In overly congested airports requests for landing and take-off slots are allocated according to the IATA World Scheduling Guidelines (WSG). A central concept of these guidelines is the prioritization of the satisfaction of the requested slots according to a hierarchy that recognizes historic usage rights of slots. A number of criteria have been proposed in the literature to optimize airport slot allocation decisions. Multi-objective programming models have been proposed to investigate the trade-offs of the slot allocation objectives for the same level of the slot hierarchy. However, the literature currently lacks models that can study in a systematic way the trade-offs among the scheduling objectives across all levels of the hierarchy and the airport schedule as a whole. To close the existing literature gap, we are proposing a new tri-objective slot allocation model (TOSAM) that considers total schedule displacement, maximum schedule displacement and demand-based fairness, and we introduce a multi-level, multi-objective algorithm to solve it. We are using real world slot request and airport capacity data to demonstrate the applicability of the proposed approach. Our computational results suggest that the systematic consideration of the interactions among the objectives of the different levels of the slot hierarchy, results to improved schedule-wide slot scheduling performance. In particular, we found that small sacrifices made for the attainment of the scheduling objectives of the upper echelons of the slot hierarchy, result in significant improvements of the schedule-wide objectives.