Multi criteria decision making for process parametric optimization of a milling process using the marcos method and different weighing methods

ABSTRACT

The cutting force, surface roughness, tool life, materials removal rate are generally evaluated by the efficiency of the cutting methods used in the industry. The machining process selected to machine a workpiece providing minimum surface roughness, maximum material removal rate, minimum cutting force, are considered to be highly efficient. However, in an industry, in specific the machining condition, the objective function gives contradictory requirements. In these cases, Multi Criteria Decision Making process is adopted to ensure equal importance for all the objective functions. In this paper, multi-criteria decision making study is presented for machining of steel using milling machine. The weights of the criteria are determined by four different methods, namely; equal weight, Rank Order Centroid (ROC) method, Rank Sum (RS) weighing method and Entropy weight. The Measurement Alternative and Ranking according to COmpromise Solution (MARCOS) method is applied for multi-criteria decision making. The best alternative is evaluated and the effects of ordering the criteria on decision making have been discovered.

Keywords:
MARCOS; Entropy method; ROC weight; RS Weight; Equal weight

1. INTRODUCTION

ARULDOSS et al. [¹] surveyed on multi-criteria decision making techniques and its applications. It is observed that AHP technique provides advantage with limited consistency whereas TOPSIS, ELECTRE methods the consistency is not controlled. He also recommended TOPSIS is exception in its simplicity and usage for larger number of alternatives. SUN et al. [²] discovered Optimal cutting parameters for Aviation workpiece by MCDM techniques. TOPSIS-ASIM (Adversarial Interpretive Structural Modelling) methods are combined to determine the best optimal cutting parameters. The errors are in the acceptable level between the original results and other relative errors and it is proved that the method is highly reliable. DUC TRUNG et al. [³] employed different weighting methods for analyzing the multi-criteria decision making techniques for milling, turning, grinding operations. It is observed that the weighting criteria plays a major role in the ranking of the alternatives and the ranking is not same for all approaches. Also it is concluded that Entropy method and equal weight method provides best ranking method in the implementation of multi criteria decision making technique. ÇALIŞKAN et al. [⁴] employed multi-criteria decision making technique for material selection for the tool holder working under hard milling conditions. VIKOR, TOPSIS and EXPROM2 are employed to rank the alternatives and weighting of the criteria is performed by compromised weighting method. It is concluded that the MCDM can be used a solution for a real time material selection problem. DAS and CHAKRABORTY [⁵] employed new MCDM tools, multi-attributive ideal-real comparative analysis (MAIRCA), multi-attributive border approximation area comparison (MABAC), measurement alternatives and ranking according to compromise solution (MARCOS) and compromise ranking of alternatives from distance to ideal solution (CRADIS) methods to optimize end milling process. Better results are predicted at optimal parameters based on level-averaging methods. AKULA and KHAN [⁶] optimized support structures and build orientation in masked stereo lithography for dental bridges using MAIRCA technique. The use of this MCDM result in overall 34% reduction in support structure compared to system generated structures. This improved the reduction in material up to 13% and 12% reduction in printing cost. Effective optimization of build orientation for dental bridges with minimal support structures is facilitated. AHIJITH KUMAR et al. [⁷] investigated tool wear and surface quality of hardened tool steel using fuzzy MARCOS analysis and Response surface methodology. The ranking of parameters using sensitivity analysis and a novel MEREC integrated fuzzy MACROS approach. Turning process parameters are studied and ANOVA analysis and regression models are carried out along with RSM approach to determine the optimal turning parameters. KUMAR et al. [⁸] used MARCOS technique for coating material selection in tooling industries. Seven Weight criteria change are tested and ranked appropriately to determine the best optimal coating material based on the result obtained from sensitivity analysis. KAMILLA et al. [⁹] employed MARCOS-based techniques to maximize resistance spot welding of dissimilar materials for stainless steel and aluminum alloy). The particle diameter and tensile-shear strength were most significantly influenced by the welding current. The optimized parameters were validated by confirmatory experiments. BISWAL et al. [¹⁰], BALRAJ et al. [¹¹], CHAKRABORTY and CHAKRABORTY [¹²], KALITA et al. [¹³], SHAMUGHASUNDAR et al. [¹⁴], ALI et al. [¹⁵] have employed Taguchi- MARCO method for optimization of multi objective optimization problems for several machining processes. The ranking of the parameters are done using sensitivity analysis and best optimal parameters are selected and validated.

