IDEAS home Printed from https://ideas.repec.org/a/eee/reensy/v239y2023ics095183202300409x.html
   My bibliography  Save this article

Minimizing the maximal reliable path with a nodal interdiction model considering resource sharing

Author

Listed:
  • Xiang, Yin

Abstract

This study presents a novel maximal reliable path interdiction (MRPI) problem in application to traffic inspection and intercepting invading attackers. This problem differs from traditional MRPI problems in that (1) interdiction acts on nodes, (2) binary interdiction variables are relaxed as integer variables, (3) the interdict effect is endogenously determined, and (4) resource sharing is considered among nodes. This problem is addressed as a two-player (i.e., defender–attacker) Stackelberg game, in which the defender seeks to minimize the attack's utility by coordinating inspection resources among nodes, and the attacker seeks to maximize the intrusion probability by selecting the maximal reliable path. To solve this problem, an improved Benders decomposition algorithm is proposed. Specifically, we improve the basic Benders decomposition algorithm in two ways: (1) To enhance Benders decomposition cuts and reduce iterations, a local search procedure is applied when solving the subproblem, and (2) to accelerate solving the master problem, an innovative two-stage method based on a relaxed linear programming model and a greedy algorithm is proposed. The algorithm is then tested in different sizes of grid networks and compared with other algorithms. The results show that the improved Benders decomposition algorithm performs very well. Finally, the MRPI model is also applied in a real-world north Xinjiang border network. The results verify the correctness and efficiency of the solution method.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:reensy:v:239:y:2023:i:c:s095183202300409x
    DOI: 10.1016/j.ress.2023.109495
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S095183202300409X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ress.2023.109495?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. Kelly J. Cormican & David P. Morton & R. Kevin Wood, 1998. "Stochastic Network Interdiction," Operations Research, INFORMS, vol. 46(2), pages 184-197, April.
    2. Davis, Lauren B. & Samanlioglu, Funda & Qu, Xiuli & Root, Sarah, 2013. "Inventory planning and coordination in disaster relief efforts," International Journal of Production Economics, Elsevier, vol. 141(2), pages 561-573.
    3. Eli Gutin & Daniel Kuhn & Wolfram Wiesemann, 2015. "Interdiction Games on Markovian PERT Networks," Management Science, INFORMS, vol. 61(5), pages 999-1017, May.
    4. Wu, Yipeng & Chen, Zhilong & Dang, Junhu & Chen, Yicun & Zhao, Xudong & Zha, Lvying, 2022. "Allocation of defensive and restorative resources in electric power system against consecutive multi-target attacks," Reliability Engineering and System Safety, Elsevier, vol. 219(C).
    5. 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.
    6. Scaparra, Maria P. & Church, Richard L., 2008. "An exact solution approach for the interdiction median problem with fortification," European Journal of Operational Research, Elsevier, vol. 189(1), pages 76-92, August.
    7. Yaghlane, Asma Ben & Azaiez, M. Naceur & Mrad, Mehdi, 2019. "System survivability in the context of interdiction networks," Reliability Engineering and System Safety, Elsevier, vol. 185(C), pages 362-371.
    8. Paola Cappanera & Maria Paola Scaparra, 2011. "Optimal Allocation of Protective Resources in Shortest-Path Networks," Transportation Science, INFORMS, vol. 45(1), pages 64-80, February.
    9. Akgün, Ibrahim & Tansel, Barbaros Ç. & Kevin Wood, R., 2011. "The multi-terminal maximum-flow network-interdiction problem," European Journal of Operational Research, Elsevier, vol. 211(2), pages 241-251, June.
    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. Li, Qing & Li, Mingchu & Tian, Yuan & Gan, Jianyuan, 2023. "A risk-averse tri-level stochastic model for locating and recovering facilities against attacks in an uncertain environment," Reliability Engineering and System Safety, Elsevier, vol. 229(C).
    12. Xiaodan Xie & Felipe Aros‐Vera, 2022. "An interdependent network interdiction model for disrupting sex trafficking networks," Production and Operations Management, Production and Operations Management Society, vol. 31(6), pages 2695-2713, June.
    13. Yongjia Song & Siqian Shen, 2016. "Risk-Averse Shortest Path Interdiction," INFORMS Journal on Computing, INFORMS, vol. 28(3), pages 527-539, August.
    14. Le Thi Khanh Hien & Melvyn Sim & Huan Xu, 2020. "Mitigating Interdiction Risk with Fortification," Operations Research, INFORMS, vol. 68(2), pages 348-362, March.
    15. Gerald G. Brown & W. Matthew Carlyle & Robert C. Harney & Eric M. Skroch & R. Kevin Wood, 2009. "Interdicting a Nuclear-Weapons Project," Operations Research, INFORMS, vol. 57(4), pages 866-877, August.
    16. P. M. Ghare & D. C. Montgomery & W. C. Turner, 1971. "Optimal interdiction policy for a flow network," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 18(1), pages 37-45, March.
    17. Li, Qing & Li, Mingchu & Zhang, Runfa & Gan, Jianyuan, 2021. "A stochastic bilevel model for facility location-protection problem with the most likely interdiction strategy," Reliability Engineering and System Safety, Elsevier, vol. 216(C).
    18. Wu, Yipeng & Chen, Zhilong & Gong, Huadong & Feng, Qilin & Chen, Yicun & Tang, Haizhou, 2021. "Defender–attacker–operator: Tri-level game-theoretic interdiction analysis of urban water distribution networks," Reliability Engineering and System Safety, Elsevier, vol. 214(C).
    19. 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.
    20. Enayaty-Ahangar, Forough & Rainwater, Chase E. & Sharkey, Thomas C., 2019. "A Logic-based Decomposition Approach for Multi-Period Network Interdiction Models," Omega, Elsevier, vol. 87(C), pages 71-85.
    21. 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.
    22. Kosanoglu, Fuat & Bier, Vicki M., 2020. "Target-oriented utility for interdiction of transportation networks," Reliability Engineering and System Safety, Elsevier, vol. 197(C).
    23. Karabulut, Ezgi & Aras, Necati & Kuban Altınel, İ., 2017. "Optimal sensor deployment to increase the security of the maximal breach path in border surveillance," European Journal of Operational Research, Elsevier, vol. 259(1), pages 19-36.
    24. Lazar Babu, Vellara L. & Batta, Rajan & Lin, Li, 2006. "Passenger grouping under constant threat probability in an airport security system," European Journal of Operational Research, Elsevier, vol. 168(2), pages 633-644, January.
    25. Li, Qing & Li, Mingchu & Gong, Zhongqiang & Tian, Yuan & Zhang, Runfa, 2022. "Locating and protecting interdependent facilities to hedge against multiple non-cooperative limited choice attackers," Reliability Engineering and System Safety, Elsevier, vol. 223(C).
    26. Richard Wollmer, 1964. "Removing Arcs from a Network," Operations Research, INFORMS, vol. 12(6), pages 934-940, December.
    27. Haywood, Adam B. & Lunday, Brian J. & Robbins, Matthew J., 2022. "Intruder detection and interdiction modeling: A bilevel programming approach for ballistic missile defense asset location," Omega, Elsevier, vol. 110(C).
    28. 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.
    29. Juan S. Borrero & Oleg A. Prokopyev & Denis Sauré, 2019. "Sequential Interdiction with Incomplete Information and Learning," Operations Research, INFORMS, vol. 67(1), pages 72-89, January.
    30. 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.
    31. Cen Song & Jun Zhuang, 2018. "Modeling Precheck Parallel Screening Process in the Face of Strategic Applicants with Incomplete Information and Screening Errors," Risk Analysis, John Wiley & Sons, vol. 38(1), pages 118-133, January.
    32. Ghorbani-Renani, Nafiseh & González, Andrés D. & Barker, Kash & Morshedlou, Nazanin, 2020. "Protection-interdiction-restoration: Tri-level optimization for enhancing interdependent network resilience," Reliability Engineering and System Safety, Elsevier, vol. 199(C).
    Full references (including those not matched with items on IDEAS)

