![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
−
−
⊕ = ⊕ = + + +
⊗ = ⊗ =
− = − = − − −
÷ = ÷ =
= =](https://image.slidesharecdn.com/hybridmcdmforsupplierselection-230110162256-9d649f02/85/HybridMCDMforSupplierSelection-pdf-9-320.jpg)
![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](https://image.slidesharecdn.com/hybridmcdmforsupplierselection-230110162256-9d649f02/85/HybridMCDMforSupplierSelection-pdf-11-320.jpg)
HybridMCDMforSupplierSelection.pdf
- 1. See discussions, stats, and author profiles for this publication at: https://www.researchgate.net/publication/264821318 A hybrid MCDM approach to supplier selection Article in International Journal of Engineering Management and Economics · January 2012 DOI: 10.1504/IJEME.2012.052403 CITATIONS 8 READS 367 11 authors, including: Mani Ilangkumaran K. S. Rangasamy College of Technology 35 PUBLICATIONS 934 CITATIONS SEE PROFILE Loganathan Thirulogasundar Larsen and Toubro 1 PUBLICATION 8 CITATIONS SEE PROFILE Km Mouleeshwaran K. S. Rangasamy College of Technology 1 PUBLICATION 8 CITATIONS SEE PROFILE M. Boopathi Raja K. S. Rangasamy College of Technology 4 PUBLICATIONS 94 CITATIONS SEE PROFILE All content following this page was uploaded by Nizamuddin Pallikadath on 26 June 2019. The user has requested enhancement of the downloaded file.
- 2. Int. J. Engineering Management and Economics, Vol. X, No. Y, xxxx 1 Copyright © 200x Inderscience Enterprises Ltd. A hybrid MCDM approach to supplier selection M. Ilangkumaran*, M. Dinesh, M.M. Jegan, T. Loganathan, K.M. Mouleeshwaran, V. Sasirekha, Boopathi Raja, Nizamuddin Pallikadath, S. Praveen Kumar, T. Ruban Sundara Raj and C.N.S. Siddharatha Department of Mechatronics Engineering, K.S. Rangasamy College of Technology, Tiruchengode – 637 215, Namakkal, Tamil Nadu, India E-mail: [email protected] E-mail: [email protected] E-mail: [email protected] E-mail: [email protected] E-mail: [email protected] E-mail: [email protected] E-mail: [email protected] E-mail: [email protected] E-mail: [email protected] E-mail: [email protected] E-mail: [email protected] *Corresponding author Abstract: An organisation’s progress strongly depends on the selection of an appropriate supplier. The selection of suitable supplier is a multi criteria decision making (MCDM) problem, which is based on several qualitative, quantitative and even conflicting criteria. This paper aims to propose a hybrid MCDM technique for the supplier selection problem. The fuzzy analytical hierarchy process (FAHP) is used to analyse the structure of supplier selection problem and to determine the weights of the criteria. The preference ranking organisation method for enrichment evaluation (PROMETHEE) is used to obtain the final ranking of the suppliers. The effectiveness of the proposed FAHP-PROMETHEE method is compared to AHP-PROMETHEE and it is illustrated using a real-time case study from a refrigerator manufacturing industry. Keywords: AHP; fuzzy set theory; FST; preference ranking organisation method for enrichment evaluation; PROMETHEE; multi criteria decision making; MCDM; supplier selection. Reference to this paper should be made as follows: Ilangkumaran, M., Dinesh, M., Jegan, M.M., Loganathan, T., Mouleeshwaran, K.M. Sasirekha, V., Raja, B., Pallikadath, N., Praveen Kumar, S., Ruban Sundara Raj, T. and Siddharatha, C.N.S. (xxxx) ‘A hybrid MCDM approach to supplier selection’, Int. J. Engineering Management and Economics, Vol. X, No. Y, pp.000–000.
