2 European Journal of Operational Research 48 (1990) 2-8 North-Holland An overview of the Analytic Hierarchy Process and its applications Luis G. Vargas Joseph M. Katz Graduate School of Business, University of Pittsburgh, Pittsburgh, PA 15260, USA 1. Introduction: Principles and axioms The Analytic Hierarchy Process (AHP) is a theory of measurement for dealing with quantifia- ble and/or intangible criteria that has found rich applications in decision theory, conflict resolution and in models of the brain. It is based on the principle that, to make decisions, experience and knowledge of people is at least as valuable as the data they use. Decision applications of the AHP are carried out in two phases: hierarchic design and evalua- tion. The design of hierarchies requires experience and knowledge of the problem area. Two decision makers would normally structure two different hierarchies of the same problem. Thus a hierarchy is not unique. On the other hand, even when two people design the same hierarchy, their prefer- ences may yield different courses of action. How- ever, a group of people can work together to reach consensus on both the hierarchy (design) and on the judgments and their synthesis (evaluation). The evaluation phase is based on the concept of paired comparisons. The elements in a level of the hierarchy are compared in relative terms as to their importance or contribution to a given crite- rion that occupies the level immediately above the elements being compared. This process of com- parison yields a relative scale of measurement of the priorities or weights of the elements. That is, the scale measures the relative standing of the elements with respect to a criterion independently of any other criterion or element that may be considered for comparison. These relative weights sum to unity. The comparisons are performed for Received November 1989 the elements in a level with respect to all the elements in the level above. The final or global weights of the elements at the bottom level of the hierarchy are obtained by adding all the contribu- tions of the elements in a level with respect to all the elements in the level above. This is known as the principle of hierarchic composition. While there is an infinite number of ways of synthesizing the weights of the alternatives and the weights of the criteria, the additive aggregation rule of the AHP has the advantage of intuitive understanding of the apportionment of the whole into its parts. A useful feature of the AHP is its applicability to the measurement of intagible criteria along with tangible ones through ratio scales. In addition, by breaking a problem down into its constituent parts and relating them in a logical fashion from the large, descending in gradual steps, to the smaller and smaller, one is able to connect through simple paired comparison judgments the small to the large. The AHP is a tool that has found uses in a wide range of problem areas from simple personal to complex and capital intensive decisions. The success of the theory is a consequence of its sim- plicity and robustness. The axioms of the theory are as follows: Axiom 1: (Reciprocal Comparison). The deci- sion maker must be able to make comparisons and state the strength of his preferences. The intensity of these preferences must satisfy the reciprocal condition: If A is x times more preferred than B, then B is 1/x times more preferred than A. Axiom 2: (Homogeneity). The preference are represented by means of a bounded scale. Axiom 3: (Independence). When expressing preferences, criteria are assumed independent of the properties of the alternatives. 0377-2217/90/$03.50 © 1990 - Elsevier Science Publishers B.V. (North-Holland)