Abstract: The gap between supply and demand in healthcare service is becoming more and more serously with the improvement of medical requirements. Moreover, one of the most significant problems is the shortage of bed capacity around the world. Furthermore, most patients should go through a treatment stage and recovery stage in medical service procedure which has not been studied sufficiently. In this paper, a resource allocation study of healthcare beds is present that formulates patient’s medical service process by a two-stage queuing model. The two-stage queuing model includes a compulsory treatment stage and a recovery stage. Firstly, dividing the state of healthcare service system into three situations, the probability equations of the treatment queuing are gotten by supplementary variable method under the fixed service number constraint respectively, then the partial differential equations is solved by characteristic equation method with boundary conditions and the probability expression of healthcare service system state. Using this expression, the customer deny probability and average recovery service time can be further calculated. Furthermore, considering the risk factors that a new patient is unable to get treatment and the patients who has recovered are early discharged due to bed capacity shortage, the medical bedroom allocation model is developed based on the queuing indexes, and dynamic programming analysis is given. Finally, the numerical analysis is to implement according to Chinese Health Statistics data and the simulation data. The result shows that the traditional one-stage model has a significant difference allocation result compared with our two-stage model, and patient’s arrival rate has significant impact on optimal bed allocation in the proposed model. Furthermore, management insights are provided according to numerical result and further work is given in conclusion. This study can be used to improve the efficiency of healthcare resource and be extend to support the similar researches about two-stage service system.

Key words: hospital bed management, queuing, capacity analysis, healthcare operations management