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A 2-Approximation Algorithm for the Multi-vehicle Scheduling Problem on a Path with Release and Handling Times

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Algorithms — ESA 2001 (ESA 2001)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2161))

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Abstract

In this paper, we consider a scheduling problem of vehicles on a path. Let G = (V, E) be a path, where V = {v 1, v 2,..., v n } is its set of n vertices and E = {{v j, v j+1 | j = 1, 2,..., n-1} is its set of edges. There are m identical vehicles (1 ≤ m ≤ n). The travel times w(v j, v j+1) (= w(v j+1,v j)) are associated with edges {v j, v j+1} ∈ E. Each job j which is located at each vertex v j ∈ V has release time r j and handling time h j. Any job must be served by exactly one vehicle. The problem asks to find an optimal schedule of m vehicles that minimizes the maximum completion time of all the jobs. The problem is known to be NP-hard for any fixed m ≥ 2. In this paper, we give an O(mn 2) time 2-approximation algorithm to the problem, by using properties of optimal gapless schedules.

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Author information

Authors and Affiliations

  1. Kyoto Institute of Technology, Matsugasaki, Sakyo, Kyoto, 606-8585, Japan

    Yoshiyuki Karuno

  2. Toyohashi University of Technology, Tempaku-cho, Toyohashi, 441-8580, Japan

    Hiroshi Nagamochi

Authors
  1. Yoshiyuki Karuno
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  2. Hiroshi Nagamochi
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Editor information

Editors and Affiliations

  1. Department of Mathematics and Computer Science and Heinz Nixdorf Institute, Paderborn University, 33095, Paderborn, Germany

    Friedhelm Meyer auf der Heide

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© 2001 Springer-Verlag Berlin Heidelberg

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Karuno, Y., Nagamochi, H. (2001). A 2-Approximation Algorithm for the Multi-vehicle Scheduling Problem on a Path with Release and Handling Times. In: auf der Heide, F.M. (eds) Algorithms — ESA 2001. ESA 2001. Lecture Notes in Computer Science, vol 2161. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44676-1_18

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  • DOI: https://doi.org/10.1007/3-540-44676-1_18

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-42493-2

  • Online ISBN: 978-3-540-44676-7

  • eBook Packages: Springer Book Archive

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