Issue 
Manufacturing Rev.
Volume 9, 2022



Article Number  3  
Number of page(s)  13  
DOI  https://doi.org/10.1051/mfreview/2022003  
Published online  01 February 2022 
Research Article
Multicriteria decision making under the MARCOS method and the weighting methods: applied to milling, grinding and turning processes
Faculty of Mechanical Engineering, Hanoi University of Industry, Vietnam
^{*} email: doductrung@haui.edu.vn
Received:
14
October
2021
Accepted:
15
January
2022
The efficiency of cutting machining methods is generally evaluated through many parameters such as surface roughness, material removal rate, cutting force, etc. A machining process is considered highly efficient when it meets the requirements for these parameters, such as ensuring small surface roughness, high material removal rate, or small cutting force, etc. However, for each specific machining condition, sometimes the objective functions give contradictory requirements. In this case, it is necessary to implement multicriteria decision making, i.e., make a decision to ensure harmonization of all required objectives. In this paper, a multicriteria decisionmaking study is presented for three common machining methods: milling, grinding, and turning. In each machining method, the weights of the criteria were determined by four different methods, including Equal weight, ROC weight, RS weight and Entropy weight. The MARCOS method was applied for multicriteria decision making. The best alternative was found to be the same as the weights were determined using the Equal weight and Entropy weight methods. In the remaining two weighting methods, the best alternative found depends on the order where the criteria were arranged, not these methods themselves. Direction for further research has been suggested in this study as well.
Key words: Multicriteria decision making / MARCOS method / multicriteria / weight
© D. Duc Trung, Published by EDP Sciences 2022
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
1 Introduction
In practice, the need to ensure multiple criteria simultaneously is always a requirement for machining processes. For example, when processing by cutting methods, it often requires small surface roughness, significant MRR, long tool life, small cutting force, etc. However, the above requirements are not always achieved at the same time, but sometimes they contradict each other. For example, the highspeed turning process to increase productivity often reduces tool life [1], or when grinding, the increase of the cutting depth to increase cutting productivity leads to the rise of the cutting force, the wheel wear rate as well as the spindle vibration [2]. In this case, it is necessary to carry out decisionmaking to ensure the harmonization of the set goals.
In practice, milling, turning, and grinding are three common machining methods. These methods account for a large volume in manufacturing mechanical products. Also, machines for the mentioned machining types are available [3]. As a result, there have been many studies with the use of different mathematical tools on multicriteria decision making when implementing these machining methods.
There have been a number of multicriteria decisionmaking methods that have been used to make multicriteria decisions for milling processes such as: using the RIM method to solve the multiobjective optimization problem of steel milling SKD11 to ensure simultaneously minimum surface roughness and cutting force, and maximum MRR [4]; the TOPSIS method is used when milling Ti6Al4V alloy to ensure the minimum surface roughness and maximum MRR [5]; using the PIV method to ensure the minimum surface roughness and the maximum MRR simultaneously when milling SCM440 steel [6]; the MOORA method was used to provide simultaneous surface roughness and three components of cutting force, and maximum MRR when milling Ti6Al4V alloy [7]; the TOPSIS method and the WASPAS method were applied for getting simultaneously the minimum surface roughness and dimensional deviation, and the maximum MRR when milling steel EN31 [8]; the VIKOR method has been applied to simultaneously optimize the minimum surface texture and three cutting force components, and the maximum MRR when milling aluminum alloy AA3105 [9], etc.
With the grinding method, several studies have been done in multicriteria decision making. The works include using TOPSIS method to ensure simultaneously the minimum surface roughness, the minimum wheel shaft vibration, and the maximum MRR when grinding DIN 1.2379 steel [2]; applying the MOORA method and COPRAS method to get both the minimum surface roughness, and the maximum MRR when grinding SKD11 steel [10]; using the PSI method to ensure the minimum values of two surface texture parameters (Ra, Rz), and the maximum MRR when grinding SCM400 steel [11], etc.
