Physics-aware Truck and Drone Delivery Planning Using Optimization & Machine Learning

TL;DR

This paper presents a novel integrated optimization and machine learning approach for truck and drone delivery planning that explicitly models drone physics, resulting in more efficient and environmentally friendly last-mile delivery solutions.

Contribution

It introduces a new joint formulation and solution method that combines physics-aware drone trajectory modeling with neural network predictors for improved delivery planning.

Findings

Outperforms state-of-the-art benchmarks ignoring drone physics.

Reduces delivery tour duration and drone energy consumption.

Potential for significant cost savings and environmental benefits.

Abstract

Combining an energy-efficient drone with a high-capacity truck for last-mile package delivery can benefit operators and customers by reducing delivery times and environmental impact. However, directly integrating drone flight dynamics into the combinatorially hard truck route planning problem is challenging. Simplified models that ignore drone flight physics can lead to suboptimal delivery plans. We propose an integrated formulation for the joint problem of truck route and drone trajectory planning and a new end-to-end solution approach that combines optimization and machine learning to generate high-quality solutions in practical online runtimes. Our solution method trains neural network predictors based on offline solutions to the drone trajectory optimization problem instances to approximate drone flight times, and uses these approximations to optimize the overall truck-and-drone delivery plan by augmenting an existing order-first-split-second heuristic. Our method explicitly incorporates key kinematics and energy equations in drone trajectory optimization, and thereby outperforms state-of-the-art benchmarks that ignore drone flight physics. Extensive experimentation using synthetic datasets and real-world case studies shows that the integration of drone trajectories into package delivery planning substantially improves system performance in terms of tour duration and drone energy consumption. Our modeling and computational framework can help delivery planners achieve annual savings worth millions of dollars while also benefiting the environment.