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A tutorial in irregular shape packing problems

Author

Listed:
  • J A Bennell

    (University of Southampton)

  • J F Oliveira

    (Universidade do Porto)

Abstract

Cutting and packing problems have been a core area of research for many decades. Irregular shape packing is one of the most recent variants to be widely researched and its history extends over 40 years. The evolution of solution approaches to this problem can be attributed to increased computer power and advances in geometric techniques as well as more sophisticated and insightful algorithm design. In this paper we will focus on the latter. Our aim is not to give a chronological account or an exhaustive review, but to draw on the literature to describe and evaluate the core approaches. Irregular packing is combinatorial and as a result solution methods are heuristic, save a few notable exceptions. We will explore different ways of representing the problem and mechanisms for moving between solutions. We will also propose where we see the future challenges for researchers in this area.

Suggested Citation

  • 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.
    • Handle: RePEc:pal:jorsoc:v:60:y:2009:i:1:d:10.1057_jors.2008.169
    DOI: 10.1057/jors.2008.169
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    References listed on IDEAS

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    1. 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.
    2. Egeblad, Jens & Nielsen, Benny K. & Odgaard, Allan, 2007. "Fast neighborhood search for two- and three-dimensional nesting problems," European Journal of Operational Research, Elsevier, vol. 183(3), pages 1249-1266, December.
    3. Jakobs, Stefan, 1996. "On genetic algorithms for the packing of polygons," European Journal of Operational Research, Elsevier, vol. 88(1), pages 165-181, January.
    4. Stoyan, Yu. G. & Novozhilova, M. V. & Kartashov, A. V., 1996. "Mathematical model and method of searching for a local extremum for the non-convex oriented polygons allocation problem," European Journal of Operational Research, Elsevier, vol. 92(1), pages 193-210, July.
    5. Dyckhoff, Harald, 1990. "A typology of cutting and packing problems," European Journal of Operational Research, Elsevier, vol. 44(2), pages 145-159, January.
    6. Gomes, A. Miguel & Oliveira, Jose F., 2006. "Solving Irregular Strip Packing problems by hybridising simulated annealing and linear programming," European Journal of Operational Research, Elsevier, vol. 171(3), pages 811-829, June.
    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. Edmund Burke & Robert Hellier & Graham Kendall & Glenn Whitwell, 2006. "A New Bottom-Left-Fill Heuristic Algorithm for the Two-Dimensional Irregular Packing Problem," Operations Research, INFORMS, vol. 54(3), pages 587-601, June.
    9. Dowsland, Kathryn A. & Vaid, Subodh & Dowsland, William B., 2002. "An algorithm for polygon placement using a bottom-left strategy," European Journal of Operational Research, Elsevier, vol. 141(2), pages 371-381, September.
    10. Burke, E.K. & Hellier, R.S.R. & Kendall, G. & Whitwell, G., 2007. "Complete and robust no-fit polygon generation for the irregular stock cutting problem," European Journal of Operational Research, Elsevier, vol. 179(1), pages 27-49, May.
    11. Gomes, A. Miguel & Oliveira, Jose F., 2002. "A 2-exchange heuristic for nesting problems," European Journal of Operational Research, Elsevier, vol. 141(2), pages 359-370, September.
    12. Julia A. Bennell & Kathryn A. Dowsland, 2001. "Hybridising Tabu Search with Optimisation Techniques for Irregular Stock Cutting," Management Science, INFORMS, vol. 47(8), pages 1160-1172, August.
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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. Sato, André Kubagawa & Martins, Thiago Castro & Gomes, Antonio Miguel & Tsuzuki, Marcos Sales Guerra, 2019. "Raster penetration map applied to the irregular packing problem," European Journal of Operational Research, Elsevier, vol. 279(2), pages 657-671.
    3. Nascimento, Paulo Jorge & Silva, Cristóvão & Antunes, Carlos Henggeler & Moniz, Samuel, 2024. "Optimal decomposition approach for solving large nesting and scheduling problems of additive manufacturing systems," European Journal of Operational Research, Elsevier, vol. 317(1), pages 92-110.
    4. 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.
    5. Umetani, Shunji & Murakami, Shohei, 2022. "Coordinate descent heuristics for the irregular strip packing problem of rasterized shapes," European Journal of Operational Research, Elsevier, vol. 303(3), pages 1009-1026.
    6. Josef Kallrath & Tatiana Romanova & Alexander Pankratov & Igor Litvinchev & Luis Infante, 2023. "Packing convex polygons in minimum-perimeter convex hulls," Journal of Global Optimization, Springer, vol. 85(1), pages 39-59, January.
    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. Jie Fang & Yunqing Rao & Xusheng Zhao & Bing Du, 2023. "A Hybrid Reinforcement Learning Algorithm for 2D Irregular Packing Problems," Mathematics, MDPI, vol. 11(2), pages 1-17, January.
    9. 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.
    10. 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).
    11. Kimms, Alf & Király, Hédi, 2023. "An extended model formulation for the two-dimensional irregular strip packing problem considering general industry-relevant aspects," European Journal of Operational Research, Elsevier, vol. 306(3), pages 1202-1218.
    12. 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.
    13. Toledo, Franklina M.B. & Carravilla, Maria Antónia & Ribeiro, Cristina & Oliveira, José F. & Gomes, A. Miguel, 2013. "The Dotted-Board Model: A new MIP model for nesting irregular shapes," International Journal of Production Economics, Elsevier, vol. 145(2), pages 478-487.
    14. 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.
    15. Lastra-Díaz, Juan J. & Ortuño, M. Teresa, 2024. "Mixed-integer programming models for irregular strip packing based on vertical slices and feasibility cuts," European Journal of Operational Research, Elsevier, vol. 313(1), pages 69-91.
    16. Silva, Allyson & Coelho, Leandro C. & Darvish, Maryam & Renaud, Jacques, 2022. "A cutting plane method and a parallel algorithm for packing rectangles in a circular container," European Journal of Operational Research, Elsevier, vol. 303(1), pages 114-128.
    17. Cherri, Luiz Henrique & Carravilla, Maria Antónia & Ribeiro, Cristina & Toledo, Franklina Maria Bragion, 2019. "Optimality in nesting problems: New constraint programming models and a new global constraint for non-overlap," Operations Research Perspectives, Elsevier, vol. 6(C).
    18. Donald Jones, 2014. "A fully general, exact algorithm for nesting irregular shapes," Journal of Global Optimization, Springer, vol. 59(2), pages 367-404, July.
    19. Elkeran, Ahmed, 2013. "A new approach for sheet nesting problem using guided cuckoo search and pairwise clustering," European Journal of Operational Research, Elsevier, vol. 231(3), pages 757-769.

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