Sparsest packing of two-dimensional objects. Issue 13 (3rd July 2021)

• Record Type: Journal Article
• Authors: Romanova, Tatiana; Pankratov, Alexander; Litvinchev, Igor; Plankovskyy, Sergiy; Tsegelnyk, Yevgen; Shypul, Olga
• Is Part Of: International journal of production research. Volume 59:Issue 13(2021)
• Page Start: 3900
• Page End: 3915
• Publication Date: 2021-07-03
• Subjects: sparsest packing -- balancing conditions -- mathematical modelling -- nonlinear optimisation; Factory management -- Periodicals; 658.57
• DOI: 10.1080/00207543.2020.1755471
• Languages: English
• ISSNs: 0020-7543

Abstract

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.