Nursevendor Problem: Personnel Staffing in the Presence of Endogenous Absenteeism

The problem of determining nurse staffing levels in a hospital environment is a complex task because of variable patient census levels and uncertain service capacity caused by nurse absenteeism. In this paper, we combine an empirical investigation of the factors affecting nurse absenteeism rates with an analytical treatment of nurse staffing decisions using a novel variant of the newsvendor model. Using data from the emergency department of a large urban hospital, we find that absenteeism rates are consistent with nurses exhibiting an aversion to higher levels of anticipated workload. Using our empirical findings, we analyze a single-period nurse staffing problem considering both the case of constant absenteeism rate (exogenous absenteeism) as well as an absenteeism rate that is a function of the number of nurses scheduled (endogenous absenteeism). We provide characterizations of the optimal staffing levels in both situations and show that the failure to incorporate absenteeism as an endogenous effect results in understaffing.