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superadditive functions

RAIRO - Operations Research (1)

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On the minimum cost multiple-source unsplittable flow problem
Meriema Belaidouni, Walid Ben-Ameur
Journal:

RAIRO - Operations Research / Volume 41 / Issue 3 / July 2007

Published online by Cambridge University Press:

21 August 2007, pp. 253-273

Print publication:

July 2007
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The minimum cost multiple-source unsplittable flow problem isstudied in this paper. A simple necessary condition to get asolution is proposed. It deals with capacities and demands and canbe seen as a generalization of the well-known semi-metriccondition for continuous multicommdity flows. A cutting planealgorithm is derived using a superadditive approach. Theinequalities considered here are valid for single knapsackconstraints. They are based on nondecreasing superadditivefunctions and can be used to strengthen the relaxation of anyinteger program with knapsack constraints. Some numericalexperiments confirm the efficiency of the inequalities introducedin the paper.