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In supply chains, the variability in the replenishment orders often increases as demand infor-mation travels upstream in the supply chain, from the retailer towards the factory and the sup-pliers. This phenomenon has been recognized as the bullwhip effect (Lee, Padmanabhan, and Whang 1997) and observed in many industries such as Campbell Soup’s (Fisher et al. 1997), HP and Proctor & Gamble(Lee, Padmanabhan, and Whang 1997), fast moving consumer goods (Zotteri 2012), and car manufacturing (Klug 2013). Forrester (1958) was mostly the first to study this problem through a set of simulation experiments using system dynamics and called it demand amplification. Forrester analyzed the behavior of a linear supply chain under various internal conditions as well as its response to external changes and shocks, and found that the structure, policies, and interactions within a supply chain cause demand variability amplification. Other researchers developed simulation games to illustrate the bullwhip effect existence and its negative impacts in supply chains (Sterman, 1989; Chen and Samroengraja, 2000; Jacobs, 2000; Machuca and Barajas, 1997). Towill, Zhou, and Disney (2007) indicated that the bullwhip effect could lead to stock-outs, large and expensive capacity utilization swings, lower quality products, and considerable production/transport costs.

Lee et al. (1997) identified five fundamental causes of the bullwhip effect: demand signal processing, non-zero lead-time, order batching, price fluctuations and rationing and shortage gaming. Of our particular interest is the demand signal processing in which forecasting meth-ods and replenishment rules (inventory control policy) are jointly applied to identify when and how much to order. Burbi...

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...attern under the influence of three inventory policies: an inventory-on-hand policy, an installation-stock policy, and an echelon-stock policy. They proved analytically that the installation-stock and echelon-stock policies are more stable than the inventory-on-hand policy. Chandra and Grabis (2005) adopted a simulation modeling ap-proach to investigate the impact of a materials requirements planning (MRP) based inventory management approach on the bullwhip effect and inventory performance for the most down-stream supply chain unit. They argued that the MRP approach is comparable to the traditional order-up-to approach. Dejonckheere et al. (2003) proved through a control theoretic approach that the bullwhip effect is guaranteed in the order-up-to model irrespective of the forecasting method used and state this without making any assumptions about the demand pattern.

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