Abstract
This article introduces the subject of terrorism and counter-terrorism by means of a two-person bimatrix game that provides some insight into the behaviour of the two players. We then examine three important areas in counter-terrorism tasks: the detection of terrorist cells and how to render them inoperable, the fortification of assets in order to protect them from terrorist attacks and the optimal evacuation of people from an area affected by terrorism. Basic mathematical models are formulated and demonstrated. This article concludes with some thoughts on potential extensions of the models presented here.
Similar content being viewed by others
References
Abrahms, M. (2008) What terrorists really want: Terrorist motives and counterterrorism strategy. International Security 31 (4): 78–105.
Artificial Intelligence Lab. (2011) The university of Arizona, http://ai.arizona.edu/research/terror/, accessed 24 November 2011.
Bard, J.F. (1998) Practical Bilevel Optimization. Nonconvex optimization and its applications. Vol. 30. Dordrecht: Kluwer Academic.
Barr, D. and Baker, A. (2001) Getting the message from ‘eco-terrorists’: Mystery group takes its campaign East. New York Times 8 January: A15.
Bier, V., Oliveros, S. and Samuelson, L. (2007) Choosing what to protect: Strategic defensive allocation against an unknown attacker. Journal of Public Economic Theory 9 (4): 563–587.
Bobeica, M., Jéral, J.-P., Garcia, T. and Best, C. (2008) A quantitative analysis of ‘root causes of conflict’. In: H.C. Chen, E. Reid, J. Sinai, A. Silke and B. Ganor (eds.) Terrorism Informatics: Knowledge Management and Data Mining for Homeland Security. New York: Springer-Verlag, pp. 115–139.
Carley, K. et al (2003) BioWar: Scalable multi-agent social and epidemiological simulation of bioterrorism events. NAACSOS Conference 2003, Day 4, Electronic Publication, Pittsburgh, PA, IEEESMCA03-11-0274, http://www.casos.cs.cmu.edu/publications/papers/carley_2003_biowarscalablemulti.pdf, accessed 24 November 2011.
Carley, K.M., Lee, J.-S. and Krackhardt, D. (2002) Destabilizing networks. Connections 24 (3): 79–92.
Charters, D.A. (2007) 9/11: Seven years into history. The Journal of Conflict Studies 27 (2): 173–187.
Church, R.L. and Scaparra, M.P. (2007) Protecting critical assets: The r-interdiction median problem with fortification. Geographical Analysis 39 (2): 129–146.
Church, R.L., Scaparra, M.P. and Middleton, R.S. (2004) Identifying critical infrastructure: The median and covering facility interdiction problems. Annals of the Association of American Geographers 94 (3): 491–502.
Dempe, S. (2002) Foundations of Bilevel Programming. New York, Boston, Dordrecht, London, Moscow: Kluwer Academic Publishers.
de Silva, F.N. and Eglese, R.W. (2000) Integrating simulation modelling and GIS: Spatial decision support systems for evacuation planning. The Journal of the Operational Research Society 51 (4): 423–430.
Eiselt, H.A. (1985) A location problem with minimax objective. In: H. Noltemeier (ed.) Proceedings of the WG ’85: International Workshop on Graphtheoretic Concepts in Computer Science. West Germany: Universitätsverlag R. Trauner, Linz, pp. 85–99.
Eiselt, H.A. (1986) Continuous maximin knapsack problems with GLB constraints. Mathematical Programming 36 (1): 114–121.
Eiselt, H.A. (1998) Perception and information in a competitive location model. European Journal of Operational Research 108 (1): 94–105.
Eiselt, H.A. and Sandblom, C.-L. (eds.) (2004) Decision Analysis, Location Models, and Scheduling Problems. Berlin/Heidelberg/New York: Springer-Verlag.
Farley, J.D. (2003) Breaking Al Qaeda cells: A mathematical analysis of counterterrorism operations (a guide for risk assessment and decision making). Studies in Conflict and Terrorism 26 (6): 399–411.
