A hybrid genetic algorithm-queuing multi-compartment model for optimizing inpatient bed occupancy and associated costs.

Abstract

Explore how efficient intelligent decision support systems, both easily understandable and straightforwardly implemented, can help modern hospital managers to optimize both bed occupancy and utilization costs. This paper proposes a hybrid genetic algorithm-queuing multi-compartment model for the patient flow in hospitals. A finite capacity queuing model with phase-type service distribution is combined with a compartmental model, and an associated cost model is set up. An evolutionary-based approach is used for enhancing the ability to optimize both bed management and associated costs. In addition, a "What-if analysis" shows how changing the model parameters could improve performance while controlling costs. The study uses bed-occupancy data collected at the Department of Geriatric Medicine - St. George's Hospital, London, period 1969-1984, and January 2000. The hybrid model revealed that a bed-occupancy exceeding 91%, implying a patient rejection rate around 1.1%, can be carried out with 159 beds plus 8 unstaffed beds. The same holding and penalty costs, but significantly different bed allocations (156 vs. 184 staffed beds, and 8 vs. 9 unstaffed beds, respectively) will result in significantly different costs (£755 vs. £1172). Moreover, once the arrival rate exceeds 7 patient/day, the costs associated to the finite capacity system become significantly smaller than those associated to an Erlang B queuing model (£134 vs. £947). Encoding the whole information provided by both the queuing system and the cost model through chromosomes, the genetic algorithm represents an efficient tool in optimizing the bed allocation and associated costs. The methodology can be extended to different medical departments with minor modifications in structure and parameterization.