A dual ascent approach to the fixed-charge capacitated network design problem

In this paper we consider the problem of constructing a network over which a number of commodities are to be transported. Fixed costs are associated to the construction of network arcs and variable costs are associated to routing of commodities. In addition, one capacity constraint is related to each arc. The problem is to determine a network design that minimizes the total cost; i.e., it balances the construction and operating costs. A dual ascent procedure for finding improved lower bounds and near-optimal solutions for the fixed-charge capacitated network design problem is proposed. The method is shown to generate tighter lower bounds than the linear programming relaxation of the problem.