Algorithmic Advances for 1.5-Dimensional Two-Stage Cutting Stock Problem
The Cutting Stock Problem (CSP) is an optimization challenge that involves dividing large objects into smaller components while considering various managerial objectives. The problem’s complexity can differ based on factors such as object dimensionality, the number of cutting stages required, and an...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2024-12-01
|
| Series: | Algorithms |
| Subjects: | |
| Online Access: | https://www.mdpi.com/1999-4893/18/1/3 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832589375913852928 |
|---|---|
| author | Antonio Grieco Pierpaolo Caricato Paolo Margiotta |
| author_facet | Antonio Grieco Pierpaolo Caricato Paolo Margiotta |
| author_sort | Antonio Grieco |
| collection | DOAJ |
| description | The Cutting Stock Problem (CSP) is an optimization challenge that involves dividing large objects into smaller components while considering various managerial objectives. The problem’s complexity can differ based on factors such as object dimensionality, the number of cutting stages required, and any technological constraints. The demand for coils of varying sizes and quantities necessitates intermediate splitting and slitting stages to produce the finished rolls. Additionally, relationships between orders are affected by dimensional variations at each stage of processing. This specific variant of the problem is known as the One-and-a-Half Dimensional Two-Stage Cutting Stock Problem (1.5-D TSCSP). To address the 1.5-D TSCSP, two algorithmic approaches were developed: the Generate-and-Solve (G&S) method and a hybrid Row-and-Column Generation (R&CG) approach. Both aim to minimize total trim loss while navigating the complexities of the problem. Inspired by existing problems in the literature for simpler versions of the problem, a set of randomly generated test cases was prepared, as detailed in this paper. An implementation of the two approaches was used to obtain solutions for the generated test campaign. The simpler G&S approach demonstrated superior performance in solving smaller instances of the problem, while the R&CG approach exhibited greater efficiency and provided superior solutions for larger instances. |
| format | Article |
| id | doaj-art-0b4b5adcdf134999bf827319ea5553ce |
| institution | Kabale University |
| issn | 1999-4893 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Algorithms |
| spelling | doaj-art-0b4b5adcdf134999bf827319ea5553ce2025-01-24T13:17:25ZengMDPI AGAlgorithms1999-48932024-12-01181310.3390/a18010003Algorithmic Advances for 1.5-Dimensional Two-Stage Cutting Stock ProblemAntonio Grieco0Pierpaolo Caricato1Paolo Margiotta2Dipartimento di Ingegneria dell’Innovazione, Università del Salento, 73100 Lecce, ItalyDipartimento di Ingegneria dell’Innovazione, Università del Salento, 73100 Lecce, ItalyDipartimento di Ingegneria dell’Innovazione, Università del Salento, 73100 Lecce, ItalyThe Cutting Stock Problem (CSP) is an optimization challenge that involves dividing large objects into smaller components while considering various managerial objectives. The problem’s complexity can differ based on factors such as object dimensionality, the number of cutting stages required, and any technological constraints. The demand for coils of varying sizes and quantities necessitates intermediate splitting and slitting stages to produce the finished rolls. Additionally, relationships between orders are affected by dimensional variations at each stage of processing. This specific variant of the problem is known as the One-and-a-Half Dimensional Two-Stage Cutting Stock Problem (1.5-D TSCSP). To address the 1.5-D TSCSP, two algorithmic approaches were developed: the Generate-and-Solve (G&S) method and a hybrid Row-and-Column Generation (R&CG) approach. Both aim to minimize total trim loss while navigating the complexities of the problem. Inspired by existing problems in the literature for simpler versions of the problem, a set of randomly generated test cases was prepared, as detailed in this paper. An implementation of the two approaches was used to obtain solutions for the generated test campaign. The simpler G&S approach demonstrated superior performance in solving smaller instances of the problem, while the R&CG approach exhibited greater efficiency and provided superior solutions for larger instances.https://www.mdpi.com/1999-4893/18/1/3manufacturing technology managementtwo-stage CSP1.5-D CSProw-and-column generationguillotine |
| spellingShingle | Antonio Grieco Pierpaolo Caricato Paolo Margiotta Algorithmic Advances for 1.5-Dimensional Two-Stage Cutting Stock Problem Algorithms manufacturing technology management two-stage CSP 1.5-D CSP row-and-column generation guillotine |
| title | Algorithmic Advances for 1.5-Dimensional Two-Stage Cutting Stock Problem |
| title_full | Algorithmic Advances for 1.5-Dimensional Two-Stage Cutting Stock Problem |
| title_fullStr | Algorithmic Advances for 1.5-Dimensional Two-Stage Cutting Stock Problem |
| title_full_unstemmed | Algorithmic Advances for 1.5-Dimensional Two-Stage Cutting Stock Problem |
| title_short | Algorithmic Advances for 1.5-Dimensional Two-Stage Cutting Stock Problem |
| title_sort | algorithmic advances for 1 5 dimensional two stage cutting stock problem |
| topic | manufacturing technology management two-stage CSP 1.5-D CSP row-and-column generation guillotine |
| url | https://www.mdpi.com/1999-4893/18/1/3 |
| work_keys_str_mv | AT antoniogrieco algorithmicadvancesfor15dimensionaltwostagecuttingstockproblem AT pierpaolocaricato algorithmicadvancesfor15dimensionaltwostagecuttingstockproblem AT paolomargiotta algorithmicadvancesfor15dimensionaltwostagecuttingstockproblem |