Deriving weights from pair-wise comparison matrices by goal programming

Derivation of weights from pairwise comparison matrices (PCMs) is the most important task in the Analytic Hierarchy Process. Traditionally, eigenvector method, least squares and logarithmic least squares methods are used to derive the weights from PCMs. In this paper, a goal programming method has been proposed to derive the weights from PCMs. This new method has been contrasted with the least squares and logarithmic least squares methods on various properties of ratio-scale matrices. A number of advantages of goal programming method over the least squares and logarithmic least squares methods are also pointed out. Finally, the proposed method has been illustrated by means of numerical examples.