Measuring and avoiding the bullwhip effect: a control theoretic approach

An important contributory factor to the bullwhip effect (i.e. the variance amplification of order quantities observed in supply chains) is the replenishment rule implemented by supply chain members. We analyse the bullwhip effect induced by the use of different forecasting methods in order-up-to replenishment policies. We not only quantify the variance amplification, but we prove that the bullwhip effect is guaranteed irrespective of the forecasting method used. Avoiding the bullwhip effect consequently means avoiding the order-up-to policies. In a second part of the paper we introduce a general decision rule that avoids variance amplification and succeeds in generating smooth ordering patterns, even when demand has to be forecasted. The methodology is based on control systems engineering and allows us to gain important insights in the dynamic behaviour of replenishment rules.status: publishe