A Hybrid Constraint Programming Approach for Nurse Rostering Problems Rong Qu and Fang He 1 Abstract: Due to the complexity of nurse rostering problems (NRPs), Constraint Pro- gramming (CP) approaches on their own have shown to be ineffective in solving these highly constrained problems. We investigate a two-stage hybrid CP approach on real world benchmark NRPs. In the first stage, a constraint satisfaction model is used to generate weekly rosters consist of high quality shift sequences satisfying a subset of constraints. An iterative forward search is then adapted to extend them to build complete feasible solutions. Variable and value selection heuristics are employed to improve the efficiency. In the sec- ond stage, a simple Variable Neighborhood Search is used to quickly improve the solution obtained. The basic idea of the hybrid approach is based on the observations that high qual- ity nurse rosters consist of high quality shift sequences. By decomposing the problems into solvable sub-problems for CP, the search space of the original problems are significantly reduced. The results on benchmark problems demonstrate the efficiency of this hybrid CP approach when compared to the state-of-the-art approaches in the literature. 1. Introduction Due to their complexity and importance in real world modern hospitals, nurse ros- tering problems (NRPs) have been extensively studied in both Operational Re- search and Artificial Intelligence societies for more than 40 years [6,10,13]. Most NRPs in real world are NP-hard [16] and are particularly challenging as a large set of different rules and specific nurse preferences need to be satisfied to warrant high quality rosters for nurses in practice. Other wide range of heterogeneous and specific constraints makes the problem over-constrained and hard to solve effi- ciently. NRPs consist of generating rosters where required shifts are assigned to nurses over a scheduling period satisfying a number of constraints [6,10]. These con- straints are usually defined by regulations, working practices and preferences of nurses in different countries. They are usually categorised into two groups: hard constraints and soft constraints, as defined below:  Hard constraints must be satisfied in order to obtain feasible solutions for use in practice. A roster satisfying all hard constraints is usually termed feasible. A common hard constraint is to assign all shifts required to the limited num- ber of nurses. Rong Qu and Fang He, School of Computer Science, University of Nottingham, Jubilee Campus, Nottingham, NG8 1BB, UK, email: {rxq|fxh}@cs.nott.ac.uk