is more than
the acceptable value, inconsistency of judgements within that matrix will occur and the
evaluation process should therefore be reviewed, reconsidered and improved.
9. 8 M. Ilangkumaran et al.
Table 4 Average RCI based on matrix size
S. no. 1 2 3 4 5 6 7 8 9 10
RCI 0 0 0.52 0.89 1.11 1.25 1.35 1.40 1.45 1.49
4 Fuzzy set theory
The expressions such as ‘not very clear’, ‘probably so’, and ‘very likely’, are used often
in daily life, and they more or less represent some degree of uncertainty of human
thought. The FST proposed by Zadeh (1965), is an important concept that is applied in
the scientific environment and it has been available to other fields as well. Consequently,
the fuzzy theory has become a useful tool for automating human activities with
uncertainty-based information. Therefore, this research incorporates the fuzzy theory for
the performance measurement by evaluators’ subjective judgements. The FST resembles
human reasoning with use of approximate information and certainty to generate decisions
and it is a better approach to convert linguistic variables into fuzzy numbers under
ambiguous assessments. The FST which is incorporated with AHP allows a more
accurate description of decision making process.
The uncertain comparison ratios are expressed as fuzzy sets or fuzzy numbers. The
evaluation criterion in the judgement matrix and weight vector is represented by
triangular fuzzy numbers. A fuzzy number is a special fuzzy set F = {(x, μF(x), x € R}
where x takes its value on the real line R1: – ∞ < x < + ∞ and µF(x) is a continuous
mapping from R1 to the close interval [0, 1]. A triangular fuzzy number (TFN) can be
denoted as M = (l, m, u). The TFN can be represented as follows:
0, , ,
, ,
( )
, ,
0,
A
x l
x l
l x m
m l
μ x
u x
m x u
u m
x u
⎧
⎪ −
⎪ ≤ ≤
⎪ −
= ⎨
−
⎪ ≤ ≤
⎪ −
⎪ >
⎩
(5)
According to the nature of TFN, it can be defined as a triplet (l, m, u). The TFN can be
represented as ( , , ),
A L M U
= where L and U represent the fuzzy probability between the
lower and upper boundaries of evaluation. The two fuzzy numbers 1 1 1 1
( , , )
A L M U
= and
2 2 2 2
( , , )
A L M U
= are assumed.
( ) ( ) ( )
( ) ( ) ( )
( ) ( ) ( )
( ) ( ) ( )
( ) ( )
1 2 1 1 1 2 2 2 1 2 1 2 1 2
1 2 1 1 1 2 2 2 1 2 1 2 1 2
1 2 1 1 1 2 2 2 1 2 1 2 1 2
1 2 1 1 1 2 2 2 1 2 1 2 1 2
1
1
1 1 1 1 1 1
1
, , , , , ,
, , , , , ,
, , , , , ,
, , , , , ,
, , 1 ,1 ,1
A A L M U L M U L L M M U U
A A L M U L M U L L M M U U
A A L M U L M U L L M M U U
A A L M U L M U L L M M U U
A L M U U M L
−
−
⊕ = ⊕ = + + +
⊗ = ⊗ =
− = − = − − −
÷ = ÷ =
= =
10. A hybrid MCDM approach to supplier selection 9
4.1 Construction of the fuzzy judgement matrix
The crisp pair-wise comparison matrix A is fuzzified using the triangular fuzzy number
(TFN) M = (l, m, u), l and u represent lower and upper bound range respectively that
might exist in the preferences expressed by the decision maker. The membership function
of the TFNs M1, M3, M5, M7, and M9 are used to represent the assessment from equally
preferred (M1), moderately preferred (M3), strongly preferred (M5), very strongly
preferred (M7), and extremely preferred (M9). This paper employs a TFN to express the
membership functions of the aforementioned expression values on five scales which are
used for FAHP listed in Table 3 and graphically expressed in Figure 2.
