Teknomekanik.
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June 2024 e-ISSN: 2621-8720 p-ISSN: 2621-9980 Comparison of MCDM methods effectiveness in the selection of plastic injection molding machines Do Duc Trung1.
Branislav DudiN2.
Duong Van Duc1.
Nguyen Hoai Son1 and Aleksandar Aonja3 School of Mechanical and Automotive Engineering.
Hanoi University of Industry.
Hanoi.
VIETNAM Faculty of Management.
Comenius University Bratislava.
SLOVAKIA Faculty of Economics and Engineering Management.
Novi Sad.
SERBIA A The Author.
Published by Universitas Negeri Padang.
This is an open-access article under the: https://creativecommons.
org/licenses/by/4.
* Corresponding Author: branislav.
dudic@fm.
Received January 4th 2024.
1st Revised March 16th 2024.
2nd Revised April 18th 2024.
Accepted April Cite this https://doi.
org/10.
24036/teknomekanik.
Abstract: In each specific problem of finding the best solution among many available options, where each option has multiple criteria, multi criteria decision making methods are considered equally effective when they converge to the same optimal solution.
Proximity Indexed Value.
Preference Selection Index.
Faire Un Choix Adyquat .
n Frenc.
, and Collaborative Unbiased Rank List Integration are four Multi Criteria Decision Making methods with very different characteristics.
All these four methods have been used a lot in recent times.
The effectiveness of these four methods have been confirmed to be comparable to other multi criteria decision making methods in many However, the comparison of these four methods with each other has never been performed in any studies.
This article is performed to fill that gap.
These four methods have been used to find to the best option among five types of plastic injection molding machine.
Ten criteria have been chosen to describe each alternative.
Two different methods that have been used to calculate the weights for the criteria are the MEAN weight method and the CRiteria Importance Through Intercriteria Correlation weight method.
Different scenarios have been created to compare the effectiveness of these four methods.
The results have shown that the four multi criteria decision making methods mentioned above are equally effective in the selection of plastic injection molding machines.
Among the five types of plastic injection molding machines, namely JSW J350EII-SPA ANBE-002-02.
Meiki M-200B-SJ.
Meiki M-350C-DF-SJ.
JSW J350E II, and JSW J550E-C5, the JSW J550E-C5 is the best type.
Keywords: MCDM.
PIV Method.
PSI Method.
FUCA Method.
CURLI Method.
Introduction Nowadays, the number of MCDM (Multi Criteria Decision Makin.
methods has exceeded 200, and they are used a lot to find the best option among available options in many different fields .
The purpose of applying MCDM methods is to find the best option among available options.
Therefore, the methods are considered to be equally effective when they find the same best option .
, .
, .
MCDM methods are divided into four main groups, the first group is the methods that need to normalize data and determine the weights for criteria .
alled group I), the second group is the methods that need to normalize data but do not need to determine the weights for criteria .
roup II), the third group is the methods that do not need to normalize data but need to determine the weights for criteria .
, the fourth group is the methods that need neither data normalization nor determining the weights for criteria .
roup IV).
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PIV (Proximity Indexed Valu.
is a method that belongs to group I, this method has an advantage of minimizing rank reversal .
, .
, .
, .
PSI (Preference Selection Inde.
is a method that belongs to group II, this method is known to be the method that can be combined with many data normalization methods.
Which means when using many data normalization methods to combine with it, it still find the same best option .
Another advantage of the PSI method is that because it does not need to determine the weights for criteria so this method is very useful in solving problems where there is a conflict about the importance of criteria .
, .
FUCA (Faire Un Choix Adyqua.
is a method that belongs to group i and is known to have a simpler algorithm than other methods .
In some studies, it was found that the best option determined by the FUCA method does not depend on the weights of criteria .
CURLI (CRiteria Importance Through Intercriteria Correlatio.
is the only method that belongs to group IV.
The significant advantage of this method is when using it, it is not necessary to normalize data and determine the weights for criteria .
