中文摘要：

本文研究静态市场下的以质保期和价格为决策变量的最优控制决策问题。考虑了初次购买和重复购买两个过程以及重复购买过程是否受价格影响两种情况。模型中的生产成本考虑了产品生产过程中的学习效应,质保成本使用了免费维修质保策略并假设产品两次故障之间的时间服从韦伯分布。在完整建模的基础上,应用最大化原理对基本模型进行了求解,之后本文给出了一种基本模型的具体应用场景,并运用Lingo11软件进行了数值试验。最后对主要研究结论进行了应用讨论。

英文摘要：

In this paper, a decision model is developed to determine the optimal price and warranty length for a static demand market. The demand function of the model characterizes both the repurchasing process and the initial purchase process. The cost functions consider both the learning effect and free repair war- ranty policy. And it is assumed that the time between two failures follows Weibull distribution. Two sce- narios are provided, which are based on whether the repurchasing process is affected by price. The maxi- mum principle method is used to obtain optimal solutions. The optimal policies for a special case are fur- ther investigated and Lingoll is used to do some numerical tests. In this paper, it is found that price and warranty have to be considered in the same time, the best policy is to set high price and long warranty in the beginning and reduce them along the product life circle. Considering the repurchasing process, manu- facture can get more profit and consumer can have better warranty. Finally, the management implication get from the model solutions is discussed.