IDEAS home Printed from https://ideas.repec.org/a/inm/oropre/v61y2013i1p199-213.html
   My bibliography  Save this article

Design of Survivable Networks Using Three- and Four-Partition Facets

Author

Listed:
  • Yogesh Agarwal

    (Indian Institute of Management, Prabandh Nagar, Lucknow 226 013, India)

Abstract

This paper considers the problem of designing a multicommodity network with single facility type subject to the requirement that under failure of any single edge, the network should permit a feasible flow of all traffic. We study the polyhedral structure of the problem by considering the multigraph obtained by shrinking the nodes, but not the edges, in a k -partition of the original graph. A key theorem is proved according to which a facet of the k -node problem defined on the multigraph resulting from a k -partition is also facet defining for the larger problem under a mild condition. After reviewing the prior work on two-partition inequalities, we develop two classes of three-partition inequalities and a large number of inequality classes based on four-partitions. Proofs of facet-defining status for some of these are provided, while the rest are stated without proof. Computational results show that the addition of three- and four-partition inequalities results in substantial increase in the bound values compared to those possible with two-partition inequalities alone. Problems of 35 nodes and 80 edges with fully dense traffic matrices have been solved optimally within a few minutes of computer time.

Suggested Citation

  • Yogesh Agarwal, 2013. "Design of Survivable Networks Using Three- and Four-Partition Facets," Operations Research, INFORMS, vol. 61(1), pages 199-213, February.
    • Handle: RePEc:inm:oropre:v:61:y:2013:i:1:p:199-213
    DOI: 10.1287/opre.1120.1147
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/opre.1120.1147
    Download Restriction: no
    File URL: https://libkey.io/10.1287/opre.1120.1147?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Martin Grötschel & Clyde L. Monma & Mechthild Stoer, 1992. "Computational Results with a Cutting Plane Algorithm for Designing Communication Networks with Low-Connectivity Constraints," Operations Research, INFORMS, vol. 40(2), pages 309-330, April.
    2. 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.
    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 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.
    5. 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.
    6. Kennington, Jeffery L. & Olinick, Eli V. & Spiride, Gheorghe, 2007. "Basic mathematical programming models for capacity allocation in mesh-based survivable networks," Omega, Elsevier, vol. 35(6), pages 629-644, December.
    7. Sara Mattia, 2012. "Solving survivable two-layer network design problems by metric inequalities," Computational Optimization and Applications, Springer, vol. 51(2), pages 809-834, March.
    8. BIENSTOCK, Daniel & CHOPRA, Sunil & GÜNLÜK, Oktay & TSAI, Chih-Yang, 1998. "Minimum cost capacity installation for multicommodity network flows," LIDAM Reprints CORE 1391, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    9. Thomas L. Magnanti & Prakash Mirchandani & Rita Vachani, 1995. "Modeling and Solving the Two-Facility Capacitated Network Loading Problem," Operations Research, INFORMS, vol. 43(1), pages 142-157, February.
    10. 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.
    11. Clyde L. Monma & David F. Shallcross, 1989. "Methods for Designing Communications Networks with Certain Two-Connected Survivability Constraints," Operations Research, INFORMS, vol. 37(4), pages 531-541, August.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Agarwal, Y.K. & Venkateshan, Prahalad, 2016. "Near optimal design of wavelength routed optical networks," European Journal of Operational Research, Elsevier, vol. 250(3), pages 990-1000.
    2. Nigam, Ashutosh & Agarwal, Yogesh K., 2014. "Optimal relay node placement in delay constrained wireless sensor network design," European Journal of Operational Research, Elsevier, vol. 233(1), pages 220-233.
    3. Agarwal, Y.K. & Aneja, Y.P. & Jayaswal, Sachin, 2022. "Directed fixed charge multicommodity network design: A cutting plane approach using polar duality," European Journal of Operational Research, Elsevier, vol. 299(1), pages 118-136.
