Numerical scales generated individually for analytic hierarchy process

Because individual interpretations of the analytic hierarchy process (AHP) linguistic scale vary for each user, this study proposes a novel framework that AHP decision makers can use to generate numerical scales individually, based on the 2-tuple linguistic modeling of AHP scale problems. By using the concept of transitive calibration, individual characteristics in understanding the AHP linguistic scale are first defined. An algorithm is then proposed for detecting the individual characteristics from the linguistic pairwise comparison data that is associated with each of the AHP individual decision makers. Finally, a nonlinear programming model is proposed to generate individual numerical scales that optimally match the obtained individual characteristics. Two well-known numerical examples are re-examined using the proposed framework to demonstrate its validity.     

An analytic network process approach to operationalization of five forces model

The five forces model has been one of the most influential frameworks for strategic management. In contrast to its importance as a centerpiece of textbooks, however, it has attracted less attention from both academic researchers and practicing managers. This is due to its innate weakness, difficulty in operationalization. The vital requisites for operationalizing the five forces model are to deal with it as a complex system composed of interrelated forces and their sub-forces, and to prioritize them with consideration of their interdependency. The tenet of this study is the requisites can be achieved through the analytic network process (ANP). The ANP, which is a generalization of the analytic hierarchy process (AHP), produces priorities of elements in a complex network model with consideration of interdependency among elements. The five forces model is transformed into a network model of the ANP. The ANP procedure is then carried out to obtain the priority weights of the forces. Combining the derived weights and ratings on the forces produces the state-of-industry-competition index (SICI) values that represent the overall competitive condition of a given industry. The working of the proposed approach is provided with the help of a case study example of the Web portal Industry of Korea. The proposed ANP approach is expected to expand the five forces model into a workable system of analysis by improving its analytical power.     

Fuzzy analytic hierarchy process: Fallacy of the popular methods

The fuzzy Analytic Hierarchy Process (fuzzy AHP) is a very popular decision making method and literally thousands of papers have been published about it. However, we find the basic logic of this approach has problems. From its methodology, the definition and operational rules of fuzzy numbers not only oppose the main logic of fuzzy set theory, but also oppose the basic principles of the AHP. In dealing with the outcomes, fuzzy AHP does not give a generally accepted method to rank fuzzy numbers and a way to check the validity of the results. Besides, we discuss the validity of the Analytic Hierarchy/Network Process (AHP/ANP) in complex and uncertain environments and find that fuzzy ANP is a false proposition because there is no fuzzy priority in the super matrix which provides the basis for the ANP. Although fuzzy AHP has been applied in many cases and cited hundreds of times, we hoped that those who use fuzzy AHP would understand the problems associated with this method.     

Integrated analytic hierarchy process and its applications – A literature review

Due to its wide applicability and ease of use, the analytic hierarchy process (AHP) has been studied extensively for the last 20 years. Recently, it is observed that the focus has been confined to the applications of the integrated AHPs rather than the stand-alone AHP. The five tools that commonly combined with the AHP include mathematical programming, quality function deployment (QFD), meta-heuristics, SWOT analysis, and data envelopment analysis (DEA). This paper reviews the literature of the applications of the integrated AHPs. Related articles appearing in the international journals from 1997 to 2006 are gathered and analyzed so that the following three questions can be answered: (i) which type of the integrated AHPs was paid most attention to? (ii) which area the integrated AHPs were prevalently applied to? (iii) is there any inadequacy of the approaches? Based on the inadequacy, if any, some improvements and possible future work are recommended. This research not only provides evidence that the integrated AHPs are better than the stand-alone AHP, but also aids the researchers and decision makers in applying the integrated AHPs effectively.     

