Analytic Hierarchy Process: an introduction with examples and resources

Submitted by Richard Taylor | published 24th Jan 2012 | last updated 22nd Sep 2020
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Analytic Hierarchy Process (AHP) is  a type of multi-criteria assessment (MCA) technique for analyzing complex decisions. It was developed in the early 1980s to help decision-makers find the option that best suits their goal and understanding of the ‘problem’. Nowadays it is applied in a wide variety of fields (mainly engineering, business strategic management, education, quality assessment)

The method is is used to compare the set of options, using participants data, experience and judgment, and converting these into numerical values. It allows them to compare in a rational and consistent way diverse elements that are often difficult to measure (AHP measures intangibles in relative terms)

It evaluates various elements by comparing them to one another two at a time (pairwise comparison). Comparisons are made using a scale of ‘absolute judgements’ that represents how much more one element dominates another with respect to a given reference point.

AHP is very flexible and can be adapted to different needs and contexts. Criteria (or attributes) can be decided in advance or through a participatory process (increase transparency and dialogue). Criteria can be tangible and intangible, can have subcriteria and be as many as necessary. The process can involve as many participants as required. The number of alternatives to evaluate can also vary.

Implementing the AHP exercise with CIFOR researchers in Bogor (September 2011)

Decision situations

Decision situations to which the AHP can be applied include:

  • Choice - The selection of one alternative from a given set of alternatives, usually multiple decision criteria involved
  • Ranking - Putting a set of alternatives in order from most to least desirable
  • Prioritization - Determining the relative merit of a set of alternatives, as opposed to selecting a single one or merely ranking them
  • Resource allocation - Distributing resources among a set of alternatives
  • Benchmarking – Comparing processes in one organization with those of other best-of-breed organizations
  • Quality management - Dealing with the multidimensional aspects of quality and quality improvement
  • Conflict resolution - Settling disputes between actors with apparently incompatible goals or positions

Source: Wikipedia. Retrieved from

Implementing the AHP exercise with CIFOR researchers in Bogor (September 2011)

Application of the method

AHP Step 1:Define

  • Define the ‘problem’, the need and purpose of the decision (goal)
  • List the alternatives to evaluate (options)
  • Set up the criteria and sub-criteria (attributes)
  • Define the stakeholders and groups to involve in the process

AHP Step 2: Structure

  • Structure the Decision Hierarchy
  • Set up the hierarchy using the elements defined in Step 1
  • Goal on the top level, criteria in the intermediate level, set of options in the lowest level

Example Hierarchy set up in Step 2, Lekie case study

AHP Step 3: Pairwise Comparison

  • Compare elements to one another, two at a time, with respect to their impact/ importance on an element above them in the hierarchy
  • Use numerical values to conduct the pairwise comparisons, constructing a set of pairwise comparison matrices. Values in cells that are diagonal are mathematical inverses of each other
  • Several matrices to compare the options (alternatives) with respect to each criteria, and the criteria with respect to the goal

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Matrix of adaptation options (alternatives) proposed for Lekie case study (done with CIFOR researchers in Bogor, September 2011). This can be used for the pairwise comparison of options in relation to criteria (one such matrix could be used for each criteria) in STEP 3.

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Matrix of some example criteria which can be used for the pairwise comparison of criteria in relation to the decision goal. I.e. the relative importance of each criteria for the goal.

In the cells of the matrix*, corresponding to each pair of criteria, the preference values can be entered:

(Value / interpretation)

1 – Equal

3 – Slightly or moderately greater import

5 – Strongly more important

7 – Very strongly

9 – Extremely

* In the matrices used in ADx exercise (pictured above) we used half of the cells only to record this information.

AHP Step 4: Calculate relative priorities

  • Values in step 3 are processed to obtain numerical priorities or weights given to the elements
  • Mathematically, AHP derives priorities using the values of the principal right eigenvectors of the comparison matrices
  • Priorities are absolute numbers between zero and one, without units or dimensions
  • A priority .200 for a criteria has twice the weight in reaching the goal as one criteria with priority .100
  • Depending on the problem at hand, a priority or weight can refer to importance, or preference, or likelihood

AHP Step 5: Aggregate priorities

Aggregate relative priorities to produce overall priorities (final evaluation metrics) which sum to 1.000.

Compare the final results:

  • as trend data
  • in ranks (normalising the priorities)
  • in categories (significant difference between aggregates can be predefined eg. a difference of 0.15)
  • as progress targets

AHP drawbacks

Results change as new options/ alternatives are considered in the analysis. However, some criteria are not independent so this can bias or complicate the way in which they are assessed (clusters can be formed). Also, AHP can become complicated if lots of criteria and options are considered.

In conclusion, the AHP method is used in a variety of problem domains, it is widely used and is published in many studies and research papers. It is technically valid and practically useful. It can promote discussion among participants and capture different points of view. It can compare tangibles and intangibles. To compensate drawbacks, it can be used in combination with other (objective and subjective) methods.

Application to adaptation decision-making

AHP has been used to support adaptation decision-making in many different contexts, including:

Adaptation options for resiliency planning in the Kalika Municipality in Nepal

Irrigated agriculture in the Guadiana Basin, Spain

Climate Adaptation in Greater Banjul, Gambia

Note that the method does not seem to need any particular modification for use in adaptation projects but (as always) users need to be aware of the conditions of applicability of the method.

Further resources


Seminal reference: The Analytic Hierarchy Process for Decisions in a Complex World (Thomas Saaty 1982, revised ed. 2000)


Some useful portals with tools/software for AHP: