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Stochastic Network Interdiction

Author

Listed:
  • Kelly J. Cormican

    (Naval Postgraduate School, Monterey, California)

  • David P. Morton

    (The University of Texas at Austin, Austin, Texas)

  • R. Kevin Wood

    (Naval Postgraduate School, Monterey, California)

Abstract

Using limited assets, an interdictor attempts to destroy parts of a capacitated network through which an adversary will subsequently maximize flow. We formulate and solve a stochastic version of the interdictor's problem: Minimize the expected maximum flow through the network when interdiction successes are binary random variables. Extensions are made to handle uncertain arc capacities and other realistic variations. These two-stage stochastic integer programs have applications to interdicting illegal drugs and to reducing the effectiveness of a military force moving materiel, troops, information, etc., through a network in wartime. Two equivalent model formulations allow Jensen's inequality to be used to compute both lower and upper bounds on the objective, and these bounds are improved within a sequential approximation algorithm. Successful computational results are reported on networks with over 100 nodes, 80 interdictable arcs, and 180 total arcs.

Suggested Citation

  • Kelly J. Cormican & David P. Morton & R. Kevin Wood, 1998. "Stochastic Network Interdiction," Operations Research, INFORMS, vol. 46(2), pages 184-197, April.
    • Handle: RePEc:inm:oropre:v:46:y:1998:i:2:p:184-197
    DOI: 10.1287/opre.46.2.184
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    References listed on IDEAS

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    1. C. C. Huang & W. T. Ziemba & A. Ben-Tal, 1977. "Bounds on the Expectation of a Convex Function of a Random Variable: With Applications to Stochastic Programming," Operations Research, INFORMS, vol. 25(2), pages 315-325, April.
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