Cutting and packing problems for irregular objects with continuous rotations: mathematical modelling and non-linear optimization

Yuriy Stoyan, Alexander Pankratov and Tatiana Romanova
Additional contact information
Yuriy Stoyan: Institute for Mechanical Engineering Problems of the National Academy of Sciences of Ukraine, Kharkov, Ukraine
Alexander Pankratov: Institute for Mechanical Engineering Problems of the National Academy of Sciences of Ukraine, Kharkov, Ukraine
Tatiana Romanova: Institute for Mechanical Engineering Problems of the National Academy of Sciences of Ukraine, Kharkov, Ukraine

Journal of the Operational Research Society, 2016, vol. 67, issue 5, 786-800

Abstract: We further improve our methodology for solving irregular packing and cutting problems. We deal with an accurate representation of objects bounded by circular arcs and line segments and allow their continuous rotations and translations within rectangular and circular containers. We formulate a basic irregular placement problem which covers a wide spectrum of packing and cutting problems. We provide an exact non-linear programming (NLP) model of the problem, employing ready-to-use phi-functions. We develop an efficient solution algorithm to search for local optimal solutions for the problem in a reasonable time. The algorithm reduces our problem to a sequence of NLP subproblems and employs optimization procedures to generate starting feasible points and feasible subregions. Our algorithm allows us to considerably reduce the number of inequalities in NLP subproblems. To show the benefits of our methodology we give computational results for a number of new challenger and the best known benchmark instances.

Date: 2016
References: Add references at CitEc
Citations: View citations in EconPapers (7)

Downloads: (external link)
http://www.palgrave-journals.com/jors/journal/v67/n5/pdf/jors201594a.pdf Link to full text PDF (application/pdf)
http://www.palgrave-journals.com/jors/journal/v67/n5/full/jors201594a.html Link to full text HTML (text/html)
Access to full text is restricted to subscribers.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:pal:jorsoc:v:67:y:2016:i:5:p:786-800

Ordering information: This journal article can be ordered from
http://www.springer. ... search/journal/41274

Access Statistics for this article

Journal of the Operational Research Society is currently edited by Tom Archibald and Jonathan Crook

More articles in Journal of the Operational Research Society from Palgrave Macmillan, The OR Society
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().