    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. Yan, Xihong & Ren, Xiaorong & Nie, Xiaofeng, 2022. "A budget allocation model for domestic airport network protection," Socio-Economic Planning Sciences, Elsevier, vol. 82(PB).
    2. 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.
    3. Beck, Yasmine & Ljubić, Ivana & Schmidt, Martin, 2023. "A survey on bilevel optimization under uncertainty," European Journal of Operational Research, Elsevier, vol. 311(2), pages 401-426.
    4. 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.
    5. 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.
    6. 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.
    7. 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).
    8. Jabarzare, Ziba & Zolfagharinia, Hossein & Najafi, Mehdi, 2020. "Dynamic interdiction networks with applications in illicit supply chains," Omega, Elsevier, vol. 96(C).
    9. 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.
    10. Li, Qing & Li, Mingchu & Tian, Yuan & Gan, Jianyuan, 2023. "A risk-averse tri-level stochastic model for locating and recovering facilities against attacks in an uncertain environment," Reliability Engineering and System Safety, Elsevier, vol. 229(C).
    11. 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.
    12. 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.
    13. Leitner, Markus & Ljubić, Ivana & Monaci, Michele & Sinnl, Markus & Tanınmış, Kübra, 2023. "An exact method for binary fortification games," European Journal of Operational Research, Elsevier, vol. 307(3), pages 1026-1039.
    14. Utsav Sadana & Erick Delage, 2023. "The Value of Randomized Strategies in Distributionally Robust Risk-Averse Network Interdiction Problems," INFORMS Journal on Computing, INFORMS, vol. 35(1), pages 216-232, January.
    15. 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.
    16. Parajuli, Anubhuti & Kuzgunkaya, Onur & Vidyarthi, Navneet, 2017. "Responsive contingency planning of capacitated supply networks under disruption risks," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 102(C), pages 13-37.
    17. Bhatt, Sneha Dhyani & Sinha, Ankur & Jayaswal, Sachin, 2024. "The capacitated r-hub interdiction problem with congestion: Models and solution approaches," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 185(C).
    18. Li, Qing & Li, Mingchu & Gong, Zhongqiang & Tian, Yuan & Zhang, Runfa, 2022. "Locating and protecting interdependent facilities to hedge against multiple non-cooperative limited choice attackers," Reliability Engineering and System Safety, Elsevier, vol. 223(C).
    19. 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.
    20. Bloch, Francis & Chatterjee, Kalyan & Dutta, Bhaskar, 2023. "Attack and interception in networks," Theoretical Economics, Econometric Society, vol. 18(4), November.

    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:eee:reensy:v:239:y:2023:i:c:s095183202300409x. 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: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/reliability-engineering-and-system-safety .

    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.