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Multistart Branch and Bound for Large Asymmetric Distance-Constrained Vehicle Routing 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 chapter we revise and modify an old branch-and-bound method for solving the asymmetric distance-constrained vehicle routing problem suggested by Laporte et al. in 1987. It is based on reformulating distance-constrained vehicle routing problem into a travelling salesman problem and use of assignment problem as a lower bounding procedure. In addition, our algorithm uses the best-first strategy and new tolerance-based branching rules. Since our method was fast but memory consuming, it could stop before optimality is proven. Therefore we introduce the randomness, in case of ties, in choosing the node of the search tree. If an optimal solution is not found, we restart our procedure. In that way we get multistart branch-and-bound method. As far as we know instances we solved exactly (up to 1,000 customers) are much larger than instances considered for other VRP models from the recent literature. So, despite its simplicity, this proposed algorithm is capable of solving the largest instances ever solved in the literature. Moreover, this approach is general and may be used in solving other types of vehicle routing problems.

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Authors and Affiliations

  1. Brunel University, Uxbridge, Middlesex, UB8 3PH, UK

    Samira Almoustafa & Nenad Mladenović

  2. Lamih-Universite de Valenciennes, Valenciennes, France

    Said Hanafi

Authors
  1. Samira Almoustafa
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  2. Said Hanafi
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  3. Nenad Mladenović
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Corresponding author

Correspondence to Samira Almoustafa .

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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Almoustafa, S., Hanafi, S., Mladenović, N. (2013). Multistart Branch and Bound for Large Asymmetric Distance-Constrained Vehicle Routing 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_2

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