Quantifying the Bullwhip Effect in a Seasonal Supply Chain with Stochastic Lead Time

Abstract In this study, we quantify the bullwhip effect in a seasonal two echelon supply chain with stochastic lead time. The bullwhip effect is the phenomenon of demand variability amplification when one moves away from the customer to the supplier in a supply chain. The amplification effect poses very severe problems for a supply chain. The retailer faces external demand for a single product from end customers where the underlying demand process is a seasonal autoregressive moving average, SARMA (1,0)X(0,1) s demand process. And the retailer employs a base stock periodic review policy to replenish its inventory from the upstream party every period using the minimum mean-square error forecasting technique. In order to quantify the bullwhip effect in a seasonal supply chain, we use the ratio of the variance of retailer’s order quantities experienced by the supplier to the actual variance of demand quantities from the customers. After the bullwhip effect is obtained, we investigate what parameters have an impact on the bullwhip effect and how large each parameter affects it. Specifically, we show that seasonal phenomenon plays an important role for the bullwhip effect in a seasonal supply chain.