A Stochastic Programming Approach for Integrated Nurse Staffing and Assignment

The renowned nursing shortage has attracted much attention from national level law makers, state legislatures, commercial organizations, and researchers due to its direct impact on the quality of patient care. High workloads and undesirable schedules are two major issues that cause nurses’ job dissatisfaction. The focus of this paper is to find nondominated solutions to an integrated nurse staffing and assignment problem that minimize two criteria, which are excess workload on nurses and nurse staffing cost. Initially, we present a stochastic integer programming model with an objective to minimize excess workload subject to a hard budget constraint. Accordingly, we develop three solution approaches, which are Benders’ decomposition, Lagrangian relaxation with Benders’ decomposition, and nested Benders’ decomposition. We vary the maximum allowable staffing cost in the budget constraint in Benders’ decomposition and nested Benders’ decomposition, and we relax the budget constraint and penalize staffing cost in the Lagrangian relaxation with Benders’ decomposition approach. We collect nondominated bicriteria solutions from the algorithms. We demonstrate the effectiveness of the model and algorithms with a computational study based upon data from two medical-surgical units at a Northeast Texas hospital. A float assignment policy is also evaluated. Finally, areas of future research are discussed.