A Benders Decomposition Method for Two-Stage Stochastic Network Design Problems

This paper describes a Benders decomposition algorithm capable of efficiently solving large-scale instances of the well-known multi-commodity capacitated network design problem with demand uncertainty. The problem is important because it models many real-world applications, including telecommunications, transportation, and logistics. This problem has been tackled in the literature with meta-heuristics and exact methods, but many benchmark instances, even though of moderate size, remain unsolved. To successfully apply Benders method to these instances, we propose various acceleration techniques, including the use of cutting planes, partial decomposition, heuristics, stronger cuts, reduction and warm-start strategies. Extensive computational experiments on benchmark instances were conducted to evaluate the efficiency and robustness of the algorithm as well as of the proposed strategies. The numerical results confirm the superiority of the proposed algorithm over existing ones. We dedicate this work to Professor Jacques F. Benders who left this world January 2017.