Models for the two-dimensional rectangular single large placement problem with guillotine cuts and constrained pattern

Autor(es)

Martin, Mateus ^[1] ; Birgin, Ernesto G. ^[2] ; Lobato, Rafael D. ^[2] ; Morabito, Reinaldo ^[1] ; Munari, Pedro ^[1]

Afiliação do(s) autor(es)

^[1] Univ Fed Sao Carlos, Dept Prod Engn, Via Washington Luiz Km 235, BR-13565905 Sao Carlos, SP - Brazil

^[2] Univ Sao Paulo, Dept Comp Sci, Sao Paulo - Brazil

• Tipo de documento: Artigo Científico
• Fonte: International Transactions in Operational Research; v. 27, n. 2 JULY 2019.
• Citações Web of Science: 2

Resumo

In this paper, we address the constrained two-dimensional rectangular guillotine single large placement problem (2D\_R\_CG\_SLOPP). This problem involves cutting a rectangular object to produce smaller rectangular items from orthogonal guillotine cuts. In addition, there is an upper limit on the number of copies that can be produced of each item type. To model this problem, we propose a new pseudopolynomial integer nonlinear programming (INLP) formulation and obtain an equivalent integer linear programming (ILP) formulation from it. Additionally, we developed a procedure to reduce the numbers of variables and constraints of the integer linear programming (ILP) formulation, without loss of optimality. From the ILP formulation, we derive two new pseudopolynomial models for particular cases of the 2D\_R\_CG\_SLOPP, which consider only two-staged or one-group patterns. Finally, as a specific solution method for the 2D\_R\_CG\_SLOPP, we apply Benders decomposition to the proposed ILP formulation and develop a branch-and-Benders-cut algorithm. All proposed approaches are evaluated through computational experiments using benchmark instances and compared with other formulations available in the literature. The results show that the new formulations are appropriate in scenarios characterized by few item types that are large with respect to the object's dimensions. (AU)

• Processo FAPESP: 13/07375-0 - CeMEAI - Centro de Ciências Matemáticas Aplicadas à Indústria
• Beneficiário: Francisco Louzada Neto
• Modalidade de apoio: Auxílio à Pesquisa - Centros de Pesquisa, Inovação e Difusão - CEPIDs
• Processo FAPESP: 16/01860-1 - Problemas de corte, empacotamento, dimensionamento de lotes, programação da produção, roteamento, localização e suas integrações em contextos industriais e logísticos
• Beneficiário: Reinaldo Morabito Neto
• Modalidade de apoio: Auxílio à Pesquisa - Temático
• Processo FAPESP: 12/23916-8 - Empacotamento de elipsoides
• Beneficiário: Rafael Durbano Lobato
• Modalidade de apoio: Bolsas no Brasil - Doutorado
• Processo FAPESP: 16/08039-1 - Problemas de Corte Bidimensional Guilhotinado e Restrito: Formulações Matemáticas e Métodos de Solução
• Beneficiário: Mateus Pereira Martin
• Modalidade de apoio: Bolsas no Brasil - Doutorado