### Abstract

In this paper, we consider the set partitioning polytope and we begin by applying the reformulation-linearization technique of Sherali and Adams (1990, 1994) to generate a specialized hierarchy of relaxations by exploiting the structure of this polytope. We then show that several known classes of valid inequalities for this polytope, as well as related tightening and composition rules, are automatically captured within the first-and second-level relaxations of this hierarchy. Hence, these relaxations provide a unifying framework for a broad class of such inequalities. Furthermore, it is possible to implement only partial forms of these relaxations from the viewpoint of generating tighter relaxations that delete the underlying linear programming solution to the set partitioning problem, based on variables that are fractional at an optimum to this problem.

Original language | English |
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Pages (from-to) | 153-167 |

Number of pages | 15 |

Journal | Discrete Applied Mathematics |

Volume | 68 |

Issue number | 1-2 |

Publication status | Published - 1996 Jun 12 |

Externally published | Yes |

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### Keywords

- Cutting planes
- Reformulation-linearization technique
- Set partitioning polytope
- Valid inequalities

### ASJC Scopus subject areas

- Computational Theory and Mathematics
- Applied Mathematics
- Discrete Mathematics and Combinatorics
- Theoretical Computer Science

### Cite this

*Discrete Applied Mathematics*,

*68*(1-2), 153-167.