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Matheuristics for the irregular bin packing problem with free rotations

Author

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  • Martinez-Sykora, A.
  • Alvarez-Valdes, R.
  • Bennell, J.A.
  • Ruiz, R.
  • Tamarit, J.M.

Abstract

We present a number of variants of a constructive algorithm able to solve a wide variety of variants of the Two-Dimensional Irregular Bin Packing Problem (2DIBPP). The aim of the 2DIBPP is to pack a set of irregular pieces, which may have concavities, into stock sheets (bins) with fixed dimensions in such a way that the utilization is maximized. This problem is inspired by a real application from a ceramic company in Spain. In addition, this problem arises in other industries such as the garment industry or ship building. The constructive procedure presented in this paper allows both free orientation for the pieces, as in the case of the ceramic industry, or a finite set of orientations as in the case of the garment industry. We explicitly model the assignment of pieces to bins and compare with the more common strategy of packing bins sequentially. There are very few papers in the literature that address the bin packing problem with irregular pieces and to our knowledge this is the first to additionally consider free rotation of pieces with bin packing. We propose several Integer Programing models to determine the association between pieces and bins and then we use a Mixed Integer Programing model for placing the pieces into the bins. The computational results show that the algorithm obtains high quality results in sets of instances with different properties. We have used both industry data and the available data in the literature of 2D irregular strip packing and bin packing problems.

Suggested Citation

  • Martinez-Sykora, A. & Alvarez-Valdes, R. & Bennell, J.A. & Ruiz, R. & Tamarit, J.M., 2017. "Matheuristics for the irregular bin packing problem with free rotations," European Journal of Operational Research, Elsevier, vol. 258(2), pages 440-455.
    • Handle: RePEc:eee:ejores:v:258:y:2017:i:2:p:440-455
    DOI: 10.1016/j.ejor.2016.09.043
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    References listed on IDEAS

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    1. H. Terashima-Marín & P. Ross & C. Farías-Zárate & E. López-Camacho & M. Valenzuela-Rendón, 2010. "Generalized hyper-heuristics for solving 2D Regular and Irregular Packing Problems," Annals of Operations Research, Springer, vol. 179(1), pages 369-392, September.
    2. Wascher, Gerhard & Hau[ss]ner, Heike & Schumann, Holger, 2007. "An improved typology of cutting and packing problems," European Journal of Operational Research, Elsevier, vol. 183(3), pages 1109-1130, December.
    3. Eunice López-Camacho & Gabriela Ochoa & Hugo Terashima-Marín & Edmund Burke, 2013. "An effective heuristic for the two-dimensional irregular bin packing problem," Annals of Operations Research, Springer, vol. 206(1), pages 241-264, July.
    4. Jakobs, Stefan, 1996. "On genetic algorithms for the packing of polygons," European Journal of Operational Research, Elsevier, vol. 88(1), pages 165-181, January.
    5. Alvarez-Valdes, R. & Martinez, A. & Tamarit, J.M., 2013. "A branch & bound algorithm for cutting and packing irregularly shaped pieces," International Journal of Production Economics, Elsevier, vol. 145(2), pages 463-477.
    6. J A Bennell & J F Oliveira, 2009. "A tutorial in irregular shape packing problems," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 60(1), pages 93-105, May.
    7. Bennell, Julia A. & Oliveira, Jose F., 2008. "The geometry of nesting problems: A tutorial," European Journal of Operational Research, Elsevier, vol. 184(2), pages 397-415, January.
    8. F. Parreño & R. Alvarez-Valdes & J. Oliveira & J. Tamarit, 2010. "A hybrid GRASP/VND algorithm for two- and three-dimensional bin packing," Annals of Operations Research, Springer, vol. 179(1), pages 203-220, September.
    9. Martinez-Sykora, Antonio & Alvarez-Valdes, Ramon & Bennell, Julia & Tamarit, Jose Manuel, 2015. "Constructive procedures to solve 2-dimensional bin packing problems with irregular pieces and guillotine cuts," Omega, Elsevier, vol. 52(C), pages 15-32.
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    Cited by:

