In this paper we propose two solution methods that can effectively handle the multifunction worker assignment problem in U-shaped production lines under the strategy of man-hour reduction applied by Lean Production Systems. This particular man-machine assignment problem aims at minimizing the number of workers within a certain cycle time. The two procedures proposed utilize the spacefilling curve technique as a means to visit all machines without violating the zone constraint minus; machines must be allocated in such a way that the walking routes of any two workers are not crossed. Computational experiments show that both algorithms perform well at determining the minimal workforce required to run a production line under certain parameters -walking times, machine operating times and cycle time. The model is deterministic, i.e., all parameters are assumed to be known with certainty.