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A note on “Reducing the number of binary variables in cutting stock problems”

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Abstract

This study proposes a deterministic model to solve the two-dimensional cutting stock problem (2DCSP) using a much smaller number of binary variables and thereby reducing the complexity of 2DCSP. Expressing a 2DCSP with \(m\) stocks and \(n\) cutting rectangles requires \(2n^{2}+n(m+1)\) binary variables in the traditional model. In contrast, the proposed model uses \(n^{2}+n\lceil {\log _2 m}\rceil \) binary variables to express the 2DCSP. Experimental results showed that the proposed model is more efficient than the existing model.

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Acknowledgments

The authors would like to thank the editor and anonymous referee for providing most valuable comments for us to improve the quality of this manuscript. This research was supported by the project granted by ROC NSC 99-2221-E-030-005- and NSC 100-2221-E-030 -009-.

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Authors and Affiliations

  1. Department of Information Management, College of Management, Fu Jen Catholic University, No.510, Jhongjheng Road, Sinjhuang City, Taipei County, 242, Taiwan

    Hao-Chun Lu

  2. Department of Information Management, Chung Hua University, 707, Sec.2, WuFu Road, Hsinchu, 300, Taiwan

    Yu-Chien Ko

  3. Institute of Information Management, National Chiao Tung University, Management Building 2, 1001 Ta-Hsueh Road, Hsinchu, 300, Taiwan, ROC

    Yao-Huei Huang

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  1. Hao-Chun Lu
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Correspondence to Yao-Huei Huang.

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Lu, HC., Ko, YC. & Huang, YH. A note on “Reducing the number of binary variables in cutting stock problems”. Optim Lett 8, 569–579 (2014). https://doi.org/10.1007/s11590-012-0598-x

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