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# Matheuristics for the irregular bin packing problem with free rotations

Martinez-Sykora, A., Alvarez-Valdes, R., Bennell, J., Ruiz, R. and Tamarit, J.M. (2017) Matheuristics for the irregular bin packing problem with free rotations. European Journal of Operational Research, 258 (2), 440-455.

Record type: Article

## Abstract

We present a number of variants of a constructive algorithm able to solve a wide variety of variants of the Two-Dimensional Irregular Bin Packing Problem (2DIBPP). The aim of the 2DIBPP is to pack a set of irregular pieces, which may have concavities, into stock sheets (bins) with fixed dimensions in such a way that the utilization is maximized. This problem is inspired by a real application from a ceramic company in Spain. In addition, this problem arises in other industries such as the garment industry or ship building. The constructive procedure presented in this paper allows both free orientation for the pieces, as in the case of the ceramic industry, or a finite set of orientations as in the case of the garment industry. We explicitly model the assignment of pieces to bins and compare with the more common strategy of packing bins sequentially. There are very few papers in the literature that address the bin packing problem with irregular pieces and to our knowledge this is the first to additionally consider free rotation of pieces with bin packing. We propose several Integer Programing models to determine the association between pieces and bins and then we use a Mixed Integer Programing model for placing the pieces into the bins. The computational results show that the algorithm obtains high quality results in sets of instances with different properties. We have used both industry data and the available data in the literature of 2D irregular strip packing and bin packing problems.

Text
BCP-EJOR.pdf - Accepted Manuscript

Accepted/In Press date: 25 September 2016
e-pub ahead of print date: 28 September 2016
Published date: 16 April 2017

## Identifiers

Local EPrints ID: 400806
URI: http://eprints.soton.ac.uk/id/eprint/400806
ISSN: 0377-2217
PURE UUID: 3421e7f1-d0dc-4711-a54c-608746ce94b9
ORCID for A. Martinez-Sykora: orcid.org/0000-0002-2435-3113

## Catalogue record

Date deposited: 27 Sep 2016 15:06

## Contributors

Author: R. Alvarez-Valdes
Author: J. Bennell
Author: R. Ruiz
Author: J.M. Tamarit