  We study the nurse staffing problem under random nurse demand and
absenteeism. While the demand uncertainty is exogenous (stemming from the
random patient census), the absenteeism uncertainty is \emph{endogenous}, i.e.,
the number of nurses who show up for work partially depends on the nurse
staffing level. For quality of care, many hospitals have developed float pools,
i.e., groups of hospital units, and trained nurses to be able to work in
multiple units (termed cross-training) in response to potential nurse shortage.
In this paper, we propose a distributionally robust nurse staffing (DRNS) model
that considers both exogenous and endogenous 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. Furthermore, we
optimize the float pool design to reduce cross-training while achieving
specified target staffing costs. The numerical case studies, based on the data
of a collaborating hospital, suggest that the units with high absenteeism
probability should be pooled together.
