International Journal of Engineering Trends and Technology (IJETT) – Volume 34 Number 8- April 2016
Cookware material selection by multi-criteria
decision making (MCDM) methods
Javier Martínez-Gómez#1, Gonzalo Guerrón*2, Ricardo A. Narvaez C*3.
1
Instituto Nacional de Eficiencia Energética y Energías Renovables (INER),
Adress: 6 de Diciembre N33-32, Quito, Ecuador. Tel +593 (0) 2 3931390 ext: 2079,
Abstract - Material selection has great importance
in design and development of the products. The
success and competitiveness of the producers also
depends on the selected material. This paper reports
of the application of different preference rankingbased MCDM method for the base of an induction
cookware for the National Efficient Cooking
Program of Ecuador which tries to replace liquefied
petroleum gas cookers for induction cookers.
Selection of an appropriate material is necessary for
improve the efficiency in the system cookwareinduction cooker. This efficiency is measured with
the energy efficiency, cost saving, high heating rate,
and workability. The MCMD method implemented is
operational competitiveness rating analysis (OCRA).
The criteria weighting was performed by
compromised weighting method composed of
analytic hierarchy process (AHP) and Entropy
methods. Using these methods, a list of all the
possible choices from the best to the worst suitable
materials is obtained taking into account different
material selection criteria. According to the results,
Ni would be the best material for the base of an
induction pot.
Keywords- Multi-criteria decision making methods,
MCDM, induction heating, induction cookware,
National Efficient Cooking Program, Ecuador.
I. INTRODUCTION
Material selection is one of the most challenging
issues in the design and development of products,
and it is also critical for the success and
competitiveness of the manufacturing organizations
[1, 2] Material selection for engineering design
needs a clear understanding of the functional
requirement for each individual component/product
and various important criteria also need to be
considered [3, 4] The improper selection of one
material could negatively affect productivity,
profitability and reputation of an organization
because of the growing demands for extended
producer responsibility. The objectives and criteria
in the material selection process are observed to be
often in conflicts and it involves trade-offs amongst
decisive factors, such as desired properties,
operating environment, production process, cost,
market value, availability of supplying sources and
product performance [1, 2]
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The objectives and criteria in the material
selection process are observed to be often in
conflicts and it involves trade-offs amongst decisive
factors, such as desired properties, operating
environment, production process, cost, market value,
availability of supplying sources and product
performance [5-7]. Thus, the material selection
process can be regarded as a multi-criteria decisionmaking (MCDM) problem. Hence, a systematic and
efficient approach to material selection is necessary
in order to select the best alternative for a given
engineering application [8, 9]. Thus, efforts need to
be extended to identify those criteria that influence
material selection for a given engineering
application to eliminate unsuitable alternatives and
select the most appropriate alternative using simple
and logical methods [10, 11].
Currently Ecuador is running a world pioneer
campaign called “National Efficient Cooking
Program” (NECP), which aims the migration of 3
million of liquefied petroleum gas (LPG) based
cookers to electric induction cookers, in order to
enhance the security of energy supply and reduce
emissions of greenhouse gases and other pollutants
[12, 13] A cookware manufacturing project for
induction cookers is necessary to accomplish these
policies, it is expected to fabricate and use 3 million
of induction cookware sets between 2014 and 2016
[12, 13]. To make the selection of materials for an
induction cookware is necessary to keep the
interplay between the requirements of design,
materials and processing.
This research focuses on selecting an alternative
material which best fits the technological
requirements to make high efficiency induction
cookware and has a good price for the consumer
than the conventional stainless steel 430 to improve
the overall efficiency of the induction cooker. This
paper solves the problem of selecting the material
for the base using recent mathematical tools and
techniques for accurate ranking of the alternative
materials for the base of an induction cookware
using OCRA method. The criteria weighting was
performed by compromised weighting method
composed of AHP and Entropy methods. For these
methods, a list of all the possible choices from the
best to the worst suitable materials is obtained,
taking into account different material selection
criteria. The rankings of the candidate materials
derived using these four methods prove the universal
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International Journal of Engineering Trends and Technology (IJETT) – Volume 34 Number 8- April 2016
applicability of these methods as efficient tools for
material selection decision-making.
II. MATERIALS AND METHODS
Definition of the decision making problem. The
induction heating is based on the static magnetic
field principle. Induction cooking heats a cooking
vessel by magnetic induction, instead of by thermal
conduction from a flame, or an electrical heating
element. In an induction cooker, a coil of copper
wire is placed under the cooking pot and an
alternating electric current is passed through it
(Figure 1). The resulting oscillating magnetic field
induces a magnetic flux which repeatedly
magnetizes the pot, treating it like a loss magnetic
core of a transformer. This produces large eddy
currents in the cookware, which because of the
resistance of the pot, heats it by the Joule effect.
