Benders-and-cut algorithm for fixed-charge capacitated network design problem

We develop a Benders-and-cut algorithm for fixed-charge capacitated network design problem which incorporates both Benders cuts and polyhedral cuts into an implicit branch-and-bound algorithm. The algorithm is tested over a wide range of problem instances with varying sizes and traffic conditions. It is shown that this new algorithm's performance is competitive compared with existing algorithms, and that Benders cuts are more effective under heavy traffic load, while cut set inequalities are more effective under light traffic load.