Dynamic analysis of a two-stage supply chain—a switched system theory approach

This paper investigates the dynamics of a two-stage supply chain consisting of one retailer and one distributor with order-up-to control policy. A discrete time state space model is developed to analyze the system. Due to the constraints of the distributor’s capacity, the supply chain turns out to be an autonomous switched system corresponding to the shipment policy of the distributor. The stability of the system studied is analyzed using switched system theory and discrete system control theory for the practical perspective. This study shows that the system will exhibit stable, periodic, and divergent behavior with different order policy parameters due to the switching mechanism within the system. The relationship between dynamics and cost is investigated, and insights are obtained about the control of the supply chain.

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