Figure 2 Fuzzy triangular membership function
5 PROMETHEE method
Preference function-based outranking method is a special type of MCDM tool that can
provide a ranking ordering of the decision options. The PROMETHEE method was
developed by Brans and Vincke (1985). PROMETHEE I method can provide a partial
ordering of the decision alternatives whereas PROMETHEE II method can derive the full
ranking of the alternatives. In this paper, the PROMETHEE II method is employed to
obtain the full ranking of the suppliers for a given industrial application.
The procedural steps involved in PROMETHEE II are enlisted below:
Step 1 First of all, a committee of decision makers is formed. In the decision making
committee, there are three decision makers; fuzzy rating of each decision maker
can be represented as TFN with membership function.
Step 2 The appropriate crisp score is chosen for evaluating supplier alternatives. The
crisp score is tabulated in Table 8.
Step 3 Based on the questionnaire, the suitable crisp score is assigned for alternative
suppliers by each decision maker. Then the decision matrix is formed.
11. 10 M. Ilangkumaran et al.
Step 4 Normalise the decision matrix using the following equation:
[ ] [ ]
min max min ( 1,2, , : 1,2, , )
ij ij ij ij ij
R X X X X i n j m
= − − = =
… … (6)
where Xij is the performance measure of ith
alternative with respect to jth
criterion.
For non-beneficial criteria, equation (1) can be rewritten as follows:
[ ] [ ]
max max min
ij ij ij ij ij
R X X X X
= − − (7)
Step 5 Calculate the evaluative differences of ith
alternative with respect to other
alternatives. This step involves the calculation of differences in criteria values
between different alternatives pair-wise.
Step 6 Calculate the preference function, Pj(i, i′).
It may be very tough for decision makers to select the suitable preference
function for each criterion by Brans and Mareschal proposal. In order to reduce
the overburden of decision makers, the simplified preference function model by
Athawale and Chakraborty (2010) is implemented here.
( , ) 0
j ij i j
P i i if R R ′
′ = ≤ (8)
( , )
j ij i j ij i j
P i i R R if R R
′ ′
′ = − > (9)
Step 7 Calculate the aggregated preference function taking the criteria weights into
account.
Aggregated preference function,
( ) ( ) [ ]
1 1
, ,
m m
j j j
j j
π i i W P i i W
= =
⎡ ⎤
′ ′
= ⎡ × ⎤
⎢ ⎥
⎣ ⎦
⎢ ⎥
⎣ ⎦
∑ ∑ (10)
where Wj is the relative importance (weight) of jth
criterion.
Step 8 Determine the leaving and entering outranking flows as follows:
Leaving (or positive) flow for ith
alternative,
( ) ( )
1
1
( ) ,
1
n
i
i π i i i i
n
+
′=
′ ′
= ≠
− ∑
φ (11)
Entering (or negative) flow for ith
alternative,
( ) ( )
1
1
( ) ,
1
n
i
i π i i i i
n
−
′=
′ ′
= ≠
− ∑
φ (12)
where n is the number of alternatives.
Here, each alternative faces (n – 1) number of other alternatives. The leaving
flow expresses how much an alternative dominates the other alternatives, while
the entering flow denotes how much an alternative is dominated by the other
alternatives. Based on these outranking flows, the PROMETHEE I method can
provide a partial pre-order of the alternatives whereas the PROMETHEE II
12. A hybrid MCDM approach to supplier selection 11
method can give the complete pre-order by using a net flow, though it loses
much information of preference relations.
Step 9 Calculate the net outranking flow for each alternative.
The net outranking flow is computed through the difference between leaving
flow and entering flow of each alternatives.
( ) ( ) ( )
i i i
− + −
′ ′ ′
= −
φ φ φ (13)
Step 10 Determine the ranking of all the considered alternatives depending on the values
of φ(i).The higher value of φ(i), the better is the alternative. Thus, the best
alternative is the one having the highest φ(i) value.
6 Application of the proposed model
The objective of this section is to explain how supplier selection decisions are made using
the proposed model. This research study is applied for a refrigerator manufacturing
industry which is located in southern part of India. The industry is well reputed for
manufacturing of efficient refrigerators in and around India. The manufacturing of single
refrigerator involves assembling of 750 different components together. Therefore, it is
impossible to produce such large number of components in a single manufacturing unit.