Freeman, L. (1977) A set of measures of centrality based on betweenness. Sociometry 40 (1): 35–41.
Frey, B.S., Luechinger, S. and Stutzer, A. (2007) Calculating tragedy: Assessing the costs of terrorism. Journal of Economic Surveys 21 (1): 1–24.
Galvao, R.D. and Marianov, V. (2011) Lagrangean relaxation-based techniques for solving facility location problems. In: H.A. Eiselt and V. Marianov (eds.) Foundations of Location Analysis. New York: Springer-Verlag, pp. 391–420.
Ghosh, A. and Buchanan, A. (1988) Multiple outlets in a duopoly: A first entry paradox. Geographical Analysis 20 (2): 111–121.
Gross, O. and Wagner, R. (1950) A continuous Colonel Blotto game. Research memorandum, The Rand Corporation RM-408.
Gutfraind, A. (2009) Understanding terrorist organizations with a dynamic model. Studies in Conflict and Terrorism 32 (1): 45–59.
Hamacher, H. and Tjandra, S. (2002) Mathematical modeling of evacuation problems: A state of the art. In: M. Schreckenberg and S.D. Sharma (eds.) Pedestrian and Evacuation Dynamics. Berlin, Germany: Springer-Verlag, pp. 227–266.
Hartnell, B. and Gunther, G. (2009) Security of underground resistance movements. In: N. Memon, J.D. Farley, D.L. Hicks and T. Rosenorn (eds.) Mathematical Methods in Counterterrorism. Vienna, Austria: Springer-Verlag, pp. 185–204.
Hoffman, B. (2006) Inside Terrorism. New York: Columbia University Press.
Klerks, P. (2001) The network paradigm applied to criminal organisations: Theoretical nitpicking or a relevant doctrine for investigators? Recent developments in The Netherlands. Connections 24 (3): 53–65.
Krebs, V. (2008) Connecting the dots: Connecting two identified terrorists, http://www.orgnet.com/tnet.html, accessed 24 November 2011.
Krebs, V.E. (2002) Mapping networks of terrorist cells. Connections 24 (3): 43–52.
List of designated terrorist organizations. (2011). http://en.wikipedia.org/wiki/Terrorist_groups, accessed 24 November 2011.
Lu, Q., Huang, Y. and Shekhar, S. (2003) Evacuation planning: A capacity constrained routing approach. Proceedings of the 1st NSF/NIJ conference on Intelligence and security informatics. Berlin, Heidelberg: Springer-Verlag.
Martello, S. and Toth, P. (1990) Knapsack Problems: Algorithms and Computer Implementations. Chichester, UK: Wiley-Interscience.
McGehee, R.W. (1983) Deadly Deceits: My 25 Years in the CIA. New York: Sheridan Square Publications.
Michael, G. and Wahba, K.M. (2001) Transcript of Usama Bin Laden Video Tape. 13 December, http://www.defense.gov/news/Dec2001/d20011213ubl.pdf, accessed 29 November 2011.
Milgram, S. (1967) The small world problem. Psychology Today 1 (1): 60–67.
Niskanen, W.A. (1968) The peculiar economics of bureaucracy. The American Economic Review 58 (2): 293–305.
Orgnet.com. (2011) Social network analysis. A brief introduction, http://www.orgnet.com/sna.html, accessed 24 November 2011.
Osman, M.S. (2009) Evacuation route optimization models for low-rise building groups. Dissertation thesis at Department of Industrial and Systems Engineering, NC A&T State University, North Carolina.
Osman, M.S, Ram, B., Stanfield, P., Davis, L., Samanlioglu, F. and Bhadury, J. (2009) Optimization models for distributed scheduling for disaster area logistics. Proceedings of the IEEE International Conference on Service Operations, Logistics, and Informatics, Chicago, IL.
Perry, R.W., Lindell, M.K. and Greene, M. (1981) Evacuation Planning in Emergency Management. Lexington, KY: Lexington Books.
