Optimal Scheduling of Nursing Shifts : A Case Study on Work Scheduling at Haukeland University Hospital

Abstract

This thesis presents a nurse scheduling problem tailored to characteristics common of Norwegian hospitals. The problem involves allocating nurses to specific shifts to ensure coverage of demand, while respecting work regulations and accounting for balance of workload, general nurse preferences and fairness. We formulate models for the nurse scheduling problem in line with the scheduling principles at Haukeland University Hospital and solve them using mathematical programming techniques. The purpose lies in the attempt to present a more efficient approach to the problem, compared to the manual scheduling approach currently utilized at the hospital. The method involves formulating a mixed integer programming model, which is implemented computationally in an optimization software. Multiple decision models are produced to represent two different forms of schedules, one cyclical and one calendar based. The model for the cyclical schedule can be optimized directly using the solver of the software. The model for the calendar-based schedule is more complex and is therefore solved by designing a decomposition heuristic approach to find a good solution in a reasonable computational time. The conclusion is that the schedules derived from the decision models are viable, with emphasis on the considerable time savings compared to the current scheduling approach at Haukeland. Currently, the hospital uses a manual method which takes approximately four to six weeks to create a schedule, whereas the models proposed in this thesis are able to derive an optimal solution within two hours. The models manage to effectively account for many criteria, including work regulations, fairness, balance of workload and preferred practices. The work in this thesis has been conducted through close cooperation with a representative from the staffing department at Haukeland, and the solutions derived from the models are able to capture their considerations in practice to a large extent. Our work has contributed to giving staff at Haukeland insight on how optimization and computational tools can be used to deal with their complex work scheduling problem.