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 used by supply chain members. First the bullwhip effect induced by the use of different forecasting methods in order-up-to replenishment policies is analysed. Variance amplification is quantified and we prove that the bullwhip effect is guaranteed in the order-up-to model irrespective of the forecasting method used. Thus, when production is inflexible and significant costs are incurred by frequently switching production quantities up and down, order-up-to policies may no longer be desirable or even achievable. In the second part of the paper a general decision rule is introduced 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 important insights to be gained about the dynamic behaviour of replenishment rules.