Year: 2026
Type: article
Abstract: Combining an energy-efficient drone with a high-capacity truck for last-mile package delivery can reduce delivery times and environmental impact. However, directly integrating drone flight dynamics into the combinatorially challenging truck-route planning problem is difficult. Simplified models that ignore drone flight physics can lead to poor drone flying duration estimates and suboptimal delivery plans. We propose an integrated formulation for the joint problem of truck-route and drone-trajectory planning, together with a physics-aware, surrogate-assisted heuristic planning framework that combines optimization and machine learning to generate high-quality solutions within practical online runtimes. Our approach trains neural network predictors on offline solutions of a modified drone-only trajectory model to approximate drone flying durations, combines these predictions with the corresponding truck travel durations to obtain synchronized operation duration estimates, and then embeds the resulting estimates into an augmented order-first, split-second heuristic for truck-and-drone planning. The framework explicitly incorporates key kinematics and energy relationships in drone trajectory optimization and outperforms benchmark methods that use simplified approximations of drone flying durations. Extensive computational experiments on synthetic instances and real-world case studies show that integrating drone trajectories into package-delivery planning can substantially reduce tour duration and drone energy consumption. Overall, the proposed modeling and computational framework provides a practically scalable and operationally impactful way to incorporate flight-physics awareness into truck-and-drone delivery planning.
Source: Computers & Operations Research
Authors: Yineng Sun, Armin Fügenschuh, Vikrant Vaze
Language: English
Subfield: Industrial and Manufacturing Engineering
Field: Engineering
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,570
OpenAlex ID: W7213358133