Multicriteria decision making methods have also been applied for optimization of the turning process. Some results can be listed as follows: the TOPSIS method was used to ensure the minimum surface roughness and the maximum MRR simultaneously when turning EN8 steel [12]; the VIKOR method was used to ensure simultaneously the minimum surface roughness, the minimum workpiece vibration and cutting force, and the maximum MRR when turning EN 10503 [13]; the VIKOR method was applied to ensure simultaneous the minimum surface roughness, the minimum cutting power, and the maximum MRR when turning AISI 1040 steel [14]; the MOORA method was used to ensure the minimum cutting force, and the minimum dimensional deviation when turning Al6026T9 aluminum alloy [15]; The COPRAS method was used to ensure that the cutting power, the workpiece vibration, and the surface roughness were minimum when turning ASTM A36 steel [16]. Moreover, the PSI method was applied to simultaneously ensure the minimum surface roughness and the maximum MRR when turning EN24 [17]; the WASPAS method was used to ensure simultaneously the minimum surface roughness, the minimum cutting heat, the minimum cutting energy, and the tool wear, and the maximum MRR when turning AISI D3 [18] steels, etc.
From the above analysis, it can be seen that multicriteria decision making methods (TOPSIS, VIKOR, MOORA, etc.) have been exploited a lot in multicriteria decision making for milling, turning, grinding processes. This proves the great role of these methods in multicriteria decision making of machining processes. Therefore, it is very necessary and useful to apply a certain new method to make multicriteria decisions for mechanical processing processes.
MARCOS is a multicriteria decisionmaking method first proposed in 2020 [19]. Although it has only been published for a short time, this method has been applied in a number of studies such as: selection of intermediate models of transport between countries in the Danube region [20]; solving multiobjective problems to reduce risks in road traffic [21]; selection of loading/unloading machines in small warehouses [22]; selection of employees for a shipping company [23]; cost calculation in construction [24]. However, up to now, there have been no studies applying the MARCOS method to multicriteria decision making for cutting methods. This is the first reason why this study was chosen.
Most multicriteria decisionmaking methods require weighting of criteria (except for a few methods such as PSI [25], CURLI [26]). However, for each different weighting method, the criteria also have different weights. In addition, the weight of the criteria greatly affects the ranking of alternatives [27]. Therefore, if only one weighting method is used to implement multicriteria decision making, the best solution may not be the best. Therefore, to ensure that an alternative is the best, multicriteria decision making is required when the weights of the criteria are determined by several different methods. Besides, determining the weight according to the Entropy weight method has been used in many studies, and is considered a method with high accuracy [28,29]. Therefore, this method along with three weight determination methods including Equal weight, ROC weight, and RS weight are selected to solve the multiobjective optimization problem. The application of all four methods of determining weights will increase the reliability of multicriteria decision making. This is the second reason for conducting this study.
In fact, there is a method to determine the weight where the weight of the criteria does not depend on the ordering of the criteria. In addition, there are methods where the weight of the indicators depends heavily on the ordering of the indicators (this issue will also be clarified in the next section). This is the third reason for doing this study.
From the above analysis, in this study, the MARCOS method will be applied for multicriteria decision making for a milling process, a grinding process, and a turning process. In each case, the weight of the criteria is also determined by four different methods. In which, the data of the milling process is carried out by the experimental process of the author of this study, while the data of the grinding process and the turning process are obtained from published studies. The main objective of this study is to determine the stability of finding the best solution using the MARCOS method for different weighting methods as well as for the order of the criteria. This is also the reason why all three methods of milling, turning and grinding have been mentioned in this study.
2 The MARCOS method
The steps to implement multicriteria decision making according to the MARCOS method are as follows [19]:
Step 1: Building the initial matrix according to the following formula:$$X=\left[\begin{array}{ccc}\hfill {x}_{11}\hfill & \hfill \cdots \hfill & \hfill {x}_{1n}\hfill \\ \hfill {x}_{21}\hfill & \hfill \cdots \hfill & \hfill {x}_{2n}\hfill \\ \hfill \vdots \hfill & \hfill \cdots \hfill & \hfill \vdots \hfill \\ \hfill {x}_{m1}\hfill & \hfill \cdots \hfill & \hfill {x}_{mn}\hfill \end{array}\right]$$(1)where, m is the number of options, n is the number of criteria, x_{mn} is the value of the n criterion in m.
