Integer linear programming for a cutting problem in the wood‐processing industry: a case study

Koch, Sören; König, S.; Wäscher, Gerhard

doi:10.1111/j.1475-3995.2009.00704.x

Cited by 19 publications

(10 citation statements)

References 9 publications

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“…O primeiro artigo que se refere ao problema de corte de estoque com as sobras aproveitáveis encontradas na literatura foi proposto por Brown em 1971 [3], mas somente posteriormente, esse problema foi abordado diretamente. Algumas abordagens de solução para PCESA podem ser encontradas em, Roodman [14], Scheithauer [15], Gradisar et al [9], Abuabara e Morabito [1], Nicola [12], Cherri et al [4], Koch et al [10], Cherri et al [5], Arenales et al [2] e entre outros.…”

Section: Introductionunclassified

Problema de Corte de Estoque Unidimensional com Sobras Aproveitáveis: Solução via Metaheurística GRASP

Poldi

Rios

2020

Tend. Mat. Apl. Comput.

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Recebido em 3 de fevereiro de 2020 / Aceito em 9 de julho de 2020 RESUMO. Neste artigo apresentamos um estudo sobre o Problema de Corte de Estoque com Sobras Aproveitáveis (PCESA) unidimensional. O Problema de Corte de Estoque (PCE) consiste em cortar um conjunto de objetos, disponíveis em estoque, para produzir um conjunto de itens em quantidades e tamanhos especificados. O PCESAé um PCE no qual nem todas as sobras de um processo de corte são consideradas perdas, ou seja, quando uma sobra for maior que um determinado comprimento, ela retorna ao estoque para ser usada nos processos de corte subsequentes. Assim, o objetivo do problema abordadoé otimizar os planos de corte a serem aplicados em objetos padronizados e objetos não padronizados (sobras de cortes anteriores); atender a demanda conhecida de itens menores, de forma a minimizar a perda de material, controlando a quantidade de retalhos gerados. Para resolver este problema, duas heurísticas e três versões da metaheurística Greedy Randomized Adaptive Search Procedure (GRASP) foram desenvolvidas. Testes computacionais foram realizados para os procedimentos propostos em instâncias da literatura. As abordagens propostas para a solução apresentaram boas soluções em relação ao número de sobras geradas.

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Section: Introductionunclassified

Problema de Corte de Estoque Unidimensional com Sobras Aproveitáveis: Solução via Metaheurística GRASP

Poldi

Rios

2020

Tend. Mat. Apl. Comput.

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“…Aiming to reduce operating costs, several aspects of the cutting process may be taken into account, and returning leftovers to stock so they can be used in future orders is one of them (see, for example, Koch et al. () and Chen et al. (), where the usage of leftovers in the wood‐processing and plastic‐film industries are considered).…”

Section: Introductionmentioning

confidence: 99%

The multiperiod two‐dimensional non‐guillotine cutting stock problem with usable leftovers

Birgin

Romão

Ronconi

2019

Int Trans Operational Res

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A mixed integer linear programing model for the two‐dimensional non‐guillotine cutting problem with usable leftovers was recently introduced by Andrade et al. The problem consists in cutting a set of ordered items using a set of objects of minimum cost and, within the set of solutions of minimum cost, maximizing the value of the usable leftovers. Since the concept of usable leftovers assumes they can potentially be used to attend new arriving orders, the problem is extended to the multiperiod framework in this work. In this way, the decision at each instant does not minimize in a myopic way the cost of the objects required to attend the orders of the current instant; but it aims to minimize the overall cost of the objects up to the considered time horizon. Some variants of the proposed model are analyzed and numerical results are presented.

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“…One‐dimensional cutting/packing problems that allow the provision of residual pieces have been studied by different authors (Roodman, ; Scheithauer, ; Gradisar et al., , ; Sinuany‐Stern and Weiner, ; Gradisar and Trkman, ; Trkman and Gradisar, ; Cherri et al., , ; Dimitriadis and Kehris, ; Cui and Yang, ; Bang‐Jensen and Larsen, ). Examples of applications of one‐dimensional cutting problems with usable leftovers were reported in, for example, the textile industry (Gradisar et al., ), the agricultural light aircraft manufacturing (Abuabara and Morabito, ), and the wood‐processing industry (Koch et al., ). To the best of our knowledge, all studies reported in the literature focused on one‐dimensional residual bin‐packing problems, the exception being the recent published paper (Andrade et al., ) that deals with two‐dimensional nonguillotine cutting problems with usable leftovers.…”

Section: Introductionmentioning

confidence: 99%

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

Andrade

Birgin

Morábito

2014

Int Trans Operational Res

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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.

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Integer linear programming for a cutting problem in the wood‐processing industry: a case study

Cited by 19 publications

References 9 publications

Problema de Corte de Estoque Unidimensional com Sobras Aproveitáveis: Solução via Metaheurística GRASP

Problema de Corte de Estoque Unidimensional com Sobras Aproveitáveis: Solução via Metaheurística GRASP

The multiperiod two‐dimensional non‐guillotine cutting stock problem with usable leftovers

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

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