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443
Advances in Production Engineering & Management
ISSN 1854-6250
Volume 16 | Number 4 | December 2021 | pp 443–456
Journal home: apem-journal.org
https://doi.org/10.14743/apem2021.4.412
Original scientific paper
A multi-criteria decision-making in turning process using the
MAIRCA, EAMR, MARCOS and TOPSIS methods:
A comparative study
Trung, D.D.a,*, Thinh, H.X.b
aFaculty of mechanical engineering, Hanoi Univeristy of Industry, Vietnam
bCenter for mechanical engineering, Hanoi Univeristy of Industry, Vietnam
A B S T R A C T
A R T I C L E I N F O
Multi-criteria decision-making is important and it affects the efficiency of a
mechanical processing process as well as an operation in general. It is under-
stood as determining the best alternative among many alternatives. In this
study, the results of a multi
-criteria decision-
making study are presented. In
which, sixteen experiments on turning process were carried
out. The input
parameters of the experiments are the cutting speed, the feed speed, and the
depth of cut. After conducting the experiments, the surface roughness and the
material removal rate (MRR) were determined. To determine which experi-
ment guarantees
the minimum surface roughness and maximum MRR simul-
taneously, four multi
-criteria decision-
making methods including the MAIR-
CA, the EAMR, the MARCOS, and the TOPSIS were used. Two methods the
Entropy and the MEREC were used to determine the weights for the criteria.
The combination of four multi
-
criteria making decision methods with two
determination methods of the weights has created eight ranking solutions for
the experiments, which is the novelty of this study. An amazing result was
obtained that all eight solutions all determined the same best experiment.
From the obtained results, a recommendation was proposed that the multi
-
criteria making decision methods and the weighting methods using in this
study can also be used for multi
-criteria making decisio
n in other cases, other
processes.
Keywords:
Turning;
Material
removal rate (MRR);
Surface
roughness;
Multi
-criteria decision-making
(MCDM);
Multi
Atributive Ideal-Real Com-
parative
Analysis (MAIRCA);
Evaluation
by an Area-based
Method
of Ranking (EAMR);
Measurement
of Alternatives and
Ranking
according to Compromise
Solution
(MARCOS);
Technique
for Order of Preference
by
Similarity to Ideal Solution
(TOPSIS);
Entropy;
Method
based on the Removal
Effects
of Criteria (MEREC)
*
Corresponding author:
doductrung@haui.edu.vn
(Trung, D.D.)
Article history:
Received
19 November 2021
Revised
8 December 2021
Accepted
9 December 2021
Content from this work may be used under the terms of
the Creative Commons Attribution 4.0 International
Licence (CC BY 4.0). Any further distribution of this work
must maintain attribution to the author(s) and the title of
the work, journal citation and DOI.
1. Introduction
Multi-criteria decision-making methods are used in many fields. These methods help to compare
alternatives and find the best one [1]. For a mechanical machining process as well as a turning
process, multi-criteria decision-making is very important. It can be said that because among
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Advances in Production Engineering & Management 16(4) 2021
many input parameters to evaluate the turning process, sometimes there are parameters that
the objective function sets for them are often opposite. For example, when high-speed turning to
improve machining productivity, the tool wear rate is also large, causing the decrease of the tool
life [2]. To increase the MRR, it is necessary to increase the feed rate and the depth of cut, but
this increases the surface roughness [3]. Besides, to reduce the tool wear rate, it is necessary to
increase the flow and the concentration of the coolant to reduce the cutting heat. However, doing
that will not only increase the manufacturing cost but also affect the environment. In addition,
increasing the machining productivity will often increase the cutting tool vibration, and lead to
the reduction of the tool life and increase the surface roughness [4], etc. For the above reasons,
many studies on multi-criteria decision-making for turning process have been carried out.