They should have some specific properties in order
to maintain their function during heating. A cooking
vessel must be made of, or contain, a ferromagnetic
metal such as cast iron or some stainless steels.
However, copper, non-magnetic stainless steels, and
aluminum vessels can be placed on a ferromagnetic
interface disk which improve the thermal diffusivity
of a conventional hotplate. In order to meet all these
requirements, the most important material property
is considered to be cost ($/Kg), the low values of
which are desired in order to provide a competitive
advantage among manufacturers. The second
property required is high values of relative
permeability (µ) due to magnetize the base of the pot.
A high Thermal diffusivity (α), which indicates how
fast heat is transferred through and out of the
material, is important. Yield strength (Y) for the
workability cookware is desired in order to decrease
the energy required to build the cookware and be a
good cookware. Electric conductivity (σ) is
important for the eddy current generated in the base
of the pot. Density (ρ) is important to reduce the
weight of the base of the pot. Thermal conductivity
(λ) to transfer heat from one part of the pan to
another very quickly and efficiently. Finally Specific
Heat (Cp) is important to the thermal energy transfer.
Among these eight criteria, the cost, yield strength,
electric conductivity and density are a non-beneficial
properties. Eight alternatives for the base of an
induction cookware were taken into consideration:
Permalloy 80, No oriented Electrical Steel ASTM
A677, Mumetal, AISI 430 stainless steel, AISI 410
stainless steel, cast iron, Co and Ni. The properties
required for the base of an induction cookware
alternatives with their quantitative data are given in
Table I and their average values were used.
Figure 1.
Working principle of induction
effect over magnetic pot bases
Table 1. Material properties for the base of an induction cookware [9-15]
(1) Permalloy 80 (80 %
Ni, 4% Mo, 16% Fe)
37.50
(2) ASTM A677 Steel
M-47 No oriented
Electrical Steel
(3) Mumetal (77% Ni.
4% Mo. 14% Fe. 5% Cu)
0.975
11550
18.20
300
2.70
7.75
65.00
0.46
38.00
127500
7.65
715
1.695
8.74
33.50
0.495
(4) AISI 430
1.50
850
6.95
513.5
1.60
7.80
24.90
0.46
(5) AISI 410
2.00
850
6.90
1180
1.70
7.80
24.70
0.46
(6) Cast Iron
0.125
425
7.40
385
9.00
7.18
26.60
0.505
(7) Co
30.00
155
21.85
225
1.60
8.80
84.60
0.44
(8) Ni
18.00
670
19.85
52
1.125
8.89
79.00
0.455
Thermal
diffusivity [·106
m2 s-1] (α)
7.90
Yield strength
[MPa] (Y)
321
Electric
conductivity
[·107 S m-1] (σ)
1.71
Specific Heat
[kJ kg-1 K]
( )
0.50
Relative
permeability
( )
190000
Material cost
($ Kg-1)
Material
Density
[g cm-3] (ρ)
8.24
Thermal
conductivity
[W mK-1] (λ)
32.50
III. MULTI-CRITERIA DECISION MAKING METHODS
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International Journal of Engineering Trends and Technology (IJETT) – Volume 34 Number 8- April 2016
IV. I. CRITERIA WEIGHTING.
The criteria weights are calculated using a
compromised weighting method where the AHP and
Entropy methods were combined in order to take
into account the subjective and objective weights of
the criteria and to obtain more reasonable weight
coefficients. The synthesis weight for the jth criteria
is:
(1)
The consistency of the results is resumed by the
pairwise comparison of alternatives. Matrix can
be ranked as 1 and
= n.
3)
Consistency assessment
In order to analyze the consistency of the results it
is necessary to distinguish the importance of
alternatives among them. In equations (4) and (5) is
shown the consistency indexes required to validate
the results.
(4)
where αj is the weight of jth criteria obtained via
AHP method and βj is the weight of jth criteria
obtained through Entropy method.
III. I. I. ANALYTIC HIERARCHY PROCESS (AHP)
This method set weights of an alternative over
others. The mathematical model was developed by
[16].
The AHP approach depends on [16]: 1) Hierarchy
rank, 2) Comparison among selection criteria, 3)
Assessing consistency in results.
1)
Hierarchy rank. Every alternative
is assigned a value in order to identify its
importance in an application. The ranking is
composed by three levels: a). general objective.
b). criteria for every alternative. c). alternatives
to regard [16].
2)
Comparison among alternatives.
The weight of criteria respect to other is set in
this section. To quantify its coefficient it is
required the experience and knowledge of the
assessing team or technician. [16], classified the
importance parameters show in Table II. The
values 2, 4, 6 and 8 are applied to differentiate
slightly differing judgements. The comparison
among n criteria is resume in matrix A (
),
the global arrange is expressed in equation (2).
