Analytic Hierarchy Process (AHP)

The Analytic Hierarchy Process (AHP) is structured for decision-making in complex environments as a theory of measurement through pairwise comparisons. In this process the problem is broken down into hierarchy of criteria or attributes that are more easily analyzed and compared independently

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.


  • Duration
    Long (more than 1 hour)
  • Complexity:
  • Group size:
    5 to 50 persons

Description Long

The Analytic Hierarchy Process (AHP) is a multi-criteria decision-making approach based on mathematics and psychology, which was introduced by Thomas L. Saaty in 1980's. The AHP is a decision support technique that facilitates solving complex decision problems. In this method there exists a multi-level hierarchical structure of objectives, criteria, subcriteria, and alternatives, providing a comprehensive and rational framework for structuring a decision problem. The AHP method represents and quantifies its elements and relates those elements to overall goals, and evaluates alternative solutions. Participants are able to develop relative weights (Priorities) in order to distinguish the significane level of the criteria by ranking them on different scales (e.g. scales from 1 to 10, percents). AHP has particular application in group decision-making, and is used in a wide variety of decision situations, in fields such as government, business, industry, healthcare, and education.



  1. This is about making a decision in a hierarchical process, therefore ideas have to be collected in a previous step.


  1. Define the problem clearly and specify the solution to be obtained.
  2. Structure the hierarchy from the overall managerial goals through relevant intermediate levels (Criteria) to the level where problems would be solved (Alternatives).
  3. Create a pair wise comparison matrix of the relative contribution or impact of each element on each governing objective or criterion in the adjacent upper level.
  4. Obtain all n(n-1)/2 judgments specified by the set of matrices in step 3.
  5. Synthesize the comparative judgments to determine the relative value of elements.
  6. Repeat step 3, 4, and 5 for all levels and clusters in the hierarchy.
  7. Apply the matrix computation among the relative value of elements in each level to determine the priority of elements in the lowest level with respect to the goal in the highest level.

Hints from experience

Note that some of the criteria could be contrasting; however, choose the one, which achieves the most suitable trade-off among the different criteria.


B. Llamas, M. Arribas, E. Hernandez and L.F. Mazadiego (2014). Pre-Injection Phase: Site Selection and Characterization. CO2 Sequestration and Valorization, Mr. Victor Esteves (Ed.), ISBN: 978-953-51-1225-9, InTech, DOI: 10.5772/57405. Retrieved 5 August 2015 from,,. Analytic Hierarchy Process. Retrieved 7 August 2015, from

Rebernik, M., & Hojnik, B. B. (2008). Module 4: Idea evaluation methods and techniques. Ekonomska-poslovna fakulteta. Retrieved 7 August 2015, from

Saaty, T. (1980). The analytic hierarchy process. New York: McGraw-Hill International Book Co.

Saaty, T. L. (2008). Decision making with the analytic hierarchy process. International journal of services sciences, 1(1), 83-98. DOI: 10.1504/IJSSCI.2008.017590

Triantaphyllou, E., & Mann, S. H. (1995). Using the analytic hierarchy process for decision making in engineering applications: some challenges. International Journal of Industrial Engineering: Applications and Practice, 2(1), 35-44. Retrieved 6 August 2015 from,

Wollmann, D., Steiner, M. T. A., Vieira, G. E., & Steiner, P. A. (2014). Details of the analytic hierarchy process technique for the evaluation of health insurance companies. Production, 24(3), 583-593. Retrieved 5 August from,

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