Article ID: | iaor19991401 |
Country: | United States |
Volume: | 46 |
Issue: | 2 |
Start Page Number: | 184 |
End Page Number: | 197 |
Publication Date: | Mar 1998 |
Journal: | Operations Research |
Authors: | Wood R. Kevin, Morton David P., Cormican Kelly J. |
Keywords: | programming: probabilistic, game theory |
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.