Enhancing efficiency in photo chemical machining: a multivariate decision-making approach

Enhancing efficiency in photo chemical machining: a multivariate decision-making approach Gaurav Sapkota 1 , Ranjan Kumar Ghadai 2 *, Robert Čep 3 *, G. Shanmugasundar 4 , Jasgurpreet Singh Chohan 5 and Kanak Kalita 6 * 1 Department of Mechanical Engineering, Sikkim Manipal Institute of Technology, Sikkim Manipal University, Gangtok, India, 2 Department of Mechanical and Industrial Engineering, Manipal Institute of Technology, Manipal Academy of Higher Education, Manipal, India, 3 Department of Machining, Assembly and Engineering Metrology, Faculty of Mechanical Engineering, VSB-Technical University of Ostrava, Ostrava, Czechia, 4 Department of Mechanical Engineering, Sri Sairam Institute of Technology, Chennai, India, 5 Department of Mechanical Engineering and University Centre for Research and Development, Chandigarh University, Mohali, India, 6 Department of Mechanical Engineering, Vel Tech Rangarajan Dr. Sagunthala R&D Institute of Science and Technology, Avadi, India Non-Traditional Machining (NTM) outperforms traditional processes by offering superior geometric and dimensional accuracy, along with a better surface finish. Photo Chemical Machining (PCM) represents one such NTM process, using chemical etching for material removal. PCM finds substantial application in the creation of microchannels in pharmaceutical, chemical and energy industries. Several input parameters—such as etchant concentration, etching time and etchant temperature—profoundly influence the machining’s quality and efficiency. Therefore, the optimization of these parameters is crucial. This study presents a comparative analysis of five Multiple Criteria Decision Making (MCDM) techniques—Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS), Multi-Objective Optimization on the basis of Ratio Analysis (MOORA), Additive Ratio Assessment (ARAS), Weighted aggregated sum product assessment method (WASPAS) and Multi-Attributive Border Approximation Area Comparison Method (MABAC)—for the optimization of the PCM process. Key performance metrics considered are Material Removal Rate (MRR), Surface Roughness (SR), Undercut (Uc) and etch factor (EF). The weights of these criteria were calculated using the Criterion-Induced Aggregation Technique (CRITIC) and was compared with other popular methods like MEREC, Entropy and equal weights. MRR and EF are seen as beneficial criteria, while SR and Ucare perceived as cost criteria. Optimum process parameters were identified as 850 g/ L etchant concentration, 40 min etching time and 70°C etchant temperature. Two of the three employed MCDM techniques agreed on these optimal parameters, reinforcing the findings. Furthermore, a strong correlation was observed amongst the employed MCDM techniques, further validating the results. KEYWORDS photochemical machining, MCDM, TOPSIS, MOORA, ARAS, non-traditional machining OPEN ACCESS EDITED BY Sabina Luisa Campanelli, Politecnico di Bari, Italy REVIEWED BY Krzysztof Żak, Opole University of Technology, Poland Leijie Fu, Xi’an Technological University, China *CORRESPONDENCE Ranjan Kumar Ghadai, [email protected] Robert Čep, [email protected] Kanak Kalita, [email protected] RECEIVED 20 October 2023 ACCEPTED 31 January 2024 PUBLISHED 13 February 2024 CITATION Sapkota G, Ghadai RK, Čep R, Shanmugasundar G, Chohan JS and Kalita K (2024), Enhancing efficiency in photo chemical machining: a multivariate decisionmaking approach. Front. Mech. Eng 10:1325018. doi: 10.3389/fmech.2024.1325018 COPYRIGHT © 2024 Sapkota, Ghadai, Čep, Shanmugasundar, Chohan and Kalita. