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

Miguel Lejeune () and Wenbo Ma ()
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Wenbo Ma: Department of Decision Sciences, George Washington University, Washington, District of Columbia 20052

Operations Research, 2025, vol. 73, issue 1, 86-108

Abstract: We propose a new stochastic emergency network design model that uses a fleet of drones to quickly deliver naloxone in response to opioid overdoses. The network is represented as a collection of M / G / K queueing systems in which the capacity K of each system is a decision variable, and the service time is modeled as a decision-dependent random variable. The model is a queuing-based optimization 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 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 generalizability and show that the problem of minimizing the average response time of a collection of M / G / K queueing systems with unknown capacity K is always MILP-representable. We design an outer approximation branch-and-cut algorithmic framework that is computationally efficient and scales well. The analysis based on real-life data reveals that drones can in Virginia Beach: (1) decrease the response time by 82%, (2) increase the survival chance by more than 273%, (3) save up to 33 additional lives per year, and (4) provide annually up to 279 additional quality-adjusted life years.

Keywords: Policy Modeling and Public Sector OR; opioid overdose; drone delivery; optimization-based queueing model; survival chance; mixed-integer nonlinear programming; stochastic network design (search for similar items in EconPapers)
Date: 2025
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