Analysis of Lagrangian lower bounds for a graph partitioning problem

Date
1999
Authors
Adil, G. K.
Ghosh, J. B.
Advisor
Supervisor
Co-Advisor
Co-Supervisor
Instructor
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
Journal Title
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Volume Title
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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.

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Keywords
Cellular manufacturing, Group technology, Heuristic methods, Integer programming, Mathematical models, VLSI circuits, Graph partitioning problem, Lagrangian lower bounds, Graph theory
Citation
Published Version (Please cite this version)