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      Analysis of Lagrangian lower bounds for a graph partitioning problem

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      Author(s)
      Adil, G. K.
      Ghosh, J. B.
      Date
      1999
      Source Title
      Operations Research
      Print ISSN
      0030-364X
      Electronic ISSN
      1526-5463
      Publisher
      Institute for Operations Research and the Management Sciences (INFORMS)
      Volume
      47
      Issue
      5
      Pages
      785 - 788
      Language
      English
      Type
      Article
      Item Usage Stats
      248
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      254
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      Abstract
      Recently, Ahmadi and Tang (1991) demonstrated how various manufacturing problems can be modeled and solved as graph partitioning problems. They use Lagrangian relaxation of two different mixed integer programming formulations to obtain both heuristic solutions and lower bounds on optimal solution values. In this note, we point to certain inconsistencies in the reported results. Among other things, we show analytically that the first bound proposed is trivial (i.e., it can never have a value greater than zero) while the second is also trivial for certain sparse graphs. We also present limited empirical results on the behavior of this second bound as a function of graph density.
      Keywords
      Cellular manufacturing
      Group technology
      Heuristic methods
      Integer programming
      Mathematical models
      VLSI circuits
      Graph partitioning problem
      Lagrangian lower bounds
      Graph theory
      Permalink
      http://hdl.handle.net/11693/25215
      Published Version (Please cite this version)
      https://doi.org/10.1287/opre.47.5.785
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