In the just-in-time context, parts are often processed by a single-unit production and conveyance system (called "ikko nagash" in Japanese) without conveyors. The U-shaped layout, in which each multi-function worker takes charge of several machines, has been introduced as an implementation of this concept. Presently the layout is gaining an increasing popularity due to the low running cost. In this paper, first we deal with the U-shaped production line with a single multi-function worker. We derive his waiting time and a cycle time of the line when processing times of items, operation times, and his walking times between machines are constants. Then we deal with a U-shaped production line with multiple workers. We derive the overall cycle time of this line, and consider an optimal worker allocation problem that minimizes the overall cycle time when the number of workers is given. In particular, it is shown that the U-shaped layout is superior to the linear layout for lines with one or two workers. We also discuss the case where those processing, operation and walking times are stochastic.