Declarative Modelling of Fair Hierarchical Task Allocation Using Answer Set Programming

Task allocation is a well-known optimization problem that has been widely addressed using techniques such as Integer Programming (IP) and nature-inspired algorithms. However, many existing approaches lack flexibility and contextual awareness, especially in scenarios requiring fairness and hierarchical compliance. This research proposes an optimized Answer Set Programming (ASP) model for the Fair Hierarchical Task Allocation (FHTA) problem. The model incorporates knowledge-based reasoning to support context-specific constraints and generates stable models (answer sets) that satisfy both fairness and organizational hierarchy. A generate-and-test methodology is employed, wherein candidate solutions are produced and evaluated against a set of hard and soft constraints. A realistic problem scenario involving academic task assignment was formalized in ASP, using the Potassco toolkit (Clingo). The performance of the model was evaluated across varying problem sizes, specifically by changing the number of tasks and personnel involved. Metrics such as CPU time and total runtime were recorded. The results show that the ASP model performs efficiently for moderately sized instances and effectively achieves fair and hierarchical task allocation. This work demonstrates that ASP provides a scalable, explainable, and flexible framework for solving complex task allocation problems in hierarchical organizations.