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      The multi-terminal maximum-flow network-interdiction problem

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      Author
      Akgün, İ.
      Tansel, B. Ç.
      Wood, R. K.
      Date
      2011
      Source Title
      European Journal of Operational Research
      Print ISSN
      0377-2217
      Volume
      211
      Issue
      2
      Pages
      241 - 251
      Language
      English
      Type
      Article
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      Abstract
      This paper defines and studies the multi-terminal maximum-flow network-interdiction problem (MTNIP) in which a network user attempts to maximize flow in a network among K ≥ 3 pre-specified node groups while an interdictor uses limited resources to interdict network arcs to minimize this maximum flow. The paper proposes an exact (MTNIP-E) and an approximating model (MPNIM) to solve this NP-hard problem and presents computational results to compare the models. MTNIP-E is obtained by first formulating MTNIP as bi-level min-max program and then converting it into a mixed integer program where the flow is explicitly minimized. MPNIM is binary-integer program that does not minimize the flow directly. It partitions the node set into disjoint subsets such that each node group is in a different subset and minimizes the sum of the arc capacities crossing between different subsets. Computational results show that MPNIM can solve all instances in a few seconds while MTNIP-E cannot solve about one third of the problems in 24 hour. The optimal objective function values of both models are equal to each other for some problems while they differ from each other as much as 46.2% in the worst case. However, when the post-interdiction flow capacity incurred by the solution of MPNIM is computed and compared to the objective value of MTNIP-E, the largest difference is only 7.90% implying that MPNIM may be a very good approximation to MTNIP-E. © 2011 Elsevier B.V. All rights reserved.
      Keywords
      Integer programming
      Network flows
      Network interdiction
      OR in military
      Computational results
      Disjoint subsets
      Flow capacity
      Flow network
      Integer program
      Maximum flows
      Min-max
      Mixed-integer programs
      Multi terminals
      Network flows
      Network interdiction
      Network users
      NP-HARD problem
      Objective function values
      OR in military
      Worst case
      Computational complexity
      Rough set theory
      Integer programming
      Permalink
      http://hdl.handle.net/11693/21908
      Published Version (Please cite this version)
      http://dx.doi.org/10.1016/j.ejor.20http://dx.doi.org/10.12.011
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      • Department of Industrial Engineering 677
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