A Hybrid Mathematical-Simulation Approach to Hospital Beds Capacity Optimization for COVID-19 Pandemic Conditions

The COVID-19 pandemic was an unforeseen threat to human survival, and the efficiency of the health sector faced a severe challenge. The lack of hospital beds was one of the most critical concerns, and optimizing the capacity of hospital beds was considered one of the key issues. Due to the ageing of the population and the occasional occurrence of environmental and health crises, the demand for health services and the need for improved planning and administration are increasing daily. Therefore, the optimal allocation of hospital resources particularly the number of beds the essential criterion for a medical center’s capacity can substantially reduce patient waiting time and treatment costs, and improve services. An ideal multi-objective integer programming problem is presented in this study for optimizing the number of hospital beds and reducing costs of the length of stay and length of hospital stay. The problem also considers constraints relating to critical circumstances given the Corona’s prevalence. Moreover, the optimal answer is obtained using a simulation model mathematical optimization and a simulation-based optimization approach. The optimal value of the objective function was obtained at $90,516k for 1 month, with a productivity rate of 65%. In the simulation model, the waiting time was calculated to be 13,701.22 min in 1 month, whereas the mathematical model calculated it as 2230.8 min in the second period. These figures were instrumental in highlighting the efficiency of the bed allocation strategy under real-world conditions. The total cost for bed development and maintenance was estimated to range from $13k to $26.5k across the periods. Due to the ageing of the population and the occasional occurrence of environmental and health crises, the demand for health services and the need for improved planning and administration are increasing daily. Therefore, the optimal allocation of hospital resources, particularly the number of beds and the essential criterion for a medical center’s capacity, can substantially reduce patient waiting time and treatment costs and improve services. An ideal multi-objective integer programming problem is presented in this study for optimizing the number of hospital beds and reducing costs of the length of stay and length of hospital stay. The problem also considers constraints relating to critical circumstances, given the Corona’s prevalence. Moreover, the optimal answer is obtained using a simulation model, mathematical optimization, and a simulation-based optimization approach. For this purpose, mathematical modelling was used to minimize patients’ waiting time, hospitalizations, and maintenance costs of existing beds and purchasing a new bed. Following that, real-world conditions were introduced into the problem using the simulation model and information acquired from one month of hospitalization of patients during the Coronavirus outbreak at Imam Hussein Hospital in Tehran. After comparing mathematical and simulated models, the OptQuest simulation-based optimization technique revealed the ideal number of hospital beds.