Robust Defibrillator Deployment Under Cardiac Arrest Location Uncertainty via Row-and-Column Generation

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, thus shortening the time between collapse and treatment. 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 an intuitive sample average approximation by 9%-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. Funding: This research was partially supported by the National Science Foundation [CMMI 1265671], the National Natural Science Foundation of China [Grants 71210002 and 71332005], the Natural Sciences and Engineering Research Council of Canada, and the Ontario Ministry of Training, Colleges and Universities. Supplemental Material: The electronic companion is available at https://doi.org/10.1287/opre.2017.1660. Keywords: robust optimization * row-and-column generation * healthcare operations * facility location
1. Introduction Sudden cardiac arrest is a leading cause of death in North America and is responsible for more than 400,000 deaths each year (Heart and Stroke Foundation 2013, Mozaffarian [...]