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A problem in network interdiction

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  • Bruce Golden

Abstract

Suppose we are given a network G=(V,E) with arc distances and a linear cost function for lengthening arcs. In this note, we consider a network‐interdiction problem in which the shortest path from source node s to sink node t is to be increased to at least τ units via a least‐cost investment strategy. This problem is shown to reduce to a simple minimum‐cost‐flow problem. Applications and generalizations are discussed, including the multiple‐destination case.

Suggested Citation

  • Bruce Golden, 1978. "A problem in network interdiction," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 25(4), pages 711-713, December.
    • Handle: RePEc:wly:navlog:v:25:y:1978:i:4:p:711-713
    DOI: 10.1002/nav.3800250412
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    Cited by:

    1. Harald Held & Raymond Hemmecke & David L. Woodruff, 2005. "A decomposition algorithm applied to planning the interdiction of stochastic networks," Naval Research Logistics (NRL), John Wiley & Sons, vol. 52(4), pages 321-328, June.
    2. Eli Towle & James Luedtke, 2018. "New solution approaches for the maximum-reliability stochastic network interdiction problem," Computational Management Science, Springer, vol. 15(3), pages 455-477, October.
    3. Kelly M. Sullivan & David P. Morton & Feng Pan & J. Cole Smith, 2014. "Securing a border under asymmetric information," Naval Research Logistics (NRL), John Wiley & Sons, vol. 61(2), pages 91-100, March.
    4. Smith, J. Cole & Song, Yongjia, 2020. "A survey of network interdiction models and algorithms," European Journal of Operational Research, Elsevier, vol. 283(3), pages 797-811.
    5. Bloch, Francis & Chatterjee, Kalyan & Dutta, Bhaskar, 2023. "Attack and interception in networks," Theoretical Economics, Econometric Society, vol. 18(4), November.
    6. Young‐Soo Myung & Hyun‐Joon Kim, 2007. "Network disconnection problems in a centralized network," Naval Research Logistics (NRL), John Wiley & Sons, vol. 54(7), pages 710-719, October.
    7. Abumoslem Mohammadi & Javad Tayyebi, 2019. "Maximum Capacity Path Interdiction Problem with Fixed Costs," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 36(04), pages 1-21, August.
    8. Nguyen, Di H. & Smith, J. Cole, 2022. "Network interdiction with asymmetric cost uncertainty," European Journal of Operational Research, Elsevier, vol. 297(1), pages 239-251.
    9. Juan S. Borrero & Leonardo Lozano, 2021. "Modeling Defender-Attacker Problems as Robust Linear Programs with Mixed-Integer Uncertainty Sets," INFORMS Journal on Computing, INFORMS, vol. 33(4), pages 1570-1589, October.
    10. Brian Lunday & Hanif Sherali, 2012. "Network interdiction to minimize the maximum probability of evasion with synergy between applied resources," Annals of Operations Research, Springer, vol. 196(1), pages 411-442, July.
    11. Noam Goldberg, 2017. "Non‐zero‐sum nonlinear network path interdiction with an application to inspection in terror networks," Naval Research Logistics (NRL), John Wiley & Sons, vol. 64(2), pages 139-153, March.
    12. Shahram Morowati-Shalilvand & Sedaghat Shahmorad & Kamal Mirnia & Javad Mehri-Tekmeh, 2021. "Quickest flow over time network interdiction: mathematical formulation and a solution method," Operational Research, Springer, vol. 21(2), pages 1179-1209, June.
    13. Sushil Gupta & Martin K. Starr & Reza Zanjirani Farahani & Mahsa Mahboob Ghodsi, 2020. "Prevention of Terrorism–An Assessment of Prior POM Work and Future Potentials," Production and Operations Management, Production and Operations Management Society, vol. 29(7), pages 1789-1815, July.
    14. Chaya Losada & M. Scaparra & Richard Church & Mark Daskin, 2012. "The stochastic interdiction median problem with disruption intensity levels," Annals of Operations Research, Springer, vol. 201(1), pages 345-365, December.
    15. Claudio Contardo & Jorge A. Sefair, 2022. "A Progressive Approximation Approach for the Exact Solution of Sparse Large-Scale Binary Interdiction Games," INFORMS Journal on Computing, INFORMS, vol. 34(2), pages 890-908, March.
    16. Kübra Tanınmış & Markus Sinnl, 2022. "A Branch-and-Cut Algorithm for Submodular Interdiction Games," INFORMS Journal on Computing, INFORMS, vol. 34(5), pages 2634-2657, September.
    17. Tayyebi, Javad & Mitra, Ankan & Sefair, Jorge A., 2023. "The continuous maximum capacity path interdiction problem," European Journal of Operational Research, Elsevier, vol. 305(1), pages 38-52.
    18. Kosanoglu, Fuat & Bier, Vicki M., 2020. "Target-oriented utility for interdiction of transportation networks," Reliability Engineering and System Safety, Elsevier, vol. 197(C).
    19. Tony H. Grubesic & Timothy C. Matisziw & Alan T. Murray & Diane Snediker, 2008. "Comparative Approaches for Assessing Network Vulnerability," International Regional Science Review, , vol. 31(1), pages 88-112, January.

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