An application of stochastic programming method for nurse scheduling problem in real word hospital

• Modeling nurse scheduling problem which considers uncertainties.
• Sample Average Approximation (SAA) method is used to obtain an optimal schedule.
• A case study conducted in Department of Heart Surgery in Razavi Hospital.
• The main objective of the model is to minimize the total costs.
• The problem SNSP was formulated using the recourse model.

Given its complexity and relevance in healthcare, the well-known Nurse Scheduling Problem (NSP) has been the subject of several researches and different approaches have been used for its solution. The importance of this problem comes from its critical role in healthcare processes as NSP assigns nurses to daily shifts while respecting both the preferences of the nurses and the objectives of hospital. Most models in NSP literature have dealt with this problem in a deterministic environment, while in the real-world applications of NSP, the vagueness of information about management objectives and nurse preferences are sources of uncertainties that need to be managed so as to provide a qualified schedule. In this study, we propose a stochastic optimization model for the Department of Heart Surgery in Razavi Hospital, which accounts for uncertainties in the demand and stay period of patients over time. Sample Average Approximation (SAA) method is used to obtain an optimal schedule for minimizing the regular and overtime assignment costs, with the numerical experiments demonstrating the convergence of statistical bounds and moderate sample size for a given numerical experiment. The results confirm the validity of the model.