- 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
- 15. 14 M. Ilangkumaran et al. Table 6 Fuzzy comparison matrix of criteria using TFN C1 C2 C3 C4 C5 C6 C7 C8 C9 C1 (1, 1, 1) (1, 3, 5) (3, 5, 7) (1, 3, 5) (0.33, 1, 1) (1, 3, 5) (1, 3, 5) (1, 1, 1) (1, 3, 5) C2 (0.2, 0.33, 1) (1, 1, 1) (3, 5, 7) (1, 3, 5) (0.2, 0.33, 1) (1, 3, 5) (0.2, 0.33, 1) (1, 1, 1) (3, 5, 7) C3 (0.14, 0.2, 0.33) (0.14, 0.2, 0.33) (1, 1, 1) (0.14, 0.2, 0.33) (0.14, 0.2, 0.33) (0.33, 1, 1) (0.2, 0.33, 1) (0.2, 0.33, 1) (0.33, 1, 1) C4 (0.2, 0.33, 1) (0.2, 0.33, 1) (3, 5, 7) (1, 1, 1) (0.2, 0.33, 1) (1, 3, 5) (0.2, 0.33, 1) (0.33, 1, 1) (1, 3, 5) C5 (1, 1, 3) (1, 3, 5) (3, 5, 7) (1, 3, 5) (1, 1, 1) (3, 5, 7) (1, 3, 5) (1, 1, 1) (3, 5, 7) C6 (0.2, 0.33, 1) (0.2, 0.33, 1) (1, 1, 3) (0.2, 0.33, 1) (0.14, 0.2, 0.33) (1, 1, 1) (1, 1, 1) (0.33, 1, 1) (1, 3, 5) C7 (0.2, 0.33, 1) (1, 3, 5) (1, 3, 5) (1, 3, 5) (0.2, 0.33, 1) (1, 1, 1) (1, 1, 1) (0.33, 1, 1) (1, 3, 5) C8 (1, 1, 1) (1, 1, 1) (1, 3, 5) (1, 1, 3) (1, 1, 1) (1, 1, 3) (1, 1, 3) (1, 1, 1) (3, 5, 7) C9 (0.2, 0.33, 1) (0.14, 0.2, 0.33) (1, 1, 3) (0.2, 0.33, 1) (0.14, 0.2, 0.33) (0.2, 0.33, 1) (0.2, 0.33, 1) (0.14, 0.2, 0.33) (1, 1, 1) Sum (4.14, 4.85, 10.33) (5.68, 12.06, 19.66) (17, 29, 45) (6.54, 14.86, 26.33) (3.35, 4.59, 6.91) (9.53, 18.33, 29) (5.8, 10.32, 19) (5.33, 7.53, 8.33) (14.33, 29, 43)
- 16. A hybrid MCDM approach to supplier selection 15 Table 7 Results obtained with AHP and fuzzy AHP AHP crisp weights FAHP crisp weights C1 0.202368 0.178002 C2 0.11595 0.120028 C3 0.035137 0.035390 C4 0.085725 CI = 0.113638 0.088179 CI = 0.113638 C5 0.226695 (RI = 1.45) 0.222079 (RI = 1.45) C6 0.060016 CR = CI/RI = 0.078371 0.064692 CR = CI/RI = 0.078371 C7 0.117076 0.110614 C8 0.124191 0.141792 C9 0.032842 0.039224 Sum 1 1 Table 8 Linguistic scale for the rating of alternatives Scale of importance Worst Poor Good Fair Best Crisp score 0.00 2.50 5.00 7.50 10.00 Table 9 Rating of alternatives under nine criteria C1 C2 C3 C4 C5 C6 C7 C8 C9 S1 2.50 1.67 7.50 5.00 6.67 7.50 3.33 1.67 1.67 S2 6.67 4.17 0.83 8.33 5.83 4.17 7.50 5.00 7.50 S3 5.00 8.33 6.67 5.00 7.50 5.00 5.00 5.83 0.00 S4 5.83 3.33 3.33 5.00 0.83 3.33 5.00 5.83 2.50 Table 10 Normalised decision matrix C1 C2 C3 C4 C5 C6 C7 C8 C9 S1 0.00 0.00 1.00 0.00 0.88 1.00 0.00 0.00 0.22 S2 1.00 0.38 0.00 1.00 0.75 0.20 1.00 0.80 1.00 S3 0.60 1.00 0.88 0.00 1.00 0.40 0.40 1.00 0.00 S4 0.80 0.25 0.37 0.00 0.00 0.00 0.40 1.00 0.33 Table 11 Preference function for all pair of alternatives C1 C2 C3 C4 C5 C6 C7 C8 C9 (S1, S2) 0.00 0.00 1.00 0.00 0.00 0.93 0.00 0.00 0.00 (S1, S3) 0.00 0.00 0.20 0.00 0.00 0.86 0.00 0.00 0.28 (S1, S4) 0.00 0.00 0.70 0.00 0.75 1.00 0.00 0.00 0.00 (S2, S1) 1.00 0.30 0.00 1.00 0.00 0.00 1.00 0.64 0.72 (S2, S3) 0.45 0.00 0.00 1.00 0.00 0.00 0.54 0.00 1.00 (S2, S4) 0.18 0.05 0.00 1.00 0.75 0.07 0.54 0.00 0.50 (S3, S1) 0.55 1.00 0.00 0.00 0.25 0.00 0.46 1.00 0.00 (S3, S2) 0.00 0.70 0.80 0.00 0.25 0.07 0.00 0.36 0.00