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms. Frontiers in Mechanical Engineering frontiersin.org01 TYPE Original Research PUBLISHED 13 February 2024 DOI 10.3389/fmech.2024.1325018 1 Introduction As the demand for superior dimensional and geometric accuracy rises, various non-traditional machining processes are gaining industrial prominence. The manufacturing of microfluidic devices in pharmaceutical and biotechnological industries necessitates exceptional dimensional accuracies, achievable only through a select few non-traditional machining processes (Wangikar et al., 2019). One such process is Photo-Chemical Machining (PCM), which employs photochemical etching for material removal, enabling the machining of intricate shapes with high dimensional accuracy. PCM leverages highly accelerated yet controlled corrosion to remove material from the bulk (Wangikar et al., 2017). Recently, PCM has garnered significant interest from the scientific community due to its advantages, such as high dimensional accuracy, negligible residual stress and improved surface finish. Agrawal et al. (Agrawal et al., 2021) utilized PCM to machine SS-430 and conducted parametric optimization using Taguchi-Grey Relation Analysis to identify optimum process parameters. Their findings indicated that a lower concentration TABLE 1 Weights allocated under different methods. Weight allocation method EF MRR SR Uc MEREC 0.1132 0.3095 0.4173 0.1600 CRITIC 0.2243 0.2650 0.2200 0.2907 Entropy 0.0743 0.1172 0.6376 0.1708 Equal 0.2500 0.2500 0.2500 0.2500 FIGURE 1 Plot of Euclidean distance versus alternatives for weights calculated by (A) MEREC, (B) CRITIC, (C) Entropy and (D) Equal weights. Frontiers in Mechanical Engineering frontiersin.org02 Sapkota et al. 10.3389/fmech.2024.1325018 of etchant combined with high temperature and etching time yielded optimum results. Misal et al. (Misal et al., 2017) employed ferric chloride as an etchant to machine Inconel 718 using the PCM process, observing that the etchant’s temperature and etching time significantly influenced surface roughness. Given PCM’s diverse applications, it is crucial to select optimum process parameters directly impacting machining quality. MultiCriteria Decision Making (MCDM) techniques are widely used in various fields of study for process parameter optimization. Das and Chakraborty (Das and Chakraborty, 2022) applied a Grey Correlation-based EDAS technique for PCM, Laser-Assisted Jet Electro-Chemical Machining and Abrasive Water Jet Drilling process optimization. They accurately predicted optimum process parameters and confirmed these using regression equations. Chakraborty et al. (Chakraborty et al., 2020) used the MultiAttributive Border Approximation Area Comparison Method (MABAC) approach to select the best non-traditional machining process. They successfully tested the method’s validity through two different scenarios, concluding that rough numbers could be effectively used with the MABAC technique for MCDM problems. Deosant et al. (Deosant et al., 2021) integrated the AHP with the Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) method to select suitable non-traditional micro-machining processes. Their study