The TOPSIS is the most used method for multi-criteria decision-making in many different
fields [5, 6]. This method has also been used for multi-criteria decision-making for turning pro-
cesses in many studies. These studies usually focus on selecting optimal input process parame-
ters to ensure multiple criteria at the same time such as: Ensuring the minimum surface rough-
ness and the maximum MRR when processing Glass fiber reinforced polyester materials (GFRP)
[7]; Ensuring all of six parameters of the surface roughness (including Rq, Ra, Rt, Rku, Rz, Rsm) have
the same minimum value when turning GFRP materials [8]; Ensure the minimum surface rough-
ness (Ra and Rz) and the maximum MRR when turning EN19 steel [9]; Simultaneously ensuring
the minimum surface roughness and tool wear rate, and the maximum MRR when turning 1030
steel [10]; Simultaneously ensuring the minimum surface roughness, the cutting force, the tool
wear and the cutting heat, and the maximum MRR when turning pure Titanium [11]. Ensuring
the minimum surface roughness, the cutting force and the tool wear when turning CP-Ti grade II
material [12]; Simultaneously ensuring the minimum surface roughness, the cutting force, the
tool wear and the cutting temperature when turning Ti-6Al-4V alloy [13]; Simultaneously ensur-
ing the minimum surface roughness, and the maximum MRR when turning AISI D2 steel [14];
Simultaneously ensuring the minimum surface roughness, and the maximum MRR when turning
Al 6351 alloy [15]; Simultaneously ensuring the minimum surface roughness, the minimum
roundness deviation and the minimum tool wear when turning 9XC steel [16], etc. Recently, the
TOPSIS method and six other methods including the SAW, the WASPAS, the VIKOR, the MOORA,
the COPRAS, and the PIV, have been used in multi-criteria decision-making when turning
150Cr14 steel and the best option was received for all of methods [17].
In the last few years, scientists have also proposed new decision-making methods. Three of
those methods are MAIRCA, EAMR, and MARCOS methods.
The MAIRCA method was first introduced in 2018 [18]. The outstanding advantage of this
method over other methods is that the objectives can be in both qualitative and quantitative
types. There have been several studies which applied this method to multi-criteria decision-
making. For example, determining the most effective time (year) in mergers and acquisitions of
companies in Turkey during the period 2015-2019 [19]; determining the best performing airline
out of eleven emerging airlines from Turkey, Mexico, China, Indonesia and Brazil [20]; selecting
a partner for a food company in Turkey [21]; preventing the Covid-19 epidemic to the sustaina-
ble development of OECD countries [22].
The EAMR method was discovered in 2016 [23]. This method has been used for a number of
studies such as: selecting partners to hire for logistics [24]; selecting contract types of health
care services [25]; deciding the order quantity for each supplier to ensure environmental crite-
ria [26].
The MARCOS method was first used in 2019 [27]. This method has been applied in several
studies such as: in the selection of intermediate modes of transport between countries in the
Danube region [28]; for minimizing risks in the transportation [29], in selection of lifting equip-
ment for services in warehouses [30]; for the selection of human resources for transportation
companies [31], or for the cost selection in the construction [32].
Although the three methods MAIRCA, EAMR and MARCOS have been used in some studies as
described above, so far there has been no research on the application of any of these methods
for multi-criteria decision-making for the turning process. The combination of three methods
A multi-criteria decision-making in turning process using the MAIRCA, EAMR, MARCOS and TOPSIS methods: A …
Advances in Production Engineering & Management 16(4) 2021
445
(MAIRCA, EAMR and MARCOS) with TOPSIS method is the basis for assessing the accuracy of the
results obtained. This is the first reason for doing this study.
When performing multi-criteria decisions, an important task is to determine the weights for
the criteria. This has a great influence on the ranking order of the alternatives [33]. If it is done
by the decision maker, the accuracy achieved is not high because it depends on the knowledge as
well as the subjective thoughts of that person. If it is determined by consulting the experts, its
accuracy will depend on the experience of the experts as well as the way the questionnaires are
presented, which is also very time consuming and high cost [34]. To overcome these limitations,
it is necessary to determine the weights for the criteria based on mathematical models. In this
way, the weight of the criteria is determined independent of the subjectivity of the decision
maker. The Entropy is known as a method of determining weights with high accuracy, which has
been used in many cases. When it is necessary to compare multi-criteria decision-making meth-
ods, the Entropy method is also recommended to use to determine the weights for the criteria
[17].