(5)
Where:
: Number of selection criteria.
: Random index.
: Consistency index.
: Consistency relationship.
Largest eigenvalue.
If
should be greater than 0.1, otherwise, the
importance coefficient (1-9) has to be set again and
recalculated (8).
III. I. II. ENTROPY METHOD.
Entropy measures the uncertainty in the
information formulated using probability theory. The
description of the method is explained by [17].
Equation (6) shows the decision matrix A of multicriteria problem with
alternatives and criteria:
;
;
(6)
Where
=1
(2)
Afterwards, from matrix it is determined the
relative priority among properties. The eigenvector
is the weight importance and it corresponds with
the largest eigenvector (
):
(3)
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is the performance value of the
alternative to the
criteria.
The normalized decision matrix
is calculated
(7), in order to determine the weights by the Entropy
method.
(7)
The Entropy value
obtained as:
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of
criteria can be
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International Journal of Engineering Trends and Technology (IJETT) – Volume 34 Number 8- April 2016
(12)
(8)
Where
is a constant that guarantees
and m is the number of alternatives.
The degree of divergence (
) of the average
information contained by each criterion can be
obtained from Eq. (9):
(9)
Thus, the weight of Entropy of
defined as:
(13)
III. II. OCRA METHOD.
OCRA uses an intuitive method for incorporating
the decision maker’s preferences about the relative
importance of the criteria [18]. In OCRA method, in
the first step, the preference ratings with respect to
non- beneficial or input criteria are determined; in
the second step, the preference ratings of the output
criteria are determined and in the last step, the
overall preference ratings of the available
alternatives are evaluated where both the cardinal
and ordinal data are used. The general OCRA
procedure is described as below [18]:
Step 1: Compute the preference ratings with
respect to the non- beneficial criteria. The aggregate
performance of
alternative with respect to all the
input criteria is calculated using the following
equation:
j=1.2.….n)
Where
indicates the number of
beneficial attributes or output criteria and
is
calibration constant or weight importance of
output criteria. The higher an alternative’s score for
an output criterion, the higher is the preference for
that alternative. It can be mentioned that
Step 4: Calculate the linear preference rating for
the output criteria using the following equation:
(14)
Step 5: Compute the overall preference ratings.
The overall preference rating for each alternative
is calculated by scaling the
so that
the least preferable alternative receives a rating of
zero.
The overall preference rating ( ) is calculated as
follows:
(i=1.2.….m.
(15)
(11)
The alternatives are ranked according to the
values of the overall preference rating. The
alternative with the highest overall performance
rating receives the first rank.
Where
is the measure of the relative
performance of
alternative and
is the
performance score of ith alternative with respect to
input criterion. If
alternative is preferred to
alternative with respect to
criterion, then
indicates the
difference in performance scores for criterion ,
between
alternative and the alternative whose
score for criterion is the highest among all the
alternatives considered.
Step 2: Calculate the linear preference rating for
the input criteria.
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to the least preferable alternative. represents the
aggregate preference rating for
alternative with
respect to the input criteria.
Step 3: Compute the preference ratings with
respect to the beneficial criteria. The aggregate
performance for
alternative on all the beneficial
or output criteria is measured using the following
expression:
criteria can be
(10)
. Then term
This linear scaling is done to assign a zero rating
V. RESULTS AND DISCUSSION
The results for weights of each criteria were
computed by the AHP method and Entropy method.
V. I. CRITERIA WEIGHTING
The weight of each alternative was assigned
according to the AHP method. The comparison
among properties of every alternative are in Table 1
(4), (5). The properties identification appears under
the name of each property as ($ kg-1). (µ). (α). (Y).
(σ). (ρ). (λ). and ( ). In Table 2 is can be showed
the scale of relative importance used in the AHP
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International Journal of Engineering Trends and Technology (IJETT) – Volume 34 Number 8- April 2016
method. In Table 3, the decision matrix generated is
shown which take into account the importance of
each criteria. The most important criteria to generate
the matrix was considered ( ); slightly more
important was taken (µ); strongly more important
was considered (α) and (Y); demonstrably more
important were taken (σ) and (ρ); extreme more
important were considered (λ), and (
). The
coefficients were assigned based on the heating
principle on induction cookers. The results are
consistent due to the value of the consistency index
(CI = 0.0489) and the consistency ratio (CR =
0.0347) which are lower than the limit 0.1.
At the final step, the compromised weights of the
criteria ( ) were calculated using the Eq. (1). In
Table 4, the weight coefficient of every criterion was
determined based in results of AHP and Entropy
methods. On one hand, the most representative
values are relative permeability 46.10% and cost
28.40%. On the other hand, less than 30% of the
overall weight is distributed in (α), (Y), (σ), (ρ), (λ),
( ).
