Department of Industrial Engineering2024-11-1020081091-985610.1287/ijoc.1070.02372-s2.0-61349126068http://dx.doi.org/10.1287/ijoc.1070.0237https://hdl.handle.net/20.500.14288/15937We propose an exact solution method for a routing and capacity installation problem in networks. Given an input graph, the problem is to route traffic from a set of source nodes to a sink node and to install transmission facilities on the edges of the graph to accommodate the flow at minimum cost. We give a branch-and-bound algorithm that solves relaxations obtained by approximating the noncontinuous cost function by its lower convex envelope. The approximations are refined by branching on the flow ranges on selected edges. Our computational experiments indicate that this method is effective in solving moderate-size problems and provides very good candidate solutions early in the branch-and-bound tree.Computer ScienceArtificial intelligenceOperations researchManagement scienceJournal Article1526-5528255504700008Q37142