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A Polynomial Time Approximation Scheme for the Multi-vehicle Scheduling Problem on a Path with Release and Handling Times

  • Yoshiyuki Karuno
  • Hiroshi Nagamochi
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2223)

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, . . . , vn} 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 vehicles (1 ≤ mn). 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 vjGBV has release time rj and handling time hj . Any job must be processed 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 present a polynomial time approximation scheme A ε to the problem with a fixed m. Our algorithm can be extended to the case where G is a tree so that a polynomial time approximation scheme is obtained if m and the number of leaves in G are fixed

Keywords

Schedule Problem Completion Time Release Time Optimal Schedule Edge Weight 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Yoshiyuki Karuno
    • 1
  • Hiroshi Nagamochi
    • 2
  1. 1.Kyoto Institute of TechnologyKyotoJapan
  2. 2.Toyohashi University of TechnologyToyohashiJapan

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