Models for the two-dimensional level strip packing problem – a review and a computational evaluation

Abstract

The two-dimensional level strip packing problem has received little attention from the scientific community. To the best of our knowledge, the most competitive model is the one proposed in 2004 by Lodi et al., where the items are packed by levels. In 2015, an arc flow model addressing the two-dimensional level strip cutting problem was proposed by Mrad. The literature presents some mathematical models, despite not addressing specifically the two-dimensional level strip packing problem, they are efficient and can be adapted to the problem. In this paper, we adapt two mixed integer linear programming models from the literature, rewrite the Mrad’s model for the strip packing problem and add well-known valid inequalities to the model proposed by Lodi et al. Computational results were performed on instances from the literature and show that the model put forward by Lodi et al. with valid inequalities outperforms the remaining models with respect to the number of optimal solutions found.

Keywords:

• cutting and packing problems
• guillotine cutting
• level packing
• integer programming

Acknowledgments

The authors would like to thank the Center of Mathematical Sciences Applied to Industry – CeMEAI (CEPID FAPESP No. 2013/07375-0), the National Council for Scientific and Technological Development (CNPq) and the Universidade Federal da Grande Dourados (UFGD).

Disclosure statement

No potential conflict of interest was reported by the author(s).