  We quantify the bullwhip effect (which measures how the variance in
replenishment orders is amplified as the orders move up the supply chain) when
random demands and random lead times are estimated using the industrially
popular moving average forecasting method. We assume that the lead times
constitute a sequence of independent identically distributed random variables
and correlated demands are described by a first order autoregressive process.
We obtain an expression that reveals the impact of demand and lead time
forecasting on the bullwhip effect. We draw a number of conclusions on the
behavior of the bullwhip effect with respect to the demand auto-correlation and
the number of past lead times and demands used in the forecasts. Furthermore we
find the maxima and minima of the bullwhip measure as a function of the demand
auto-correlation.
