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A Two-Sided Optimization for Theater Ballistic Missile Defense

Author

Listed:
  • Gerald Brown

    (Operations Research Department, Naval Postgraduate School, Monterey, California 93943)

  • Matthew Carlyle

    (Operations Research Department, Naval Postgraduate School, Monterey, California 93943)

  • Douglas Diehl

    (Operations Research Department, Naval Postgraduate School, Monterey, California 93943)

  • Jeffrey Kline

    (Operations Research Department, Naval Postgraduate School, Monterey, California 93943)

  • Kevin Wood

    (Operations Research Department, Naval Postgraduate School, Monterey, California 93943)

Abstract

We describe JOINT DEFENDER, a new two-sided optimization model for planning the pre-positioning of defensive missile interceptors to counter an attack threat. In our basic model, a defender pre-positions ballistic missile defense platforms to minimize the worst-case damage an attacker can achieve; we assume that the attacker will be aware of defensive pre-positioning decisions, and that both sides have complete information as to target values, attacking-missile launch sites, weapon system capabilities, etc. Other model variants investigate the value of secrecy by restricting the attacker’s and/or defender’s access to information. For a realistic scenario, we can evaluate a completely transparent exchange in a few minutes on a laptop computer, and can plan near-optimal secret defenses in seconds. JOINT DEFENDER’s mathematical foundation and its computational efficiency complement current missile-defense planning tools that use heuristics or supercomputing. The model can also provide unique insight into the value of secrecy and deception to either side. We demonstrate with two hypothetical North Korean scenarios.

Suggested Citation

  • Gerald Brown & Matthew Carlyle & Douglas Diehl & Jeffrey Kline & Kevin Wood, 2005. "A Two-Sided Optimization for Theater Ballistic Missile Defense," Operations Research, INFORMS, vol. 53(5), pages 745-763, October.
  • Handle: RePEc:inm:oropre:v:53:y:2005:i:5:p:745-763
    DOI: 10.1287/opre.1050.0231
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    References listed on IDEAS

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    1. Guillermo Owen, 1969. "Minimization of Fatalities in a Nuclear Attack Model," Operations Research, INFORMS, vol. 17(3), pages 489-505, June.
    2. Jerome Bracken & Peter S. Brooks & James E. Falk, 1987. "Robust preallocated preferential defense," Naval Research Logistics (NRL), John Wiley & Sons, vol. 34(1), pages 1-22, February.
    3. James T. Moore & Jonathan F. Bard, 1990. "The Mixed Integer Linear Bilevel Programming Problem," Operations Research, INFORMS, vol. 38(5), pages 911-921, October.
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    Cited by:

    1. Nedialko B. Dimitrov & Gerald Brown & Matthew Carlyle, 2013. "A Real-World Network Modeling Project," INFORMS Transactions on Education, INFORMS, vol. 14(1), pages 4-12, September.
    2. Jayaswal, Sachin & Sinha, Ankur, 2022. "Bilevel Optimization: Applications, Models and Solution Approaches," IIMA Working Papers WP 2022-05-02, Indian Institute of Management Ahmedabad, Research and Publication Department.
    3. 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.
    4. David L. Alderson & Gerald G. Brown & W. Matthew Carlyle, 2015. "Operational Models of Infrastructure Resilience," Risk Analysis, John Wiley & Sons, vol. 35(4), pages 562-586, April.
    5. 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).
    6. Peiqiu Guan & Jun Zhuang, 2015. "Modeling Public–Private Partnerships in Disaster Management via Centralized and Decentralized Models," Decision Analysis, INFORMS, vol. 12(4), pages 173-189, December.
    7. Shan, Xiaojun & Zhuang, Jun, 2013. "Hybrid defensive resource allocations in the face of partially strategic attackers in a sequential defender–attacker game," European Journal of Operational Research, Elsevier, vol. 228(1), pages 262-272.
    8. Ankur Sinha & Zhichao Lu & Kalyanmoy Deb & Pekka Malo, 2020. "Bilevel optimization based on iterative approximation of multiple mappings," Journal of Heuristics, Springer, vol. 26(2), pages 151-185, April.
    9. Zhuang, Jun & Bier, Vicki M. & Alagoz, Oguzhan, 2010. "Modeling secrecy and deception in a multiple-period attacker-defender signaling game," European Journal of Operational Research, Elsevier, vol. 203(2), pages 409-418, June.
    10. Bo An & Fernando Ordóñez & Milind Tambe & Eric Shieh & Rong Yang & Craig Baldwin & Joseph DiRenzo & Kathryn Moretti & Ben Maule & Garrett Meyer, 2013. "A Deployed Quantal Response-Based Patrol Planning System for the U.S. Coast Guard," Interfaces, INFORMS, vol. 43(5), pages 400-420, October.
    11. Antoniou, Margarita & Sinha, Ankur & Papa, Gregor, 2024. "δ-perturbation of bilevel optimization problems: An error bound analysis," Operations Research Perspectives, Elsevier, vol. 13(C).
    12. Michael J. Armstrong, 2014. "Modeling Short-Range Ballistic Missile Defense and Israel's Iron Dome System," Operations Research, INFORMS, vol. 62(5), pages 1028-1039, October.
    13. Mohammad E. Nikoofal & Mehmet Gümüs, 2015. "On the value of terrorist’s private information in a government’s defensive resource allocation problem," IISE Transactions, Taylor & Francis Journals, vol. 47(6), pages 533-555, June.
    14. Kathryn Merrick & Medria Hardhienata & Kamran Shafi & Jiankun Hu, 2016. "A Survey of Game Theoretic Approaches to Modelling Decision-Making in Information Warfare Scenarios," Future Internet, MDPI, vol. 8(3), pages 1-29, July.
    15. 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.
    16. Gokhan Karakose & Ronald G. McGarvey, 2019. "Optimal Detection of Critical Nodes: Improvements to Model Structure and Performance," Networks and Spatial Economics, Springer, vol. 19(1), pages 1-26, March.
    17. Gerald G. Brown & Walter C. DeGrange & Robert F. Dell & Ronald D. Fricker, 2015. "ASP, Art and Science of Practice: Educating Military Operations Research Practitioners," Interfaces, INFORMS, vol. 45(2), pages 175-186, April.
    18. Mark Horner & Michael Widener, 2011. "The effects of transportation network failure on people’s accessibility to hurricane disaster relief goods: a modeling approach and application to a Florida case study," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 59(3), pages 1619-1634, December.
    19. Jie Xu & Jun Zhuang, 2016. "Modeling costly learning and counter-learning in a defender-attacker game with private defender information," Annals of Operations Research, Springer, vol. 236(1), pages 271-289, January.
    20. Bier, Vicki M. & Hausken, Kjell, 2013. "Defending and attacking a network of two arcs subject to traffic congestion," Reliability Engineering and System Safety, Elsevier, vol. 112(C), pages 214-224.
    21. Chen Wang & Vicki M. Bier, 2016. "Quantifying Adversary Capabilities to Inform Defensive Resource Allocation," Risk Analysis, John Wiley & Sons, vol. 36(4), pages 756-775, April.
    22. 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.
    23. Nikoofal, Mohammad E. & Zhuang, Jun, 2015. "On the value of exposure and secrecy of defense system: First-mover advantage vs. robustness," European Journal of Operational Research, Elsevier, vol. 246(1), pages 320-330.
    24. Boaz I. Kaminer & Joseph Z. Ben‐Asher, 2010. "A methodology for estimating and optimizing effectiveness of Non‐Independent Layered Defense," Systems Engineering, John Wiley & Sons, vol. 13(2), pages 119-129, June.

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