Tools of mathematical modeling of arbitrary object packing problems
Tools of mathematical modeling of arbitrary object packing problems
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.
mathematical modeling, cutting and packing, phi-function, geometry, nofit polygon
343-368
Bennell, J.
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Scheithauer, G.
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Stoyan, Y.
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Romanova, T.
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7 November 2010
Bennell, J.
38d924bc-c870-4641-9448-1ac8dd663a30
Scheithauer, G.
20048fd2-0af4-4c61-9aff-87c6e6aa8ff0
Stoyan, Y.
cdfc8474-9402-44a0-b856-09d5e2f5dc57
Romanova, T.
fc983dc2-e442-41b5-824a-d61e2574e693
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), .
(doi:10.1007/s10479-008-0456-5).
Abstract
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
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Local EPrints ID: 154612
URI: http://eprints.soton.ac.uk/id/eprint/154612
PURE UUID: 1839e2d5-fa33-45eb-a991-b82a910b6edf
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Date deposited: 25 May 2010 15:16
Last modified: 14 Mar 2024 01:34
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Author:
J. Bennell
Author:
G. Scheithauer
Author:
Y. Stoyan
Author:
T. Romanova
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