Dynamical transition in random supply chain

We present the stochastic model of the supply chain composed of u series machines and buffers. Each machine has an adaptation time (delay) different from the other and each buffer has a capacity of storage different from the other. We extend the deterministic supply chain model to the stochastic one in which the adaptation time and storage's capacity are random parameters. We study the effect of the random parameters on the dynamical behavior of the production process. It is found that the production process in the random supply chain is unstable when the mean value of the adaptation time is higher than the threshold. The phase diagram (region map) is given for the random supply chain.