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A Stochastic Cutting Stock Procedure: Cutting Rolls of Insulating Tape

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  • D. Sculli

    (University of Hong Kong)

Abstract

This paper develops a one-dimensional cutting stock procedure which will minimize material wastage when a batch of small pieces are cut from several long pieces. The problem differs from the classical one-dimensional cutting stock problem in that the dimensions of the material to be cut are random variables due to fringe defects caused by the production process. Examples of such processes include the production of flat glass, laminated board, corrugated board, adhesive tape, carpeting, and insulating tape. The cutting procedure inevitably generates some material wastage and process delays caused by the need to set cutting knives in required positions. The approach followed in this paper is to minimize material wastage when cutting a batch of identical rolls of insulating tape from several long rolls with stationary cutting knives. An exact solution is presented for the case in which the variability of defects at both ends is independently distributed and the two distributions differ by a location parameter only. An approximate solution is also presented when the two end defect distributions differ by both scale and location parameters. The wastage resulting from the use of these procedures is then compared with the wastage generated when the positioning of the knives is altered every time an original piece is cut. This comparison enables management to decide when the positioning of the cutting knives should be fixed.

Suggested Citation

  • D. Sculli, 1981. "A Stochastic Cutting Stock Procedure: Cutting Rolls of Insulating Tape," Management Science, INFORMS, vol. 27(8), pages 946-952, August.
    • Handle: RePEc:inm:ormnsc:v:27:y:1981:i:8:p:946-952
    DOI: 10.1287/mnsc.27.8.946
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    Cited by:

    1. Douglas Alem & Pedro Munari & Marcos Arenales & Paulo Ferreira, 2010. "On the cutting stock problem under stochastic demand," Annals of Operations Research, Springer, vol. 179(1), pages 169-186, September.
    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. Cherri, Adriana Cristina & Cherri, Luiz Henrique & Oliveira, Beatriz Brito & Oliveira, José Fernando & Carravilla, Maria Antónia, 2023. "A stochastic programming approach to the cutting stock problem with usable leftovers," European Journal of Operational Research, Elsevier, vol. 308(1), pages 38-53.
    4. Beraldi, P. & Bruni, M.E. & Conforti, D., 2009. "The stochastic trim-loss problem," European Journal of Operational Research, Elsevier, vol. 197(1), pages 42-49, August.
    5. 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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