Abstract: The choice of inventory management mode by the core enterprise in the supply chain will affect the income of upstream and downstream members and the operation efficiency of the system. Considering a supply chain composed of a supplier, a third-party logistics service provider (TPLSP) and a retailer, when both parties of supply and demand outsource logistics services to the TPLSP jointly and share freight costs, the impact of the introduction of vendor-managed inventory (VMI) and consignment inventory (CI) on system operation and contracts design is explored. A sequential non-cooperative game model is built in which the TPLSP is the leader while the supplier and the retailer are followers under three different inventory management modes, i.e., traditional retailer managed inventory (RMI), retailer-managed-consignment inventory (RMCI) by only introducing the CI mode and vendor-managed-consignment inventory (VMCI) by introducing both the VMI and the CI mode. Then, it is proved that the equilibrium solutions of the order or consignment quantity are exist and unique under all inventory modes and discuss the changes of the equilibrium result with the retailer's freight sharing ratio and transfer payment price. Horizontally Comparing of the equilibrium results under the three modes and the optimal results under the centralized decision-making, it is found that the equilibrium order quantity under the RMI mode is always lower than that under the RMCI mode and the centralized decision-making mode, while the order quantity under other inventory management modes is not necessarily lower than that under the centralized decision-making mode. Under different inventory modes, the size of the relationship between the order quantity or the consignment quantity and the system’s total expected profit depends on the category marginal (gross marginal) contribution ratio of the supplier and the retailer. This shows that in the supply chain environment, the income structure and profit level of the upstream and downstream enterprises has an important influence on the inventory decision and the selection of inventory modes. Moreover, in most cases, the equilibrium order quantity under different inventory modes is not equal to the optimal order quantity under centralized decision-making mode, so the system's total expected profit will suffer from different degrees of loss. A bidirectional regulation contract is introduced between the retailer and the supplier. By adjusting the value range of contract parameters, perfect coordination of supply chain can be achieved in three modes, and the parameter conditions of Pareto improvement in each mode are given. The conclusions of this paper provide a theoretical basis for exploring the influences of VMCI management mode and logistics joint outsourcing on the supply chain decision-making and contracts-designing, and the choice of the inventory management mode.

Key words: logistics outsourcing; inventory management mode; third-party logistics service provider; supply chain