Analytic Hierarchy Process

The Analytic Hierarchy Process (AHP) is a decision making technique developed by Thomas Saaty. He claimed AHP allows for the rational evaluation of pros and cons concerning different alternative solutions to a multi-goal problem.

AHP is based on a series pairwise comparions and then those comparisons are checked for internal consistency. The procedure can be summarized as:

1. Decision makers are asked their preferences of attributes of alternatives. For example, if the alternatives are comparing potential real-estate purchases, the investors might say they prefer location over price and price over timing.
2. Then they would be asked if the location of alternative "A" is preferred to that of "B", which has the preferred timing, and so on.
3. This creates a matrix which is evaluated by using eigenvalues to check the consistency of the responses. This produces a "consistency coefficient" where a value of "1" means all preferences are internally consistent. This value would be lower, however, if decision makers said X is preferred to Y, Y to Z but Z is preferred to X (such a position is internally inconsistent).

It is this last step that that causes many users to believe that AHP is theoretically well founded.

Criticisms

AHP has had many challenges to its theoretical and practical shortcomings from those who have a more thurough grounding in all the decision sciences. Some have maintained that AHP assigns arbitrary or ordinal measures to the pairwise comparisons. Proponents maintain that while this is true of the 'verbal' mode of AHP, it has been demonstrated that in situations where there is adequate variety and redundancy, accurate ratio scale priorities can be derived from such judgments.

Proponents claim that it could be used by Aircraft engineers to evaluate alternative wing designs and actuaries can use it to evaluate risks. However, in those fields specific models already exist that make AHP unnecessary and innacurate. AHP, for example, cannot compute the value of a premium in the way that an actuary does. Such methods have to use specific mathematical theorems unique to that field.

AHP, like many systems based on pairwise comparisons, can produce "rank reversal" outcomes. That is a situation where the order of preference is, for example, A, B, C then D. But if C is eliminated for other reasons, the order of A and B could be reversed so that the resulting priority is then B, A, then D. It has been proven that any pairwise comparison system will still have rank-reversal solutions even when the pair preferences are consistent Proponents argue that rank reversal may still be desirable but this is also controversial. Given the example, this would be the position that if C were elliminated, the preference of A over B should be switched.

Another strong theoretical problem of AHP was found by Perez, et. al. This has to do with what they identify as an "indiferent criterion" flaw. Indiferent criterion requires that once A, B, C and D are ranked according to criteria, say, W, X, Y, adding another criterion for which A, B, C, and D are equal, should have no bearing on the ranks. Yet, Perez et al prove that such an outcome is possible. Note that this flaw, too, is a shortcoming of any pairwise comparison process, not just AHP. But AHP's consistency-checking methods offer no guarantee such flaws cannot occur, since there are solution sets with these flaws even when preferences are consistent.

Many alternatives to AHP are economically viable, especially for larger, riskier decision. Methods from decision theory and various economic modeling methods can be applied. A scoring method that has a superior track record of improving decisions was developed by Egon Brunswik in the 1950's. Other methods such as Applied Information Economics quantify risk, cost and value in economically meaningful terms even where AHP considers them to be "immeasurable".

We can use Criterium Decision Plus for calculation in this AHP method