Maximizing Survival to Time-Sensitive Medical Events with Drone Logistics

We propose a novel queueing optimization model for the design of a drone network delivering automated external defibrillators in response to out-of-hospital cardiac arrests (OHCA). The network is modeled as a collection of M/G/1 queues in which the occurrence of OHCA is modelled as a Poisson process while the drone service times and the arrival of OHCA requests at drone bases are random variables whose distribution parameters are determined endogenously. The model takes the form of an integer nonlinear model with fractional and bilinear terms and minimizes the average response time which is conducive to maximizing the chance of survival of OHCA patients. We derive a mixed-integer linear programming (MILP) reformulation and propose a modular exact solution method that includes a warm-start and an optimality-based bound tightening (OBBT) module. In particular, we propose four new MILP and feasibility OBBT models that can derive multiple bounds at once. We also devise a persistency-based heuristic to solve very large instances. We use real cardiac arrest data for Virginia Beach (i) to ascertain the computational efficiency and scalability of our approach, (ii) to derive practical insights about the impact of delivery mode, network capacity, and drone technology on response time and probability of survival, and (iii) to showcase the need to properly model the dependency of the response time on the utilization of the drones and to endogenize the response time and the OHCA arrival rate at drone stations.