This paper deals with the replica placement problem on fully homogeneous tree networksknownasthe Replica Placementoptimizationproblem. Theclient requests are known beforehand, while the number and location of the servers are to be determined. We investigate the latter problem using the Closest access policy when adding QoS and bandwidth constraints. In this paper, we state that the extension of Closest/Homogeneous with QoS to bandwidth keeps polynomial. This is an important cognition, as the postulated constraints are of different nature. QoS is a constraint that belongs to a node locally, whereas bandwidth constraints have a global influence on the resources. We propose an optimal algorithm in two passes using dynamic programming.