A NALYSIS O F S UPPLIER’S P ERFORMANCE T HROUGH F PIR /F NIR A ND M EMBERSHIP D EGREE T RANSFORMATION

Dhinaharan Nagamalai et al. (Eds) : CSTY, SIGI, AI, MaVaS - 2015
pp. 67–79, 2015. © CS & IT-CSCP 2015 DOI : 10.5121/csit.2015.50907
ANALYSIS OF SUPPLIER’S PERFORMANCE
THROUGH FPIR/FNIR AND MEMBERSHIP
DEGREE TRANSFORMATION
S.Hemalatha1
K. Ram Babu2
K.Narayana Rao3
K.Venkatasubbaiah4
1
Department of Mechanical Engg, Lendi Institute of Engineering and
Technology, Vizianagaram- 535 005
2
Department of Mechanical Engg, Andhra University, Visakhapatnam-530 007
3
Government Model Residential Polytechnic, Paderu-531024
4
Department of Mechanical Engg, Andhra University, Visakhapatnam-530 007
ABSTRACT
In today’s highly competitive business environment, evaluation of suppliers is the prime function
of the purchasing department of the organization. It is due to the fact that high percentage of the
material cost for manufacturing of a product is involved. Identification of decision criteria and
methods for supplier evaluation are appearing to be the important research area in the
literature. In this paper, hybrid methodology of Fuzzy positive Ideal rating /Fuzzy Negative
Ideal rating and Membership Degree Transformation- M (1, 2, 3) is proposed for evaluation of
supplier’s performance. A wide literature review is made and six selection criteria namely:
Cost, Quality, Service, Business performance, Technical Capability and Delivery performance
are considered for evaluation. A detailed application of the proposed methodology is illustrated.
The proposed methodology is useful not only to judge the overall performance of the supplier
but also to know which criteria/sub-criteria need to be improved.
KEYWORDS
Membership Degree transformation; Fuzzy positive Ideal Rating; Fuzzy Negative Ideal Rating;
Supplier performance;
1. INTRODUCTION
The traditional business functions need to be coordinated to achieve customer satisfaction, value,
profitability, and competitive advantage for individual companies and the entire supply chain.
One of the functions that have been singled out as important in the coordination processes of the
individual firms and supply chain is purchasing.
Cheraghi et al (2002) presented the critical success factors (CSFs) for supplier selection reported
in the literature emanating from the seminal work of Dickson (1966) and provide an update based
on reviewing more than 110 research papers. The authors indicated significant change in the
relative importance of various critical success factors in the research reported during 1966-1990
versus 1990-2001. Supplier selection and their performance evaluation is one of the important

68 Computer Science & Information Technology (CS & IT)
drivers of supply chain performance. Uses of suitable criteria with appropriate methodologies are
necessary for performance evaluation of a supplier. In the literature, it is observed that supplier
selection and evaluation methods were based on quoted price, quality, business relations, lead
time etc., constitute a multi-criteria or multi-objective decision making problem. The overall
objective of the supplier selection process is to identify, evaluate, contract with the suppliers and
optimum quota allocation to the suppliers. Boer et al (2001) made a review on decision methods
on supplier selection based on academic literature. Byun (2001) presented Analytical Hierarch
Process (AHP) approach for vendor selection and identified supplier reliability, product quality
and supplier experiences are the critical factors for effective supplier selection in Korean
automobiles. Muralidharan et al (2002) suggested guidelines for comparing supplier attributes
using a five-point rating scale and developed aggregation technique for combining group
member’s preferences into one consensus for supplier rating. In the supplier selection process,
organizations judge the supplier’s ability to meet the requirements of the organization to survive
in the intensely competitive global economy. Dulmin and Mininno (2003) used multi-criteria
decision analysis method in supplier selection problem using PROMETHEE and GAIA
methodology. Rajkumar and Ray (2004) identified attributes and factors relevant for
performance evaluation of suppliers through fuzzy inference system of the MATLAB fuzzy logic
tool box. Venkatasubbaiah and Narayana Rao (2004) considered thirty three sub-criteria under six
main criteria reported in the literature in four decision hierarchy levels for supplier selection using
AHP. Very often, experts opinion is the prominent characteristic of multi-criteria decision
making problems and this impreciseness of human’s judgments can be handled through the fuzzy
sets theory developed by Zadeh (1965). Fuzzy set theory effectively incorporates imprecision
and subjectivity into the model formulation and solution process. Chen et al (2006) adopted
TOPSIS concept in fuzzy environment to incorporate imprecision and subjectivity into the model
formulation and solution process to determine the ranking order of the suppliers. The author
considered the factors such as quality, price, and flexibility and delivery performance. Lee et al
(2007) adopted Fuzzy Analytic Hierarchy Process (FAHP) to analyze the importance of multiple
factors by incorporating the experts’ opinions to select Thin Film Transistor Liquid Crystal
Display (TFT-LCD) suppliers. Narayana Rao et al (2007) illustrated fuzzy outranking technique
for selection of supplier using minimum and gamma operators for aggregating the concordance
and discordance indices of the alternative suppliers to arrive the ranking of suppliers with
credibility values. Shouhua Yuan et al (2008) proposed DEA, AHP and fuzzy set theory to
evaluate the overall performance of suppliers of a manufacturing company. Enyinda et al (2010)
adopted analytic hierarchy process (AHP) model and implemented using Expert Choice Software
for a supplier selection problem in a generic pharmaceutical organization. Elanchezhian et al
(2010) adopted analytical network process (ANP) and TOPSIS method for select the best vendor.
Jitendra Kumar and Nirjhar Roy (2010), adopted a hybrid model using analytic hierarchy process
(AHP) and neural networks (NNs) theory to assess vendor performance. Yucel and Guneri (2011)
assessed the supplier selection factors through fuzzy positive ideal rating and negative ideal rating
to handle ambiguity and fuzziness in supplier selection problem and developed a new weighted
additive fuzzy programming approach. Yang and Jiang (2012) proposed AHM (Analytic
Hierarchy Method) and M(1,2,3) methodology to evaluate the supply chains’ overall
performance. Durga Prasad et al (2012) proposed and illustrated the methodology for evaluating
the efficiency and performance of the suppliers using Data Envelopment Analysis (DEA)
technique. Amindoust (2012) proposed and illustrated ranking methodology in fuzzy environment
with sustainable supplier selection criteria/sub-criteria. Abbasi et al (2013) proposed a framework
and applied QFD/ANP to rank the relative importance of the key attributes in selection of
suppliers. Galankashi et al (2013) presented supplier Selection for Electrical Manufacturing
Companies Based on Different Supply Chain Strategies using AHP. Eshtehardian et al (2013),

