On the bullwhip effect of Order-Up-To policies for ARMA(2,2) demand and arbitrary lead-times


A number of papers have recently appeared that investigate the bullwhip effect (the variance amplification of ordering decisions in the supply chain) produced by the order-up-to replenishment policy. An adapted policy, with a proportional inventory feedback controller, has shown improved bullwhip behavior. The dynamic behavior of this so-called proportional order-up-to policy has been investigated for arbitrary lead-times and several demand models such as i.i.d. demand and auto-regressive moving average AR(1) and ARMA(1,1) models. The provided insights indicate that for a correct choice of the feedback parameter the bullwhip effect can always be avoided. But at the same time, less attractive properties of this policy become clear. Herein we investigate the behavior of the proportional order up to policy for ARMA(2,2) demand under arbitrary lead-times. In order to compensate possible weaknesses, we propose another replenishment rule that takes into account the characteristics of the demand in a superior manner. Both policies are compared for several parameter settings of the ARMA(2,2) model. Finally, the consequences of our adaptation to the proportional order-up-to policy are discussed.

Pre-prints of the 14th International Working Seminar on Production Economics, Igls, AUSTRIA, 20th-24th February, 55-64