MEREC is a weighting method which introduced in 2021 [35]. This method has been used to
determine the weights for criteria such as: decision-making to determine the location of logistics
distribution centers [36]; decision-making for documental classification [37]; etc. However, up
to now this method has not been used to determine the weights for criteria in turning processes.
The simultaneous use of two methods (the MEREC and the Entropy) to determine weights is the
basis for evaluating stability when determining the best solution of multi-criteria decision-
making methods. This is the second reason for doing this study.
Surface roughness and MRR are two commonly used parameters to evaluate turning process-
es. The reason is that the surface roughness has a great influence on the workability and durabil-
ity of the products through the wear resistance, the chemical corrosion resistance, and the accu-
racy of the joint (for tight joints) [3], while MRR is an important factor to evaluate the cutting
productivity [38]. Besides, determining the values of these parameters is also simpler than other
that of parameters, such as the cutting force, the cutting temperature, or the vibration in the
cutting process. This is the reason why this study will also use the surface roughness and MRR as
two indicators to evaluate turning process.
This study presents the results of experimental research on turning process with two param-
eters to evaluate the turning process, namely surface roughness and MRR. In addition, the En-
tropy and the MEREC are two methods used to determine the weights for the criteria (surface
roughness and MRR). Also, four methods including the MAIRCA, the EAMR, the MARCOS, and the
TOPSIS will be used to make multi-criteria decision for turning process. The purpose of multi-
criteria decision-making is to ensure simultaneous minimum surface roughness and maximum
MRR.
2. Used methods of multi-criteria decision-making
2.1 The MAIRCA method
The steps to implement multi-criteria decision-making according to the MAIRCA method are as
follows [18].
Step 1: Building the initial matrix according to the following equation:
=
(1)
where m is the number of options; n is the number of criteria; xmn is the value of the n criterion in
m.
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Step 2: Determining the priority for an indicator. When the decision maker is neutral, the role of
the indicators is the same (no priority is given to any). Then the priority for the criteria is the
same and is calculated as follows:
=
, j = 1, 2, …,
n
(2)
Step 3: Calculating the quantities tpij according to the equation:
= ,
i
= 1, 2, …,
m
;
j
= 1, 2,…,
n
(3)
where wj is the weight of the j-th criterion.
Step 4: Calculating the quantities trij according to the equations:
=
if
j
is the criterion the bigger the better
(4)
=
if
j
is the criterion as small as better
(5)
Step 5: Calculating the quantities gij according to the equation:
=
(6)
Step 6: Summing the gj values according to the equation:
=
(7)
Ranking the options according to the principle that the one with the smallest Qi is the better.
2.2 The EAMR method
The steps according to the EAMR method are summarized as follows [23].
Step 1: Building a decision matrix:
=
(8)
where 1 ≤ d ≤ k, k is the number of decision makers; d is the index representing the decision maker d.
Step 2: Calculating the mean value of each alternative for each criterion according to the equa-
tion:
= 1
+
++
(9)
It should be noted that k is the index of the k decision maker, not the exponent.
Step 3: Determining the weights for the criteria. At this step, each decision maker can choose a
different weighting method.
Step 4: Calculating the average weighted value for each criterion according to the equation:
= 1
+ ++
(10)
Step 5: Calculating nij values according to the equation:
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Advances in Production Engineering & Management 16(4) 2021
447
=
(11)
in which, ej is determined by the equation:
=max{,…,}
(12)
Step 6: Calculating the normalized weight values according to the equation:
=
(13)
Step 7: Calculating the normalized score for the criteria:
=
+
++
if j is the criterion the bigger the better
(14)
=
+
++
if j is the criterion as small as better
(15)
Step 8: The rank of value (RV) is found based on and .
Step 9: Calculating the evaluation score for the options according to the equation:
= ()
(16)
The solution with the largest Si will be the best one, which is the ranking principle of the
EAMR method.
2.3 The MARCOS method
The steps to implement multi-criteria decision-making according to the MARCOS method are as
follows [27].
Step 1: Similar to step 1 of the MAIRCA method.
