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Determination of Relative Importance of Raw Materials in Textile Spinning Industry Using GA-TOPSIS Hybrid Approach

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This paper presents an idea to combine Genetic Algorithm (GA) optimization heuristic with TOPSIS multi-criteria decision making method to render it an optimization capability in a multi criteria setting. The relative importance or weights of different fibre criteria for the selection of raw materials i.e. cotton fibres in textile spinning industry are determined using the hybrid GA-TOPSIS method. Six quality parameters of fibres viz., strength, elongation, upper half mean length, length uniformity, fineness and short fibre content are regarded as the criteria for cotton selection in an attempt to achieve maximum strength of the yarn. GA has been applied to search the optimum set of weights for various cotton fibre criteria by means of maximizing the rank correlation coefficient obtaining from the two methods of ranking such as TOPSIS quality index of different types of cottons and strength of the yarns spun from them. The investigation indicates that the criteria weights for cotton selection can be obtained with a reasonable degree of agreement. The obtained weights signify the actual contribution of different cotton fibre properties on yarn strength. The result shows that the fibre strength has maximum contribution on yarn strength followed by fibre length parameters and fineness. Fibre elongation has least contribution on yarn strength. The proposed approach is flexible and can be modified with ease depending upon the technology of spinning being followed in the industry. Moreover, it can universalize itself into the far wider domain of multi-criteria decision making problems.
Content may be subject to copyright.
November 2012
Vol.
V
&
lssue No.
11
November 2012
DETERMINATION
OF
RELATTVE
IMPORTANCE
OF
RAW MATERIALS
IN
TEXTILE SPINNING
INDUSTRY USING GA-TOPSIS
I{YBRID
APPROACH
Subhasis
Das
Dr.Anindya Ghosh
Dr. Abhijit Majumdar
Dr' DebamalYa Banerjee
Abstract
This
paper presents an idea to combine Gmetic
Algorithm
(GA)
optimization
heuristic with TOPSIS multi-criteria decision making
method to
render it an optimization
capability in a multi
criteria setting.
The relative importance or weights of dffirentfibre
criteriafor the selection of
raw
materials i.e. cottonfibres
in textile spinning
industry are determined
using the hybrid GA-TOPSIS method.
Six
quality
parameters
offibres viz.,
strength,
elongation, upper
half mean length, length
uniformity,finmess and shortfibre
conlent
are regarded as the criteriafor
cotton
selection in
an attempt
to
achieve
maximum strength
of the
yarn.
GA has
been applied to search the optimum set of weights
for
various
cottonfibre criteria
by
meaw of maximizing the
rank correlation coeficient
obtainingfrom the
two methods of ranking
such as TOPSIS
quality
index of dffirmt types of
cottons and strength
of the
yarns
spun
from
them.
The investigation indicates that the criteria weights
for
cotton selection can be obtained with a
reasonable degree
ofagreement. The obtainedweights
signifi
the actual contribution ofdifferent cottonfibre
properties
onyarn strength.
The result
shows that
the
fibre
strength has muirinum
contribution
on
yarn
strength
followed
by
fibre
length
parameters
and
fineness.
Fibre
elongation
has
least contribution
onyam strength.
The
proposed approach isflexible and can be
modffiedwith
ease depending upon the technologt ofspinning
beingfollowed
in the industry.
Moreover, it can universalize
itself into thefar wider domain of multi-criteria decision making
problems.
Key word: Cotton,
genetic
algorithm,
raw material, spinning
industry, TOPSIS.
1.
INTRODUCTION
Decision
making
in the textile
spinning
industry
for raw
material
(cotton
fibre) selection
is a
complex
problem
involving
assessment
of
a wide
range
of
alternative
cottons
based on
a
set of criteria
encompassing
the
fibre
properties
such
as
fibre
bundle
strength,
fibre bundle elongation,
fibre
length, length
uniformity
index,
fibre
fineness
(a
measure of
mass
per
unit
length
of
cotton
fibre) and short
fibre
content.
It is
a
key
strategic
point
since
the
raw materials bear
the
bulk
of
total
production
cost
in a cotton spinning
industry
which
is a typical
high volume but
low
profit
turner
[1].However,
the
nature
of
raw
material
selection
decision,
in
most
of
the
cases,
is
very
crude
and unstructured.
Occasionally,
the
indices
like Fibre
Quality
Index
(FQI),
Spinning
Consistency
Index
(SCI)
and
Premium
Discount
Index
(PDI)
have been
practiced
in
the
textile spinning
industry
for the cotton
fibre selection
12-61.
The
main advantage
of
using
these
indices
is their computational
simplicity;
however, selection
of
cottons based
on
these
indices
is not beyond
criticism.
These indices by
and
large depend on
the
particular
range of
cottons
used
to
formulate
the equations
and seldom
universalize
themselves
to subsume
the
intricate
multiv arrate
nature of cotton
fiber
properties. As an example
SCI
regression
equation
originally
deduced
from the
fibre
properties
of
Pima and Upland
cottons
may not
replicate a
good
fit with
the
Indian cotton.
