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An Approximation Algorithm for the Three Depots Hamiltonian Path Problem

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Optimization Theory, Decision Making, and Operations Research Applications

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 31))

Abstract

In this paper, we propose an approximation algorithm for solving the three depots Hamiltonian path problem (3DHPP). The problem studied can be viewed as a variant of the well-known Hamiltonian path problem with multiple depots (cf., Demange [Mathématiques et Informatique, Gazette, 102 (2004)] and Malik et al. [Oper. Res. Lett. 35, 747–753 (2007)]). For the 3DHPP, we show the existence of a \(\frac{3} {2}\)-approximation algorithm for a broad family of metric cases which also guarantees a ratio r < 2 in the general metric case. The proposed algorithm is mainly based on extending the construction scheme already used by Rathinam et al. [Oper. Res. Lett. 38, 63–68 (2010)]. The aforementioned result is established for a variant of the three-depot problem, that is, when costs are symmetric and satisfy the triangle inequality.

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References

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Authors and Affiliations

  1. Picardie University, 33 Rue Saint Leu, 80039, Amiens Cedex 1, France

    Aristotelis Giannakos & M’hand Hifi

  2. Faculty of Science Tizi Ouzon, Mouloud Mammeri University, Tizi-Ouzou, Algeria

    Rezika Kheffache

  3. University of Technology, Bab Ezzouar, Algeria

    Rachid Ouafi

Authors
  1. Aristotelis Giannakos
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  2. M’hand Hifi
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  3. Rezika Kheffache
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  4. Rachid Ouafi
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Corresponding author

Correspondence to Aristotelis Giannakos .

Editor information

Editors and Affiliations

  1. , Faculty of Engineering, Aristotle University of Thessaloniki, Thessaloniki, 54124, Greece

    Athanasios Migdalas

  2. , Economical and Social Sciences, University of Macedonia, Loggou-Tourpali, Naoussa, 59200, Greece

    Angelo Sifaleras

  3. , Department of Applied Informatics, University of Macedonia, Egnatia St. 156, Thessaloniki, 54006, Greece

    Christos K. Georgiadis

  4. , Department of Marketing and Operations M, University of Macedonia, Agiou Dimitriou 49, Edessa, 58200, Greece

    Jason Papathanasiou

  5. , Department of Applied Informatics, University of Macedonia, Egnatia Street 156, Thessaloniki, 54006, Greece

    Emmanuil Stiakakis

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Giannakos, A., Hifi, M., Kheffache, R., Ouafi, R. (2013). An Approximation Algorithm for the Three Depots Hamiltonian Path Problem. In: Migdalas, A., Sifaleras, A., Georgiadis, C., Papathanasiou, J., Stiakakis, E. (eds) Optimization Theory, Decision Making, and Operations Research Applications. Springer Proceedings in Mathematics & Statistics, vol 31. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-5134-1_25

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