Optimizing Truck-Drone Routing in Last-Mile Delivery Based on a Two-Index Stage-Based Formulation

Le Thi Hong Le1, , HopTrinhThi1, Trịnh Thị Anh Loan1
1 Hong Duc University

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Abstract

This paper investigates the Flying Sidekick Traveling Salesman Problem (FSTSP), a breakthrough solution for last-mile logistics. We propose a Mixed-Integer Linear Programming (MILP) model based on a 2-index stage-based formulation. Unlike traditional arc-based models, this approach assigns customers to ordered stages, significantly reducing the number of binary variables and automatically eliminating subtour constraints. Numerical experiments on the Niels Agatz (2018) benchmark datasets with up to 45 customers demonstrate that the model achieves superior performance in terms of convergence time and solution quality. Finally, the study suggests a future research direction by integrating this model into the Construct-Merge-Solve & Adapt (CMSA) hybrid metaheuristic framework to address larger-scale problems.

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References

[1]. Joerss, M., et al. (2016). Parcel delivery: The future of last mile. McKinsey & Company.
[2]. Figliozzi, M. A. (2017). Lifecycle greenhouse gas emissions of drones versus ground delivery vehicles. Transportation Research Part D: Transport and Environment, 52, 285-297.
[3]. Murray, C. C., & Chu, A. G. (2015). The flying sidekick traveling salesman problem: Optimization of drone-assisted parcel delivery. Transportation Research Part C: Emerging Technologies, 54, 86-109.
[4]. Agatz, N., et al. (2018). Optimization approaches for the traveling salesman problem with drone. Transportation Science, 52(4), 965-981.
[5]. Ha, Q. M., et al. (2018). On the min-cost Traveling Salesman Problem with Drone. Transportation Research Part C, 86, 597-621.
[6]. Dell’Amico, M., et al. (2020). Modeling the flying sidekick traveling salesman problem with drone stations. Computers & Operations Research, 120, 104954.
[7]. Savelsbergh, M. W., & Van Woensel, T. (2016). 50th anniversary invited article-city logistics: Challenges and opportunities. Transportation Science, 50(2), 579-590.
[8]. Poikonen, S., et al. (2017). The vehicle routing problem with drones: Extended models and case studies. Journal of the Operational Research Society, 68(12), 1563-1574.
[9]. Jeong, H. Y., et al. (2019). A truck-drone hybrid delivery model considering autonomous pathways and battery capacity. Sustainability, 11(5), 1455.