RANDOM CONSISTENCY INDICES FOR ANALYTIC HIERARCHY PROCESSES

Levon R. Hayrapetyan
Houston Baptist University

ABSTRACT

Analytic Hierarchy Process (AHP) is a powerful multi-objective decision making tool
originally developed by Tomas Saaty (Saaty, 1980). It allows selecting overall the best choice
among all possible alternatives based on multiple objectives. The relative importance (weights) of
all objectives and the relative desirability of each choice with respect to each objective are
calculated based on pairwise comparison matrices created by the decision maker. The validity of
the results generated by AHP is determined by the level of consistency of each pairwise
comparison matrix used. The consistency is measured as a ratio of the consistency index and the
corresponding random index. The consistency indices are calculated based on pairwise
comparison matrices, whereas the random indices are generated using simulations. The literature
provides random indices for a limited matrix sizes only. This study presents an Excel-based
simulation, which can generate random index for any matrix size.

Keywords: Analytic-Hierarchy Process, Decision Support System, Multi-Objective Decision Making,
Consistency Index, Random Index.