Irregular packing problems: A review of mathematical models

Autor(es)

Leao, Aline A. S. ^[1] ; Toledo, Franklina M. B. ^[1] ; Oliveira, Jose Fernando ^[2] ; Carravilla, Maria Antonia ^[2] ; Alvarez-Valdes, Ramon ^[3]

Afiliação do(s) autor(es)

^[1] Univ Sao Paulo, Inst Math & Comp Sci, Sao Carlos - Brazil

^[2] Univ Porto, Fac Engn, INESC TEC, Porto - Portugal

^[3] Univ Valencia, Dept Stat & Operat Res, Valencia - Spain

• Tipo de documento: Artigo de Revisão
• Fonte: European Journal of Operational Research; v. 282, n. 3, p. 803-822, MAY 1 2020.
• Citações Web of Science: 2

Resumo

Irregular packing problems (also known as nesting problems) belong to the more general class of cutting and packing problems and consist of allocating a set of irregular and regular pieces to larger rectangular or irregular containers, while minimizing the waste of material or space. These problems combine the combinatorial hardness of cutting and packing problems with the computational difficulty of enforcing the geometric non-overlap and containment constraints. Unsurprisingly, nesting problems have been addressed, both in the scientific literature and in real-world applications, by means of heuristic and metaheuristic techniques. However, more recently a variety of mathematical models has been proposed for nesting problems. These models can be used either to provide optimal solutions for nesting problems or as the basis of heuristic approaches based on them (e.g. matheuristics). In both cases, better solutions are sought, with the natural economic and environmental positive impact. Different modeling options are proposed in the literature. We review these mathematical models under a common notation framework, allowing differences and similarities among them to be highlighted. Some insights on weaknesses and strengths are also provided. By building this structured review of mathematical models for nesting problems, research opportunities in the field are proposed. (C) 2019 Elsevier B.V. All rights reserved. (AU)

• Processo FAPESP: 12/21176-7 - Formulações matemáticas para o problema de corte de peças irregulares
• Beneficiário: Aline Aparecida de Souza Leão
• Linha de fomento: Bolsas no Brasil - Pós-Doutorado
• Processo FAPESP: 13/07375-0 - CeMEAI - Centro de Ciências Matemáticas Aplicadas à Indústria
• Beneficiário: José Alberto Cuminato
• Linha de fomento: Auxílio à Pesquisa - Centros de Pesquisa, Inovação e Difusão - CEPIDs
• Processo FAPESP: 18/07240-0 - Incerteza em problemas de cortes e empacotamentos: planeamento robusto e replaneamento otimizado na produção e nos transportes
• Beneficiário: Franklina Maria Bragion de Toledo
• Linha de fomento: Auxílio à Pesquisa - Regular