| Full text | |
| Author(s): |
Leao, Aline A. S.
[1]
;
Toledo, Franklina M. B.
[1]
;
Oliveira, Jose Fernando
[2]
;
Carravilla, Maria Antonia
[2]
;
Alvarez-Valdes, Ramon
[3]
Total Authors: 5
|
| Affiliation: | [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
Total Affiliations: 3
|
| Document type: | Review article |
| Source: | European Journal of Operational Research; v. 282, n. 3, p. 803-822, MAY 1 2020. |
| Web of Science Citations: | 2 |
| Abstract | |
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) | |
| FAPESP's process: | 13/07375-0 - CeMEAI - Center for Mathematical Sciences Applied to Industry |
| Grantee: | Francisco Louzada Neto |
| Support Opportunities: | Research Grants - Research, Innovation and Dissemination Centers - RIDC |
| FAPESP's process: | 12/21176-7 - Mathematical formulations for nesting problem |
| Grantee: | Aline Aparecida de Souza Leão |
| Support Opportunities: | Scholarships in Brazil - Post-Doctoral |
| FAPESP's process: | 18/07240-0 - Uncertainty in cutting and packing problems: robust planning and optimized replanning in manufacturing and transportation |
| Grantee: | Franklina Maria Bragion de Toledo |
| Support Opportunities: | Regular Research Grants |