Step 2: Constructing an initial matrix that expands by adding an ideal solution (AI) and the oppo-
site solution to the ideal solution (AAI) :
=
AAI
A
A
A
AI
(17)
where:
AAI = min (); i = 1, 2, …, m; j = 1, 2, …, n if j is the criterion the bigger the better.
AAI = max (); i = 1, 2, …, m; j = 1, 2, …, n if j is the criterion as small as better.
AI = max (); i = 1, 2, …, m; j = 1, 2, …, n if j is the criterion the bigger the better.
AI = min (); i = 1, 2, …, m; j = 1, 2, …, n if j is the criterion as small as better.
Step 3: Calculating the normalized values according to the following equations:
=
if
j
is the criterion as small as better
(18)
=
if
j
is the criterion the bigger the better
(19)
Step 4: Calculating the weighted normalized values using the equation:
=
(20)
where wj is the weight of the criterion j.
Step 5: Calculating coefficients Ki+ and Ki- by the following equations:
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Advances in Production Engineering & Management 16(4) 2021
=
(21)
=
(22)
where Si, SAAI and SAI are the sum of the values of cij, xaai and xai, respectively; with i = 1, 2,..., m.
Step 6: Calculating functions f(Ki+) and f(Ki-) by:
()=
+
(23)
()=
+
(24)
Step 7: Calculating function f(Ki) according to the following equation and rank the alternatives:
()= +
1 + 1()
()+1()
()
(25)
Ranking the solutions according to the best solution is the one with the largest value of the
function f(Ki).
2.4 The TOPSIS method
The steps performed in the TOPSIS method are described as follows [39, 40].
Step 1: Similar to step 1 of the MAIRCA method.
Step 2: Calculating the normalized values of kij according to the equation:
=
(26)
Step 3: Calculating the weighted normalized values using the equation:
=×
(27)
Step 4: Determine the best solution A+ and the worst solution A- for the criteria according to the
equations:
= ,, … , , … ,
(28)
= ,, … , , … ,
(29)
wherein and are the best and worst values of the j criterion, respectively.
Step 5: Calculating values and by the following equations:
=
i
= 1, 2, …,
m
(30)
=
i
= 1, 2, …,
m
(31)
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449
Step 6: Calculating values by:
=
i =
1, 2, …,
m;
0 1
(32)
Step 7: Rank the alternatives according to the principle that the one with the largest Ci* is the
best one.
3. Used methods of determining the weight
3.1 The Entropy method
Determining the weights of the indicators by the Entropy method is performed according to the
following steps [41].
Step 1: Determining the normalized values for the indicators:
ij
=
ij
+
ij
(33)
Step 2: Calculating the value of the Entropy measure for each indicator:
=ij ×ln(
ij
)
1
ij
×ln 1
ij
(34)
Step 3: Calculating the weight for each indicator:
=1
1
(35)
3.2 The MEREC method
The steps to determine the weights according to the MEREC method are as follows: [35]:
Step 1: Similar to step 1 of the MAIRCA method.
Step 2: Calculating the normalized values using the following equations:
=
if j is the criterion the bigger the better
(36)
=
if j is the criterion as small as better
(37)
Step 3: Calculating the overall efficiency of the alternatives by the following equation:
= ln 1 + 1
ln
(38)
Step 4: Calculating the efficiency of the alternatives according to the equation:
= ln 1 + 1
lnh
,
(39)
Step 5: Calculating the absolute value of the deviations using the equation:
=
(40)
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Step 6: Calculating the weight for the criteria according to the equation:
=
(41)
4. Used materials and execution of turning experiment
The experimental setup is described as follows: A conventional lathe ECOCA SJ460 (Taiwan) was
used for the experiment. Besides, SKS3 steel samples with a diameter of 32 mm and a length of
260 mm were selected. In addition, three input parameters including cutting speed, feed rate
and depth of cut were investigated. The Taguchi method was used to design an orthogonal ma-
trix of 16 experimental runs (Table 1). After conducting the experiment, the MRR values were
calculated according to the Eq. 42:
MRR =
(mm3/s)
(42)
where nw is the number of revolutions of the part per minute; dw is the diameter of the work-
piece; fd is the feed rate, and ap is the depth of cut (mm).
