Measuring the Bullwhip Effect with Material Flow Data: Biases and Remedies

The bullwhip effect is a well-known phenomenon of demand information distortion in supply chains. To measure the bullwhip effect in a supply chain, researchers often resort to material flow data, i.e., shipments and sales data, as proxies for order and demand information. In this paper, we study the accuracy of such an approximated bullwhip measure and provide remedies for correcting the estimation biases. In a single-stage system with independently and identically distributed (i.i.d.) demand, it is known that there is no bullwhip effect under a base-stock policy. However, we show that the bullwhip measure based on material flow data always overestimates the actual bullwhip effect in this case. Specifically, the variance of shipments is always greater than that of sales, and the difference has a simple expression that comprises on-hand inventory and backorders. We further extend the analysis to a two-stage system with i.i.d. demand and a single-stage system with correlated demand. For both systems, we derive conditions under which the overestimation occurs. Our study suggests that the accuracy of the material bullwhip measure is driven by four factors: stocking level, lead time, supply chain location, and demand correlation. Interestingly, we find that the biases in the material bullwhip measure can be corrected by simple remedies based on the sample autocovariances of the sales and shipment data. Our debiasing methods can be further generalized to serial systems with an arbitrary number of stages under i.i.d. demand.