Facility Location under Uncertainty and Spatial Data Analytics in Healthcare

Out-of-hospital cardiac arrest (OHCA) is a significant public health issue and treatment, namely, cardiopulmonary resuscitation and defibrillation, is very time-sensitive. Public access defibrillation programs, which deploy automated external defibrillators (AEDs) for bystander use in an emergency, have been shown to reduce the time to defibrillation and improve survival rates. The focus of this thesis is on data-driven decision making aimed at improving survival from OHCA by analyzing cardiac arrest risk and optimizing AED deployment. This work establishes a unique marriage of data analytics and facility location optimization to address both the demand (cardiac arrest) and supply (AED) sides of the AED deployment problem. In the demand side, we analyze the spatiotemporal trends of OHCAs in Toronto and show that the OHCA risk is stable at the neighborhood level over time. In other words, high risk areas tend to remain high risk, which supports focusing public health resources for cardiac arrest intervention and prevention in those areas to increase the efficiency of these scarce resources and improve the long-term impact. In the supply side, we develop a comprehensive modeling framework to support data-driven decision making in the deployment of public location AEDs, with the ultimate goal of increasing the likelihood of AED usage in a cardiac arrest emergency. As a part of this framework, we formulate three optimization models that consider probabilistic coverage of cardiac arrests using AEDs and address specific, real-life scenarios about AED retrieval and usage. Our models generalize existing location models and incorporate differences in bystander behavior. The models are mixed integer nonlinear programs, and a contribution of this work lies in the development of mixed integer linear formulation equivalents and tight and easily computable bounds. Next, we use kernel density estimation to derive a spatial probability distribution of cardiac arrests that is used for optimization and model evaluation. Using data from Toronto, Canada, we show that optimizing AED deployment outperforms the existing approach by 40% in coverage and substantial gains can be achieved through relocating existing AEDs. Our results suggest that improvements in survival and cost-effectiveness are possible with optimization.