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 expectedlevels of bed utilization. However, uncertainty in the patient’s length of stay and bed availability challengethe accomplishment of that objective. This research addresses the off-line admission planning problem withuncertain length of stay. We study the coordinated decisions of scheduling and allocation for the patient-to-roomadmission problem assuming heterogeneous patient types and time-varying capacity. The objective is to maximizethe weighted sum of the patient’s admission benefit while reducing the cost of overstay. We present adistributionally robust optimization (DRO) framework that is distribution-free; it considers that known informationis limited only to the first moment and the support set of the true probability distribution. The frameworkis robust against the infinite set of probability distribution functions that could represent the stochastic process ofthe patient’s length of stay. To test the performance of the proposed DRO approach, we compared it withbenchmark models employing a real data set from a public hospital in Chile. The results show that our approachoutperforms the evaluated models in both reliability and computational efficiency. We provide insights topractitioners and hospital decision-makers to anticipate admission decisions while considering the randomness ofthe length of stay at the tactical-operational level.