Step 2: Constructing an expanded initial matrix by adding an ideal alternative (AI) and the antiideal alternative (AAI).$$X=\begin{array}{c}\hfill AAI\hfill \\ \hfill {A}_{1}\hfill \\ \hfill {A}_{2}\hfill \\ \hfill \vdots \hfill \\ \hfill {A}_{m}\hfill \\ \hfill AI\hfill \end{array}\left[\begin{array}{ccc}\hfill {x}_{aa1}\hfill & \hfill \cdots \hfill & \hfill {x}_{aan}\hfill \\ \hfill {x}_{11}\hfill & \hfill \cdots \hfill & \hfill {x}_{1n}\hfill \\ \hfill {x}_{21}\hfill & \hfill \cdots \hfill & \hfill {x}_{2n}\hfill \\ \hfill \vdots \hfill & \hfill \vdots \hfill & \hfill \vdots \hfill \\ \hfill {x}_{m1}\hfill & \hfill \cdots \hfill & \hfill {x}_{mn}\hfill \\ \hfill {x}_{ai1}\hfill & \hfill \cdots \hfill & \hfill {x}_{ain}\hfill \end{array}\right]$$(2)
In which: $AAI=\mathrm{\backslash rm\; min}\left(x{}_{ij}\right)$; i = 1, 2, …, m; j = 1, 2, …, n if j is the larger the better.
AAI = max(x_{ij}); i = 1, 2, …, m; j = 1, 2, …, n if j is the smaller the better.
AI = max(x_{ij}); i = 1, 2, …, m; j = 1, 2, …, n if j is the larger the better.
AI = min(x_{ij}); i = 1, 2, …, m; j = 1, 2, …, n if j is the smaller the better.
Step 3: Normalizing the expanded initial matrix according to the formula.$${n}_{ij}=\frac{{x}_{AI}}{{x}_{ij}}\text{if}j\text{is the smaller the better.}$$(3) $${n}_{ij}=\frac{{x}_{ij}}{{x}_{AI}}\text{if}j\text{is the lager the better.}$$(4)
Step 4: Building a normalized matrix taking into account the weights of the criteria, with the normalized value calculated according to the formula.$${v}_{ij}={n}_{ij}\cdot {w}_{j}$$(5)where w_{j} is the weight of the criterion j.
Step 5: Calculating coefficients K_{i}^{+} and K_{i}^{−} according to the formula.$${K}_{i}^{}=\frac{{S}_{i}}{{S}_{AAI}}$$(6) $${K}_{i}^{+}=\frac{{S}_{i}}{{S}_{AI}}$$(7)
In which: S_{i}, S_{AAI} and S_{AI} are the sum of the values of v_{ij}, x_{aai} and x_{ai}, respectively, where i = 1, 2, …., m.
Step 6: Calculate the functions f(K_{i}^{+}) and f(K_{i}^{}) according to the formula.$$f\left({K}_{i}^{}\right)=\frac{{K}_{i}^{+}}{{K}_{i}^{+}+{K}_{i}^{i}}$$(8) $$f\left({K}_{i}^{+}\right)=\frac{{K}_{i}^{}}{{K}_{i}^{+}+{K}_{i}^{i}}$$(9)
Step 7: Calculating the function f (Ki) according to the following formula and rank the alternatives.$$f\left({K}_{i}\right)=\frac{{K}_{i}^{+}+{K}_{i}^{}}{1+\frac{1f\left({K}_{i}^{+}\right)}{f\left({K}_{i}^{+}\right)}+\frac{1f\left({K}_{i}^{}\right)}{f\left({K}_{i}^{}\right)}}$$(10)
Ranking the alternatives according to the larger f (Ki) the better.
3 Method of determining the weight
3.1 Equal weight method
Equal weight method is used to calculate the weight according to the following formula [30].
In which, n is the number of objectives.
