In this paper, we deal with the physical layer impairments (PLIs) in optical burst switching (OBS). In particular we present a formulation of the routing and regenerator placement and dimensioning (RRPD) problem for a feasible translucent OBS (T-OBS) network architecture. Since addressing the joint RRPD problem results in an extremely complex undertaking, we decouple the problem, and hence, we eventually provide formal models to solve routing and RPD separately in the socalled R+RPD problem. Thus, making use of mixed integer linear programming (MILP) formulations, we first address the routing problem with the aim of minimizing congestion in bottleneck network links, and second, we tackle the issue of performing a sparse placement of electrical regenerators in the network. Since the RPD formulation requires high computational effort for large problem instances, we also propose two alternative heuristic strategies that provide good near-optimal solutions within reasonable time limits. To be precise, we evaluate the trade-off between optimality and complexity provided by these methods. Finally, we conduct a series of simulation experiments on the T-OBS network that prove that the R+RPD strategies effectively deal with burst losses caused by the impact of PLIs, and therefore, ensure that the overall T-OBS network performance remains unaffected.