Network interdiction to minimize the maximum probability of evasion with synergy between applied resources
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In this paper, we model and solve the network interdiction problem of minimizing the maximum probability of evasion by an entity traversing a network from a given source to a designated terminus, while incorporating novel forms of superadditive synergy between resources applied to arcs in the network. Inspired primarily by operations to coordinate Iraqi and U.S. security forces seeking to interdict an evader attempting to avoid detection while transiting part of the nearly rectilinear street network in East Baghdad, this study motivates and examines either linear or concave (nonlinear) synergy relationships between the applied resources within our formulations. We also propose an alternative model for sequential overt and covert deployment of subsets of interdiction resources, and conduct theoretical as well as empirical comparative analyses between models for purely overt (with or without synergy) and composite overt-covert strategies to provide insights into absolute and relative threshold criteria for recommended resource utilization. Our empirical results confirm the value of tactical patience regarding decisions on the covert utilization of resources for network interdiction. Furthermore, considering non-integral and integral resource allocations, we identify (theoretically and empirically) parametric characteristics of instances that exhibit the relative worth of employing partially covert operations. Under the relatively more practical scenario involving integral resource allocations, we demonstrate that the composite overt-covert strategy of deploying resources has a greater potential to improve over a purely overt resource deployment strategy, both with and without synergy, particularly when costs are positively correlated, resources are plentiful, and a sufficiently high ratio of covert to overt resources exists. Moreover, should an interdictor be able to ascertain an optimal evader path, the potential and magnitude of this relative improvement for the overt-covert resource allocation strategy is significantly greater.
- Bailey, M. D., Shechter, S. M., Schaefer, A. J. (2006) SPAR: stochastic programming with adversarial recourse. Operations Research Letters 34: pp. 307-315 CrossRef
- Bayrak, H., Bailey, M. (2008) Shortest path network interdiction with asymmetric information. Networks 52: pp. 133-140 CrossRef
- Bazaraa, M. S., Sherali, H. D., Shetty, C. M. (2006) Nonlinear programming: theory and algorithms. Wiley, Hoboken CrossRef
- Brown, S. S. (1980) Optimal search for a moving target in discrete time and space. Operations Research 28: pp. 1275-1289 CrossRef
- Brown, G., Carlyle, M., Salmerón, J., Wood, R. K. (2006) Defending critical infrastructure. Interfaces 36: pp. 530-544 CrossRef
- Brown, G. G., Harney, R. C., Skroch, E. M., Wood, R. K. (2009) Interdicting a nuclear-weapons project. Operations Research 57: pp. 866-877 CrossRef
- Cormican, K. J. (1995). Computational methods for deterministic and stochastic network interdiction problems. Master’s Thesis, US Naval Postgraduate School, Monterey, CA.
- Cormican, K. J., Morton, D. P., Wood, R. K. (1998) Stochastic network interdiction. Operations Research 46: pp. 184-197 CrossRef
- Dempe, S. (2002) Foundations of bilevel programming. Kluwer Academic, Dordrecht
- Ford, L. R., Fulkerson, D. R. (1956) Maximal flow through a network. Canadian Journal of Mathematics 8: pp. 399-404 CrossRef
- Ford, L. R., & Fulkerson, D. R. (1955). A simple algorithm for finding maximal network flows and an application to the Hitchcock problem. Project rand research memorandum, RM-1604, Santa Monica, CA.