Furthermore,
these
indices
comprise
of
the
linear combinations
of cotton
fibre
properties;
however,
there
exists
a highly non-linear
relationship in
practice.
These
indices
often
fail
to
produce
desired
results
due to their
inherent
drawbacks.
This may
lead
to the
rejection
of the
delivered
goods
due
to nonconformance
with respect to
some
quality parameters.
Thus,
the
traditional
methods
of cotton
fibre
selection
need
to be
replaced
by
an
approach
having
sound substratum of
scientific
principle
and methodology. There
are number of
criteria which
govern
the
quality
of
the
cotton.
A
particular
type
of cotton
may
have an
edge
over
the
others with
respect to a
particular
criterion;
nevertheless,
the
relative
dominance
may
be offset when another
criterion
is
taken
note
of.
Therefore, the
cotton
fibre selection invokes
Multi-Criteria Decision Making
(MCDM)
as the feasible method.
An MCDM
method
deals with
the selection ofoptimal alternatives
according
to their
preferential
rank
under
the
presence
of
a
finite
number
of
decision
criteria. There are many MCDM methods
available
namely,
Weighted
Sum
Model
(WSM)
t7l,
Weighted
Product
Method
(WPM)[81,
Analytic Hierarchy Process
(AHP)
[9],
Multiplicative AHPI10],
Revised AHP
[11],
Technique
for
Order
Preference
by Similarity to
Ideal
Solution
(TOPSIS)
U2l,
Elimination and Choice Translating Reality
(ELECTRE)
[13]
etc.
An
MCDM
problem
is
commonly expressed
in
the
form
of
a
matrix known as
the
decision
matrix
(Table
1).
A
decision
matrix is a
(mxn)
matrix in
which
element
xij
indicates the
performance
of alternative Ai
when
it is
evaluated
in terms of
decision
cntenln
C"
'.r
here
n.
Nurnerical
it,
gr
J:t:
r
'.i
|
,
15
its
relatil
e
imp..runce
sucir
Table
l. Derision
matrir
i-
l.1.3.....
m,
andj:1,2,3)...,
arisched
to
each
criterion
based
on
that*',
-1.
for
a
\ICDM
problem
November
2012
selection
criteria
regarding
the
fibre
properties
so as
to
reayze
the
maxrmization
of
yarn
strength.
The proposed
method
is
a
new
one
which
hitherto
not
reported
anywhere.
The
optimum
criteria
weights
as
obtained
by
this
method give
a
quantitative
estimation
of
the
percentage
contribution
of
cotton
fibre
properties
on
yarn
strength.
2.
TOPSIS
METHOD
TOPSIS
is
one
of
the
popular
methods
of
MCDM
developed
by
Hwang
and
Yoon
Uzl.
It
is
used
when
a
set
of
alternatives
(say
cotton
fibres)
has
to
be ranked
in
terms
of a
set
of
decision
criteria
(for
example,
cotton
fibre properties).
The
basic
philosophy
of TOPSIS
is
that
the
selected
alternative
should
have
the
shortest
distance
(in
a
geometrical
sense)
from
the
ideal
solution
and
longest
distance
from
the
worst
solution.
The
positive
ideal
solution
supposedly
has
the
best
performance
scores
in
all
the
decision
criteria.
On
the
other
hand,
negative
ideal
solution
has
worst
performance
score
on
all
the
decision
criteria.
The
ranking
of
an
alternative
is
determined
based
on its
geometric
distance
from
the positive
ideal
solution
and
negative
ideal
solution.
The
organrzation
of this
method
is
illustrated
by
the
following
steps:
Step
1:
Construction
of the
decision
matrix
This
step
produces
decision
matrix
D
of
criteria
and
alternative
based
on information
available
regarding
the
problem.
If
the
number
of
alternatives
is
m
and
number
of
criteria
is
n,
then
decision
matrix
having
an
order
of mxn
is
represent
as follows:
xtt
xtz
x
zt
x
zz
xt,
x^
zn
!;1fii..+.i:):,
ili'ii#jii;,,
,ctful; Cr C2
t
ci
,TI
:1:r;iiiliiilililii,illili
r+ffiil
\\eights
ol
*l
*j
W1
X.,
xln
|'
al
t
v
x2i
x2n
t-
i
\
XU
Xit't
I
Xmn
The
numerical
u
eiehts
are
usually
determinedbythe
stan
dardized
coefficients
rp
crretTicients)
of independent
variables
in linear
multiple
resression
analr-sis.
Cheng
and
Cheng
used
beta
coefficient
analr
sis
of multiple
regression
equation
to
determine
the
weights
of
r
arious
cotton
fibre properties
for
predicting
the
cotton
)'arn
strensrh
bl'
case
based
reasoning
system
Ll4l.
The
standardized
coefficients
are
the
estimates
resulting
from
an
analysis
carried
out on the
variables
that have
been
standar
drzed
by
subtracting
their
respective
means
and
dividing
by their
standard
der iations.
The
standardtzed
coefficient
refers
to
the
change
in
the
standard
deviation
of
the
dependent
variable
with
a
unit
change
in
standard
deviation
of an independent
vanable.
