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

Yanasse, Horácio Hideki; Morábito, Reinaldo

doi:10.1080/00207540601011543

Cited by 29 publications

(14 citation statements)

References 34 publications

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“…Figure 2 shows four types of n-groups patterns: (a) 1-group, (b) 2-groups, (c) 3i-groups and (d) 3t-groups. Since most of the cutting patterns used in Factory V are n-group, Faccio and Rangel (2009) conducted a computational study of the mixed integer programming models presented by Yanasse and Morabito (2008) to generate n-group patterns (n = 1, 2, 3) with data from Factory V. The results showed that the generated cutting patterns have waste within the requirements of the industry (average waste between 1.1 and 2.5 %). The best results were obtained with the 3t-group cutting patterns.…”

Section: D Cutting Pattern Generationmentioning

confidence: 99%

A heuristic approach to minimize the number of saw cycles in small-scale furniture factories

2015

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This paper addresses a two-dimensional cutting stock problem arising in furniture factories. The problem involves the simultaneous optimization of two, usually conflicting, objectives: minimizing the total number of objects and maximizing the cutting machine productivity in terms of the number of objects that are simultaneously cut. A heuristic algorithm to solve the problem is proposed based on variables and constraints generation. The main idea is to add, in a dynamic way, bounds to the frequency of some chosen cutting patterns. At each iteration a solution is generated and at the end we have a set of non-dominated solutions. A computational study was conducted using real data from a small-scale furniture factory. The results show that the proposed algorithm finds solutions that are as good as or better than the ones used in practice in the furniture factory.

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Section: D Cutting Pattern Generationmentioning

confidence: 99%

A heuristic approach to minimize the number of saw cycles in small-scale furniture factories

2015

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“…Recently, many studies have focused on special classes of cutting patterns, such as the p-group, T-shaped, or p-staged, due to the impractical computational time and particular characteristics of certain cutting machines (Yanasse and Morabito 2008, Cui and Yang 2011, Wy and Kim 2011. However, far fewer studies have considered exact algorithms for non-staged CTDC because non-staged CTDC is more difficult to solve than any other type of TDC (i.e., it is more difficult than UTDC or staged TDC).…”

Section: Introductionmentioning

confidence: 99%

An improved best-first branch-and-bound algorithm for constrained two-dimensional guillotine cutting problems

Yoon

Ahn

Kang

2013

International Journal of Production Research

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The constrained two-dimensional cutting problem involves maximising the sum of the profits obtained from small rectangular pieces cut from a large rectangular plate where the number of each type of cut piece cannot exceed a prescribed quantity. This paper proposes a best-first branch-and-bound algorithm to find the optimal solution to the problem. The proposed algorithm uses an efficient method to remove the duplicate patterns, and it improves the existing upper bounds. It also prevents the construction of dominated patterns and introduces a new bounding strategy that can prune more than one node at a time. Computational results are compared with a well-known exact algorithm to demonstrate the efficiency of the proposed algorithm. The proposed algorithm is as fast as or faster than the existing algorithm and reduces the average computing time by up to 99% for benchmark problems. For some problems, it can also find optimal solutions that existing algorithms are not able to find.

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“…Otherwise, if two different cut sets are used, then it is denoted as 2‐group, since the strips have to be separated in two different groups before being processed. This concept can be extended and the term p ‐group is used to denote the case when the number of different cut sets is limited by an integer value p (Yanasse and Morabito, ). The general two‐staged case with unlimited p value is also referred to as free .…”

Section: Introductionmentioning

confidence: 99%

Constrained two‐dimensional guillotine cutting problem: upper‐bound review and categorization

Russo¹,

Boccia

Sforza³

et al. 2019

Int Trans Operational Res

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In the two‐dimensional (2D) cutting (2DC) problem, a large rectangular sheet has to be dissected into smaller rectangular pieces with the aim of maximizing the total profit associated with the extracted pieces. When the number of copies of each piece to be extracted is bounded, it is referred to as constrained 2DC (C2DC) problem. The C2DC has been widely studied by the operations research community for its applications and theoretical issues. In this work, we recall the best exact and heuristic solving approaches for the C2DC and we provide a review and a categorization of the available upper bounds. We also discuss improvements and combinations of these upper bounds and give directions for their effective exploitation. Finally, we demonstrate the loss of accuracy of several exact methods present in literature because of the effect of the used antiredundancy strategies on the implemented bounding criteria. This work, based on more than 90 contributions, has a twofold target. For researchers working in C2DC, it provides a useful insight on the topic. For expert practitioners, it represents a systematic collection of the main findings and achievements, posing also the basis for future research.

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

Cited by 29 publications

References 34 publications

A heuristic approach to minimize the number of saw cycles in small-scale furniture factories

A heuristic approach to minimize the number of saw cycles in small-scale furniture factories

An improved best-first branch-and-bound algorithm for constrained two-dimensional guillotine cutting problems

Constrained two‐dimensional guillotine cutting problem: upper‐bound review and categorization

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