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An Integer Linear Programming based heuristic for the Capacitated m-Ring-Star Problem

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  • Naji-Azimi, Zahra
  • Salari, Majid
  • Toth, Paolo

Abstract

We address the Capacitated m-Ring-Star Problem in which the aim is to find m rings (simple cycles) visiting a central depot, a subset of customers and a subset of potential (Steiner) nodes, while customers not belonging to any ring must be “allocated” to a visited (customer or Steiner) node. Moreover, the rings must be node-disjoint and the number of customers allocated or visited in a ring cannot be greater than a given capacity Q. The objective is to minimize the total visiting and allocation costs. The Capacitated m-Ring-Star Problem is NP-hard, since it generalizes the Traveling Salesman Problem.

Suggested Citation

  • Naji-Azimi, Zahra & Salari, Majid & Toth, Paolo, 2012. "An Integer Linear Programming based heuristic for the Capacitated m-Ring-Star Problem," European Journal of Operational Research, Elsevier, vol. 217(1), pages 17-25.
    • Handle: RePEc:eee:ejores:v:217:y:2012:i:1:p:17-25
    DOI: 10.1016/j.ejor.2011.08.026
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    References listed on IDEAS

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    1. Baldacci, R. & Dell'Amico, M., 2010. "Heuristic algorithms for the multi-depot ring-star problem," European Journal of Operational Research, Elsevier, vol. 203(1), pages 270-281, May.
    2. S. Lin & B. W. Kernighan, 1973. "An Effective Heuristic Algorithm for the Traveling-Salesman Problem," Operations Research, INFORMS, vol. 21(2), pages 498-516, April.
    3. 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.
    4. Labbe, Martine & Laporte, Gilbert & Rodriguez Martin, Inmaculada & Gonzalez, Juan Jose Salazar, 2005. "Locating median cycles in networks," European Journal of Operational Research, Elsevier, vol. 160(2), pages 457-470, January.
    5. 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.
    6. John R. Current & David A. Schilling, 1989. "The Covering Salesman Problem," Transportation Science, INFORMS, vol. 23(3), pages 208-213, August.
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    Cited by:

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    3. Baldacci, Roberto & Hoshino, Edna A. & Hill, Alessandro, 2023. "New pricing strategies and an effective exact solution framework for profit-oriented ring arborescence problems," European Journal of Operational Research, Elsevier, vol. 307(2), pages 538-553.
    4. Agustín Montero & Juan José Miranda-Bront & Isabel Méndez-Díaz, 2017. "An ILP-based local search procedure for the VRP with pickups and deliveries," Annals of Operations Research, Springer, vol. 259(1), pages 327-350, December.
    5. Calvete, Herminia I. & Galé, Carmen & Iranzo, José A., 2013. "An efficient evolutionary algorithm for the ring star problem," European Journal of Operational Research, Elsevier, vol. 231(1), pages 22-33.
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