    1. Parreño, F. & Alonso, M.T. & Alvarez-Valdes, R., 2020. "Solving a large cutting problem in the glass manufacturing industry," European Journal of Operational Research, Elsevier, vol. 287(1), pages 378-388.
    2. Parreño, F. & Alvarez-Valdes, R., 2021. "Mathematical models for a cutting problem in the glass manufacturing industry," Omega, Elsevier, vol. 103(C).
    3. Longhui Meng & Liang Ding & Ray Tahir Mushtaq & Saqib Anwar & Aqib Mashood Khan, 2024. "Efficient Packing of 2D Irregular Parts: A Hybrid Approach Incorporating a Modified Genetic Algorithm and Image Processing," Mathematics, MDPI, vol. 12(22), pages 1-21, November.
    4. Igor Kierkosz & Maciej Łuczak, 2019. "A one-pass heuristic for nesting problems," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 29(1), pages 37-60.
    5. Qiang Luo & Yunqing Rao, 2022. "Improved Sliding Algorithm for Generating No-Fit Polygon in the 2D Irregular Packing Problem," Mathematics, MDPI, vol. 10(16), pages 1-18, August.
    6. Germán Pantoja-Benavides & David Álvarez-Martínez & Francisco Parreño Torres, 2024. "The Normalized Direct Trigonometry Model for the Two-Dimensional Irregular Strip Packing Problem," Mathematics, MDPI, vol. 12(15), pages 1-25, August.
    7. Leao, Aline A.S. & Toledo, Franklina M.B. & Oliveira, José Fernando & Carravilla, Maria Antónia & Alvarez-Valdés, Ramón, 2020. "Irregular packing problems: A review of mathematical models," European Journal of Operational Research, Elsevier, vol. 282(3), pages 803-822.
    8. Yainier Labrada-Nueva & Martin H. Cruz-Rosales & Juan Manuel Rendón-Mancha & Rafael Rivera-López & Marta Lilia Eraña-Díaz & Marco Antonio Cruz-Chávez, 2021. "Overlap Detection in 2D Amorphous Shapes for Paper Optimization in Digital Printing Presses," Mathematics, MDPI, vol. 9(9), pages 1-22, May.
    9. Hu, Xiaoxuan & Zhu, Waiming & Ma, Huawei & An, Bo & Zhi, Yanling & Wu, Yi, 2021. "Orientational variable-length strip covering problem: A branch-and-price-based algorithm," European Journal of Operational Research, Elsevier, vol. 289(1), pages 254-269.
    10. Abraham, Gyula & Dosa, Gyorgy & Hvattum, Lars Magnus & Olaj, Tomas Attila & Tuza, Zsolt, 2023. "The board packing problem," European Journal of Operational Research, Elsevier, vol. 308(3), pages 1056-1073.
    11. Hagspihl, Thomas & Kolisch, Rainer & Fontaine, Pirmin & Schiffels, Sebastian, 2024. "Apron layout planning–Optimal positioning of aircraft stands," Transportation Research Part B: Methodological, Elsevier, vol. 179(C).
    12. Longhui Meng & Liang Ding & Aqib Mashood Khan & Ray Tahir Mushtaq & Mohammed Alkahtani, 2024. "Optimizing Two-Dimensional Irregular Pattern Packing with Advanced Overlap Optimization Techniques," Mathematics, MDPI, vol. 12(17), pages 1-19, August.
    13. Bennell, J.A. & Cabo, M. & Martínez-Sykora, A., 2018. "A beam search approach to solve the convex irregular bin packing problem with guillotine guts," European Journal of Operational Research, Elsevier, vol. 270(1), pages 89-102.
    14. Griffiths, Valeriya & Scanlan, James P. & Eres, Murat H. & Martinez-Sykora, Antonio & Chinchapatnam, Phani, 2019. "Cost-driven build orientation and bin packing of parts in Selective Laser Melting (SLM)," European Journal of Operational Research, Elsevier, vol. 273(1), pages 334-352.
    15. Jäck, Christian & Gönsch, Jochen, 2024. "How to load your auto carrier. A hybrid packing approach for the auto-carrier loading problem," European Journal of Operational Research, Elsevier, vol. 315(3), pages 1167-1181.
    16. Marco Ghirardi & Fabio Salassa, 2022. "A simple and effective algorithm for the maximum happy vertices problem," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(1), pages 181-193, April.

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