We study a continuous version of the capacity and flow assignment problem(CFA) where the design cost is combined with an average delay measureto yield a non convex objective function coupled with multicommodity flowconstraints. A separable convexification of each arc cost function is proposedto obtain approximate feasible solutions within easily computable gaps fromoptimality. On the other hand, DC (difference of convex functions) programming can be usedto compute accurate upper bounds and reduce the gap.The technique is shown to be effective when topology is assumedfixed and capacity expansion on some arcs is considered.
