IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v189y2008i1p76-92.html
   My bibliography  Save this article

An exact solution approach for the interdiction median problem with fortification

Author

Listed:
  • Scaparra, Maria P.
  • Church, Richard L.

Abstract

Systematic approaches to security investment decisions are crucial for improved homeland security. We present an optimization modeling approach for allocating protection resources among a system of facilities so that the disruptive effects of possible intentional attacks to the system are minimized. This paper is based upon the p-median service protocol for an operating set of p facilities. The primary objective is to identify the subset of q facilities which, when fortified, provides the best protection against the worst-case loss of r non-fortified facilities. This problem, known as the r-interdiction median problem with fortification (IMF), was first formulated as a mixed-integer program by Church and Scaparra [R.L. Church, M.P. Scaparra, Protecting critical assets: The r-interdiction median problem with fortification, Geographical Analysis 39 (2007) 129-146]. In this paper, we reformulate the IMF as a maximal covering problem with precedence constraints, which is amenable to a new solution approach. This new approach produces good approximations to the best fortification strategies. Furthermore, it provides upper and lower bounds that can be used to reduce the size of the original model. The reduced model can readily be solved to optimality by general-purpose MIP solvers. Computational results on two geographical data sets with different structural characteristics show the effectiveness of the proposed methodology for solving IMF instances of considerable size.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:ejores:v:189:y:2008:i:1:p:76-92
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377-2217(07)00505-X
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    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. Richard Church, 2003. "COBRA: A New Formulation of the Classic p-Median Location Problem," Annals of Operations Research, Springer, vol. 122(1), pages 103-120, September.
    2. Osman Alp & Erhan Erkut & Zvi Drezner, 2003. "An Efficient Genetic Algorithm for the p-Median Problem," Annals of Operations Research, Springer, vol. 122(1), pages 21-42, September.
    3. S. L. Hakimi, 1964. "Optimum Locations of Switching Centers and the Absolute Centers and Medians of a Graph," Operations Research, INFORMS, vol. 12(3), pages 450-459, June.
    4. Richard Wollmer, 1964. "Removing Arcs from a Network," Operations Research, INFORMS, vol. 12(6), pages 934-940, December.
    5. James T. Moore & Jonathan F. Bard, 1990. "The Mixed Integer Linear Bilevel Programming Problem," Operations Research, INFORMS, vol. 38(5), pages 911-921, October.
    6. Alberto Caprara & Paolo Toth & Matteo Fischetti, 2000. "Algorithms for the Set Covering Problem," Annals of Operations Research, Springer, vol. 98(1), pages 353-371, December.
    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. 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.
    2. Snežana Tadić & Mladen Krstić & Željko Stević & Miloš Veljović, 2023. "Locating Collection and Delivery Points Using the p -Median Location Problem," Logistics, MDPI, vol. 7(1), pages 1-17, February.
    3. Wangshu Mu & Daoqin Tong, 2020. "On solving large p-median problems," Environment and Planning B, , vol. 47(6), pages 981-996, July.
    4. 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.
    5. 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.
    6. Kenneth Carling & Mengjie Han & Johan Håkansson, 2012. "Does Euclidean distance work well when the p-median model is applied in rural areas?," Annals of Operations Research, Springer, vol. 201(1), pages 83-97, December.
    7. Amir Khakbaz & Ali Nookabadi & S. Shetab-bushehri, 2013. "A Model for Locating Park-and-Ride Facilities on Urban Networks Based on Maximizing Flow Capture: A Case Study of Isfahan, Iran," Networks and Spatial Economics, Springer, vol. 13(1), pages 43-66, March.
    8. Comber, Alexis & Dickie, Jennifer & Jarvis, Claire & Phillips, Martin & Tansey, Kevin, 2015. "Locating bioenergy facilities using a modified GIS-based location–allocation-algorithm: Considering the spatial distribution of resource supply," Applied Energy, Elsevier, vol. 154(C), pages 309-316.
    9. Dayanna Rodrigues da Cunha Nunes & Orivalde Soares da Silva Júnior & Renata Albergaria de Mello Bandeira & Yesus Emmanuel Medeiros Vieira, 2023. "A Robust Stochastic Programming Model for the Well Location Problem: The Case of The Brazilian Northeast Region," Sustainability, MDPI, vol. 15(14), pages 1-21, July.
    10. Alcaraz, Javier & Landete, Mercedes & Monge, Juan F., 2012. "Design and analysis of hybrid metaheuristics for the Reliability p-Median Problem," European Journal of Operational Research, Elsevier, vol. 222(1), pages 54-64.
    11. Deniz Aksen & Nuray Piyade & Necati Aras, 2010. "The budget constrained r-interdiction median problem with capacity expansion," 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. 18(3), pages 269-291, September.
    12. 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.
    13. Mehdi Firoozbakht & Hamidreza Vosoughifar & Alireza Ghari Ghoran, 2019. "Coverage intensity of optimal sensors for common, isolated, and integrated steel structures using novel approach of FEM-MAC-TTFD," International Journal of Distributed Sensor Networks, , vol. 15(8), pages 15501477198, August.
    14. 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.
    15. Yates, Justin & Batta, Rajan & Karwan, Mark & Casas, Irene, 2012. "Establishing public policy to protect critical infrastructure: Finding a balance between exposure and cost in Los Angeles County," Transport Policy, Elsevier, vol. 24(C), pages 109-117.
    16. ReVelle, C.S. & Eiselt, H.A. & Daskin, M.S., 2008. "A bibliography for some fundamental problem categories in discrete location science," European Journal of Operational Research, Elsevier, vol. 184(3), pages 817-848, February.
    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. Sergio García & Martine Labbé & Alfredo Marín, 2011. "Solving Large p -Median Problems with a Radius Formulation," INFORMS Journal on Computing, INFORMS, vol. 23(4), pages 546-556, November.
    19. 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.
    20. Antiopi Panteli & Basilis Boutsinas & Ioannis Giannikos, 2021. "On solving the multiple p-median problem based on biclustering," Operational Research, Springer, vol. 21(1), pages 775-799, March.

    More about this item

    Statistics

    Access and download statistics

    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:ejores:v:189:y:2008:i:1:p:76-92. 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: http://www.elsevier.com/locate/eor .

    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.