2. EXPERIMENTAL METHODOLOGY

Experimental setup is an important task to be built for analyzing the results and determine the adequacy of MARCOS method for different weighing methods. Milling operation is performed on the SKS3 steel for conducting the experiments using TiN coated cutting tool. The cutting tool provides high harness, high wear resistance, low chipping rate and high toughness during the machining process. CNC milling machine shown in Figure 1 is used to perform the experiments. CNC milling machine is equipped with rigid spindle capable of operating at speeds 6000-8000 rpm and is driven by 7.5kW spindle motor. The machine provides precise motion along the x-axis, y-axis and z-axis with a working travel of 500 × 400 × 400 mm ensuring accurate control of cutting parameters. A tool holding system are stable machine table are provided to carry out the experiments with high precision and repeatability. The surface roughness is measured using Mitutoyo surface tester as shown in Figure 2. The work material and the 20 mm diameter milling cutter preferred for milling operation are shown in the Figure 3 and Figure 4 respectively. The cutting speed, feed rate, cutting width and depth of cut are considered as the process parameter in milling process.

Figure 1
CNC milling machine.

Figure 2
Surface roughness tester.

Figure 3
Work material.

Figure 4
End mill cutter.

Four input process parameters are selected with three levels as shown in the Table 1. The parameters are selected in such a way that these parameters can maximize the material removal rate and provide high quality, optimized tool life, process stability and high productivity. The previous researchers have selected these levels of process parameters and validated through several trial runs to validate whether these parameters meet the quality requirements. The levels for the factors are selected in such a way that they will ensure stable cutting conditions without inducing excessive tool wear. Lower levels indicates the conservative machining with safe operational limits. The cutting speed range of 80–120 m/min was chosen to have stable cutting conditions without excessive tool wear. The feed and the depth of cut are selected in appropriate ranges to ensure safe engagement of cutting tool and good surface integrity.

Table 1
Process parameters and its levels.

CUTTING PARAMETERS	LEVEL 1	LEVEL 2	LEVEL 3
Cutting speed (vc), m/min	80	100	120
Feed rate (f), mm/rev	0.05	0.1	0.15
Cutting width (a), mm	4	8	12
Depth of cut (d), mm	0.1	0.3	0.5

The surface roughness and material removal rate are measured as the responses. MRR is calculated according the formula given in Equation (1). Surface roughness is measured using a contact type surface roughness tester and three values are taken at multiple locations and the average value is recorded here. Taguchi experimental design is used in this work to conduct the experiments and here four input parameters are selected with three levels of each parameter. As per the Taguchi design, orthogonal matrix L9 is selected and nine experiments are conducted and the experimental data is presented in Table 2. L9 orthogonal array is primarily selected for saving the resources and efficiency, when dealing with three parameter and three levels. Also L9 orthogonal array are simpler to manage and analyze and it is best for limited number of factors is sufficient for the desired information. The objective of this study is to minimize the surface roughness and maximize the material removal rate simultaneously. The number of experiments are limited to maintain experimental feasibility and ensure reliable and repeatable measurements under controlled machining conditions. Since surface roughness and material removal rate are considered as the primary indicators of surface quality and productivity in machining applications, they are focused in this work. Also the other machining response such as cutting force, tool wear, vibration are also important in the assessment of process performance during the machining operations. However, incorporating all response will increase the complexity of the problem to achieve and effective balance between machining quality and efficiency. From the experimental data in Table 2, it is observed that the minimum surface roughness has the minimum value in experimental number #8 and maximum material removal rate has the maximum value in experimental number #3. This provides a contradictory decision and it is necessary to perform multi criteria decision making to find which experimental run will provide minimum surface roughness and maximum material removal rate simultaneously.

