In this paper we consider an SS/TDMA system with

uplink beams,

downlink beams, and

transponders. An optimal time slot assignment algorithm for any

and any traffic matrix is presented, where optimality means achieving the minimal possible total duration for the given traffic matrix. The number of switching matrices generated by the algorithm is bounded above by

for

and

otherwise. Extensive simulation results on randomly generated matrices are carried out, showing that the average number of switching matrices generated is substantially lower than the bounds.