This paper presents a scenario-oriented optimization model and solution algorithm to solve the joint routing/capacity assignment problem for computer networks. The advantage of this model is that failures are directly dealt with at the design stage. The model helps to find a suitable trade-off between capacity assignment and performance in the event of failures. As accounting for major failures can be very time consuming, we introduce parallelism as a tool to solve this type of problem. Two parallel versions of the algorithm were implemented. Both parallel versions were found to be extremely efficient in reducing computational time, the one presenting two levels of parallelization was found more suitable for larger networks.