Bounds and approximations for cycle times of a U-shaped production line

In this paper, we deal with a U-shaped production line with a single multi-function worker in a JIT production system. We assume that the processing times of items, operation times, and walking times of the worker between machines are sequences of mutually independent and generally distributed random variables. We derive upper and lower bounds for the expected cycle time of the line, and propose approximate formulae using these bounds. Numerical examples show that these approximations give less than two percent errors for the cases tested.