So, the industry is likely to outsource the production of some components to other
medium or small manufacturing units. Already the industry has realised that quality
matters more than the quantity. Therefore, the industry has adopted the outsourcing
technique to meet its needs of quality. The efficient suppliers of an industry not only
determine the quality, but also help the industry to improve the competitive strategy by
reducing the production cost. Even if there is any delay in delivery of a component, it
may affect the supply chain adversely. Hence the industry needs a number of criteria to
evaluate the alternative suppliers. So, there is a need of systematic approach for assessing
the supplier of every component to establish the standard of the product. The four
different suppliers namely S1, S2, S3 and S4 are considered for purchasing a cooling fan.
A decision making committee which includes three decision makers namely D1, D2 and
D3 is formed to assign the most suitable linguistic values for evaluating criteria of
alternative suppliers.
6.1 Identification of necessary criteria
The evaluation criteria are determined according to the view of decision making team and
literature survey. The criteria are described as follow:
• Quality (C1): The ability of a product to perform its functions.
• Delivery time (C2): The criterion regarding how efficient and responsive a supplier
would be in delivery of a component within a given time.
• Performance history (C3): It is a measure of past performance of a supplier firm
based on the other criteria.
13. 12 M. Ilangkumaran et al.
• Production capability (C4): The criterion regarding quantity of components, the
supplier can produce in a stipulated time.
• Price (C5): It is cost of a component procuring from supplier.
• Technical capability (C6): It is technology or automation level of a supplier, which
is directly related to the quality of their products.
• Financial position (C7): It is a consideration of economical stability of an
organisation.
• Geographical location (C8): It is a consideration of distance between suppliers and
the procuring industry.
• Flexibility (C9): It considers the fitness of a supplier in response to changing
demand.
6.2 Formation of decision hierarchy
Identified criteria and supplier alternatives are used to frame the decision hierarchy as
shown in Figure 3. The supplier selection process includes three levels in the decision
hierarchy structure. With overall objective of the decision process ‘the selection of best
supplier’ is kept at the first level. The criteria are at the second level and the alternative
suppliers are at the third level of the hierarchy.
Figure 3 Hierarchical structure of supplier selection problem
6.3 Computation of criteria weights using AHP and FAHP
After the approval of decision hierarchy for the SSP, the weights of the criteria to be used
in the evaluation process are calculated by using AHP and FAHP method. In this phase,
formation of individual pair-wise comparison matrix is assigned as a task for the experts
in the decision making team by using the scale given in Tables 2 and 3. The questionnaire
design is presented in Appendix 1 to form a pair-wise comparison matrix. The pair-wise
comparison matrix of the evaluation criteria using crisp scale and triangular fuzzy scale
14. A hybrid MCDM approach to supplier selection 13
are tabulated in Tables 5 and 6. The calculated CI, CR and weights of the criteria for
AHP and FAHP are tabulated in Table 7.
6.4 Determination of final rank of alternatives
Step 1 A company is looking forward to select the best supplier among the four supplier
alternatives namely S1, S2, S3 and S4. A committee of three decision makers
D1, D2, and D3 is formed to conduct the evaluation and select the most suitable
supplier.
Step 2 The second step is to define linguistic variables and their corresponding crisp
scores. The evaluators are involved in expressing the rating of alternatives with
respect to each criterion in linguistic variables. The crisp score for
PROMETHEE calculation is tabulated in Table 8.
Step 3 The questionnaire designs are presented in Appendix 2 to evaluate the alternative
suppliers according to selection criteria. The ratings of four alternatives under
nine criteria, made by three decision makers, are aggregated by averaging and
tabulated in Table 9.
Step 4 According to equations (6) and (7), the weighted normalised decision matrix is
computed and tabulated in Table 10.
Step 5 The preference functions are calculated for all the pairs of alternatives, using
equations (8) and (9), and are tabulated in Table 11.
Step 6 Table 12 exhibits the aggregated preference function values for all the paired
alternatives, as calculated using equation (10) for both AHP and FAHP weights.
Step 7 The leaving and the entering flows for different supplier alternatives are
computed using equations (11) and (12) respectively, and obtained values are
tabulated in Table 13 using AHP and FAHP weights.