Table 2
Experimental data.

EXPT. NO	CUTTING SPEED, Vc, m/min	FEED RATE, f, mm/rev	CUTTING WIDTH, a, mm	DEPTH OF CUT, d. mm	SURFACE ROUGHNESS Ra (µM)	MRR (mm3/min)
1	80	0.05	4	0.1	1.254	145.763
2	80	0.1	8	0.3	2.147	368.224
3	80	0.15	12	0.5	1.549	968.364
4	100	0.05	8	0.5	0.985	526.267
5	100	0.1	12	0.1	0.589	265.321
6	100	0.15	4	0.3	1.254	399.247
7	120	0.05	12	0.3	1.691	312.251
8	120	0.1	4	0.5	0.495	219.368
9	120	0.15	8	0.1	1.264	375.364

(1) $$MRP=\frac{1}{\pi .d}1000\ast v_C\ast f\ast a\ast d$$

3. DETERMINATION OF THE WEIGHTS OF THE CRITERIA

3.1. Equal weight method

In equal weight method, the weights of each criterion are determined by the Equation (2).

(2) $$w_j=\frac{1}{n}$$

where n is the number of objectives.

In this study, two responses are studied and the weights of the criteria of the response for surface roughness and material removal rate are assigned as 0.5.

3.2. Rank order centroid method

In ROC method, the weights of the objectives are calculated based on the Equation (3)

(3) $$w_j=\frac{1}{n}{\displaystyle \sum {}_{k=1}^n}\frac{1}{k}$$

In this method, the important criterion assigns the highest weight and the least criterion assigns the least weight. The sum of the weights of all criterion is equal to 1. The weight drops non-linearly with rank in this method. In this study, there are two responses (n = 2) and the weights are measured for surface roughness and material removal rate. The weight of the criteria for surface roughness and material removal rate are found to be 0.75 and 0.25 respectively.

3.3. Rank sum weighing method

In RS method, the weights of the each criterion are determined by the Equation (4).

$$w_j=\frac{2\left(n+1-i\right)}{n\left(n+1\right)}$$

In this method, the weight drops linearly with rank. The highest criterion gets the largest weight and the lowest ranked criterion gets the smallest weight. In this study, weight of the criterion for surface roughness and material removal rate are found to be 0.667 and 0.333 respectively.

3.4. Entropy method

Entropy method weights of the each criterion are defined from the data dispersion. The larger weights to the criterion show more variation across the alternatives. The lower weights will have lesser information and all alternatives have the same values and unable to distinguish them. The criterions are normalized to compare them fairly. Entropy method does not depend on the order of the criteria. The weight of objectives corresponding to different methods are given in Table 3. TRANG et al. [¹⁶] observed that, these weights significantly influences the ranking stability of the alternatives when evaluated using various MCDM methodologies. TRUNG et al. [¹⁷] discussed that the machine selection is an important role and also a complex task, which involves several parameters which needs to considered optimally. MCDM methodologies and probability theory are used in appropriate selection of the machine tool to provide efficient production. TRUNG [¹⁸] discovered that the efficient material removal rate with low surface finish are typically a tedious combination and this leads to multi criteria decision making to determine the optimal cutting parameters. Several MCDM methodologies such as EDAS, MARCOS, PIV, MOORA and TOPSIS are used to determine the best alternate solutions for milling operations. DUC TRANG [¹⁹] used MCDM methodology in determining the minimum cutting force and maximum material removal rate. Entropy method is employed to determine the weights of the criteria and the best set of experiment is determined and validated. DUC TRANG [²⁰] conducted sixteen experiments in a turning process to determine the optimal combination of experiments providing minimum surface roughness and maximum material removal rate. Pareto Edgeworth Grierson (PEG), Preference selection index (PSI) and Collaborative Unbiased Rank List Integration (CURLI) are used for multi criteria decision making of the alternatives. SEKAR et al. [²¹] used MCDM technique in optimizing M-Sand material supplier selection in construction industry. The weight of each criterion are determined by Analytical Hierarchy Process (AHP) and fuzzy AHP and TOPSIS model is used to rank the alternatives. DEA model was used to integrate and balance the qualitative and quantitative sustainable suppliers. THIRUMALAI and SENTHILKUMAAR [²²] investigated the Multi Criteria Decision Making technique in the determination of optimal process parameters in turning operation. The four weighing methods viz., Equal weight method. ROC method, RS method and Entropy method are employed in this work to evaluate the robustness of the MARCOS decision by combining all perspectives. Four weighting methods are employed to ensure that the final ranking is stable and not depends on a single weighting philosophy.

