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

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  • 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
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    References listed on IDEAS

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    1. Steve Alpern & Thomas Lidbetter, 2014. "Searching a Variable Speed Network," Mathematics of Operations Research, INFORMS, vol. 39(3), pages 697-711, August.
    2. Steve Alpern & Thomas Lidbetter, 2013. "Mining Coal or Finding Terrorists: The Expanding Search Paradigm," Operations Research, INFORMS, vol. 61(2), pages 265-279, April.
    3. Baston, Vic & Kikuta, Kensaku, 2019. "A search problem on a bipartite network," European Journal of Operational Research, Elsevier, vol. 277(1), pages 227-237.
    4. Robbert Fokkink & Thomas Lidbetter & László A. Végh, 2019. "On Submodular Search and Machine Scheduling," Management Science, INFORMS, vol. 44(4), pages 1431-1449, November.
    5. 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.
    6. 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.
    7. Matteo Fischetti & Paolo Toth, 1997. "A Polyhedral Approach to the Asymmetric Traveling Salesman Problem," Management Science, INFORMS, vol. 43(11), pages 1520-1536, November.
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