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