Abstract: The vendor-buyer integrated production-inventory system is an important component of the supply chain operation. So far, more and more literatures have been interested on this theme. However, all the shipment policies hitherto been presented have obviously defects which will lose the optimal order scheme. In this paper, the marginal analysis method is used to analyzed the relationship between the change of order quantity and system inventory cost. Firstly, the buyer's quantities of the twice adjacent orders are adjusted while keeping their whole quantity unchanged. Then, both the producer's and the buyer's inventory and their inventory cost are recalculated. Finally, a "three phase" rule of the best order strategy of this system can be deduced. First stage is the increase ordering stage during the first part of the producer's production. And the buyer needs to increase the ordering quantity according to the ratio of the productivity and the demand rate. The second stage is the equal ordering stage during the second part of the producer's production. And the buyer will make several ordering with certain equal ordering quantity in this stage. The third stage is the equal ordering stage after the vendor's production, which means the buyer will make several ordering with equal ordering quantity after production. According to this characteristic, the corresponding mathematical model of ordering strategy can be constructed by only six variables, which include the quantity and the times of ordering during the various stages. Compared with the other direct mathematical model with every possible number of the order and their ordering quantities, not only the variables of the model are reduced, but also the solution process is become relatively simple. Finally, two simulation examples commonly used in many literatures are analyzed. And the result shows that this strategy can actually find the optimal solution while other strategies lost.

Key words: two-echelon supply chain, vendor-buyer, integrated system, three-phase synchronized shipment