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An approximation algorithm for a special case of the asymmetric travelling salesman problem

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  • Maksim Barketau
  • Erwin Pesch

Abstract

We consider the following optimisation problem that we encountered during the consolidation process of trains in a container transhipment terminal as well as in the intermediate storage of containers in sea ports in order to accelerate the loading and unloading of the vessels. There are n ordered pairs of points in the m -dimensional metric space: . The problem is to find a permutation of numbers minimising the function where is the metric of the space. The problem can be considered as a special case of the asymmetric travelling salesman problem. As for Euclidean, Manhattan and Chebyshev metric the problem is NP-hard (as a generalisation of the well-known TSP problem) we propose the simple approximation algorithm with the approximation guarantee equal to 3. The approximation guarantee is tight as will be shown by a sequence of instances for which the approximation ratio converges to 3.

Suggested Citation

  • Maksim Barketau & Erwin Pesch, 2016. "An approximation algorithm for a special case of the asymmetric travelling salesman problem," International Journal of Production Research, Taylor & Francis Journals, vol. 54(14), pages 4205-4212, July.
    • Handle: RePEc:taf:tprsxx:v:54:y:2015:i:14:p:4205-4212
    DOI: 10.1080/00207543.2015.1113327
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    References listed on IDEAS

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    1. P. M. Dearing & R. L. Francis, 1974. "A Minimax Location Problem on a Network," Transportation Science, INFORMS, vol. 8(4), pages 333-343, November.
    2. P. M. Dearing & R. L. Francis, 1974. "A Network Flow Solution to a Multifacility Minimax Location Problem Involving Rectilinear Distances," Transportation Science, INFORMS, vol. 8(2), pages 126-141, May.
    3. Nils Boysen & Florian Jaehn & Erwin Pesch, 2011. "Scheduling Freight Trains in Rail-Rail Transshipment Yards," Transportation Science, INFORMS, vol. 45(2), pages 199-211, May.
    4. Nils Boysen & Malte Fliedner & Florian Jaehn & Erwin Pesch, 2013. "A Survey on Container Processing in Railway Yards," Transportation Science, INFORMS, vol. 47(3), pages 312-329, August.
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