highlighted electrical discharge machining as the most effective technique among the various techniques considered. Kalita et al. (Kalita et al., 2022) conducted a comparative study of various MCDM techniques for milling process optimization. They TABLE 2 TOPSIS rank under various weight. Sr. No. MEREC CRITIC Entropy Equal CCiRank CCiRank CCiRank CCiRank 1 0.2996 25 0.4487 24 0.2970 25 0.4105 25 2 0.6808 7 0.6635 5 0.7044 7 0.6703 5 3 0.6892 6 0.6181 7 0.7148 6 0.6400 7 4 0.5182 20 0.5478 9 0.5601 19 0.5377 13 5 0.1453 27 0.3373 26 0.0990 26 0.2890 26 6 0.7781 5 0.7509 1 0.7800 5 0.7647 2 7 0.6671 8 0.5045 16 0.6840 8 0.5382 12 8 0.5840 16 0.4609 22 0.5849 16 0.4867 21 9 0.4502 23 0.5248 13 0.4108 23 0.5071 20 10 0.6009 12 0.5026 17 0.6360 11 0.5204 15 11 0.4536 22 0.4500 23 0.4266 22 0.4473 24 12 0.6002 13 0.4860 21 0.5897 14 0.5107 18 13 0.5073 21 0.4363 25 0.5122 21 0.4491 23 14 0.5923 14 0.4997 18 0.5876 15 0.5182 17 15 0.8820 1 0.7233 2 0.9067 2 0.7649 1 16 0.5843 15 0.4896 20 0.5950 13 0.5090 19 17 0.5556 19 0.5096 15 0.5473 20 0.5190 16 18 0.1962 26 0.2598 27 0.0621 27 0.2348 27 19 0.6379 10 0.5304 11 0.6403 10 0.5545 10 20 0.5596 18 0.5099 14 0.5807 17 0.5271 14 21 0.6383 9 0.5399 10 0.6318 12 0.5630 9 22 0.6158 11 0.5265 12 0.6452 9 0.5432 11 23 0.5699 17 0.6088 8 0.5714 18 0.6007 8 24 0.3616 24 0.4956 19 0.3207 24 0.4662 22 25 0.8709 2 0.7044 3 0.9199 1 0.7410 3 26 0.8683 3 0.6751 4 0.9025 3 0.7181 4 27 0.8324 4 0.6184 6 0.8688 4 0.6664 6 Frontiers in Mechanical Engineering frontiersin.org03 Sapkota et al. 10.3389/fmech.2024.1325018 used entropy weight calculation with six MCDM techniques and compared the ranks obtained, suggesting that objective weight calculation performs better with robust data. Shanmugasundar et al. (Shanmugasundar et al., 2022) utilized Method Based on the Removal Effects of Criteria (MEREC) weight calculation with various MCDM techniques for industrial robot selection, presenting a comparative study among various MCDM techniques to identify the drawbacks and advantages of the techniques used. Kumari and Acherjee (Kumari and Acherjee, 2022) applied a Criterion-Induced Aggregation Technique (CRITIC)—COmbinative Distance-based ASsessment (CODAS)-based technique to select the best nonconventional machining process among eight processes based on six different criteria. Their method’s comparison with established methods demonstrated good performance. Pathapalli et al. (Pathapalli et al., 2020) developed an aluminium composite using the stir casting process and optimized turning process parameters using Multi-Objective Optimization on the basis of Ratio Analysis (MOORA) and weighted aggregated sum product assessment method (WASPAS) techniques. A comparative study revealed that both techniques work well for turning parameter optimization. Goswami et al. (Goswami et al., 2021) used an Additive Ratio Assessment (ARAS)-TOPSIS hybrid MCDM technique for robot selection among twelve industrial robots based on five contrasting criteria, suggesting that objective weight determination techniques are free from decision-maker biases and, thus, superior to subjective methods. From the aforementioned literature, it is clear that MCDM techniques are widely used for selecting optimum process TABLE 3 Ranking using MOORA. Sr. No. MEREC CRITIC Entropy Equal yiRank yiRank yiRank yiRank 1 0.1131 3 0.0596 3 0.1728 3 0.0678 3 2 0.0459 24 0.0242 27 0.0701 21 0.0275 26 3 0.0435 