Table 3
Weights of objective corresponding to different methods.

WEIGHTING METHODS	CRITERIA
	RA	MRR
Equal weight method	0.5	0.5
ROC weight	0.75	0.25
RS weight method	0.667	0.333
Entropy method	0.6618	0.3382

4. MULTI CRITERIA DECISION MAKING FOR MILLING PROCESS (MARCOS METHOD)

The objective of the study is to demonstrate the practical applicability of the machining parameters of a milling process using the MARCOS method and different weighting methods. This work demonstrates effective and systematic application of existing methods to practical machining problem characterized by conflicting performance objectives. The multiple criteria weighing schemes combined with MARCOS method examines the influence of variation in criteria with the decision outcomes. This comparative weighing analysis provides valuable insights to the industrialists for selection of economical and optimal machining conditions. Multi-criteria decision making is used to determine the best optimal solution among the several alternatives with several constraints. Common multi-criteria decision making techniques are classified as multi-attribute decision making and multi-objective decision making. Analytical Hierarchy Process (AHP), Technique for order preference by similarity to Ideal solution (TOPSIS), VIKOR, ELECTRE are the common methods of multi-criteria decision making. Measurement of Alternatives and Ranking according to the compromised solution (MARCOS) is a new MCDM technique used in this work to rank the alternatives. The ranking is done by comparing the alternatives with an ideal and anti-ideal solution. The steps followed in MARCOS are given in Figure 5.

Figure 5
Steps in MARCOS method for multi-criteria decision making.

5. RESULTS AND DISCUSSION

The Equation (2) is used to build the expanded initial matrix with ideal solutions (AI) and anti-ideal solutions (AAI). Equation (3) is used to build the normalized matrix and equation (3) is used to build the weighted normalized matrix by assigning weights to the each criteria as discussed above. In this work, the weights are assigned to each criterion using equal weight method, ROC method, RS method, Entropy method. The expanded initial matrix, normalized matrix and normalized weight matrix is presented in Tables 4–6 respectively.

Table 4
Expanded initial matrix.

EXPT. NUMBER	SURFACE ROUGHNESS	MATERIAL REMOVAL RATE
AAI	2.147	145.763
1	1.254	145.763
2	2.147	368.224
3	1.549	968.364
4	0.985	526.267
5	0.589	265.321
6	1.254	399.247
7	1.691	312.251
8	0.495	219.368
9	1.264	375.364
AI	0.495	968.364

Table 5
Normalized matrix.

EXPT. NUMBER	SURFACE ROUGHNESS	MATERIAL REMOVAL RATE
AAI	0.2306	0.1505
1	0.3947	0.1505
2	0.2306	0.3803
3	0.3196	1.0000
4	0.5025	0.5435
5	0.8404	0.2740
6	0.3947	0.4123
7	0.2927	0.3225
8	1.0000	0.2265
9	0.3916	0.3876
AI	1.0000	1.0000

Table 6
Normalized matrix with weights.