, .
, .
, .
, .
These four methods are confirmed to be equally effective as other methods in many different cases.
In table 1, a summary of some contents related to this statement is presented.
Table 1.
Some MCDM methods that were confirmed to be equally effective in each case MCDM methods PIV.
ARAS (Additive Ratio ASsessmen.
MOORA (Multi Objective Optimization on the basis of Ratio Analysi.
MABAC (Multi-Attributive Border Approximation area Compariso.
PIV.
AHP (Analytic Hierarchy Proces.
COPRAS (COmplex PRroportional ASsessmen.
WEDBA (Weighted Euclidean Distance Based Approac.
PIV.
SAW.
MAUT (Multi Attribute Utility Theor.
PIV.
TOPSIS.
WASPAS.
COPRAS Cases for application Ref.
Choosing location to build garment factory in Tyrkiye .
Choosing online learning website .
Identify the Country worst affected by the Covid 19 pandemic Choosing location to build warehouse Choosing personnel for manager PSI.
SAW
PSI.
CODAS (COmbinative Distance- Choosing personnel of textile company based Assessmen.
in Denizli Choosing the Country with the best PSI.
EDAS
tourism potential Choosing air conditioner, washing FUCA.
CURLI
machine, drone Choosing metal grinder, metal drilling FUCA.
CURLI
machine, metal milling machine CURLI.
PROMETHEE
(Preference Choosing material to manufacture Ranking Organization Method for protective panel on car Enrichment Evaluatio.
EDAS
CURLI.
EDAS.
TOPSIS.
PROMETHEE
Choosing material to manufacture gear CURLI.
VIKOR
Choosing material for cutting tool CURLI.
CRADIS (Compromise Ranking of Choosing wood milling machine, wood Alternatives from Distance to Ideal sawing machine, wood planer Solutio.
CURLI.
VIKOR.
TOPSIS
Choosing grinding wheel CURLI.
TOPSIS
Choosing supplier Teknomekanik.
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Thus, it can be seen that the four methods PIV.
PSI.
FUCA, and CURLI have been confirmed to be as effective as other MCDM methods in many different cases.
However, there was no document that has been proceeded to compare these four methods.
This study has been performed to fill this When using two methods PIV and FUCA, the determination of the weights for criteria is necessary.
However, the weights for criteria also have a great influence on the ranks of alternatives .
, .
For the comparison between PIV method and FUCA method to be general, two different weighting methods have been used.
MEAN weight is the first method to be used.
According to this method, all criteria have the same weight.
It is the simplest method among weighting methods .
, .
, .
PSI and CURLI are two methods that do not need to calculate the weights for criteria, so the combination of the MEAN weight method with two methods PIV and FUCA to compare with PSI and CURLI is considered a suitable approach.
The second weighting method that has been used is the CRITIC (CRiteria Importance Through Intercriteria Correlatio.
This is the weighting method for criteria that consider the correlation between criteria .
, .
, .
, .
, .
For plastic injection molding machine, many parameters have correlation with each other.
For example, the diameter size of screw is related to the maximum pressing force, or spindle motor power is related to maximum pressing force, or the diameter size of screw is related to spindle moter power, etc.
Therefore, the application of the CRITIC method is considered to be suitable to calculate the weights for criteria that are correlated with each other of plastic injection molding The plastic injection molding machine has been chosen as the subject of this study because selecting an appropriate plastic injection molding machine is crucial for plastic manufacturing A precise injection molding machine not only enhances productivity but also ensures the quality of the final products.
This is because a suitable plastic injection molding machine can optimize the manufacturing process, minimize material waste, and maximize operational efficiency.
Additionally, plastic injection molding machine can be utilized in various applications such as plastic packaging production, shaping industrial products, and even in the medical field.
Therefore, searching for and selecting the right plastic injection molding machine is a crucial step for the success of a plastic manufacturing business.
This study aims to achieve two goals.
The first objective is to compare the effectiveness of four methods: PIV.