- 17. 16 M. Ilangkumaran et al. Table 11 Preference function for all pair of alternatives (continued) C1 C2 C3 C4 C5 C6 C7 C8 C9 (S3, S4) 0.00 0.75 0.50 0.00 1.00 0.14 0.00 0.00 0.00 (S4, S1) 0.82 0.25 0.00 0.00 0.00 0.00 0.46 1.00 0.22 (S4, S2) 0.00 0.00 0.30 0.00 0.00 0.00 0.00 0.36 0.00 (S4, S3) 0.27 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.50 Table 12 Aggregated preference function (a, b) (S1, S2) (S1, S3) (S1, S4) (S2, S1) (S2, S3) (S2, S4) π(a, b) for AHP weight 0.09 0.07 0.25 0.54 0.27 0.38 π(a, b) for FAHP weight 0.10 0.07 0.26 0.53 0.27 0.38 (S3, S1) (S3, S2) (S3, S4) (S4, S1) (S4, S2) (S4, S3) π(a, b) for AHP weight 0.46 0.22 0.34 0.38 0.06 0.07 π(a, b) for FAHP weight 0.46 0.22 0.34 0.38 0.06 0.07 Table 13 Leaving and entering flow using AHP weight Flows using AHP weight Flows using FAHP weight Suppliers S1 S2 S3 S4 S1 S2 S3 S4 Leaving flow (φ+ ) 0.41 1.20 1.02 0.51 0.43 1.18 1.03 0.51 Entering flow (φ– ) 1.38 1.36 0.41 0.98 1.37 0.38 0.41 0.97 Table 14 Net outranking flows Suppliers Net outranking flow (φ) using AHP Net outranking flow (φ) using FAHP S1 –0.97 –0.95 S2 0.84 0.80 S3 0.60 0.62 S4 –0.47 –0.47 Table 15 Ranking of alternatives Suppliers Net outranking flow (φ+ ) using AHP AHP-PROMETHEE ranking Net outranking flow(φ+ ) using FAHP FAHP-PROMETHEE ranking S1 –0.97 4 –0.95 4 S2 0.84 1 0.80 1 S3 0.60 2 0.62 2 S4 –0.47 3 –0.47 3 S3 0.60 2 0.62 2 S4 –0.47 3 –0.47 3
- 18. A hybrid MCDM approach to supplier selection 17 Table 16 Sensitivity analysis Weights Net outflow values Condition w1 w2 w3 w4 w5 w6 w7 w8 w9 S1 S2 S3 S4 Main 0.1780 0.1200 0.0354 0.0882 0.2221 0.0647 0.1106 0.1418 0.0392 –0.9475 0.7957 0.6178 –0.4660 1 0.1200 0.1780 0.0354 0.0882 0.2221 0.0647 0.1106 0.1418 0.0392 –0.9004 0.6803 0.7703 –0.5502 2 0.0354 0.1200 0.1780 0.0882 0.2221 0.0647 0.1106 0.1418 0.0392 –0.3395 0.2628 0.7997 –0.7230 3 0.0882 0.1200 0.0354 0.1780 0.2221 0.0647 0.1106 0.1418 0.0392 –0.8251 0.9181 0.5441 –0.6371 4 0.2221 0.1200 0.0354 0.0882 0.1780 0.0647 0.1106 0.1418 0.0392 –1.0737 0.8458 0.5438 –0.3159 5 0.0647 0.1200 0.0354 0.0882 0.2221 0.1780 0.1106 0.1418 0.0392 –0.3638 0.5044 0.5651 –0.7057 6 0.1106 0.1200 0.0354 0.0882 0.2221 0.0647 0.1780 0.1418 0.0392 –0.9171 0.8261 0.6240 –0.5329 7 0.1418 0.1200 0.0354 0.0882 0.2221 0.0647 0.1106 0.1780 0.0392 –0.9575 0.7332 0.6737 –0.4494 8 0.0392 0.1200 0.0354 0.0882 0.2221 0.0647 0.1106 0.1418 0.1780 –0.7122 0.8769 0.3961 –0.5608 9 0.1780 0.0354 0.1200 0.0882 0.2221 0.0647 0.1106 0.1418 0.0392 –0.6555 0.6479 0.5031 –0.4956 10 0.1780 0.0882 0.0354 0.1200 0.2221 0.0647 0.1106 0.1418 0.0392 –0.9300 0.9025 0.5079 –0.4804
- 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.
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- 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 View publication stats