The cutting stock problem — a survey

Cheng, Chun-Hao; Feiring, Bruce R.; Cheng, Tao

doi:10.1016/0925-5273(94)00045-x

Cited by 96 publications

(47 citation statements)

References 98 publications

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“…An extensive literature on the CuSPPs and their applications has developed since. For example, Golden in [8] gives an abstract description of a variety of different solution methods; in [2] Chen et al discuss a number of solution methods, and Dyckhoff in [5] lists a number of solution methods and applications and presents a systematic categorization of cutting and packing problems.…”

Section: Description Of the Problemmentioning

confidence: 99%

Approximating Multi-Objective Hyper-Heuristics for Solving 2D Irregular Cutting Stock Problems

Gómez

Terashima-Marín

2010

Advances in Soft Computing

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Abstract. This article presents a method based on the multi-objective evolutionary algorithm NSGA-II to approximate hyper-heuristics for solving irregular 2D cutting stock problems under multiple objectives. In this case, additionally to the traditional objective of minimizing the number of sheets used to fit a finite number of irregular pieces, the time required to perform the placement task is also minimized, leading to a bi-objective minimization problem with a tradeoff between the number of sheets and the time required for placing all pieces. We solve this problem using multi-objective hyper-heuristics (MOHHs), whose main idea consists of finding a set of simple heuristics which can be combined to find a general solution for a wide range of problems, where a single heuristic is applied depending on the current condition of the problem, instead of applying a unique single heuristic during the whole placement process. The MOHHs are approximated after going through a learning process by mean of the NSGA-II, which evolves combinations of condition-action rules producing at the end a set of Pareto-optimal MOHHs. We tested the approximated MMOHHs on several sets of benchmark problems, having outstanding results for most of the cases.

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Section: Description Of the Problemmentioning

confidence: 99%

Approximating Multi-Objective Hyper-Heuristics for Solving 2D Irregular Cutting Stock Problems

Gómez

Terashima-Marín

2010

Advances in Soft Computing

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“…However, in recent years, fewer papers have been published in this area, despite the large potential for applications, including time organization in administration, memory management in computer systems, etc. For a recent survey, see Cheng et al (1994). In contrast to this situation, industrial needs seem to be increasing because of the increasingly competitive business environment.…”

Section: Introductionmentioning

confidence: 99%

Approximation Algorithms to Solve Real-Life Multicriteria Cutting Stock Problems

Chen¹,

Antonio

1999

Operations Research

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This paper addresses a real-life unidimensional cutting stock problem. The objective is not only to minimize trim loss, as in traditional cutting stock problems, but also to minimize cutting time. A variety of technical constraints are taken into account. These constraints often arise in the iron and steel cutting industry. Since cutting stock problems are well known to be NP-hard, it is prohibitive to obtain optimal solutions. We develop approximation algorithms for different purposes: quick response algorithms for individual customer requirement planning to build a quotation, and elaborate algorithms to provide a production plan for the next day. These latter algorithms are submitted to less strict computation time limitations. Computational results show that our algorithms improve by 8% the performance of our partner company where the cutting plan had been carried out manually by very experienced people. Numerical comparison for small sized problems shows that these algorithms provide solutions very close to optimal. These algorithms have been implemented in the company.

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“…Also several objectives can be considered [5,[8][9][10]:  element alignment (orthogonal or arbitrary),  efficient usage of available resources (e.g., number of cuts, scrap percentage) and  (real world) application constraints [23].…”

Section: Introductionmentioning

confidence: 99%

“…Most of these problems are geometry-dependent (e.g., facility layout, vehicle routing, packing, or cutting stock problems) [4][5][6][7][8][9]. Solving them calls for a colourful variability of geometry representation, search methods (i.e., algorithms), and objectives selection.…”

Section: Introductionmentioning

confidence: 99%

“…The geometry-dependent problem solving involves selection of elements (resources), dimensions of shapes (1D, 2D, 3D, or nD), and its representation [5,[8][9][10]:  1D (one-dimensional shapes): bars [11];  2D (two-dimensional shapes): rectangles, trapezoids, circles, convex, concave and irregular shapes [7,[12][13][14][15][16][17][18];  3D (three-dimensional shapes) [19,20];  nD (n-dimensional shapes) [21,22].…”

Section: Introductionmentioning

confidence: 99%

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A Universal CAD System for Cutting Stock Problem

Kovačić¹,

Brezočnik²

2017

Int. j. simul. model.

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In this research the universal system using CAD geometry for solving of cutting stock problem is proposed. The system consists of the three main modules: geometry definition module, objective definition module, and the search strategy module. In the first module the reference points and orientation of parts and stock are defined. In the second module some constraints such as the quantity of the desired type of parts to be placed on the stock can be taken into account. The third module contains the search strategy. For the purpose of this research, the genetic algorithm was used as the search method. For illustration of the generality of the proposed approach, three practical examples for solving orthogonally and irregularly-shaped cutting stock problems are presented. The parts which are to be cut from stock-material with minimal loss and also the stock-material itself are presented as CAD geometries without any kind of geometrical constraints (i.e., concavity, convexity, sections, and holes). In the presented approach the AutoCAD environment was used. The AutoLISP in-house developed system for cutting stock problem was integrated into the AutoCAD. The developed system is without any kind of geometrical constraints and thus highly applicable in the practice. The presented approach can be developed also in other CAD systems where the application programming interfaces (API) are available.

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The cutting stock problem — a survey

Cited by 96 publications

References 98 publications

Approximating Multi-Objective Hyper-Heuristics for Solving 2D Irregular Cutting Stock Problems

Approximating Multi-Objective Hyper-Heuristics for Solving 2D Irregular Cutting Stock Problems

Approximation Algorithms to Solve Real-Life Multicriteria Cutting Stock Problems

A Universal CAD System for Cutting Stock Problem

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