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The Capacitated m -Ring-Star Problem

Author

Listed:
  • R. Baldacci

    (Dipartimento di Elettronica, Informatica e Sistemistica, University of Bologna, 47023 Cesena, Italy)

  • M. Dell'Amico

    (Dipartimento di Scienze e Metodi dell'Ingegneria, University of Modena and Reggio Emilia, 42100 Reggio Emilia, Italy)

  • J. Salazar González

    (Departamento de Estadistica, Investigacíon Operativa y Computacíon, Facultad de Matemáticas, Universidad de La Laguna, 38271 La Laguna, Tenerife, Spain)

Abstract

The Capacitated m -Ring-Star Problem (C m RSP) is the problem of designing a set of rings that pass through a central depot and through some transition points and/or customers, and then assigning each nonvisited customer to a visited point or customer. The number of customers visited and assigned to a ring is bounded by an upper limit: the capacity of the ring. The objective is to minimize the total routing cost plus assignment costs. The problem has practical applications in the design of urban optical telecommunication networks. This paper presents and discusses two integer programming formulations for the C m RSP. Valid inequalities are proposed to strengthen the linear programming relaxation and are used as cutting planes in a branch-and-cut approach. The procedure is implemented and tested on a large family of instances, including real-world instances, and the good performance of the proposed approach is demonstrated.

Suggested Citation

  • R. Baldacci & M. Dell'Amico & J. Salazar González, 2007. "The Capacitated m -Ring-Star Problem," Operations Research, INFORMS, vol. 55(6), pages 1147-1162, December.
    • Handle: RePEc:inm:oropre:v:55:y:2007:i:6:p:1147-1162
    DOI: 10.1287/opre.1070.0432
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    References listed on IDEAS

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    1. Gouveia, Luis, 1995. "A result on projection for the vehicle routing ptoblem," European Journal of Operational Research, Elsevier, vol. 85(3), pages 610-624, September.
    2. 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.
    3. R. Baldacci & E. Hadjiconstantinou & A. Mingozzi, 2004. "An Exact Algorithm for the Capacitated Vehicle Routing Problem Based on a Two-Commodity Network Flow Formulation," Operations Research, INFORMS, vol. 52(5), pages 723-738, October.
    4. Gerhard Reinelt, 1991. "TSPLIB—A Traveling Salesman Problem Library," INFORMS Journal on Computing, INFORMS, vol. 3(4), pages 376-384, November.
    5. J. Beasley & E. Nascimento, 1996. "The Vehicle Routing-Allocation Problem: A unifying framework," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 4(1), pages 65-86, June.
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    Cited by:

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    4. 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.
    5. Baldacci, Roberto & Hill, Alessandro & Hoshino, Edna A. & Lim, Andrew, 2017. "Pricing strategies for capacitated ring-star problems based on dynamic programming algorithms," European Journal of Operational Research, Elsevier, vol. 262(3), pages 879-893.
    6. Pereira, Armando Honorio & Mateus, Geraldo Robson & Urrutia, Sebastián Alberto, 2022. "Valid inequalities and branch-and-cut algorithm for the pickup and delivery traveling salesman problem with multiple stacks," European Journal of Operational Research, Elsevier, vol. 300(1), pages 207-220.
    7. Mads Jepsen & Simon Spoorendonk & Stefan Ropke, 2013. "A Branch-and-Cut Algorithm for the Symmetric Two-Echelon Capacitated Vehicle Routing Problem," Transportation Science, INFORMS, vol. 47(1), pages 23-37, February.
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    10. Xujin Chen & Xiaodong Hu & Xiaohua Jia & Zhongzheng Tang & Chenhao Wang & Ying Zhang, 0. "Algorithms for the metric ring star problem with fixed edge-cost ratio," Journal of Combinatorial Optimization, Springer, vol. 0, pages 1-25.
    11. Wang, Mengtong & Zhang, Canrong & Bell, Michael G.H. & Miao, Lixin, 2022. "A branch-and-price algorithm for location-routing problems with pick-up stations in the last-mile distribution system," European Journal of Operational Research, Elsevier, vol. 303(3), pages 1258-1276.
    12. Alessandro Hill & Roberto Baldacci & Edna Ayako Hoshino, 2019. "Capacitated ring arborescence problems with profits," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 41(2), pages 357-389, June.
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