Step 8 The net outranking flow values for different alternative suppliers are tabulated in
Table 14.
Table 5 Pair-wise comparison matrix for criteria
C1 C2 C3 C4 C5 C6 C7 C8 C9
C1 1.00 3.00 5.00 3.00 1.00 3.00 3.00 1.00 3.00
C2 0.33 1.00 5.00 3.00 0.33 3.00 0.33 1.00 5.00
C3 0.20 0.20 1.00 0.20 0.20 1.00 0.33 0.33 1.00
C4 0.33 0.33 5.00 1.00 0.33 3.00 0.33 1.00 3.00
C5 1.00 3.00 5.00 3.00 1.00 5.00 3.00 1.00 5.00
C6 0.33 0.33 1.00 0.33 0.20 1.00 1.00 1.00 3.00
C7 0.33 3.00 3.00 3.00 0.33 1.00 1.00 1.00 3.00
C8 1.00 1.00 3.00 1.00 1.00 1.00 1.00 1.00 5.00
C9 0.33 0.20 1.00 0.33 0.20 0.33 0.33 0.20 1.00
19. 18 M. Ilangkumaran et al.
7 Results and sensitivity analysis
The net flow of various alternatives is computed through the difference between leaving
flow and entering flow of the alternatives are tabulated in Table 15. Based on the net flow
(φ), the ranking of the suppliers in the descending order are S2, S3, S4 and S1. It is
evident that the supplier 2 (S2) is the best supplier. To analyse the performance of the
suppliers under varying criteria weights, sensitivity analysis is carried out. The motive of
sensitivity analysis is to determine the impact on the alternatives, while exchanging the
criterion weight. To perform sensitivity analysis, ten conditions are framed by
exchanging the weights of criteria. The main condition denotes the performance of each
supplier with the original weights of criteria. For each condition, the net flow (φ) value of
the suppliers is calculated and tabulated in Table 16. The result is graphically represented
using the Figure 4. According to Table 16, S1 has the highest φ value of –0.3395 from
–0.9475 when the first and the third criteria weights are exchanged in condition 2. S1 has
the lowest value of –1.0737 when the first and the fifth criteria weights are exchanged in
condition 4. S2 will have the highest φ value of 0.9181 from 0.7957 when the first and
the fourth criteria weights are exchanged in condition 3. It will have the lowest value of
0.2628 when the first and third criteria weights are exchanged in condition 2. S3 will
have the highest φ value of 0.7997 from 0.6178 when the first and the third criteria
weights are exchanged in condition 2. It will have the lowest value of 0.3961 when the
first and ninth criteria weights are exchanged in condition 8. S4 will have the highest φ
value of –0.3159 from –0.4660 when the first and the fifth criteria weights are exchanged
in condition 4. It will have the lowest value of –0.7230 when the first and third criteria
weights are exchanged in condition 2. On the other hand, the supplier S2 will be selected
if the conditions 3, 4, 6, 7, 8, 9 and 10 are met. The supplier S3 will be selected if the
conditions 1, 2 and 5 are met. These combinations of different criteria weights can help
the decision maker in the decision making process.
8 Conclusions
The objective of this study is that the hybrid MCDM technique can be implemented in
supplier selection problem to choose the best supplier based on various conflicting
criteria. The supplier selection process incorporates both qualitative and quantitative
criteria and it may be difficult for the decision makers to express the values for
qualitative criteria. To eliminate the difficulty in decision making, the values for the
qualitative criteria have been taken as linguistic terms and they are converted into TFNs.
The fuzzy numbers used in fuzzy AHP helps to improve the consistency of decision
making process compared to the traditional AHP approach. The ranking of suppliers
obtained from the PROMETHEE method provides a solution for the industries to select
the appropriate supplier. The group decision making used in PROMETHEE method
eliminates the inaccuracy and inconsistency of the decisions made by a single decision
maker. For future research, mathematical modelling can be incorporated in this study for
multiple sourcing.