Computer Science & Information Technology (CS & IT) 69
presented a decision support system to the supplier selection in the construction and civil
engineering companies using AHP and ANP simultaneously. Om pal et al (2013) presented
review on supplier selection criteria and methods basing on research reported in the supply chain
management area. Deshmukh and Vasudevan (2014) explored criteria that are important for green
supplier selection, as evident in literature and gathered from discussions with experts. Ergün and
Atalay (2014) proposed FAHP and FTOPSIS for evaluation of suppliers of an electronic
company.
From the review of literature, it is observed that there is limited research in group decision
approach for prioritizing the supplier selection criteria in fuzzy environment. Further,
classification of a supplier belongs to a particular class basing on the data mining technology is
also limited. In lieu of this, a hybrid methodology is proposed for evaluation of supplier’s
performance and illustrated by considering the supplier of a pharmaceutical company. In the
methodology, Fuzzy positive Ideal Rating and Fuzzy Negative Ideal rating approach is adopted to
find out the importance weights of criteria/sub-criteria. Then, Membership transformation
method – M(1,2,3) is adopted to find out the grade of overall performance of a supplier. Proposed
methodology is explained in section two. Numerical Illustration is presented in section three.
Results and discussion is made in section four. Finally, the conclusions are summarized with
future scope in section five.
2. METHODOLOGY
Step 1: Establish Evaluation Index System of Supplier Performance
An Organization has to identify criteria for supplier selection to evaluate whether the supplier fits
its competitive strategy and supply chain strategy .The total performance of the supplier depends
on the capabilities in each criteria/sub criteria and the relative importance given to them.
Step 2: Determine importance weights of the criteria/sub criteria
Fuzzy Positive Ideal Rating (FPIR) and Fuzzy Negative Ideal Rating (FNIR) are used to compute
the weights of the criteria/sub criteria (Yucel and Guneri, 2011).
Step 3: Membership Transformation through “Effective, Comparison and
Composition”
Membership transformation method – M(1,2,3) proposed by Hua and Ruan (2009) as discussed in
the following steps is adopted to determine the evaluation matrix of the alternative.
Step 3.1: Determine Evaluation Membership ( )jk Qµ
Percentage of satisfaction among the domain experts under each class is considered as evaluation
matrix of each criterion.
( )jk Qµ =membership of jth
sub-criteria of the criteria group ‘Q’ belonging to the kth
fuzzy
membership class.

