Measuring the Bullwhip Effect: Discrepancy and Alignment Between Information and Material Flows

The bullwhip effect is a phenomenon commonly observed in supply chains. It describes how demand variance amplifies from a downstream site to an upstream site due to demand information distortion. Two different bullwhip effect measures have been used in the literature. Theorists analyze the bullwhip effect based on the information flow (i.e., order and demand information), whereas most empiricists measure it according to the material flow (i.e., shipment and sales data). It is unclear how much the discrepancy between these two measures is, and, if significant, how to reconcile the discrepancy. In this paper, we illustrate and quantify the discrepancy under three inventory systems. For the system with stationary demand and ample supply, we show that the bullwhip effect measure based on the material-flow data is always greater than that based on the information flow. For the system with correlated demand and for the system with supply shortages, we derive conditions under which the material flow measure is either greater or less than the information flow measure. We find that the discrepancy is driven by four factors: stocking level, lead time, demand correlation, and supply service level. We further propose a method to reduce the discrepancy by using the sample variances of aggregated sales data. Our method works for common demand processes with short-range dependence, and it does not require the knowledge of the underlying base-stock levels.