Analytic Hierarchy Process Model

Fundamentals

The analytic hierarchy process (AHP) comprises a hierarchy of levels (e.g., goals, criteria, and alternatives). At each level, manager(s) examine each entity on a level across all combination of pairs for the subordinate level. For example, if the goal was to select a car to purchase, one of the criteria for selecting that car might be fuel economy. To determine a priority of cars for a given criterion, each car would be compared to all other alternative cars in terms of that particular criterion. In this case, a hybrid sedan (40 mpg) would be considered more preferable than a midsize sport utility vehicle (25 mpg). This would be repeated for all criteria (e.g., storage space, price, maintenance cost, styling, etc.). Then, each criterion would be evaluated against all other criteria. Once all comparisons have been made (and the rating and ranking have been completed), the range of decisions (choice of cars) will have been prioritized according to the criteria.

The following is the general process by which the AHP is applied in a decision-making context. AHP uses the following basic format to elicit key information about the decision problem:

• Describe the problem to be considered.
• Develop a hierarchy for the problem under consideration. A basic AHP hierarchy might include objectives at the top level, criteria at the next level, and alternatives at the lowest level. There can be more or fewer levels.
• Given this hierarchy, a set of pairwise comparisons are developed (such that for each level of the hierarchy, there are n[n−1]/2 judgments to be made using a relative scale). For example, if there are two items being compared, A and B, the decision maker would be asked which element is preferred, more important, etc. Then, the decision maker would indicate the strength of that relationship: equal, moderate, strong, very strong, or extreme (and the following absolute numbers are assigned: 1, 3, 5, 7, or 9, respectively). For example, if A is considered moderately more important than B, it would be assigned the value 3 to indicate that it is three times more important than B. Conversely, B is one third as important as A (the reciprocal). Pairwise comparisons are made for each level of the hierarchy.

Once pairwise-comparison judgments have been made, a solution technique is used to identify the principle eigenvalues for each item in a particular level of the hierarchy. These eigenvalues correspond to the relative weight assigned to each item. The relative weights can be combined across the various levels (e.g., decision criteria) to determine the most preferred alternative (according to the decision-maker’s judgments from the pairwise comparisons).

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