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A representation problem for a rectangular cutting-stock model

Marinescu D.

Foundations of Computing and Decision Sciences

2007

Vol. 32, No. 3

239-250

First we give a representation of a rectangular cutting-stock model by two kinds of graphs, Gdand Gr, which describe the vertical and the horizontal relations between the elements of the model. Studying the properties of these graphs we are able to describe the cutting-stock model with the help of a trivalent matrix with the elements from the set {0,1,2}. To this purpose we introduce a trivalent product of two matrices and we show how the geometrical properties of a cutting-stock model are represented by algebraic properties of this trivalent matrix. Such a kind of representation is useful for the generation of all cutting-stock models and for the representation of these models by a two-dimensiona! language.