Standardization
of the
coefficients
suggests
the
order
in
which
the
independent
variables
have
a
dominant
eflect
on
the
dependent
variable.
u'hen
the r
ariables
are measured
in
difrerent
units
of
measurement.
Sometimes.
such
standar
dizatron
can
be
ambiguous
because
a unit
change
of
standard
deviation
in
one
independent
r
ariable
has
no
reason
to
be
equivalent
to a
similar
change
in
another
one. Moreover,
a
linear
combination
of
the
independent
variables
is
assumed
to formulate
the
regression
equation;
however,
this
assumption
may
not
be
true
in
most
of
the real
world
problems.
Occasionally,
the
numerical
weights
are
determined
based
on
.'
; rtln-ellgineering
approaches
as
experience
of the
decision
rkr:s
Saarv
recommended
the
evaluation
of the
weights
for
ditlere::
::rreria
throughAnalytic
Hierarchy
process
(AHp)
t9].
In
this
:r.e::.,d.
the rneights
are
determined
by
constructing
a
pair-rn
rs:
;,r:i:rison
matrix
for
criteria.
Majumdar
et
al
tl5-
16]
cornraie
i
\
.inrrr..r.s
\ICDM
methods
to
determine
the
quality
r-alue
of c,l:Tcn
i-L're
br
assigning
the
commensurate
weights
to
the
dltlerent
:b:g
;r-ireria
based
on
Saafy's
AHp
method
and
found
that
T(IPSIS
,,.eiCs
the
best
result
tl5].
Nevertheless,
AHP
is
also
en
e\p,e:ri:.i
L'ased
evaluation
of the
weights.
An
engineering
apprca;h
',i
;';1C
'rener
be
adopted
for
determination
of
weights
in preli:in;i
l,,r',
r
ntari-ergineering
one.
This
work
attempts
to
solr
e
the
pi'..b";:r
rrf
determining
the
relative
importance
or
u
eight,
ic'r
\
a:trL-S i--r-iteria
using
a
hybrid
Genetic
Algorithm
(GA
I-TOPSIS
rFprr
e;h.
.{ssignment
of
weights
for
various
fibre
cntena
rs l
t:3;-;uisire
tbr
the
selection
of
cottons
using
an
\f
CD\n
:re::c'd
-
r
--"
:_ In
this
study,
cotton
fibre
selection
probienn
cr \[CD\f
tas
'reen
r--onsidered
with
an
aim
to
optimize
the
relatir
e lrlpq-,nsn;e
trr
\\
e
iehts
of different
x
mn
where
xij
denotes
the
performance
measure
ofthe
i-th
alternative
in
terms
of the
j-th
criterion.
step 2:
construction
of
the
normalized
decision
matrix
In
this
step
the
decision
matrix
is
converted
to a
norrn
ahzed
decision
matrix
R.
An
element
rij
of
the
norunahzed,
decision
matrix
is
calculated
as
follows:
DI
X
*I
X
^2
r..
U
(1)
(2)
and
Ttz
"'
Tr,
Yzz
"
'
T2n
(3)
I
T*z
"'T*,
\r
Tzt
r
m
^:[
ro-
Step
3:
construction
of
the
weighted
normalized
matrix
Nbvember
2012
The
weighted
normalizedmatrix
(V)
is obtained by
multiplying
each column of
the nonnalized decision
matrix R with the
associated
criteria weight coffesponding
to that column.
Therefore,
(4)
Where
00
wr0
0 0... wn
-
relative
weight of
ith
criteria
and
solution.
Step 5: Calculation
of
the
separation measure
The n-dimensional
Euclidean
distance method is
next
applied
to measure
the
separation
distance
of each
alternative from
the
ideal
solution and negative
ideal
solution. Thus,
for the
distance
from
the
ideal
solution
we have:
where Si*
is
the distance
of each alternative
from
the
ideal
solution. Similarly,
for
the
distance
from
the
negative-ideal
solution we have:
for
i
-L,2,3.,
ffi
(1
1)
where Si-
is
the
distance
of each alternative from
the negative-
ideal
solution.
Step 6:
Estimation
of the relative
closeness to
the
ideal
solution
In this
step
the
relative
closeness
(Ci*)
value
of each
alternative
with respect to
the ideal
solution is
defined as following
equation:
rt
sr-
L'r*:
,
(12)
S,-
+E-
where
I
>
Ci*
>
0, and
i
:
1,2,3...,
m.
Step 7:
Ranking
of
the
alternatives
in
preference
order
A11 the alternatives
are now
arranged in a
descending
order
according
to the
value
of Ci*.
Therefore,
the best alternative
is
the one that has
the
shortest
distance to the ideal
solution.
The
previous
definition
can also
be used to
demonstrate that
any alternative
which has the
shortest
distance
from
the ideal
solution
is
also
guaranteed
to have the longest
distance
from the
negative-ideal
solution.
3.
GENETIC
ALGORTTHM
(GA)
Over the
last few
decades the field
of
optimization
has
changed
by the
introduction
of a number
of
non-traditional
optimization
algorithms
which are
based
on the concept
ofnatural
phenomena.