- Fulkerson, D. R., Harding, G. C. (1977) Maximizing the minimum source-sink path subject to a budget constraint. Mathematical Programming 13: pp. 116-118 CrossRef
- Golden, B. (1978) A problem in network interdiction. Naval Research Logistics Quarterly 25: pp. 711-713 CrossRef
- Hausken, K. (2011) Strategic defense and attack of series systems when agents move sequentially. IIE Transactions 43: pp. 483-504 CrossRef
- Held, H., Hemmecke, R., Woodruff, D. L. (2005) A decomposition algorithm applied to planning the interdiction of stochastic networks. Naval Research Logistics 52: pp. 321-328 CrossRef
- Hemmecke, R., Schultz, R., Woodruff, D. L. Interdicting stochastic networks with binary effort. In: Woodruff, D. L. eds. (2003) Network interdiction and stochastic integer programming. Kluwer Academic, Norwell, pp. 69-84 CrossRef
- Israeli, E., Wood, R. K. (2002) Shortest-path network interdiction. Networks 40: pp. 97-111 CrossRef
- Koopman, B. O. (1979) Search and its optimization. The American Mathematical Monthly 86: pp. 527-540 CrossRef
- Lim, C., Smith, J. C. Algorithms for network interdiction and fortification games. In: Chinchuluun, A., Pardalos, P. M., Migdalas, A., Pitsoulis, L. eds. (2008) Pareto optimality, game theory and equilibria. Springer, New York, pp. 609-644
- Lim, C., Smith, J. C. (2007) Algorithms for discrete and continuous multicommodity flow network interdiction problems. IIE Transactions 39: pp. 15-26 CrossRef
- Lunday, B. J. (2010). Resource allocation on networks: nested event tree optimization, network interdiction, and game theoretic methods. Doctoral Dissertation, Virginia Tech, Blacksburg, VA.
- Lunday, B. J., Sherali, H. D. (2011) A dynamic network interdiction problem. Informatica 21: pp. 553-574
- Lunday, B. J., & Sherali, H. D. (2011b). Network flow interdiction models and algorithms with resource synergy considerations. Manuscript, Grado Department of Industrial and Systems Engineering, Virginia Polytechnic Institute and State University, Blacksburg, VA.
- Meijers, E. (2005) Polycentric urban regions and the quest for synergy: is a network of cities more than the sum of the parts?. Urban Studies 42: pp. 765-781 CrossRef
- Morton, D. P., Pan, F., Saeger, K. J. (2007) Models for nuclear smuggling interdiction. IIE Transactions 39: pp. 3-14 CrossRef
- Napier, R. W., Gershenfeld, M. K. (1993) Groups: theory and experiences. Houghton Mifflin Company, Boston
- Nagurney, A., Woolley, T. Environmental and cost synergy in supply chain network integration in mergers and acquisitions. In: Ehrgott, M., Naujoks, B., Stewart, T., Wallenius, J. eds. (2010) Multiple criteria decision making for sustainable energy and transportation systems. Proceedings of the 19th international conference on multiple criteria decision making. Springer, Berlin, pp. 51-78
- Nehme, M. V. (2009). Two-person games for stochastic network interdiction: models, methods, and complexities. Doctoral Dissertation, University of Texas, Austin, TX.
- Pan, F., Charlton, W. S., Morton, D. P. A stochastic program for interdicting smuggled nuclear material. In: Woodruff, D. L. eds. (2003) Network interdiction and stochastic integer programming. Kluwer Academic, Norwell, pp. 1-19 CrossRef
- Royset, J. O., Wood, R. K. (2007) Solving the bi-objective maximum-flow network-interdiction problem. INFORMS Journal on Computing 19: pp. 175-184 CrossRef
- Sherali, H. D., Lunday, B. J. (2010) Equitable apportionment of railcars within a pooling agreement for shipping automobiles. Transportation Research. Part E 47: pp. 263-283 CrossRef
- Unsal, O. (2010). Two-person zero-sum network-interdiction game with multiple inspector types. Master’s Thesis, Naval Postgraduate School, Monterey, CA.
- Eye, A., Schuster, C., Rogers, W. M. (1998) Modelling synergy using manifest categorical variables. International Journal of Behavioral Development 22: pp. 537-557 CrossRef
- Washburn, A., Wood, R. K. (1995) Two-person zero-sum games for network interdiction. Operations Research 43: pp. 243-251 CrossRef
- Wood, R. K. (1993) Deterministic network interdiction. Mathematical and Computer Modelling 17: pp. 1-18 CrossRef
- Network interdiction to minimize the maximum probability of evasion with synergy between applied resources
Annals of Operations Research
Volume 196, Issue 1 , pp 411-442
- Cover Date
- Print ISSN
- Online ISSN
- Springer US
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- Resource allocation
- Minimax flow problems
- Network evasion
- Network interdiction
- Overt and covert strategies
- Industry Sectors