Effect of worker sequence on cycle time in a U-shaped line with chase mode

In this paper, a U-shaped line with multiple machines is considered, where each of multiple heterogeneous workers is allocated to one of machines as his/her starting position along the line. The chase mode is assumed, in which workers deal with all tasks and walk around on the same route. Periodicity of cycle time of a U-shaped line in chase mode is discussed, where periodicity means that time necessary for each worker to walk around is cyclic and depends on the order of worker's sequence. When it is periodic, the overall cycle time on the output of products becomes greater than the fundamental cycle time of the system, which is the maximum among total task times on workers and machines divided by the number of workers. It is shown that if there are just two workers then there is no periodicity of cycle time. Examples for three worker case show that the order of workers on the line sometimes highly influences on the length and periodicity of cycle time. The sufficient conditions under which there is no periodicity are derived for three or more worker cases.