3.2 ROC weight method
In the ROC weight method, the weights of the objectives are calculated based on the following formula [31].$${w}_{j}=\frac{1}{n}{\displaystyle \sum _{k=1}^{n}}\frac{1}{k}$$(12)
3.3 RS weight method
In the RS weight method, the weight is determined by the following formula [31].$${w}_{j}=\frac{2\left(n+1i\right)}{n\left(n+1\right)}$$(13)
3.4 Entropy weight method
In the entropy weight method, the weights of the objectives can be found by the following steps [32].
Step 1. Determining the normalized values for objectives:$${p}_{\text{ij}}=\frac{{y}_{\text{ij}}}{m\text{+}{\sum}_{i=1}^{m}{y}_{\text{ij}}^{2}}$$(14)
where y_{ij} is the value of criterion j corresponding to test's run i; m is the number of experiments.
Step 2. Calculating the value of the Entropy measure for each criteria.$$\begin{array}{l}{e}_{\text{j}}={\sum}_{i=1}^{m}\left[{p}_{\text{ij}}\times {\text{ln}(\text{p}}_{\text{ij}})\right]\\ \left(1{\sum}_{i=1}^{m}{p}_{\text{ij}}\right)\times \mathrm{ln}\left(1{\sum}_{i=1}^{m}{p}_{\text{ij}}\right)\end{array}$$(15)
Step 3. Calculating the weight for each criteria.$${w}_{j}=\frac{1{e}_{j}}{{\sum}_{j=1}^{m}\left(1{e}_{j}\right)}.$$(16)
From the above formulas, it can be seen that, with the Equal weight method and the Entropy weight method, the weights do not depend on the order of the criteria. However, for the other two methods (ROC weight and RS weight), the weight depends on the order of the criteria.
The following example will illustrate that: There are two criteria C_{1}, and C_{2}. If the criteria are arranged in the order C_{1}, C_{2}, then when determining the weight for them by ROC weight method, the weight value of C_{1} is 0.75, the weight value of C_{2} is 0.25. If using the RS weight method, the weighted value of C_{1} is 0.6667, the weighted value of C_{2} is 0.3333. However, if the criteria are ranked in the order C_{2}, C_{1}, then according to the ROC weight method, the weighted value of C_{2} is 0.75, the weighted value of C_{1} is 0.25. If using the RS weight method, the weighted values of C_{2} are 0.6667, and of C_{1} are 0.3333. Thus, when using the ROC weight method and the RS weight method, the weight of the objectives depends on the ordering of the criteria. Does this issue affect the ranking of alternatives? This content will be clarified in the next part of the article.
4 Multicriteria decision making for milling
4.1 Milling experiment
It is very important to build the setup and conduct the experiment, as well as analyze its results. These things need to be done carefully because they will affect the accuracy of the experiment. However, the main purpose of this study is to determine the stability of the MARCOS method for different weighting methods. The experimental setup can be described as follows: SKS3 steel was used during the test. This is a widely used steel for making dies, cutters, etc. due to its high hardness, high wear resistance. Steel samples are available in length, width and height of 120 mm, 40 mm and 40 mm respectively. The cutting tool used in this study is a TiN coated cutter. This is a cutting tool with high hardness, wear resistance, high toughness, and low chipping rate during machining [33,34]. The cutter body has a diameter of 20 mm, on which two symmetrical cutting pieces are mounted. The experiment was designed according to the Taguchi method with four input parameters that are variable variables in each experiment. Each input parameter was selected with three levels of values as shown in Table 1 [34,35]. The experiments were performed on a 3axis CNC milling machine TXC540 (Taiwan).
The experimental matrix is shown in Table 2. The experiments were performed according to the experimental plan in this table. The MRR is calculated according to formula (17), where d is the tool diameter, v_{c} is the cutting speed, f is the feed rate, a_{r} is the cutting width, a_{p} is the depth of cut. The surface roughness was measured with an SJ201. The response values of the experiments have also been included in Table 2.$$MRR=\frac{1}{\pi \cdot d}\cdot 1000\cdot {v}_{c}\cdot f\cdot {a}_{r}\cdot {a}_{p}$$(17)
The purpose of the study is to determine the experiment to ensure the minimum Ra and maximum MRR simultaneously. However, the experimental results (Tab. 2) show that Ra has the smallest value in experimental run #8, but MRR has the largest value in run #3. Therefore, it is necessary to perform multicriteria decision making to determine the experimental run where Ra is considered to be “smallest” and MRR is considered “maximum”.
