The Analytic Hierarchy Process: A Mathematical Model for Decision Making Problems

The ability to make the right decision is an asset in many areas and lines of profession including social work, business, national economics, and international security. However, decision makers often have difficulty choosing the best option since they might not have a full understanding of their preferences, or lack a systematic approach to solve the decision making problems at hand. The Analytic Hierarchy Process (AHP) provides a mathematical model that helps the decision makers arrive at the most logical choice, based on their preferences. We investigate the theory of positive, reciprocal matrices, which provides the theoretical justification of the method of the AHP. At its heart, the AHP relies on three principles: Decomposition, Measurement of preferences, and Synthesis. Throughout the first five chapters of this thesis, we use a simple example to illustrate these principles. The last chapter presents a more sophisticated application of the AHP, which in turn illustrates the Analytic Network Process, a generalization of the AHP to systems with dependence and feedback