Packing Oblique 3D Objects

Alexander Pankratov, Tatiana Romanova and Igor Litvinchev
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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
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
Igor Litvinchev: Faculty of Mechanical and Electrical Engineering, Graduate Program in Systems Engineering, Nuevo Leon State University (UANL), 66450 Monterrey, Mexico

Mathematics, 2020, vol. 8, issue 7, 1-17

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.

Keywords: packing; irregular 3D objects; quasi-phi-function s; nonlinear optimization (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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