The following MCDM methods are available, many of which are implemented by specialized decision-making software. Multi-criteria Decision Making techniques has been selected in this research the following:
1.1 Analytic Hierarchy Process (AHP)
Many researchers used AHP, an extensively utilized MDCM method due to its wide applicability and great flexibility, to organize and analyze complex decisions (Ho and Ma, 2018). AHP was developed by Saaty in 1980 and since then it had been studied widely by many researchers in almost all the applications related with MCDM in the last 20 years. According to Steuer and Na (2003), the AHP was adopted in education, engineering, government, industry, management, manufacturing, personal, political, social, and sports. Furthermore, AHP can be integrated with other techniques such as: mathematical programming, quality function deployment (QFD), meta-heuristics, SWOT (strengths, weaknesses, opportunities, and threats) analysis, and data envelopment analysis (DEA). The integrated AHP techniques are mainly constructed to account for the real-world resource limitation beside the qualitative and quantitative factors. These integrated methods would result in a more realistic and promising decision than the stand-alone AHP.
AHP comprise of three main operations including hierarchy construction, priority analysis, and consistency verification. First step in the AHP method is developing a multiple hierarchical levels structure with a goal at the top level, the criteria at the second level and the alternatives at the third level. Second step is determining the relative importance of different criteria with respect to the goal based on the decision maker’s knowledge and experience which is known as the pair-wise comparison matrix. The pair-wise comparison matrix size is equivalent to the number of criteria n used in the decision making and the diagonal value should always be one. For instance, every two criteria in the second level are compared at each time with respect to the goal, whereas every two attributes of the same criteria in the third level are compared at a time with respect to the corresponding criterion. Finally, a consistency verification operation, which is regarded as one of the most advantages of the AHP, is carried out to guarantee the judgments are consistent since the comparisons are carried out through subjective judgements. The verification operation measures the degree of consistency among the pairwise comparisons by computing the consistency ratio. If the computed ratio exceeds a certain limit, the decision maker should review the pairwise comparison. Once all pairwise comparisons are carried out at every level, and are proved to be consistent, the judgments can then be synthesized to find out the priority ranking of each criterion and its attributes.
Although AHP is considered one of the most widely used MCDM methods, it has been criticized mainly for the rank reversals issue and the order preservation condition violation (Ho and Ma, 2018). The issue of rank reversals means that adding or deleting an alternative would change the relative rankings of the other alternatives (Belton and Gear, 1983). Accordingly, some researchers suggested various AHP modifications to avoid the AHP rank reversals (Schenkerman 1994; Wang and Elhag, 2006) [4,5]. On the other hand, other researchers have agreed that rank reversal is an intrinsically legitimate phenomenon not only because the measurements are made in relative terms but also it has been observed to occur in practice (Forman, 1993; Saaty, 1994; Vargas, 1994; Millet and Saaty, 2000; Saaty, 2013). Finally, Wang et al. (2009) concluded that the order preservation condition violation is due to the inconsistencies between elements of the pairwise comparison matrix, which is not detected by the inconsistency measurement used for the matrix as a whole (Kulakowski, 2015).