Benders decomposition for network design covering problems

We consider two covering variants of the network design problem. are given a set origin/destination pairs, called O/D and each such pair is covered if there exists path in from origin to destination whose length not larger than threshold. In first problem, Maximal Covering Network Design one must determine that maximizes total fulfilled demand pairs subject budget constraint on costs network. second Partial cost minimized while lower bound covered. After presenting formulations, we develop Benders decomposition approach solve problems. Further, several stabilization methods cuts as well addition cut-set inequalities master also impact adding an initial solution our methods. Computational experiments show efficiency these different aspects.