The multi-terminal maximum-flow network-interdiction problem
Author
Akgün, İ.
Tansel, B. Ç.
Wood, R. K.
Date
2011Source Title
European Journal of Operational Research
Print ISSN
0377-2217
Volume
211
Issue
2
Pages
241 - 251
Language
English
Type
ArticleItem Usage Stats
91
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views
93
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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 programmingNetwork 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/11693/21908Published Version (Please cite this version)
http://dx.doi.org/10.1016/j.ejor.20http://dx.doi.org/10.12.011Collections
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