基于Poisson分布需求的两级零售系统最优订货策略

考虑由一个分销中心和N个零售商组成的两级分销库存系统．假设两级库存补充均采取周期订货策略，在每个零售商处的客户需求是随机的，且服从Poisson分布．当给定的某一货物缺货时，顾客愿意等待特别订货的概率是一确定的常数，在满足给定的客户服务水平的条件下，寻求该供应链总费用的最小化．对库存费用的计算进行了精确的推导，并且得到了最优的订货策略．最后给出了一个算例，根据所得到的公式由电子表格获得了两级最优库存水平．

Optimizing order strategies of two-echelon retailer system with Poisson distributions

The two-echelon distribution system containing one single distribution center (DC) and N stores is considered.The customer demand at each store is assumed random and follows a Poisson distribution.When a stockout occurs,customers are willing to wait for their order to be filled with a known probability for a given item.The DC and stores are assumed to perform periodic review and order strategies,and the replenishment lead times equal to zero.The unit holding costs at the store level and at the DC are different.Our object is to minimize the total cost in the supply chain under the restriction of given customer service level.Our formulation is an exact calculation of inventory cost to get optimum order policies.An example is given out whose optimum solution can be obtained easily by using spreadsheet.