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This paper presents some analytical results on production and order dynamics in the context of a discrete-time VMI supply chain system composed of one retailer and one manufacturer. We firstly derive the lower bound and upper bound on the range of inventory fluctuations for the retailer under unknown demand. We prove that the production fluctuations can be interestingly smoothed and stabilized independent of the delivery frequency of the manufacturer used to satisfy the retailer’s demand, even if the retailer subsystem is unstable. The sufficient and necessary stability condition for the whole supply chain system is obtained. To further explore the production fluctuation problem, the bullwhip effect under unknown demand is explored based on a transfer function model with the purpose of disclosing the influences of parameters on production fluctuations. Finally, simulation experiments are used to validate the theoretical results with respect to inventory and production fluctuations.

Inventory and Production Dynamics in a Discrete-Time Vendor-Managed Inventory Supply Chain System