Bullwhip and anti-bullwhip effects in a supply chain

The anti-bullwhip effect, coined by Li et al. in 2005 based on the findings in a simulation study, is the contrary effect of the well-known bullwhip effect. Although there is ample empirical evidence that suggests both effects exist, current literature has not yet provided an integrated framework to address how the two effects are related with each other. By extending the classic work of Lee, Padmanabhan, and Whang of 1997 to a multi-stage supply chain, we derive closed-form formula to analytically describe how the two effects originate initially and then evolve over time and space in the supply chain. Our results show both the bullwhip effect and the anti-bullwhip effect can occur when facing different end-customer demands. However, the magnitude of these effects gradually decreases when moving upstream. We also show the impact of long lead-time on increasing the magnitude of information transformation at the next stage and simultaneously decreasing the magnitude at higher stages. These analytical results provide a theoretical explanation to most simulation findings of Li et al.'s 2005 work and can be used by researchers and practitioners to examine the empirical data and design innovate marketing strategies to convert the unwelcome bullwhip effect into the anti-bullwhip effect.