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

  • Authors:

  • A. Sedeño-Noda;C. González-Martín;S. Alonso-Rodríguez

  • Affiliations:

  • Departamento de Estadística, Investigación Operativa y Computación (DEIOC), Universidad de La Laguna, La Laguna, Spain 38271;Departamento de Estadística, Investigación Operativa y Computación (DEIOC), Universidad de La Laguna, La Laguna, Spain 38271;Departamento de Estadística, Investigación Operativa y Computación (DEIOC), Universidad de La Laguna, La Laguna, Spain 38271

  • Venue:
  • Computational Optimization and Applications
  • Year:
  • 2010

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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.