Analytic hierarchy process

Analytic Hierarchy Process (AHP), a multiple criteria analysis tool developed by Prof. Saaty, is a relative measurement theory that provides the objective mathematics to process the subjective and personal judgment of individual or group in decision making. Salient features of AHP weighting process are given here further details may also be found in Saaty (1980). The priority weight vector (w) of n elements measured in ratio scale is derived in AHP from a positive reciprocal square matrix A  

Decision makers are asked to respond to n(n -1) / 2 pairwise comparisons in which two elements at a time are compared with respect to their parent criteria. The relative dominance values (flj.) are then elicited from the said respondents using the so-called Saaty s fundamental 9-point scale. After the pairwise comparison matrix A is filled up with those value judgments Aj., the relative weights (w) of the elements are computed from the normalized right eigenvector associated to the principal eigenvalue (2 ) of A as shown in the following equations  

For a perfectly consistent pairwise comparative judgment matrix, the X.is equal to n. 

Note that the eigenvector method also yields a natural measure of consistency as described by the following equation  

Here is a numerical example to illustrate how weights are derived from a 3x3 pairwise comparison matrix A  

The analytic hierarchy process (AHP), developed by Saaty (1980), is a multicriteria decision making method for ranking alternatives. Using AHP, the DM can assess not only quantitative but also various qualitative factors, such as financial stability, feeling of trust, etc. in the supplier selection process. The buyer establishes a set of evaluation criteria and AHP uses these criteria to rank the different suppliers. AHP can enable the DM to represent the interaction of multiple factors in complex and unstructured situations. AHP does not require the scaling of criteria values. 

Multiple Criteria Decision Making in Supply Chain Management 

This chapter reviews the Analytic Hierarchy Process (AHP) method and explains how this method is applied to generate the weights for each category on the DDSC 

The first step in using the AHP to analyze a decision problem is to hierarchically break down the decision problem (objective) into its constituent components and identify the alternatives to be evaluated. The resulting hierarchy consists of the overall objective (goal) and one or more levels of sub-objectives. The alternatives to be evaluated are added at the lowest level of the hierarchy. According to Saaty (1980, pp. 79-83) a cluster should not contain more than 7 elements because results from psychological tests show that 1+1-2 are the maximum number of elements a person can effectively compare simultaneously. 

For cases where a large number of alternatives has to be evaluated, absolute measurement provides a second evaluation option that does not require a pairwise comparison of alternatives (cf. Saaty 2005, pp. 369-372). Also, methods to reduce the number of comparisons below n(n-l)/2 in large hierarchies while still ensuring a sufficient level of accuracy have been developed (cf. Millet and Harker 1990). 

To allow for interdependencies and feedback between the various elements constituting a decision support model, Saaty (1996) extended the AHP into the more general Analytic Network Process (ANP). A brief exposition of the ANP can be found in Saaty (2005, pp. 382-405) and Cheng et al. (2005) provide application examples. A case study of using the ANP 

Additionally, a scale that allows for comparisons exceeding one order of magnitude and functionality to include hard data are included in the Expert Choice software (cf. Forman and Selly 2002, p. 67 and pp. 140-144). Haines (1998) proposes approaches to accommodate cases where the decision maker is uncertain about his preferences and prefers to assign intervals of preference instead of single points. 

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Weighted scoring methods, such as Kepner-Tregoe Decision Analysis and the Analytical Hierarchy Process (AHP)... 

Saaty T.L. (1980) The Analytic Hierarchy Process. McGra.vf-HiR, Hew York. 

Chapter 4 covers the site selection and site controlling phase. Consequently, it deals with the assessment of individual production sites based on primarily qualitative criteria. Alternative Multiple Attribute Decision Analysis methods are reviewed and a decision support model employing the Analytic Hierarchy Process, which can be used both for site selection problems and as a controlling tool to perform site portfolio rankings of entire production networks, is proposed. Experiences from application in industry are reported. 

Analytic Hierarchy Process Eigenvector Method (cf. Saaty 1980, pp. 165-197)... 

The objective was to develop a site assessment model based on the Analytic Hierarchy Process that can be used both for site selection and site ranking/controlling purposes. While the different application situations to some extent require different criteria the intention was to develop a model as uniform as possible to achieve consistency in site strategy processes. 

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Eagan, P. and Weinberg, L., Application of analytic hierarchy process techniques to streamlined life-cycle analysis of two anodizing processes, Environ. Sci. Technol., 33, 1495-1500, 1999. 

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Case-based reasoning Analytical hierarchy process... 

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