Balance constraints reduction of large-scale linear programming problems

Balance constraints reduction of large-scale linear programming problems

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Article ID: iaor19941122
Country: Switzerland
Volume: 43
Issue: 1/4
Start Page Number: 149
End Page Number: 170
Publication Date: Oct 1993
Journal: Annals of Operations Research
Authors:
Abstract:

This paper describes a method and the corresponding algorithms for simplification of large-scale linear programming models. It consists of the elimination of the balance constraints (i.e. constraints with zero RHS term). The idea is to apply some linear transformations to the original problem in order to nullify the balance constraints. These transformations are able to simultaneously eliminate more balance rows. The core of this contribution is the introduction of the reduction matrix and the associated theorems on the equivalent linear programs (original and reduced). The numerical experiments with this method of simplification proved this approach to be beneficial for a large class of LP problems.

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