The Analytic Hierarchy Process (AHP) provides the underlying decision process that powers Decision Lens. AHP helps decision makers find one that best suits their goal and their understanding of the problem. It provides a comprehensive and rational framework for structuring a decision problem, for representing and quantifying its elements, for relating those elements to overall goals, and for evaluating alternative solutions.

1. Define the problem and specify the solution desired.

2. Organize the problem as a hierarchy. In doing this, participants explore the aspects of the problem at levels from general to detailed, then express it in the multileveled way that the AHP requires. As they work to build the hierarchy, they increase their understanding of the problem, of its context, and of each other's thoughts and feelings about both.

3. Construct a pairwise comparison matrix of the relevant contribution or impact of each element on each governing criterion in the next higher level. In this matrix, pairs of elements are compared with respect to a criterion in the superior level. In comparing two elements most people prefer to give a judgment that indicates the dominance as a whole number. The matrix has one position to enter that number and another to enter its reciprocal. Thus if one element does not contribute more than another, the other must contribute more than it. This number is entered in the appropriate position in the matrix and its reciprocal is entered in the other position. An element on the left is by convention examined regarding its dominance over an element at the top of the matrix.

4. Obtain all judgments required to develop the set of matrices in step 3. If there are many people participating, the task for each person can be made simple by appropriate allocation of effort, which we describe in a later chapter. Multiple judgments can be synthesized by using their geometric mean.

5. Having collected all the pairwise comparison data and entered the reciprocals together with unit entries down the main diagonal, the priorities are obtained and consistency is tested.

6. Perform steps 3, 4, and 5 for all levels and clusters in the hierarchy.

7. Use hierarchical composition (synthesis) to weight the vectors of priorities by the weights of the criteria, and take the sum over all weighted priority entries corresponding to those in the next lower level and so on. The result is an overall priority vector for the lowest level of the hierarchy. If there are several outcomes, their geometric average may be taken.

8. Evaluate consistency for the entire hierarchy by multiplying each consistency index by the priority of the corresponding criterion and adding the products. The result is divided by the same type of expression using the random consistency index corresponding to the dimensions of each matrix weighted by the priorities as before. The consistency ratio of the hierarchy should be 10 percent or less. If it is not, the quality of information should be improved─ perhaps by revising the manner in which questions are posed to make the pairwise comparisons. If this measure fails to improve consistency, it is likely that the problem has not been accurately structured ─ that is, similar elements have not been grouped under a meaningful criterion. A return to step 2 is then required, although only the problematic parts of the hierarchy may need revision.

## Comments