| Full text | |
| Author(s): |
Martin, Mateus
;
Morabito, Reinaldo
;
Munari, Pedro
Total Authors: 3
|
| Document type: | Journal article |
| Source: | INTERNATIONAL JOURNAL OF PRODUCTION RESEARCH; v. 60, n. 6, p. 20-pg., 2021-02-09. |
| Abstract | |
We address two variants of the two-dimensional guillotine cutting problem that appear in different manufacturing settings that cut defective objects. Real-world applications include the production of flat glass in the glass industry and the cutting of wooden boards with knotholes in the furniture industry. These variants assume that there are several defects in the object, but the items cut should be defective-free; the cutting pattern is limited to two guillotine stages; and the maximum number of copies per item type in the pattern can be limited. The first variant deals with exact 2-stage patterns, while the second with exact 1-group patterns. To effectively solve these problems, we propose a Constraint Programming (CP) based algorithm as well as different Integer Linear Programming (ILP) formulations. The first presented formulations are extensions of the modelling approach of [Martin, M., E. G. Birgin, R. D. Lobato, R. Morabito, and P. Munari. 2020. "Models for the Two-Dimensional Rectangular Single Large Placement Problem with Guillotine Cuts and Constrained Pattern." International Transactions in Operational Research 27: 767-793. doi:] for the case with defects, while the others are novel and more elaborate formulations based on the relative position of the items. We evaluate these three approaches with computational experiments using a set of benchmark instances from the literature. The results show that the approaches find optimal and near-optimal solutions in short processing times for several types of problem instances. (AU) | |
| FAPESP's process: | 16/08039-1 - Two-Dimensional Cutting Problems: Mathematical Formulations and Solution Methods |
| Grantee: | Mateus Pereira Martin |
| Support Opportunities: | Scholarships in Brazil - Doctorate |
| FAPESP's process: | 20/00747-2 - New formulations for the minimization open stacks problems and related |
| Grantee: | Mateus Pereira Martin |
| Support Opportunities: | Scholarships in Brazil - Post-Doctoral |
| 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: | 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 Opportunities: | Research Projects - Thematic Grants |