A large-scale analytic hierarchy process including incomplete information and multiple evaluators and its application to personnel administration evaluation system

The conventional AHP supposes that several objects are completely compared by a single evaluator and hence, we can not directly apply it to an evaluation system with a lot of number of alternatives/criteria and multiple evaluators. Applying it to a personnel administration evaluation system in a section of an organization, we are faced with the problem of a large number of alternatives and multiple evaluators. There are several project teams in the section of the organization and all employees belong to each team. Because all project leaders compare some pairs of members within each team, multiple evaluators carry out a part of overall pairwise comparisons among all employees. This study develops a framework of AHP which is available to the evaluation system including multiple evaluators and a lot of alternatives or criteria. Dealing with a lot of alternatives or criteria, we do not assume complete pairwise comparisons and we permit different pairwise comparison values of the same pair by several evaluators. In order to determine priority weights of alternatives(criteria), we propose the logarithmic least squared method with the input-data of such pairwise comparison values. We show that the proposed framework of AHP is a geometric mean method in the case where a single evaluator compares all pair of alternatives. We prove that it is a group AHP which deals with the geometric mean among multiple comparison values of the same pair as the representative pairwise comparison value. We apply the framework of AHP to a personnel evaluation in software company in order to illustrate its validity.