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Survivable capacitated network design problem: new formulation and Lagrangean relaxation

Author

Listed:
  • M Ríos

    (Universidad Católica de Chile)

  • V Marianov

    (Universidad Católica de Chile)

  • M Gutierrez

    (Universidad Católica de Chile)

Abstract

This work is focused on the analysis of the survivable capacitated network design problem. This problem can be stated as follows: Given a supply network with point-to-point traffic demands, specific survivability requirements, a set of available capacity ranges and their corresponding discrete costs for each arc, find minimum cost capacity expansions such that these demands can be met even if a network component fails. Solving this problem consists of selecting the links and their capacity, as well as the routings for each demand in every failure situation. This type of problem can be shown to be NP-hard. A new linear mixed-integer mathematical programming formulation is presented. An effective solution procedure based on Lagrangean relaxation is developed. Comparison heuristics and improvement heuristics are also described. Computational results using these procedures on different sizes of randomly generated networks are reported.

Suggested Citation

  • M Ríos & V Marianov & M Gutierrez, 2000. "Survivable capacitated network design problem: new formulation and Lagrangean relaxation," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 51(5), pages 574-582, May.
    • Handle: RePEc:pal:jorsoc:v:51:y:2000:i:5:d:10.1057_palgrave.jors.2600913
    DOI: 10.1057/palgrave.jors.2600913
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    Citations

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    Cited by:

    1. Morlok, Edward K. & Chang, David J., 2004. "Measuring capacity flexibility of a transportation system," Transportation Research Part A: Policy and Practice, Elsevier, vol. 38(6), pages 405-420, July.
    2. M Riis & A J V Skriver & S F Møller, 2005. "Internet protocol network design with uncertain demand," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 56(10), pages 1184-1195, October.
    3. Kenneth Martínez & David Claudio, 2023. "Expanding Fundamental Boundaries between Resilience and Survivability in Systems Engineering: A Literature Review," Sustainability, MDPI, vol. 15(6), pages 1-27, March.
    4. Majbah Uddin & Nathan Huynh, 2019. "Reliable Routing of Road-Rail Intermodal Freight under Uncertainty," Networks and Spatial Economics, Springer, vol. 19(3), pages 929-952, September.
    5. Fateme Fotuhi & Nathan Huynh, 2017. "Reliable Intermodal Freight Network Expansion with Demand Uncertainties and Network Disruptions," Networks and Spatial Economics, Springer, vol. 17(2), pages 405-433, June.
    6. Ukkusuri, Satish V. & Patil, Gopal, 2009. "Multi-period transportation network design under demand uncertainty," Transportation Research Part B: Methodological, Elsevier, vol. 43(6), pages 625-642, July.
    7. Garg, Manish & Smith, J. Cole, 2008. "Models and algorithms for the design of survivable multicommodity flow networks with general failure scenarios," Omega, Elsevier, vol. 36(6), pages 1057-1071, December.

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