Improving the Robustness of Nurse Schedules in a Real-Life Instance - a Quantitative Analysis Based on Simulation and Rescheduling Under Uncertainty
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Nurse schedules are subject to uncertainties in both the demand and supply of nurses, which often change on a daily basis. The demand depends on the number and severity of the patients admitted, while the supply depends on the number of absent employees. Schedules are usually created manually, taking only expected values and insights from previous periods into account. This makes it difficult to create schedules that always meet demand. We define a schedule's robustness as its stability, or capability to absorb unexpected events, as well as its flexibility, or capability to be reestablished when demand exceeds supply. If a schedule is not robust, it might be necessary to make multiple daily changes to the schedule, which is costly, time-consuming for the managers and inconvenient to the employees. It is therefore desirable to identify means to make schedules more robust. In this thesis, we study this robustness, using real-life data from the Department of Neonatal Intensive Care (DNIC) at St. Olavs Hospital. We define a baseline MIP scheduling model used to make nurse schedules subject to the rules, regulations and preferences at DNIC. We also propose multiple proactive scheduling strategies intended to increase the schedule robustness, which are added to the baseline model. To imitate the uncertainties, we define models simulating the demand and supply of nurses, based on probability distributions calculated using historical data provided by DNIC. Both the simulation results and an initial schedule are used as inputs to a rolling horizon rescheduling model, which uses mixed integer programming to solve the daily rescheduling problem using the same rescheduling actions as are used in practice at DNIC. Finally, we evaluate the robustness of multiple schedules using various stability and flexibility measures. Using the proactive scheduling strategies proposed, we significantly outperform the baseline model in terms of robustness in three out of four cases. We also combine the best strategies into one model, successfully boosting the performance further. The best performing strategies include 1) assign a reasonable buffer of employees in excess of minimum demand on all shifts; 2) assign excess capacity to the shifts where employees who are extra vulnerable to absence are scheduled, and 3) allow employees to work extra weekends in exchange for extra off days. Another key insight obtained is the optimal duration of the replanning period when rescheduling. Using the robustness measures, we show that the longer the duration of the replanning period is, the more efficiently the schedule is reestablished.