Selection of technology acquisition mode using the analytic network process

Selecting the appropriate acquisition mode for a required technology, is one of the critical strategic decisions in formulating a technology strategy. Although a number of factors were found to be influential in the choice of technology acquisition mode, it still remains a void in the literature how to make a strategic decision, based on a huge set of those factors with the help of a systematic approach. This study deals with the selection of technology acquisition mode as a multiple criteria decision making (MCDM) problem. The proposed solution to the problem in this study, is the analytic network process (ANP) approach. Since the ANP is a MCDM method that can accommodate interdependency among decision attributes, it is capable of providing priorities of alternatives with consideration of interrelationships among strategic factors. The 21 influential factors identified from the empirical studies are included as sub-criteria in the ANP model, and they are grouped into five criteria: capability, strategy, technology, market, and environment. The final decision can be made based on the resulting priorities of the alternative acquisition modes. The proposed approach is expected to effectively aid decision making on which mode is adopted for acquisition of required technologies. A case of a software company is presented for the illustration of the proposed approach.     

On the use of information criteria in analytic hierarchy process

In this article, we discuss how the model-selection procedures such as Akaike's information criteria (AIC) can be used for selecting the most appropriate one out of several existing statistical models in the literature for the judgment data used in analytic hierarchy process (AHP). Furthermore, once the appropriate model is selected, a procedure is proposed on the basis of AIC for statistical ranking of the alternatives. This ranking procedure does not suffer from the problem of intransitivity and can be based on non-normal distribution. It enables one to obtain the detailed pattern for the ordered priorities of the alternatives in the decision process involving AHP.     

Solving multiattribute design problems with analytic hierarchy process and conjoint analysis: An empirical comparison

We consider the multiattribute design problem (MADP) which contains a considerable number of alternatives, resulting from the combination of a limited number of discrete levels of several quantitative and/or qualitative attributes. In order to solve such problems, the preferences of individual decision makers have to be measured. Though a considerable number of methods is available from different research areas, only a subset is applicable to MADP.In this paper, we report on an empirical study which considered the problem of designing a university and involved more than 300 respondents. Because of this large-scale design, we performed a paper-and-pencil investigation and selected methods which could concisely be applied in such a setting: the analytic hierarchy process (AHP) and the conjoint analysis (CA).The results show that both methods give useful models of the respondents' preferences. However, inspecting the utility functions determined in detail reveals considerable discrepancies between them. Most of the measures used for comparison indicate AHP to be the better choice for the special decision situation considered. In order to get a more general recommendation, we categorize different types of MADP and discuss the applicability of AHP and CA.     

On modeling dynamic priorities in the analytic hierarchy process using compositional data analysis

In a rapidly changing environment, the priorities derived using the analytic hierarchy process (AHP) approach at one point in time might very likely change in the near future. Thus, in order to adapt to such ever-changing environment, it is of primary importance to be able to follow the change over time as to enable the system to respond differently and continuously over time of its operation. This paper proposes the use of a time-based compositional forecasting method, which is based on the idea of exponential smoothing, to deal with the AHP priority dynamics. The proposed method is particularly useful when there is a limited number of historical data, and might be considered to be more effective and time-efficient compared to that of multivariate time series method. It was also shown that the proposed method provides much greater adaptability in modeling the AHP priorities change over time compared to that of recently developed methods in compositional data research field. The shortcoming of Saaty’s dynamic judgment approach and some limitations of the other existing methods will be discussed. Finally, to substantiate the validity of the proposed method and to give some practical insights, an illustrative case study is provided.     

A Thurstonian view of the analytic hierarchy process

The application of deterministic decision models in situations characterized by noise and uncertainty is likely to produce results of questionable value. In this paper, some very simple probabilistic models are developed and substituted for the deterministic scales used in the Analytic Hierarchy Process (AHP). It is shown that the use of these probabilistic models can extend the domain of AHP to situations, such as consensual or group decision making, that possess significant amounts of uncertainty. In addition, explicit measures of the variation present in the evaluation of decision alternatives and attributes are obtained.     

Scales and methods for deriving weights in the analytic hierarchy process

Scales and methods for deriving weights of objects being compared used in the analytic hierarchy process (AHP) are theoretically studied. Results are formulated as theorems, which can be applied by a decision maker to choose AHP parameters in solving practical problems.     