20. A hybrid MCDM approach to supplier selection 19
References
Ahire, S.L. and Rana, D.S. (1995) ‘Selection of TQM pilot projects using an MCDM approach’,
International Journal of Quality and Reliability Management, Vol. 12, No. 1, pp.61–81.
Al Harbi, K.M. (2001) ‘Application of AHP in project management’, International Journal of
Project Management, Vol. 19, No. 4, pp.19–27.
Al Khalil, M.I. (2002) ‘Selecting the appropriate project delivery method using AHP’,
International Journal of Project Management, Vol. 20, No. 6, pp.469–474.
Albayrak, E. and Erensal, Y.C. (2004) ‘Using analytic hierarchy process (AHP) to improve human
performance: an application of multiple criteria decision making problem’, Journal of
Intelligent Manufacturing, Vol. 15, No. 4, pp.491–503.
Almeida, A.T. (2007) ‘Multicriteria decision model for outsourcing contracts selection based on
utility function and ELECTRE method’, Computers & Operations Research, Vol. 34, No. 12,
pp.3569–3574.
Athawale, V.M. and Chakraborty, S. (2010) ‘Facility location selection using PROMETHEE II
method’, Paper presented at the International Conference on Industrial Engineering and
Operational Management, Bangladesh, 9–10 January.
Bahurmoz, A.M.A. (2003) ‘The analytic hierarchy process at DarAl-Hekma’, Saudi Arabia
Interfaces, Vol. 33, No. 4, pp.70–78.
Bellman, R.E. and Zadeh, L.A. (1970) ‘Decision making in a fuzzy environment’, Management
Science, Vol. 17, No. 4, pp.141–164.
Boer, L., Wegen, L. and Telgen, J. (1998) ‘Outranking methods in support of supplier selection’,
European Journal of Purchasing & Supply Management, Vol. 4, No. 2, pp.109–118.
Brad, J.F. (1986) ‘A multi-objective methodology for selecting sub-system automation options’,
Management Science, Vol. 32, No. 12, pp.1628–1641.
Brans, J.P. and Vincke, PH. (1985) ‘A preference ranking organization method’, Management
Science, Vol. 31, No. 6, pp.647–656.
Ceha, R. and Ohta, H. (1994) ‘The evaluation of air transportation network based on multiple
criteria’, Computers and Industrial Engineering, Vol. 27, Nos. 1–4, pp.249–252.
Chan, F.T.S. (2003) ‘Interactive selection model for supplier selection process an AHP’,
International Journal of Production Research, Vol. 41, No. 15, pp.3549–3579.
Chan, F.T.S. and Chan, H.K. (2010) ‘An AHP model for selection of suppliers in the fast changing
fashion market’, Int. J. Adv. Manuf. Technol., Vol. 51, Nos. 9–12, pp.1195–1207.
Chang, C.L., Wei, C.C. and Lee, Y.H. (1999) ‘Failure mode and effects analysis using fuzzy
method and grey theory’, Kybernetes, Vol. 28, No. 9, pp.1072–1080.
Cheng, J., Lee, C. and Tang, C. (2009) ‘An application of fuzzy Delphi and fuzzy AHP on
evaluating wafer supplier in semiconductor industry’, WSEAS Transactions on Information
Science and Applications, Vol. 6, No. 5, pp.756–767.
Deng, H. (1999) ‘Multi criteria analysis with fuzzy pair-wise comparison’, International Journal of
Approximate Reasoning, Vol. 21, No. 3, pp.215–231.
Dickson, G.W. (1966) ‘An analysis of vendor selection system and decisions’, Journal of
Purchasing, Vol. 2, No. 1, pp.5–17.
Gencer, C. and Gürpinar, D. (2007) ‘Analytic network process in supplier selection: a case study in
an electronic firm’, Applied Mathematical Modelling, Vol. 31, No. 11, pp.2475–2486.
Haq, N. and Kannan, G. (2006) ‘Fuzzy analytical hierarchy process for evaluating and selecting a
vendor in a supply chain model’, Int. J. Adv. Manuf. Technol., Vol. 29, Nos. 7–8, pp.826–835.
