IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v8y2020i7p1130-d382786.html
   My bibliography  Save this article

Packing Oblique 3D Objects

Author

Listed:
  • Alexander Pankratov

    (Department of Mathematical Modeling and Optimal Design, Institute for Mechanical Engineering Problems of the National Academy of Sciences of Ukraine, 2/10, Pozharsky str., 61046 Kharkiv, Ukraine
    Department of Department of Systems Engineering of Kharkiv National University of Radio Electronics, Nauky Ave. 14, 61166 Kharkiv, Ukraine)

  • Tatiana Romanova

    (Department of Mathematical Modeling and Optimal Design, Institute for Mechanical Engineering Problems of the National Academy of Sciences of Ukraine, 2/10, Pozharsky str., 61046 Kharkiv, Ukraine
    Department of Department of Systems Engineering of Kharkiv National University of Radio Electronics, Nauky Ave. 14, 61166 Kharkiv, Ukraine)

  • Igor Litvinchev

    (Faculty of Mechanical and Electrical Engineering, Graduate Program in Systems Engineering, Nuevo Leon State University (UANL), 66450 Monterrey, Mexico)

Abstract

Packing irregular 3D objects in a cuboid of minimum volume is considered. Each object is composed of a number of convex shapes, such as oblique and right circular cylinders, cones and truncated cones. New analytical tools are introduced to state placement constraints for oblique shapes. Using the phi-function technique, optimized packing is reduced to a nonlinear programming problem. Novel solution approach is provided and illustrated by numerical examples.

