  In this article we quantify the bullwhip effect (the variance amplification
in replenishment orders) when demands and lead times are predicted in a simple
two-stage supply chain with one supplier and one retailer. In recent research
the impact of stochastic order lead time on the bullwhip effect is
investigated, but the effect of needing to predict / estimate the lead time is
not considered in the supply chain models. Under uncertainty conditions it is
necessary to estimate the lead time for a member of the supply chain to place
an order. We find a new cause of the bullwhip effect in the form of lead time
forecasting and we give an exact form of the bullwhip effect measure (the ratio
of variances) when demands and lead times are predicted by moving averages. In
the bullwhip effect measure we discover two terms amplifying the effect which
are the result of lead time estimation