Jadidi, O., Hong, T.S., Firouzi, F., Yusuff, R.M. and Zulkifli, N. (2008) ‘TOPSIS and fuzzy
multi-objective model integration for supplier selection problem’, Journal of Achievements in
Materials and Manufacturing Engineering, Vol. 31, No. 2, pp.762–769.
21. 20 M. Ilangkumaran et al.
Lai, L., Wong, B.K. and Cheung, W. (2002) ‘Group decision making in a multiple criteria
environment: a case using the AHP in the software selection’, European Journal of
Operational Research, Vol. 137, No. 1, pp.134–144.
Libertore, M.J. (1987) ‘An extension of analytic hierarchical process for industrial R&D project
selection and resource allocation’, IEEE Transactions on Engineering Management, Vol. 34,
No. 1, pp.12–18.
Mikhailov, L. (2003) ‘Deriving priorities from fuzzy pair wise comparison judgments’, Fuzzy Sets
and Systems, Vol. 134, No. 3, pp.365–385.
Mohammady, P. and Amid, A. (2010) ‘Integrated fuzzy VIKOR and fuzzy AHP model for supplier
selection in an agile and modular virtual enterprise; application of FMCDM on service
companies’, The Journal of Mathematics and Computer Science, Vol. 1, No. 4, pp.413–434.
Nordggrd, D.E., Heggset, J. and Ostgulen, E. (2003) ‘Handling maintenance priorities using multi
criteria decision making’, IEEE Bologna Power Tech Conference.
Parthiban, P., Punniyamoorthy, M., Mathiyalagan, P. and Dominic, P.D.D. (2009) ‘A hybrid
decision model for the selection of capital equipment using AHP in conjoint analysis under
fuzziness’, International Journal of Enterprise Network Management, Vol. 3, No. 2,
pp.112–129.
Raju, K.S. and Pillai, C.S.R. (1999) ‘Multi-criteria decision making in river basin planning and
development’, European Journal of Operational Research, Vol. 112, No. 2, pp.249–257.
Rezqallah, H.R., Hamad, I., Al-Abdul, W. and Duffuaa, S.O. (1999) ‘The use of an analytical
hierarchy process in pavement maintenance priority ranking’, Journal of Quality in
Maintenance Engineering, Vol. 5, No. 1, pp.25–39.
Rouyendegh, B.D. and Erkan, T.M. (2012) ‘Selecting the best supplier using analytic hierarchy
process (AHP) method’, African Journal of Business Management, Vol. 6, No. 4,
pp.1455–1462.
Saaty, T.L. (1980) The Analytic Hierarchy Process, McGraw-Hill, New York, NY.
Sevkli, M. (2010) ‘An application of the fuzzy ELECTRE method for supplier selection’,
International Journal of Production Research, Vol. 48, No. 12, pp.339–3405.
Shahanaghi, K. and Yazdian, S.A. (2009) ‘Vendor selection using a new fuzzy group TOPSIS
approach’, Journal of Uncertain Systems, Vol. 3, No. 3, pp.221–231.
Shemshadi, A., Toreihi, M., Shirazi, H. and Tarokh, M.J. (2011) ‘Supplier selection based on
supplier risk: an ANP and fuzzy TOPSIS approach’, The Journal of Mathematics and
Computer Science, Vol. 2, No. 1, pp.111–121.
Socorro, G.C.M. and Teresa, L.M. (2009) ‘Selection of a cleaning system for engine maintenance
based on the analytic hierarchy process’, Computers and Industrial Engineering, Vol. 56,
No. 4, pp.1442–1451.
Tahriri, F., Osman, M.R., Ali, A. and Yusuff, R.M. (2008) ‘A review of supplier selection methods
in manufacturing industries’, Suranaree J. Sci. Technol., Vol. 15, No. 3, pp.201–208.
Tam, M.C.Y. and Tummala, V.M.R. (2001) ‘An application of the AHP in vendor selection of a
telecommunications system’, The International Journal of Management Science, Vol. 29,
No. 2, pp.171–182.
Teeravaraprug, J. (2008) ‘Outsourcing and vendor selection model based on Taguchi loss function’,
Songklanakarin J. Sci. Technol., Vol. 30, No. 4, pp.523–530.