Input parameters.
Orthogonal matrix L9 and experimental results.
4.2 Determining the weights for the criteria
Formula (11) is used to determine the weights for the criteria according to the Equal weight method. The weight of each criterion is determined by 0.5.
Formula (12) is used to determine the weight of the criteria according to the ROC weight method. The weights of the criteria Ra, MRR were found to be 0.75 and 0.25, respectively.
Formula (13) is used to determine the weight of the criteria according to the RS weight method. The weights of the criteria Ra, MRR were found to be 0.6667 and 0.3333, respectively.
The weights for the criteria Ra and MRR according to the Entropy method are calculated according to the formulas (14) to (17) and the results are 0.6618 and 0.3382, respectively.
4.3 Applying the MARCOS method for multicriteria decision making
Formula (1) is used to determine the original matrix. This matrix is the last two columns in Table 2.
Formula (2) is used to build the expanded initial matrix. The results are presented in Table 3.
Formulas (3), (4) are used to determine the normalized matrix. The results are presented in Table 4.
Formula (5) is used to build a normalized matrix taking into account the weights of the criteria. In which, the weight of the criteria is determined by the equal weight method (i.e. w_{j} = 0.5, with j = 1÷2). The results are presented in Table 5.
Apply formulas (6), (7), (8), (9) and (10) to calculate the respective values K_{i}^{−}, K_{i}^{+}, f (K_{i}^{−}), f (K_{i}^{+}) and f (K_{i}). The results are presented in Table 6. The results of ranking the alternatives according to the value of f(K_{i}) have also been included in this table.
Proceeding in the same way, the alternatives corresponding to different weighting methods (ROC weight, RS weight, Entropy weight) are ranked as shown in Table 7.
The results in Table 7 show that, with different weighting methods, the ranking results of the alternatives are also different. This is in complete agreement with the comment in [27]. However, it is surprising to find that with all four different weighting methods, A_{8} is still determined to be the best solution, and A_{1} is still considered the worst solution. The data in Table 2 demonstrates that the MRR at A_{1} is significantly lower than that at other alternatives. Hence, it is appropriate to conclude that A_{1} is the worst alternative. In contrast, Ra at A_{8} is the lowest among the eight alternatives, while the MRR at A_{8} is only lower than the MRR at A_{3}. For that reason, A_{8} is considered as the best. This is explained by the fact that the MARCOS method considers the ideal solution (AI) and the antiideal solution (AAI). In addition, when the weight of the criteria is determined by the RS method and the Entropy method, the ranking order of the alternatives is completely identical.
Expanded initial matrix.
Normalized matrix.
Normalized matrix with weights.
Some parameters in MARCOS and ranking of alternatives.
Ranking of alternatives for different weighting methods
5 Multicriteria decision making for grinding process
In this section, the results of the steel grinding test SCM400 [11] were used. In this experiment, nine experiments with the Taguchi design were conducted. At each experiment, the part speed, feed rate, and depth of cut were changed. In addition, surface roughness (Ra, Rz) was measured and MRR was calculated with each experiment. The results of this experiment are presented in Table 8. In this study, the PSI method for multicriteria decision making was used. The purpose of this study is to identify one experiment out of a total of nine experiments where Ra and Rz are the smallest and the MRR is the largest. However, in this study, the author did not compare the MARCOS method and the PSI method, but determined the stability of the multicriteria decision making by the MARCOS method when using the identification methods assign different weights.
The weights of the criterias have been determined according to four methods including the Equal weight, the ROC weight, the RS weight, and the Entropy weight and the results are presented in Table 9.
With four sets of weights of the criteria as shown in Table 9, the MARCOS method is applied to rank the alternatives. The results obtained are presented in Table 10.
The ranking results of the alternatives in Table 10 show that, with different weighting methods, the ranking results of the options are also different [27]. However, with all four different weighting methods, A_{4} was determined to be the best solution. In addition, when using the Equal weight method, the ROC weight method, and RS weight method, A_{2} is the worst option. According to the data in Table 8, both Ra and Rz at A_{4} are the lowest among nine experiments. As a result, A_{4} is found as the best solution. On the contrary, Rz is the highest and Ra is also great (only lower than Ra at A_{6}) at A2. Therefore, it is appropriate to conclude that A_{2} is the worst option.
