The supply chain network is a complex nonlinear system that may have a chaotic behavior. This network involves multiple entities that cooperate to meet customers demand and control network inventory. Although there is a large body of research on measurement of chaos in the supply chain, no proper method has been proposed to control its chaotic behavior. Moreover, the dynamic equations used in the supply chain ignore many factors that affect this chaotic behavior. This paper offers a more comprehensive modeling, analysis, and control of chaotic behavior in the supply chain. A supply chain network with a centralized decision-making structure is modeled. This model has a control center that determines the order of entities and controls their inventories based on customer demand. There is a time-varying delay in the supply chain network, which is equal to the maximum delay between entities. Robust control method with linear matrix inequality technique is used to control the chaotic behavior. Using this technique, decision parameters are determined in such a way as to stabilize network behavior.
Supply chain network (SCN) is a complex nonlinear system and may have a chaotic behavior. This network involves multiple entities that cooperate to satisfy customers demand and control network inventory. The policy of each entity in demand forecast and inventory control, and constraints and uncertainties of demand and supply (or production) significantly affects the complexity of its behavior. In this paper, a supply chain network is investigated that has two ordering policies: smooth ordering policy and a new policy that is designed based on proportional-derivative controller. Two forecast methods are used in the network: moving average (MA) forecast and exponential smoothing (ES) forecast. The supply capacity of each entity is constrained. The effect of demand elasticity, which is the result of marketing activities, is involved in the SCN. The inventory adjustment parameter and demand elasticity are the most important decision parameters in the SCN. Overall, four scenarios are designed for modeling and analyzing the chaotic behavior of the network and in each scenario the maximum Lyapunov exponent is calculated and drawn. Finally, the best scenario for decision-making is obtained.2010 Mathematics Subject Classification. Primary: 35C20, 35P20; Secondary: 93D15.
Abstract:A supply chain network (SCN) is a complex nonlinear system involving multiple entities. The policy of each entity in decision-making and the uncertainties of demand and supply (or production) significantly affect the complexity of its behavior. Although several studies have presented information about the measurement of chaos in the supply chain, there has not been an appropriate way to control the chaos in it. In this paper, the chaos control problem is considered for a SCN with a time-varying delay between its entities. The innovation of this paper is the more comprehensive modeling, analysis, and control of chaotic behavior in the system. The proposed model has a control center to determine the orders of entities and control their inventories. Customer demand is modeled as an unknown exogenous disturbance. A robust H ∞ control method is designed to control its chaotic behavior in terms of a certain linear matrix inequality technique that can be readily solved using the MATLAB LMI toolbox. By using this technique and calculating the maximum Lyapunov exponent, decision parameters are determined in such a way that the behavior of the SCN is stable.
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