An adaptation of Dantzig-Wolfe decomposition applied to fuzzy multicommodity flow problems

In this work, a novel method that solves a class of linear programming problems with uncertain costs in the objective function is proposed. This method is an adaptation of the classical Dantzig-Wolfe decomposition method. This kind of problem has a special structure in the set of constraints such as multicommodity flow problems, which can be modeled by a graph whose nodes represent points of supply and demand of the commodities. Besides, the graphs modeled by real-world problem can have uncertainties both its structure and the its parameters. The objective of this work is to achieve the flow of each commodity that has minimum cost and satisfies the capacity and flow conservation constraints. An illustrative numerical example illustrating the solution approach is solved and analyzed to show the efficiency of this proposed method.