The Nurse Scheduling Problem in the Covid-19 Pandemic: A Stochastic Programming Approach

The nurse scheduling problem (NSP) in different work shifts in medical centers is one of the essential issues in the health care systems. In general, nurses have various preferences for working in different shifts, and there are considerations for overtime and activity on holidays. During the Covid-19 pandemic, various problems, such as fatigue due to high workload or nurses suffering from this disease are led to a shortage of the required number of nurses in work shifts. Using skilled float nurses in shifts is one of the appropriate solutions in case of workforce shortage. Moreover, equipping nurses with appropriate equipment to deal with coronavirus, such as gowns, masks, etc., is mandatory and costly for hospitals in the context of the Covid-19 pandemic. In this paper, a mixed-integer linear programming (MILP) model is presented to minimize deviations from fixed nurses' preferences for the shift and day, salaries of fixed nurses during regular hours and overtime, salaries of floating nurses, and equipment costs, in the Covid-19 pandemic conditions. It is assumed that the number of nurses required per shift in a working day is uncertain, and a stochastic mathematical model is proposed. The model is solved using scenario generation and scenario reduction methods. Furthermore, the proposed models are investigated using real data that are gathered from a hospital located in Mazandaran province, Iran. The results show that uncertainty should be considered in the NSP.