Table 2. Scale of relative importance
Definition
Equal importance
Moderate importance
Strong importance
Very strong importance
Extreme importance
Intermediate importance
Intensity of importance
1
3
5
7
9
2, 4, 6, 8
Table 3. Comparison among criteria for balanced scales AHP
method
($/Kg)
( )
(α)
(Y)
(σ)
(ρ)
(λ) (
)
1.00
3.00 5.00 5.00 7.00 7.00 9.00 9.00
0.33
1.00 3.00 3.00 5.00 5.00 7.00 7.00
0.20
0.33 1.00 1.00 3.00 3.00 5.00 5.00
0.20
0.33 1.00 1.00 3.00 3.00 5.00 5.00
0.14
0.20 0.33 0.33 1.00 1.00 3.00 3.00
0.14
0.20 0.33 0.33 1.00 1.00 3.00 3.00
0.11
0.14 0.20 0.20 0.33 0.33 1.00 1.00
0.11
0.14 0.20 0.20 0.33 0.33 1.00 1.00
Table 4. Criteria weighting by the AHP (
), balanced scales
($/Kg)
(µ)
(α)
(Y)
(σ)
(ρ)
0.401
0.22
0.11
0.11
0.05
0.05 0.02 0.02
0.096
0.28
0.10
0.05
0.02
0.17 0.10 0.17
0.285
0.46
0.09
0.04
0.01
0.07 0.01 0.03
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(λ)
entropy (
) and compromised weighting (
) methods
V. II. OCRA METHOD.
The aggregate performance of the alternatives
with respect to all the input criteria is calculated with
equation (11) from data from Table I. Applying
equation (13), the aggregate achievement of the
alternatives on all the beneficial or output criteria are
then determined and subsequently, the linear
preference ratings for the output criteria are
calculated. Finally, the overall preference rating for
each alternative material is determined using
equation (15). The detailed computations of this
method are illustrated in Table 5. In this method, the
ranking of material alternatives is obtained as 8-4-72-3-1-6-5, which suggests that Ni attains the top
rank. AISI 430 is the second best choice and AISI
410 has the last rank and Cast iron is the second last
rank.
Table 5. Computation details for OCRA method
Material
1
2
3
4
5
6
7
8
2.054
615.645
186.508
646.296
644.660
650.724
583.586
609.479
0.000
613.591
184.454
644.242
642.606
648.669
581.532
607.425
0.956
0.056
0.712
0.016
0.026
0.010
0.155
0.094
0.947
0.047
0.702
0.006
0.016
0.000
0.145
0.085
0.000
612.691
184.209
643.301
641.676
647.722
580.730
606.562
VI. DISCUSSION
In this research it has been observed that the
MCDM are an important tool to recognize and
identify the best alternative in a bunch of several of
them. These methods can adapt to different sort of
environments and conditions that would affect the
final result and that is why these approaches are
applied in different areas of science, engineering and
management [19, 20] In this case, we take advantage
of MCDM methods in order know the best
alternative for the materials of the base in an
induction cookware. Ni attains the top rank. AISI
430 is the second best choice and AISI 410 has the
last rank and Cast iron is the second last rank. This
results are in agreement with the results exposed by
[21] which developed a Magnetic material selection
using multiple attribute decision making approach.
Where, it has been applied magnetics properties for
the material selection as the magnetic permeability.
(Cp)
VII.
CONCLUSIONS
In this paper the material selection problem for
the base of an induction cookware has been solved
utilizing a decision model. The weighting of the
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Rank
8
4
7
2
3
1
6
5
International Journal of Engineering Trends and Technology (IJETT) – Volume 34 Number 8- April 2016
material properties was performed using the
compromised weighting method
composes of the
AHP and Entropy methods. Ranking scores which
were used to rank the alternative materials were
obtained as results of the methods. In this case, we
take advantage of MCDM in order to contribute to
the Ecuadorian government in the new model of
energetic management (matrix). According to the
results. Ni would be the best material for the base of
an induction pot. This material is adequate for its
high permeability in order to induce Eddy currents
and generate heat. The trend in the results has
changed only in OCRA method due to the wide
range of variability in the magnitude of every
criterion.
It was validated that the MCDM approach is a
viable tool in solving the complex material selection
decision problems. The model which was developed
for material selection of the base of the cookware
can be applied on other mechanical components for
material selection problems.
ACKNOWLEDGEMENTS
The authors of this research acknowledge to the
Secretaría Nacional de Planificación y Desarrollo
(SENPLADES) for financing the execution of the
present research. This work was sponsored by the
Prometeo project of the Secretaria de Educación
Superior. Ciencia. Tecnología e Innovación
(SENESCYT) held in the Republic of Ecuador. The
information necessary to complete this work was
given by the Ministerio de Electricidad y Energía
Renovable (MEER) of Ecuador
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