A representation problem for a rectangular cutting-stock model

• Autorzy: Marinescu D.
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

cutting-stock problem; covering problem; two-dimensional languages; trivalent product

• Wydawca: Wydawnictwo Politechniki Poznańskiej
• Czasopismo: Foundations of Computing and Decision Sciences
• Rocznik: 2007
• Tom: Vol. 32, No. 3
• Strony: 239--250
• Opis fizyczny: Bibliogr. 7 poz.

Twórcy

autor

Marinescu D.

• TRANSILVANIA University of Brasov, B-dul Eroilor, No. 29, Brasov, Romania,

Bibliografia

• [1] Ahuja R. K., Magnali T., 1., Orlin J. B. Network Flows: Theory, Algorithms and Applications. Prentice Hall, Englewood, Cliffs, N.J., 1993.
• [2] Chen W. K., Theory of nets: Flows in Nefrvorks. John Wiley & Sons, New York, 1990.
• [3] Iacob P, Marinescu D, Luca C, L-Shape room Proceedings of WMSC1A, Oriando, Florida, USA, 2005, VolIU, pp. 175-179.
• [4] Macii E., A discussion of the explicit Methods for transitive closure computation based on matrix multiplication. Proceedings of ASILOMAR-29, IEEE, 1996, pp 799-801
• [5] Marinescu D., Graphs attached to a rectangular cutting-stock model (French). Itinerant Seminar of Functional Equations, Approximation and Convexity, ClujNapoca, 1988, Preprint No. 6pp. 209 -212.
• [6] Marinescu D., Properties of the matrices attached to a rectangular cutting-stock model (French). Bulletin of the Transilvania University of Brasov seria C, Vol XXXIV, 1992, pp 41-48.
• [7] Marinescu D., A monotonie array grammar for a two-dimensional cutting-stock problem. Proceedings of the third Colloquium on Logic, Language, Mathematics,and Linguistics, Brasov, 1991 pp 51-60.