Design and Optimization Methods for Elective Hospital Admissions

Abstract

Hospitals typically lack effective enterprise level strategic planning of bed and care resources, contributing to bed census levels that are statistically "out of control.'' This system dysfunction manifests itself in bed block, surgical cancellation, ambulance diversions and operational chaos. This is the classic Hospital Admission Scheduling and Control (HASC) problem, which has been addressed in its entirety only through inexact simulation-based search heuristics. This paper develops new analytical models of controlled hospital census that can, for the first time, be incorporated into a Mixed Integer Programming model to optimally solve the strategic planning/scheduling portion of the HASC. Our new solution method coordinates elective admissions with other hospital subsystems to reduce system congestion. We formulate a new Poisson-arrival-location model (PALM) based on an innovative stochastic location process that we developed and call the Patient Temporal Resource Needs (PATTERN) model. We further extend the PALM approach to the class of deterministic controlled-arrival-location models (d-CALM) and develop linearizing approximations to stochastic blocking metrics. This work provides the theoretical foundations for an efficient scheduled admissions planning system as well as a practical decision support methodology to stabilize hospital census.

Keywords: Hospital Admissions and Bed Management, Stochastic Patient Flow Modeling, Mixed Integer Programming, Census Smoothing, Stochastic Arrival-Location Models