A COMPARATIVE STUDY OF THE
TRADITIONAL AND MULTIPLE-CRITERIA
DECISION-MAKING APPROACHES
Abhijit Majumdar 1
,
Prabal Kumar Majumdar 2
&
Bijan Sarkar 31
College of Textile
Technology, Berhampore 742 101, India
Email:
abhitextile@rediffmail.com 2
College of Textile
Technology, Serampore 712 201, India
Email:
pkm5@rediffmail.com 3
Department
of Production Engineering, Jadavpur University
Kolkata
700 032, India Email:
bijonsarkar@email.com
Abstract
This paper presents a comparative study of the methods used
to determine the
technological
value or overall quality of cotton fibre. Three existing
methods, namely the
fibre
quality index (FQI), the spinning consistency index (SCI) and
the premium-discount
index
(PDI) have been considered, and a new method has been proposed
based on a multiple-criteria
decision-making (MCDM) technique. The efficacy of these
methods was determined
by conducting a rank correlation analysis between the
technological values of
cotton
and yarn strength. It was found that the rank correlation
differs widely for the three
existing
methods. The proposed method of MCDM (multiplicative AHP)
could enhance
the
correlation between the technological value of cotton and yarn
strength.
Key words:
analytic hierarchy process, cotton fibre, fibre quality
index, premium-discount index,
spinning
consistency index, technological value
Introduction
Determining the technological value of cotton fibre is an
interesting field of textile research. The quality
of
final yarn is largely influenced (up to 80%) by the
characteristics of raw cotton [1]. However, the
level
to which various fibre properties influence yarn quality is
diverse, and also changes depending
on
the yarn manufacturing technology. Besides, a cotton may have
conflicting standards in terms of
different
quality criteria. Therefore, the ranking or grading of cotton
fibres in terms of different quality
criteria
will certainly not be the same. This will make the situation
more complex, and applying multiple-criteria
decision-making (MCDM) methods can probably deliver a
plausible solution. The solution
must produce an index of technological value or overall
quality of cotton fibre, and the index
should
incorporate all the important fibre parameters. The weights of
the fibre parameters should be
commensurate
with their importance on the final yarn quality.
Traditionally,
three fibre parameters have been used to determine the quality
value of cotton fibre. These
are grade, fibre length and fibre fineness. The development of
fibre testing instruments such as
the
High Volume Instrument (HVI) and the Advanced Fibre
Information System (AFIS) has
revolutionised
the concept of fibre testing. With the HVI it is pragmatically
possible to determine most of
the quality characteristics of a cotton bale within two
minutes. Based on the HVI results, composite
indexes
such as the fibre quality index (FQI) and spinning consistency
index (SCI) can be used to determine
the technological value of cotton; this can play a pivotal
role in an engineered fibre selection
programme
[2-3]. In this paper, a new
method of determining the technological value of cotton using
a multiplicative analytic
hierarchy process (multiplicative AHP) of the MCDM method is
postulated. The technological
value
of cotton was also determined by the three traditional
methods, namely the fibre quality index
(FQI),
the spinning consistency index (SCI) and the premium-discount
index (PDI). The ranking of cotton fibres produced by these
four methods was compared with the ranking of final yarn
tenacity, and a rank
correlation analysis was carried out.
Overview of MCDM and AHP
Multiple Criteria Decision Making is a well-known branch of
Operations Research (OR), which deals
with
decision problems involving a number of decision criteria and
a finite number of alternatives.
Various
MCDM techniques, such as the weighted sum model (WSM), the
weighted product model (WPM),
the analytic hierarchy process (AHP), the revised AHP, the
technique for order preference by
similarity
to an ideal solution (TOPSIS), and elimination and choice
translating reality (ELECTRE), can
be
used in engineering decision-making problems, depending upon
the complexity of the situation [4-
8]
The Analytic Hierarchy Process (AHP), introduced by Saaty
[9-12], is one of the most frequently
discussed
methods of MCDM. Although some researchers [13-16] have raised
concerns over the theoretical
basis of AHP, it has proven to be an extremely useful
decision-making method. The reason
for
AHP's popularity lies in the fact that it can handle the
objective as well as subjective factors, and
the
criteria weights and alternative scores are elicited through
the formation of a pair-wise comparison
matrix,
which is the heart of the AHP.
