In this paper we propose a scenario-oriented optimization model and solution algorithm to assess the capacity and the routing of computer networks. The advantage of this model is that failures are directly incorporated into the design procedure. As accounting for important failures can be very time consuming, we introduce parallelism as a tool to solve this type of problem. Two parallel versions of the algorithms were implemented. Results on some key test networks show that explicitly considering reliability at the design level has a definite impact on cost and network robustness.