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Tools of mathematical modeling of arbitrary object packing problems

Bennell, J., Scheithauer, G., Stoyan, Y. and Romanova, T. (2010) Tools of mathematical modeling of arbitrary object packing problems Annals of Operations Research, 179, (1), pp. 343-368. (doi:10.1007/s10479-008-0456-5).

Record type: Article


The article reviews the concept of and further develops phi-functions (?-functions) as an efficient tool for mathematical modeling of two-dimensional geometric optimization problems, such as cutting and packing problems and covering problems. The properties of the phi-function technique and its relationship with Minkowski sums and the nofit polygon are discussed. We also describe the advantages of phi-functions over these approaches. A clear definition of the set of objects for which phi-functions may be derived is given and some exceptions are illustrated. A step by step procedure for deriving phi-functions illustrated with examples is provided including the case of continuous rotation.

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Published date: 7 November 2010
Keywords: mathematical modeling, cutting and packing, phi-function, geometry, nofit polygon


Local EPrints ID: 154612
PURE UUID: 1839e2d5-fa33-45eb-a991-b82a910b6edf

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Date deposited: 25 May 2010 15:16
Last modified: 18 Jul 2017 12:46

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Author: J. Bennell
Author: G. Scheithauer
Author: Y. Stoyan
Author: T. Romanova

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