A Fairness-Based Heuristic Technique for Long-Term Nurse Scheduling

We present a new heuristic long-term solution to the Nurse Scheduling Problem (NSP). Nurse scheduling requires the satisfaction of a set of constraints: Hard constraints that must be satisfied, and soft constraints that are specified by the nurses according to their preferences. The quality of a technique is measured by the level of satisfaction of those constraints, which we measure using a penalty system. We propose a three-phase solution based on the way nurses trade shifts: In the first phase, we generate a schedule that satisfies all the hard constraints irrespective of the individual nurses. Then, each nurse is matched to her optimal schedule. Finally, we satisfy as many of the soft constraints as possible using shift swapping between the different nurses' schedules. We analyze the performance of our technique and it obtained satisfactory results in reasonable time compared to a brute-force generated optimal schedule that takes an extremely long time to generate. We extended the scheduling technique to multiple scheduling periods by carrying the old penalties accumulated by a nurse to her new schedule. This guarantees fairness over the long term, and decreased the variance in overall penalties by over 50% compared to independently scheduling each schedule period.