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A characterization of irreducible infeasible subsystems in flow networks

Author(s)
Joormann, Imke; Pfetsch, Marc E.; Orlin, James B
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Abstract
Infeasible network flow problems with supplies and demands can be characterized via violated cut-inequalities of the classical Gale-Hoffman theorem. Written as a linear program, irreducible infeasible subsystems (IISs) provide a different means of infeasibility characterization. In this article, we answer a question left open in the literature by showing a one-to-one correspondence between IISs and Gale-Hoffman-inequalities in which one side of the cut has to be weakly connected. We also show that a single max-flow computation allows one to compute an IIS. Moreover, we prove that finding an IIS of minimal cardinality in this special case of flow networks is strongly NP-hard.
Date issued
2016-08
URI
http://hdl.handle.net/1721.1/111098
Department
Sloan School of Management
Journal
Networks
Publisher
Wiley Blackwell
Citation
Joormann, Imke et al. “A Characterization of Irreducible Infeasible Subsystems in Flow Networks.” Networks 68, 2 (June 2016): 121–129 © 2016 Wiley Periodicals, Inc
Version: Author's final manuscript
ISSN
0028-3045
1097-0037

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