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We propose a new stochastic emergency network design model that uses a fleetof drones to quickly deliver naxolone in response to opioid overdoses. Thenetwork is represented as a collection of M/G/K queuing systems in which thecapacity K of each system is a decision variable and the service time ismodelled as a decision-dependent random variable. The model is anoptimization-based queuing problem which locates fixed (drone bases) and mobile(drones) servers and determines the drone dispatching decisions, and takes theform of a nonlinear integer problem, which is intractable in its original form.We develop an efficient reformulation and algorithmic framework. Our approachreformulates 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 theaverage response time of a network of M/G/K queuing systems with unknowncapacity K is always MILP-representable. We design two algorithms anddemonstrate that the outer approximation branch-and-cut method is the mostefficient and scales well. The analysis based on real-life overdose datareveals that drones can in Virginia Beach: 1) decrease the response time by78%, 2) increase the survival chance by 432%, 3) save up to 34 additional livesper year, and 4) provide annually up to 287 additional quality-adjusted lifeyears.

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