Details of AHP methodology
Step 1:
Develop the hierarchical structure of the problem. The
overall objective or goal of the problem is
positioned
at the top of the hierarchy, and the decision alternatives are
placed at the bottom. Between
the
top and bottom levels are found the relevant attributes of the
decision problem such as criteria and
sub-criteria.
The number of levels in the hierarchy depends on the
complexity of the problem.
Step 2:
Generate relational data for comparing the alternatives.
This requires the decision maker to formulate
pair-wise
comparison matrices of elements at each level in the hierarchy
relative to each activity at the
next,
higher level. In AHP, if a problem involves
M
alternatives and
N
criteria, then the decision maker
has
to construct N
judgment
matrices of alternatives of
M
x M order and one judgment matrix of
criteria
of N x N order.
Finally, the decision matrix of
M
x N order is formed by using the relative scores
of the alternatives with respect
to each criterion. In AHP, the relational scale of real
numbers from 1 to 9 and
their reciprocals are used to assign preferences in a
systematic manner. When comparing two
criteria
(or alternatives) with respect to an attribute in a higher
level, the relational scale proposed by
Saaty
[9-12] is used. The scale is shown in Table 1.
Results and Discussion
The technological value
of cotton fibre derived by various methods, as well as the
rank correlation coefficient
(Rs)
between the technological value of cotton and yarn tenacity,
are shown in Tables 8 and 9. It is
observed that the Rs
ranges
from a very low value of 0.098 to a very high value of 0.817.
In general, the
Rs
values were the lowest for the
FQI model and highest for the PDI model. The proposed
multiplicative
AHP model, which can be considered as a variant of the
traditional FQI model, demonstrates
a reasonably good Rs
value
of 0.738 and 0.716 for 22 Ne and 30 Ne respectively. The
SCI model shows a moderate
Rs
value of 0.401 and 0.459 for 22
Ne and 30 Ne respectively. The
traditional FQI model is basically a multiplicative model
where all the criteria weights
(Wj)
are considered to be unity. However,
in practice this assumption is totally void, as the influence
of various fibre properties on yarn
properties will not be identical. Therefore, in a
multiplicative type model, proper
emphasis must be given to the weights of different decision
criteria. This modification is introduced
here in the multiplicative AHP model resulting in enhanced
Rs
values.
From
Table 9, one may be tempted to conclude that in the given
problem, the premium-discount index is
the best method to determine the technological value of
cotton. However, in the premium-discount
index
model, the decision maker receives a clear idea of the
influence of fibre properties on yarn
tenacity
from the standardised 'â
' coefficient values. The real
accuracy of the premium-discount index
model
can be judged by subjecting it to some new test samples, which
were not used for developing the
regression equation relating the fibre properties and yarn
tenacity. In case of the multiplicative
AHP
model, the relative weights of the cotton fibre properties are
obtained from the pair-wise comparison
matrix, where entries were made based on the past experience
of the decision maker, without
having any specific knowledge of the present case. Therefore,
the multiplicative AHP is a very flexible
tool, and can be used in any situation where the
decision-maker has some prior knowledge of
the
problem.
Conclusions
A new multiplicative AHP
model has been proposed to determine the technological value
of cotton. The proposed method uses
a variant of the traditional FQI formula, and enhances the
rank correlation between the
technological value of cotton and yarn tenacity. The
incorporation of proper weights of cotton
properties in the multiplicative formula is more logical than
having the same weight for all the cotton
properties. The past experience of the decision-maker plays a
key role in determining the criteria
weights in the proposed multiplicative AHP method. Of the four
methods considered here, the premium-discount
index method shows maximum rank correlation between the
technological value of cotton
and yarn tenacity. The multiplicative AHP, SCI and FQI models
are the remaining three methods, in
the order of descending rank correlation. Similar studies
could also be initiated using other MCDM
methods.
-
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