Facts and fictions about the analytic hierarchy process

Journal of Multi-Criteria Decision Analysis, 2012

During the last few decades, several multi-criteria decision analysis methods have been proposed to help in selecting the best compromise alternatives. Among them, analytic hierarchy process (AHP) and its applications have attracted much attention from academics and practitioners. However, since the early 1980s, critics have raised questions regarding its proper use. One of them concerns the unacceptable changes in the ranks of the alternatives, called rank reversal, upon changing the structure of the decision. Several modifications were suggested to preserve ranks. In this paper, a classification scheme and a comprehensive literature review are presented in order to uncover, classify and interpret the current research on AHP methodologies and rank reversals. On the basis of the scheme, 61 scholarly papers from 18 journals are categorized into specific areas. The specific areas include the papers on the topics of adding/deleting alternatives and the papers published in adding/deleting criteria. The scholarly papers are also classified by (1) year of publication, (2) journal of publication, (3) authors' geographic location and (4) using the AHP in association with other methods. It is hoped that the paper can meet the needs of researchers and practitioners for convenient references of AHP methodologies and rank reversals and hence promote the future of rank reversal research.

2018

This paper examines the pattern of development of the AHP research. The Analytic Hierarchy Process (AHP) was introduced by T.L. Saaty, is an effective tool for dealing with complex decision making, and may aid the decision maker to set priorities and make the best decision. The analytic hierarchy process (AHP) is a theory of measurement through pairwise comparisons and relies on the judgments of experts to derive priority scales, these scales that measure intangibles in relative terms. The ratio scales are derived from the principal Eigen vectors and the consistency index is derived from the principal Eigen value.

Journal of Risk and Financial Management

The benefits, opportunities, costs, and risks (BOCR) model is a multiple-criteria decision-making (MCDM) model used to elicit a mutually exclusive and collectively exhaustive set of criteria. As an acronym proposed in the theory of the analytic hierarchy process (AHP), the BOCR model has received attention from users of this MCDM method. A state-of-the-art review, an approach to a literature review that is more comprehensive than a rapid review but not as exhaustive as a systematic literature review, was performed with the Scopus database. The overwhelming majority of documents found on BOCR were practical applications, but they were from diverse areas, including business, computer science, and engineering. It is proposed that two main kinds of contributions for future research on BOCR should be methodological and practical.

Proceedings of the International Symposium on the Analytic Hierarchy Process, 1999

The seven pillars of the AHP, some highlights of which are discussed in the paper, are: 1) ratio scales derived from reciprocal paired comparisons; 2) paired comparisons and the psychophysical origin of the fundamental scale used to make the comparisons; 3) conditions for sensitivity of the eigenvector to changes in judgments; 4) homogeneity and clustering to extend the scale from 1-9 to 1-Go; 5) additive synthesis of priorities, leading to a vector of multi-linear forms as applied within the decision structure of a hierarchy or the more general feedback network to reduce multi-dimensional measurements to a uthdimensional ratio scale; 6) allowing rank preservation (ideal mode) or allowing rank reversal (distributive mode); and 7) group decision making using a mathematically justifiable way for synthesizing individual judgments which allows the construction of a cardinal group decision compatible with the individual preferences.

This paper serves as an introduction to the Analytic Hierarchy Process -A multicriteria decision making approach in which factors are arranged in a hierarchic structure. The principles and the philosophy of the theory are summarized giving general background information of the type of measurement utilized, its properties and applications.

Decisions involve many intangibles that need to be traded off. To do that, they have to be measured along side tangibles whose measurements must also be evaluated as to, how well, they serve the objectives of the decision maker. The Analytic Hierarchy Process (AHP) is a theory of measurement through pairwise comparisons and relies on the judgements of experts to derive priority scales. It is these scales that measure intangibles in relative terms. The comparisons are made using a scale of absolute judgements that represents, how much more, one element dominates another with respect to a given attribute. The judgements may be inconsistent, and how to measure inconsistency and improve the judgements, when possible to obtain better consistency is a concern of the AHP. The derived priority scales are synthesised by multiplying them by the priority of their parent nodes and adding for all such nodes. An illustration is included.

European Journal of operational research, 2006

This article presents a literature review of the applications of Analytic Hierarchy Process (AHP). AHP is a multiple criteria decision-making tool that has been used in almost all the applications related with decision-making. Out of many different applications of AHP, this article covers a select few, which could be of wide interest to the researchers and practitioners. The article critically analyses some of the papers published in international journals of high repute, and gives a brief idea about many of the referred publications. Papers are categorized according to the identified themes, and on the basis of the areas of applications. The references have also been grouped region-wise and year-wise in order to track the growth of AHP applications. To help readers extract quick and meaningful information, the references are summarized in various tabular formats and charts.

Journal of Applied Information Science, 2017

In this paper, we first reviews different measurement scales (Linear, Power, Geometric, Logarithmic, Root square, Inverse linear, and Balanced) adopted in Analytic Hierarchy Process (AHP). then, with reduction of different measurement scale ranges to: left position (i.e., for linear measurement scale: 1-3), middle position (4-6), right position (7-9), left & middle position (1-6), middle & right position (4-9), and perfect ranges (1-9), the effects of different measurement scale on priorities and discrimination level (to discriminate an important alternative from others) of alternatives are investigated. The findings of this paper reveal that first, in 39 possibilities out of 42 cases, the same ranking (A1>A2>A3) with different intensities were obtained, and in 3 possibilities rank reversal are happened. Next, the geometric measurement scale in all ranges and particularly in perfect range have the best performance in discriminating an important alternative than others. Moreover, only the left position and perfect ranges in the most of measurement scales have the best performance in discriminating an important alternative from others.

Management practice has tended to focus on uni-dimensional goals such as profit maximization or share value maximization. Analytic tools covered in business schools have also, for the most part, supported this orientation. Management science tools, for example, typically involve seeking optimal solutions based on quantitative and objective criteria. Management problems often have qualitative and subjective criteria embedded in them, however. Also, several stakeholders can be impacted by any one decision, making it important to incorporate various criteria in decision-making. A tool that can incorporate multiple quantitative and qualitative criteria in a meaningful and rational way was developed by Thomas Saaty in the late 70s called the analytic hierarchy process or AHP. In 2008, Saaty received the INFORMS Impact Prize for his development of the Analytic Hierarchy Process. Management scholars as well as practitioners have been arguing for the use of this tool for contentious, ethics-laden oriented or stakeholder-oriented decision-making. The paper advocates for the teaching of AHP in all OR and management science courses. This will enable management students to implement decisions with a broader view.