Drone scheduling for parcel delivery with an access grade to stops on a fixed truck route
DOI: 10.1299/jamdsm.2024jamdsm0021
archive: archived pipeline: cataloged verified
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Summary
This paper addresses the scheduling problem for a truck-drone parcel delivery system, specifically focusing on minimizing the total duration (makespan) of a carrier truck serving a fixed set of customers. The system consists of a single truck acting as a mobile depot for multiple identical drones, each with a unit capacity. The truck follows a fixed, ordered route of stops, and drones must launch and retrieve at the same stop for each sortie. The authors introduce a novel "access grade" parameter to generalize existing models, which typically assume unrestricted access to any truck stop for drone launches. This parameter imposes a flight time bound, partitioning stops into "nearer" and "farther" subsets, requiring drones to launch only from nearer stops. This generalization allows the model to simulate constraints such as limited battery capacity or operational restrictions on drone range. The study formulates the problem using Integer Programming (IP). The authors first review the underlying IP formulation for the unrestricted model and then modify it to incorporate the access grade parameter. The generalized IP formulation minimizes the sum of the truck’s standing times at all stops, subject to constraints ensuring each customer is served exactly once and that drone flight times do not exceed the bound defined by the access grade. Theoretical analysis demonstrates that the problem remains NP-hard, even for small numbers of drones. Furthermore, the authors show that the ratio of the optimal total duration under strict access constraints (nearest stops only) to the unrestricted case can grow arbitrarily large, indicating that strict access grades can significantly reduce the efficiency of drone utilization. Numerical experiments were conducted using randomly generated instances with 50 customers, 10 truck stops, and varying numbers of drones (1 to 20). The Gurobi Optimizer was used to solve the IP formulations within a 3,600-second time limit. Results indicate that the maximum allowable flight time increases with the access grade parameter, with the largest jump occurring between the first and second grades. The study identifies a "minimal integer for equivalent access," the lowest access grade that yields the same optimal total duration as the unrestricted model. These findings highlight the trade-off between operational constraints and system efficiency, providing a framework for optimizing truck-drone logistics under realistic flight limitations.
Provenance
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| Stage | Outcome | Tool | Model | Prompt | Attempts | Completed |
|---|---|---|---|---|---|---|
| discover | success | DOAJ | — | — | 1 | 2026-06-24 |
| archive | success | unpaywall | — | — | 1 | 2026-06-26 |
| extract | success | cached | — | — | 2 | 2026-06-26 |
| clean | success | clean | — | — | 1 | 2026-06-25 |
| chunk | success | chunk | — | — | 1 | 2026-06-25 |
| embed | success | embed | Qwen/Qwen3-Embedding-8B | — | 1 | 2026-06-25 |
| promote | success | — | — | — | 1 | 2026-06-24 |
| summarize | success | llm | qwen3.6-27b-prismaquant | summ-v5 | 1 | 2026-06-26 |
| tag | success | vector_similarity | — | — | 6 | 2026-06-25 |
| verify | success | — | — | — | 1 | 2026-06-26 |
Summary generated by qwen3.6-27b-prismaquant on 2026-06-26; verification: verified.
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