Of these, GAmimics nature's
evolutionary
principles
to
drive
its
search
towards
an
optimal solution
[19].
One
of
the outstanding
differences between
GA and classical
optimrzation algorithms
is
that the
latter
use a
point-by-point
approach, where
one
solution
in
each
iteration
is
modified to a
different
(hopefully
better) solution
and
eventually
the outcome
becomes
a local
optimized solution,
whereas the
GA works with a
population
of solutions
in
each iteration, instead
of a
single solution.
As
multiple
solutions are
processed
simultaneously, it is
very
likely
that the expected optimized
GA solution
should
turn
out to be
a
global
one.
,S.-
:
I
0...0
0... 0
w1
0
0
W-
Z*,-1
,S-
=
I
wtTtt
wzTtz ... wrTt,
wtTzt wzTzz ... wrTz,
V_
(s)
wtT*t wz
T*z
...wn
rmn
vt,
v2n
v*n
'),
r=1,
2,3,...,*\
A*
={(
-=,uli=
/),
(ry",,1i
:
{rr-
,v2*)....,rrn*\
vtz
vzz
vm
vtt
vzt
V*1
2
Hence an
element
vij of the weighted
representing as:
vrj: wj
rtj
(6)
norrnalized matrix V is
Step
4: Determination of
the ideal
and the
solutions
(7)
negative-ideal
The ideal, denoted
as
,
and the
negative-ideal, denoted
as
,
solutions are defined
as follows:
eJ
(8)
,
={(
min
,ult./),(-=
,uli
er'),
t
-\2,3,...,*\
=
{u,
,v2- ).....rrr-\
(e)
:1,
2, 3,. ..,
n
and
j
is associated with benefit
3,...,
fr
and
j
is associated
with
cost
or
loss
where,
J-
{
j
criteria)
J'_{j:1,2,
criteria).
For the benefit criteria,
the
decision
maker
wants
to
have
the
maximum value
among
the alternatives.
Therefore,
indicates
the
ideal
solution.
Similarly,
indicates the
negative ideal
Il,,
j=l
GA
is
a
heuristic
search
algorithm
that
can
be
applied
when
the
dimension
of the
data
space
is
too
large
for
an
exhaustive
search.
GA
proceeds
first
b1
randomll,'
generating
an
initial
population
oi
indir
iduals.
rr
hich
should
ideally
cover
the
domain
to
e\plore
Each
:ndir
idual
is represented
by
a
binary
coded
stnng
or
ch:oirtrSt-rtrc
encoding
a
possible
solution
in
the
data
space.
.{t
e\
en
:teration
step
or
seneration,
the
individuals
in
the
current
Flopulation
are
tested
according
to
the
fitness
function.
Tt-r
torrr
a
neI,\
population
(the
next
generation),
good
individuals
are
se'ected
according
to
their
fitness,
which
is
termed
as
reprcCJc:ion.
Selection
alone
cannot
introduce
new
individuals
intc
the prrpulation,
which
is
necessary
in
order
to
make
the
strlut:on
es
independ.ent
of
the
initial
population
as
possible.
\e,,r
inCir
iduals
in
the
search
space
are
thus generated
by
fw'o
operations:
crossover
and
mutation.
Crossover
concerns
two
selected
indn
iduals
(parents)
that
exchange
parts
of
their
chronlosome
to
form
fwo
new
individuals
(offsprings).
The
crosso\
er
operation
is
not
always
applied
to
all
selected
chromosomes.
The
application
of
crossover
is governed
by
a
crossover
probabiliry",
denoted
by
pc.
If pc
is
too
large,
then
the
structure
of a
high
quality
solution
could
be
prematurely
destroved.
on
the
contrary,
a
too
small pc
reduces
the
searching
efficiencr,.
Generally,
pc
is
chosen
between
0.5
and
0.g.
The
mutation
operation
is
used
as
a
means
to
achieve
a local
change
around
the
current
solution.
Thus,
if
a
solution
gets
stuck
at
the
local
minimum,
mutation
may
help
it
to
come
out
of
this
siluation
and
consequently,
it
may
jump
to
global
basin.
The
mutation
consists
in
flipping
bits
of individual's
strings
at
random
and u'ith
some
small probability,
termed
as
mutation
probabilin
(pm).
If pm
is
too
small,
then
new
gene
segment
could
not
be
induced,
whereas
if
pm
is
too
big,
then
the
genetic
evolution
Ceeenerates
into
a
random
local
search.
Gener
ally,pm
is
chosen
b'eru
een
0.001
and
0. 1.
4.
DE\-ELOP\IE\T
OF
FIVtsR.TD
GA-TOPSTS
&{ETF{OD
FOR
OPTI}IIZ
\TTOI\
OF
CR.NTE}RIA
WENGHTS
II{
COTTO\
SE
LECTION
PROtsI,EM
The
relatir
e
importance
or
weights
of
different
fibre
criteria
for
the
selection
of
conon
fibres
are
determined
using
the
hybrid
GA-TOPSIS
method.
