Checkerboard pattern: proposals for its generation

Yanasse, Horácio Hideki; Katsurayama, Daniel Massaru

doi:10.1111/j.1475-3995.2005.00488.x

Cited by 15 publications

(7 citation statements)

References 16 publications

(15 reference statements)

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Heuristic solutions can be obtained by approaches focusing on the two-staged case, either free (Lodi and Monaci, 2003;Hifi an M'Hallah, 2005;Macedo et al, 2010;Mrad et al, 2012) or pgroup (Yanasse and Katsurayama, 2005;Yanasse and Morabito, 2006;, and on the three-staged case (Puchinger and Raidl, 2007;Silva et al, 2010;Cui et al, 2015b). Besides these papers, other simplifications have been proposed with the aim of reducing the solution space through the elimination of intricate cutting schemes.…”

Section: Heuristic and Metaheuristic Approachesmentioning

confidence: 99%

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

Russo¹,

Boccia

Sforza³

et al. 2019

Int Trans Operational Res

View full text Add to dashboard Cite

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.

show abstract

Section: Heuristic and Metaheuristic Approachesmentioning

confidence: 99%

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

Russo¹,

Boccia

Sforza³

et al. 2019

Int Trans Operational Res

View full text Add to dashboard Cite

show abstract

“…For the one-dimensional cutting stock problem, the subproblem is a regular knapsack problem ( Gilmore & Gomory, 1961,1963Martello & Toth, 1990 ). Considering higher dimensions for the subproblems, other solution methods have also been proposed in the literature ( Arenales & Morabito, 1995;Christofides & Whitlock, 1977;Yanasse & Katsurayama, 2005 ).…”

Section: Decision Variablesmentioning

confidence: 99%

Classification and literature review of integrated lot-sizing and cutting stock problems

Melega

Araújo

Jans

2018

European Journal of Operational Research

View full text Add to dashboard Cite

a b s t r a c tThe aim of this paper is to classify the literature related to the integration between the lot-sizing and cutting stock problem. A deterministic mathematical model, that considers multiple dimensions of integration and comprises several aspects found in practice, is proposed. This model is used as a framework to classify the current literature in this field. The main classification of the literature is organized around two types of integration. In a planning horizon which consists of multiple periods, the inventory provides a link between the periods. This integration across time periods constitutes the first type of integration. The proposed model also considers the production of different types of items at three different levels: objects are fabricated or purchased and next cut into pieces which are then assembled into final products. The integration between these three production levels constitutes the second type of integration. The classification indicates that, even though many papers in the current literature analyze an integrated lot-sizing and cutting stock problem, they vary widely with respect to the level of integration on the time and production level dimensions. Furthermore, our analysis indicates that the current models also consider varying assumptions with respect to the inventory, the production capacities and the setups. Finally, we point out some possible interesting areas for future research. (R. Jans). that might correspond to customer requests, and a decision related to the cutting stock problem is needed. Part of the smaller reels can be cut again into paper sheets, according to some decision related to the lot size for the papers sheets. In the furniture industry, wooden plates are produced or purchased from different suppliers, and a decision about the size of the lots to be produced or purchased from each supplier must be taken. Then, these wooden plates are cut into several wooden parts (in a two-dimensional cutting stock process) to be assembled into the final products. A decision about the size of the lots of final products is also needed, and consequently there are three levels of decisions. Other examples can be found in the fiberglass industry, where fiberglass plates are cut to manufacture printed circuit boards and in the aluminium industry, where aluminium profiles are cut to make several window types. The basic idea of the integrated lot-sizing and cutting stock problem is to consider, simultaneously, the decisions related to both problems so as to capture the interdependency between these decisions in order to obtain a better global solution. Several papers from the literature present computational results showing the benefits of considering an integrated approach instead of taking decisions separately

show abstract

“…Solution approaches for two‐stage two‐dimensional cutting stock problems based on two phases are common in the literature, as for example in Farley (), Riehme et al. (), Hifi (), Morabito and Garcia (), and Yanasse and Katsurayama (). For the case in which the set of items has few items of identical size, authors have proposed alternatives for the rounding of relaxed solutions of the simplex method (Wäscher and Gau, ; Poldi and Arenales, ) or greedy heuristics combined with column‐generation procedures (Hinxman, ; Poldi and Arenales, ) that may not work well for two‐stage two‐dimensional bin‐packing problems.…”

Section: Two‐stage Bin‐packing Models Without Leftoversmentioning

confidence: 99%

Two‐stage two‐dimensional guillotine cutting stock problems with usable leftover

Andrade

Birgin

Morábito

2014

Int Trans Operational Res

View full text Add to dashboard Cite

In this study, we solve the nonexact two-stage two-dimensional guillotine cutting problem considering usable leftovers, in which stock plates remainders of the cutting patterns (nonused material or trim loss) can be used in the future, if they are large enough to fulfill future demands for items (ordered smaller plates). This cutting problem can be characterized as a residual bin-packing problem because of the possibility of putting back into stock residual pieces, as the trim loss of each cutting/packing pattern does not necessarily represent waste of material depending on its size. Two bilevel mathematical programming models to represent this nonexact two-stage two-dimensional residual bin-packing problem are presented. The models basically consist of cutting/packing the ordered items using a set of plates of minimum cost and, among all possible solutions of minimum cost, choosing one that maximizes the value of the generated usable leftovers. Because of special characteristics of these bilevel models, they can be reformulated as one-level mixed integer programming models. Results of some numerical experiments are presented to show that the models represent appropriately the problem and illustrate their performance.

show abstract

Checkerboard pattern: proposals for its generation

Cited by 15 publications

References 16 publications

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

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

Classification and literature review of integrated lot-sizing and cutting stock problems

Two‐stage two‐dimensional guillotine cutting stock problems with usable leftover

Contact Info

Product

Resources

About