We consider a multi-stage production system with finite buffers under the so-called repetitive-service blocking mechanism, modelled by a tandem queueing system with blocking. The objective is to find to which stage each server should be assigned in order to maximize the throughput. For this server assignment problem we first derive a throughput upper bound which is found to be very close to the exact one to be used as a substitute measure. Based on this measure we show that the rules of placing the worst servers from the outermost stages by Yamazaki et al. ( 1989) for the case of no buffers, are effective for the case with buffers of equal size. For the general case with buffers of different sizes, we propose an algorithm based on the observation that our throughput upper bound can be increased fastest by placing the fastest servers around the smallest buffered stage. Effectiveness of this algorithm as well as the proposed rules are well demonstrated by the extensive computational experiments conducted with a number of test examples ranging up to five stages.