## 2 Literature Review
This has continued to be a trend in the last three years because the literature is replete with examples of its use in widely varying fields (e.g., [41; 42; 43; 44; 45; 46; 47; 48; 49]). Since TOPSIS is another widely used approach, setting up a hybrid approach that uses both TOPSIS and AHP (AHP-TOPSIS) as the rival approach is an important experimental design of this study. GTMA, since proposed, has also become an increasing popular MADM approach. Graph theory, which forms the basis for GTMA, is centuries old. To the authors' best knowledge, the first application of graph theory was in a study by [PERSON] in 1736 [50]. A decade ago, [PERSON] proposed an idea that used graph theory [51] for MADM, and the method was further systematized as the known graph theory and matrix approach (GTMA) as a formal decision-making method [52]. GTMA represents the performance attributes (of each alternative) in a digraph, translates it into the matrix representation and calculates the permanent functional value of which as the basis for ranking [53]. Note that, during this process, the permanent function, and neither the determinant function nor the permutation function (which totally differs in its meaning), is used to provide the complete information of the assessed alternative without any loss (see [51]). Some recent studies have successfully resolved the selection decisions or alternative ranking problems using this method [54; 55; 56; 57; 58]. Within the scope of GTMA, in addition to the abovementioned articles, there have been studies using the AHP-GTMA hybrid approach [59; 60; 61]. These works are all published after 2012 because of the youngness (recency) of the AHP-GTMA approach. However, to the authors' knowledge, the applications of this method is relatively few (in comparison with the widely used AHP-TOPSIS). The above literature study addresses the standpoint of this study. First, methodologically, each MADM model prioritizes the alternatives using a different internal solution logic. This is reflexive to the claim that \"algorithms (for MADM) differ in their approach to selecting the 'best' solution, so this leads to 'inconsistency in the results'\" [7]. However, in the literature, it is also noted that \"there is neither a strong reason to reject a particular school of MCDM, nor a convincing argument to give general preference to one of the many methods\" [62]. In this sense, the necessity for further scrutiny of whether the relatively recent AHP-GTMA approach is effective to aid the selection decision problems in industrial practice (which may answer the main research question of this study) should be addressed. Second, AHP-GTMA and AHP-TOPSIS share a former phase of AHP. This is important to make a solid basis for the comparison works. The fact the rival approach shares a common former phase with the benchmarked approach can control the \"inconsistency in the results\", which is a positive antecedence for the comparisons. Third, AHP-TOPSIS has been a \"widely used\" approach, in contrast to AHP-GTMA whose applications are relatively few. The literature contains many examples of the application of AHP-TOPSIS (the articles cited are very limited). It is a mature and widely used method so it is credible. This justifies the appropriateness of using AHP-TOPSIS as the rival approach. Note that this is not a comment on the relative merits of these two approaches, but is a claim made based on the observed number of cases (i.e., it has been used again and again for selection problems), although such popularity of AHP-TOPSIS could be attributed to the length of time during which it has been used. For example, in a recent study [63], the school of MODM proposed a hybrid mathematical programming approach to solve the site selection and capacity planning problem for the establishment of wind farms. However, in another recent study [49], the school of MADM also successfully used AHP-TOPSIS as an effective MADM modeling method to aid the decision for the selection of solar farms.