A mat-heuristic based solution approach for an extended nurse rostering problem with skills and units

The Nurse Rostering Problem (NRP) is a combinatorial optimization problem that deals with assignment of nurses to shifts based on a set of constraints. The real-life NRP applications are difficult to solve because of the fact that the problem is NP-hard. In this paper, we focus on two main aspects of the problem, model and solution methodology. Firstly, we propose a novel model that also considers unit assignments. Majority of the studies in the literature accounts for nurse, day, and shift assignments. Due to skill and experience levels, not every nurse can be assigned to every unit. Therefore, accounting for unit assignments helps the model to be more accurate in terms of real-life scenarios. Lastly, we propose a new mathematical based heuristic that combines Integer Programming (IP) and Discrete Particle Swarm Optimization (PSO). IP is used to generate initial schedules and PSO further improves the schedule. Any infeasibility is corrected by IP along the process. IP and PSO coordinate until final stopping criterion. Computational experiments on test data show that the proposed algorithm generates near optimal solutions.