A variable neighborhood search based matheuristic for nurse rostering problems

A practical nurse rostering problem, which arises at a ward of an Italian private hospital, is considered. In this problem, it is required each month to generate the nursing staff shifts subject to various requirements. A matheuristic approach is introduced, based on a set of neighborhoods searched by a commercial integer programming solver within a defined global time limit. Generally speaking, a matheuristic algorithm is a heuristic algorithm that uses non trivial optimization and mathematical programming tools to explore the solutions space with the aim of analyzing large scale neighborhoods. The solutions computed by the proposed procedure are compared to the solutions achieved by the pure solver within the same time limit. The results show that the proposed solution approach outperforms the solver in terms of solution quality.