Abstract: From a control theory perspective,based on a generic replenishment rule that is APIOBPCS policy,the paper derives an analytical expression for bullwhip effect.It clearly shows that bullwhip effect can be reduced by increasing gain of the discrepancy in the inventory position and pipeline position,and by increasing the average age of the forecast and reducing the production lead-time.Then this paper also derives an analytical expression for the variance of inventory position.When this analytical expression is applied together with the bullwhip expression,the balance between both bullwhip effect and inventory variance for a range of weightings is discussed.According to these balances,the production and inventory controllers can design suitable supply chain system.

Key words: bullwhip effect, supply chains, z-transforms, APIOBPCS