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A new strategy for the undirected two-commodity maximum flow problem

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Abstract

We address the two-commodity maximum flow problem on undirected networks. As a result of a change of variables, we introduce a new formulation that solves the problem through classical maximum flow techniques with only one-commodity. Therefore, a general strategy, based on this change of variables, is defined to deal with other undirected multi-commodity problems. Finally, we extend the single objective problem to a bicriteria environment. We show that the set of efficient solutions of the biobjective undirected two-commodity maximum flow problem is the set of alternative optimum solutions of the undirected two-commodity maximum flow problem. In addition, we prove that the set of efficient extreme points in the objective space has, at most, cardinality two.

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  1. Departamento de Estadística, Investigación Operativa y Computación (DEIOC), Universidad de La Laguna, 38271, La Laguna, Tenerife, Spain

    A. Sedeño-Noda, C. González-Martín & S. Alonso-Rodríguez

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  1. A. Sedeño-Noda
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  2. C. González-Martín
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  3. S. Alonso-Rodríguez
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Correspondence to A. Sedeño-Noda.

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Sedeño-Noda, A., González-Martín, C. & Alonso-Rodríguez, S. A new strategy for the undirected two-commodity maximum flow problem. Comput Optim Appl 47, 289–305 (2010). https://doi.org/10.1007/s10589-008-9214-5

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  • DOI: https://doi.org/10.1007/s10589-008-9214-5

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