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On the Optimal Cutting of Defective Sheets

Author

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  • Susan G. Hahn

    (IBM Corporation, New York, New York)

Abstract

A method is developed for cutting up sheets with defective areas into given pieces while minimizing waste. The sheets, the pieces, and the defects are all rectangles, these latter to be identified by the coordinates of two opposite corners in a coordinate system attached to the sheet. The cutting is done in in three stages. If the length of the sheet is along the x -axis, the first cuts are made parallel to the y -axis, obtaining “sections.” The sections are then cut into “strips” parallel to the x -axis, and, finally, the strips into “pieces” parallel to the y -axis. The procedure uses dynamic programming, which requires a value to be attached to each size. The computer program senses the defects and fits pieces into the clear portion of the sheet in such a way that the total value is a maximum. In order to shorten machine time, some simplifying shortcuts are made.

Suggested Citation

  • Susan G. Hahn, 1968. "On the Optimal Cutting of Defective Sheets," Operations Research, INFORMS, vol. 16(6), pages 1100-1114, December.
    • Handle: RePEc:inm:oropre:v:16:y:1968:i:6:p:1100-1114
    DOI: 10.1287/opre.16.6.1100
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    Cited by:

    1. Felix Prause & Kai Hoppmann-Baum & Boris Defourny & Thorsten Koch, 2021. "The maximum diversity assortment selection problem," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 93(3), pages 521-554, June.
    2. Vasko, Francis J. & Newhart, Dennis D. & Stott, Kenneth Jr., 1999. "A hierarchical approach for one-dimensional cutting stock problems in the steel industry that maximizes yield and minimizes overgrading," European Journal of Operational Research, Elsevier, vol. 114(1), pages 72-82, April.
    3. Vera Neidlein & Andrèa C. G. Vianna & Marcos N. Arenales & Gerhard Wäscher, 2008. "The Two-Dimensional, Rectangular, Guillotineable-Layout Cutting Problem with a Single Defect," FEMM Working Papers 08035, Otto-von-Guericke University Magdeburg, Faculty of Economics and Management.
    4. Celia Glass & Jeroen Oostrum, 2010. "Bun splitting: a practical cutting stock problem," Annals of Operations Research, Springer, vol. 179(1), pages 15-33, September.
    5. Suliman, S.M.A., 2006. "A sequential heuristic procedure for the two-dimensional cutting-stock problem," International Journal of Production Economics, Elsevier, vol. 99(1-2), pages 177-185, February.
    6. Gonçalves, José Fernando & Wäscher, Gerhard, 2020. "A MIP model and a biased random-key genetic algorithm based approach for a two-dimensional cutting problem with defects," European Journal of Operational Research, Elsevier, vol. 286(3), pages 867-882.
    7. de Gelder, E.R. & Wagelmans, A.P.M., 2007. "The two-dimensional cutting stock problem within the roller blind production process," Econometric Institute Research Papers EI 2007-47, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    8. Claudio Arbib & Fabrizio Marinelli & Mustafa Ç. Pınar & Andrea Pizzuti, 2022. "Robust stock assortment and cutting under defects in automotive glass production," Production and Operations Management, Production and Operations Management Society, vol. 31(11), pages 4154-4172, November.

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