A Variable Neighbourhood Search for Nurse Scheduling with Balanced Preference Satisfaction

The nurse scheduling problem (NSP) is a combinatorial optimisation problem widely tackled in the literature. Recently, a new variant of this problem was proposed, called nurse scheduling problem with balanced preference satisfaction (NSPBPS). This paper further investigates this variant of the NSP as we propose a new algorithm to solve the problem and obtain a better balance of overall preference satisfaction. Initiall, the algorithm converts the problem to a bottleneck assignment problem and solves it to generate an initial feasible solution for the NSPBPS. Posteriorly, the algorithm applies the Variable Neighbourhood Search (VNS) metaheuristic using two sets of search neighbourhoods in order to improve the initial solution. We empirically assess the performance of the algorithm using the NSPLib benchmark instances and we compare our results to other results found in the literature. The proposed VNS algorithm exhibits good performance by achieving solutions that are fairer (in terms of preference satisfaction) for the majority of the scenarios.