Dynamic and flexible staff deployment in accident and emergency departments using simulation-based optimization

Accident and emergency departments experience overcrowding due to staff shortages as well as to variations in patient arrivals and the time required to treat them. Several policies have been developed by hospitals to ensure that patients are not put at clinical risk during overcrowding. These policies suggest flexing nurses from different duties to the overcrowded section. However, the policies do not indicate the details of when exactly the flexing should be activated. We develop a mathematical model to find the optimum levels of triage and treatment queue lengths after which flexing should be activated. The performance indicators of the department are the waiting time targets and the disturbance due to nurse flexing. Because of the lack of closed-form formulations, we propose simulation optimization to solve the problem. By analyzing the model structure, we develop an efficient search procedure of the discrete solution space. We show the application of the proposed method using the data of a large hospital in the UK under different parameter settings. The results show that hospital management should focus on increasing the number of treatment nurses rather than flexing the nurses, and the queue of the service stream that requires tighter staffing should be controlled by an upper limit.