Multiple Objective Simulation Optimization for Emergency Department Resource Allocation

Abstract

Emergency departments (EDs) are among the most intensive and dynamic departments in hospital systems. This study considers the resource allocation problem at the ED of a hospital with two objective functions: the length of stay (LS) and wasted resources. The numbers of doctors, nurses, lab technicians, and other medical equipment must be constantly determined to effectively operate EDs with the two objective functions, representing the satisfaction of patients and unnecessary costs, respectively. The ED system is evaluated with a discrete event simulation (DES) model. Furthermore, a Pareto optimal set of solutions is approximated using the quantile-relaxed multiple objective probabilistic branch and bound (QR-MOPBnB), which was developed as an extension algorithm of MOPBnB to improve efficiency. QR-MOPBnB iteratively branches the solution space into subregions and identifies the subregions that are the most promising to be close to the Pareto optimal set. Using QR-MOPBnB, the trade-off between the LS and wasted resources is illustrated for decision makers to appropriately determine the ideal design based on their preferences, and the relaxed Pareto optimal set with statistical quality assurance provides further insights similar to those obtained through sensitivity analysis.