PSI.
FUCA and CURLI, when used to select plastic molding machines.
The second objective is to identify the best plastic injection molding machine among the five available types.
The motivation of this research is to broaden the understanding of the effectiveness of MCDM methods.
The results of the study will provide a solid foundation for users when deciding to employ a specific MCDM method to solve a particular problem.
Material dan methods Block diagram of the process Determining the best type of plastic injection molding machine is conducted as illustrated in Figure From the information about various types of molding machines, two MCDM methods without using criteria weights .
ncluding PSI and CURLI) will be employed to rank the alternatives.
Also, from the information about the machines, weighting criteria using two methods.
MEAN and CRITIC, will be performed.
Subsequently, two MCDM methods requiring criteria weighting .
ncluding PIV and FUCA) will be utilized to rank the alternatives.
A summary of the steps applying each method is presented in subsections 2.
2 through 2.
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Figure 1.
Block diagram of the process for determining the best type of plastic injection molding The PIV method Let m be the number of alternatives to be ranked, n is the number of criteria of each alternative, yij is the value of criterion j of alternative i, with i= 1ym, j = 1yn, ranking the alternatives when using the PIV method is performed in the following sequence .
Step 1: Calculate the normalized values according to equation .
ycuycnyc = Oo Ocyco ycn=1 ycycnyc Step 2: Calculate the weighted normalized values of the criteria according to equation .
ycOycnyc = ycyc y ycuycnyc Step 3: Calculate the quantities ui according to two equations .
For the larger the better criteria, the formula .
will be used.
The equation .
will be used for the smaller the better ycycn = yuOmax Oe yuOycn ycycn = yuOycn Oe yuOmin Step 4: Equation .
is used to calculate the scores of alternatives.
di = Eu ui j =1 Step 5: Alternatives are ranked in ascending order of their score.
The PSI method The order of ranking alternatives when using the PSI method is as follows .
Step 1: Normalize data according to two equations .
The equations .
are applied respectively when criteria are the larger the better and the smaller the better.
Teknomekanik.
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June 2024 e-ISSN: 2621-8720 p-ISSN: 2621-9980 ycuycnyc = yc ycoycaycu yc ycycycoycnycu ycuycnyc = .
ycycnyc Step 2: The average of normalized data is calculated according to equation .
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Step 3: The quantities Aj.
EIj.
Aj are calculated according to equations .
, .
yucyc = Ocycuycn=1.
cuycnyc Oe yc.
OIyc = .
Oe yucyc ] AyeU = OIyeU Ocyea yeU=ya OIyeU Step 4: Equation .
is used to calculate the scores for alternatives.
yco ycEycIyayc = Oc ycuycnyc .
Ayc yc=1 Step 5: The descending order of the scores of alternatives is the ranks of the alternatives.
The FUCA method To rank the alternatives when using the FUCA method, the following sequence must be followed .
Step 1: Rank the alternatives for each criterion.
Let rij be the rank of the alternatives, rij = 1 if the criterion j of the alternative i is the best.
Otherwise, rij = m if the criterion j of the alternative i is the worst.
Step 2: Equation .
is used to calculate the score of each alternative.
ycu ycycn = Oc ycycnyc .
ycyc yc=1 Step 3: The ranks of alternatives are determined in ascending order of their scores.
The CURLI method The sequence to apply the CURLI method is as follows .
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June 2024 e-ISSN: 2621-8720 p-ISSN: 2621-9980 Step 1: For each criterion, construct a square matrix of level m and score the alternatives.
The scoring of alternatives .
or each criterio.
is performed as follows.
For example, in the cell corresponding to column 1 and row 2, the value of the alternative 1 is better than that of the alternative 2, then score 1 in that cell.
Another example, if in the cell corresponding to column 2 and row 1, the value of the alternative 2 is worse that that of the alternative 1, then score -1 in that cell.
As another example, if in the cell corresponding to column 2 and row m, the value of the alternative 2 is equal to that of the alternative m, then score 0 in that cell, etc.
