Solving nurse scheduling problems aided by vectorization of matrices

The nurse scheduling problem, known to be NP-hard, is modeled as an integer linear programming (ILP) problem. A constraint regarding the demand for a given number of nurses of different grades makes the problem complicated. Finding feasible solutions is often difficult. Applying vectorization of matrices, the ILP model is transformed into a standard ILP model. The coefficient matrix in constraints is then able to be precalculated, and therefore the solution process becomes easier while larger problem instances can be solved. Better solutions were obtained to 10 real data instances of nurse scheduling while the computational time was generally reduced. The transformation method based on the vectorization of matrices could be successfully applied to solving other non-standard ILP models.