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Technical note: the expected length of an orderly path

Author

Listed:
  • Heather S. Lutz

    (Penn State University)

  • Trevor S. Hale

    (Texas A&M University)

  • Faizul Huq

    (Ohio University)

Abstract

Logistics planners often need to estimate length of a path through n random points. The problem has connections to geographical surveys, Steiner tree problems, traveling salesman problems, Amazon.com and Alibaba.cn drone aircraft multi-package outbound delivery paths, and aircraft sorties. In this effort, we utilize two applied probability tenets in concert to derive a closed form model for the expected distance between orderly pairs of randomly distributed delivery locations across some region. Indeed, by themselves each of the two tenets offer little help but when utilized simultaneously they elucidate the problem. Then, this expected distance is multiplied by (n − 1) to estimate the total length of the associated orderly path (albeit not the optimal path) through the n points. This total path length estimate, in turn, provides decision makers with a better information for distribution and logistics planning.

Suggested Citation

  • Heather S. Lutz & Trevor S. Hale & Faizul Huq, 2020. "Technical note: the expected length of an orderly path," Annals of Operations Research, Springer, vol. 289(2), pages 463-472, June.
    • Handle: RePEc:spr:annopr:v:289:y:2020:i:2:d:10.1007_s10479-019-03327-7
    DOI: 10.1007/s10479-019-03327-7
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    References listed on IDEAS

    as
    1. Trevor S. Hale & Faizul Huq & Heather Lutz & Carles Moslares, 2015. "On the expected distance of a random walk," International Journal of Mathematics in Operational Research, Inderscience Enterprises Ltd, vol. 7(3), pages 241-250.
    2. Morganna Carmem Diniz & Edmundo de Souza e Silva & H. Richard Gail, 2002. "Calculating the Distribution of a Linear Combination of Uniform Order Statistics," INFORMS Journal on Computing, INFORMS, vol. 14(2), pages 124-131, May.
    3. Rodney Vaughan, 1984. "Approximate Formulas for Average Distances Associated with Zones," Transportation Science, INFORMS, vol. 18(3), pages 231-244, August.
    4. Barreto,Humberto & Howland,Frank, 2006. "Introductory Econometrics," Cambridge Books, Cambridge University Press, number 9780521843195, October.
    5. S. Lin & B. W. Kernighan, 1973. "An Effective Heuristic Algorithm for the Traveling-Salesman Problem," Operations Research, INFORMS, vol. 21(2), pages 498-516, April.
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    Cited by:

    1. Martin Wiegand & Saralees Nadarajah, 2024. "On the expected length of an orderly path," OPSEARCH, Springer;Operational Research Society of India, vol. 61(2), pages 963-971, June.

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