25 0.0279 26 0.0664 22 0.0260 27 4 0.0691 9 0.0364 19 0.1055 9 0.0414 13 5 0.1562 1 0.0824 1 0.2387 1 0.0936 1 6 0.0399 26 0.0342 22 0.0518 23 0.0322 24 7 0.0463 23 0.0522 8 0.0708 20 0.0449 11 8 0.0629 13 0.0533 6 0.0962 13 0.0458 8 9 0.0931 5 0.0491 9 0.1422 5 0.0557 5 10 0.0556 17 0.0322 24 0.0849 17 0.0333 22 11 0.0896 6 0.0473 10 0.1369 6 0.0537 6 12 0.0622 14 0.0549 5 0.0951 14 0.0472 7 13 0.0754 7 0.0398 16 0.1152 7 0.0452 10 14 0.0632 12 0.0436 12 0.0966 12 0.0379 18 15 0.0481 22 0.0412 15 0.0204 26 0.0388 16 16 0.0621 15 0.0395 17 0.0949 15 0.0372 20 17 0.0702 8 0.0370 18 0.1073 8 0.0421 12 18 0.1541 2 0.0813 2 0.2355 2 0.0923 2 19 0.0547 18 0.0428 14 0.0835 18 0.0368 21 20 0.0648 11 0.0342 21 0.0990 11 0.0388 17 21 0.0561 16 0.0440 11 0.0857 16 0.0379 19 22 0.0543 19 0.0309 25 0.0830 19 0.0325 23 23 0.0674 10 0.0355 20 0.1029 10 0.0404 15 24 0.1083 4 0.0571 4 0.1654 4 0.0649 4 25 0.0379 27 0.0333 23 0.0196 27 0.0306 25 26 0.0504 21 0.0431 13 0.0251 25 0.0407 14 27 0.0510 20 0.0530 7 0.0311 24 0.0456 9 Frontiers in Mechanical Engineering frontiersin.org04 Sapkota et al. 10.3389/fmech.2024.1325018 parameters in multi-objective problems. Although these techniques have been extensively applied across various domains, the optimization of PCM process parameters using MCDM techniques remains underexplored. Moreover, a comparative study of various MCDM techniques in the PCM process using objective weight determination methods has yet to be conducted. The current study attempts to bridge this gap by comparing five MCDM techniques—TOPSIS, MOORA, ARAS, WASPAS, and MABAC—using four different objective weight determination techniques namely, CRITIC, MEREC, Entropy along with equal weights to optimize PCM process parameters. Additionally, a correlation analysis is presented to elucidate the similarities and differences between the techniques employed. 2 Materials and methods 2.1 Experimental procedure The experimental data for this study were derived from Agarwal and Kamble (Agrawal and Kamble, 2019). Stainless Steel-304 (SS304) was selected as the substrate material for the PCM process. The etchant was prepared by dissolving ferric chloride in water, with precise weighing of ferric chloride to ensure the desired concentration. Prior to the application of the photoresist coating, the specimen was thoroughly cleaned with acetone and water. The coated material and phototool were then exposed to UV light. The portions not covered by the phototool and exposed to UV light remained unetched post-machining. TABLE 4 Rank Calculation using ARAS. Sl. No. MEREC CRITIC Entropy Equal KiRank KiRank KiRank KiRank 1 3.1932 12 2.0379 24 5.4508 4 2.1792 21 2 2.5375 23 2.0565 23 3.3205 22 2.0907 23 3 2.6082 21 2.1742 21 3.3797 21 2.1791 22 4 2.4145 25 1.7280 27 3.7915 18 1.8141 27 5 4.2585 2 2.6062 6 7.3384 2 2.7626 4 6 2.6877 18 2.3081 16 3.1157 23 2.3277 16 7 2.9408 16 2.4411 13 3.7971 17 2.3772 13 8 3.2796 8 2.5989 7 4.4636 10 2.5503 8 9 3.7655 4 2.7394 3 5.4017 5 2.8067 2 10 2.6113 20 2.0343 25 3.7189 19 2.0253 25 11 3.6807 5 2.6926 4 5.3287 6 2.7149 5 12 3.4629 6 2.7640 2 4.5642 8 2.7125 6 13 3.1993 11 2.3937 14 4.6656 7 2.3890 12 14 3.2359 9 2.5239 9 4.3750 11 2.4968 10 15 2.4158 24 2.3038 17 2.3163 25 2.2544 19 16 3.0039 14 2.3380 15 4.1831 13 2.3210 17 17 3.2799 7 2.5059 10 4.5507 9 2.5095 9 18 4.9003 1 3.2256 1 7.8854 1 3.2919 1 19 3.0770 13 2.4702 11 4.0460 16 2.4397 11 20 2.9117 17 