Stochastic analysis of a U-shaped production line with multiple workers

In a conveyor system for mass production as in the Ford system, each station processes just one item in one cycle time, where the cycle time is the time-interval between two successive outputs. In a Just-In-Time production system, a single-unit production and conveyance system is applied to a part production line without conveyors, and multi-function workers and a U-shaped layout of machines have been introduced. The multi-function worker takes charge of multiple machines. In this paper, we consider a U-shaped line with multiple multi-function workers, each of which is responsible for several machines. We formulate it into a marked Petri net, which has a convex property of a generalized semi-Markov process. This shows that the cycle times of two different systems are comparable in the sense of an increasing convex order. We also show the reversibility of the system, that is, the expected cycle time of the reversed system where each worker operates items and walks in the reversed order of stations is the same as that of the original system.