Weights of objectives corresponding to different weighting methods.
Ranking of alternatives for different weighting methods.
6 Multicriteria decision making for turning process
In this section, 6063 aluminum turning test results [36] were used. In which, twentyseven experiments were designed according to the Taguchi method with input parameters as part speed, feed amount, depth of cut, and percentage of TiC additive in lubricant. At each experiment, surface roughness (Rz), cutting force (Fc), and MRR were calculated. The obtained results are shown in Table 11. In this study, the WASPAS method and the MOORA method were also used for multicriteria decision making to determine the experiment that simultaneously ensures the largest MRR, Fc and Rz are the smallest. However, the comparison of the MARCOS methods, the WASPAS method, and the MOORA method was not performed, but only the stability assessment of multicriteria decisionmaking was carried out by the MARCOS method corresponding to the identified methods different weights.
Four methods Equal weight, ROC weight, RS weight and Entropy weight were again used to determine the weights for the criteria, and the results are presented in Table 12. The MARCOS method was also applied to rank the indicators. The plans and results are presented in Table 13.
The ranking results of the alternatives in Table 13 also show that, with different weighting methods, the ranking results of the alternatives are also different [27]. However, alternative A_{16} was determined to be the best option, and alternative A_{21} was still determined to be the worst option. From the data in Table 11, the MRR is remarkably high (only lower than the MRR at A_{18}) and the Fc and Rz at A_{16} by are fairly low at A_{16}. This contributes to the conclusion that A_{16} is the best alternative.
From the ranking results of the three machining processes (milling, grinding, turning) (Tables 7, 10 and 13), as well as from the content discussed about them, the MARCOS method always determines the best test for although the weights of the criteria are determined by different methods. Furthermore, although the number of experiments is different in the milling, grinding and turning cases, the best alternative in each case is defined to be the same using the different weighting methods. This is explained by the fact that the MARCOS method refers to the ideal and antiideal alternatives [19].
However, if the weights of the indicators are determined by the Equal weight method or the Entropy weight method, their values do not depend on the order of the criteria. However, with two methods ROC weight and RS weight, the result is different. The question is when the criteria are arranged in different order, will it make the ranking of the different criteria or not. Tables 14–16 present the ranking results of the plans for milling, grinding, and turning when the order of criteria is arranged in different ways.
Table 14 shows:
When the order of criteria is arranged in the order Ra to MRR, then A_{8} is considered the best option in both cases where the weight is determined by ROC weight method and RS weight method. According to experimental data in Table 2, A_{8} is the solution with the smallest Ra (Ra = 0.326 μm).
When the order of criteria is arranged in the order MRR to Ra, A_{3} is determined to be the best option. At A_{3}. In Table 2, the MRR also has the largest value (MRR = 1145,916 mm^{3}/min).
This is considered as the result of ranking the options that have oriented towards the priority for the criterion ranked in the top position. Specifically, when the criteria are arranged in the order Ra to MRR, the best solution is also the one with the smallest Ra. Besides, when the criteria are arranged in order of MRR to Ra, the best solution is also the one with the largest MRR. It is easy to see that the best solution depends on the ordering of the criteria, not on the weighting method.
From the Table 15, it was reported that:
When the criteria are arranged in the order Ra, Rz to MRR (column (1) and column (7)), then A_{4} is determined to be the best option. From Table 8, in run A_{4}, both Ra and Rz have the smallest value (Ra = 0.38 μm, Rz = 1.77 μm).
When the criteria are arranged in the order Ra, MRR to Rz (column (2) and column (8)), A_{5} is determined to be the best solution with which Ra is very small (Ra = 0.42 μm), and MRR is the largest (MRR = 141.277 mm^{3}/min).
In columns (3), (4), (9) and (10) are the results of ranking methods when Rz is selected as the first criterion. In all four cases, A_{4} is determined to be the best solution, and in this case, Rz also has the smallest value.
