Cutting and Packing

Álvarez-Valdés, Ramón; Carravilla, Maria Antónia; Oliveira, José Fernando

doi:10.1007/978-3-319-07124-4_43

Cited by 7 publications

(7 citation statements)

References 80 publications

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“…Alvarez‐Valdes et al. ( 2018 ) give a general overview about 2D‐CPPs, where the authors discuss aspects such as dimensionality, geometry, as well as additional characteristics and constraints defining different variants of 2D‐CPPs. Besides, a broad overview of the main heuristic techniques used to tackle 2D‐CPPs is also provided.…”

Section: Literature Reviewmentioning

confidence: 99%

On the optimal layout of a dining room in the era of COVID‐19 using mathematical optimization

Contardo

Costa

2022

Int Trans Operational Res

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We consider the problem of maximizing the number of people that a dining room can accommodate provided that the chairs belonging to different tables are socially distant. We introduce an optimization model that incorporates several characteristics of the problem, namely: the type and size of surface of the dining room, the shapes and sizes of the tables, the positions of the chairs, the sitting sense of the customers, and the possibility of adding space separators to increase the capacity. We propose a simple, yet general, set‐packing formulation for the problem. We investigate the efficiency of space separators and the impact of considering the sitting sense of customers in the room capacity. We also perform an algorithmic analysis of the model, and assess its scalability to the problem size, the presence of (or lack thereof) room separators, and the consideration of the sitting sense of customers. We also propose two constructive heuristics capable of coping with large problem instances otherwise intractable for the optimization model.

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Section: Literature Reviewmentioning

confidence: 99%

On the optimal layout of a dining room in the era of COVID‐19 using mathematical optimization

Contardo

Costa

2022

Int Trans Operational Res

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“…In the following decade, a survey on general two-dimensional packing problems was proposed by Alvarez-Valdes et al [1]. Surveys on specific problems, variants, and methodologies were produced by Lodi et al [30] (2D-BPP and 2D-SPP), Silva et al [44] (pallet loading problem, a variant of the 2D-BPP in which one has to pack, with orthogonal rotations, the maximum number of identical items into a single bin), Oliveira et al [40] (2D-SPP), Christensen et al [14] (approximation and online algorithms), and Russo et al [41] (upper bounds for problems with guillotine cuts).…”

Section: Surveys and Typologiesmentioning

confidence: 99%

“…The coordinates F(i) = (x i , y i ) represent the position where the bottom-left corner of each i ∈ I is placed. Constraints (1) impose that each item is entirely inside the bin, while constraints (2) forbid overlapping between pairs of items. Constraints (1) and ( 2) impose that items have fixed orientation (i.e., cannot be rotated), but they can be adapted to consider the popular variant (discussed in Sect.…”

Section: Introductionmentioning

confidence: 99%

2DPackLib: a two-dimensional cutting and packing library

et al. 2021

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Two-dimensional cutting and packing problems model a large number of relevant industrial applications.The literature on practical algorithms for such problems is very large. We introduce the , a library on two-dimensional orthogonal cutting and packing problems. The library makes available, in a unified format, 25 benchmarks from the literature for a total of over 3000 instances, provides direct links to surveys and typologies, and includes a list of relevant links.

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“…The irregular strip packing problem (ISP), or often called the nesting problem, is the one of the representative cutting and packing problems that emerges in a wide variety of industrial applications, such as garment manufacturing, sheet metal cutting, furniture making and shoe manufacturing [Alvarez-Valdes et al, 2018, Scheithauer, 2018. This problem is categorized as the two-dimensional, irregular open dimensional problem in Dyckhoff [1990], Wäscher et al [2007].…”

Section: Introductionmentioning

confidence: 99%

Coordinate descent heuristics for the irregular strip packing problem of rasterized shapes

Umetani¹,

Murakami²

2021

Preprint

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We consider the irregular strip packing problem of rasterized shapes, where a given set of pieces of irregular shapes represented in pixels should be placed into a rectangular container without overlap. The rasterized shapes enable us to check overlap without any exceptional handling due to geometric issues, while they often require much memory and computational effort in high-resolution. We develop an efficient algorithm to check overlap using a pair of scanlines that reduces the complexity of rasterized shapes by merging consecutive pixels in each row and column into strips with unit width, respectively. Based on this, we develop coordinate descent heuristics that repeat a line search in the horizontal and vertical directions alternately. Computational results for test instances show that the proposed algorithm obtains sufficiently dense layouts of rasterized shapes in high-resolution within a reasonable computation time.

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Cutting and Packing

Cited by 7 publications

References 80 publications

On the optimal layout of a dining room in the era of COVID‐19 using mathematical optimization

On the optimal layout of a dining room in the era of COVID‐19 using mathematical optimization

2DPackLib: a two-dimensional cutting and packing library

Coordinate descent heuristics for the irregular strip packing problem of rasterized shapes

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