Ti, L.Y., Chia, L.L., Hsiao, C.Y. and Gwo, H.T. (2010) ‘A novel hybrid MCDM approach for
outsourcing vendor selection: a case study for a semiconductor company in Taiwan’, Expert
Systems with Applications, Vol. 37, No. 7, pp.4796–4804.
Yang, J.L., Chiu, H.N., Tzeng, G. and Yeh, R.H. (2008) ‘Vendor selection by integrated fuzzy
MCDM techniques with independent and interdependent relationships’, Information Sciences,
Vol. 178, No. 21, pp.4166–4183.
Yurdakul, M. (2004) ‘AHP is the strategic decision-making tool to justify machine tool selection’,
Journal of Materials Processing Technology, Vol. 146, No. 3, pp.365–376.
22. A hybrid MCDM approach to supplier selection 21
Zadeh, L.A. (1965) ‘Fuzzy sets’, Information and Control, Vol. 8, No. 3, pp.338–353.
Zhang, T., He, Q., Zhang, H. and Li, Y. (2011) ‘Applying combined AHP-QFD method in new
product development: a case study in developing new sports earphone’, International
Conference on Management Science and Industrial Engineering (MSIE), pp.80–85.
Appendix 1
Questionnaire design for development FAHP model for supplier selection
process
Read the following questions and put check marks on the pair wise comparison matrices.
If a criterion on the left is more important than the matching one on the right, put the
check mark to the left of the importance ‘Equal’ under the importance level. If a criterion
on the left is less important than the matching one on the right, put your check mark to
the right of the importance ‘Equal’ under the importance level.
With respect to quality
Q1 How important is the quality (C1) when it is compared with delivery time (C2)?
Q2 How important is the quality (C1) when it is compared with performance history
(C3)?
Q3 How important is the quality (C1) when it is compared with production capability
(C4)?
Q4 How important is the quality (C1) when it is compared with price (C5)?
Q5 How important is the quality (C1) when it is compared with technical capability
(C6)?
Q6 How important is the quality (C1) when it is compared with financial position
(C7)?
Q7 How important is the quality (C1) when it is compared with geographical location
(C8)?
Q8 How important is the quality (C1) when it is compared with flexibility (C9)?
With respect to delivery time
Q9 How important is the delivery time (C2) when it is compared with performance
history (C3)?
Q10 How important is the delivery time (C2) when it is compared with production
capability (C4)?
Q11 How important is the delivery time (C2) when it is compared with price (C5)?
Q12 How important is the delivery time (C2) when it is compared with technical
capability (C6)?
23. 22 M. Ilangkumaran et al.
Q13 How important is the delivery time (C2) when it is compared with financial
position (C7)?
Q14 How important is the delivery time (C2) when it is compared with geographical
location (C8)?
Q15 How important is the delivery time (C2) when it is compared with flexibility (C9)?
With respect to performance history
Q16 How important is the performance history (C3) when it is compared with
production capability (C4)?
Q17 How important is the performance history (C3) when it is compared with price
(C5)?
Q18 How important is the performance history (C3) when it is compared with technical
capability (C6)?
Q19 How important is the performance history (C3) when it is compared with financial
position (C7)?
Q20 How important is the performance history (C3) when it is compared with
geographical location (C8)?
Q21 How important is the performance history (C3) when it is compared with
flexibility (C9)?
With respect to production capability
Q22 How important is the production capability (C4) when it is compared with price
(C5)?
Q23 How important is the production capability (C4) when it is compared with
technical capability (C6)?
Q24 How important is the production capability (C4) when it is compared with
financial position (C7)?
Q25 How important is the production capability (C4) when it is compared with
geographical location (C8)?
Q26 How important is the production capability (C4) when it is compared with
flexibility (C9)?
With respect to price
Q27 How important is the price (C5) when it is compared with technical capability
(C6)?
Q28 How important is the price (C5) when it is compared with financial position (C7)?
Q29 How important is the price (C5) when it is compared with geographical location
(C8)?
Q30 How important is the price (C5) when it is compared with flexibility (C9)?
