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Zbl 1125.90382
Stoyan, Yurij; Scheithauer, Guntram; Gil, Nikolay; Romanova, Tatiana
$\Phi$-functions for complex 2D-objects.
(English)
[J] 4OR 2, No. 1, 69-84 (2004). ISSN 1619-4500; ISSN 1614-2411/e

Summary: Within two-dimensional cutting and packing problems with irregular shaped objects, the concept of $\Phi$-functions has been proven to be very helpful for several solution approaches. In order to construct such $\Phi$-functions a previous work [{\it Yu. G. Stoyan} et al., Appl. Math. 29, No. 2, 199--218 (2002; Zbl 1053.90009)], in which so-called primary objects are considered, is continued. Now $\Phi$-functions are constructed for pairs of objects which can be represented as a finite combination (union, intersection, complement) of primary objects which allows the handling of arbitrary shaped objects by appropriate approximations of sufficient accuracy.
MSC 2000:
*90B80 Discrete location and assignment
90C26 Nonconvex programming

Keywords: Cutting and packing; mathematical modelling; optimization; 2D placement problems

Citations: Zbl 1053.90009

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