A branch &amp; bound algorithm for cutting and packing irregularly shaped pieces

Álvarez-Valdés, Ramón; Martínez, Antonio; Tamarit, José Manuel

doi:10.1016/j.ijpe.2013.04.007

Cited by 79 publications

(67 citation statements)

References 18 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Fischetti and Luzzi [5] were the first to propose a MIP model to the problem. Alvarez-Valdes et al [1] defined some structures used in [5] and developed a branch-and-bound algorithm to solve the model. Santoro and Lemos [11] proposed a MIP model to convex polygons with some limitations: the polygons can have up to eight edges and their opposite edges must be parallel.…”

Section: Introductionmentioning

confidence: 99%

MIP models for the irregular strip packing problem: new symmetry breaking constraints

2017

View full text Add to dashboard Cite

Abstract. The irregular strip packing problem consists in minimizing the length used to cut a set of pieces from a board with fixed width. Recently, a mixed integer programming model was proposed for the problem, but it may allow a large number of symmetric solutions. In this paper, new symmetry breaking constraints are proposed to improve the model. Computational experiments were performed for instances with convex pieces. The results show the proposed formulation is better than the previous one for most instances, since it improves lower bounds and reduces run-time and number of nodes explored to prove optimality.

show abstract

Section: Introductionmentioning

confidence: 99%

MIP models for the irregular strip packing problem: new symmetry breaking constraints

2017

View full text Add to dashboard Cite

show abstract

“…These constraints were proposed by Alvarez-Valdes et al (2013) in their horizontal slices formulation and use the edges of the NFP to form the no-overlap constraints. Prior to solving the MIP, construct the NFP of p and each piece…”

Section: Problem Descriptionmentioning

confidence: 99%

Constructive procedures to solve 2-dimensional bin packing problems with irregular pieces and guillotine cuts

Martínez-Sykora

Álvarez-Valdés

Bennell

et al. 2015

Omega

View full text Add to dashboard Cite

This paper presents an approach for solving a new real problem in Cutting and Packing. At its core is an innovative mixed integer programme model that places irregular pieces and defines guillotine cuts. The two-dimensional irregular shape bin packing problem with guillotine constraints arises in the glass cutting industry, for example, the cutting of glass for conservatories. Almost all cutting and packing problems that include guillotine cuts deal with rectangles only, where all cuts are orthogonal to the edges of the stock sheet and a maximum of two angles of rotation are permitted. The literature tackling packing problems with irregular shapes largely focused on strip packing i.e. minimizing the length of a single fixed width stock sheet, and does not consider guillotine cuts. Hence, this problem combines the challenges of tackling the complexity of packing irregular pieces with free rotation, guaranteeing guillotine cuts that are not always orthogonal to the edges of the stock sheet, and allocating pieces to bins. To our knowledge only one other recent paper tackles this problem. We present a hybrid algorithm that is a constructive heuristic that determines the relative position of pieces in the bin and guillotine constraints via a mixed integer programme model. We investigate two approaches for allocating guillotine cuts at the same time as determining the placement of the piece, and a two phase approach that delays the allocation of cuts to provide flexibility in space usage. Finally we describe an improvement procedure that is applied to each bin before it is closed. This approach improves on the results of the only other publication on this problem, and gives competitive results for the classic rectangle bin packing problem with guillotine constraints.

show abstract

“…Alvarez-Valdes et al (2013) reviewed the mixed-integer models presented in Sections 2.2.2 and 2.2.3 and dened a procedure to design the slices of Fischetti and Luzzi (2009) model. Furthermore, they lifted the bound constraints (2.21)-(2.23) and developed a branch-and-cut method to solve the model proposed by Fischetti and Luzzi (2009).…”

Section: A Linear Model Based On Compaction Strategiesmentioning

confidence: 99%

“…Figure 2.14: Slices generated in the exterior region of a not polygon dened by pieces i and j (based on Alvarez-Valdes et al (2013)). …”

Section: Alvarez-valdes Et Al (2013) Approachmentioning

confidence: 99%

“…by Alvarez-Valdes et al (2013), who also developed a branch and bound algorithm to solve the problem and extended a linear compaction model designed by Gomes and Oliveira (2006) for a mixed-integer programming model that represents the whole problem. Although all such models accurately represent the problem, they demand complex geometric structures not easy to be obtained.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Nesting problems

Cherri¹

View full text Add to dashboard Cite

A branch & bound algorithm for cutting and packing irregularly shaped pieces

Cited by 79 publications

References 18 publications

MIP models for the irregular strip packing problem: new symmetry breaking constraints

MIP models for the irregular strip packing problem: new symmetry breaking constraints

Constructive procedures to solve 2-dimensional bin packing problems with irregular pieces and guillotine cuts

Nesting problems

Contact Info

Product

Resources

About