IDEAS home Printed from https://ideas.repec.org/a/spr/orspec/v47y2025i1d10.1007_s00291-024-00785-9.html
   My bibliography  Save this article

Two-indexed formulation of the traveling salesman problem with multiple drones performing sidekicks and loops

Author

Listed:
  • Alexander Rave

    (Catholic University Eichstätt-Ingolstadt)

Abstract

Aerial drone delivery has great potential to improve package delivery time, as drones can fly autonomously over obstacles at a possibly higher speed than trucks. The benefits of drones in delivery can even be increased in a truck-and-drone tandem where a truck carries multiple drones and releases them at advantageous places, i.e., the traveling salesman problem with multiple drones (TSPmD). We focus on a general version of this problem with makespan minimization, where the drones have two options after serving the customer: they can return to any node the truck visits at a later stage (sidekick) or return to the same node they were launched from (loop) — even at the depot. We introduce an efficient two-indexed mixed-integer linear program (MILP) for this TSPmD and show how to adapt the MILP to cover two problem variants, namely the multiple flying sidekick traveling salesman problem and the traveling salesman problem with drone. Our MILP formulation is an efficient formulation, as it outperforms eight state-of-the-art MILP formulations for these problem variants in nearly all larger instances. In a numerical study, we provide new optimal solutions with up to 28 nodes for benchmark purposes. Moreover, we analyze the impact of allowing drone loops on makespan minimization in general and at the depot. We find that loops mainly become relevant when drones travel faster than trucks, resulting in average makespan savings of up to 2.7%.

Suggested Citation

  • Alexander Rave, 2025. "Two-indexed formulation of the traveling salesman problem with multiple drones performing sidekicks and loops," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 47(1), pages 67-104, March.
  • Handle: RePEc:spr:orspec:v:47:y:2025:i:1:d:10.1007_s00291-024-00785-9
    DOI: 10.1007/s00291-024-00785-9
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00291-024-00785-9
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.

    File URL: https://libkey.io/10.1007/s00291-024-00785-9?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:orspec:v:47:y:2025:i:1:d:10.1007_s00291-024-00785-9. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.