Application of Benders decomposition method in solution of a fixed-charge multicommodity network design problem avoiding congestion

In this paper, a new variable partitioning strategy in Benders decomposition method is applied that enables us to deal with a wide class of mixed-integer nonlinear programming problems including fixed-charge multicommodity network design (FMND) problems under congestion effects. It is proved that the proposed technique for an FMND problem leads to a simple branch-and-bound algorithm such that each node of the branching tree includes a single conic quadratic representable problem consisting of only continuous (flow) variables. Preliminary numerical results are reported.