The biobjective undirected two-commodity minimum cost flow problem

The biobjective undirected two-commodity minimum cost flow problem

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Article ID: iaor20061803
Country: Netherlands
Volume: 164
Issue: 1
Start Page Number: 89
End Page Number: 103
Publication Date: Jul 2005
Journal: European Journal of Operational Research
Authors: , ,
Keywords: programming: multiple criteria
Abstract:

We address the two-commodity minimum cost flow problem considering two objectives. We show that the biobjective undirected two-commodity minimum cost flow problem can be split into two standard biobjective minimum cost flow problems using the change of variables approach. This technique allows us to develop a method that finds all the efficient extreme points in the objective space for the two-commodity problem solving two biobjective minimum cost flow problems. In other words, we generalize the Hu's theorem for the biobjective undirected two-commodity minimum cost flow problem. In addition, we develop a parametric network simplex method to solve the biobjective problem.

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