The surface roughness was also determined at each test using an SJ-201 equipment. Table 1
shows the obtained results of surface texture and MRR.
From Table 1, the minimum surface roughness is 0.455 µm in option A13, but the maximum
value of MRR is 362.046 mm3/s in option A7. It is therefore necessary to define an alternative
where the surface roughness is considered to be the “minimum” and the MRR is considered the
“maximum”. This work can only be done by using mathematical methods in decision-making,
and of course a mandatory job is also to determine the weights for the criteria. These two im-
portant contents will be presented in section 5 of this paper.
Table 1 Orthogonal experimental matrix L16 and the response
Trial.
Actual value
Responses
nw (rev/min)
fd (mm/rev)
ap (mm)
Ra (µm)
MRR (mm3/s)
A1
588
0.092
0.4
0.572
36.255
A2
588
0.167
0.6
1.395
98.717
A3
588
0.292
0.8
2.704
230.144
A4
588
0.302
1.0
2.897
297.531
A5
740
0.092
0.6
0.532
68.441
A6
740
0.167
0.4
1.166
82.824
A7
740
0.292
1.0
2.662
362.046
A8
740
0.302
0.8
2.602
299.555
A9
833
0.092
0.8
0.542
102.724
A10
833
0.167
1.0
1.372
233.083
A11
833
0.292
0.4
2.301
163.018
A12
833
0.302
0.6
2.502
252.902
A13
1050
0.092
1.0
0.455
161.855
A14
1050
0.167
0.8
1.082
235.041
A15
1050
0.292
0.6
2.221
308.228
A16
1050
0.302
0.4
2.211
212.522
5. Results and discussion
5.1 Determining the weights for criteria
Eqs. 33 to 35 were used to determine the weights for the criteria according to the Entropy
method. The weights of Ra and MRR are 0.6149 and 0.3851, respectively.
Eqs. 36 to 41 were applied to determine the weights for the criteria according to the MEREC
method. The results have determined that the weights of Ra and MRR are 0.7042 and 0.2958,
respectively.
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5.2 Multi-criteria decision-making with the use of the entropy method for determining the weights
of the criteria
Applying the MAIRCA method
Eq. 1 was used to build the initial matrix, which is the last two columns in Table 1.
Eq. 2 was applied to determine the priority for the criteria. As the criteria are considered
equal, that is, the decision maker does not give importance to one criterion over the other.
Therefore, the priority for both criteria Ra and MRR is equal to 1/16 = 0.0625.
Eq. 3 was applied to determine the value of parameter , with the weight of the criteria de-
fined in section 5.1. The result has determined the value of Ra and MRR are 0.0384 and
0.0241 respectively.
Eqs. 4 and 5 was used to calculate the values of ; apply Eq. 6 to calculate ; apply Eq. 7 to
calculate Qi. All these values have been included in Table 2. The results of ranking options ac-
cording to the value of Qi have also been included in this table.
Table 2 Several MAIRCA parameters and ratings
Trial.
Rank
Ra
MRR
Ra
MRR
A1
0.0366
0.0000
0.0018
0.0241
0.0259
6
A2
0.0236
0.0046
0.0148
0.0195
0.0342
9
A3
0.0030
0.0143
0.0354
0.0097
0.0451
16
A4
0.0000
0.0193
0.0384
0.0048
0.0432
14
A5
0.0372
0.0024
0.0012
0.0217
0.0229
4
A6
0.0272
0.0034
0.0112
0.0206
0.0318
8
A7
0.0037
0.0241
0.0347
0.0000
0.0347
10
A8
0.0046
0.0195
0.0338
0.0046
0.0384
11
A9
0.0371
0.0049
0.0014
0.0192
0.0205
3
A10
0.0240
0.0145
0.0144
0.0095
0.0240
5
A11
0.0094
0.0094
0.0291
0.0147
0.0438
15
A12
0.0062
0.0160
0.0322
0.0081
0.0403
13
A13
0.0384
0.0093
0.0000
0.0148
0.0148
1
A14
0.0286
0.0147
0.0099
0.0094
0.0193
2
A15
0.0106
0.0201
0.0278
0.0040
0.0318
7
A16
0.0108
0.0130
0.0276
0.0110
0.0387
12
Applying the EAMR method
Eq. 8 was applied to build decision matrix. If the number of decision makers is k, then each per-
son has a different decision matrix (possibly due to different experimental results). However, in
this study, there is only one set of results shown in Table 1, i.e. k equals 1. Therefore, this step of
EAMR method is similar to step 1 of MAIRCA method, which means that the main decision ma-
trix is the last two columns in Table 1.
