TY - GEN

T1 - On the sum constraint

T2 - 8th International Conference on Principles and Practice of Constraint Programming, CP 2002

AU - Yunes, Tallys H.

N1 - Publisher Copyright:
© Springer-Verlag Berlin Heidelberg 2002.
Copyright:
Copyright 2020 Elsevier B.V., All rights reserved.

PY - 2002

Y1 - 2002

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.

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U2 - 10.1007/3-540-46135-3_6

DO - 10.1007/3-540-46135-3_6

M3 - Conference contribution

AN - SCOPUS:84957026851

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

Y2 - 9 September 2002 through 13 September 2002

ER -