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Top1. Introduction
In the past decade, researchers have probed into the “Bullwhip effect” in supply chains. However, along with the complication of the structures of supply chains, we find it increasingly important to take bullwhip effect into account when we do researches about supply chains with a view of entropy complexity. Bullwhip effect refers to the phenomenon that the orders are amplified within each level from downstream demand to upstream. Nowadays, this phenomenon becomes especially significant in many industries, such as automotive, commodities, electronic equipment, fast food industries etc. Previous literature has shown that the bullwhip effect can lead to wrong judgments for both retailers and suppliers, especially in the aspect of inventory. And it also can add production cost and cause inactive transportation (Lee, Padmanabhan, & Whang, 1997b). In other words, the bullwhip effect in product orders not only contributes to adding cost and possibilities of inventory oscillations for upstream, but also unavoidably results in larger inventory costs for downstream (Hoberg, Bradley, & Thonemann, 2007).
The bullwhip effect has so many negative influences, accompanying it brings about special concern: how to reduce or eliminate it. In this regard, many scholars have already set foot on these issues.
“Bullwhip effect” was put forward by Lee et al. (1997a). He demonstrated the five factors causes the bullwhip effect in supply chains, which include demand signal processing, non-zero lead-time, order batching, supply shortages and price fluctuation. To begin with, Kahn quantified the bullwhip effect by using the first-order autoregressive demand process (Kahn, 1987). Graves researched the bullwhip effect in supply chains with an integrated moving average process (Graves, 1999). Chen studied the influence of the methods of exponential smoothing (ES) and MA forecasting on the bullwhip effect in supply chain including one supplier and one retailer (Chen, Drezner, Ryan, Simchi-Levi, 2000a; 2000b). XU developed the ES forecasting method for the lead-time demand in his papers about the bullwhip effect (Xu, Dong, Evers, 2001). Alwan studied the bullwhip effect for the lead-time demand with MMSE-optimal forecasting technique and demand process following a positively or negatively correlated process (Ahmad, 2007). Wang compared the bullwhip effect using correct, MA and EWMA method in a single-stage supply chain (Wang, 2010). Wang published papers about two kinds of fuzzy demand through a revenue-sharing contract (Wang, Li, Du & Wang, 017).
According to preceding studies, many scholars also analyzed the coefficient of the demand forecast on the bullwhip effect subsequently. For example, Zhang studied the impact of bullwhip effect with a first-order autoregressive process and an order up to inventory policy, which indicated that different parameters influence the bullwhip effect to a great extent (Zhang, Cavusgil & Roath, 2003). Luong investigated the effect of autoregressive coefficient and lead time on the bullwhip effect in a supply chain and the demand forecast was performed with the first-order autoregressive model AR(1), he examined the upper limit of the bullwhip effect and demonstrated the upper limit mainly depends on the autoregressive coefficient (Luong, 2007), which is similar to the paper once used by Chen. Duc studied the effects of autoregressive coefficient, the moving average parameter and the lead time on the bullwhip effect with the inventory policy interpreted as first order mixed autoregressive-moving average model (Duc, Luong & Kim, 2008). These results are helpful because they are able to identify whether the bullwhip effect is infinite.