Stability and transition in multiple production lines

We present the dynamical model of the multiple production lines composed of M parallel and u series machines. We extend the single-series production line model to the multiple production lines. We study the effect of the multiple lines on the dynamical behavior of the production process. We apply the linear stability analysis to the production process in the multiple lines. The linear stability criterion is derived for the production system with the multiple lines. It is shown that the production process in the multiple lines is more unstable than that in the single line. The phase diagram (region map) is given for the multiple production lines. The nonlinear instability and dynamical transition are investigated by using computer simulation. It is shown that the dynamical transitions occur between the stable and oscillatory productions.