The Research on Stability of Supply Chain under Variable Delay Based on System Dynamics

With the swift development of modern science and network technology and fortified trend of economics globalization, the cooperation between supply chain partners is happening with increasing frequency and the cooperation difficulty increased correspondingly. Supply chain is a complex system which involves multiple entities encompassing activities of moving goods and adding value from the raw material stage to the final delivery stage. Feedback, interaction, and time delay are inherent to many processes in a supply chain, making it a dynamics system. Because of the dynamics and complex behaviors in the supply chain, the study on the stability of supply chain has become an independent research field only in last decade. At the same time, the great development of control theory and system dynamics provides an effective way to understand and solve the complexity of evolution in the supply chain system. The research on stability of supply chain was put forward during the studying of bullwhip effect. According to the paper of Holweg & Disney (2005), the development of the research on stability of supply chain and bullwhip effect can be divided into six stages: 1. Production and Inventory Control (before 1958) Nobel laureate Herbert Simon (1952) first suggested a PIC model based on Laplace transform methods and differential equations. In the model, Simon used first order lag to describe the delay of stock replenishment. Vassian (1955) built continuous time PIC model using Z transform. Magee (1958) solved the problems of inventory management and control in order-up-to inventory policy. At this stage, early PIC models were built based on control theory and the dynamics characteristics of PIC systems were discussed. 2. Smoothing production (1958-1969) In the early 1960s, Forrester (1958, 1961) built the original dynamics models of the supply chain using DYNAMO (Dynamic Modeling) language. He revealed the counterintuitive phenomenon of fluctuations in supply chain. The methods Jay Forrester proposed have gradually developed into system dynamics methodology which is used to research on dynamics characteristics of supply chain systems. For the bullwhip effect in discrete-time supply chain systems, analytical expression of the change in inventory under order-up-to policy was presented based on certain demand forecasting method (Deziel&Eilon,1967). At

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