0 score will also be filled in the cells that lie in the main diagonal of matrix.
The scoring matrix for criterion j is denoted by the matrix Qi.
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Step 2: The scoring matrix of the alternatives for all the criteria will be formed by adding all the matrices Qi together.
This matrix is called matrix Q, which means Q = Q1 Q2 A Qj A Qm.
Step 3: Arrange the matrix Q by repositioning the rows and columns so that the part above the main diagonal has no cells with positive score.
After rearranging, the alternative that is positioned in row 1 is considered the best alternative.
The weighting methods The MEAN weight method is the method where the weights of criteria are equal .
, 17, .
The CRITIC method is used to calculate the weights of criteria according to equations .
, .
, .
, .
, .
yayc = yuayc Oc.
Oe ycycnyc ) .
yc=1 ycOyc = yayc Ocycuyc=1 yayc Where: Aj and rij are the standard deviation of criterion j and the correlation coefficient between the two criteria, respectively.
Types of plastic injection molding machine Five types of plastic injection molding machine have been chosen for ranking with product codes JSW J350EII-SPA ANBE-002-02.
Meiki M-200B-SJ.
Meiki M-350C-DF-Sj.
JSW J350E II, and JSW J550E-C5.
These five types of machine have been denoted by the letters A.
D and E.
To rank the machine types, ten criteria have been used to describe each product type including the minimum height of the mold that can be mounted on the machine .
, the maximum height of the mold that can be mounted on the machine .
, the screw diameter .
, the mold pressing force .
, the pressing stroke .
, the width of the base plate .
, the length of the base plate .
, the spindle motor .
W), the maximum mold opening .
, and selling price .
illion Vietnam don.
These ten criteria are denoted by the symbols from C1 to C10, respectively.
C1 and C10 are the smaller the better criteria, the remaining eight criteria are the larger the better criteria.
The minimum and maximum mold heights that the machine can accommodate determine its capability to work with molds of varying sizes.
The diameter of the screw directly impacts the plastic molding efficiency, while the mold clamping force dictates the machine's ability to precisely inject plastic into the mold.
The stroke length needs to be determined to ensure the machine can effectively handle different sizes and shapes of products.
The size of the mold base plate must be compatible with both the mold and the machine to avoid mismatch or Teknomekanik.
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The main axis motor needs to be sufficiently powerful to ensure stable and efficient machine operation, especially when dealing with large-sized molds or highpressure plastic molding requirements.
The maximum mold opening distance needs to be determined to ensure the machine can accommodate large-sized molds and adjust the opening distance flexibly.
Finally, the cost is crucial for evaluating the feasibility and economic viability of investing in an injection molding machine.
In table 2, the information of five types of plastic injection molding machine has been presented.
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Table 2.
Types of plastic injection molding machine Alt.
C10
We can see that machine B has two criteria C1 and C10 are the best.
machine C has two criteria C6 and C7 are the best.
machine E has six criteria C2.
C3.
C4.
C5.
C8.
C9 are the best.
Two machines A and D do not have any best criteria.
Thus, the best machine type will not be found only base on observing the data in table 2.
The best machine type can only be found when using multi-criteria decision-making methods to rank the machine types.
Four methods PIV.
PSI.
FUCA and CURLI will be used to perform this task, respectively.
To apply both PIV and FUCA methods, it is necessary to calculate the weights for the criteria first.
Results and discussion Determination of the wights for criteria According to the MEAN weight method, each criterion will have a weight of 0.
To calculate the weights of the criteria according to the CRITIC method, the determination of the correlation coefficients between two criteria have been calculated online, the results are summarized in table Table 3.
Correlation coefficients between the criteria
Citeria
C10
C10
The standard deviations of the criteria have also been calculated.
The Ci values and wj weights have also been calculated according to the formulas .
All the data have been summarized in Teknomekanik.
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Some parameters in the CRITIC method
Application of the PIV method
C10
Apply the formula .
