The minimum cost multiple-source unsplittable flow problem is studied in this paper. A simple necessary condition to get a solution is proposed. It deals with capacities and demands and can be seen as a generalization of the well-known semi-metric condition for continuous multicommdity flows. A cutting plane algorithm is derived using a superadditive approach. The inequalities considered here are valid for single knapsack constraints. They are based on nondecreasing superadditive functions and can be used to strengthen the relaxation of any integer program with knapsack constraints. Some numerical experiments confirm the efficiency of the inequalities introduced in the paper.
Mots-clés : network flows, integer programming, superadditive functions
@article{RO_2007__41_3_253_0,
author = {Belaidouni, Meriema and Ben-Ameur, Walid},
title = {On the minimum cost multiple-source unsplittable flow problem},
journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
pages = {253--273},
publisher = {EDP-Sciences},
volume = {41},
number = {3},
year = {2007},
doi = {10.1051/ro:2007023},
mrnumber = {2348001},
language = {en},
url = {http://archive.numdam.org/articles/10.1051/ro:2007023/}
}
TY - JOUR AU - Belaidouni, Meriema AU - Ben-Ameur, Walid TI - On the minimum cost multiple-source unsplittable flow problem JO - RAIRO - Operations Research - Recherche Opérationnelle PY - 2007 SP - 253 EP - 273 VL - 41 IS - 3 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/ro:2007023/ DO - 10.1051/ro:2007023 LA - en ID - RO_2007__41_3_253_0 ER -
%0 Journal Article %A Belaidouni, Meriema %A Ben-Ameur, Walid %T On the minimum cost multiple-source unsplittable flow problem %J RAIRO - Operations Research - Recherche Opérationnelle %D 2007 %P 253-273 %V 41 %N 3 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/ro:2007023/ %R 10.1051/ro:2007023 %G en %F RO_2007__41_3_253_0
Belaidouni, Meriema; Ben-Ameur, Walid. On the minimum cost multiple-source unsplittable flow problem. RAIRO - Operations Research - Recherche Opérationnelle, Tome 41 (2007) no. 3, pp. 253-273. doi : 10.1051/ro:2007023. http://archive.numdam.org/articles/10.1051/ro:2007023/
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