  Sudden cardiac arrest is a significant public health concern. Successful
treatment of cardiac arrest is extremely time sensitive, and use of an
automated external defibrillator (AED) where possible significantly increases
the probability of survival. Placement of AEDs in public locations can improve
survival by enabling bystanders to treat victims of cardiac arrest prior to the
arrival of emergency medical responders. However, since the exact locations of
future cardiac arrests cannot be known a priori, AEDs must be placed
strategically in public locations to ensure their accessibility in the event of
an out-of-hospital cardiac arrest emergency. In this paper, we propose a
data-driven optimization model for deploying AEDs in public spaces while
accounting for uncertainty in future cardiac arrest locations. Our approach
involves discretizing a continuous service area into a large set of scenarios,
where the probability of cardiac arrest at each location is itself uncertain.
We model uncertainty in the spatial risk of cardiac arrest using a polyhedral
uncertainty set that we calibrate using historical cardiac arrest data. We
propose a solution technique based on row-and-column generation that exploits
the structure of the uncertainty set, allowing the algorithm to scale
gracefully with the total number of scenarios. Using real cardiac arrest data
from the City of Toronto, we conduct an extensive numerical study on AED
deployment public locations. We find that hedging against cardiac arrest
location uncertainty can produce AED deployments that outperform a intuitive
sample average approximation by 9 to 15%, and cuts the performance gap with
respect to an ex-post model by half. Our findings suggest that accounting for
cardiac arrest location uncertainty can lead to improved accessibility of AEDs
during cardiac arrest emergencies and the potential for improved survival
outcomes.
