Drone-Delivery Network for Opioid Overdose: Nonlinear Integer Queueing-Optimization Models and Methods
Operations Research · 2025 · Volume 73 · Issue 1
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 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 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. Funding: M. A. Lejeune acknowledges the support of the National Science Foundation [Grant ECCS-2114100] and the Office of Naval Research [Grant N00014-22-1-2649]. Supplemental Material: The online appendices are available at https://doi.org/10.1287/opre.2022.0489 .
Keywords
Policy Modeling and Public Sector OR, opioid overdose, drone delivery, optimization-based queueing model, survival chance, mixed-integer nonlinear programming, stochastic network design
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