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An exact approach for the r-interdiction covering problem with fortification

Author

Listed:
  • Marcos Costa Roboredo

    (Universidade Federal Fluminense)

  • Luiz Aizemberg

    (Banco Nacional do Desenvolvimento)

  • Artur Alves Pessoa

    (Universidade Federal Fluminense)

Abstract

In this paper we treat the r-interdiction covering problem with fortification (RICF). The environment of this problem is composed of a set of customers J and a set of facilities I. For each customer j, there is set of facilities containing the facilities that can cover the demand of j. The system efficiency is given by the sum of the total covered demand. The facilities are subject to interdictions. When a facility is interdicted, it can not cover the demand of any customer. To mitigate the negative impact of the interdictions on the system efficiency, the system planner can fortify a subset of facilities. If a facility is fortified then it can not be interdicted. The RICF consists of choosing q facilities to be fortified knowing that r not fortified facilities will be interdicted at the worst case. We propose a branch-and-cut algorithm for the problem. Our results are compared with the exact method found in the literature, being faster for the most instances, mainly the large ones.

Suggested Citation

  • Marcos Costa Roboredo & Luiz Aizemberg & Artur Alves Pessoa, 2019. "An exact approach for the r-interdiction covering problem with fortification," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 27(1), pages 111-131, March.
    • Handle: RePEc:spr:cejnor:v:27:y:2019:i:1:d:10.1007_s10100-017-0494-7
    DOI: 10.1007/s10100-017-0494-7
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    References listed on IDEAS

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    1. Yuan, Wei & Zhao, Long & Zeng, Bo, 2014. "Optimal power grid protection through a defender–attacker–defender model," Reliability Engineering and System Safety, Elsevier, vol. 121(C), pages 83-89.
    2. 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.
    3. Roboredo, Marcos Costa & Pessoa, Artur Alves, 2013. "A branch-and-cut algorithm for the discrete (r∣p)-centroid problem," European Journal of Operational Research, Elsevier, vol. 224(1), pages 101-109.
    4. Gerald Brown & Matthew Carlyle & Javier Salmerón & Kevin Wood, 2006. "Defending Critical Infrastructure," Interfaces, INFORMS, vol. 36(6), pages 530-544, December.
    5. Lawrence V. Snyder & Zümbül Atan & Peng Peng & Ying Rong & Amanda J. Schmitt & Burcu Sinsoysal, 2016. "OR/MS models for supply chain disruptions: a review," IISE Transactions, Taylor & Francis Journals, vol. 48(2), pages 89-109, February.
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    Cited by:

    1. Yiyong Xiao & Pei Yang & Siyue Zhang & Shenghan Zhou & Wenbing Chang & Yue Zhang, 2020. "Dynamic Gaming Case of the R-Interdiction Median Problem with Fortification and an MILP-Based Solution Approach," Sustainability, MDPI, vol. 12(2), pages 1-17, January.
    2. 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.

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