Eq. 9 was used to calculate the mean value of the alternatives for each criterion. For k equals
1, then = .
Eq. 10 was applied to calculate the average weight for the criteria. Since k equals 1, so = .
Eq. 11 was used to calculate nij values; apply Eq. 12 to calculate ej values. Also, Eq. 13 was
used to calculate .
Eqs. 14 and 15 were applied to calculate the respective values Gi.
Eq. 16 was used to calculate the Si values.
The results of calculating these quantities are presented in Table 3. The results of ranking the
alternatives according to the value of Si have also been compiled into this table.
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Table 3 EAMR parameters and ratings
Trial.
nij
vij
Gi
Si
Rank
Ra
MRR
Ra
MRR
Ra
MRR
A1
0.1974
0.1001
0.1214
0.0386
0.1214
0.0386
0.3176
16
A2
0.4815
0.2727
0.2961
0.1050
0.2961
0.1050
0.3546
15
A3
0.9334
0.6357
0.5739
0.2448
0.5739
0.2448
0.4265
12
A4
1.0000
0.8218
0.6149
0.3165
0.6149
0.3165
0.5147
11
A5
0.1836
0.1890
0.1129
0.0728
0.1129
0.0728
0.6447
9
A6
0.4025
0.2288
0.2475
0.0881
0.2475
0.0881
0.3560
14
A7
0.9189
1.0000
0.5650
0.3851
0.5650
0.3851
0.6816
7
A8
0.8982
0.9719
0.5523
0.3743
0.5523
0.3743
0.6777
8
A9
0.1871
0.3333
0.1150
0.1283
0.1150
0.1283
1.1156
3
A10
0.4736
0.7562
0.2912
0.2912
0.2912
0.2912
1.0000
4
A11
0.7943
0.5289
0.4884
0.2037
0.4884
0.2037
0.4170
13
A12
0.8637
0.8205
0.5311
0.3160
0.5311
0.3160
0.5950
10
A13
0.1571
0.5251
0.0966
0.2022
0.0966
0.2022
2.0939
1
A14
0.3735
0.7626
0.2297
0.2937
0.2297
0.2937
1.2787
2
A15
0.7667
1.0000
0.4714
0.3851
0.4714
0.3851
0.8169
6
A16
0.7632
1.0000
0.4693
0.3851
0.4693
0.3851
0.8206
5
Applying the MARCOS method
Eq. 17 has been applied to determine the ideal solution (AI) and the opposite solution to the
ideal solution (AAI). Accordingly, in the ideal solution, the values of Ra and MRR are 0.455 µm
and 362.046 mm3/min, respectively. At the opposite solution, the values of Ra and MRR are
2.897 µm and 36.255 mm3/min, respectively.
Calculating the normalized values uij according to the Eqs. 18 and 19.
The normalized value considering the weight cij is calculated according to the Eq. 20.
The coefficients Ki+ and Ki- were calculated according to Eqs. 21 and 22.
The value of f(Ki+) that has been calculated by Eq. 23 is equal to 0.9025. Also, the value of f(Ki-)
has been calculated by Eq. 24 is equal to 0.0975.
Eq. 25 has been applied to calculate the values of f(Ki ).
The results of calculating these quantities are presented in Table 4. The ranking results of the
alternatives are also presented in this table.
