Performance Measurement of Individual Manufacturing Firm Under Fuzzy Performance Index Model

International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056
Volume: 04 Issue: 07 | July -2017 www.irjet.net p-ISSN: 2395-0072
© 2017, IRJET | Impact Factor value: 5.181 | ISO 9001:2008 Certified Journal | Page 557
Performance measurement of individual manufacturing firm under
fuzzy performance index model
Bhuneshwar Kumar Dixena1, Raghavendra Singh Kashyap2
M-Tech Scholar1, Assistant Professor2
Department of Mechanical Engg,
Dr. C.V. Raman University, Kota, Bilaspur, (C.G.), India
---------------------------------------------------------------------***---------------------------------------------------------------------
Abstract - In last decade, each firm has begun to establish
the production with rapid rate in compensating the high
demand of goods with rich-quality of service level. In order
to respond these, many firm perceived the necessity to
balance the production chain of organization. In the
presented research work, a 2nd second level hierarchical
Lean-Resilient supply chain module structure has been
constructed, where Fuzzy Performance Index model has
been applied to assess the overall performance of crank and
shaft vendor firm.
Key Words: Benchmarking, L-R (Leanness-Resilient)
Supply Chain, Performance Measurement (PM), Fuzzy
Performance Index (FPI).
1. INTRODUCTION
Supply Chain Management (SCM) is described as the
procedure of planning and executing, and at the same time
managing the supply chain by the mainly efficient potential
way. Supply chain management involves controlling of
finished products from the source of origin the consumption
level. The conventional supply chain concerned with two or
more firms, which were enabled the connection among the
consumers and the vendors. In this conventional technique,
therefore the finished products are delivered to the
purchasers through a chain of warehouses. SC is a system of
business that are involved, through upstream and
downstream connection, in the dissimilar procedure and
actions, which create worth in the term of goods and
services in the hands of the final purchasers.
SCM integrate vendors, goods producers, warehouses and
stores, in order that goods / services are produced and
distributed to the consumers at right quantity, at right
site, at right time, at right price by removing the system
wide price while fulfilling the service level requirement of
customers. Performance measurement is counted as vital
constituent of effective forecast and controlling as well as
decision making. It provides essential criticisms or
information to expose growth, augment in enthusiasm and
identify problems. Performance measurement is consider as
a part of methods, metrics, courses and systems , used in
firms to explain strategies into tactics, observe
implementation, and supply insight to get better
financial and operations. Supply chain management
networking is shown in Fig.1.
Fig.1. Supply chain management networking
2. FUZZY SET THEORY:
Prof. Zadeh proposed the concept of fuzzy logic in 1965.
Fuzzy logic theory is a control tool and technique, which
encompasses the data by allowing partial set membership
rather than crisp set membership or non-membership.
Fuzzy logic deals with the concept of partial truth, where
the truth value may range between completely true and
completely false. Fuzzy logic found their application where
the valuable information is neither completely true nor
completely false, or which are partly true and partly false
(Sahu et al., 2015a, b, Sahu et al., 2016c, Sahu et al., 2017b,
e).
Fuzzy logic deals with reasoning that is approximate
rather than fixed and exact. Compared to traditional
binary sets. Fuzzy logic variables may have a truth value
that ranges in degree between 0 and 1.
3. RESEARCH OBJECTIVES:
After reviewing the content of research gap, It is observed
that, many philosophies were introduced in loop of supply
chain management in order to solve various problems of
industrial sectors i.e. assessment of resiliency of supplier
against disasters, waste management equipments
availability in evaluated manufacturing firms, green
performance, responses of firms towards their clients etc.

Amongst proposed SC philosophies, Lean-Resilient (L-R)
strategies of SC worked seminal to solve many problems of
firms. Performance measurement is utilized as a tool to
quantify overall efficiency cum effectiveness via Lean-
Resilient (L-R) assist to reduce the waste and assess the
capability of firm against disasters. After literature survey,
it is realized that there is need to develop a multi criterion
decision making performance appraisement hierarchical
module (constituted by mixing the segregated Lean-
Resilient L-R 2nd layers of SC measures / drivers and their
corresponding interrelated metrics conjunctive with Fuzzy
Performance Index model in purpose to estimation the
overall performance of individual firm.
4. METHODS:
Considering an L-R, 2nd level appraisement hierarchical
module, included criterion at 1st and 2nd level followed
below said notations to compute the performances of
Choice / Alternative crank manufacturing and shaft
manufacturing firms.
iC = th
i
1st level assessment index; 1,2,..., .i m
ijC = th
j
2nd level assessment index which is under th
i
1st level assessment index
iC ; 1,2,..., .j n
The calculated fuzzy rating of individual 1st level
assessment criterion-attribute can be computed as (Equa.
7), (Lin et al., 2006, Sahu et al., 2014).
 
