Hospital-wide reactive scheduling of nurses with preference considerations

This paper presents a new methodology for reactively scheduling nurses in light of shift-by-shift imbalances in supply and demand. In most hospitals, the nursing staff is given a midterm schedule that specifies their work assignments for up to 6 weeks at a time. However, emergencies, call-outs, and normal fluctuations in personnel requirements can play havoc with the schedule. As a result, it is necessary to make short-term adjustments, either by reallocating resources when shortages exist or by cancelling assignments when demand drops. The need to take into account individual preferences further complicates the process. The problem associated with making the daily adjustments is formulated as an Integer Program (IP) and solved within a rolling horizon framework. The idea is to consider 24 hours at a time, but to only implement the results for the first 8 hours. The IP is then re-solved for the next 24 hours after several hours have elapsed and new data are available, and so on. Initial attempts to solve 50-nurse problems with a commercial code proved to be unsuccessful and led to the development of a branch-and-price algorithm. Included in the algorithm are a feasibility heuristic to find the upper bounds and a cut generation procedure to improve the lower bound computations. A set-covering-type IP was used to find upper bounds and mixed-integer rounding cuts were used to tighten the relaxed feasible region. Although the effectiveness of all but the set covering heuristic proved to be marginal, most problem instances with up to 200 nurses were solved within 10 minutes.