Relaxation of Coverage Constraints in Hospital Personnel Rostering

Hospital personnel scheduling deals with a large number of constraints of a different nature, some of which need to be satisfied at all costs. It is, for example, unacceptable not to fully support patient care needs and therefore a sufficient number of skilled personnel has to be scheduled at any time. In addition to personnel coverage constraints, nurse rostering problems deal with time-related constraints arranging work load, free time, and personal requests for the staff. Real-world nurse rostering problems are usually over-constrained but schedulers in hospitals manage to produce solutions anyway. In practice, coverage constraints, which are generally defined as hard constraints, are often relaxed by the head nurse or personnel manager. The work presented in this paper builds upon a previously developed nurse rostering system that is used in several Belgian hospitals. In order to deal with widely varying problems and objectives, all the data in the model are modifiable by the users. We introduce a set of specific algorithms for handling and even relaxing coverage constraints, some of which were not supposed to be violated in the original model. The motivation is that such practices are common in real scheduling environments. Relaxations enable the generation of better-quality schedules without enlarging the search space or the computation time.