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Optimal capacitated ring trees

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  • HILL, Alessandro
  • VOß, Stefan

Abstract

We study a new network design model combining ring and tree structures under capacity constraints. The solution topology of this capacitated ring tree problem (CRTP) is based on ring trees which are the union of trees and 1-trees. The objective is the minimization of edge costs but could also incorporate other types of measures. This overall problem generalizes prominent capacitated vehicle routing and Steiner tree problem variants. Two customer types have to be connected to a distributor ensuring single and double node connectivity, respectively, while installing optional Steiner nodes. The number of ring trees and the number of customers supplied by such a single structure are bounded. After embedding this combinatorial optimization model in existing network design concepts, we develop a mathematical formulation and introduce several valid inequalities for the CRTP that are separated in our exact algorithm. Additionally, we use local search techniques to tighten the obtained upper bounds. For a set of literature-derived instances we consider various reliability scenarios and present computational results.

Suggested Citation

  • HILL, Alessandro & VOß, Stefan, 2014. "Optimal capacitated ring trees," Working Papers 2014012, University of Antwerp, Faculty of Business and Economics.
    • Handle: RePEc:ant:wpaper:2014012
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    File URL: https://repository.uantwerpen.be/docman/irua/d9597f/145286.pdf
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    References listed on IDEAS

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    1. Naji-Azimi, Zahra & Salari, Majid & Toth, Paolo, 2010. "A heuristic procedure for the Capacitated m-Ring-Star problem," European Journal of Operational Research, Elsevier, vol. 207(3), pages 1227-1234, December.
    2. Roberto Baldacci & Paolo Toth & Daniele Vigo, 2010. "Exact algorithms for routing problems under vehicle capacity constraints," Annals of Operations Research, Springer, vol. 175(1), pages 213-245, March.
    3. Matteo Fischetti & Juan José Salazar González & Paolo Toth, 1997. "A Branch-and-Cut Algorithm for the Symmetric Generalized Traveling Salesman Problem," Operations Research, INFORMS, vol. 45(3), pages 378-394, June.
    4. HILL, Alessandro, 2014. "Multi-exchange neighborhoods for the capacitated ring tree problem," Working Papers 2014011, University of Antwerp, Faculty of Business and Economics.
    5. Letchford, Adam N. & Nasiri, Saeideh D. & Theis, Dirk Oliver, 2013. "Compact formulations of the Steiner Traveling Salesman Problem and related problems," European Journal of Operational Research, Elsevier, vol. 228(1), pages 83-92.
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    1. HILL, Alessandro, 2014. "Multi-exchange neighborhoods for the capacitated ring tree problem," Working Papers 2014011, University of Antwerp, Faculty of Business and Economics.
    2. HILL, Alessandro & VOß, Stefan, 2014. "Generalized local branching heuristics and the capacitated ring tree problem," Working Papers 2014020, University of Antwerp, Faculty of Business and Economics.

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    More about this item

    Keywords

    Capacitated ring tree problem; Steiner tree; Ring tree; Vehicle routing; Survivable network design; Integer programming;
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