When MRR is selected as the first criterion (columns (5), (6), (11), (12)), then A_{3} is determined as the best option. At A_{3}, MRR also has the largest value.
Thus, from Table 15, it can be seen that the best solution is towards the one in which the first ranking criterion achieves the best results. Specifically, if Ra is sorted as the number one criterion, then the best alternative will have the smallest Ra, or if the sorted MRR is the number one criterion, the best alternative will have the largest MRR. In addition, the bestdetermined alternative depends on the ordering of the criteria and not on the weighting method.
From Table 16 it can be noted that:
In columns (1), (2), (7) and (8), when MRR is selected as the number one indicator, A_{16} is the best option. From Table 11 it can be seen that in this alternative, the MRR also has the largest value (MRR = 6924 mm^{3}/min).
In columns (3), (4), (9) and (10), when Rz is selected as the first indicator, A_{11} is considered the best option. In this option, Rz also has the small value among the total of 27 solutions. Rz in plan A_{11} is equal to 4.01 μm, only a very small amount greater than Rz in plans A_{7}, A_{10}, A_{22}.
When Fc is ranked as the number one criterion (column (5), (6), (11), (12)), A_{11} is also determined to be the best option. In this alternative, Fc also has the smallest value among the total of 27 options, Fc = 110 (N).
The solution is determined to be the best depending only on the ordering of the criteria, not on the weighting method. This can also be due to the issue of mentioning the ideal alternative under the MARCOS method.
Weights of criteria corresponding to different weighting methods.
Ranking of alternatives for different weighting methods.
Ranking of alternatives of milling according to the arrangement of criteria.
Ranking of alternatives of grinding process according to the arrangement of criteria.
Ranking of alternatives of turning process according to the arrangement of criteria.
7 Conclusions
In this study, multicriteria decision making for three different machining processes including milling, grinding and turning was performed. In each process, the weights of the indicators were determined according to four methods including the Equal weight method, the ROC weight method, the RS weight method, and Entropy weight method. The MARCOS alternative was first applied to multicriteria decision making for mechanical processing. The effect of ordering the criteria on decision making to choose the best option has also been carefully considered, and some very interesting issues have been discovered. Some conclusions are drawn after applying all three machining methods as follows:
When the weights of the criteria are determined by the Equal weight method and the Entropy weight method, the weighted values of the alternative do not depend on the ranking order of the criteria and the best solution is always indicated systematically between the two methods.
When the weights of the alternatives are determined by methods where the value of the weights depends on the arrangement of the criteria (the ROC weight, and the RS weight criteria), the best solution is determined depending on the sort order of the criteria. When the same ordering of the criteria, the best solution is determined uniformly for both methods.
When using two methods including the ROC weight method and the RS weight method, if the best alternative is to give priority to any criteria, that criteria need to be ranked at the first position in the order of ranking criteria.
By referring to the ideal alternative, it appears that the MARCOS method always determines the best solution when the different weighting methods are used.
Evaluation of the stability of the alternative rank using the different weighting methods as well as comparison of the MARCOS method with other multicriteria decision making methods, such as TOPSIS, MOORA, VIKOR, etc. are necessary to be carried out in the future.
Abbreviations
MARCOS: Measurement Alternatives and Ranking according to COmpromise Solution
TOPSIS: Technique for Order of Preference by Similarity to Ideal Solution
MOORA: Multi Objective Optimization on the basis of Ratio Analysis.
WASPAS: Weighted Aggregated Sum Product ASsessment
VIKOR: Vlsekriterijumska optimizacija I KOmpromisno Resenje
COPRAS: COmplex Proportional ASsessment.
PSI: Preference Selection Index
CURLI: Collaborative Unbiased Rank List integration
Ra: The arithmetical mean deviation of the assessed profile
Rz: The minimum value of the profile maximum height
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Cite this article as: Do Duc Trung, Multicriteria decision making under the MARCOS method and the weighting methods: applied to milling, grinding and turning processes, Manufacturing Rev. 9, 3 (2022)
All Tables
Ranking of alternatives of grinding process according to the arrangement of criteria.
Ranking of alternatives of turning process according to the arrangement of criteria.
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