An approximability result of the multi-vehicle scheduling problem on a path with release and handling times

Authors:
Yoshiyuki Karuno;Hiroshi Nagamochi
Affiliations:
Department of Mechanical and System Engineering, Kyoto Institute of Technology, Matsugasaki, Sakyo, Kyoto 606-8585, Japan;Department of Information and Computer Sciences, Toyohashi University of Technology, Toyohashi, Aichi 441-8580, Japan
Venue:
Theoretical Computer Science
Year:
2004

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Abstract

In this paper, we consider a scheduling problem of vehicles on a path G with n vertices and n - 1 edges. There are m identical vehicles. Each vertex in G has exactly one job. Any of the n jobs must be processed by some vehicle. Each job has a release time and a handling time. With the edges, symmetric travel times are associated. The problem asks to find an optimal schedule of the 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 show that the problem with a fixed m admits a polynomial time approximation scheme. 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.