The Dotted-Board Model: A new MIP model for nesting irregular shapes

Franklina M.B. Toledo, Maria Antónia Carravilla, Cristina Ribeiro, José F. Oliveira and A. Miguel Gomes

International Journal of Production Economics, 2013, vol. 145, issue 2, 478-487

Abstract: The nesting problem, also known as irregular packing problem, belongs to the generic class of cutting and packing (C&P) problems. It differs from other 2-D C&P problems in the irregular shape of the pieces. This paper proposes a new mixed-integer model in which binary decision variables are associated with each discrete point of the board (a dot) and with each piece type. It is much more flexible than previously proposed formulations and solves to optimality larger instances of the nesting problem, at the cost of having its precision dependent on board discretization. To date no results have been published concerning optimal solutions for nesting problems with more than 7 pieces. We ran computational experiments on 45 problem instances with the new model, solving to optimality 34 instances with a total number of pieces ranging from 16 to 56, depending on the number of piece types, grid resolution and the size of the board. A strong advantage of the model is its insensitivity to piece and board geometry, making it easy to extend to more complex problems such as non-convex boards, possibly with defects. Additionally, the number of binary variables does not depend on the total number of pieces but on the number of piece types, making the model particularly suitable for problems with few piece types. The discrete nature of the model requires a trade-off between grid resolution and problem size, as the number of binary variables grows with the square of the selected grid resolution and with board size.

Keywords: Cutting and packing; Nesting; Irregular packing; Mixed-integer programming models (search for similar items in EconPapers)
Date: 2013
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (13)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0925527313001722
Full text for ScienceDirect subscribers only

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:eee:proeco:v:145:y:2013:i:2:p:478-487

DOI: 10.1016/j.ijpe.2013.04.009

Access Statistics for this article

International Journal of Production Economics is currently edited by Stefan Minner

More articles in International Journal of Production Economics from Elsevier
Bibliographic data for series maintained by Catherine Liu ().