### Abstract

The global constraint sum can be used as a tool to implement summations over sets of variables whose indices are not known in advance. This paper has two major contributions. On the theoretical side,we present the convex hull relaxation for the sum constraint in terms of linear inequalities, whose importance in the context of hybrid models is then justified. On the practical side, we demonstrate the applicability of the sum constraint in a scheduling problem that arises as part of the development of new products in the pharmaceutical and agrochemical industries. This problem can be modeled in two alternative ways: by using the sum constraint in a natural and straight forward manner, or by using the element constraint in a trickier fashion. With the convex hull relaxation developed earlier, we prove that the linear relaxation obtained from the former model is tighter than the one obtained from the latter.Moreover, our computational experiments indicate that the CP modelbased on the sum constraint is significantly more efficient as well.

Original language | English (US) |
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Title of host publication | Principles and Practice of Constraint Programming- CP 2002 - 8th International Conference, CP 2002, Proceedings |

Editors | Pascal Van Hentenryck |

Publisher | Springer Verlag |

Pages | 80-92 |

Number of pages | 13 |

ISBN (Print) | 3540441204, 9783540441205 |

State | Published - Jan 1 2002 |

Externally published | Yes |

Event | 8th International Conference on Principles and Practice of Constraint Programming, CP 2002 - Ithaca, United States Duration: Sep 9 2002 → Sep 13 2002 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 2470 |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 8th International Conference on Principles and Practice of Constraint Programming, CP 2002 |
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Country | United States |

City | Ithaca |

Period | 9/9/02 → 9/13/02 |

### Fingerprint

### ASJC Scopus subject areas

- Computer Science(all)
- Theoretical Computer Science

### Cite this

*Principles and Practice of Constraint Programming- CP 2002 - 8th International Conference, CP 2002, Proceedings*(pp. 80-92). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 2470). Springer Verlag.

**On the sum constraint : Relaxation and applications.** / Yunes, Tallys.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Principles and Practice of Constraint Programming- CP 2002 - 8th International Conference, CP 2002, Proceedings.*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 2470, Springer Verlag, pp. 80-92, 8th International Conference on Principles and Practice of Constraint Programming, CP 2002, Ithaca, United States, 9/9/02.

}

TY - GEN

T1 - On the sum constraint

T2 - Relaxation and applications

AU - Yunes, Tallys

PY - 2002/1/1

Y1 - 2002/1/1

N2 - The global constraint sum can be used as a tool to implement summations over sets of variables whose indices are not known in advance. This paper has two major contributions. On the theoretical side,we present the convex hull relaxation for the sum constraint in terms of linear inequalities, whose importance in the context of hybrid models is then justified. On the practical side, we demonstrate the applicability of the sum constraint in a scheduling problem that arises as part of the development of new products in the pharmaceutical and agrochemical industries. This problem can be modeled in two alternative ways: by using the sum constraint in a natural and straight forward manner, or by using the element constraint in a trickier fashion. With the convex hull relaxation developed earlier, we prove that the linear relaxation obtained from the former model is tighter than the one obtained from the latter.Moreover, our computational experiments indicate that the CP modelbased on the sum constraint is significantly more efficient as well.

AB - The global constraint sum can be used as a tool to implement summations over sets of variables whose indices are not known in advance. This paper has two major contributions. On the theoretical side,we present the convex hull relaxation for the sum constraint in terms of linear inequalities, whose importance in the context of hybrid models is then justified. On the practical side, we demonstrate the applicability of the sum constraint in a scheduling problem that arises as part of the development of new products in the pharmaceutical and agrochemical industries. This problem can be modeled in two alternative ways: by using the sum constraint in a natural and straight forward manner, or by using the element constraint in a trickier fashion. With the convex hull relaxation developed earlier, we prove that the linear relaxation obtained from the former model is tighter than the one obtained from the latter.Moreover, our computational experiments indicate that the CP modelbased on the sum constraint is significantly more efficient as well.

UR - http://www.scopus.com/inward/record.url?scp=84957026851&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84957026851&partnerID=8YFLogxK

M3 - Conference contribution

SN - 3540441204

SN - 9783540441205

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 80

EP - 92

BT - Principles and Practice of Constraint Programming- CP 2002 - 8th International Conference, CP 2002, Proceedings

A2 - Van Hentenryck, Pascal

PB - Springer Verlag

ER -