中文摘要：

针对多等级产品的动态定价问题,将顾客分为两类：1顾客只购买固定等级的产品;2顾客以一定的概率在不同等级的产品之间进行选择。在此基础上,利用动态规划方法,建立了多等级产品的动态定价模型,给出了收益函数及最优定价策略的性质。最后,通过数值算例进行了最优定价策略的有效性验证,结果表明：各等级产品的最优价格随自身库存和其他产品库存的增加单调不增;随剩余时间的增加单调不减,且质量等级较高的产品最优价格也较高。

英文摘要：

For the dynamic pricing for the multi-class products,the customers are classified into two types：the first type of customers purchases only the fixed class of products and the second type of customers chooses between different classes of products with a certain probability.Then a dynamic pricing model for the multi-class products is established using dynamic programming.The properties of the objective function and the optimal pricing strategy are given.A numerical example demonstrates the availability of the optimal pricing strategy,and the results show that the optimal price of each class product is non-increasing with the increase of its own inventory and the other classes productsinventories,non-decreasing with the increase of the remaining time,and the optimal price of a higher quality class product is also higher than that of a lower quality class product.