IDEAS home Printed from https://ideas.repec.org/a/spr/jcomop/v32y2016i3d10.1007_s10878-015-9905-7.html
   My bibliography  Save this article

The Canadian Tour Operator Problem on paths: tight bounds and resource augmentation

Author

Listed:
  • Sabine Büttner

    (University of Kaiserslautern)

  • Sven O. Krumke

    (University of Kaiserslautern)

Abstract

In the prize-collecting travelling salesman problem, we are given a weighted graph $$G=(V,E)$$ G = ( V , E ) with edge weights $$\ell :E\rightarrow \mathbb {R}_+$$ ℓ : E → R + , a special vertex $$r\in V$$ r ∈ V , penalties $$\pi :V\rightarrow \mathbb {R}_+$$ π : V → R + and the goal is to find a closed tour $$T$$ T such that $$r\in V(T)$$ r ∈ V ( T ) and such that the cost $$\ell (T)+\pi (V\setminus V(T))$$ ℓ ( T ) + π ( V \ V ( T ) ) , which is the sum of the edges in the tour and the cost of the vertices not spanned by $$T$$ T , is minimized. We consider an online variant of the prize-collecting travelling salesman problem related to graph exploration. In the Canadian Tour Operator Problem the task is to find a closed route for a tourist bus in a given network $$G=(V,E)$$ G = ( V , E ) in which some edges are blocked by avalanches. An online algorithm learns from a blocked edge only when reaching one of its endpoints. The bus operator has the option to avoid visiting each node $$v\in V$$ v ∈ V by paying a refund of $$\pi (v)$$ π ( v ) to the tourists. The goal consists of minimizing the sum of the travel costs and the refunds. We study the problem on a simple (weighted) path and prove tight bounds on the competitiveness of deterministic algorithms. Specifically, we give an algorithm with competitive ratio equal to the golden ratio $$\phi =(1+\sqrt{5})/2$$ ϕ = ( 1 + 5 ) / 2 . We also study the effect of resource augmentation, where the online algorithm either pays a discounted cost for traversing edges or for the penalties.

Suggested Citation

  • Sabine Büttner & Sven O. Krumke, 2016. "The Canadian Tour Operator Problem on paths: tight bounds and resource augmentation," Journal of Combinatorial Optimization, Springer, vol. 32(3), pages 842-854, October.
  • Handle: RePEc:spr:jcomop:v:32:y:2016:i:3:d:10.1007_s10878-015-9905-7
    DOI: 10.1007/s10878-015-9905-7
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10878-015-9905-7
    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/s10878-015-9905-7?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.

    References listed on IDEAS

    as
    1. Patrick Jaillet & Michael R. Wagner, 2008. "Generalized Online Routing: New Competitive Ratios, Resource Augmentation, and Asymptotic Analyses," Operations Research, INFORMS, vol. 56(3), pages 745-757, June.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Davood Shiri & Vahid Akbari & F. Sibel Salman, 2024. "Online algorithms for ambulance routing in disaster response with time-varying victim conditions," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 46(3), pages 785-819, September.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Zhang, Huili & Tong, Weitian & Xu, Yinfeng & Lin, Guohui, 2015. "The Steiner Traveling Salesman Problem with online edge blockages," European Journal of Operational Research, Elsevier, vol. 243(1), pages 30-40.
    2. Cong Chen & Huili Zhang & Yinfeng Xu, 2022. "Online machine minimization with lookahead," Journal of Combinatorial Optimization, Springer, vol. 43(5), pages 1149-1172, July.
    3. Zhang, Huili & Tong, Weitian & Lin, Guohui & Xu, Yinfeng, 2019. "Online minimum latency problem with edge uncertainty," European Journal of Operational Research, Elsevier, vol. 273(2), pages 418-429.
    4. Davood Shiri & Hakan Tozan, 2022. "Online routing and searching on graphs with blocked edges," Journal of Combinatorial Optimization, Springer, vol. 44(2), pages 1039-1059, September.
    5. Xu, Jun & Wang, Jun-Qiang & Liu, Zhixin, 2022. "Parallel batch scheduling: Impact of increasing machine capacity," Omega, Elsevier, vol. 108(C).
    6. Dimitris Bertsimas & Patrick Jaillet, & Sébastien Martin, 2019. "Online Vehicle Routing: The Edge of Optimization in Large-Scale Applications," Operations Research, INFORMS, vol. 67(1), pages 143-162, January.
    7. Ananya Christman & William Forcier & Aayam Poudel, 2018. "From theory to practice: maximizing revenues for on-line dial-a-ride," Journal of Combinatorial Optimization, Springer, vol. 35(2), pages 512-529, February.
    8. Devansh Jalota & Dario Paccagnan & Maximilian Schiffer & Marco Pavone, 2023. "Online Routing Over Parallel Networks: Deterministic Limits and Data-driven Enhancements," INFORMS Journal on Computing, INFORMS, vol. 35(3), pages 560-577, May.
    9. Wen, Jian & Nassir, Neema & Zhao, Jinhua, 2019. "Value of demand information in autonomous mobility-on-demand systems," Transportation Research Part A: Policy and Practice, Elsevier, vol. 121(C), pages 346-359.
    10. Shiri, Davood & Akbari, Vahid & Hassanzadeh, Ali, 2024. "The Capacitated Team Orienteering Problem: An online optimization framework with predictions of unknown accuracy," Transportation Research Part B: Methodological, Elsevier, vol. 185(C).
    11. Bakker, Hannah & Dunke, Fabian & Nickel, Stefan, 2020. "A structuring review on multi-stage optimization under uncertainty: Aligning concepts from theory and practice," Omega, Elsevier, vol. 96(C).
    12. Alonso Tabares, Diego & Mora-Camino, Felix & Drouin, Antoine, 2021. "A multi-time scale management structure for airport ground handling automation," Journal of Air Transport Management, Elsevier, vol. 90(C).
    13. Pillac, Victor & Gendreau, Michel & Guéret, Christelle & Medaglia, Andrés L., 2013. "A review of dynamic vehicle routing problems," European Journal of Operational Research, Elsevier, vol. 225(1), pages 1-11.
    14. Melih Çelik & Özlem Ergun & Pınar Keskinocak, 2015. "The Post-Disaster Debris Clearance Problem Under Incomplete Information," Operations Research, INFORMS, vol. 63(1), pages 65-85, February.
    15. Xingang Wen & Yinfeng Xu & Huili Zhang, 2015. "Online traveling salesman problem with deadlines and service flexibility," Journal of Combinatorial Optimization, Springer, vol. 30(3), pages 545-562, October.
    16. Güneş Erdoğan & Maria Battarra & Gilbert Laporte, 2014. "Scheduling twin robots on a line," Naval Research Logistics (NRL), John Wiley & Sons, vol. 61(2), pages 119-130, March.
    17. Davood Shiri & Vahid Akbari & F. Sibel Salman, 2024. "Online algorithms for ambulance routing in disaster response with time-varying victim conditions," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 46(3), pages 785-819, September.

    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:jcomop:v:32:y:2016:i:3:d:10.1007_s10878-015-9905-7. 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.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with 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.