Quantifying the effect of batch size and order errors on the bullwhip effect using simulation

The bullwhip effect is the observed amplification in order-size variance for upstream nodes in a supply chain. Lee et al. (1997 Lee, HL, Padmanabhan, V and Whang, SJ. (1997). Information distortion in a supply chain: the bullwhip effect. Management Science, 43: pp. 546–558[Web of Science ®] , [Google Scholar], Management Science, 43, pp. 546–558) identified four causes for a single-product demand: (1) nodes updating their forecasts independently; (2) order batching; (3) price fluctuations; and (4) rationing. Chen et al. (2000 Chen, F, Ryan, JK and Simchi-Levi, D. (2000). Quantifying the bullwhip effect in a simple supply chain: the impact of forecasting, leadtimes, and information. Management Science, 46: pp. 436–443[Web of Science ®] , [Google Scholar], Management Science, 46, 436–443) provided a lower bound of the impact of the first cause. We contribute by quantifying the impact of the other three causes individually through simulation. We require any order to be an integer multiple of the batch size and posit price fluctuations and rationing as causing random i.i.d. errors or deviations from the optimal order size. We find with high R2 that the increase in order variance over a “core” order variance (when none of the four causes is present) is directly proportional to the square of the batch size and to the variance of the order deviations.