Multi-modal delivery systems are a promising solution to the challenges posed by the increasing demand of e-commerce. Due to the potential benefit drones can have on logistics networks such as delivery systems, some countries have taken steps towards integrating drones into their airspace. In this paper we aim to quantify this potential by developing a mathematical model for a multi-modal delivery system composed of trucks and drones. We propose an optimization formulation that can be efficiently solved in order to design socially-optimal routing and allocation policies. We incorporate both societal cost in terms of road congestion and parcel delivery latency in our formulation. Our model is able to quantify the effect drones have on mitigating road congestion, and can solve for the path routing needed to minimize the chosen objective. To accurately capture the effect of stopping trucks on road latency, we use SUMO simulations and derive a mathematical latency function for roads shared by trucks and cars. Based on this, we show that the proposed framework is computationally feasible to scale due to its reliance on convex quadratic optimization techniques.
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