EXPT. NUMBER	EQUAL WEIGHT METHOD		ROC WEIGHT METHOD		RS WEIGHT METHOD		ENTROPY METHOD
	SURFACE ROUGHNESS	MATERIAL REMOVAL RATE	SURFACE ROUGHNESS	MATERIAL REMOVAL RATE	SURFACE ROUGHNESS	MATERIAL REMOVAL RATE	SURFACE ROUGHNESS	MATERIAL REMOVAL RATE
AAI	0.115277	0.075263	0.172916	0.037631	0.15378	0.05017	0.152581	0.050908
1	0.197368	0.075263	0.296053	0.037631	0.263289	0.05017	0.261237	0.050908
2	0.115277	0.190127	0.172916	0.095063	0.15378	0.126739	0.152581	0.128602
3	0.159781	0.5	0.239671	0.25	0.213147	0.3333	0.211485	0.3382
4	0.251269	0.27173	0.376904	0.135865	0.335193	0.181135	0.33258	0.183798
5	0.420204	0.136994	0.630306	0.068497	0.560552	0.091321	0.556182	0.092663
6	0.197368	0.206145	0.296053	0.103073	0.263289	0.137416	0.261237	0.139437
7	0.146363	0.161226	0.219545	0.080613	0.195248	0.107473	0.193726	0.109053
8	0.5	0.113267	0.75	0.056634	0.667	0.075504	0.6618	0.076614
9	0.195807	0.193813	0.29371	0.096907	0.261206	0.129196	0.25917	0.131095
AI	0.5	0.5	0.75	0.25	0.667	0.3333	0.6618	0.3382

The ranking of the alternatives with different weighting methods are calculated and presented in Table 7(a-d). The results in Table 7, shows that ranking of the alternatives are different for different weighting methods. It is observed that in RS, ROC and entropy method, experimental run 2 is the best optimal solution and experimental run 8 is the worst solution. However, in equal weight method, experimental run 3 is observed to be optimal best solution and experimental run 1 is observed as the worst solution. The experimental data in Table 2 demonstrates the MRR is significantly lower that all alternatives and hence it could be concluded experimental run 8 is the worst solution among all alternatives. In contrast, surface roughness at experimental run 8 is found to be lowest along all the alternatives while MRR at experimental run 8 is lower than MRR at experimental run 3.

Table 7(a)
Ranking of alternatives using equal weight method.

EXPT. NUMBER	MARCOS PARAMETERS					RANK
	Ki-	Ki+	f(ki-)	f(ki+)	f(ki)
1	0.101458833	0.272631	0.271215	0.728785	0.728785	1
2	0.14194439	0.305404	0.317302	0.682698	0.682698	2
3	0.579716496	0.659781	0.467703	0.532297	0.532297	9
4	0.41074612	0.522999	0.439891	0.560109	0.560109	6
5	0.452993443	0.557198	0.448423	0.551577	0.551577	7
6	0.263142097	0.403514	0.39472	0.60528	0.60528	5
7	0.144643788	0.307589	0.319844	0.680156	0.680156	3
8	0.52225735	0.613267	0.459926	0.540074	0.540074	8
9	0.24597955	0.38962	0.387004	0.612996	0.612996	4

Table 7(b) Ranking of alternatives using ROC weight method.

EXPT. NUMBER	MARCOS PARAMETERS					RANK
	Ki-	Ki+	f(ki-)	f(ki+)	f(ki)
1	0.156028	0.333684	0.318611	0.681389	0.681389	3
2	0.072804	0.267979	0.213638	0.786362	0.786362	1
3	0.353605	0.489671	0.419323	0.580677	0.580677	6
4	0.382861	0.512769	0.427477	0.572523	0.572523	7
5	0.618496	0.698803	0.469518	0.530482	0.530482	8
6	0.238917	0.399125	0.374454	0.625546	0.625546	5
7	0.113563	0.300158	0.274491	0.725509	0.725509	2
8	0.755077	0.806634	0.483494	0.516506	0.516506	9
9	0.228141	0.390617	0.368708	0.631292	0.631292	4

Table 7(c) Ranking of alternatives using RS weight method.

EXPT. NUMBER	MARCOS PARAMETERS					RANK
	Ki-	Ki+	f(ki-)	f(ki+)	f(ki)
1	0.138594	0.313459	0.306588	0.693412	0.693412	3
2	0.097262	0.280518	0.257458	0.742542	0.742542	1
3	0.430924	0.546447	0.440902	0.559098	0.559098	7
4	0.393134	0.516328	0.432271	0.567729	0.567729	6
5	0.563202	0.651872	0.463513	0.536487	0.536487	8
6	0.248062	0.400706	0.382359	0.617641	0.617641	5
7	0.125121	0.302722	0.292447	0.707553	0.707553	2
8	0.676918	0.742504	0.476897	0.523103	0.523103	9
9	0.235134	0.390403	0.375893	0.624107	0.624107	4

Table 7(d) Ranking of alternatives using entropy method.

