Exact Algorithms for the Multicommodity Uncapacitated Fixed-Charge Network Design Problem

We present two exact algorithms based on Benders decomposition for solving the multicommodity uncapacitated fixed-charge network design problem. The first implements Benders decomposition within a branch-and-cut framework. We present implementation techniques crucial for the algorithm's efficiency such as cut selection criteria and core point definition and highlight their impact on the solution time. Our second algorithm combines a cut-and-solve strategy with Benders decomposition. We also describe a slope scaling metaheuristic to efficiently obtain high quality solutions. We perform extensive computational experiments on benchmark instances to compare the efficiency of the proposed algorithms. Both exact algorithms provide a speedup between one and two orders of magnitude compared to a state-of-the-art general-purpose MIP solver.