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One-Dimensional Cutting Stock Problem with Cartesian Coordinate Points

Received: 29 September 2016     Accepted: 22 December 2016     Published: 24 October 2017
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Abstract

The cutting stock problem is used in many industrial processes and recently has been considered as one of the most important research topics. It is basically describes in two ways, One –dimensional and Two-dimensional Cutting Stock Problems (CSP). An optimum cutting stock problem can be defined as cutting a main sheet into smaller pieces while minimizing the total wastage of the raw material or maximizing overall profit obtained by cutting smaller pieces from the main sheet. In this study, One-dimensional CSP is discussed. Modified Brach and Bound algorithm for One-dimensional cutting stock problem is coded and programmed in the Matlab programming environment to generate feasible cutting patterns. At the same time, Cartesian coordinate points are derived from the developed algorithm. In our approach, the case study is pertained to the real data used at L.H. Chandrasekara & Brothers (Pvt Ltd) in Sri Lanka for its production.

Published in International Journal of Systems Science and Applied Mathematics (Volume 2, Issue 5)
DOI 10.11648/j.ijssam.20170205.14
Page(s) 99-104
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2017. Published by Science Publishing Group

Keywords

One-Dimensional CSP, Brach and Bound Algorithm, Matlab Software, Cartesian Coordinate Points

References
[1] P. C. Gilmore and R. E. Gomary, “A Linear Programming Approach to the Cutting Stock Problem”, Operations Research, Vol. 9, No. 2 (1961), 849-859.
[2] P. C. Gilmore and R. E. Gomary, “A Linear Programming Approach to the Cutting Stock Problem – Part II”, Operations Research, Vol. 11, No. 6 (1963), 863-888.
[3] R. Morbito and V. Garcia, “A Cutting Stock Problemin Hardboard Industry- Case Study”, Computer Operations Research, Vol. 25, No. 6 (1997), 469-485.
[4] Saad M. A. Suliman, “Pattern Generating Procedure for the Cutting Stock Problem”, International Journal of Production Economics 74(2001) 293-301.
[5] G. Belov and G. Scheithauer, “A cutting plane algorithm for the one-dimensional cutting stock problem with multiple stock lengths”, European Journal of Operational Research 141 (2002) 274–29.
[6] JakobPuchinger, Gunther R. Raidl and Gabriele Koller, “Solving a Real-World Glass Cutting Problem”.
[7] L. Fern´andez, L. A. Fern´andez, C. Pola, “Integer Solutions to Cutting Stock Problems”, 2nd International Conference on Engineering Optimization, Sep 6-9, 2010.
[8] W. N. P Rodrigo, W. B Daundasekera and A. A. I Perera, “Pattern Generation for One-dimensional Cutting Stock Problem”, Peradeniya University Research Session (PURSE), 2011.
[9] W. N. P. Rodrigo, W. B. Daundasekera and A. A. I. Perera, “Modified Method for One-dimensional Cutting Stock Problem”, Science Publishing Group 2015;3(3); 12-17.
[10] W. N. P. Rodrigo, W. B. Daundasekera and A. A. I. Perera, “A Method for Two-Dimensional Cutting Stock Problem with Triangular Shape Items”, British Journal of Mathematics and Computer Science 2013;3(4);750-771.
Cite This Article
  • APA Style

    Niluka Rodrigo, Sium Shashikala. (2017). One-Dimensional Cutting Stock Problem with Cartesian Coordinate Points. International Journal of Systems Science and Applied Mathematics, 2(5), 99-104. https://doi.org/10.11648/j.ijssam.20170205.14

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    ACS Style

    Niluka Rodrigo; Sium Shashikala. One-Dimensional Cutting Stock Problem with Cartesian Coordinate Points. Int. J. Syst. Sci. Appl. Math. 2017, 2(5), 99-104. doi: 10.11648/j.ijssam.20170205.14

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    AMA Style

    Niluka Rodrigo, Sium Shashikala. One-Dimensional Cutting Stock Problem with Cartesian Coordinate Points. Int J Syst Sci Appl Math. 2017;2(5):99-104. doi: 10.11648/j.ijssam.20170205.14

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  • @article{10.11648/j.ijssam.20170205.14,
      author = {Niluka Rodrigo and Sium Shashikala},
      title = {One-Dimensional Cutting Stock Problem with Cartesian Coordinate Points},
      journal = {International Journal of Systems Science and Applied Mathematics},
      volume = {2},
      number = {5},
      pages = {99-104},
      doi = {10.11648/j.ijssam.20170205.14},
      url = {https://doi.org/10.11648/j.ijssam.20170205.14},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijssam.20170205.14},
      abstract = {The cutting stock problem is used in many industrial processes and recently has been considered as one of the most important research topics. It is basically describes in two ways, One –dimensional and Two-dimensional Cutting Stock Problems (CSP). An optimum cutting stock problem can be defined as cutting a main sheet into smaller pieces while minimizing the total wastage of the raw material or maximizing overall profit obtained by cutting smaller pieces from the main sheet. In this study, One-dimensional CSP is discussed. Modified Brach and Bound algorithm for One-dimensional cutting stock problem is coded and programmed in the Matlab programming environment to generate feasible cutting patterns. At the same time, Cartesian coordinate points are derived from the developed algorithm. In our approach, the case study is pertained to the real data used at L.H. Chandrasekara & Brothers (Pvt Ltd) in Sri Lanka for its production.},
     year = {2017}
    }
    

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    T1  - One-Dimensional Cutting Stock Problem with Cartesian Coordinate Points
    AU  - Niluka Rodrigo
    AU  - Sium Shashikala
    Y1  - 2017/10/24
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    DO  - 10.11648/j.ijssam.20170205.14
    T2  - International Journal of Systems Science and Applied Mathematics
    JF  - International Journal of Systems Science and Applied Mathematics
    JO  - International Journal of Systems Science and Applied Mathematics
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    AB  - The cutting stock problem is used in many industrial processes and recently has been considered as one of the most important research topics. It is basically describes in two ways, One –dimensional and Two-dimensional Cutting Stock Problems (CSP). An optimum cutting stock problem can be defined as cutting a main sheet into smaller pieces while minimizing the total wastage of the raw material or maximizing overall profit obtained by cutting smaller pieces from the main sheet. In this study, One-dimensional CSP is discussed. Modified Brach and Bound algorithm for One-dimensional cutting stock problem is coded and programmed in the Matlab programming environment to generate feasible cutting patterns. At the same time, Cartesian coordinate points are derived from the developed algorithm. In our approach, the case study is pertained to the real data used at L.H. Chandrasekara & Brothers (Pvt Ltd) in Sri Lanka for its production.
    VL  - 2
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    ER  - 

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Author Information
  • Department of Mathematics, University of Peradeniya, Peradeniya, Sri Lanka

  • Department of Mathematics, University of Peradeniya, Peradeniya, Sri Lanka

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