Design and analysis of ambulance diversion policies

Overcrowding of Emergency Departments (EDs) put the safety of patients at risk. Decision makers implement Ambulance Diversion (AD) as a way to relieve congestion and ensure timely treatment delivery. However, ineffective design of AD policies reduces the accessibility to emergency care and adverse events may arise. The objective of this dissertation is to propose methods to design and analyze effective AD policies that consider performance measures that are related to patient safety. First, a simulation-based methodology is proposed to evaluate the mean performance and variability of single-factor AD policies in a single hospital environment considering the trade-off between average waiting time and percentage of time spent on diversion. Regression equations are proposed to obtain parameters of AD policies that yield desired performance level. The results suggest that policies based on the total number of patients waiting are more consistent and provide a high precision in predicting policy performance. Then, a Markov Decision Process model is proposed to obtain the optimal AD policy assuming that information to start treatment in a neighboring hospital is available. The model is designed to minimize the average tardiness per patient in the long run. Tardiness is defined as the time that patients have to wait beyond a safety time threshold to start receiving treatment. Theoretical and computational analyses show that there exists an optimal policy that is of threshold type, and diversion can be a good alternative to decrease tardiness when ambulance patients cause excessive congestion in the ED. Furthermore, implementation of AD policies in a simulation model that accounts for several relaxations of the assumptions suggests that the model provides consistent policies under multiple scenarios. Finally, a genetic algorithm is combined with simulation to design effective policies for multiple hospitals simultaneously. The model has the objective of minimizing the time that patients spend in non-value added activities, including transportation, waiting and boarding in the ED. Moreover, the AD policies are combined with simple ambulance destination policies to create ambulance flow control mechanisms. Results show that effective ambulance management can significantly reduce the time that patients have to wait to receive appropriate level of care.