    4. Kohar, Amit & Jakhar, Suresh Kumar & Agarwal, Yogesh K., 2023. "Strong cutting planes for the capacitated multi-pickup and delivery problem with time windows," Transportation Research Part B: Methodological, Elsevier, vol. 176(C).
    5. Yogesh Kumar Agarwal & Prahalad Venkateshan, 2019. "New Valid Inequalities for the Optimal Communication Spanning Tree Problem," INFORMS Journal on Computing, INFORMS, vol. 31(2), pages 268-284, April.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Agarwal, Y.K. & Venkateshan, Prahalad, 2014. "Survivable network design with shared-protection routing," European Journal of Operational Research, Elsevier, vol. 238(3), pages 836-845.
    2. Yogesh K. Agarwal, 2002. "Design of Capacitated Multicommodity Networks with Multiple Facilities," Operations Research, INFORMS, vol. 50(2), pages 333-344, April.
    3. 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.
    4. Ioannis Gamvros & Bruce Golden & S. Raghavan, 2006. "The Multilevel Capacitated Minimum Spanning Tree Problem," INFORMS Journal on Computing, INFORMS, vol. 18(3), pages 348-365, August.
    5. 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.
    6. Kennington, Jeffery L. & Olinick, Eli V. & Spiride, Gheorghe, 2007. "Basic mathematical programming models for capacity allocation in mesh-based survivable networks," Omega, Elsevier, vol. 35(6), pages 629-644, December.
    7. Bernard Fortz & Martine Labbé & Francesco Maffioli, 2000. "Solving the Two-Connected Network with Bounded Meshes Problem," Operations Research, INFORMS, vol. 48(6), pages 866-877, December.
    8. Sara Mattia & Michael Poss, 2018. "A comparison of different routing schemes for the robust network loading problem: polyhedral results and computation," Computational Optimization and Applications, Springer, vol. 69(3), pages 753-800, April.
    9. 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.
    10. Sridhar, Varadharajan & Park, June S., 2000. "Benders-and-cut algorithm for fixed-charge capacitated network design problem," European Journal of Operational Research, Elsevier, vol. 125(3), pages 622-632, September.
    11. Morten Riis & Kim Allan Andersen, 2002. "Capacitated Network Design with Uncertain Demand," INFORMS Journal on Computing, INFORMS, vol. 14(3), pages 247-260, August.
    12. Ellis L. Johnson & George L. Nemhauser & Martin W.P. Savelsbergh, 2000. "Progress in Linear Programming-Based Algorithms for Integer Programming: An Exposition," INFORMS Journal on Computing, INFORMS, vol. 12(1), pages 2-23, February.
    13. Daniel Bienstock & Olga Raskina & Iraj Saniee & Qiong Wang, 2006. "Combined Network Design and Multiperiod Pricing: Modeling, Solution Techniques, and Computation," Operations Research, INFORMS, vol. 54(2), pages 261-276, April.
    14. Andrew P. Armacost & Cynthia Barnhart & Keith A. Ware, 2002. "Composite Variable Formulations for Express Shipment Service Network Design," Transportation Science, INFORMS, vol. 36(1), pages 1-20, February.
    15. Keely L. Croxton & Bernard Gendron & Thomas L. Magnanti, 2007. "Variable Disaggregation in Network Flow Problems with Piecewise Linear Costs," Operations Research, INFORMS, vol. 55(1), pages 146-157, February.
    16. Tianyu Wang & Igor Averbakh, 2022. "Network construction/restoration problems: cycles and complexity," Journal of Combinatorial Optimization, Springer, vol. 44(1), pages 51-73, August.
    17. Sara Mattia, 2013. "The robust network loading problem with dynamic routing," Computational Optimization and Applications, Springer, vol. 54(3), pages 619-643, April.
    18. Grit Claßen & Arie M. C. A. Koster & David Coudert & Napoleão Nepomuceno, 2014. "Chance-Constrained Optimization of Reliable Fixed Broadband Wireless Networks," INFORMS Journal on Computing, INFORMS, vol. 26(4), pages 893-909, November.
    19. Anantaram Balakrishnan & Gang Li & Prakash Mirchandani, 2017. "Optimal Network Design with End-to-End Service Requirements," Operations Research, INFORMS, vol. 65(3), pages 729-750, June.
    20. Mervat Chouman & Teodor Gabriel Crainic & Bernard Gendron, 2018. "The impact of filtering in a branch-and-cut algorithm for multicommodity capacitated fixed charge network design," EURO Journal on Computational Optimization, Springer;EURO - The Association of European Operational Research Societies, vol. 6(2), pages 143-184, June.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:inm:oropre:v:61:y:2013:i:1:p:199-213. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.