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On Coordinated Drone-Courier Logistics for Intra-city Express Services

Shuiwang Chen, Kai Wang, Lingxiao Wu, Wei Qi

TL;DR

The paper tackles the last-meter delivery challenge in dense urban areas by proposing a coordinated drone-courier system that confines drone operations to vertiport networks while couriers handle first-/last-mile stops. It develops a unified hub location-queueing optimization model, featuring a nonlinear queueing term $f(\rho)=\frac{\rho}{1-\rho}$ that yields a partly convex, partly concave feasible region, and then solves it with an exact adaptive discretization algorithm that alternates conservative and relaxed linearizations to obtain optimality guarantees. Using real data from SF Express, the approach demonstrates scalable, optimal solutions that yield cost and time savings through drone turnover and improved coordination, with a concentrated vertiport structure that enhances pooling and reduces deadheading. The study delivers actionable managerial insights on vertiport placement, demand consolidation, and the balance between drone capabilities and courier costs, while laying out a roadmap for future research in generalized coordinated unmanned-human logistics systems. Overall, the work advances the design and operation of intra-city express networks by integrating strategic vertiport location with tactical drone-courier dynamics in a rigorously solved optimization framework.

Abstract

Problem definition: Drones, despite being acknowledged as a transformative force in the city logistics sector, are unable to execute the \textit{last-meter delivery} (unloading goods directly to customers' doorsteps) due to airspace restrictions and safety concerns. To leverage advancements and overcome the limitations of drones in providing intra-city express services, we introduce a coordinated drone-courier logistics system where drones operate within a closed network among vertiports, while couriers connect customers to the drone delivery system. This paper aims to shed light on this coordinated system in terms of system feasibility, network interactivity, and long-term sustainability. Methodology/Results: We develop an integrated optimization model to optimize the network planning of the coordinated logistics system. The interplay between network planning and tactical operations is mirrored by a queueing network model, resulting in the nonlinear and nonconvex (partially convex and partially concave) feasible region of the optimization model. An iterative exact algorithm that tightens lower and upper bounds by adaptively refining the linear approximations of nonlinear constraints is developed to provide optimality-guaranteed solutions with finite convergence. The computational experiments demonstrate the scalability and robustness of our algorithm across various network configurations and scenarios.Managerial implications: The case study, based on a real-world dataset from SF Express, a logistics giant in China, validates that the coordinated logistics system efficiently attains cost and time savings by leveraging the effective turnover of drones and the coordination between drones and couriers. The optimal network design features a concentrated structure, streamlining demand consolidation and reducing deadhead repositioning.

On Coordinated Drone-Courier Logistics for Intra-city Express Services

TL;DR

The paper tackles the last-meter delivery challenge in dense urban areas by proposing a coordinated drone-courier system that confines drone operations to vertiport networks while couriers handle first-/last-mile stops. It develops a unified hub location-queueing optimization model, featuring a nonlinear queueing term that yields a partly convex, partly concave feasible region, and then solves it with an exact adaptive discretization algorithm that alternates conservative and relaxed linearizations to obtain optimality guarantees. Using real data from SF Express, the approach demonstrates scalable, optimal solutions that yield cost and time savings through drone turnover and improved coordination, with a concentrated vertiport structure that enhances pooling and reduces deadheading. The study delivers actionable managerial insights on vertiport placement, demand consolidation, and the balance between drone capabilities and courier costs, while laying out a roadmap for future research in generalized coordinated unmanned-human logistics systems. Overall, the work advances the design and operation of intra-city express networks by integrating strategic vertiport location with tactical drone-courier dynamics in a rigorously solved optimization framework.

Abstract

Problem definition: Drones, despite being acknowledged as a transformative force in the city logistics sector, are unable to execute the \textit{last-meter delivery} (unloading goods directly to customers' doorsteps) due to airspace restrictions and safety concerns. To leverage advancements and overcome the limitations of drones in providing intra-city express services, we introduce a coordinated drone-courier logistics system where drones operate within a closed network among vertiports, while couriers connect customers to the drone delivery system. This paper aims to shed light on this coordinated system in terms of system feasibility, network interactivity, and long-term sustainability. Methodology/Results: We develop an integrated optimization model to optimize the network planning of the coordinated logistics system. The interplay between network planning and tactical operations is mirrored by a queueing network model, resulting in the nonlinear and nonconvex (partially convex and partially concave) feasible region of the optimization model. An iterative exact algorithm that tightens lower and upper bounds by adaptively refining the linear approximations of nonlinear constraints is developed to provide optimality-guaranteed solutions with finite convergence. The computational experiments demonstrate the scalability and robustness of our algorithm across various network configurations and scenarios.Managerial implications: The case study, based on a real-world dataset from SF Express, a logistics giant in China, validates that the coordinated logistics system efficiently attains cost and time savings by leveraging the effective turnover of drones and the coordination between drones and couriers. The optimal network design features a concentrated structure, streamlining demand consolidation and reducing deadhead repositioning.
Paper Structure (54 sections, 6 theorems, 47 equations, 8 figures, 8 tables, 2 algorithms)

This paper contains 54 sections, 6 theorems, 47 equations, 8 figures, 8 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Background
  3. Contributions and Outline
  4. Literature Review
  5. Coordinated City Logistics
  6. Drone Delivery Network Planning
  7. Hub Location-Queueing Problem
  8. Problem Statement and Model Formulation
  9. Problem Description and Assumptions
  10. Model Formulation
  11. Network Planning.
  12. Service Level Management.
  13. Traffic Flow Management.
  14. Drone Operations.
  15. Full Formulation
  16. ...and 39 more sections

Key Result

Proposition 1

Let $Z[\cdot]$ denote an optimum a model. $[G_C]$ provides an upper bound on $Z[G^*]$, while $[G_R]$ provides a lower bound on $Z[G^*]$, i.e., $Z[G_R] \leq Z[G^*] \leq Z[G_C]$.

Figures (8)

  • Figure 1: Sample of Coordination Logistics Systems. (a) Meituan. (b) Hive Box
  • Figure 2: Traditional Dedicated Courier-based and Coordinated Drone-Courier Logistics Networks
  • Figure 3: Closed and Open queueing Network for Drone Operations
  • Figure 4: Convex Function $h(\cdot)$ and Concave Function $g(\cdot)$, with Their Piecewise Linear Approximations
  • Figure 5: Illustration of Discretization
  • ...and 3 more figures

Theorems & Definitions (7)

  • Proposition 1
  • Theorem 1
  • Proposition 2
  • Proposition 3
  • Proposition 4
  • Remark 1
  • Theorem 2