Efficiently interdicting a time-expanded transshipment network
Derbes, H. Dan
Wood, R. Kevin
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A network interdictor' has a limited supply of resource with which to disrupt a network user's" flow of supplies in a capacitated transshipment network. The interdictor's problem of minimizing the maximum flow through the network is a difficult- to-solve integer programming problem but we show that a heuristic based on Lagrangian relaxation is very effective in approximately solving the problem. We implement algorithms in C to approximately solve both the static (without considering time) and dynamic network interdiction problems. Static test networks range in size from 25 nodes and 64 arcs to 400 nodes and 1519 arcs. Using an IBM Rs/6000 Model 590 workstation, we find optimal solutions for seven of 12 test networks and solve the largest problem in only 31.0 seconds. We model a dynamic network in time-expanded form in order to assign time weights of 0 or 1 to flow, include repair time of interdicted arcs, and provide a schedule to the network interdictor that identifies arcs and time periods for interdictions. Dynamic networks range in size from 525 nodes and 1, 344 arcs to 40,400 nodes and 153,419 arcs (in time-expanded form). We find near- optimal solutions in 13 of 24 test networks and solve the largest network in 1729.5 seconds
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