Table 4 MARCOS parameters and ratings
Trial.
uij
cij
K+ K- f
(
Ki
)
Rank
Ra
MRR
Ra
MRR
A1
0.7955
0.1001
0.4891
0.0386
0.00146
0.01348
0.00144
4
A2
0.3262
0.2727
0.2006
0.1050
0.00084
0.00780
0.00083
15
A3
0.1683
0.6357
0.1035
0.2448
0.00096
0.00890
0.00095
13
A4
0.1571
0.8218
0.0966
0.3165
0.00114
0.01055
0.00113
10
A5
0.8553
0.1890
0.5259
0.0728
0.00165
0.01529
0.00163
3
A6
0.3902
0.2288
0.2399
0.0881
0.00090
0.00838
0.00090
14
A7
0.1709
1.0000
0.1051
0.3851
0.00135
0.01252
0.00134
6
A8
0.1749
0.8274
0.1075
0.3186
0.00118
0.01088
0.00116
9
A9
0.8395
0.2837
0.5162
0.1093
0.00173
0.01598
0.00171
2
A10
0.3316
0.6438
0.2039
0.2479
0.00125
0.01154
0.00123
8
A11
0.1977
0.4503
0.1216
0.1734
0.00081
0.00753
0.00081
16
A12
0.1819
0.6985
0.1118
0.2690
0.00105
0.00973
0.00104
11
A13
1.0000
0.4471
0.6149
0.1722
0.00217
0.02010
0.00215
1
A14
0.4205
0.6492
0.2586
0.2500
0.00140
0.01299
0.00139
5
A15
0.2049
0.8514
0.1260
0.3279
0.00125
0.01159
0.00124
7
A16
0.2058
0.5870
0.1265
0.2261
0.00097
0.00901
0.00096
12
Applying the TOPSIS method
Eq. 26 was used to calculate the normalized values of kij. The normalized values taking into ac-
count the weight lij are calculated according to the Eq. 27.
The A+ value of Ra and MRR has been determined by Eq. 28, with values of 0.0366 and 0.1597
respectively.
A multi-criteria decision-making in turning process using the MAIRCA, EAMR, MARCOS and TOPSIS methods: A …
Advances in Production Engineering & Management 16(4) 2021
453
The A- value of Ra that MRR has also been determined by Eq. 29 is 0.2331 and 0.0160 respec-
tively.
The values Si+ and Si- have been calculated according to the Eqs. 30 and 31, respectively.
The value Ci* has been calculated by Eq. 32.
The results of calculating these quantities are presented in Table 5. The ranking results of the
alternatives are also presented in this table.
Table 5 TOPSIS parameters and ratings
Trial.
kij
lij
Si+ Si- Ci*
Rank
Ra
MRR
Ra
MRR
A1
0.0748
0.0415
0.0460
0.0160
0.1440
0.1871
0.5650
6
A2
0.1825
0.1131
0.1122
0.0436
0.1386
0.1240
0.4721
9
A3
0.3538
0.2637
0.2176
0.1015
0.1901
0.0869
0.3138
15
A4
0.3791
0.3409
0.2331
0.1313
0.1985
0.1153
0.3673
14
A5
0.0696
0.0784
0.0428
0.0302
0.1297
0.1908
0.5954
5
A6
0.1526
0.0949
0.0938
0.0365
0.1358
0.1408
0.5090
7
A7
0.3483
0.4148
0.2142
0.1597
0.1776
0.1450
0.4495
10
A8
0.3405
0.3432
0.2094
0.1322
0.1749
0.1186
0.4040
11
A9
0.0709
0.1177
0.0436
0.0453
0.1146
0.1917
0.6259
3
A10
0.1795
0.2670
0.1104
0.1028
0.0932
0.1503
0.6174
4
A11
0.3011
0.1868
0.1851
0.0719
0.1725
0.0737
0.2992
16
A12
0.3274
0.2897
0.2013
0.1116
0.1716
0.1007
0.3699
13
A13
0.0595
0.1854
0.0366
0.0714
0.0883
0.2041
0.6980
1
A14
0.1416
0.2693
0.0871
0.1037
0.0754
0.1703
0.6932
2
A15
0.2906
0.3531
0.1787
0.1360
0.1441
0.1317
0.4777
8
A16
0.2893
0.2435
0.1779
0.0938
0.1559
0.0954
0.3795
12
5.3 Multi-criteria decision-making with the use of the MEREC method for determining the weights
of the criteria
Doing the same as in section 5.2, the results of ranking options according to four multi-criteria
decision-making methods (MAIRCA, EAMR, MARCOS and TOPSIS) when the weights are deter-
mined by the MEREC method (presented in section 5.1) are presented in Table 6. In addition, the
ranking results of the alternatives when the weights are determined by the Entropy method (in
Tables 2, 3, 4, 5) have also been summarized in Table 6.
