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), 343-368. (doi:10.1007/s10479-008-0456-5).


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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.

Item Type: Article
Digital Object Identifier (DOI): doi:10.1007/s10479-008-0456-5
ISSNs: 0254-5330 (print)
1572-9338 (electronic)
Keywords: mathematical modeling, cutting and packing, phi-function, geometry, nofit polygon
Subjects: H Social Sciences > H Social Sciences (General)
Divisions : University Structure - Pre August 2011 > School of Management
ePrint ID: 154612
Accepted Date and Publication Date:
7 November 2010Published
Date Deposited: 25 May 2010 15:16
Last Modified: 31 Mar 2016 13:25
An Investigation of Cutting/Packing and Planning using Automated Algorithm Selection
Funded by: EPSRC (GR/S52421/01)
April 2004 to August 2007

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