Invited ReviewThe state-of-the-art integrations and applications of the analytic hierarchy process
Introduction
Because of its simplicity, ease of use, and great flexibility, the analytic hierarchy process (AHP) has been studied extensively and used in nearly all applications related to multiple criteria decision-making (MCDM) since its development (Saaty, 1980). Because Ho (2008) observed in his literature review article that integrated AHP can result in a more realistic and promising decision than a stand-alone AHP, we focus only on integrated AHP approaches and conduct a follow-up literature review study to Ho (2008) to explore the new trends and advances of the integrated AHP and its applications from the perspective of operations/supply chain management from 2007 to 2016.
In the last decade, i.e., 2007–2016, five journal articles reviewing the literature of AHP have been published. Ho (2008) reviewed 66 journal articles published between 1997 and 2006. Ho concluded that the most popular integrated AHP approaches are the integrated AHP-GP and integrated AHP-QFD approaches and that the most widely applied area of the integrated AHP approaches is logistics. Transportation route selection, supplier/subcontractor selection, facility location selection, and scheduling plan selection are the most common problems addressed in logistics. Liberatore and Nydick (2008) reviewed 50 journal articles published between 1981 and 2006 that applied AHP to medical and health care decision-making. Those authors classified the articles into seven categories and determined that the AHP was most widely applied to project and technology evaluation and selection. Sipahi and Timor (2010) reviewed 232 journal articles published between 2005 and 2009 and concluded that applications of AHP are dominant in manufacturing. Supplier selection, supply chain evaluation, location selection, system selection or evaluation, and strategy evaluation are the most common problems addressed in manufacturing. In addition, those authors reported that the most frequently used integrated AHP approach is the integration of AHP and simulation. Subramanian and Ramanathan (2012) reviewed 291 journal articles published from 1999 to 2009 that applied the stand-alone and integrated AHP approaches in operations management. Their paper presented three major research findings. First, product and process design and supply chain management are the two most addressed decision themes. Second, applications of integrated AHP approaches in operations management occur more frequently than stand-alone AHP. Third, the applications of AHP in the manufacturing sector received more attention than in the service sector. Unlike the above four articles, Ishizaka and Labib (2011) reviewed the developments of AHP since its inception, including problem modeling, pairwise comparisons, judgment scales, derivation methods, consistency indices, incomplete matrices, synthesis of weights, sensitivity analysis, and group decisions.
Although the previously mentioned review articles make significant contributions to the literature of AHP, two significant knowledge gaps remain that motivated us to conduct this study. First, none of these review articles are sufficiently recent to include the many new studies published after 2009. Second, the previously mentioned review articles focus primarily on the commonly studied stand-alone and integrated AHP approaches during a certain period of time. None of these review articles provide a comparative analysis or analyze development trends. To fill these gaps, this paper presents a review of relevant journal articles appearing between 2007 and 2016 to analyze the integrations and applications of AHP and then compare these articles with those published between 1997 and 2006 (Ho, 2008).
There is no doubt that AHP is one of the most popular MCDM approaches (Ho, 2008). At the same time, AHP has been criticized considerably for the issue of rank reversals and the violation of a so-called condition of order preservation (COP). First, the issue of rank reversals means that the relative rankings of the other alternatives would change if an alternative is added or deleted (Belton & Gear, 1983). Since the early 1980 s, there are two types of reactions about this issue. One group of researchers has suggested various modifications to avoid rank reversals in AHP (e.g., Schenkerman, 1994, Wang and Elhag, 2006). Maleki and Zahir (2013) reviewed 61 scholarly papers from 18 journals on AHP methodologies and rank reversals. Another group of researchers has defended 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. Therefore, there is no need to adjust AHP to avoid rank reversals (Forman, 1993, Millet and Saaty, 2000, Saaty, 1994 Saaty, 2013, Vargas, 1994).
Second, Bana e Costa and Vansnick (2008) criticized that the eigenvector method in AHP, used for deriving priorities, violates the COP: “For all alternatives x1, x2, x3, x4, such that x1 dominates x2 and x3 dominates x4, if the evaluator's judgments indicate the extent to which x1 dominates x2 is greater than the extent to which x3 dominates x4, then the vector of priorities w should be such that not only w(x1) > w(x2) and w(x3) > w(x4) (preservation of order of preference) but also that w(x1)/w(x2) > w(x3)/w(x4) (preservation of order of intensity of preference)” (Saaty, 2013). Wang, Chin, and Luo (2009) used the concept of overall judgments to re-examine Bana e Costa and Vansnick's numerical examples, and revealed that Bana e Costa and Vansnick's criticism is invalid. Kulakowski (2015) argued that Bana e Costa and Vansnick's criticism is not the inherent problem of the prioritization procedure followed in AHP. Instead, the problem 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).
The remainder of the paper is organized as follows: Section 2 provides an introduction to the research methodology. Section 3 presents various integrated AHP approaches and their applications. Section 4 discusses the observations and compares this paper's conclusions with observations in Ho (2008). Section 5 proposes future research directions. Finally, Section 6 concludes the paper.
Section snippets
Research methodology
Because this paper is a follow-up literature review to Ho (2008), which reviewed journal articles published between 1997 and 2006, we will focus on journal articles published from 2007 to 2016. The research methodology is illustrated in Fig. 1. First, the search term was defined. A title/abstract/keyword search with the term “Analytic Hierarchy Process” was used in the search process. Second, various academic databases were utilized to identify the journal articles, including EBSCOhost,
Integrated AHP and fuzzy set theory
Fuzzy set theory has been widely used in conjunction with AHP because fuzzy set theory enables decision-makers to render interval judgments and consider uncertainty or fuzziness. Twenty articles applied the integrated AHP and fuzzy (AHP-fuzzy) approach, as shown in Table 1. The articles can be classified into five categories: supplier evaluation and selection, product/process evaluation and selection, business information system assessment, project assessment, and others.
A number of researchers
Observations and discussions
In this paper, 88 journal articles published between 2007 and 2016 that studied integrated AHP approaches were reviewed. The methods integrated with the AHP include fuzzy set theory, DEA, mathematical programming, QFD, simulation, and some others. These integrated AHP approaches and their applications are summarized in Tables 1–7. Based on the 88 journal articles, five questions can be answered: (1) Which type of integrated AHP approach received the most attention? (2) Which application areas
Future work
Based on the observations in Section 4, room remains for integrated AHP approaches, particularly the integrations with multiple methods, to be published in high-ranking international journals. Therefore, in this section, some recommendations are directed to scholars regarding the new applications of the newly integrated AHP approaches.
First, supply chain risk management has been one of the “hot” research topics in the field of operations/supply chain management and has attracted significant
Conclusions
This paper, as a follow-up study to Ho (2008), reviewed the literature on the integrated AHP approaches and applications published between 2007 and 2016 and compared the findings to studies published in the previous decade, i.e., 1997–2006. In addition to the searching and filtering criteria used in Ho (2008), this paper focused on those articles published in international journals with high ranking, including A/A* journals on the Australian Business Deans Council (ABDC) journal list, and/or
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