Table 6 Ranking of alternatives by two methods of determining weight
Trial.
Entropy weight
MEREC weight
MAIRCA
EAMR
MARCOS
TOPSIS
MAIRCA
EAMR
MARCOS
TOPSIS
A1
6
16
4
6
5
16
4
5
A2
9
15
15
9
8
15
14
8
A3
16
12
13
15
16
12
15
16
A4
14
11
10
14
15
11
10
14
A5
4
9
3
5
3
9
3
4
A6
8
14
14
7
7
14
12
7
A7
10
7
6
10
10
7
7
10
A8
11
8
9
11
12
8
9
12
A9
3
3
2
3
2
3
2
3
A10
5
4
8
4
6
4
6
6
A11
15
13
16
16
14
13
16
15
A12
13
10
11
13
13
10
13
13
A13
1
1
1
1
1
1
1
1
A14
2
2
5
2
4
2
5
2
A15
7
6
7
8
9
6
8
9
A16
12
5
12
12
11
5
11
11
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454
Advances in Production Engineering & Management 16(4) 2021
The ranking results of the options in Table 6 show that:
• With three methods MAIRCA, MARCOS, and TOPSIS: for different weighting methods, the
ranking order of options is also different [33].
• All four multi-criteria decision-making methods identify A13 as the best option. This result
is consistent when the weights of the criteria are determined by two different methods.
• The order of ranking the alternatives according to the EAMR method is completely the
same when using two different weighting methods. This shows that the EAMR method has
very high stability in ranking the alternatives.
• To ensure the "minimum" surface roughness and "maximum" MRR at the same time, the
values of cutting speed, feed rate and cutting depth are 1050 rev/min, 0.092 mm/rev and
1.0 mm respectively.
6. Conclusion
This paper presents the results of an experimental study on the SKS3 steel turning process, with
a total of 16 experiments designed according to the orthogonal matrix by the Taguchi method.
Three cutting parameters were selected for the process input. Besides, surface roughness and
MRR were selected as two parameters to evaluate turning process. Four methods including the
MAIRCA, the EAMR, the MARCOS, and the TOPSIS were used for multi-criteria decision-making.
The determination of the weights for the criteria was done by two methods Entropy and MEREC.
From the results of the study, some conclusions are drawn as follows:
• For the first time, three methods including MAIRCA, EAMR, MARCOS are used to make
multi-criteria decision for turning process. An excellent result has been obtained that all
three methods as well as the TOPSIS method have consistently identified a best alternative.
• The MEREC method is applied for the first time in this study to determine the weights for
the criteria of the turning process. The use of weights determined by the Entropy method
or the MEREC method does not affect the determination of the best solution in all four cas-
es where the different methods are used. Thus, with this study, determining the best solu-
tion when using four methods (MAIRCA, EAMR, MARCOS and TOPSIS) does not depend on
the method of determining the weights.
• When using the Entropy method, for different multi-criteria decision-making methods, the
same best solution can be determined [17]. In addition, when using two methods Entropy
and MEREC, for different decision-making methods, the best solutions still only one option.
• To determine the best option when making a multi-criteria decision, the weighted method
is Entropy and (or) MEREC should be used.
• The order of ranking the alternatives when using the EAMR method is completely the
same when using two different weighting methods. This shows the use of the EAMR meth-
od to rank the alternatives for high stability. This can be explained that when applying this
method, the weights of the criteria were normalized according to Eq. 13.
• The above conclusions are drawn based on the results of this study. To solidify them, there
is a need for some more studies in which other weighting options are considered, in other
machining processes.
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