IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v285y2020i3p965-976.html
   My bibliography  Save this article

Search and Delivery Man Problems: When are depth-first paths optimal?

Author

Listed:
  • Alpern, Steve
  • Lidbetter, Thomas

Abstract

Let h be a probability measure on the nodes and arcs of a network Q, viewed either as the location of a hidden object to be found or as the continuous distribution of customers receiving packages. We wish to find a trajectory starting from a specified root, or depot O that minimizes the expected search or delivery time. We call such a trajectory optimal. When Q is a tree, we ask for which h there is an optimal trajectory that is depth-first, and we find sufficient conditions and in some cases necessary and sufficient conditions on h. A consequence of our analysis is a determination of the optimal depot location in the Delivery Man Problem, correcting an error in the literature. We concentrate mainly on the search problem, with the Delivery Man Problem arising as a special case.

Suggested Citation

  • Alpern, Steve & Lidbetter, Thomas, 2020. "Search and Delivery Man Problems: When are depth-first paths optimal?," European Journal of Operational Research, Elsevier, vol. 285(3), pages 965-976.
    • Handle: RePEc:eee:ejores:v:285:y:2020:i:3:p:965-976
    DOI: 10.1016/j.ejor.2020.02.026
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221720301442
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ejor.2020.02.026?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. Steve Alpern & Thomas Lidbetter, 2013. "Mining Coal or Finding Terrorists: The Expanding Search Paradigm," Operations Research, INFORMS, vol. 61(2), pages 265-279, April.
    2. Baston, Vic & Kikuta, Kensaku, 2019. "A search problem on a bipartite network," European Journal of Operational Research, Elsevier, vol. 277(1), pages 227-237.
    3. Robbert Fokkink & Thomas Lidbetter & László A. Végh, 2019. "On Submodular Search and Machine Scheduling," Management Science, INFORMS, vol. 44(4), pages 1431-1449, November.
    4. Steve Alpern & Vic Baston & Shmuel Gal, 2008. "Network search games with immobile hider, without a designated searcher starting point," International Journal of Game Theory, Springer;Game Theory Society, vol. 37(2), pages 281-302, June.
    5. Lidbetter, Thomas, 2013. "Search games with multiple hidden objects," LSE Research Online Documents on Economics 55103, London School of Economics and Political Science, LSE Library.
    6. Matteo Fischetti & Paolo Toth, 1997. "A Polyhedral Approach to the Asymmetric Traveling Salesman Problem," Management Science, INFORMS, vol. 43(11), pages 1520-1536, November.
    7. Steve Alpern & Thomas Lidbetter, 2014. "Searching a Variable Speed Network," Mathematics of Operations Research, INFORMS, vol. 39(3), pages 697-711, August.
    Full references (including those not matched with items on IDEAS)

    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. Lidbetter, Thomas, 2020. "Search and rescue in the face of uncertain threats," European Journal of Operational Research, Elsevier, vol. 285(3), pages 1153-1160.
    2. Yolmeh, Abdolmajid & Baykal-Gürsoy, Melike, 2021. "Weighted network search games with multiple hidden objects and multiple search teams," European Journal of Operational Research, Elsevier, vol. 289(1), pages 338-349.
    3. Bui, Thuy & Lidbetter, Thomas, 2023. "Optimal patrolling strategies for trees and complete networks," European Journal of Operational Research, Elsevier, vol. 311(2), pages 769-776.
    4. Hellerstein, Lisa & Lidbetter, Thomas, 2023. "A game theoretic approach to a problem in polymatroid maximization," European Journal of Operational Research, Elsevier, vol. 305(2), pages 979-988.
    5. Garrec, Tristan & Scarsini, Marco, 2020. "Search for an immobile hider on a stochastic network," European Journal of Operational Research, Elsevier, vol. 283(2), pages 783-794.
    6. Robbert Fokkink & Ken Kikuta & David Ramsey, 2017. "The search value of a set," Annals of Operations Research, Springer, vol. 256(1), pages 63-73, September.
    7. Vic Baston & Kensaku Kikuta, 2015. "Search games on a network with travelling and search costs," International Journal of Game Theory, Springer;Game Theory Society, vol. 44(2), pages 347-365, May.
    8. Steve Alpern & Thomas Lidbetter, 2019. "Approximate solutions for expanding search games on general networks," Annals of Operations Research, Springer, vol. 275(2), pages 259-279, April.
    9. Robbert Fokkink & Thomas Lidbetter & László A. Végh, 2019. "On Submodular Search and Machine Scheduling," Management Science, INFORMS, vol. 44(4), pages 1431-1449, November.
    10. Lidbetter, Thomas, 2017. "On the approximation ratio of the Random Chinese Postman Tour for network search," European Journal of Operational Research, Elsevier, vol. 263(3), pages 782-788.
    11. Bastián Bahamondes & Mathieu Dahan, 2024. "Hide-and-Seek Game with Capacitated Locations and Imperfect Detection," Decision Analysis, INFORMS, vol. 21(2), pages 110-124, June.
    12. Garrec, Tristan, 2019. "Continuous patrolling and hiding games," European Journal of Operational Research, Elsevier, vol. 277(1), pages 42-51.
    13. Ben Hermans & Roel Leus & Jannik Matuschke, 2022. "Exact and Approximation Algorithms for the Expanding Search Problem," INFORMS Journal on Computing, INFORMS, vol. 34(1), pages 281-296, January.
    14. Bui, Thuy & Lidbetter, Thomas & Lin, Kyle Y., 2024. "Optimal pure strategies for a discrete search game," European Journal of Operational Research, Elsevier, vol. 313(2), pages 767-775.
    15. Felix Happach & Lisa Hellerstein & Thomas Lidbetter, 2022. "A General Framework for Approximating Min Sum Ordering Problems," INFORMS Journal on Computing, INFORMS, vol. 34(3), pages 1437-1452, May.
    16. Baston, Vic & Kikuta, Kensaku, 2019. "A search problem on a bipartite network," European Journal of Operational Research, Elsevier, vol. 277(1), pages 227-237.
    17. Steve Alpern, 2017. "Hide-and-Seek Games on a Network, Using Combinatorial Search Paths," Operations Research, INFORMS, vol. 65(5), pages 1207-1214, October.
    18. Furini, Fabio & Persiani, Carlo Alfredo & Toth, Paolo, 2016. "The Time Dependent Traveling Salesman Planning Problem in Controlled Airspace," Transportation Research Part B: Methodological, Elsevier, vol. 90(C), pages 38-55.
    19. Wettergren, Thomas A., 2021. "Game-based modeling of independent searchers who share a common goal," Applied Mathematics and Computation, Elsevier, vol. 391(C).
    20. D Soler & E Martínez & J C Micó, 2008. "A transformation for the mixed general routing problem with turn penalties," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 59(4), pages 540-547, April.

    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:eee:ejores:v:285:y:2020:i:3:p:965-976. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/eor .

    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.