中文摘要：

考虑一个报童模型中多类顾客的库存分配问题，将顾客按照他们愿意支付价格的高低划分为不同级别。零售商在销售期初决定产品订货量，并在销售期内决定接受或者拒绝不同顾客的需求，以最大化销售期内的期望总利润。将销售期分成大量足够小的时间单位，通过建立一个反向Bellman动态规划方程，以优化每个时间单位内的库存分配策略，并得到了零售商最优的期初订货量。通过与没有库存分配策略下零售商的期望利润进行比较，算例分析得出库存分配策略可以大幅提高零售商的利润。这主要是因为通过库存分配可以使得零售商从高端顾客中获取更多利润，同时能够减小期初的订货量，以节约采购成本和库存持有成本。

英文摘要：

This paper studies an inventory rationing in a newsboy problem with multiple customer class. The customer classes are distinguished by their purchasing price, and the firm either fulfills demand or denies the demand. Through discrediting the selling season into a large number of smaller intervals and using a finite difference equation to approximate the optimality equation, this paper characterizes the retailer＇s optimal rationing policy, which is depended on the inventory level and rest time. Under the optimal rationing policy, the expected profit function is concave in the order quantity, and there exists an optimal order quantity to maximize the expected profit. Through comparing with the First-Come-First-Served （FCFS） policy, the numerical analyses illustrates that the inventory rationing policy can improve the firm＇s profit significantly. This is because that the retailer can obtain more profit from the profitable customers by ensuring the high fill rate. Meantime, the order quantity under rationing policy is less than that under the FCFS policy, and then the retailer can benefit from the rationing policy by saving the purchasing cost and holding cost.