Response Time Minimization for Cardiac Arrests

Abstract

Cardiac arrests are a significant health concern in the United States, as more than 350,000 occur annually and 90% of them are fatal. Providing quick access to automated external defibrillators is paramount since irreversible damage to vital organs occurs within minutes without cardiopulmonary resuscitation and defibrillation. We propose a novel optimization model to design a network of drones delivering automated external defibrillators in response to out-of-hospital cardiac arrests. The network is modeled as a collection of queues in which the occurrence of cardiac arrests is modeled as a Poisson process while the drone service times and the arrival of cardiac arrest requests at drone bases are random variables whose distribution parameters are determined endogenously. The model is formulated as a fractional integer problem with bilinear terms and minimizes the average response time which is conducive to maximizing the chance of survival of patients. We derive a mixed-integer linear reformulation and develop an exact solution method that includes a warm-start approach and new optimality-based bound tightening models. We use real-life cardiac arrest data (i) to derive healthcare insights about the impact of delivery mode and drone technology on response time and probability of survival, (ii) to showcase the dependency of the service rate and response time on the utilization of drones and the need to endogenize the response time, and (iii) to ascertain the computational efficiency and scalability of our approach. The cross-validation analysis confirms the robustness of the model and its applicability to unseen out-of-hospital cardiac arrest data.