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A Practical Application of the Generalized Cutting Stock Algorithm

Author

Listed:
  • W. D. D. Madhavee

    (Department of Mathematics, University of Colombo, Colombo 3, Sri Lanka)

  • N. Saldin

    (Department of Mathematics, University of Colombo, Colombo 3, Sri Lanka)

  • U. C. Vaidyarathna

    (Department of Mathematics, University of Colombo, Colombo 3, Sri Lanka)

  • C. J. Jayawardene

    (Department of Mathematics, University of Colombo, Colombo 3, Sri Lanka)

Abstract

A watered-down version of the cutting stock algorithm has existed for a few centuries before the industrial revolution but no real formulation or solution to the problem was known other than for a few heuristic algorithms used under specific cases pertaining to the logging industry. The first formulations and solutions of the cutting stock problem was published about 6 decades ago by Gilmore and Gomory in the Operation research journal [1]. In that, they have explained the concept by using crude optimization techniques which are not applicable to most conditions found in the contemporary business environment. Our research project involves cut-ting wooden sheets and wooden rods of specific dimensions based on the requirements of the customers of Moratuwa Timber Work (MTW). The main focus of this paper is to find the optimal cutting patterns by minimizing the wastage and the trim loss. This is achieved with the aid of a web enabled database, using Java codes and Lingo programs.

Suggested Citation

  • W. D. D. Madhavee & N. Saldin & U. C. Vaidyarathna & C. J. Jayawardene, 2018. "A Practical Application of the Generalized Cutting Stock Algorithm," Academic Journal of Applied Mathematical Sciences, Academic Research Publishing Group, vol. 4(3), pages 15-21, 03-2018.
    • Handle: RePEc:arp:ajoams:2018:p:15-21
    DOI: arpgweb.com/?ic=journal&journal=17&info=aims
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    References listed on IDEAS

    as
    1. J. E. Beasley, 1985. "An Exact Two-Dimensional Non-Guillotine Cutting Tree Search Procedure," Operations Research, INFORMS, vol. 33(1), pages 49-64, February.
    2. P. C. Gilmore & R. E. Gomory, 1961. "A Linear Programming Approach to the Cutting-Stock Problem," Operations Research, INFORMS, vol. 9(6), pages 849-859, December.
    3. Lodi, Andrea & Martello, Silvano & Monaci, Michele, 2002. "Two-dimensional packing problems: A survey," European Journal of Operational Research, Elsevier, vol. 141(2), pages 241-252, September.
    4. P. C. Gilmore & R. E. Gomory, 1963. "A Linear Programming Approach to the Cutting Stock Problem---Part II," Operations Research, INFORMS, vol. 11(6), pages 863-888, December.
    5. Cintra, G.F. & Miyazawa, F.K. & Wakabayashi, Y. & Xavier, E.C., 2008. "Algorithms for two-dimensional cutting stock and strip packing problems using dynamic programming and column generation," European Journal of Operational Research, Elsevier, vol. 191(1), pages 61-85, November.
    6. A. H. G. Rinnooy Kan & J. R. De Wit & R. Th. Wijmenga, 1987. "Nonorthogonal Two-Dimensional Cutting Patterns," Management Science, INFORMS, vol. 33(5), pages 670-684, May.
    7. P. C. Gilmore & R. E. Gomory, 1965. "Multistage Cutting Stock Problems of Two and More Dimensions," Operations Research, INFORMS, vol. 13(1), pages 94-120, February.
    8. Haessler, Robert W. & Sweeney, Paul E., 1991. "Cutting stock problems and solution procedures," European Journal of Operational Research, Elsevier, vol. 54(2), pages 141-150, September.
    9. Vahrenkamp, Richard, 1996. "Random search in the one-dimensional cutting stock problem," European Journal of Operational Research, Elsevier, vol. 95(1), pages 191-200, November.
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