Multi-objective student nurse allocation problem during training using exact and hybrid heuristic–metaheuristic methods

Assigning nursing students to clinical training wards while satisfying operational, educational, and institutional constraints is a difficult multi-objective combinatorial optimization problem known as the student nurse allocation problem (SNAP). Based on real-world scheduling requirements gathered from expert interviews and university practice, this study develops a mixed-integer programming model for SNAP. The optimization criteria are minimizing the total completion time across wards and minimizing ward switching across courses. Two solution approaches are proposed: the augmented epsilon-constraint (AUGMECON) method for obtaining exact non-dominated solutions in small-size instances and a constructive-heuristic-guided NSGA-II algorithm (CH-NSGA-II) for larger instances. Computational experiments were conducted on generated instances with different sizes and on a real-world case study. In small-size instances, the AUGMECON and CH-NSGA-II were evaluated using computational time and distance-based indicator. For larger generated instances, CH-NSGA-II was compared with a randomized constructive heuristic (RCH) baseline using the normalized hypervolume indicator. The results show that CH-NSGA-II generated non-dominated solutions in shorter computational times than AUGMECON for the tested small-size instances. In the larger instances, CH-NSGA-II achieved higher normalized hypervolume values than RCH across all tested problem groups, indicating improved Pareto-front quality compared with the randomized constructive baseline. In the real-world case, the best reported solution reduced the total completion time across wards by 30.9% compared with the available manual schedule, while satisfying the considered hard constraints. The results suggest that CH-NSGA-II can support clinical placement scheduling in nursing education by providing alternative trade-off solutions for decision makers.