A subproblem-centric model and approach to the nurse scheduling problem

The number of hospitals in Japan exceeds 10,000, and every month nurses are scheduled to shifts in about 30,000 units in total. There is serious demand for automating this scheduling task. In this paper, we introduce a mathematical programming formulation of the nurse scheduling problem in Japan, and develop a meta-heuristic approach to solve the problem. This scheduling problem is a hard combinatorial problem due to tight constraints involving such factors as the skill level of a team, the need to balance workload among nurses, and the consideration of nurses' preferences, even though the number of the nurses to be scheduled is not large, at between 20 and 40. The performance of our approach is demonstrated by the successful solution of data taken from actual scheduling problems. The proposed model and approach can be adapted for the majority of hospitals in Japan, as well as for some hospitals in other countries, and is likely applicable to many other scheduling problems in the fields of business and logistics.Key words.nurse scheduling – block-angular problem – subproblem – integer programming – relaxation – tabu search – branch-and-boundMathematics Subject Classification (1991):20E28, 20G40, 20C20