Pinker, E.J. (2009) A mathematical analysis of short-term responses to threats of terrorism. In: N. Memon, J.D. Farley, D.L. Hicks and T. Rosenorn (eds.) Mathematical Methods in Counterterrorism. Vienna, Austria: Springer-Verlag, pp. 141–160.
Political Research Associates. (2010) The roots of the leaderless resistance concept, http://www.publiceye.org/liberty/terrorism/insurgency/cells.html, accessed 24 November 2011.
Posner, R.A. (2008) Privacy, surveillance, and law. The University of Chicago Law Review 75 (1): 245–260.
Rapoport, D. (2004) The four waves of modern terrorism. In: A. Cronin and J. Ludes (eds.) Attacking Terrorism. Washington DC: Georgetown University Press, pp. 46–73.
Rhodes, C.J. (2009) Inference approaches to constructing covert social network topologies. In: N. Memon, J.D. Farley, D.L. Hicks and T. Rosenorn (eds.) Mathematical Methods in Counterterrorism. Vienna, Austria: Springer-Verlag, pp. 127–140.
Rodriguez, J.A. (2005) The March 11th Terrorist Network: In its weakness lies its strength. WP EPP-LEA: 03, http://www.ub.edu/epp/wp/11m.PDF, accessed 24 November 2011.
Sageman, M. (2004) Understanding Terror Networks. Philadelphia, PA: University of Pennsylvania Press.
Sageman, M. (2008) Leaderless Jihad. Philadelphia, PA: University of Pennsylvania Press.
Sandler, R. and Enders, W. (2004) An economic perspective on transnational terrorism. European Journal of Political Economy 20 (2): 301–316.
Sherali, H.D., Carter, T.B. and Hobeika, A.G. (1991) A location-allocation model and algorithm for evacuation planning under hurricane/flood conditions. Transportation Research Part B: Methodological 25 (6): 439–452.
Silke, A. (2008) Research on terrorism: A review of the impact of 9/11 and the global war on terrorism. In: H.C. Chen, E. Reid, J. Sinai, A. Silke and B. Ganor (eds.) Terrorism Informatics: Knowledge Management and Data Mining for Homeland Security. New York: Springer-Verlag, pp. 27–50.
Skillicorn, D. (2009) Extracting knowledge from graph data in adversarial settings. In: N. Memon, J.D. Farley, D.L. Hicks and T. Rosenorn (eds.) Mathematical Methods in Counterterrorism. Vienna, Austria: Springer-Verlag, pp. 33–54.
State Department. (2011). Foreign terrorist organizations. http://www.state.gov/, accessed 24 November 2011.
The Age. (2004). UN calculates the cost of terrorism. http://www.theage.com.au/articles/2004/08/27/1093518081060.html, accessed 24 November 2011.
Waeckerle, J.F. (1991) Disaster planning and response. New England Journal of Medicine 324 (12): 815–821.
Waldau, N., Gattermann, P., Knoflacher, H. and Schreckenberg, M. (eds.) (2006) Pedestrian and Evacuation Dynamics ‘05. Berlin/Heidelberg, Germany: Springer-Verlag.
Weinberg, L. and Eubank, W. (2010) An end to the fourth wave of terrorism? Studies in Conflict & Terrorism 33 (7): 594–602.
WordIQ. (2010). Red Army Faction – Definition. http://www.wordiq.com/definition/Red_Army_Faction, accessed 24 November 2011.
Acknowledgements
This research was in part supported by a grant from the Natural Sciences & Engineering Research Council of Canada under grant number 0009160. This support is gratefully acknowledged. The insightful comments of an anonymous referee are much appreciated. They helped streamline the exposition.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Eiselt, H., Bhadury, J. & Burkey, M. An optimization-based framework for modelling counter-terrorism strategies. OR Insight 26, 7–31 (2013). https://doi.org/10.1057/ori.2011.24
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1057/ori.2011.24