2.2909 18 4.1807 14 2.3134 18 21 3.2309 10 2.5925 8 4.1856 12 2.5615 7 22 2.6505 19 2.0798 22 3.7008 20 2.0745 24 23 2.9815 15 2.2690 20 4.1729 15 2.3317 15 24 3.8471 3 2.6910 5 5.8198 3 2.8011 3 25 2.0255 27 2.0020 26 1.8579 27 1.9397 26 26 2.3465 26 2.2808 19 2.1475 26 2.1974 20 27 2.5730 22 2.4596 12 2.5579 24 2.3633 14 Frontiers in Mechanical Engineering frontiersin.org05 Sapkota et al. 10.3389/fmech.2024.1325018 Agarwal and Kamble (Agrawal and Kamble, 2019) identified three input variables that were of prime significance following an extensive literature survey. These three input parameters: concentration of etchant, etching time and temperature of the etchant were varied between three levels to conduct 27 experimental runs based on Taguchi orthogonal array experimental design. Concentration of etchant was measured in gm/ltrs and denotes the strength of etchant, etching time was measured in minutes and denotes the time for which the material was exposed to the etchant. Etchant was also used in an elevated temperature to expedite the process of chemical etching and the temperature was measured in °C. Three levels of all these factors are presented in Table A1. The Material Removal Rate (MRR), Surface Roughness (SR), Etch Factor (EF) and Undercut (Uc) were measured and documented (Table A2). 2.2 Multi criteria decision making Five MCDM techniques namely, TOPSIS, MOORA, ARAS, WASPAS, and MABAC methods were used to identify the compromise optimum values of responses variables. Weight of the response variables were calculated using CRITIC, MEREC and Entropy methods and a comparison was made with the case when equal weights are assigned to all criteria. All the MCDM techniques used in the current work are discussed in detail in the TABLE 5 Rank calculation using WASPAS. Sl. No. MEREC CRITIC Entropy Equal QWASPAS Rank QWASPAS Rank QWASPAS Rank QWASPAS Rank 1 1.1487 25 1.3471 10 1.4392 23 1.2842 10 2 1.7259 6 1.4929 6 2.3152 6 1.5082 6 3 1.7035 7 1.3873 8 2.3015 7 1.4203 7 4 1.3775 16 1.4123 7 1.8604 13 1.3770 9 5 0.9557 26 1.0889 24 1.0931 26 1.0464 26 6 2.1055 5 1.7097 5 2.8347 5 1.7533 5 7 1.5822 8 1.1891 15 2.0904 8 1.2248 15 8 1.3599 18 1.0804 25 1.7064 19 1.1010 23 9 1.2876 21 1.2485 12 1.4759 22 1.2401 13 10 1.3943 15 1.1384 20 1.8798 12 1.1538 21 11 1.2128 24 1.0950 23 1.4208 24 1.0952 24 12 1.4212 13 1.1331 21 1.7440 16 1.1560 20 13 1.2239 22 1.0409 26 1.5329 21 1.0474 25 14 1.3976 14 1.1422 19 1.7434 17 1.1585 19 15 4.0787 3 2.5674 3 6.2574 3 2.7672 3 16 1.3658 17 1.1224 22 1.7532 15 1.1380 22 17 1.3504 19 1.1629 18 1.6612 20 1.1725 18 18 0.9210 27 0.8940 27 0.9755 27 0.8808 27 19 1.5068 10 1.2069 14 1.9252 10 1.2316 14 20 1.3394 20 1.1680 17 1.7384 18 1.1841 17 21 1.5217 9 1.2269 13 1.9074 11 1.2515 12 22 1.4450 12 1.1867 16 1.9328 9 1.2034 16 23 1.4655 11 1.3852 9 1.8394 14 1.3796 8 24 1.2223 23 1.2803 11 1.3911 25 1.2567 11 25 6.9396 1 3.9391 1 11.4063 1 4.3407 1 26 6.0844 2 3.4833 2 9.7714 2 3.8277 2 27 3.7577 4 2.3030 4 5.7128 4 2.4909 4 Frontiers in Mechanical Engineering frontiersin.org06 Sapkota et al. 10.3389/fmech.2024.1325018 following sections. It should be noted here that for all the methods discussed, in an MCDM problem having malternatives and n criteria, the decision matrix is a matrix X[xij]mxn;where xij is the performance value associated with the ith alternative under j th criterion. 