Two-stage multi-objective optimization for ICU bed allocation under multiple sources of uncertainty

Abstract

Due to the impact of COVID-19, a significant influx of emergency patients inundated the intensive care unit (ICU), and as a result, the treatment of elective patients was postponed or even cancelled. This paper studies ICU bed allocation for three categories of patients (emergency, elective, and current ICU patients). A two-stage model and an improved Non-dominated Sorting Genetic Algorithm II (NSGA-II) are used to obtain ICU bed allocation. In the first stage, bed allocation is examined under uncertainties regarding the number of emergency patients and their length of stay (LOS). In the second stage, in addition to including the emergency patients with uncertainties in the first stage, it also considers uncertainty in the LOS of elective and current ICU patients. The two-stage model aims to minimize the number of required ICU beds and maximize resource utilization while ensuring the admission of the maximum number of patients. To evaluate the effectiveness of the model and algorithm, the improved NSGA-II was compared with two other methods: multi-objective simulated annealing (MOSA) and multi-objective Tabu search (MOTS). Drawing on data from real cases at a hospital in Lyon, France, the NSGA-II, while catering to patient requirements, saves 9.8% and 5.1% of ICU beds compared to MOSA and MOTS. In five different scenarios, comparing these two algorithms, NSGA-II achieved average improvements of 0%, 49%, 11.4%, 9.5%, and 17.1% across the five objectives.