Random number of arrivals and random length of stays make the number of patients in a hospital unit behave as a stochastic process. This makes the determination of the optimum size of the bed capacity more difficult. The number of admissions per day, service level and occupancy level are key control parameters that affect the optimum size of the required bed capacity. In this study a new stochastic approximation is developed and applied to a unit of a teaching hospital. Data between 2000 and 2004 was used to obtain the necessary probability distribution functions. Mathematical relationships between the control parameters and size of the bed capacity are obtained using generated data from a constructed simulation model. Nonlinear mathematical models are then used to determine the optimum size of the required bed capacity based on target levels of the control parameters, and a profit and loss analysis is performed.