2.2.1 CRITIC weight calculation CRITIC was proposed by Diakoulaki et al. (Diakoulaki et al., 1995) in 1995 as an objective weight determination method. The primary advantage of objective weighting method is that it omits any preferences that the decision maker might have with respect to any criteria. The internal contrasts within a criterion and conflict intensity between criteria are assessed to assign weights to them using CRITIC method. StepsinvolvedinCRITICmethodareasfollows: Step 1: Formulation of the decision matrix. Step 2: Decision matrix is normalized using Eq. 1, rij xij-xworst j xbest j-xworst j (1) Step 3: Pearson Correlation Coefficient is used to determine the degree of correlation. It is calculated using Eq. 2 CFjk m i1rij- rj  rik- rk ()  m i1rij- rj  2m i1rik- rk () 2 (2) TABLE 6 Rank calculation using MABAC. Sl. No. MEREC CRITIC Entropy Equal SiRank SiRank SiRank SiRank 1−0.1945 25 −0.0127 14 −0.1428 25 −0.0341 17 2 0.1021 6 0.1564 7 0.1484 6 0.1565 8 3 0.0737 8 0.0830 10 0.1179 7 0.0891 10 4−0.0853 23 0.0249 11 0.0260 11 0.0117 12 5−0.2810 27 −0.0915 22 −0.3333 26 −0.1184 23 6 0.2555 3 0.3086 1 0.2459 4 0.3180 1 7 0.0031 16 −0.1100 23 0.0171 13 −0.1033 22 8−0.0354 18 −0.1301 25 −0.0504 21 −0.1258 24 9 0.0653 10 0.1633 6 −0.0215 20 0.1596 7 10 −0.0820 22 −0.1229 24 −0.0045 15 −0.1280 25 11 −0.0274 17 −0.0140 16 −0.0865 24 −0.0189 16 12 0.0333 12 −0.0586 19 −0.0210 19 −0.0521 19 13 −0.0979 24 −0.1345 26 −0.0851 23 −0.1394 26 14 0.0098 15 −0.0502 18 −0.0113 17 −0.0507 18 15 0.3060 1 0.2570 2 0.3091 1 0.2739 2 16 −0.0412 20 −0.0891 21 −0.0203 18 −0.0905 21 17 0.0127 13 0.0029 13 −0.0107 16 0.0012 13 18 −0.2479 26 −0.1960 27 −0.3923 27 −0.2115 27 19 0.0393 11 −0.0193 17 0.0305 10 −0.0163 15 20 −0.0407 19 −0.0134 15 −0.0001 14 −0.0081 14 21 0.0773 7 0.0219 12 0.0406 9 0.0260 11 22 −0.0444 21 −0.0746 20 0.0196 12 −0.0785 20 23 0.0730 9 0.1683 5 0.0772 8 0.1660 4 24 0.0105 14 0.1722 3 −0.0669 22 0.1653 5 25 0.2322 4 0.1504 8 0.2968 2 0.1623 6 26 0.2801 2 0.1704 4 0.2930 3 0.1862 3 27 0.2300 5 0.0996 9 0.2299 5 0.1203 9 Frontiers in Mechanical Engineering frontiersin.org07 Sapkota et al. 10.3389/fmech.2024.1325018 Step 4: Weights of the criteria is calculated using Eqs 3,4, cjσjn k11-CFjk (3) wjcj n j1cj (4) wjis the weight of the jth criteria. 2.2.2 MEREC weight calculation MEREC is a weight evaluation method developed in 2019 by Ghorabaee et al. (Keshavarz-Ghorabaee et al., 2021)toassess weights based on deviation of performance ratings on removal of a criteria. The weights reflect the effect it has on performance rating if the criteria were omitted from the decision-making process. The procedural steps involved in this method are as follows. Step 1: A normalized decision matrix Pis formulated from the matrix Xwherein each element of the matrix Pis defined as in Eq. 5 pij min xkj  xij if jϵB pij xij max xkj  if jϵC (5) Step 2: An index Siis calculated which signifies the overall performance of the alternatives in a logarithmic scale using Eq. 6 FIGURE 2 Ranks Comparison among various weights. Frontiers in Mechanical Engineering frontiersin.org08 Sapkota et al. 10.3389/fmech.2024.1325018 Siln 1+1 mjln px ij    (6) Step 3: Similarly, an index Sij ′is calculated which signifies the overall performance of the alternatives by excluding the criteria in a logarithmic scale using Eq. 7, Sij ′ln 1+1 mk,k≠jln px ik    (7) Step 4: Absolute deviation D is calculated by subtracting one performance rating with other. Absolute value of the