Long term nurse scheduling via a decision support system based on linear integer programming: A case study at the University Hospital in Cagliari

This paper proposes a long term nurse scheduling approach based on linear integer programming. The main contribution consists in the derivation of a mathematical model that characterizes in a given time horizon, the set of feasible scheduling that satisfy a series of constraints related to contractual rules, specific local requirements, and different working conditions of nurses. When performing optimization, different goals may be imposed. Motivated by a real case study in Italy, special attention is devoted to the following three main issues: reduce the requirement of nurses from other departments, keep the number of working hours of each nurse as close as possible to a given value that is proportional to the length of the considered time horizon, and assign not isolated free days. To address the issues related to computational complexity in the case of very long time horizons and even more, to keep into account sudden variations in the availability of nurses, the proposed optimization model has been included in a Decision Support System (DSS) which allows to partition the whole time interval in several time intervals, where the scheduling is performed taking into account a series of input data that are continuously updated. A real case study is considered, namely the surgery department of the University Hospital in Cagliari, Italy. The scheduling resulting from the proposed approach is compared with that adopted by the hospital planner who currently computes it manually. It is also shown that in most of the cases, the proposed method finds out solutions not considered by the hospital planner, greatly reducing redundancies or weakness in the staff, and satisfying all the required constraints