Controlling understaffing with conditional Value-at-Risk constraint for an integrated nurse scheduling problem under patient demand uncertainty

Nursing workforce management is a challenging decision-making task in hospitals. The decisions are made across different timescales and levels from strategic long-term staffing budget to mid-term scheduling. These decisions are interconnected and impact each other, therefore are best taken by considering staffing and scheduling together. Moreover, this decision-making needs to be made in a stochastic setting to meet uncertain patient demand. A sufficient and cost-efficient staffing level with desirable schedule is essential to provide good working conditions for nurses and consequently good quality of care. On the other hand, understaffing can severely deteriorate the quality of care thus should be strictly controlled.To help with the decision making, based on our previous research we formulate in this paper an integrated nurse staffing and scheduling model under patient demand uncertainty into a two-stage stochastic programming model with an emphasis on understaffing risk control. Conditional Value-at-Risk (CVaR), a risk control measure primarily used in the financial domain, is integrated in the stochastic programming model to control understaffing risk. The IBM ILOG CPLEX solver is applied to solve the stochastic model. The model and solution approaches are tested using a case study in a real-world environment setting. We have evaluated the performance of the stochastic model and the benefit of CVaR in terms of impact on schedule quality