A generalized linear programming model for nurse scheduling

This paper presents a 0–1 column generation model with a resource constrained shortest path auxiliary problem for nurse scheduling. The master problem finds a configuration of individual schedules to satisfy the demand coverage constraints while minimizing salary costs and maximizing both employee preferences and team balance. A feasible solution of the auxiliary problem is an acceptable schedule for a given nurse, with respect to collective agreement requirements such as seniority, workload, rotations and days off. We define a new resource structure in the auxiliary problem in order to take into account the complex collective agreement rules specific to the nurse scheduling problem. This model generalizes further the previous formulations discussed in the literature and can be viewed as a general scheme for complex personnel scheduling problems, especially in the context of organizations which operate around the clock. Solution methods and preliminary test results are discussed.