Reverse logistics: a study of bullwhip in continuous time

A simple dynamic model of a hybrid manufacturing/remanufacturing system is developed. In particular the model is used to study an infinite horizon, continuous time, APIOBPCS (automatic pipeline inventory and order based production control system) model. We specifically highlight the effect of remanufacturing lead-time and the return rate on the bullwhip produced by the ordering policy. Our results clearly show that a larger return rate leads to less bullwhip, thus returns can be used to absorb demand fluctuations to some extent. Longer remanufacturing lead-times have less impact at reducing bullwhip than shorter lead-times. We conclude, within our specified system, that bullwhip is always less with returns than without returns.