, the normalized data have been calculated as shown in table 5.
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Table 5.
Normalized values in the PIV method Alt.
C10
The formula .
has been applied to calculate the weighted normalized values of the criteria.
First, the weight set of the criteria which was calculated by the MEAN weight method will be used, the results are summarized in table 6.
Table 6.
The weighted normalized values of the criteria Alt.
C10
Two formulas .
have been applied to calculate the values of uij.
The scores of the alternatives have been calculated according to the formula .
All the values that were calculated and the ranks of the alternatives have been summarized in table 7.
Table 7.
Values of uij, scores di and ranking the alternatives by the PIV method when the weights of the criteria have been calculated by the MEAN weight method Alt.
Rank
C10
Following the same procedure, the scores have been calculated and the alternatives have been ranked when the weights of the criteria have been calculated by the CRITIC weight method, as shown in table 8.
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Values of uij, scores di and ranking the alternatives by the PIV method when the weights of the criteria have been calculated by the CRITIC weight method Alt.
Rank
C10
Application of the PSI method A The Author.
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The two formulas .
have been applied to calculate the normalized data.
The data has been summarized in table 9.
Table 9.
Normalized values in the PSI method
C10
Alt.
The formulas .
, .
, .
have been applied to calculate the values of Aj.
EIj vy Aj.
The results have been summarized in table 10.
Table 10.
Some parameters in PSI
Parameters Aj
EIj
C10
The scores of the alternatives have been calculated according to the formula .
The scores of PSIi and the ranks of the alternatives have been presented in table 11.
Table 11.
Scores and ranks of the alternatives Alt.
Aj * nij
PSIi Rank
C10
Application of the FUCA method The results of ranking the alternatives for each criterion are in table 12.
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Ranking the alternatives for each criterion Alt.
C10
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Apply the formula .
to calculate the score of each alternative.
In two tables 13 and 14, the scores and ranks of the alternatives when the weights of the criteria are calculated according to two different methods are presented, respectively.
Table 13.
Ranking the alternatives when the weights of the criteria are calculated according to the MEAN weight method Alt.
C10
Rank Table 14.
Ranking the alternatives when the weights of the criteria are calculated according to the CRITIC method Alt.
Rank
C10
Application of the CURLI method The ten tables in the appendix section, from Table A1 to Table A10, represent the scoring results of the options based on each criterion.
Add the matrices Q1.
Q2.
A Q10 together, we get the matrix Q as shown in table 15.
Table 15.
Matrix Q Alt.
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The results are presented in table 16.
We notice that all cells with negative values lie above the main diagonal of the matrix.
In contrast, all the cells with positive values lie below the main diagonal of the matrix.
Thus, the swapping of rows and columns has ended.
The results of ranking the alternative have also been presented in the last column of table 16.
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Table 16.
Matrix Q after rearranging Alt.
Rank Summary of the results of ranking the plastic injection molding machine when using different methods have been presented in the chart in figure 2.
Figure 2.
Ranking the plastic injection molding machines It can be seen that in every cases.
E is always determined to be the best alternative.
Which means the four methods PIV.
PSI.
FUCA, and CURLI are equally effective.
To reinforce this statement, the ranking of plastic injection molding is further performed with different scenarios.
Generating various scenarios to assess the stability of ranking options is necessary because multiple studies have shown that when the number of options to be ranked changes, the rankings of the options may change as well.
Even an option considered the best can become the worst if any option is removed from the list of options to be ranked .
, .
, .
Four scenarios have been performed, each scenario will remove one option from the list of alternatives to be ranked.
This is how to create different scenarios that have been used in many studies .
In figure 3 to 6, the results of ranking plastic injection molding machines in four different scenarios are presented.
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Teknomekanik.
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Ranking the plastic injection molding machines after removing alternative A from the After removing A from the list of alternatives, we see that there is only one exchange in the ranks of two alternatives B and D when using the PIV method .
Thus, in this case, we also notice that the four methods PIV.
