Abstract: 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.

Key words: supply chain coordination; vendor-managed inventory; variable inventory cost; stockout-cost sharing; EOQ model