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Analytic hierarchy process

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The Analytic Hierarchy Process (AHP) is a technique for decision making where there are a limited number of choices, but where each has a number of different attributes, some or all of which may be difficult to formalize. [1] It is especially applicable when decisions are being made by a team.

AHP can assist with identifying and weighting selection criteria, analyzing the data collected for the criteria, and expediting the decision-making process. It helps capture both subjective and objective evaluation measures, providing a useful mechanism for checking the consistency of the evaluation measures and alternatives suggested by the team. [2]

The process is based on a series pairwise comparisons which are then 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.[citation needed]

Criticisms

Both the theoretical and practical soundness of AHP has been challenged. Some have maintained that AHP assigns arbitrary or ordinal measures to the pairwise comparisons.[citation needed] 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[citation needed] and actuaries can use it to evaluate risks.[citation needed] However, in those fields specific models already exist that make AHP unnecessary and inaccurate. 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 [3][4] Proponents argue that rank reversal may still be desirable but this is also controversial.[citation needed] Given the example, this would be the position that if C were eliminated, the preference of A over B should be switched.

Another strong theoretical problem of AHP was found by Perez, et. al. [5]. This has to do with what they identify as an "indifferent criterion" flaw. Indifferent 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.

See also

Thomas Saaty, developer of the Analytic Hierarchy Process.

References

  1. ^ Analytic Hierarchy Process example at cmu.edu
  2. ^ Analytical Hierarchy Process :: Overview at thequalityportal.com
  3. ^ Dyer, J. S. (1990): Remarks on the Analytic Hierarchy Process. In: Management Science, 36 (3), S. 249-258.
  4. ^ Simon French "Decision Theory: An Introduction to the Mathematics of Rationality", Ellis Horwood, Chichester, 1988.
  5. ^ J. Perez, J. Jimeno, E. Mokotoff, Another Potential Strong Shortcoming of AHP, Department of Economics, University of Alcala Spain
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