Abstract: According to the problems arising in VMI implementation,a TPL is introduced into the VMI system to build an integrated inventory model in VMI-TPL supply chain with determined demand,which consists of a manufacturer,a TPL and multiple retailers.Raw materials and finished products are both considered in the model and the optimal production and inventory policies are derived.On this basis,the effect of various parameters such as production-demand ratio(p/d) on the costs of the supply chain is discussed and the optimal policy of integrated inventory model in VMI supply chain with TPL is compared with that without TPL Through the comparison,we observe that TPL can effectively reduce the total average cost of supply chain and avoid high inventory costs and high operational risk of the manufacturer.Furthermore,we show that production demand ratio(p/d) of the manufacturer affects the performance of VMI TPL supply chain greatly; and the higher the p/d is,the be ter performance the supply chain has.

Key words: Vendor-managed Inventory(VMI), Third-Party Logistics(TPL), integrated inventory model, inventory policy