Transparent Internship Scheduling Tool with LLM-Integrated Explainability: A Comparative Analysis of MILP and the Heuristic Regret Approach

Healthcare schools must assign students to a limited number of internship places, and the process must satisfy department rotation, internship round, institution uniqueness, ward capacity, and preference rules. Manual planning is slow and automated results can also be difficult to inspect and explain. This study compares a capacity-constrained regret heuristic with mixed-integer linear programming (MILP). The heuristic uses the feasible options available at each decision, while the MILP reduces total weighted cost across the cohort. Method-specific evidence records support a separate explanation step with the Gemini 3 Model. The scheduling experiments used 133 students and produced 399 valid placements with each method. The baseline MILP cost was 5275.2, which was 3.5% below the heuristic cost of 5467.5. The median runtimes were 124.98 s for MILP and 1.10 s for the heuristic. The heuristic completed the 75% and 50% capacity cases. The corresponding MILP cases reached the ten-minute limit without a result. Regret reduced the mean heuristic cost by 1.05% against the tested no-regret variants. MILP reduced the mean and median student costs, but both methods had the same maximum student cost of 194.6. The explainability experiment used three cases, two methods, and three experts. All 18 correctness checks were positive. The heuristic received a higher mean score for alternative explanation and depth. Uncertainty scores were equal, and quality scores were similar. The results show a trade-off between cohort cost, runtime, capacity pressure, local decision evidence, and explanation detail.