PSI.
FUCA, and CURLI are equally effective because all of them determine E to be the best alternative.
Figure 4.
Ranking the plastic injection molding machines after removing alternative B from the For the scenario where B is removed from the list of alternatives, an extremely perfect result has occurred, that is the ranks of the alternatives are completely the same when using different methods .
Of course, in this case, we also find that the four methods PIV.
PSI.
FUCA and CURLI are equally effective.
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Teknomekanik.
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Ranking the plastic injection molding machines after removing alternative C from the In the scenario where C is removed from the list of alternatives, the alternatives that is ranked the 1st is completely the same when using different methods .
In this scenario, we also find that the four methods PIV.
PSI.
FUCA and CURLI are equally effective.
Figure 6.
Ranking the plastic injection molding machines after removing alternative D from the After removing D from the list of alternatives, the ranks of the remaining alternatives are also quite similar when using different methods .
In particular, the alternatives that are ranked the 1st and the 2nd are completely the same.
Thus, in this case, once again, we see that the four methods PIV.
PSI.
FUCA and CURLI are equally effective.
All the statements above are enough for us to have a solid conclusion that the four methods PIV.
PSI.
FUCA and CURLI are equally effective in the selection of the best plastic injection molding machine.
In addition, by observing five figures above, we can also make the following comments:
- The combination of the PIV method and the MEAN weight method shows that the ranking results are completely the same with when using the PSI method.
- The best alternative determined when using the PIV method does not depend on the weights of the criteria.
This is also found in some previous studies .
, .
- When using the FUCA method to rank the alternatives, the best alternative does not depend on the weights of the criteria.
This is also confirmed in some previous studies .
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Published by Universitas Negeri Padang.
This is an open-access article under the: https://creativecommons.
org/licenses/by/4.
Four MCDM methods with different characteristics are used simultaneously for the first time in this study which are the PIV method, the PSI method, the FUCA method and the CURLI method.
All these four methods are used to rank the plastic injection molding machines.
In which the PIV method and the FUCA method are used to combine with two different weighting methods.
Some conclusion are drawn as follows:
- Four methods including PIV.
PSI.
FUCA and CURLI are confirmed to be equally effective in making multi criteria decision to select plastic injection molding machine.
- When using the two methods PIV and FUCA to rank the alternatives, the best alternative to be found does not depend on the weights of the criteria.
- JSW J550E-C5 is confirmed to be the best type of plastic injection molding machine among five types of machines including JSW J350EII-SPA ANBE-002-02.
Meiki M-200B-SJ.
Meiki M350C-DF-Sj.
JSW J350E II, and JSW J550E-C5.
- Two methods have been used to calculate the weights for the criteria in this study, both of which are objective methods (MEAN and CRITIC).
This means that the opinions of decision-makers .
lastic buyer.
regarding the importance of the criteria have not been taken into account.
If one wants to consider the opinions of decision-makers on the importance of the criteria while still ensuring objectivity, it is necessary to use combined weighting methods.
Combined weighting methods are methods that combine both objective and subjective factors.
This means that weighting the criteria takes into account the opinions of decision-makers while still ensuring Some methods of this type include PIPRECIA .
and CIMAS .
- To be able to conclude whether these four methods are equally effective when they are applied in other cases, other surveys must be conducted.
Other cases can be understod as determining the weights when using other methods, or ranking other types of product .
, or the number of criteria is changed, etc.
Of course, the ways that have been used in this article can also be repeated.
Author contribution Do Duc Trung conceived the idea.
Branislav DudiN and Duong Van Duc performed calculations and analysis.
Nguyen Hoai Son drafted the initial version of the paper.
Aleksandar Aonja and Do Duc Trung provided feedback on the article.
All authors approved the final version.
Funding statement This research received no specific grant from any funding agencies in the public, commercial, or not-for-profit sectors.
Acknowledgements The manuscript has no acknowledgment.
Competing interest The authors declare no competing interest.
References