One-Dimensional Cutting Stock Problem with Cartesian Coordinate Points
International Journal of Systems Science and Applied Mathematics
Volume 2, Issue 5, September 2017, Pages: 99-104
Received: Sep. 29, 2016;
Accepted: Dec. 22, 2016;
Published: Oct. 24, 2017
Views 3185 Downloads 117
Niluka Rodrigo, Department of Mathematics, University of Peradeniya, Peradeniya, Sri Lanka
Sium Shashikala, Department of Mathematics, University of Peradeniya, Peradeniya, Sri Lanka
Follow on us
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.
One-Dimensional CSP, Brach and Bound Algorithm, Matlab Software, Cartesian Coordinate Points
To cite this article
One-Dimensional Cutting Stock Problem with Cartesian Coordinate Points, International Journal of Systems Science and Applied Mathematics.
Vol. 2, No. 5,
2017, pp. 99-104.
Copyright © 2017 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/
) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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.
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.
R. Morbito and V. Garcia, “A Cutting Stock Problemin Hardboard Industry- Case Study”, Computer Operations Research, Vol. 25, No. 6 (1997), 469-485.
Saad M. A. Suliman, “Pattern Generating Procedure for the Cutting Stock Problem”, International Journal of Production Economics 74(2001) 293-301.
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.
JakobPuchinger, Gunther R. Raidl and Gabriele Koller, “Solving a Real-World Glass Cutting Problem”.
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.
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.
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.
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.