Application of generalized Benders decomposition to a nonlinear distribution system design problem

The Benders decomposition method has been successfully applied to a classic multistage, multiproduct distribution-system design problem with fixed and linear variable costs. In other applications, however, distribution-center variable throughput costs often show nonlinearity due to economies of scale. This article extends the standard problem formulation to a nonlinear distribution-system design problem and incorporates the generalized Benders decomposition method in an efficient solution algorithm. Approximate dual prices are generated by solving linear instead of concave subproblems. Thereafter these prices are adjusted to induce a more accurate representation of the concave cost function before they are incorporated in the Benders cuts, which are used to generate new binary solutions. The computational results are encouraging.