An integrated approach for deriving priorities in analytic network process

A multiple objective programming approach for the analytic network process (ANP) is proposed to obtain all local priorities for crisp or interval judgments at one time, even in an inconsistent situation. The weakness of the ANP and fuzzy ANP (FANP) is that the complexity of generating priorities is equal to the number of comparison matrices. In the proposed approach, all sets of crisp priorities for each pairwise comparison matrix can be obtained directly. Moreover, from the outcomes of three examples, the power to reach a limiting supermatrix is less than or equal to the power of the FANP. Thus, the proposed approach can be regarded as an efficient alternative of the fuzzy ANP.     

Fuzzy analytic hierarchy process: A logarithmic fuzzy preference programming methodology

Fuzzy analytic hierarchy process (AHP) proves to be a very useful methodology for multiple criteria decision-making in fuzzy environments, which has found substantial applications in recent years. The vast majority of the applications use a crisp point estimate method such as the extent analysis or the fuzzy preference programming (FPP) based nonlinear method for fuzzy AHP priority derivation. The extent analysis has been revealed to be invalid and the weights derived by this method do not represent the relative importance of decision criteria or alternatives. The FPP-based nonlinear priority method also turns out to be subject to significant drawbacks, one of which is that it may produce multiple, even conflict priority vectors for a fuzzy pairwise comparison matrix, leading to entirely different conclusions. To address these drawbacks and provide a valid yet practical priority method for fuzzy AHP, this paper proposes a logarithmic fuzzy preference programming (LFPP) based methodology for fuzzy AHP priority derivation, which formulates the priorities of a fuzzy pairwise comparison matrix as a logarithmic nonlinear programming and derives crisp priorities from fuzzy pairwise comparison matrices. Numerical examples are tested to show the advantages of the proposed methodology and its potential applications in fuzzy AHP decision-making.     

A modified procedure for synthesising ratio judgements in the analytic hierarchy process

The analytic hierarchy process (AHP) has been widely applied to solve problems arising in group decision making, by synthesising different or conflicting judgements. However, directly synthesising conflicting judgements by calculating the geometric mean of preference weights (ratios) in AHP may not reach consensus from all members in a decision making group, especially, when those members represent the stakeholders of the decision making problem. This study proposes a new method that uses the genetic algorithm and utility function to synthesise preference weights to prevent this fallacy occurring when implementing the classical AHP approach. Using the proposed method, the final decision can be achieved with only minimally-adjusted preference weights.     

The analytic hierarchy process in medical and health care decision making: A literature review

This paper presents a literature review of the application of the analytic hierarchy process (AHP) to important problems in medical and health care decision making. The literature is classified by year of publication, health care category, journal, method of analyzing alternatives, participants, and application type. Very few articles were published prior to 1988 and the level of activity has increased to about three articles per year since 1997. The 50 articles reviewed were classified in seven categories: diagnosis, patient participation, therapy/treatment, organ transplantation, project and technology evaluation and selection, human resource planning, and health care evaluation and policy. The largest number of articles was found in the project and technology evaluation and selection category (14) with substantial activity in patient participation (9), therapy/treatment (8), and health care evaluation and policy (8). The AHP appears to be a promising support tool for shared decision making between patient and doctor, evaluation and selection of therapies and treatments, and the evaluation of health care technologies and policies. We expect that AHP research will continue to be an important component of health care and medical research.     

The analytic hierarchy process with stochastic judgements

The analytic hierarchy process (AHP) is a widely-used method for multicriteria decision support based on the hierarchical decomposition of objectives, evaluation of preferences through pairwise comparisons, and a subsequent aggregation into global evaluations. The current paper integrates the AHP with stochastic multicriteria acceptability analysis (SMAA), an inverse-preference method, to allow the pairwise comparisons to be uncertain. A simulation experiment is used to assess how the consistency of judgements and the ability of the SMAA-AHP model to discern the best alternative deteriorates as uncertainty increases. Across a range of simulated problems results indicate that, according to conventional benchmarks, judgements are likely to remain consistent unless uncertainty is severe, but that the presence of uncertainty in almost any degree is sufficient to make the choice of best alternative unclear.     

