A comparative study of exact methods for the bi-objective integer one-dimensional cutting stock problem

Abstract

This article addresses the bi-objective integer cutting stock problem in one dimension. This problem has great importance and use in various industries, including steel mills. The bi-objective model considered aims to minimize the frequency of cutting patterns to meet the minimum demand for each item requested and the number of different cutting patterns to be used, being these conflicting objectives. In this study, we apply three classic methods of scalarization: weighted sum, Chebyshev metric and \(\varepsilon \)-Constraint. This last method is developed to obtain all of the efficient solutions. Also, we propose and test a fourth method, modifying the Chebyshev metric, without the insertion of additional variables in the formulation of the sub-problems. The computational experiments with randomly generated real size instances illustrate and attest the suitability of the bi-objective model for this problem, as well as the applicability of all the proposed exact algorithms, thus showing that they are useful tools for decision makers in this area. Moreover, the modified metric method improved with respect to the performance of the classical version in the tests.

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Notes

  1. 1.

    For \(p=m\) and \(2 \cdot m\) there are many computational times close to zero, which would hinder the analyzis.

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Acknowledgements

The authors thank the reviewers, for the valuable suggestions to improve the article, and the Institute of Mathematics, Statistics and Computing Science, at UNICAMP Brazil, and FAPESP—Grants 2013/06035-0 and 2014/22665-7—for funding this research. This research was also supported by Portuguese funding from Fundação para a Ciência e a Tecnologia, under project UID/MAT/04561/2013. We want to thank Espaço da Escrita—Coordenadoria Geral da Universidade, UNICAMP—for the language services provided.

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Correspondence to Angelo Aliano Filho.

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Filho, A.A., Moretti, A.C. & Pato, M.V. A comparative study of exact methods for the bi-objective integer one-dimensional cutting stock problem. J Oper Res Soc (2017). https://doi.org/10.1057/s41274-017-0214-7

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Keywords

  • multi-objective optimization
  • multi-objective classical methods
  • one-dimensional cutting stock problem