A consideration of person-job (P-J) fit, which is a measure of the congruence between employees and their job, is recommended when solving the employee-job assignment (EJA) problem. In this paper, two types of P-J fit are proposed: (1) competency-based P-J fit, and (2) preference-based P-J fit. Competency-based P-J fit measures the overall compatibility in competencies between the employee and job profiles. Preference-based P-J fit, however, is a measure of the overall job satisfaction. Three quantitative indices are proposed to represent the two P-J fits: (1) EJA competency gap (for the competency-based P-J fit), (2) number of satisfied employees, and (3) average preference rank (both for the preference-based P-J fit). A multiple objective optimization approach is then utilized to determine the optimal EJA solution. Based on a predefined hierarchy of priorities, two solution approaches are described. From a provided illustrative example, EJA solutions from both solution approaches are determined and compared.