Step 3.2: Determine Distinguishable Weights ( ( )j Qα )
Distinguishable weight represents the normalized and quantized value obtained from the
following relation.
1
( ) ( )/ ( ) ( 1.. )=
= =∑
m
j j jj
Q v Q v Q j mα
Where
( ) 1 (1/ log( ))* ( )= −j jv Q p H Q
1
( ) ( )*log ( )
=
= −∑
p
j jk jk
k
H Q Q Qµ µ
( )jv Q = weight of the jth sub criteria of the evaluation criteria object ‘Q’ obtained from
uncertainty in the payoff information of the sub criteria
( )jH Q = Measure of uncertainty in the payoff information of the jth sub criteria of the evaluation
criteria object ‘Q’
Step 3.3: Determine Comparable sum Vector ( )kM Q
Comparable value of the sub criteria under the given criteria is determined from the following
relation
( )kM Q = 1
( )* ( )* ( )=∑
m
j j jkj
Q Q Qβ α µ
( )j Qβ = Importance Weight Vector of sub-criteria
Step 3.4: Determine Membership Vector ( )k Qµ
Membership vector of the object ‘Q’ belonging to class ‘k’ is determined from the following
relation.
( )k Qµ =
1
( ) / ( )
=
∑
p
k k
k
M Q M Q
Step 3.5: Determine Evaluation Matrix of the alternative U(S)
Membership matrix of all the criteria of the object ‘Q’ is determined and evaluation matrix is
formed as shown below.

U(S)=
( 1)
( 2)
( 3)
( 4)
..
..
 
 
 
 
 
 
 
  
 
C
C
C
C
µ
µ
µ
µ
Step 4: Determine Final membership Vector ( )Sµ
Once the evaluation matrix of the goal and the weights of the each criterion are known the
procedure is repeated from the step 3.1 to 3.5 is repeated to obtain the final membership vector of
the goal.
Step 5: Determine the grade of overall Performance (KO)
Overall performance of the alternative is determined by applying confidence recognition rule
(Confidence degree: λ >0.7)
KO = min {k|
1
( )
=
≥∑
k
k
k
Sµ λ }
3. NUMERICAL ILLUSTRATION
In this paper, supplier performance evaluation using proposed methodology is illustrated with a
numerical example. Supplier’s performance metrics taken from the literature (Venkatasubbaiah et
al., 2004; Lee et al., 2007; Narayana rao et al., 2007) are considered for performance evaluation
of supplier. The evaluation hierarchy is organized into three layers namely, Goal, Criterion layer
and sub-criterion layer as shown in fig 1.
Figure 1: Hierarchy of Evaluation Index System of Supplier performance

Evaluation of supplier performance is considered as goal. Supplier evaluation criteria namely,
Quality (Q), Cost (C), Service (S), Business performance (BP), Technical Capability (TC) and
Delivery are considered at criterion level. Sub-criteria under each criterion are given below.
Sub-criteria under Quality (Q): Product durability and Reliability (PDR); Quality systems (QS);
Percent Rejection (PR); Reputation and Position in the market (RP);
Sub-criteria under Cost (C): Competitive Pricing (CP); Unit Price (UP); Quantity Discount (QD);
Payment Terms (PT);
Sub-criteria under Service (S): Handling of Complaints (HC); Availability of product/service
(APS); Training equipment (TE); Flexibility (FL);
Sub-criteria under Business Performance (BP): Financial Stability (FS); IT usage (IT);
Management Capability (MC); Personnel Capability (PC);
Sub-criteria under Technical Capability (TC): Technical Support (TS); Technology Know How
(TKH); Understanding of Technology (UT); Performance History (PH);
3.6 Sub-criteria under Delivery Performance (DP): Delivery of Lead Time (DLT); Expeditation
of Orders (EO); Flexible Transportation Modes (FTM); Safety and Security of Components (SS);
Necessary data on the relative importance of criteria/sub-criteria gathered from discussions with
the managers of Purchasing, Logistics, Quality Control and Production departments of a
pharmaceutical company. These industries need to improve their supply chain performance by
concentrating on supplier issues to face with the uncertainty within the business environment.
3.1 Relative weights of the criteria/sub-criteria
Relative weights of criteria/sub-criteria are determined as discussed in step 2 of the methodology
section. Data is collected by discussion with the managers of Purchasing, Logistics, Quality
Control and Production departments to assess the relative importance of the criteria on the
supplier performance. Degree of relative importance of criteria is presented with the linguistic
variables: Nill-NL;Very Low- VL; Low-L; Medium Low- ML; M- Medium; Medium High-
MH; High- H;Very High- VH; Full- F; Aggregated responses of the importance of criteria and
sub-criteria in terms of the linguistic variables by the employees of different departments are
shown in the table 1.
The study considered the above criteria/sub-criteria from the literature and these are prioritized.
Relative weights of criteria and sub-criteria are determined from the aggregated responses shown
table 1 and table 2 respectively through Fuzzy Positive Ideal Rating (FPIR) and Fuzzy Negative
Ideal Rating (FNIR) approach as discussed in step 2 of the methodology section. Relative weights
of criteria and sub-criteria are shown in table 3.From table 3 it is observed that Quality criterion
is highly prioritized followed by Technical capability, Delivery Performance, Cost, Service and
Business Performance. This is due to the fact that the pharmaceutical company considers Quality
is the most important criterion that must be evaluated for successful selection of the supplier.
Technical Capability criterion is ranked second since it is an obvious consideration for any
pharmaceutical company. Relative weights of the criteria/sub-criteria are shown in fig 2