The
data
of 28
Upes
of
cotton
fibres
and
coffesponding
varns
of
two
different
linear
densities
(20
and,27
tex;
where
ter
is
defined
as
mass
in
gram
per
I
Kilometre
length
of
yarn)
made
from
each
fibre
type
in
ring
spinning
system
are
collected
from
industry.
The yarns
were
prepared
in
similar
condition.
The
fibre
data
encompasses
the
properties
such
as
strength
(FS),
elongation
(FE),
upper
half
mean
length
(LHML),
length
uniformity
index (UI),
fineness
(
mass
in
microgram
per
I
inch
length
of
fibre)
and
short
fibre
content
(SFC).
These
6
fibre properties
are
used
as
the
criteria
to
evaluate
the qualify
of
28
cottons
due
to
the
factthat
these
properties
essentially
govern
November
2012
the yarn
quality.
Strength
is
the
most
impo
rtantquality
parameter
of
a
yarn.
The
yarln
data
comprises
of
the
strength
of
yarns
for
both
liner
densities.
Table
2
illustrates
the
decision
matrix
of
cotton
fibre
properties
and
coffesponding
yarn
strengths.
The
objective
of
this
study
is
to
optimi
ze
the
relative
importance
or
weights
of
different
criteria
for
the
selection
of
cotton
fibre
in
order
to
achieve
maximum
yarn
strength.
The
fibre
criteria
such
as
FS,
FE,
UHML
and
IJI
are
regarded
as
the
benefit
cri
terra
whereas
the
fineness
and
SFC
are
considered
as
the
cost
criteria
depending
on
their positive
and
negative
influence
on
the
yarn
strength.
At
the
outset,
a
population
size
of 2000,
each
individual
of
which
consists
of
the
6
randomly
generated
elements
is
initiati
zed,.
Each
individual
of
the
population
is
converted
to
normal
rzed,
individual
by
dividing
its
every
element
with
their
sum.
The
elements
of
each
normal
rzed,individual
are
denoted
as
the
initial
solution
for
weights
(wi,
where
i:1,
2,
6)
corresponding
to
6
criteria.
Subsequently,
using
the
individual
set
of
weights,
&
population
of
decision
matrixes
each
having
28
alternatives
and
6 criterta
are
formed.
The
28
cottons
are
then
ranked
according
to
the
relative
closeness
values
(Ci*)
of
TOPSIS
for
whole
population
of
decision
matrixes.
A
separate
ranking
of
these
cottons
are
also
made
according
to
the
coffesponding
for
20
tex yarn.
The
agreement
between
these
two
ranking
methods
is
evaluated
in
terms
of rank
correlation
coefficient
(RS)
using
the
following
equation:
62a'
Rs
-l-
m(*'
-l)
(13)
where
d is
the
absolute
difference
between
the
two
ranking
methods,
and
m
is
the
total
number
of
alternatives.
RS
is
used
as
the
fitness
function
to
be
maximized,.
RS
is
evaluated
for
whole
population
from
which
the
ratio
of
the
average
fitness
value
to
the
maximum
fitness
value
(r)
is
calculated.
The population
of
weights
is
then
modified
using
different
operators
of
GA,
namely
reproduction,
cross-over
and
mutation.
A
new
population
of
decision
matrixes
is
now
formed
from
which
the
cottons
are
again
ranked
and
fitness
is
evaluated
and
r
is
recalculated.
This
completes
the
first
generation
of
GA.
The
GAruns
for
generation
after generation
until
it
satisfies
the
termination
criteria,
which
is
either
r
attains
a
desired
value
or
number
of
generations
reaches
to
a
maximum
value.
The
desired
value
of r
is
chosen
as
0.99
meanin
g
99%
of
the population
converges
to
the
optimum
fitness
value.
Maximum
number
of
generation
was
set
to
1000.
The
optimum
solution
of
GA
is
obtained
with
the
values
of
0.7
and
0.001
for
pc
and
Pffi,
respectively.
Roulette
wheel
selection
scheme
is
applied
for
reproduction
operation
to
select
the good
individuals
of
weights
from
the population
on
the
basis
of
their
fltness
information.
Uniform
cross-over
method
is
applied
to
form
new
individual
of
weights.
Fig.
I
depicts
the
flowchart
of
the
hybrid
GA-TOPSIS
method
to
optimize
the
weights
of
different
criteria
in
cotton
selection
problem.
