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Spare-Capacity Assignment For Line Restoration Using a Single-Facility Type

Author

Listed:
  • Anantaram Balakrishnan

    (The University of Texas at Austin, Austin, Texas 78712)

  • Thomas L. Magnanti

    (Massachusetts Institute of Technology, Cambridge, Massachusetts 02139)

  • Joel S. Sokol

    (Georgia Institute of Technology, Atlanta, Georgia 30332)

  • Yi Wang

    (i2 Technologies Inc., Redwood City, California 94065)

Abstract

The network restoration problem is a specialized capacitated network design problem requiring the installation of spare capacity to fully restore disrupted network flows if any edge in a telecommunications network fails. We present a new mixed-integer programming formulation for a line restoration version of the problem using a single type of capacitated facility. We examine two different models, for distinct and integrated spare-capacity systems, reflecting technologies used in synchronous transfer mode (STM) and asynchronous transfer mode (ATM) networks. The problem is NP-complete in the strong sense. We study the problem's polyhedral structure to identify strong valid inequalities that tighten the problem formulation. Our computational results on several real and randomly generated problems show that these inequalities considerably reduce the integrality gap from an average of 10% to an average of under 1%. These results indicate that strong cutting planes combined with branch-and-bound can provide efficient algorithms for solving a class of real-world problems in the telecommunications industry.

Suggested Citation

  • Anantaram Balakrishnan & Thomas L. Magnanti & Joel S. Sokol & Yi Wang, 2002. "Spare-Capacity Assignment For Line Restoration Using a Single-Facility Type," Operations Research, INFORMS, vol. 50(4), pages 617-635, August.
    • Handle: RePEc:inm:oropre:v:50:y:2002:i:4:p:617-635
    DOI: 10.1287/opre.50.4.617.2853
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    References listed on IDEAS

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    1. Geir Dahl & Mechthild Stoer, 1998. "A Cutting Plane Algorithm for Multicommodity Survivable Network Design Problems," INFORMS Journal on Computing, INFORMS, vol. 10(1), pages 1-11, February.
    2. Jeffery L. Kennington & Jason E. Whitler, 1999. "An Efficient Decomposition Algorithm to Optimize Spare Capacity in a Telecommunications Network," INFORMS Journal on Computing, INFORMS, vol. 11(2), pages 149-160, May.
    3. Jeffery L. Kennington & Mark W. Lewis, 2001. "The Path Restoration Version of the Spare Capacity Allocation Problem with Modularity Restrictions: Models, Algorithms, and an Empirical Analysis," INFORMS Journal on Computing, INFORMS, vol. 13(3), pages 181-190, August.
    4. Anantaram Balakrishnan & Thomas Magnanti & Joel Sokol & Yi Wang, 2001. "Telecommunication Link Restoration Planning with Multiple Facility Types," Annals of Operations Research, Springer, vol. 106(1), pages 127-154, September.
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    Citations

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    Cited by:

    1. Emily A Heath & John E Mitchell & Thomas C Sharkey, 2020. "Models for restoration decision making for a supply chain network after a cyber attack," The Journal of Defense Modeling and Simulation, , vol. 17(1), pages 5-19, January.
    2. Yogesh Agarwal, 2013. "Design of Survivable Networks Using Three- and Four-Partition Facets," Operations Research, INFORMS, vol. 61(1), pages 199-213, February.
    3. Timothy Matisziw & Alan Murray & Tony Grubesic, 2010. "Strategic Network Restoration," Networks and Spatial Economics, Springer, vol. 10(3), pages 345-361, September.
    4. Tianyu Wang & Igor Averbakh, 2022. "Network construction/restoration problems: cycles and complexity," Journal of Combinatorial Optimization, Springer, vol. 44(1), pages 51-73, August.
    5. Ramesh Bollapragada & Yanjun Li & Uday S. Rao, 2006. "Budget-Constrained, Capacitated Hub Location to Maximize Expected Demand Coverage in Fixed-Wireless Telecommunication Networks," INFORMS Journal on Computing, INFORMS, vol. 18(4), pages 422-432, November.
    6. Anantaram Balakrishnan & Prakash Mirchandani & Harihara Prasad Natarajan, 2009. "Connectivity Upgrade Models for Survivable Network Design," Operations Research, INFORMS, vol. 57(1), pages 170-186, February.

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