The impact of stochastic lead times on the bullwhip effect under correlated demand and moving average forecasts

摘要

We quantify the bullwhip effect (which measures how the variance inreplenishment orders is amplified as the orders move up the supply chain) whenrandom demands and random lead times are estimated using the industriallypopular moving average forecasting method. We assume that the lead timesconstitute a sequence of independent identically distributed random variablesand correlated demands are described by a first order autoregressive process.We obtain an expression that reveals the impact of demand and lead timeforecasting on the bullwhip effect. We draw a number of conclusions on thebehavior of the bullwhip effect with respect to the demand auto-correlation andthe number of past lead times and demands used in the forecasts. Furthermore wefind the maxima and minima of the bullwhip measure as a function of the demandauto-correlation.