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Heuristic for the rectangular two-dimensional single stock size cutting stock problem with two-staged patterns

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  • Cui, Yaodong
  • Zhao, Zhigang

Abstract

Two-staged patterns are often used in manufacturing industries to divide stock plates into rectangular items. A heuristic algorithm is presented to solve the rectangular two-dimensional single stock size cutting stock problem with two-staged patterns. It uses the column-generation method to solve the residual problems repeatedly, until the demands of all items are satisfied. Each pattern is generated using a procedure for the constrained single large object placement problem to guarantee the convergence of the algorithm. The computational results of benchmark and practical instances indicate the following: (1) the algorithm can solve most instances to optimality, with the gap to optimality being at most one plate for those solutions whose optimality is not proven and (2) for the instances tested, the algorithm is more efficient (on average) in reducing the number of plates used than a published algorithm and a commercial stock cutting software package.

Suggested Citation

  • Cui, Yaodong & Zhao, Zhigang, 2013. "Heuristic for the rectangular two-dimensional single stock size cutting stock problem with two-staged patterns," European Journal of Operational Research, Elsevier, vol. 231(2), pages 288-298.
    • Handle: RePEc:eee:ejores:v:231:y:2013:i:2:p:288-298
    DOI: 10.1016/j.ejor.2013.05.042
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    References listed on IDEAS

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    4. Cui, Yaodong & Huang, Baixiong, 2012. "Reducing the number of cuts in generating three-staged cutting patterns," European Journal of Operational Research, Elsevier, vol. 218(2), pages 358-365.
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    Cited by:

    1. Iori, Manuel & de Lima, Vinícius L. & Martello, Silvano & Miyazawa, Flávio K. & Monaci, Michele, 2021. "Exact solution techniques for two-dimensional cutting and packing," European Journal of Operational Research, Elsevier, vol. 289(2), pages 399-415.
    2. 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.
    3. Yi-Ping Cui & Yongwu Zhou & Yaodong Cui, 2017. "Triple-solution approach for the strip packing problem with two-staged patterns," Journal of Combinatorial Optimization, Springer, vol. 34(2), pages 588-604, August.

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