The analytic hierarchy process (AHP) is flawed as a procedure for ranking alternatives in that the rankings produced by this procedure are arbitrary. This paper provides a brief review of several areas of operational difficulty with the AHP, and then focuses on the arbitrary rankings that occur when the principle of hierarchic composition is assumed. This principle requires that the weights on the higher levels of a hierarchy can be determined independently of the weights on the lower levels. Virtually all of the published examples of the use of the AHP to evaluate alternatives relative to a set of criteria have assumed this principle. The key to correcting this flaw is the synthesis of the AHP with the concepts of multiattribute utility theory.