Efficient reorder on the basic columns in programming batches and cuts

Efficient reorder on the basic columns in programming batches and cuts

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Article ID: iaor20084483
Country: Brazil
Volume: 24
Issue: 2
Start Page Number: 323
End Page Number: 337
Publication Date: May 2004
Journal: Pesquisa Operacional
Authors: ,
Keywords: inventory, programming: linear
Abstract:

In this work the combined problem is considered, which solves simultaneously the lot sizing and the cutting stock problems. We study some properties of the matrix of constraints and how to factorize the base without losing sparsity in the simplex method context, by a static reordering of the basic columns. Numerical results simulating simplex iterations and verify the sparsity of the factorizations are presented. Numerical experiments had also proven the robustness of this strategy. We conclude that the approach of constructing of the static sparse base reordering leads to very good computational results for both: speed and robustness, in comparison with approaches which do not consider the sparse structure of the matrix of constraints.

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