MATLAB
7.Il
i
November 2012
iLffi
;isi niitii#;i##ffi ffi il#ilff #iii"r+;
rrrrA
ij
isrigl
xqrl rI rrr| ! ri ri iri lr ]ti ill
4il.ttll$tttii$lf#tnr14tr+tii:iiil.1;ir.,T';ittl"i1l,!.#iiiiil
1 tili!i:4 {Iitl4 l ii\n::ii! it}inr x i$5{iti1iF,;. lii
r#,i*&#*Gffiilili*iHri
:-rlilliiti.!ffiii#4i{tllit
:ljz.i1Ftr
l1!iL
i?liif?.ilil!.ii,ti9t$ti1]iiinrilii!tlii!iiiti.#i,iiiiiirr.nrl
.qli!r,:ii,i;i,iltiiiT{(i!.tt4iir.er(i.}il
jii,rj
;iiil.iilii#ift it1#9.85,
iitl$iiiirrllrr$t1,ft
Itnl4ii:li!ltjii!iljlli4!llliiIltIi:iIt
Weights
w1
w2
w3 w4
w5
w6 20 tex
27 tex
O
()
o-
*J
cg
A
L
h
q)
+J
t-
I 28.7
6.5 1.09 81 .0
4.4
13.8 t3.s2 14.17
2 28.s
6.6 I .15 80.2
3.s
11.9 13.64
3
28.7
5.7
1.10
79.2
3.7 18.4
12.28
4
27.5
6.3 r.07 82.8
4.5
8.4
14.06 14.7 7
5
29.2
5.3
0.98 80.0
4.5
t6.6 13.47 t3.24
6
29.0
6.7 1.05 81 .9
4.2
10.9 13.17 t4.01
7
30.3
6.7 1 .10 83.2
4.4
8.1 14.41 T4.7
5
8
28.1
6.3
I
.01
80.7 3.8 15.5 13. 10
13.35
9 30.6
6.6
t.07
83.
l 4.7
9
14.86 T5.26
10
28.7
6.7
1.05
81 .0
3.9
11.8 13.08 13.96
1l 28.3 6.5
0.97 81 .5
3.8 13.
1 13.97 15. 1
t2 29.0
6.6 1.06 80.7 3.1 11.3 13.55 14.27
13
27.7 5.5
1.05 81.s
4.7
It.7
13.82 14.18
T4
29.1
6.1 1.05 81 .7
4
n.2 13.63 14.93
15
28.6
5.7
r.04 82.4
4.2
10.8
13.22
T4.28
l6 28.r
6.1
1.03 8r.7
4.5
7.2
T3.7
5 ts.28
T7 29.0
6.0
r.04
81.4 5
6.8 14.24
15.28
18
3r.7 6.3
1.03
80.6
3.7
8.9 1 4.83 16.18
t9 29.3
6.0
1.03 81.2
4.4 8.1
14.41
1 5.98
20
29.1 6.9
1.05
83.2
4.6
s.6
14.72
ts.82
2l 30.8
6.4
I .01 8T.7
3.7 6.8 15.7
5
t6.25
22 26.7
6.9
T.04 82.6
4.8
7.5
14.t3 15.29
23 30.2
6.7
1.06 82.3
4.3
s.6
15.39 t6.72
24 29.5
6.4
r.02
8r.9
4.8
7.2 t4.99 rs.43
25 27.5
6.9
1.01 81.7
4.s
9.1
14.33 14.62
26
28.9 6.0
t.07
81.1
4.6
7.7
14.IT T5.T7
27 30.3
6.r
1.10 80.6
4.6
8.4
14.42 15.67
28 34.0
6.6
1.20
82.8
3.8
6.8
16.98 18.02
Table 2. Decision matrix of cotton
fibre
properties
and corresponding
yarn
strength
coding
is
used
to execute
the
problem
on a2.6
GHz.
PC.
5.
RESULTS
AND
DISCUSSION
5.1 Optimization
Table 3 depicts
the optimum
values
of
weights
coffesponding
to different
decision
criteria
for cotton
fibre selection
problem
as obtained
by
maximizingthe
rank
correlation
coefficient
(RS)
between
the two
ranking methods
which
are
based
on the
TOPSIS
as
13.18
13.15
well
as the strength result
of
20
tex
ring
spun
yarns
using
the
proposed
hybrid
GA-TOPSIS technique. 28
cottons
are
ranked
in accordance with the
relative
closeness
values ofTOPSIS using
the optimtzed weights.
Fig. 2
deprcts
the rank
of different
types
of cottons
resulting
from
both
the
systems.
The rank correlation
coefficient
(Rs)
is
obtained as 0.914,
which shows
a
reasonably
good
agreement between the two methods of cotton
ranking.
Fig.
3
demonstrates
the relative
closeness
value
(Ci*)
ofTOpSIS
for
28
cottons
using
the
optimum
criteria
weights.
It
is
observed
thatthe
best
alternative
(cotton
no.28)
has
a
Ci*
value
of
0.8g4.
In
contrast,
the
worst
alternative
(cotton
no.
3)
has
Ci*
value
of
0.182.
The
Ci*
values
attained
by
this
method
shows
significant
agreement
with
the
yarn
tenacity
demonstrated
in
Table
l,
which
shows
that
yarn
number
28
and
3 have
the
highest
and
November
2012
lowest
strength,
respectively,
for
both
the yarns.
Therefore,
the
resemblance
of
Ci*
value
and yarn
strength
in
addition
to
higher
RS
value
authenticate
the
results
obtained
by
the
hybrid
GA-
TOPSIS
method.
The
optimum
criteria
weights
are
actually
denoting
the
influence
of fibre properties
on
yanstrength.
