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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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    Cited by:

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    4. 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.
    5. Xujin Chen & Xiaodong Hu & Xiaohua Jia & Zhongzheng Tang & Chenhao Wang & Ying Zhang, 2021. "Algorithms for the metric ring star problem with fixed edge-cost ratio," Journal of Combinatorial Optimization, Springer, vol. 42(3), pages 499-523, October.
    6. Alessandro Hill & Stefan Voß, 2016. "Optimal capacitated ring trees," EURO Journal on Computational Optimization, Springer;EURO - The Association of European Operational Research Societies, vol. 4(2), pages 137-166, May.
    7. Zhou, Lin & Baldacci, Roberto & Vigo, Daniele & Wang, Xu, 2018. "A Multi-Depot Two-Echelon Vehicle Routing Problem with Delivery Options Arising in the Last Mile Distribution," European Journal of Operational Research, Elsevier, vol. 265(2), pages 765-778.
    8. Nicola Bianchessi & Stefan Irnich & Christian Tilk, 2020. "A Branch-Price-and-Cut Algorithm for the Capacitated Multiple Vehicle Traveling Purchaser Problem with Unitary Demand," Working Papers 2003, Gutenberg School of Management and Economics, Johannes Gutenberg-Universität Mainz.
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    10. 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.
    11. Glock, Katharina & Meyer, Anne, 2023. "Spatial coverage in routing and path planning problems," European Journal of Operational Research, Elsevier, vol. 305(1), pages 1-20.
    12. Bütün, Cihan & Petrovic, Sanja & Muyldermans, Luc, 2021. "The capacitated directed cycle hub location and routing problem under congestion," European Journal of Operational Research, Elsevier, vol. 292(2), pages 714-734.
    13. Reihaneh, Mohammad & Ghoniem, Ahmed, 2019. "A branch-and-price algorithm for a vehicle routing with demand allocation problem," European Journal of Operational Research, Elsevier, vol. 272(2), pages 523-538.
    14. Olmez, Omer Berk & Gultekin, Ceren & Balcik, Burcu & Ekici, Ali & Özener, Okan Örsan, 2022. "A variable neighborhood search based matheuristic for a waste cooking oil collection network design problem," European Journal of Operational Research, Elsevier, vol. 302(1), pages 187-202.
    15. 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.
    16. 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.
    17. Ellegood, William A. & Solomon, Stanislaus & North, Jeremy & Campbell, James F., 2020. "School bus routing problem: Contemporary trends and research directions," Omega, Elsevier, vol. 95(C).
    18. 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.
    19. 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.
    20. 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.
    21. Anupam Mukherjee & Partha Sarathi Barma & Joydeep Dutta & Goutam Panigrahi & Samarjit Kar & Manoranjan Maiti, 2022. "A multi-objective antlion optimizer for the ring tree problem with secondary sub-depots," Operational Research, Springer, vol. 22(3), pages 1813-1851, July.

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