<p>This study focuses on developing hybrid methods for the optimal and feasible solution of the panel assignment problem (PAP), which involves the fair allocation of proposals to reviewers while satisfying various constraints. The PAP is a complex combinatorial optimization problem that requires balancing fairness, efficiency, and computational feasibility. In this work, a combination of integer optimization techniques, Pareto-optimality principles, and Greedy algorithms are explored to address the challenges of panel assignment. Optimization-based methods, particularly integer programming approaches, demonstrate strong performance in identifying optimal solutions and consistently outperform previously published case studies in terms of solution quality. These methods excel at ensuring fairness and constraint satisfaction but can be computationally expensive for large-scale instances. On the other hand, Greedy algorithms provide a more computationally efficient alternative. Two variations of Greedy methods are examined: one that prioritizes solution quality at the cost of increased computational time and another that sacrifices optimality to achieve enhanced computational efficiency whilst still ensuring feasibility. Our findings indicate that while an optimized Greedy algorithm can yield near-optimal solutions, a more relaxed version offers a pragmatic balance between solution quality and computational efficiency. Additionally results show how Pareto-optimality can guide decision-making finding a balance between global optimality and maximizing commonality among reviewers who review the same proposal. The demonstrated methods and results provide valuable insights into how hybrid strategies can be tailored for practical panel assignment applications, ensuring both fairness and efficiency in panel assignment scenarios.</p>