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Integrating two-dimensional cutting stock and lot-sizing problems

Author

Listed:
  • E Silva

    (Centro de Investigação Algoritmi da Universidade do Minho, Braga, Portugal)

  • F Alvelos

    (1] Centro de Investigação Algoritmi da Universidade do Minho, Braga, Portugal[2] Escola de Engenharia, Universidade do Minho, Braga, Portugal)

  • J M Valério de Carvalho

    (1] Centro de Investigação Algoritmi da Universidade do Minho, Braga, Portugal[2] Escola de Engenharia, Universidade do Minho, Braga, Portugal)

Abstract

The two-dimensional cutting stock problem (2DCSP) consists in the minimization of the number of plates used to cut a set of items. In industry, typically, an instance of this problem is considered at the beginning of each planning time period, what may result in solutions of poor quality, that is, excessive waste, when a set of planning periods is considered. To deal with this issue, we consider an integrated problem, in which the 2DCSP is extended from the solution in only a single production planning period to a solution in a set of production planning periods. The main difference of the approach in this work and the ones in the literature is to allow sufficiently large residual plates (leftovers) to be stored and cut in a subsequent period of the planning horizon, which may further help in the minimization of the waste. We propose two integrated integer programming models to optimize the combined two-dimensional cutting stock and lot-sizing problems, minimizing the total cost, which includes material, waste and storage costs. Two heuristics based on the industrial practice to solve the problem were also presented. Computational results for the proposed models and for the heuristics are presented and discussed.

Suggested Citation

  • E Silva & F Alvelos & J M Valério de Carvalho, 2014. "Integrating two-dimensional cutting stock and lot-sizing problems," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 65(1), pages 108-123, January.
    • Handle: RePEc:pal:jorsoc:v:65:y:2014:i:1:p:108-123
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    Citations

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    Cited by:

    1. Kelly Cristina Poldi & Silvio Alexandre Araujo, 2016. "Mathematical models and a heuristic method for the multiperiod one-dimensional cutting stock problem," Annals of Operations Research, Springer, vol. 238(1), pages 497-520, March.
    2. Amanda O. C. Ayres & Betania S. C. Campello & Washington A. Oliveira & Carla T. L. S. Ghidini, 2021. "A Bi-Integrated Model for coupling lot-sizing and cutting-stock problems," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 43(4), pages 1047-1076, December.
    3. Oliveira, Washington A. & Fiorotto, Diego J. & Song, Xiang & Jones, Dylan F., 2021. "An extended goal programming model for the multiobjective integrated lot-sizing and cutting stock problem," European Journal of Operational Research, Elsevier, vol. 295(3), pages 996-1007.
    4. Kelly Poldi & Silvio Araujo, 2016. "Mathematical models and a heuristic method for the multiperiod one-dimensional cutting stock problem," Annals of Operations Research, Springer, vol. 238(1), pages 497-520, March.
    5. Melega, Gislaine Mara & de Araujo, Silvio Alexandre & Jans, Raf, 2018. "Classification and literature review of integrated lot-sizing and cutting stock problems," European Journal of Operational Research, Elsevier, vol. 271(1), pages 1-19.
    6. Gislaine Mara Melega & Silvio Alexandre de Araujo & Reinaldo Morabito, 2020. "Mathematical model and solution approaches for integrated lot-sizing, scheduling and cutting stock problems," Annals of Operations Research, Springer, vol. 295(2), pages 695-736, December.

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