Suggested Citation

  • Alexander Pankratov & Tatiana Romanova & Igor Litvinchev, 2020. "Packing Oblique 3D Objects," Mathematics, MDPI, vol. 8(7), pages 1-17, July.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:7:p:1130-:d:382786
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/8/7/1130/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/8/7/1130/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    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. 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.
    3. Giorgio Fasano, 2015. "A Modeling-Based Approach for Non-standard Packing Problems," Springer Optimization and Its Applications, in: Giorgio Fasano & János D. Pintér (ed.), Optimized Packings with Applications, edition 1, chapter 0, pages 67-85, Springer.
    4. Bortfeldt, Andreas & Wäscher, Gerhard, 2013. "Constraints in container loading – A state-of-the-art review," European Journal of Operational Research, Elsevier, vol. 229(1), pages 1-20.
    5. Hifi, Mhand & Yousef, Labib, 2019. "A local search-based method for sphere packing problems," European Journal of Operational Research, Elsevier, vol. 274(2), pages 482-500.
    6. Bortfeldt, Andreas & Gehring, Hermann, 2001. "A hybrid genetic algorithm for the container loading problem," European Journal of Operational Research, Elsevier, vol. 131(1), pages 143-161, May.
    7. Yuriy Stoyan & Alexandr Pankratov & Tatiana Romanova & Giorgio Fasano & János D. Pintér & Yurij E. Stoian & Andrey Chugay, 2019. "Optimized Packings in Space Engineering Applications: Part I," Springer Optimization and Its Applications, in: Giorgio Fasano & János D. Pintér (ed.), Modeling and Optimization in Space Engineering, pages 395-437, Springer.
    8. Yuriy Stoyan & Alexandr Pankratov & Tatiana Romanova, 2017. "Placement Problems for Irregular Objects: Mathematical Modeling, Optimization and Applications," Springer Optimization and Its Applications, in: Sergiy Butenko & Panos M. Pardalos & Volodymyr Shylo (ed.), Optimization Methods and Applications, pages 521-559, Springer.
    9. Yu. Stoyan & I. Grebennik & T. Romanova & A. Kovalenko, 2019. "Optimized Packings in Space Engineering Applications: Part II," Springer Optimization and Its Applications, in: Giorgio Fasano & János D. Pintér (ed.), Modeling and Optimization in Space Engineering, pages 439-457, Springer.
    10. A. S. Gogate & S. S. Pande, 2008. "Intelligent layout planning for rapid prototyping," International Journal of Production Research, Taylor & Francis Journals, vol. 46(20), pages 5607-5631, January.
    11. Romanova, T. & Bennell, J. & Stoyan, Y. & Pankratov, A., 2018. "Packing of concave polyhedra with continuous rotations using nonlinear optimisation," European Journal of Operational Research, Elsevier, vol. 268(1), pages 37-53.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Romanova, Tatiana & Stoyan, Yurij & Pankratov, Alexander & Litvinchev, Igor & Plankovskyy, Sergiy & Tsegelnyk, Yevgen & Shypul, Olga, 2021. "Sparsest balanced packing of irregular 3D objects in a cylindrical container," European Journal of Operational Research, Elsevier, vol. 291(1), pages 84-100.
    2. 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.
    3. Sheng, Liu & Hongxia, Zhao & Xisong, Dong & Changjian, Cheng, 2016. "A heuristic algorithm for container loading of pallets with infill boxes," European Journal of Operational Research, Elsevier, vol. 252(3), pages 728-736.
    4. Galrão Ramos, A. & Oliveira, José F. & Gonçalves, José F. & Lopes, Manuel P., 2016. "A container loading algorithm with static mechanical equilibrium stability constraints," Transportation Research Part B: Methodological, Elsevier, vol. 91(C), pages 565-581.
    5. Alonso, M.T. & Martinez-Sykora, A. & Alvarez-Valdes, R. & Parreño, F., 2022. "The pallet-loading vehicle routing problem with stability constraints," European Journal of Operational Research, Elsevier, vol. 302(3), pages 860-873.
    6. Alonso, M.T. & Alvarez-Valdes, R. & Iori, M. & Parreño, F. & Tamarit, J.M., 2017. "Mathematical models for multicontainer loading problems," Omega, Elsevier, vol. 66(PA), pages 106-117.
    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. Tian, Tian & Zhu, Wenbin & Lim, Andrew & Wei, Lijun, 2016. "The multiple container loading problem with preference," European Journal of Operational Research, Elsevier, vol. 248(1), pages 84-94.
    9. Carlos A. Vega-Mejía & Jairo R. Montoya-Torres & Sardar M. N. Islam, 2019. "Consideration of triple bottom line objectives for sustainability in the optimization of vehicle routing and loading operations: a systematic literature review," Annals of Operations Research, Springer, vol. 273(1), pages 311-375, February.
    10. German Pantoja-Benavides & Daniel Giraldo & Ana Montes & Andrea García & Carlos Rodríguez & César Marín & David Álvarez-Martínez, 2024. "Comprehensive Review of Robotized Freight Packing," Logistics, MDPI, vol. 8(3), pages 1-24, July.
    11. Ramos, António G. & Silva, Elsa & Oliveira, José F., 2018. "A new load balance methodology for container loading problem in road transportation," European Journal of Operational Research, Elsevier, vol. 266(3), pages 1140-1152.
    12. Gajda, Mikele & Trivella, Alessio & Mansini, Renata & Pisinger, David, 2022. "An optimization approach for a complex real-life container loading problem," Omega, Elsevier, vol. 107(C).
    13. Andreas Fischer & Igor Litvinchev & Tetyana Romanova & Petro Stetsyuk & Georgiy Yaskov, 2023. "Quasi-Packing Different Spheres with Ratio Conditions in a Spherical Container," Mathematics, MDPI, vol. 11(9), pages 1-19, April.
    14. I. Gimenez-Palacios & M. T. Alonso & R. Alvarez-Valdes & F. Parreño, 2021. "Logistic constraints in container loading problems: the impact of complete shipment conditions," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(1), pages 177-203, April.
    15. Araya, Ignacio & Moyano, Mauricio & Sanchez, Cristobal, 2020. "A beam search algorithm for the biobjective container loading problem," European Journal of Operational Research, Elsevier, vol. 286(2), pages 417-431.
    16. Toffolo, Túlio A.M. & Esprit, Eline & Wauters, Tony & Vanden Berghe, Greet, 2017. "A two-dimensional heuristic decomposition approach to a three-dimensional multiple container loading problem," European Journal of Operational Research, Elsevier, vol. 257(2), pages 526-538.
    17. 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.
    18. Bonet Filella, Guillem & Trivella, Alessio & Corman, Francesco, 2023. "Modeling soft unloading constraints in the multi-drop container loading problem," European Journal of Operational Research, Elsevier, vol. 308(1), pages 336-352.
    19. Gahm, Christian & Uzunoglu, Aykut & Wahl, Stefan & Ganschinietz, Chantal & Tuma, Axel, 2022. "Applying machine learning for the anticipation of complex nesting solutions in hierarchical production planning," European Journal of Operational Research, Elsevier, vol. 296(3), pages 819-836.
    20. Bortfeldt, Andreas & Wäscher, Gerhard, 2013. "Constraints in container loading – A state-of-the-art review," European Journal of Operational Research, Elsevier, vol. 229(1), pages 1-20.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:8:y:2020:i:7:p:1130-:d:382786. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.