1
1
n
ij ij
j
i n
ij
j
w U
U
w






…………………………………………………...…….…………(1)
Here
ijU represents aggregated fuzzy performance
(rating) of core derivers and
ijw represent aggregated
fuzzy importance grade with respect to attributes
ijC at
2nd level. Also,
iU represents the calculated fuzzy
performance (rating) of core derivers with respect to the
index
iC at 1st level. Thus, overall fuzzy performance
index  U FPI can be acquired as follows.
 
 
1
1
m
i i
i
m
i
i
w U
U FPI
w






…………………………………………………….………… (2)
Here
iU  rating of th
i
iC ;
iw  Importance grade of th
i
iC .
Defuzzifying the fuzzy performance importance index is
done in comparing the performance in case of numerical
value (may be set by executives of cross functional
departments of manufacturing firm).
Also the single numerical value of the fuzzy number
 4321 ,,,
~
aaaaA  based on Center of Area (COA)
technique can be articulated by following relation:
32 4
1 2 3
32 4
1 2 3
1 4
2 1 4 3
1 4
2 1 4 3
2 21 1
1 2 3 4 4 3 2 13 3
1 2 3 4
( )
( )
( )
( ) ( )
.
aa a
a a a
aa a
a a a
x x dx
defuzz A
x dx
x a a x
xdx xdx xdx
a a a a
x a a x
dx dx dx
a a a a
a a a a a a a a
a a a a




  
  


              

            
     

   
……………….…………….……(3)
5. PROPOSED LEAN-RESILIENT (L-R) SUPPLY CHAIN
EVALUATION MODEL: EMPIRICAL CASE RESEARCH:
The practical steps for measuring the performance of a
crank and shaft manufacturing firm under Lean-Resilient
(L-R) supply chain actions are presented.
Step 1: Construction of a cluster of expert’s panel for
assessing the overall Lean-Resilient (L-R) performances of
supply chain management of crank and shaft
manufacturing firm.
Step 2: Evaluation of suitable linguistic scale in terms of
appropriateness ratings and importance weight against
evaluation criterion.
Step 3: Evaluation of performance ratings as well as
weights against criterion associated with module up to
2nd level hierarchy and weight of 1st level hierarchy.
Step4: Transform the linguistic variables into
generalized trapezoidal fuzzy number set (GTFNs) and
then aggregated the assigned linguistic terms (as rating
and weights) converts into single responses.
Step 5: Applied fuzzy performance index model to
calculate the ratings of 1st level criterion.
Step 6: Estimation of overall performance of firm under
Lean-Resilient (L-R) supply chain.

