A Mixed-Integer Optimization Framework for Degree Audit and Course Allocation in Higher Education

Degree completion in higher education requires students to navigate hierarchical requirements involving course thresholds, credit limits, and logical conditions such as AND/OR and m-out-of-n rules. Some courses contribute to multiple requirements (shared), while others are exclusive (separate), complicating academic planning. Existing degree audit tools often rely on fixed, non-transparent prioritization rules and suboptimal greedy algorithms. To address these challenges, we introduce an optimization-based framework that models hierarchical structures, shared and separate requirements, and flexible satisfaction criteria. The model uses mixed-integer programming techniques and m-out-of-n logic to systematically optimize course selection and requirement satisfaction. Implemented in Pyomo with high-performance solvers, the framework scales to large datasets and provides real-world improvements in degree audit accuracy, credit utilization, and student progress insights. It offers a data-driven solution for academic planners and institutional decision-makers seeking to improve degree completion rates.