Cutting and Packing Problems: A Categorized, Application-Orientated Research Bibliography

Sweeney, Paul E; Paternoster, Elizabeth Ridenour

doi:10.1038/sj/jors/0430704

Cited by 9 publications

(6 citation statements)

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“…The first application-oriented literature review on cutting and packing problems was published by Sweeney and Paternoster (1992), including papers written since 1940. Coffman et al (2004) published a bibliography on the bin packing problem.…”

Section: Literature Reviewmentioning

confidence: 99%

A mixed‐integer linear model for the multiple heterogeneous knapsack problem with realistic container loading constraints and bins' priority

Deplano

Lersteau

Nguyễn

2019

Int Trans Operational Res

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We propose a mixed-integer linear model that solves the multiple heterogeneous knapsack problem, minimising the wasted space of the bins, taking into account their priority and considering the following constraints: non-overlapping, boundaries and positioning (both constrained and free), rotations (around the vertical axis), orthogonal displacement, weight limit, static stability, weight distribution in a pyramidal region and load bearing considering items' arbitrary centre of mass (CoM). In the experiments, the priority parameter is set to prioritise smaller bins, but the model is generic to cover other cases. We study the trade-off of adding more constraints to make the problem more realistic and the complexity of finding a solution. We introduce new metrics that facilitate the comparison of datasets used in experiments. These metrics allow the export of theoretical results in the industry. We also propose a constructive heuristic named weight first best fit to handle large-scale instances in a reasonable time.

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Section: Literature Reviewmentioning

confidence: 99%

A mixed‐integer linear model for the multiple heterogeneous knapsack problem with realistic container loading constraints and bins' priority

Deplano

Lersteau

Nguyễn

2019

Int Trans Operational Res

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“…Here we only review some closely related packing methods for packing irregular shapes in 3D space. For more comprehensive reviews on packing problems, we refer the readers to [Dyc90,SP92,DD95].…”

Section: Related Workmentioning

confidence: 99%

“…There have been extensive methods for 2D packing problems and comprehensive surveys on these methods have been provided in [Dyc90,SP92,DD95,RRS13,ZCT16]. Packing in 3D is much more difficult because of the increasing degrees of freedom in translation and rotation in 3D space.…”

Section: Introductionmentioning

confidence: 99%

Packing Irregular Objects in 3D Space via Hybrid Optimization

Chen

et al. 2018

Computer Graphics Forum

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Packing problems arise in a wide variety of practical applications. The basic problem is that of placing as many objects as possible in a non‐overlapping configuration within a given container. Problems involving irregular shapes are the most challenging cases. In this paper, we consider the most general forms of irregular shape packing problems in 3D space, where both the containers and the objects can be of any shapes, and free rotations of the objects are allowed. We propose a heuristic method for efficiently packing irregular objects by combining continuous optimization and combinatorial optimization. Starting from an initial placement of an appropriate number of objects, we optimize the positions and orientations of the objects using continuous optimization. In combinatorial optimization, we further reduce the gaps between objects by swapping and replacing the deployed objects and inserting new objects. We demonstrate the efficacy of our method with experiments and comparisons.

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“…Hundreds of studies are found in the literature dealing with cutting and packing problems and their industrial applications, as reported in the surveys and special issues in, for example, Dyckhoff and Waescher (1990), Dowsland and Dowsland (1992), Dyckhoff and Finke (1992), Lirov (1992), Sweeney and Paternoster (1992), Martello (1994a, b), Bischoff and Waescher (1995), Mukhacheva (1997), Dyckhoff et al (1997), Arenales et al (1999), Hifi (2002), Lodi et al (2002), Wang and Waescher (2002), Waescher et al (in press) and ESICUP (2006). However, only a few Two-dimensional guillotine cutting problems 6191 studies presenting mathematical programming formulations for 1-group two-dimensional guillotine cutting problems are found in the literature, for instance, Morabito and Arenales (2000), Scheithauer (2002), Yanasse and Katsurayama (2005) and Yanasse and Morabito (in press).…”

Section: Introductionmentioning

confidence: 98%

A note on linear models for two-group and three-group two-dimensional guillotine cutting problems

Yanasse

Morábito

2008

International Journal of Production Research

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Due to the particular characteristics of certain cutting machines, special classes of cutting patterns, such as 1-group, 2-group and 3-group, requiring shorter processing times appear in the furniture, hardboard and stone industries. In this study we present integer linear models to generate 2-group and 3-group constrained and unconstrained two-dimensional guillotine cutting patterns. The models are derived from the linear models for 1-group guillotine cutting patterns proposed in Yanasse, H.H. and Morabito, R., Linear models for one-group two-dimensional guillotine cutting problems. International Journal of Production Research, in press. The performances of the models were evaluated by solving a number of examples randomly generated and an actual example derived from a furniture company. These results were produced using GAMS modelling language and the CPLEX solver, and they show that the models are effective to solve problems of small and moderate size.

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Cutting and Packing Problems: A Categorized, Application-Orientated Research Bibliography

Cited by 9 publications

References 0 publications

A mixed‐integer linear model for the multiple heterogeneous knapsack problem with realistic container loading constraints and bins' priority

A mixed‐integer linear model for the multiple heterogeneous knapsack problem with realistic container loading constraints and bins' priority

Packing Irregular Objects in 3D Space via Hybrid Optimization

A note on linear models for two-group and three-group two-dimensional guillotine cutting problems

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