Nurse Staffing Under Absenteeism: A Distributionally Robust Optimization Approach

Problem definition: We study a nurse staffing problem under random nurse demand and absenteeism. Although the demand uncertainty is exogenous, the absenteeism uncertainty is decision-dependent, that is, the number of nurses who show up for work partially depends on the nurse staffing level. For quality of care, hospitals develop float pools of hospital units and train nurses to be able to work in multiple units (termed cross-training) in response to potential nurse shortages. Methodology/results: We study a distributionally robust nurse staffing (DRNS) model that considers both exogenous and decision-dependent uncertainties. We derive a separation algorithm to solve this model under a general structure of float pools. In addition, we identify several pool structures that often arise in practice and recast the corresponding DRNS model as a mixed-integer linear program, which facilitates off-the-shelf commercial solvers. Managerial implications: Through the numerical case studies, based on the data of a collaborating hospital, we found that modeling decision-dependent absenteeism improves the out-of-sample performance of staffing decisions, and such improvement is positively correlated with the value of flexibility arising from fully utilizing float pools. Funding: R. Jiang was supported in part by the National Science Foundation [Grant ECCS-1845980]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/msom.2023.0398 .