It
can
be inferred
from
Table
S:t,
rrralclmurn
n0.
of
generatinns,
r,:r,r;iatton
siee,
pt,
pne
Evaiuate
railo,
averagE
fitness
rn
axi
m
um
f
itness
No
Yes
Generate
randnffi
population
of
weights
I'l
ormalue
d
the
ureightt
construct
the pnpulatign
0f
decision
maffixes
usrng
the
normalued
ureights
Rank
the
cnttnns
usurg
TilFSIS
fsr
each
decisinn
maffrx
and
Eompare
them
rmth
the
ranhng
based
nn
yarn
sftngth
Evaluate
rank
c
orrelatin
n
coefficient
{fitness}
fsr
whnle populafion
Check
ruhether,
r
F
[.99?
Reprnduchun
Crn
s
s flrrer
htlutahnn
Modified populahon
0f
ureights
is
creahd
Normalued
the
rrueightt
Cunshuct
ner,rr pnpulation
nf
decision
matnxes
using
the
modified
normalised
Rank
the
cottsns
using
TOPSIS
for
each
decisinn
maffr:s
and
Eornpare
them
qnth
the
ranhng
based
nn
yar$
sffength
Is
generahon
(
ma:<
nn.
of
generahan?
S et,
generailofl
=
generahsn
*
I
Evaluate
rank
correlailffn
coefficient
(fitness)
for
whole
population
Figure
1.
Flowchart
of the
GA-Topsis
method.
&!,,,
November
2012
?ff
7,5
7.&
1S
!,,ffi
13
1ffi
:F
4
I
I
rfo
&=
U.9
14
-{t-
Ranft
hased
nnyflrn
strengl,h
-{-.
Rank
ba.sed
onTnpds
Jd
d
(s
F4
!i
ff
tl
t
L3 1,ffi
t+tt+n Humber
Figure 2. Rank ofcotton based on
TOPSIS and
strength data
of20 tex
yarns.
Figure 3. Relative closeness
value of cotton fibres as determined
by the TOPSIS method.
3 that
the FS
has maximum
contribution
on
yarn
strength.
This
is
attributable
to the obvious
fact that stronger
the
fibre, higher
is the
yarn
strength.
The
second
most
important fibre criterion
to determine
the
yarn
strength
is
the UI.
This
may
be ascribed
to
the
factthat
cotton
fibre with better
length uniformity
produces
more
even
yarns
having
fewer incidences of
fatal flaws
along
its length; thereby
it
causes
an
improvement of
yarn
strength.
The UHML
and SFC
are the
next two
criteria
in the
order
of
importance
which can be advocated
on
the
basis
that
during the tensile loading
of a
yaffi,
longer
fibres
ast as the
gripping
fibres
whereas
short
fibres
are
prone
to slip.
Further,
shorter
fibres result
in more hairiness;
thereby
undermine
the
yarn
strength. Nevertheless,
the
preponderance
of UI over
UHML
and
SFC
suggests that the
distribution
of
fibre length
has more impact
on the
yarn
strength than its average
values
that
define UHML and
SFC.
It
is
a
well known fact
that
finer
fibre
also
produces
stronger
yarns;
however,
the criteria
relating
to fibre
length
outperform the fineness.
The FE
shows the
least
contribution on
yarn
strength
as compared to
the other criteria.
w.g
H
ww
{d
F
ffi.'F
lrr
t/t
or [J. h
Lr
L}
s
ffi.s
-1
il
w.q
F
E
ffirc
il-l
F4
ru.p
ffi.L
\W v3 \ffi LS
C+tt+n lrTumber
??
?5
28
November
2012
I
A-
t!
14
::i
T3
Lffi
il+tt+n
Numher
&
=[.8F
+--
R ntik
b a
se
d
nn ynnl
strenglh
-il-*
E ntik
h+sed,lnTilFSIS
Figure
4.
Rank
of cotton
based
on TopsIS
and
strength
data
of 27
tex yarns.
5.2 \'alidation
For
I
alidation
of the
results
,
28
cottons
are
tanked
as
per
the
stren-qth
data
of 27
tex
ring
spun yarns
and
the
results
are
compared
with
the ranking
as
obtained
by
the
TOPSIS
method
using
the
optimized
criteria
weights.
This yields
a
value
of
0.89
for
RS.
The
result
of the
validation
is
illustrated
in
Frg.4,
tiom
u'hich
it
is
appreciable
that
the
optimrzed,
criteria
weights
as
obtained
from
the
hybrid
GA-TOPSIS
method
ean
able
to
iecipher
a
significant
agreement
for
other
set
of
yarns
as
well.
l::.e
: aiso
shows
the
values
of the
weights
for
different
fibre
-r-rr'r;,
:s
obtained
by
Majumdar
et al
[15]
based
on the
AHp
r--;
-
: i:
is
evident
from
Table
3 that
the
weights
obtained
:
-
-
; :.r
brid
GA-TOPSIS
method
are
similar
with
that
of
:---:
-';-:
'd
except
the
interchange
between
uI and
UHML.
.
:
'
-:'Srectively
for
20
and
27
texyarns,
which
are
lower
-
-
-
*
-
--
-
-
:':C
approach
is
better
over
the
experience
based
-
-
-
*
-
; :r.
i: ing
the
criteria
weights.
,.,f
the
different
fibre
criteria
obtained
by
GA-TopsIS
and
AHP
methods.
6.