6. An empirical case research of crank and shaft
manufacturing firm:
A case research of crank and shaft manufacturing firm is
carried out, where Lean-Resilient (L-R) supply chain based
appraisement module is constructed in purpose to
measure the performance of an crank and shaft
manufacturing firm. In the presented work, a decision
support system (consist of multi criterion hierarchical
module coupled with fuzzy performance index model) is
proposed to calculate the performance of said firm under
lean-resilient supply chain management strategies. In
proposed module, Lean (L) and Resilient (R) has
considered as strategy, while Technology leanness, (C1),
Work force leanness, (C2), Manufacturing management,
(C3), Collaborative planning, (C4), Resiliency, (C5) have
counted as 1st level drivers. Apart from that, Systematic
process control, (C1,1), Use of TQM tools, (C1,2),
Maintenance of machines, (C1,3), Reduction of non-value
adding cost via techniques, (C1,4), Identification and
prioritization of critical machines, (C1,5), Products
designed for easy manufacturing, (C1,6), Flexible workforce
for adaptation of new technologies, (C2,1), Multi-skilled
personnel, (C2,2), Strong employee spirit and cooperation,
(C2,3), Employee empowerment, (C2,4), Improvement
culture, (C3,1), JIT delivery to customers, (C3,2),
Optimization of processing sequence and flow in shop
floor, (C3,3), Overall Manufacturing waste reduction, (C3,4),
Material planning, (C4,1), Production planning, (C4,2),
Supplier planning, (C4,3), Distributor inventory planning,
(C4,4), Effective handling of question and answer, (C5,1),
Information discovery, (C5,2), Decision-coordination, (C5,3),
Business intelligence, (C5,4) have considered as core
drivers.
The multi level hierarchical appraisement module, shown
in Table 1. An appropriate linguistic scale is elected,
shown in Table 2, which facilitated the experts to state
their oral opinions in the terms of priority weight
(significances) and appropriateness ratings against
evaluation criterion. For computing importance and
ratings of criterion, available at different hierarchical
levels, a committee of six expert’s panel,
21, DMDM
,
3DM
54 , DMDM
and
6DM
is formed to express priority
weight (significances) and appropriateness ratings in
terms of linguistic variables against 2nd level indices,
shown in Tables 3-4 for crank and shaft manufacturing
firm.
Similarly, Expert’s panel (E) expressed their importance in
linguistic terms against 1st level criterion for alternative,
shown in Tables 5. By using trapezoidal fuzzy operators
given by (Arbos 2002), (Beamon 1999), the fuzzy
importance and ratings against individual 2nd level
criterion for alternative is aggregated, depicted in Table. 6.
Next same trapezoidal fuzzy operators given by (Arbos
2002), (Beamon 1999), is used to compute importance
against individual 1st level criterion as shown in Table 6.
Considering a Lean-Resilient (L-R) supply chain activities
2nd level appraisement hierarchical module, included
criterion at 1st and 2nd level, followed, Equation 1 is used
to compute the rating performances of 1st level and
Equation 2 for computing overall FPI, which computed as
(0.508179, 0.639028, 1.085557; 1.356745) for
alternative crank and shaft manufacturing firm. The crisp
score has computed as 0.90 by exploring (Equ. 3).
Table: 1 L-R SC performance appraisement module
Goal
1st level
driver
2nd level indices /metrics Sources
Fuzzy-
Performance
measuremen
t of a firm
under L-R
Lean (L)
strategy,C1
Technology
leanness, (C1)
Systematic process control, (C1,1) Matawale, 2016
Use of TQM tools, (C1,2) Matawale, 2016
Maintenance of machines, (C1,3) Matawale, 2016
Reduction of non-value adding cost
via techniques, (C1,4)
Matawale, 2016
Identification and prioritization of
critical machines, (C1,5) Matawale, 2016
Products designed for easy
manufacturing, (C1,6)
Matawale, 2016
Work force
leanness, (C2)
Flexible workforce for adaptation of
new technologies, (C2,1)
Sahu et al., 2015a,b
Multi-skilled personnel, (C2,2) Srivastava, 2007
Strong employee spirit and
cooperation, (C2,3)
Srivastava, 2007

supply chain,
(C)
Employee empowerment, (C2,4) Green et al., 1998
Manufacturing
management,
(C3)
Improvement culture, (C3,1) Sahu et al., 2016a,b
JIT delivery to customers, (C3,2) Sahu et al., 2016a,b
Optimization of processing sequence
and flow in shop floor, (C3,3)
Sahu et al., 2017a,c,d
Overall Manufacturing waste
reduction, (C3,4)
Sahu et al., 2017a,c,d,f,g
Resilient (R)
staregy,C2
Collaborative
planning, (C4)
Material planning, (C4,1) Sahu et al., 2017a,c,d,f,g
Production planning, (C4,2) Green et al., 1998
Supplier planning, (C4,3) Sahu et al., 2017a,b,c,d,e,f,g
Distributor inventory planning, (C4,4) Sahu et al., 2017a,b,c,d,e,f,g
Resiliency,
(C5)
Effective handling of question and
answer, (C5,1)
Sahu et al., 2017a
Information discovery, (C5,2) Sahu et al., 2017c
Decision-coordination, (C5,3) Kainumaa and Tawara 2006
Business intelligence, (C5,4) Kainumaa and Tawara 2006
Table 2: Nine-member linguistic terms and their corresponding fuzzy representations
Linguistic terms for weights Linguistic terms for performance
ratings
Fuzzy representation
DL: Definitely low DL: Definitely low (0.0, 0.0, 0.0, 0.0; 1.0)
VL: Very low VL: Very low (0.0, 0.0, 0.02, 0.07; 1.0)
L: Low L: Low (0.04, 0.10, 0.18, 0.23; 1.0)
ML: More or less low ML: More or less low (0.17, 0.22, 0.36, 0.42; 1.0)
M: Middle M: Middle (0.32, 0.41, 0.58, 0.65; 1.0)
MH: More or less high MH: More or less high (0.58, 0.63, 0.80, 0.86; 1.0)
H: High H: High (0.72, 0.78, 0.92, 0.97; 1.0)
VH: Very high VH: Very high (0.93, 0.98, 1.0, 1.0; 1.0)
DH: Definitely high DH: Definitely high (1.0, 1.0, 1.0, 1.0; 1.0)
Table 3: Weights of 2nd level indices assigned by DMs
2nd level indices Weights of 2nd level indices assigned by DMs
DM1 DM2 DM3 DM4 DM5 DM6
C11 H H VH H H VH
C12 MH H H MH H H
C13 H MH MH H MH MH
C14 MH MH MH MH MH MH
C21 VH VH DH VH VH DH
C22 H VH DH H VH DH
C23 VH H VH VH H VH
C24 DH H H DH H H
C31 MH H MH MH H MH
C32 H MH H H MH H
C33 MH M MH MH M MH
C34 MH M H MH M H

