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Vehicle scheduling on a tree with release and handling times

Author

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  • Yoshiyuki Karuno
  • Hiroshi Nagamochi
  • Toshihide Ibaraki

Abstract

In this paper, we consider a single-vehicle scheduling problem on a tree-shaped road net-work. Let T =(V,E) be a tree, where V is a set of n vertices and E is a set of edges. A task is located at each vertex v, which is also denoted as v. Each task v has release time r(v) and handling time h(v). The travel times c(u, v) and c(v, u) are associated with each edge (u, v) of E. The vehicle starts from an initial vertex v_0 of V, visits all tasks v in V for their processing, and returns to v_0 . The objective is to find a routing schedule of the vehicle that minimizes the completion time, denoted as C (i.e., the time to return to v_0 after processing all tasks). We call this problem TREE-VSP(C). We first prove that TREE-VSP(C) is NP-hard. However, we then show that TREE-VSP(C) with a depth-first routing constraint can be exactly solved in O(n log n) time. Moreover, we show that, if this exact algorithm is used as an approximate algorithm for the original TREE-VSP(C), its worst-case performance ratio is at most two. Copyright Kluwer Academic Publishers 1997

Suggested Citation

  • Yoshiyuki Karuno & Hiroshi Nagamochi & Toshihide Ibaraki, 1997. "Vehicle scheduling on a tree with release and handling times," Annals of Operations Research, Springer, vol. 69(0), pages 193-207, January.
    • Handle: RePEc:spr:annopr:v:69:y:1997:i:0:p:193-207:10.1023/a:1018928911513
    DOI: 10.1023/A:1018928911513
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    Citations

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    Cited by:

    1. Averbakh, Igor & Berman, Oded & Chernykh, Ilya, 2006. "The routing open-shop problem on a network: Complexity and approximation," European Journal of Operational Research, Elsevier, vol. 173(2), pages 531-539, September.
    2. Yuanxiao Wu & Xiwen Lu, 0. "Improved algorithms for single vehicle scheduling on tree/cycle networks," Journal of Combinatorial Optimization, Springer, vol. 0, pages 1-16.
    3. Sofie Coene & Frits C. R. Spieksma & Gerhard J. Woeginger, 2011. "Charlemagne's Challenge: The Periodic Latency Problem," Operations Research, INFORMS, vol. 59(3), pages 674-683, June.
    4. Michael Hassoun & Shraga Shoval & Eran Simchon & Liron Yedidsion, 2020. "The single line moving target traveling salesman problem with release times," Annals of Operations Research, Springer, vol. 289(2), pages 449-458, June.
    5. Yuanxiao Wu & Xiwen Lu, 2021. "Improved algorithms for single vehicle scheduling on tree/cycle networks," Journal of Combinatorial Optimization, Springer, vol. 42(3), pages 565-580, October.
    6. Herer, Yale T., 1999. "Submodularity and the traveling salesman problem," European Journal of Operational Research, Elsevier, vol. 114(3), pages 489-508, May.

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