A network D with the lower and upper bounds and the conservation constraints is given, the network D is infeasible if there is not any flow satisfying in the constrains. But what should be done if the network is infeasible? simply knowing that it is infeasible is not enough and the network must be changed in order to achieve feasibility. Consider the problem of changing the lower and upper bounds such that the sum of the violations costs from the lower and upper bounds is minimum. Reference [3] presented this problem and solved the special case with uniform costs for violating on the arcs. In this paper, the general case with arbitrary costs is considered. We call this problem the repairing problem and show it is transformed to a minimum cost flow problem on a parallel network. Thus the repairing problem can be solved using any minimum cost flow algorithm. One of the best algorithms to solve the minimum cost flow problem is the cost scaling algorithm of [2]. In this paper, by defining an especial residual network, the parallel arcs are eliminated in order to achieve a faster algorithm in practice.
