Managing the unknown: A distributionally robust model for the admission planning problem under uncertain length of stay

Abstract The admission planning problem in the inpatient service aims to provide patient access and to guarantee expected levels of bed utilization. However, uncertainty in the patient’s length of stay and bed availability challenge the accomplishment of that objective. This research addresses the off-line admission planning problem with uncertain length of stay. We study the coordinated decisions of scheduling and allocation for the patient-to-room admission problem assuming heterogeneous patient types and time-varying capacity. The objective is to maximize the weighted sum of the patient’s admission benefit while reducing the cost of overstay. We present a distributionally robust optimization (DRO) framework that is distribution-free; It considers that known information is limited only to the first moment and the support set of the true probability distribution. The framework is robust against the infinite set of probability distribution functions that could represent the stochastic process of the patient’s length of stay. To test the performance of the proposed DRO approach, we compared it with benchmark models employing a real data set from a public hospital in Chile. The results show that our approach outperforms the evaluated models in both reliability and computational efficiency. We provide insights to practitioners and hospital decision-makers to anticipate admission decisions while considering the randomness of the length of stay at the tactical-operational level.