Analytic Hierarchy Process

The Analytic Hierarchy Process (AHP) is a mathematical decision making technique that allows consideration of both qualitative and quantitative aspects of decisions. It reduces complex decisions to a series of one-on-one comparisons, then synthesizes the results.

Compared to other techniques like ranking or rating techniques, the AHP uses the human ability to compare single properties of alternatives. It not only helps decision makers choose the best alternative, but also provides a clear rationale for the choice. The process was developed in the 1970s by Thomas Saaty, then a professor at the Wharton School.

Purpose

On a daily basis, and with limited time, you need to make decisions regarding your family, your job, and many other issues. In a business or policy setting, you have to avoid emotional confrontations and pursue a rational, common denominator. Normally there are 2 to 3 proposals for the solution already under discussion, but also arguments with pros & cons. The Analytic Hierarchy Process facilitates the rational evaluation of these pros and cons. It supports the pursuit of an optimal solution in a transparent manner, via:

simple evaluation & representation of the solutions
logic arguments & clearing emotions
checking quality of your decision
little need of time for your team
high acceptance within your team

The process in theory

The Analytic Hierarchy Process relies on three fundamental assumptions:

Preferences for different alternatives depend on separate criteria which can be reasoned about independently and given numerical scores.
The score for a given criteria can be calculated from sub-criteria. That is, the criteria can be arranged in a hierarchy, and the score at each level of the hierarchy can be calculated as a weighted sum of the lower level scores.
At a given level, suitable scores can be calculated from only pairwise comparisons.

Please look at the external links

Limitations of AHP

The "separability" assumption means that AHP cannot deal with criteria that interact. (example needed here)

The "weighted sum" assumption means that AHP cannot deal with a criterion that has a threshold. For example, in a boat you might look for durability, styling, and buoyancy. A little improvement in style might compensate for a little loss in durability. However, no improvement in either durability or style could compensate for the boat being heavier than water.

The "pairwise comparison" technique gets unwieldy if there are more than a few alternatives. If there are only four alternatives, there are six pairs to consider (4*3/2). However, for 20 alternatives, there would be 190 pairs.

Example of a software implementation

The process can be described by 3 phases and 7 steps (extracted from the process of the web-instrument easy-mind respectively from the online-manual)

For demonstrating the method this example is based on:

3 criteria
2 alternatives

First phase: collect & input data

Formulate your question

(1) what is the real question and goal for your decision ?

The people

(2) which team-members have come together to make a decision?

Your aspects and criteria

(3) which criteria are really important for your question ?

1.population 2.dection

Your proposals for solution and alternatives

(4) Which possible alternatives will you seriously consider ?

Second phase: compare and evaluate data

Criterion by criterion

(5) Compare and evaluate - which criterion is more important, if compared with the other: 1 or 2 ?

The slider method allows you to compare each criterion to the others by a percentile ranking (7) .

1 by 2
2 by 3
2 by 3

For evaluating there is a scale with a spectrum of scores from 1 to 9

Alternative by criterion

(6) compare and evaluate - which alternative matches better: A or B ?

Using the slider compare each alternative to the others
in order to develop a percentile ranking (7)

A by B

for every criterion 1, 2, 3

For evaluation there is a scale with a spectrum of scores from 1 to 9

Third phase: data interpretation

Your solution

(7) answers your question

The weights of scores show your criteria in comparison to each other, combined with the evalutions in step (5)

The weights indicate your alternatives' how good do fit to a single criterion or match it. They are combined based on your evalutions in step (6) and / or (5)

Factors of inconsistency of your evalutions of criteria and alternatives

The AHP measure the logic of all your evaluations to each other by the inconsistency factor. They provide a statement about the quality of your combined solution and decision.

Eliminating contradictions in your evaluations of the criteria and alternatives

The lower your inconsistency factor is, the more conclusive your evaluations are and the fewer contradictions they contain. To be able to represent a contradiction at all, you need at least three different evaluation scores.

Test your criterion - does your solution remain stable?

Incrementally change the percentage of your criteria and observe the effects on the ranking of your alternatives

Check your alternatives - how stable is the ranking ?

Check for each criterion, to see if the calculated ranking of your alternatives looks stable. To do so, check the distance between the blue vertical line (criteria) and intersections between the red lines (alternatives).

For criteria 1

The ranking of your alternatives is relatively stable.

The distance to the next intersection is more than 20 percentage points.

Only if you modify your evaluation a lot and your criterion weight changes from 29.7 by an amount of 26.7 percentage points to 56.4 does rank reversal occur.

For criteria 2

The ranking of your alternatives is absolutely stable.

There are no relevant intersections. Modifications of Your evaluations will not cause a rank reversal.

For criteria 3