1993 Volume 5 Issue 3 Pages 516-527
In this paper, we focus on large-scale linear programming problems with the block angular structure which have been solved by the Dantzig-Wolfe decomposition method. By considering the imprecise nature of human judgements, we assume that the decision maker may have a fuzzy goal for the objective function and fuzzy constrains for the coupling constraints. Having elicited the corresponding linear membership functions through the interaction with the decision maker, we adopt the convex fuzzy decision. Then if some simple conditions are satisfied, it is shown that the formulated problem can be reduced to a number of independent linear subproblems and the overall optimal solution is directly obtained just only solving the subproblems. Even if the conditions are violated, it is clarified that the overall optimal solution is obtained by applying the Dantzig-Wolfe decomposition method.