24. A hybrid MCDM approach to supplier selection 23
With respect to technical capability
Q31 How important is the technical capability (C6) when it is compared with financial
position (C7)?
Q32 How important is the technical capability (C6) when it is compared with
geographical location (C8)?
Q33 How important is the technical capability (C6) when it is compared with flexibility
(C9)?
With respect to financial position
Q34 How important is the financial position (C7) when it is compared with
geographical location (C8)?
Q35 How important is the financial position (C7) when it is compared with flexibility
(C9)?
With respect to geographical location
Q36 How important is the geographical location (C8) when it is compared with
flexibility (C9)?
25. 24 M. Ilangkumaran et al.
Question
Criteria
Extreme
Very
strong
Strong
Moderate
Equal
Just
equal
Equal
Moderate
Strong
Very
strong
Extreme
Criteria
Q1
Quality
(C1)
Delivery
time
(C2)
Q2
Quality
(C1)
Performance
history
(C3)
Q3
Quality
(C1)
Production
capability
(C4)
Q4
Quality
(C1)
Price
(C5)
Q5
Quality
(C1)
Technical
capability
(C6)
Q6
Quality
(C1)
Financial
position
(C7)
Q7
Quality
(C1)
Geographical
location
(C8)
Q8
Quality
(C1)
Flexibility
(C9)
Q9
Delivery
time
(C2)
Performance
history
(C3)
Q10
Delivery
time
(C2)
Production
capability
(C4)
Q11
Delivery
time
(C2)
Price
(C5)
Q12
Delivery
time
(C2)
Technical
capability
(C6)
Q13
Delivery
time
(C2)
Financial
position
(C7)
Q14
Delivery
time
(C2)
Geographical
location
(C8)
Q15
Delivery
time
(C2)
Flexibility
(C9)
Q16
Performance
history
(C3)
Production
capability
(C4)
Q17
Performance
history
(C3)
Price
(C5)
Q18
Performance
history
(C3)
Technical
capability
(C6)
26. A hybrid MCDM approach to supplier selection 25
Question
Criteria
Extreme
Very
strong
Strong
Moderate
Equal
Just
equal
Equal
Moderate
Strong
Very
strong
Extreme
Criteria
Q19
Performance
history
(C3)
Financial
position
(C7)
Q20
Performance
history
(C3)
Geographical
location
(C8)
Q21
Performance
history
(C3)
Flexibility
(C9)
Q22
Production
capability
(C4)
Price
(C5)
Q23
Production
capability
(C4)
Technical
capability
(C6)
Q24
Production
capability
(C4)
Financial
position
(C7)
Q25
Production
capability
(C4)
Geographical
location
(C8)
Q26
Production
capability
(C4)
Flexibility
(C9)
Q27
Price
(C5)
Technical
capability
(C6)
Q28
Price
(C5)
Financial
position
(C7)
Q29
Price
(C5)
Geographical
location
(C8)
Q30
Price
(C5)
Flexibility
(C9)
Q31
Technical
capability
(C6)
Financial
position
(C7)
Q32
Technical
capability
(C6)
Geographical
location
(C8)
Q33
Technical
capability
(C6)
Flexibility
(C9)
Q34
Financial
position
(C7)
Geographical
location
(C8)
Q35
Financial
position
(C7)
Flexibility
(C9)
Q36
Geographical
location
(C8)
Flexibility
(C9)
27. 26 M. Ilangkumaran et al.
Appendix 2
Questionnaire design to evaluate the suppliers for development of PROMETHEE
model
Criteria Suppliers Worst (W) Poor (P) Fair (F) Good (G) Best (B)
S1
S2
S3
Quality (C1)
S4
S1
S2
S3
Delivery time (C2)
S4
S1
S2
S3
Performance history (C3)
S4
S1
S2
S3
Production capability (C4)
S4
S1
S2
S3
Price (C5)
S4
S1
S2
S3
Technical capability (C6)
S4
S1
S2
S3
Financial position (C7)
S4
S1
S2
S3
Geographical location (C8)
S4
S1
S2
S3
Flexibility (C9)
S4
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