Drone-Delivery Network for Opioid Overdose: Nonlinear Integer Queueing-Optimization Models and Methods

This study proposes an emergency network design model that uses a fleet of drones to deliver naloxone in response to opioid overdoses. The network is represented as a collection of M/G/K queueing systems with variable capacity and service time modelled as a decision-dependent random variable. The model is a complex queuing-based optimization problem which locates drone bases and dispatches drones to opioid incidents. The authors devise an efficient solution framework in which they linearize the multiple nonlinearities (fractional, polynomial, exponential, factorial terms), derive an equivalent mixed-integer linear reformulation, and design an outer approximation branch-and-cut algorithm. The authors demonstrate the generalizablity of the approach to any problem minimizing the response time of M/G/K queueing systems with unknown capacity. Tests on Virginia Beach data reveal that drones can decrease response time by 82%, increase survival chance by more than 273%, save up to 33 additional lives annually, and provide up to 279 additional quality-adjusted life years.