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Robust Optimization for the Two-Dimensional Strip-Packing Problem with Variable-Sized Bins

Author

Listed:
  • Kaiyuan Liu

    (Department of Logistics and Transportation, Shenzhen International Graduate School, Tsinghua University, Shenzhen 518055, China
    These authors contributed equally to this work.)

  • Hongyu Zhang

    (Department of Logistics and Transportation, Shenzhen International Graduate School, Tsinghua University, Shenzhen 518055, China
    These authors contributed equally to this work.)

  • Chong Wang

    (Department of Logistics and Transportation, Shenzhen International Graduate School, Tsinghua University, Shenzhen 518055, China)

  • Hui Li

    (Shenzhen Institute of Artificial Intelligence and Robotics for Society, Chinese University of Hong Kong, Shenzhen 518172, China)

  • Yongquan Chen

    (Shenzhen Institute of Artificial Intelligence and Robotics for Society, Chinese University of Hong Kong, Shenzhen 518172, China)

  • Qiong Chen

    (Navigation College, Jimei University, Xiamen 361021, China)

Abstract

The two-dimensional strip-packing problem (2D-SPP) emerges as a notable variant of the cutting and packing (C&P) problem, aiming to optimize the arrangement of small rectangular items within unique strips with a fixed width and infinite height to minimize the usage of height. Despite extensive academic exploration, applying 2D-SPP solutions in industrial settings remains challenging. Two significant issues, often overlooked in academia yet frequently encountered in industrial contexts, are the uncertain demand for items, exacerbated by the bullwhip effect, and the need for diverse types of strips to cater to varying customer needs. Our paper addresses this academia–industry gap by proposing a robust optimization model for the uncertain 2D-SPP with variable-sized bins, aiming to manage the demand fluctuations within a box uncertainty set framework. Additionally, we employ the contiguous one-dimensional relaxation technique in conjunction with column generation to tighten the lower bound of the problem, thereby augmenting solution accuracy. Furthermore, we leverage the Karush–Kuhn–Tucker (KKT) condition to transform the model into a more tractable form, subsequently leading to an exact solution. Based on datasets from a real-life plastic-cutting company, comprehensive experiments validate the effectiveness and efficiency of our proposed relaxation method and algorithm, showcasing the potential for an improved industrial application of 2D-SPP solutions.

Suggested Citation

  • Kaiyuan Liu & Hongyu Zhang & Chong Wang & Hui Li & Yongquan Chen & Qiong Chen, 2023. "Robust Optimization for the Two-Dimensional Strip-Packing Problem with Variable-Sized Bins," Mathematics, MDPI, vol. 11(23), pages 1-22, November.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:23:p:4781-:d:1288569
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    References listed on IDEAS

    as
    1. Nicos Christofides & Charles Whitlock, 1977. "An Algorithm for Two-Dimensional Cutting Problems," Operations Research, INFORMS, vol. 25(1), pages 30-44, February.
    2. Yu, Guosong & Mao, Yanling & Xiao, Jiaoliao, 2016. "A new lower bound for online strip packing," European Journal of Operational Research, Elsevier, vol. 250(3), pages 754-759.
    3. Leung, Stephen C.H. & Zhang, Defu & Sim, Kwang Mong, 2011. "A two-stage intelligent search algorithm for the two-dimensional strip packing problem," European Journal of Operational Research, Elsevier, vol. 215(1), pages 57-69, November.
    4. Puchinger, Jakob & Raidl, Gunther R., 2007. "Models and algorithms for three-stage two-dimensional bin packing," European Journal of Operational Research, Elsevier, vol. 183(3), pages 1304-1327, December.
    5. David Pisinger & Mikkel Sigurd, 2007. "Using Decomposition Techniques and Constraint Programming for Solving the Two-Dimensional Bin-Packing Problem," INFORMS Journal on Computing, INFORMS, vol. 19(1), pages 36-51, February.
    6. 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.
    7. Marco Antonio Boschetti & Lorenza Montaletti, 2010. "An Exact Algorithm for the Two-Dimensional Strip-Packing Problem," Operations Research, INFORMS, vol. 58(6), pages 1774-1791, December.
    8. Belov, G. & Scheithauer, G., 2006. "A branch-and-cut-and-price algorithm for one-dimensional stock cutting and two-dimensional two-stage cutting," European Journal of Operational Research, Elsevier, vol. 171(1), pages 85-106, May.
    9. E. K. Burke & G. Kendall & G. Whitwell, 2004. "A New Placement Heuristic for the Orthogonal Stock-Cutting Problem," Operations Research, INFORMS, vol. 52(4), pages 655-671, August.
    10. P. C. Gilmore & R. E. Gomory, 1965. "Multistage Cutting Stock Problems of Two and More Dimensions," Operations Research, INFORMS, vol. 13(1), pages 94-120, February.
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