The impact of demand parameter uncertainty on the bullwhip effect

The bullwhip effect is a very important issue for supply chains, impacting on costs and effectiveness. Academic researchers have studied this phenomenon and modelled it analytically, showing that it affects many real world industries. The analytical models generally assume that the final demand process and its parameters are known. This paper studies a two-echelon single-product supply chain with final demand distributed according to a known AR(1) process but with unknown parameters. The results show that the bullwhip effect is affected by unknown parameters and is influenced by the frequency with which parameter estimates are updated. For unknown parameters, the strength of the bullwhip effect is also influenced by the number of demand observations available to estimate the parameters. Furthermore, a negative autoregressive parameter does not always imply an anti-bullwhip effect when the parameters are unknown. An analytical approximation is proposed to mitigate the poor accuracy of existing models when the parameters of an AR(1) process are unknown, forecasts are updated but parameter estimates remain unchanged.