Table 1: Aggregated Responses on Criteria
Table 2: Aggregated Responses of Sub-criteria

Table 3: Relative weights of the criteria/sub criteria
Table 4: Evaluation Responses and Memberships

Figure 2: Relative weights of the criteria/sub-criteria
3.2 Evaluation Membership
Data on the given supplier performance sub-criteria is obtained from 75 employees of production,
Logistics, Quality control and Marketing & sales departments of the pharmaceutical company. No
of employees responded regarding the satisfaction levels in five classes and the membership
values are shown in table 4.
3.3 Evaluation matrix
Evaluation Matrix is determined as discussed in step 3 of methodology section. Evaluation matrix
of supplier’s performance is shown below.
U(S) =
( ) 0.1530 0.1400 0.3896 0.2093 0.1081
( ) 0.1632 0.1583 0.3779 0.1576 0.1429
( ) 0.2365 0.2420 0.2606 0.1422 0.1187
( ) 0.3324 0.2039 0.1825 0.1503 0.1309
( ) 0.2581 0.1901 0.2357 0.1751 0.1411
( ) 0.
 
 
 
 
= 
 
 
  
 
C
S
BP
TC
Q
DP
µ
µ
µ
µ
µ
µ 2458 0.1234 0.3459 0.1566 0.1283
 
 
 
 
 
 
 
  
 
3.4 Final membership Vector
Final membership vector of the supplier’s performance is determined as discussed in step 4 of the
methodology section. The Final membership vector of the supplier’s performance is shown
below.
( )( ) 0.2218 0.1639 0.3182 0.1699 0.1262=Sµ

3.5 Grade of Overall Performance of the supplier
From the numerical illustration, according to the final membership vector, it is observed that the
overall performance of the supplier belongs to the ‘General’ level with the confidence level of
70.39% (22.18%+16.39%+31.82%).
4. RESULTS AND DISCUSSION
Evaluation membership of supplier’s performance is shown in fig 2. From the figure, it is
understood that Technical Capability (TC) of the supplier is showing relatively high confidence
level of performances of 33.24% in ‘Very Satisfied’ level. Cost (C), Service (S), Supplier
performance in respect of Business performance (BP), Technical Capability (TC), Quality (Q),
and Delivery Performance (DP) are showing confidence levels of 38.96%, 37.79%, 26.06%,
18.25%, 23.57% and 34.59% respectively in ‘General’ level.
Figure 2: Evaluation memberships of supplier’s performance criteria
From the results of the final membership values, it can be judged that the performance of the
supplier is considered as ‘General’ level as the obtained confidence level (70.39%) is more than
the minimum confidence level of 70%. Overall confidence level with ‘Very Satisfied’ is only
22.18% indicates that the supplier should improve the performance from every criteria. In the
context of supplier evaluation for a pharmaceutical company, the suppliers need to improve
quality, technical capability and delivery performance such that the purchasing company will be
capable of rapidly responding to changes to their customer demands. Implementing continuous
quality improvement methods, making use of latest equipments and machines, implementing new
thoughts in business processes will be useful to improve the supplier’s performance
5. CONCLUSIONS
The proposed methodology is a hybrid methodology that combined the FPIR/FNIR approach with
Membership transformation method – M (1,2,3) to evaluate the performance of supplier. The
proposed methodology is useful not only to judge the overall performance of the supplier but also
to know which criteria/sub-criteria need to be increased. The proposed hybrid method is useful to
evaluate the supplier’s performance as it is affected by the subjective judgment involved in

measuring of the criteria/sub-criteria by the stake holders. The methodology maybe extended for
the supplier evaluation and selection basing on the supply chain strategy (Lean, Agile and
Leagile). To this effect, it requires critical judgment to assess the relative weights among the
criteria basing on lean, agile and leagile supply chain strategies. Also, the study can be extended
to other areas of decision making in evaluation and ranking of alternatives. Also, the performance
of the proposed method can be improved by reducing the subjective judgment in prioritizing the
factors/sub-factors.
ACKNOWLEDGEMENTS
The authors are very much thankful to the reviewer for making constructive comments to
improve the quality of the paper.
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A NALYSIS O F S UPPLIER’S P ERFORMANCE T HROUGH F PIR /F NIR A ND M EMBERSHIP D EGREE T RANSFORMATION

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