Analysis of the Bullwhip in a Hybrid System with Manufacturing/Remanufacturing

Applying control theory and simulation technique, a simply hybrid system with manufacturing /remanufacturing model is built. We study an infinite horizon, continuous time, Order-Up-To (OUT) policy. We specifically highlight the effect of remanufacturing lead-time and the return rate on the bullwhip produced by the ordering policy. We first address the stability of this system. We find that the remanufacturing lead-time and return rate have no effect on system stability. We then investigate the bullwhip. Our results clearly show that a larger return rate leads to less bullwhip. So, returns can be used to absorb demand fluctuations to some extent. However a longer remanufacturing lead-time has less impact at reducing bullwhip. Furthermore, within our specified system, we conclude that with returns, bullwhip is always less than without returns. Our results are completely analytic and exact. They are verified with simulation.