## Title data

Kartak, Vadim ; Kurz, Sascha ; Scheithauer, Guntram ; Ripatti, Artem:

**Minimal proper non-IRUP instances of the one-dimensional Cutting Stock Problem.**

*In:* Discrete Applied Mathematics.
Vol. 187
(2015)
.
- pp. 120-129.

ISSN 1872-6771

DOI: https://doi.org/10.1016/j.dam.2015.02.020

## Abstract in another language

We consider the well-known one dimensional cutting stock problem (1CSP). Based on the pattern structure of the classical ILP formulation of Gilmore and Gomory, we can decompose the infinite set of 1CSP instances, with a fixed demand n, into a finite number of equivalence classes. We show up a strong relation to weighted simple games. Studying the integer round-up property we computationally show that all 1CSP instances with n ≤ 9 are proper IRUP, while we give examples of a proper non-IRUP instances with n = 10. A gap larger than 1 occurs for n = 11. The worst known gap is raised from 1.003 to 1.0625. The used algorithmic approaches are based on exhaustive enumeration and integer linear programming. Additionally we give some theoretical bounds showing that all 1CSP instances with some specific parameters have the proper IRUP.

## Further data

Item Type: | Article in a journal |
---|---|

Refereed: | Yes |

Keywords: | bin packing problem; cutting stock problem; integer round-up property; equivalence of instances; branch and bound method; linear programming; weighted simple games |

Subject classification: | MSC: 90C10; 90B80; 90C27; 90C06; 91B12 |

Institutions of the University: | Faculties > Faculty of Mathematics, Physics und Computer Science Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematical Economics Profile Fields > Emerging Fields > Governance and Responsibility Faculties Profile Fields Profile Fields > Emerging Fields |

Result of work at the UBT: | Yes |

DDC Subjects: | 000 Computer Science, information, general works > 004 Computer science 500 Science > 510 Mathematics |

Date Deposited: | 10 Apr 2015 09:47 |

Last Modified: | 16 Mar 2023 11:51 |

URI: | https://eref.uni-bayreuth.de/id/eprint/10042 |