difference is taken as the deviation. It can be mathematically represented as in Eq. 8, DjSij ′−Si (8) Step 5: Weights of each alternative is calculated using Eq. 9, wjdj n j1dj (9) 2.2.3 Entropy weight calculation Entropy weights was adopted into MCDM problems from the concept of Shannon entropy developed by Shannon in 1948 as a concept in probabilities. This method works on the premise that the higher weight should be assigned to the criteria that carries the maximum information in a decision-making process. The procedural steps involved in this method are as follows: Step 1: The decision matrix is normalized using Eq. 10, nij aij  n i1 aij (10) Step 2: Entropy is then calculated as in Eq. 11, ej− m i1pij log pij log m(11) Step 3: The weight from the Entropy value is calculated using Eq. 12, wj1−ej n i11−ej  (12) where 1 −ejis called divergence value. 2.2.4 Technique for order of preference by similarity to ideal solution (TOPSIS) TOPSIS was initially presented by Yoon and Hwang (Yoon and Hwang, 1981) in 1981 and is among the most popular MCDM technique that has been applied in various areas of study. Distance from the ideal best and ideal worst solution in the Euclidean scale is used to identify the best alternative in this method. Steps involved in TOPSIS method are presented below: Step 1: Decision matrix is normalized using Eq. 13, nij xij  m i1x2 ij (13) Step 2: Weighted normalized matrix is calculated by multiplying the normalized decision matrix by their corresponding criteria weights using Eq. 14. rij nij ×wj(14) Step 3: Euclidean distances from the ideal best and ideal worst solutions are calculated using Eqs 15,16, S+ i n j1rij −A+ j  2 ′;A+ j max rij  for benefit criteria min rij  for cost criteria ⎧ ⎨ ⎩(15) S− i n j1rij −A− j  2 ;A− j max rij  for cost criteria min rij  for benefit criteria ⎧ ⎨ ⎩(16) Step 4: Closeness coefficient is calculated using Eq. 17 and the alternatives are ranked based on CCiin descending order. CCiS− i S+ i+S− i (17) 2.2.5 Multi-objective optimization on the basis of ratio analysis method (MOORA) MOORA was used by Chakraborty (Chakraborty, 2011) to solve decision making problem for various applications in different manufacturing environments. Brauers et al. (Brauers et al., 2008) compared various ratios and suggested that the best choice as denominator is the square root of sum of squares which is considered in MOORA. The steps involved in MOORA is same as TOPSIS until the weighted normalized decision matrix is obtained. The steps after that are as follows Step 1: After obtaining the weighted normalized decision matrix following Step 1 and Step 2 of TOPSIS, performance score is calculated as yig j1rij −n jg+1rij (18) where criteria 1 to criteria “g”are the beneficial criteria Step 2: Rank the criteria based on performance score in descending order. The highest performance score will be ranked first. 2.2.6 Additive ratio assessment (ARAS) ARAS method was presented by Zavadskas and Turskis (Zavadskas and Turskis, 2010) in the year 2010 as an MCDM technique that is simple and effective. ARAS method assumes that the effectiveness of an alternative is directly proportional to performance value under a criteria and weight of the criteria. This is the underlying principle behind the working of this technique. The steps in the ARAS method are as followsFrontiers in Mechanical Engineering frontiersin.org09 Sapkota et al. 10.3389/fmech.2024.1325018