Three-phase method for Nurse Rostering

The nurse rostering problem (NRP) aims at assigning working shift-patterns to a given number of nurses so as to satisfy a given set of constraints. Because of its great practical relevance and its computational intractability, any new effective method would be an addition to the arsenal of tools for dealing with NRP. Three ideas leading to a three-phase method constitute our contribution. Variable-fixing (VF) is the first one. This heuristic significantly reduces the problem size by discarding unpromising variables (let RNRP be the resulting reduced problem). Although RNRP is a small and sparse restricted version of the original NRP, computational experiments conducted on NSPLib dataset show that each optimal solution to RNRP is extended to an optimal or near-optimal solution to NRP. The second phase is a standard iterated local search (ILS) metaheuristic intended to create elite solutions' to RNRP. Building on the latter, the third phase defines a very small NRP which is solved with a general-purpose MIP-solver. Extended to the original NRP, the output of the last phase is the best solution found by the three-phase method. Extensive computational results are obtained on NSPLib dataset. The comparison shows that the proposed three-phase method outperforms four recent existing methods. Although slightly dominated from solution quality point of view, it is much faster than a general-purpose commercial solver.