二级供应链系统的三阶段协同订货模型

生产商-销售商联合生产库存系统是供应链的一个重要组成部分。但是目前协同条件下的相关订货策略具有明显的局限性，容易丢失真正的最优策略。本文利用边际分析法，通过改变销售商相邻两次订货量的大小来分析生产商和销售商库存费用的变化，发现销售商的订货量与系统库存费用变化量的确存在一定的规律。并且，进一步可以推导出该类系统的最优订货策略的订货量必须符合“三阶段”规律。根据该特点，只需设置各个阶段的初始订货量和订货次数等6个决策变量就可以构建订货策略的数学模型。该模型与直接求解的数学模型相比，不仅变量减少，而且其求解也相对简单。最后，利用各个文献中常用的两个实例仿真进行对比分析，验证了该策略确实能够找出其他策略丢失的最优解。

A Three-Phase Synchronized Shipment Model of Two-Echelon Supply Chain System

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.