A simulation approach for handling uncertainty in the analytic hierarchy process

Uncertainty considerations are introduced into the analytic hierarchy process (AHP). The rank order of decision alternatives depends on two types of related uncertainties: (1) uncertainty regarding the future characteristics of the decision making environment described by a set of scenarios, and (2) uncertainty associated with the decision making judgment regarding each pairwise comparison. A simulation approach for handling both types of related uncertainties in the AHP is described. The example introduced by Saaty and Kearns (1985) is extended here to include uncertainty considerations.     

Note on group consistency in analytic hierarchy process

We study the paper of Xu [Z. Xu, On consistency of the weighted geometric mean complex judgement matrix in AHP, European Journal of Operational Research 126 (2000) 683–687] for the group consistency in analytic hierarchy process of multicriteria decision-making. The purpose of this note is threefold. First, we point out the questionable results in this paper. Second, for three by three comparison matrices, we provide a patchwork for his method. Third, we constructed a counter example to show that in general his method is wrong. Numerical examples are provided to illustrate our findings. If there are four or more alternatives, then we may advise researchers to ignore his results to avoid questionable estimation of group consistency.     

Note on “Wash criterion in analytic hierarchy process”

The paper of Finan and Hurley – published in Computers and Operations Research (2002) – was re-examined, where they discussed a seemingly contradictory phenomenon resulting from the ignoring of wash criteria in the analytic hierarchy process (AHP). With that, they raised a serious challenge to the AHP methodology. However, by reviewing their arguments and example data, analyses regarding to their propositions and numerical example are presented in this paper to counter their challenge.     

Relevance assumed: a case study of balanced scorecard development using system dynamics

The balanced scorecard (BSC) has become a popular concept for performance measurement. It focuses attention of management on only a few performance measures and bridges different functional areas as it includes both financial and non-financial measures. However, doubts frequently arise regarding the quality of the BSCs developed as well as the quality of the process in which this development takes place. This article describes a case study in which system dynamics (SD) modelling and simulation was used to overcome both kinds of problems. In a two-stage modelling process (qualitative causal loop diagramming followed by quantitative simulation), a BSC was developed for management of one organizational unit of a leading Dutch insurer. This research illustrates how, through their involvement in this development process, management came to understand that seemingly contradictory goals such as customer satisfaction, employee satisfaction and employee productivity were, in fact, better seen as mutually reinforcing. Also, analysis of the SD model showed how, contrary to ex ante management intuition, performance would first have to drop further before significant improvements could be realized. Finally, the quantitative modelling process also helped to evaluate several improvement initiatives that were under consideration at the time, proving some of them to have unclear benefits, others to be very promising indeed.     

A new data envelopment analysis method for priority determination and group decision making in the analytic hierarchy process

The DEAHP method for weight deviation and aggregation in the analytic hierarchy process (AHP) has been found flawed and sometimes produces counterintuitive priority vectors for inconsistent pairwise comparison matrices, which makes its application very restrictive. This paper proposes a new data envelopment analysis (DEA) method for priority determination in the AHP and extends it to the group AHP situation. In this new DEA methodology, two specially constructed DEA models that differ from the DEAHP model are used to derive the best local priorities from a pairwise comparison matrix or a group of pairwise comparison matrices no matter whether they are perfectly consistent or inconsistent. The new DEA method produces true weights for perfectly consistent pairwise comparison matrices and the best local priorities that are logical and consistent with decision makers (DMs)’ subjective judgments for inconsistent pairwise comparison matrices. In hierarchical structures, the new DEA method utilizes the simple additive weighting (SAW) method for aggregation of the best local priorities without the need of normalization. Numerical examples are examined throughout the paper to show the advantages of the new DEA methodology and its potential applications in both the AHP and group decision making.