Automatic Constraint Weight Extraction for Nurse Rostering: A Case Study

Nurse rostering is the complex problem of scheduling the shifts of nurses in hospitals. Scheduling by hand, which is still performed in many hospitals, is a relatively intensive and time consuming task, motivating the need for automated scheduling methods. Automatic scheduling, however, typically relies on accurate constraint weights. Manually de ning constraint weights is often unintuitive even for the most experienced practitioners. In a case study we compare the amount of constraint violations of real-world manual rosters to the importance of constraints, as de ned by nurses, and observe a mismatch between the two. Based on this real-world data we attempt to automatically extract constraint weights to allow for a more e cient and straightforward transition from manual to automatic scheduling. Automatic scheduling is a constraint optimization problem that typically employs weighted sum objective functions due to their simplicity and ease of implementation. However, one disadvantage of these methods is that constraint weights are problem dependent and therefore expert knowledge is needed to set the correct weights. Many nurse rostering approaches in the literature that utilize weighted sum objective functions de ne their constraint weights with the help of health care practitioners [1]. Others simply set the weights by trial-and-error, without elaborating on the choice of values or on their e ect on the overall quality of generated schedules. Setting numerical values for the constraint weights required by automatic planners is simply not intuitive even for experienced practitioners. As part of a software training for the use of an automatic planner, head nurses in a given Belgian hospital ward were asked to manually de ne, based on their experience and intuition, the importance of all 50 constraints for their rosters. Despite their extensive experience in manually designing schedules, the head nurses found it di cult to set these abstract values. In addition, weights were chosen in only 6 discrete categories (namely 1, 200, 500, 750, 1000, 1500), where a lot of constraints have the same weight, giving a low resolution to this highly complex problem. Although the automatic planner generated schedules with low overall penalty with respect to these weights, head nurses were often more satis ed after modication of the automatically generated schedules. As a consequence, the penalty of the resulting rosters increased, suggesting that the manually de ned constraint weights do not correspond to the true importance of constraints.