IDEAS home Printed from https://ideas.repec.org/a/spr/jglopt/v67y2017i3d10.1007_s10898-016-0422-8.html
   My bibliography  Save this article

Analysis of budget for interdiction on multicommodity network flows

Author

Listed:
  • Pengfei Zhang

    (University of Arizona)

  • Neng Fan

    (University of Arizona)

Abstract

In this paper, we concentrate on computing several critical budgets for interdiction of the multicommodity network flows, and studying the interdiction effects of the changes on budget. More specifically, we first propose general interdiction models of the multicommodity flow problem, with consideration of both node and arc removals and decrease of their capacities. Then, to perform the vulnerability analysis of networks, we define the function F(R) as the minimum amount of unsatisfied demands in the resulted network after worst-case interdiction with budget R. Specifically, we study the properties of function F(R), and find the critical budget values, such as $$R_a$$ R a , the largest value under which all demands can still be satisfied in the resulted network even under the worst-case interdiction, and $$R_b$$ R b , the least value under which the worst-case interdiction can make none of the demands be satisfied. We prove that the critical budget $$R_b$$ R b for completely destroying the network is not related to arc or node capacities, and supply or demand amounts, but it is related to the network topology, the sets of source and destination nodes, and interdiction costs on each node and arc. We also observe that the critical budget $$R_a$$ R a is related to all of these parameters of the network. Additionally, we present formulations to estimate both $$R_a$$ R a and $$R_b$$ R b . For the effects of budget increasing, we present the conditions under which there would be extra capabilities to interdict more arcs or nodes with increased budget, and also under which the increased budget has no effects for the interdictor. To verify these results and conclusions, numerical experiments on 12 networks with different numbers of commodities are performed.

Suggested Citation

  • Pengfei Zhang & Neng Fan, 2017. "Analysis of budget for interdiction on multicommodity network flows," Journal of Global Optimization, Springer, vol. 67(3), pages 495-525, March.
    • Handle: RePEc:spr:jglopt:v:67:y:2017:i:3:d:10.1007_s10898-016-0422-8
    DOI: 10.1007/s10898-016-0422-8
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10898-016-0422-8
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10898-016-0422-8?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
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Jeff L. Kennington, 1978. "A Survey of Linear Cost Multicommodity Network Flows," Operations Research, INFORMS, vol. 26(2), pages 209-236, April.
    2. Kelly J. Cormican & David P. Morton & R. Kevin Wood, 1998. "Stochastic Network Interdiction," Operations Research, INFORMS, vol. 46(2), pages 184-197, April.
    3. Cynthia Barnhart & Yosef Sheffi, 1993. "A Network-Based Primal-Dual Heuristic for the Solution of Multicommodity Network Flow Problems," Transportation Science, INFORMS, vol. 27(2), pages 102-117, May.
    4. Johannes O. Royset & R. Kevin Wood, 2007. "Solving the Bi-Objective Maximum-Flow Network-Interdiction Problem," INFORMS Journal on Computing, INFORMS, vol. 19(2), pages 175-184, May.
    5. Richard Wollmer, 1964. "Removing Arcs from a Network," Operations Research, INFORMS, vol. 12(6), pages 934-940, December.
    6. 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.
    7. Qipeng P. Zheng & Siqian Shen & Yuhui Shi, 2015. "Loss-constrained minimum cost flow under arc failure uncertainty with applications in risk-aware kidney exchange," IISE Transactions, Taylor & Francis Journals, vol. 47(9), pages 961-977, September.
    8. M. Bellmore & H. J. Geenberg & J. J. Jarvis, 1970. "Multi-Commodity Disconnecting Sets," Management Science, INFORMS, vol. 16(6), pages 427-433, February.
    9. T. C. Hu, 1963. "Multi-Commodity Network Flows," Operations Research, INFORMS, vol. 11(3), pages 344-360, June.
    10. Alan Washburn & Kevin Wood, 1995. "Two-Person Zero-Sum Games for Network Interdiction," Operations Research, INFORMS, vol. 43(2), pages 243-251, April.
    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. Jabarzare, Ziba & Zolfagharinia, Hossein & Najafi, Mehdi, 2020. "Dynamic interdiction networks with applications in illicit supply chains," Omega, Elsevier, vol. 96(C).
    2. Khodakaram Salimifard & Sara Bigharaz, 2022. "The multicommodity network flow problem: state of the art classification, applications, and solution methods," Operational Research, Springer, vol. 22(1), pages 1-47, March.

