Optimal Orthogonal Subdivision of Rectangular Sheets

[+] Author and Article Information
M. Shpitalni, V. Manevich

Faculty of Mechanical Engineering, Technion-Israel Institute of Technology, Haifa, Israel 32000

J. Manuf. Sci. Eng 118(3), 281-288 (Aug 01, 1996) (8 pages) doi:10.1115/1.2831027 History: Received August 01, 1993; Revised November 01, 1994; Online January 17, 2008


The two-dimensional problem of optimal orthogonal subdivision of rectangular sheets (stock cutting) is of great interest to industry. In this paper, a new model is presented which formulates the problem in terms of integer linear programming (ILP). Using this new model, three objective functions dealing with important practical applications are formulated and demonstrated. They are: (i) selection and placement, including orientation, of rectangles on a given (single) sheet, while minimizing the unused (scrap) material; (ii) grouping the rectangles together in a predicted form, leaving a “good” and predetermined unused part of the sheet in cases where all the rectangles can be placed on a single sheet; and, (iii) optimal arrangement of rectangles on multiple sheets, including selection of the sheets to be used.

Copyright © 1996 by The American Society of Mechanical Engineers
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