Optimal Nursing Home Service Scheduling Under covid-19 Related Probabilistic Staff Shortage: A Two-stage Stochastic Programming Approach

Maintaining an appropriate staffing level is essential to providing a healthy workplace environment at nursing homes and ensuring quality care among residents. With the widespread Covid-19 pandemic, staff absenteeism frequently occurs due to mandatory quarantine and providing care to their inflicted family members. Even though some of the staff show up for work, they may have to perform additional pandemic-related protection duties. In combination, these changes lead to an uncertain reduction in the quantity of care each staff member able to provide in a future shift. To alleviate the staff shortage concern and maintain the necessary care quantity, we study the optimal shift scheduling problem for a skilled nursing facility under probabilistic staff shortage in the presence of pandemic-related service provision disruptions. We apply a two-stage stochastic programming approach to our study. Our objective is to assign staff (i.e., certified nursing aids) to shifts to minimize the total staffing cost associated with contract staff workload, the adjusted workload for the changing resident demand, and extra workload due to required sanitization. Thus, the uncertainties considered arise from probabilistic staff shortage in addition to resident service need fluctuation. We model the former source of uncertainty with a geometric random variable for each staffer. In a proof-of-the-concept study, we consider realistic COVID-19 pandemic response measures recommended by the Indiana state government. We extract payment parameter estimates from the COVID-19 Nursing Home Dataset publicly available by the Centers for Medicare and Medicaid Services (CMS). We conclude with our numerical experiments that when a skilled nursing facility is at low risk of the pandemic, the absenteeism rate and staff workload increase slightly, thus maintaining the current staffing level can still handle the service disruptions. On the other hand, under high-risk circumstances, with the sharp increase of the absence rate and workload, a care facility likely needs to hire additional full-time staff as soon as possible. Our research offers insights into staff shift scheduling in the face of uncertain staff shortages and service disruption due to pandemics and prolonged disasters.