On bullwhip in a family of order-up-to policies with 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 position feedback controller, has shown improved bullwhip behaviour. The dynamic behaviour 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 autoregressive moving average AR(1) and ARMA(1,1) models. It has been shown that, for a correct choice of the feedback parameter, the bullwhip effect can always be avoided. However, less attractive properties of this policy have also become clear. Herein, we investigate the behaviour of the proportional order up to policy for ARMA(2,2) demand with arbitrary lead-times. In order to compensate for possible weaknesses of the proportional OUT policy we propose another replenishment rule that accounts for the characteristics of the demand in a superior manner. The characteristics of both policies are compared for several parameter settings of the ARMA(2,2) model. Finally, the consequences of our full-state-feedback order-up-to policy are discussed.

International Journal of Production Economics, 121 (2), 454-463