  Due to delays in the adaptation of production or delivery rates, supply
chains can be dynamically unstable with respect to perturbations in the
consumption rate, which is known as "bull-whip effect". Here, we study several
conceivable production strategies to stabilize supply chains, which is
expressed by different specifications of the management function controlling
the production speed in dependence of the stock levels. In particular, we will
investigate, whether the reaction to stock levels of other producers or
suppliers has a stabilizing effect. We will also demonstrate that the
anticipation of future stock levels can stabilize the supply system, given the
forecast horizon is long enough. To show this, we derive linear stability
conditions and carry out simulations for different control strategies. The
results indicate that the linear stability analysis is a helpful tool for the
judgement of the stabilization effect, although unexpected deviations can occur
in the non-linear regime. There are also signs of phase transitions and chaotic
behavior, but this remains to be investigated more thoroughly in the future.