CONCLUSIONS
A
new
hybrid
approach
has
been proposed
to
determine
the
relative
importance
or
weights
of
different
flbre
criteria
for
the
selection
ofcottons
with
the
intention
ofreali
ztngmaximum
yarn
strength.
The proposed
method
uses
GA
to
search
the
best
set
of
criteria
weights
by
maximizrng
the
rank
correlation
coefficient
deriving
from
the
ranking
of
cottons
based
on
the
relative
closeness
value
of TOPSIS
and
strength
of
yarns.
Strength
data
of 20
and
27
texyarns
spun
on ring
spinning
system
are
used for
the purposes
of
opti
mrzation
and
validation,
respectively.
The
result
shows
a
significant
agreement
between
the
two
ranking
methods.
The
developed
system
is
able
to
overcome
some
of
the
drawbacks
of the
existing
cotton
fibre
selection
method.
Besides,
it
has
wide
range
of
applications
in
determining
cotton price
and
bale
management
in
textile
spinning
industry.
For
different
cotton
criteria
such
as
FS,
FE,
UHML,
UI,
flneness
and
SFC
the
obtained
values
of
optimum
weights
are
0.33,
0.05,
0.1
4,0.27,
0.08,
and
0. 13,
respectively.
These
weights
give
an
estimation
of
the percentage
contribution
of
cotton
fibre
properties
on
the
yarn
strength.
Fibre
strength
has
maximum
contribution
on
yarn
strength
followed
by
flbre
length
parameters
and
fineness.
Fibre
elongation
has
least
contribution
on
yarn
strength.
The
optimi
zed
weights
obtained
in
this
way
may
be
used
as reference
weights
for
different
fibre
criteria
while
selecting
the
cottons
with
an
MCDM
method.
The
proposed
method
is
mathematically
potent
and
flexible;
therefore,
it
can
also
be
applied
to
the
other
spinning
technologies
to
solve
similar
type
of
problem.
This
hybrid
method
can
generahze
itself
into
the
far
wider
domain
of
MCDM
problems
in
other
disciplines
as
welr.
GA-TOP$,il.ffi
ililffi
0.27
FEr::r
0.039
UH\ILrirch,
.-+
0.291
UI
190I
0.145
FF (pg,'inch)
{r.l}
0.11
SFC
(%)
r.r
l
0.145
2.
3.
4.
5.
November 2012
REFERENCES
10.
Ghosh
A, Majumdar A
and
Alam
t
Selection of Raw
materials in
Tbxtile
Spinning Industry using ELECTRE,
Industrial Engineering
J,
20I 2;
6: 6-
I
5.
El Mogahry YE.
Selecting Cotton
Fiber Properties
for
Fitting
Reliable
Equations
to
HVI Data, Tbxtile Res
J,
I99B;
sB(7): 392-397.
El Mogahzy YE, Broughton
R and Lynch
WK.
A
Statistical
Approach
for
Determining
the kchnological
Value of Cotton Using
HVI Fibre
properties,
kxtile Res
J,
1990;
60(9): 495-500.
USTER
Ir{ews
bulletin, Measurement
of the
Quality
Characteristics of Cotton
Fibre, I99I
;
3B:
2
3-3
I
.
Chellamani P,
Doraswamy
I
and
Ratnam TV Fibre
Quality
and Yarn Strength Relationships, Proceedings
of
the
30th Joint kchnological Conference Organised
by
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AUTHORS
Subhasis
Das,
Department
of
Textile
Technology,
Government
College
of
Engineering
&
Textile
Technology,
Berhampore,
West Bengal
-
7
42
I0l
E-mail:
subhasis.tex@gmai1.
com
Dr. Anindya
Ghosho
Asst. Professoq
Department
of Textile
Technology,
Government
College of
Engineering
&
Textile
Technology Berhampore,
West
Bengal
-
7 42 101
E-mail
: anindya.
text rIe@gmail.
com
Dr. Abhijit
Majumdar,
Department
of
Textile
Engineering,
Indian Institute
of
Technolo'ey,
Delhi.
Neu' Delhi
-
1 10
016
E-mail
:
majum
dar@textile.
iitd.
ac.
in
Dr. Debamalya
Banerjee,
Department
of
Production
Engineering,
Jadavpur
University,
Kolkata -700
032
E-mail
: debamalya_banerj
ee@rediffinail.
com
---rrrr____XXX
6.
B.
9.
11.
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Article
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This paper presents the grading and selection of raw materials i.e. cotton fibres in textile spinning industry using multi-criteria decision making (MCDM) approach. Generally, some quality index, based on crude formulas, are used in the textile spinning industry to evaluate the raw materials with respect to the properties of the final product i.e. yarn. These methods often fail to produce desired results due to the inherent drawbacks of the methods. In this work, the weightage of the decision criteria has been determined by the Analytic Hierarchy Process (AHP) and the Elimination and Choice Translating Reality (ELECTRE) outranking approach has been used to rank the raw materials. The proposed approach yields good rank correlation between the quality value of the raw material and the breaking strength of final yarn. Moreover, the approach is flexible and can be modified with ease depending upon the technology of spinning being used in the industry.
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