Two-dimensional cutting problems: mathematical formulations and solution methods
| Full text | |
| Author(s): |
Martin, Mateus
[1]
;
Birgin, Ernesto G.
[2]
;
Lobato, Rafael D.
[2]
;
Morabito, Reinaldo
[1]
;
Munari, Pedro
[1]
Total Authors: 5
|
| Affiliation: | [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
Total Affiliations: 2
|
| Document type: | Journal article |
| Source: | International Transactions in Operational Research; v. 27, n. 2 JULY 2019. |
| Web of Science Citations: | 0 |
| Abstract | |
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) | |
| FAPESP's process: | 13/07375-0 - CeMEAI - Center for Mathematical Sciences Applied to Industry |
| Grantee: | José Alberto Cuminato |
| Support type: | Research Grants - Research, Innovation and Dissemination Centers - RIDC |
| FAPESP's process: | 16/08039-1 - Two-dimensional cutting problems: mathematical formulations and solution methods |
| Grantee: | Mateus Pereira Martin |
| Support type: | Scholarships in Brazil - Doctorate |
| FAPESP's process: | 16/01860-1 - Cutting, packing, lot-sizing, scheduling, routing and location problems and their integration in industrial and logistics settings |
| Grantee: | Reinaldo Morabito Neto |
| Support type: | Research Projects - Thematic Grants |
| FAPESP's process: | 12/23916-8 - Ellipsoid packing |
| Grantee: | Rafael Durbano Lobato |
| Support type: | Scholarships in Brazil - Doctorate |