Measure of bullwhip effect in supply chains with first-order bivariate vector autoregression time-series demand model

With supply chains becoming increasingly global, the issue of bullwhip effect, a phenomenon attributable to demand fluctuation in the upstream section of the supply chains, has received greater attention from many researchers. However, most existing research studies on quantifying the bullwhip effect were conducted under the first-order autoregressive [AR(1)] incoming demand process or its variants as the fundamental demand process. This research work thus examines the bullwhip effect for a first-order bivariate vector autoregression [VAR(1)] demand process in a two-stage supply chain consisting of one supplier and two retailers. The impacts of the correlation parameters of the demand process, the correlation coefficient between the two error terms, and the variances of error terms on the bullwhip effect were investigated. As such, the measure of the bullwhip effect was established using an analytical approach in which the minimum mean square error (MMSE) forecasting method and the base stock policy were applied to all members of the supply chain. The number of scenarios was studied to determine the conditions in which the bullwhip effect would be present.