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International Journal of Production Research Volume 59, 2021 - Issue 13
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Articles

Sparsest packing of two-dimensional objects

Tatiana Romanovaa Department of Mathematical Modeling and Optimal Design, A. Pidgorny Institute of Mechanical Engineering Problems of the National Academy of Sciences of Ukraine, Kharkiv, UkraineCorrespondence[email protected]
ORCID Iconhttps://orcid.org/0000-0002-8618-4917
ORCID Icon,
Alexander Pankratova Department of Mathematical Modeling and Optimal Design, A. Pidgorny Institute of Mechanical Engineering Problems of the National Academy of Sciences of Ukraine, Kharkiv, UkraineORCID Iconhttps://orcid.org/0000-0002-2958-8923
ORCID Icon,
Igor Litvinchevb Faculty of Mechanical and Electrical Engineering, Nuevo Leon State University, San Nicolas de los Garza, MexicoORCID Iconhttps://orcid.org/0000-0002-1850-4755
ORCID Icon,
Sergiy Plankovskyyc Department of Aircraft Manufacturing Technology, National Aerospace University “Kharkiv Aviation Institute”, Kharkiv, UkraineORCID Iconhttps://orcid.org/0000-0003-2908-903X
ORCID Icon,
Yevgen Tsegelnykc Department of Aircraft Manufacturing Technology, National Aerospace University “Kharkiv Aviation Institute”, Kharkiv, UkraineORCID Iconhttps://orcid.org/0000-0003-1261-9890
ORCID Icon &
Olga Shypulc Department of Aircraft Manufacturing Technology, National Aerospace University “Kharkiv Aviation Institute”, Kharkiv, UkraineORCID Iconhttps://orcid.org/0000-0002-1356-5831
ORCID Icon
Pages 3900-3915 | Received 17 Dec 2019, Accepted 06 Apr 2020, Published online: 04 May 2020
 
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Abstract

The concept of the sparsest packing is introduced in this paper. The sparsest packing is aimed to place the objects in the container as distant as possible. More specifically, the minimal Euclidean distance between the objects, as well as, between the objects and the boundary of the container is maximised. This new problem statement is motivated by modern clean and energy-saving technologies such as ultrasonic hardening and finishing by detonating gas mixtures. The sparsest packing of two-dimensional objects in a circular container is considered subject to balancing conditions. The objects may have regular or irregular shapes bounded by arcs and line segments. Using the phi-function technique a mathematical model is formulated and a corresponding nonlinear programming problem is stated. A solution algorithm is proposed and computational results are presented to illustrate the approach.

Disclosure statement

No potential conflict of interest was reported by the author(s).

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