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Optimization Method for Guillotine Packing of Rectangular Items within an Irregular and Defective Slate

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  • Kaizhi Chen

    (Department of Mathematics and Computer Science, Fuzhou University, Fuzhou 350100, China
    Network System Information Security Fujian Provincial University Key Laboratory, Fuzhou University, Fuzhou 350108, China)

  • Jiahao Zhuang

    (Department of Mathematics and Computer Science, Fuzhou University, Fuzhou 350100, China
    Network System Information Security Fujian Provincial University Key Laboratory, Fuzhou University, Fuzhou 350108, China)

  • Shangping Zhong

    (Department of Mathematics and Computer Science, Fuzhou University, Fuzhou 350100, China
    Network System Information Security Fujian Provincial University Key Laboratory, Fuzhou University, Fuzhou 350108, China)

  • Song Zheng

    (College of Electrical Engineering and Automation Fuzhou University, Fuzhou University, Fuzhou 350108, China
    Key Laboratory of Industrial Automation Control Technology and Information Processing, Fuzhou University, Fuzhou 350108, China)

Abstract

Research on the rectangle packing problems has mainly focused on rectangular raw material sheets without defects, while natural slate has irregular and defective characteristics, and the existing packing method adopts manual packing, which wastes material and is inefficient. In this work, we propose an effective packing optimization method for nature slate; to the best of our knowledge, this is the first attempt to solve the guillotine packing problem of rectangular items in a single irregular and defective slate. This method is modeled by the permutation model, uses the horizontal level (HL) heuristic proposed in this paper to obtain feasible solutions, and then applies the genetic algorithm to optimize the quality of solutions further. The HL heuristic is constructed on the basis of computational geometry and level packing. This heuristic aims to divide the irregular plate into multiple subplates horizontally, calculates the movable positions of the rectangle in the subplates, determines whether or not the rectangle can be packed in the movable positions through computational geometry, and fills the scraps appropriately. Theoretical analysis confirms that the rectangles obtained through the HL heuristic are inside the plate and do not overlap with the defects. In addition, the packed rectangles do not overlap each other and satisfy the guillotine constraint. Accordingly, the packing problem can be solved. Experiments on irregular slates with defects show that the slate utilization through our method is between 89% and 95%. This result is better than manual packing and can satisfy actual production requirements.

Suggested Citation

  • Kaizhi Chen & Jiahao Zhuang & Shangping Zhong & Song Zheng, 2020. "Optimization Method for Guillotine Packing of Rectangular Items within an Irregular and Defective Slate," Mathematics, MDPI, vol. 8(11), pages 1-16, November.
  • Handle: RePEc:gam:jmathe:v:8:y:2020:i:11:p:1914-:d:438603
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    References listed on IDEAS

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    1. Chen, Chin-Sheng & Sarin, Sanjiv & Ram, Balasubramanian, 1993. "A mixed-integer programming model for a class of assortment problems," European Journal of Operational Research, Elsevier, vol. 65(3), pages 362-367, March.
    2. Andrea Lodi & Silvano Martello & Daniele Vigo, 1999. "Heuristic and Metaheuristic Approaches for a Class of Two-Dimensional Bin Packing Problems," INFORMS Journal on Computing, INFORMS, vol. 11(4), pages 345-357, November.
    3. Lodi, Andrea & Martello, Silvano & Vigo, Daniele, 1999. "Approximation algorithms for the oriented two-dimensional bin packing problem," European Journal of Operational Research, Elsevier, vol. 112(1), pages 158-166, January.
    4. Bortfeldt, Andreas, 2006. "A genetic algorithm for the two-dimensional strip packing problem with rectangular pieces," European Journal of Operational Research, Elsevier, vol. 172(3), pages 814-837, August.
    5. J. E. Beasley, 1985. "An Exact Two-Dimensional Non-Guillotine Cutting Tree Search Procedure," Operations Research, INFORMS, vol. 33(1), pages 49-64, February.
    6. Silvano Martello & David Pisinger & Daniele Vigo, 2000. "The Three-Dimensional Bin Packing Problem," Operations Research, INFORMS, vol. 48(2), pages 256-267, April.
    7. Silvano Martello & Michele Monaci & Daniele Vigo, 2003. "An Exact Approach to the Strip-Packing Problem," INFORMS Journal on Computing, INFORMS, vol. 15(3), pages 310-319, August.
    8. Jakobs, Stefan, 1996. "On genetic algorithms for the packing of polygons," European Journal of Operational Research, Elsevier, vol. 88(1), pages 165-181, January.
    9. Fabio Furini & Enrico Malaguti & Dimitri Thomopulos, 2016. "Modeling Two-Dimensional Guillotine Cutting Problems via Integer Programming," INFORMS Journal on Computing, INFORMS, vol. 28(4), pages 736-751, November.
    10. Lodi, Andrea & Martello, Silvano & Monaci, Michele, 2002. "Two-dimensional packing problems: A survey," European Journal of Operational Research, Elsevier, vol. 141(2), pages 241-252, September.
    11. Guntram Scheithauer, 2018. "Introduction to Cutting and Packing Optimization," International Series in Operations Research and Management Science, Springer, number 978-3-319-64403-5, April.
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