On bullwhip in a family of order-up-to policies with ARMA(2,2) demand and arbitrary lead-times

Abstract

. On bullwhip in a family of order-up-to policies with ARMA(2,2) demand and arbitrary lead-times. AbstractA 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.

Quantifying bullwhip effect in a closed loop supply chain

“…Gaalman and Disney [10] and Gaalman and Disney [11] studied the bullwhip effect produced by the OUT replenishment policy reacting to a stochastic ARMA(1,1) and ARMA(2,2) demand processes respectively. Duc et al [8] also quantified the impact of the bullwhip effect for a simple two-stage supply chain with one supplier and one retailer assuming that the retailer employs a base stock inventory policy, and with ARMA(1,1) demand.…”

Altruistic behaviour in a two-echelon supply chain with unmatched proportional feedback controllers

“…Recent work by Gaalman and Disney (2007) suggests that much more elegant results can be found by exploiting the "full-state-feedback" controller, a technique advocated by modern control theory. This will be explored in future research.…”

Providing a measure for bullwhip effect in a two-product supply chain with exponential smoothing forecasts

“…They showed that in some instances, bullwhip effect could be reduced when lead-time increases. Gaalman and Disney (2009) investigated behavior of the order up to policy for ARMA(2,2) demand process with arbitrary lead-time. Jaksic and Rusjan (2008) demonstrated that using some replenishment rules we could decrease the bullwhip effect.…”