Metaheuristics for Handling Time Interval Coverage Constraints in Nurse Scheduling

The problem of finding a high quality timetable for personnel in a hospital ward has been addressed by many researchers, personnel managers and schedulers over a number of years. Nevertheless, automated nurse rostering practice is not common yet in hospitals. Many head nurses are currently still spending several days per month on constructing their rosters by hand. In recent years, the emergence of larger and more constrained problems has presented a real challenge because finding good quality solutions can lead to a higher level of personnel satisfaction and to flexible organisational procedures. Compared to many industrial situations (where personnel schedules normally consist of stable periodic morning-day-night cycles) health care institutions often require more flexibility in terms of hours and shift types. The motivation for the research presented in this paper has been provided by real world hospital administrators/schedulers and the approach that we describe has been implemented in over 40 hospitals in Belgium. This paper consists of two main contributions: Modelling the real world situation more accurately than has been done in the previous literature. Presenting and evaluating an efficient and effective tabu search procedure to solve these problems (as represented in the real world model). The approach described in this paper concentrates on an advanced representation of the daily personnel requirements of healthcare institutions. We introduce ‘time interval’ personnel requirements. Instead of formulating the requirements as a number of personnel needed per shift type for each day of the planning period, time interval requirements allow for the representation of the personnel requirements per day in terms of start and end times of personnel attendance. This formulation enables the provision of a greater choice of shift work and part time work and reduces the amount of unproductive time because it enables the shifts to be split and combined. We present an algorithmic approach to handle this new formulation. We also set up a series of experiments which indicate that, not only does this approach take into account the requests and requirements of hospital schedulers, but it also generates higher quality schedules when compared with earlier approaches. The obtained results are better in the sense that various specific real world soft constraints can be satisfied by scheduling appropriate shift type combinations whereas in the shift type approach fixed shift types restricted the solution space.