Providing a Model for the Optimal Allocation of Hospital Beds Based on Markov Chain Approach (Case Study: Shiraz-Shahid-Faghihi Hospital)

As was observed in the corona crisis, in situations, such as war or natural disasters or epidemic diseases, the intensity of the applicants for medical services causes congestion problems. In this situation, due to the limited capacity of the system, queuing phenomenon for service applicants and in some cases, rejection of clients occur. Reducing the length of hospital stays by improving performance productivity can compensate for the shortage of hospital beds. In order to increase the productivity of personnel and equipment, it is necessary to eliminate unemployment and improve service scheduling. One of the ways to achieve these goals is to optimize the distribution of beds between wards. In the present study, in the form of Markov chain approach, according to the referral rate and service rate, the existing beds were allocated to different wards of the hospital to maximize service and minimize rejection of patients.

The present study is an applied study conducted in 2019 for the optimal distribution of beds between the 3 wards of Shahid Faghihi Hospital in Shiraz. The research problem was modeled in the form of Markov chain approach and assuming the referral of clients according to the continuous-time Markov chain, the model parameters value was identified. The obtained mathematical model was solved by GAMS 24.1.3 software.

The proposed model led to an improvement in ward performance in terms of reducing patient waiting time and increasing the number of admitted patients. The proposed model reduced patient rejection by 8.6 %. According to the patientschr('39') referral rate to the wards and the service rate of each ward, based on sensitivity analysis, the number of beds allocated to each of the 3 wards was determined.

Queuing theory can be applied as a tool to analyze the phenomena of the treatment system and determine the features of the waiting time, queue length, and capacity of the system. Appropriate allocation of hospital beds results in improving the efficiency and decreasing the patient rejection. Therefore, it could be useful in crisis, congestion in patients, and when increasing facilities is required.