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Tools of mathematical modelling of arbitrary object packing problems

Tools of mathematical modelling of arbitrary object packing problems
Tools of mathematical modelling of arbitrary object packing problems
The article further develops phi-functions as an efficient tool for mathematical modelling 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-funtions 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.
CORMSIS-08-15
University of Southampton
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.
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. (2008) Tools of mathematical modelling of arbitrary object packing problems (Discussion Papers in Centre for Operational Research, Management Science and Information Systems, CORMSIS-08-15) Southampton, UK. University of Southampton

Record type: Monograph (Discussion Paper)

Abstract

The article further develops phi-functions as an efficient tool for mathematical modelling 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-funtions 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: 2008

Identifiers

Local EPrints ID: 63408
URI: https://eprints.soton.ac.uk/id/eprint/63408
PURE UUID: 914f258a-76b2-4a66-bf08-083664e8f551

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Date deposited: 28 Oct 2008
Last modified: 13 Mar 2019 20:25

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