C41 H MH ML H MH ML
C42 MH M M MH M M
C43 M MH ML M MH ML
C44 MH MH L MH MH L
C51 L ML L L ML L
C52 VL ML ML VL ML ML
C53 ML L ML ML L ML
C54 DL L L DL L L
Table 4: Rating of 2nd level indices assigned by DMs
2nd level indices Rating of 2nd level indices assigned by DMs
C11 VH H MH VH H MH
C12 H M MH H M MH
C13 M H VH M H VH
C14 VH VH VH VH VH VH
C21 H VH VH H VH VH
C22 VH VH H VH VH H
C23 H M NH H M NH
C24 H M MH H M MH
C31 VH H DH VH H DH
C32 VH H DH VH H DH
C33 H VH VH H VH VH
C34 DH VH VH DH VH VH
C41 VH VH H VH VH H
C42 H H DH H H DH
C43 VH M H VH M H
C44 DH M VH DH M VH
C51 H MH H H MH H
C52 VH MH H VH MH H
C53 MH H VH MH H VH
C54 MH H DH MH H DH
Table 5: Weights of 1st level drivers assigned by DMs
1st level indices Weights of 1st level indices assigned by DMs
C1 VH DH H VH DH H
C2 H H H H H H
C3 DH VH DH DH VH DH
C4 MH H MH MH H MH
C5 MH M MH MH M MH
Table 6: Aggregated fuzzy importance weights and calculated fuzzy ratings of 1st level drivers
1st level
indices
Aggregated fuzzy importance grade, wi Computed fuzzy rating, Ui
C1 [0.638, 0.691, 0.8323, 0.898;1] [0.518, 0.642, 1.050, 1.250;1]
C2 [0.720, 0.780, 0.920, 0.970;1] [0.627, 0.808, 0.923, 1.025;1]

C3 [0.976, 0.993, 1.000, 1.000;1] [0.605, 0.748, 1.223, 1.466;1]
C4 [0.626, 0.680, 0.840, 0.896;1] [0.467, 0.624, 1.203, 1.554;1]
C5 [0.493, 0.556, 0.726, 0.790;1] [0.229, 0.458, 1.531, 2.986;1]
RESULTS:
The result has shown that evaluated fuzzy performance
is (0.508179, 0.639028, 1.085557; 1.356745;1) in term
of fuzzy scale and 0.90 in crisp value, can be compared
with the actual/standard performance of firm.
Performance can be escalated by enchaining the
performance of measures.
CONCLUSIONS:
In the presented work, the constructed multi criterion
decision making performance appraisement module
(constituted by mixing the segregated the Lean-Resilient
(L-R) SC strategy and their corresponding five (5) core
drivers and twenty two (22) interrelated metrics)
conjunctive with Fuzzy Performance Index model called
DSS (Decision Support System) has been practical
implemented on crank and shaft manufacturing firm to
estimation the overall performance of a organization. The
evaluated fuzzy performance is (0.508179, 0.639028,
1.085557; 1.356745; 1) in term of fuzzy scale and 0.90 in
crisp value, which can be compared with the actual
performance of firm. Performance can be hiked by
enchaining the performance of criterion.
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BIOGRAPHY
Bhuneshwar Kumar Dixena
is a M-Tech scholar of
Department of Mechanical
Engg, Dr. C.V. Raman
University, Kota, Bilaspur,
(C.G.), India, his current
research area is supply chain
and operations
management.

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