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

TL;DR

This paper introduces a novel stochastic network design model using drones for rapid opioid overdose response, formulating it as a complex nonlinear integer optimization problem and providing efficient solution algorithms.

Contribution

It develops a reformulation and algorithmic framework that transforms a complex nonlinear queuing optimization problem into a MILP, enabling scalable solutions for drone deployment in emergency response.

Findings

Drones can reduce overdose response time by 78%

Drones can increase survival chances by 432%

Potential to save up to 34 lives annually in Virginia Beach

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 a decision variable and the service time is modelled as a decision-dependent random variable. The model is an optimization-based queuing problem which locates fixed (drone bases) and mobile (drones) servers and determines the drone dispatching decisions, and takes the form of a nonlinear integer problem, which is intractable in its original form. We develop an efficient reformulation and algorithmic framework. 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 the most efficient and scales well. The analysis based on real-life overdose data reveals that drones can in Virginia Beach: 1) decrease the response time by 78%, 2) increase the survival chance by 432%, 3) save up to 34 additional lives per year, and 4) provide annually up to 287 additional quality-adjusted life years.