EXPT. NUMBER	MARCOS PARAMETERS					RANK
	Ki-	Ki+	f(ki-)	f(ki+)	f(ki)
1	0.136402	0.312144	0.304098	0.695902	0.695902	3
2	0.09753	0.281183	0.25753	0.74247	0.74247	1
3	0.434633	0.549685	0.441557	0.558443	0.558443	7
4	0.392816	0.516378	0.432049	0.567951	0.567951	6
5	0.559127	0.648845	0.462864	0.537136	0.537136	8
6	0.24755	0.400673	0.38189	0.61811	0.61811	5
7	0.124645	0.302779	0.291618	0.708382	0.708382	2
8	0.671581	0.738414	0.4763	0.5237	0.5237	9
9	0.234483	0.390266	0.375324	0.624676	0.624676	4

To have logical consistency with the MARCOS Results, overall ranking is considered in the final decision. Experimental run A2 is considered as the best optimal solution and it achieves overall highest rank under ROC, RS and Entropy method. Since, single response optimization leads to misleading conclusions, the multiple performance characteristics are considered in this work and optimized simultaneously. As suggested by the reviewers, the results based solely on individual response values are not considered. Experimental run A2 achieves superior overall performance since it offers a balanced compromise among all the responses considered in this work. MARCOS framework, this balanced performance gives the closer proximity to the ideal best solution and a greater separation form the ideal worst solution. In this work different weighting criterions are used and experimental run A2 is considered as the best solution and it demonstrates the robustness and stability of the decision. Practical implications also indicate that the machining conditions of the experimental run A2 are more reliable and industry viable machining conditions leading to optimal overall process parameters. Experimental run A2 achieves highest rank under ROC, RS and Entropy weighting methods, demonstrating ranking stability despite different weighting philosophies. This confirms that there is a strong compromise between machining responses towards ideal best and ideal worst solutions.

The spearmen correlation coefficient are calculated between each method and presented here. The spearmen correlation coefficient between equal weigh method and ROC weight method is found to be 0.85 and it indicates a strong positive monotonic relationship between them. The spearmen correlation coefficient between ROC weigh method and RS weight method is 0.9833 and it indicates extremely strong positive monotonic relationship between them. The spearmen correlation coefficient between RS weight method and Entropy method is 1.0 and it indicates perfect positive monotonic relationship between them. The spearmen correlation coefficient between Entropy weight method and equal weight method is 0.9 and it indicates very strong positive monotonic relationship between them. The Spearmen correlation coefficient confirms that the MARCOS rankings are stable and insensitive to the choice of weighting method and it indicates strong robustness of the decision. This validates the experimental run A2 as the reliable optimal solution. This optimal solution is governed by the overall performance consistency rather than weighting method dependency.

6. CONCLUSION

Milling operation is performed on the SKS3 steel for conducting the experiments using TiN coated cutting tool. Multi Criteria Decision Making process is adopted to ensure equal importance for all the objective functions. In this work, multi-criteria decision making study is presented for machining of steel using milling machine. The weights of the criteria are determined by four different methods, namely; equal weight, ROC weight, RS weight and Entropy weight. The Measurement Alternative and Ranking according to COmpromise Solution (MARCOS) method is applied for multi-criteria decision making. It is observed that in RS, ROC and entropy method, A2 is the best optimal solution and A8 is the worst solution. However, in equal weight method, A3 is observed to be optimal best solution and A1 is observed as the worst solution. The experiments are validated and the results are found to satisfactory.

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Publication Dates

• Publication in this collection
  23 Feb 2026
• Date of issue
  2026

History

• Received
  09 Oct 2025
• Accepted
  15 Jan 2026