库存成本变化的VMI供应链协调

提出了库存成本变化的经济订货批量(EOQ)模型，基于该模型研究了库存成本变化时供应商管理库存(VMI)系统的最优协议问题。在该系统中，订货商和供应商达成缺货成本共担协议：当缺货发生时，供应商需要向订货商支付缺货补偿。订货商和供应商分散决策，订货商通过设计协议来减少其成本，而供应商通过制定补货决策来缩小自身成本。通过与传统系统和整合系统的比较，得出了库存成本变化时VMI系统的最优补货决策和缺货成本共担协议。采用数值算例验证了分析结果。结果表明，当且仅当供应商预期成本等于整合系统的最小总成本与固定缺货罚金之和时，VMI系统与整合系统具有相同的补货决策和系统绩效，即能够实现供应链协调。

Supply Chain Coordination in Vendor-Managed Inventory Systems with Variable Inventory Cost

In the peak season of market demand, the ordering quantity of goods often exceeds the limit of warehouse capacity. The decision-maker of supply chain should consider renting warehouse. The cost of renting warehouse is probably different from that of original warehouse. When the inventory cost changes with the order quantity, how to realize the supply chain coordination is interesting. Considering a supply chain composed of a single supplier and a single retailer, an EOQ model is built with variable inventory cost for exploring an optimal vender-managed-inventory (VMI) contract to get the supply chain coordination. In the supply chain, the retailer proposes a VMI protocol. When the stockout occurs, the supplier will pay the backorder penalty. The penalty includes fixed penalty and variable penalty. Fixed penalty is independent of the quantity of shortage and variable penalty is related to the quantity of shortage. The supplier has a reservation cost, and when its own cost is less than or equal to the reservation cost, the supplier will accept the agreement. The results show that the VMI system can achieve supply chain coordination when the inventory cost changes. It is proved that if and only if the supplier’s reservation cost of the VMI system is equal to the sum of the minimum supply chain total cost of the integrated system and the fixed shortage penalty, that is, the supplier wants to bear the sum of the minimum supply chain total cost of the integrated system and the fixed shortage penalty, the VMI system and the integrated system have the same replenishment decision and system performance. The results also show that the variable inventory cost affects the replenishment decisions and system performance, and then affects the design of VMI contracts. Finally, a numerical example and a sensitivity analysis verify the results. This study is not only suitable for VMI system coordination with infinite storage capacity and limited storage capacity when inventory cost is constant, but also suitable for VMI system coordination when inventory cost changes. This research enriches the relevant theories of VMI and supply chain, and provide useful guidance for the decisions of supplier and retailer.