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On the cutting stock problem under stochastic demand

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  • Douglas Alem
  • Pedro Munari
  • Marcos Arenales
  • Paulo Ferreira

Abstract

This paper addresses the one-dimensional cutting stock problem when demand is a random variable. The problem is formulated as a two-stage stochastic nonlinear program with recourse. The first stage decision variables are the number of objects to be cut according to a cutting pattern. The second stage decision variables are the number of holding or backordering items due to the decisions made in the first stage. The problem’s objective is to minimize the total expected cost incurred in both stages, due to waste and holding or backordering penalties. A Simplex-based method with column generation is proposed for solving a linear relaxation of the resulting optimization problem. The proposed method is evaluated by using two well-known measures of uncertainty effects in stochastic programming: the value of stochastic solution—VSS—and the expected value of perfect information—EVPI. The optimal two-stage solution is shown to be more effective than the alternative wait-and-see and expected value approaches, even under small variations in the parameters of the problem. Copyright Springer Science+Business Media, LLC 2010

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  • 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.
    • Handle: RePEc:spr:annopr:v:179:y:2010:i:1:p:169-186:10.1007/s10479-008-0454-7
    DOI: 10.1007/s10479-008-0454-7
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    References listed on IDEAS

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    Cited by:

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    2. 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.
    3. Schepler, Xavier & Rossi, André & Gurevsky, Evgeny & Dolgui, Alexandre, 2022. "Solving robust bin-packing problems with a branch-and-price approach," European Journal of Operational Research, Elsevier, vol. 297(3), pages 831-843.
    4. Alysson Costa & Lana Santos & Douglas Alem & Ricardo Santos, 2014. "Sustainable vegetable crop supply problem with perishable stocks," Annals of Operations Research, Springer, vol. 219(1), pages 265-283, August.
    5. Kallrath, Julia & Rebennack, Steffen & Kallrath, Josef & Kusche, Rüdiger, 2014. "Solving real-world cutting stock-problems in the paper industry: Mathematical approaches, experience and challenges," European Journal of Operational Research, Elsevier, vol. 238(1), pages 374-389.
    6. 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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