One-Dimensional Cutting Stock Problem with Cartesian Coordinate Points

Niluka Rodrigo; Sium Shashikala

doi:doi:10.11648/j.ijssam.20170205.14

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One-Dimensional Cutting Stock Problem with Cartesian Coordinate Points

Niluka Rodrigo, Sium Shashikala

Published in International Journal of Systems Science and Applied Mathematics (Volume 2, Issue 5)

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.

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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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TY - JOUR
T1 - One-Dimensional Cutting Stock Problem with Cartesian Coordinate Points
AU - Niluka Rodrigo
AU - Sium Shashikala
Y1 - 2017/10/24
PY - 2017
N1 - https://doi.org/10.11648/j.ijssam.20170205.14
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
SP - 99
EP - 104
PB - Science Publishing Group
SN - 2575-5803
UR - https://doi.org/10.11648/j.ijssam.20170205.14
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
IS - 5
ER -

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Author Information

Niluka Rodrigo

Department of Mathematics, University of Peradeniya, Peradeniya, Sri Lanka
Sium Shashikala

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

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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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