Unavoidable transition from rigid dedicated hardware devices towards flexible containerized network services, introduced by Network Function Virtualization (NFV), brings novel opportunities while several new challenges. Meeting the expectations of NFV in post-5G networks depends on the efficient placement of the services. The online placement of the network services, demanding strict end-to-end latency requirements over the edge networks, with restricted computing resources presents a challenging problem which is worth investigating. We propose a Branch-and-Bound search approach for finding optimal placements of the network services by applying several different cost functions to maximize the service acceptance. Extensive evaluations has been carried out, and the results confirm significant improvements when we consider a fair distribution of the resources on the edge.