Measuring and Analyzing the Bullwhip Effect in a Two-Product and Two Echelon Supply Chain Using Control Theory Approach

Coordination is very important in supply chain management and it is one of the main factors in supply chain profitability. Bullwhip effect is one of the basic obstacles to achieve coordination in supply chains and reduction of this phenomenon has an important role in supply chain harmony. The other side, costs of supply chain can be mitigated and customer service level can be increased by reducing of bullwhip effect. Because measurement of bullwhip effect is very important in analysing and controlling of it, providing equations to investigate bullwhip effect behaviour based on real world supply chain conditions is necessary. The previous studies mostly concentrate on single product supply chain and few studies have been done on supply chains with more than one product. Here we quantify and investigate the bullwhip effect in a two-echelon supply chain with two products using control theory approach. Due to the relationship between demands of two products in our proposed supply chain, first order vector auto regressive model is used as demand process of the products. We also apply moving average method for lead-time demand forecasting within the "order up to" replenishment policy. We derive a closed form bullwhip measure and then bullwhip effect in a two-product supply chain is discussed and illustrated through a numerical example.