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A U-shaped production line with multiple machines and multiple workers is considered under carousel allocation in which all workers take charge of all machines in the same order. Nakade and Ohno (2003) show that, when the processing, operation and walking times are constant, the overall cycle time, which is a time interval between successive outputs of finished goods, is the greatest value of the maximal sum of the processing and operation times among machines and the time required for a worker to operate and walk around the production line without waiting for processing divided by the number of workers. In this paper, it is considered that operation times at each machine may be different between workers. If processing time is short, it is expected that the overall cycle time will be equal to the time for a worker to operate and walk around the line divided by the number of workers. However, under some specified cases, the overall cycle time is longer than that of this time, and the overall cycle time changes periodically. From numerical examples, it is shown that the order of arrivals of workers at machine 1 affects the overall cycle time. We give some properties on the periodicity of cycle times and discuss about cycle times

Periodicity of Cycle Time in a U-Shaped Production Line with Heterogeneous Workers under Carousel Allocation