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

Abstract

We propose a new stochastic emergency network design model that uses a fleet of drones to quickly deliver naxolone in response to opioid overdoses. The network is represented as a collection of M/G/K queuing systems in which the capacity K of each system is unknown ex-ante and modelled as a decision variable. The model is a bilocation-allocation optimization-based queuing problem which locates fixed (drone bases) and mobile (drones) servers and determines the drone dispatching decisions. The model takes the form of a nonlinear integer problem which is intractable in its original form. We provide a reformulation and algorithmic framework to allow for the exact solution of large instances. Our approach reformulates the multiple nonlinearities (fractional, polynomial, exponential, factorial terms) to give a mixed-integer linear programming (MILP) formulation. We demonstrate its generalizablity and show that the problem of minimizing the average response time of a network of M/G/K queuing systems with unknown capacity K is always MILP-representable. We design two algorithms and demonstrate that the outer approximation branch-and-cut method is most efficient and scales well. The data-driven analysis based on real-life overdose data reveals that the use of drones could: 1) decrease the response time by 85%, 2) increase the survival chance by 466%, 3) save up to 36 additional lives per year, and 4) provide an additional quality-adjusted life year (QALY) of up to 305 years in Virginia Beach.

Optimizing a Drone Network to Respond to Opioid Overdoses

“…13 Additionally, a pre-print by Lejune and Ma describes use of a stochastic method to improve response times by 78% in Virginia Beach. 14 Our objective in this study was to determine whether a mathematical model could be used to optimize the placement of drone bases to reduce response time to opioid overdoses. Given the locations of opioid overdoses, this mathematical model determines the number and location of drone bases to meet any specified reduction in response time.…”