Hospital emergency departments are often overcrowded, resulting in long wait times and a public perception of poor attention. Delays in transferring patients needing further treatment increases emergency department congestion, has negative impacts on their health and may increase their mortality rates. A model built around a Markov decision process is proposed to improve the efficiency of patient flows between the emergency department and other hospital units. With each day divided into time periods, the formulation estimates bed demand for the next period as the basis for determining a proactive rather than reactive transfer decision policy. Due to the high dimensionality of the optimization problem involved, an approximate dynamic programming approach is used to derive an approximation of the optimal decision policy, which indicates that a certain number of beds should be kept free in the different units as a function of the next period demand estimate. Testing the model on two instances of different sizes demonstrates that the optimal number of patient transfers between units changes when the emergency patient arrival rate for transfer to other units changes at a single unit, but remains stable if the change is proportionally the same for all units. In a simulation using real data for a hospital in Chile, significant improvements are achieved by the model in key emergency department performance indicators such as patient wait times (reduction higher than 50%), patient capacity (21% increase) and queue abandonment (from 7% down to less than 1%).

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