    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. 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.
    2. Leonardo Lozano & J. Cole Smith, 2017. "A Backward Sampling Framework for Interdiction Problems with Fortification," INFORMS Journal on Computing, INFORMS, vol. 29(1), pages 123-139, February.
    3. Dimitris Bertsimas & Ebrahim Nasrabadi & Sebastian Stiller, 2013. "Robust and Adaptive Network Flows," Operations Research, INFORMS, vol. 61(5), pages 1218-1242, October.
    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. Laan, Corine M. & van der Mijden, Tom & Barros, Ana Isabel & Boucherie, Richard J. & Monsuur, Herman, 2017. "An interdiction game on a queueing network with multiple intruders," European Journal of Operational Research, Elsevier, vol. 260(3), pages 1069-1080.
    6. 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.
    7. Zhang, Jing & Zhuang, Jun & Behlendorf, Brandon, 2018. "Stochastic shortest path network interdiction with a case study of Arizona–Mexico border," Reliability Engineering and System Safety, Elsevier, vol. 179(C), pages 62-73.
    8. Bloch, Francis & Chatterjee, Kalyan & Dutta, Bhaskar, 2023. "Attack and interception in networks," Theoretical Economics, Econometric Society, vol. 18(4), November.
    9. 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.
    10. Starita, Stefano & Scaparra, Maria Paola, 2016. "Optimizing dynamic investment decisions for railway systems protection," European Journal of Operational Research, Elsevier, vol. 248(2), pages 543-557.
    11. Rocco S., Claudio M. & Emmanuel Ramirez-Marquez, José & Salazar A., Daniel E., 2010. "Bi and tri-objective optimization in the deterministic network interdiction problem," Reliability Engineering and System Safety, Elsevier, vol. 95(8), pages 887-896.
    12. Gedik, Ridvan & Medal, Hugh & Rainwater, Chase & Pohl, Ed A. & Mason, Scott J., 2014. "Vulnerability assessment and re-routing of freight trains under disruptions: A coal supply chain network application," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 71(C), pages 45-57.
    13. Shen, Yeming & Sharkey, Thomas C. & Szymanski, Boleslaw K. & Wallace, William (Al), 2021. "Interdicting interdependent contraband smuggling, money and money laundering networks," Socio-Economic Planning Sciences, Elsevier, vol. 78(C).
    14. 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.
    15. Yongjia Song & Siqian Shen, 2016. "Risk-Averse Shortest Path Interdiction," INFORMS Journal on Computing, INFORMS, vol. 28(3), pages 527-539, August.
    16. Yan, Xihong & Ren, Xiaorong & Nie, Xiaofeng, 2022. "A budget allocation model for domestic airport network protection," Socio-Economic Planning Sciences, Elsevier, vol. 82(PB).
    17. O'Hanley, Jesse R. & Church, Richard L., 2011. "Designing robust coverage networks to hedge against worst-case facility losses," European Journal of Operational Research, Elsevier, vol. 209(1), pages 23-36, February.
    18. Jabarzare, Ziba & Zolfagharinia, Hossein & Najafi, Mehdi, 2020. "Dynamic interdiction networks with applications in illicit supply chains," Omega, Elsevier, vol. 96(C).
    19. Xiang, Yin, 2023. "Minimizing the maximal reliable path with a nodal interdiction model considering resource sharing," Reliability Engineering and System Safety, Elsevier, vol. 239(C).
    20. 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.

    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:spr:jglopt:v:67:y:2017:i:3:d:10.1007_s10898-016-0422-8. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.