静态市场下考虑重复购买的价格和质保期联合决策

doi:10.16381/j.cnki.issn1003-207x.2015.04.009

中国管理科学 ›› 2015, Vol. 23 ›› Issue (4): 70-77.doi: 10.16381/j.cnki.issn1003-207x.2015.04.009

静态市场下考虑重复购买的价格和质保期联合决策

王轩, 刘丽文

清华大学经济管理学院, 北京 100084

收稿日期:2013-07-15 修回日期:2014-02-23 出版日期:2015-04-20 发布日期:2015-04-24
作者简介:王轩(1985-), 男, (汉族), 河南人, 清华大学经济管理学院, 博士生, 研究方向:管理科学与工程.
基金资助:
国家自然科学基金资助项目(70972030)

Optimal Price and Warranty Length in the Static Demand Market Considering Repurchasing Process

WANG Xuan, LIU Li-wen

School of Economics and Management, Tsinghua University, Beijing 100084, China

Received:2013-07-15 Revised:2014-02-23 Online:2015-04-20 Published:2015-04-24

摘要/Abstract

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。

关键词: 质保期, 价格, 重复购买, 最大值原理, 最优控制, 学习效应

Abstract: 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 warranty policy. And it is assumed that the time between two failures follows Weibull distribution. Two scenarios are provided, which are based on whether the repurchasing process is affected by price. The maximum principle method is used to obtain optimal solutions. The optimal policies for a special case are further investigated and Lingo11 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, manufacture can get more profit and consumer can have better warranty. Finally, the management implication get from the model solutions is discussed.

Key words: warranty, price, repeat purchase, maximum principle, optimal control, learning effect

中图分类号:

C931

王轩, 刘丽文. 静态市场下考虑重复购买的价格和质保期联合决策[J]. 中国管理科学, 2015, 23(4): 70-77.

WANG Xuan, LIU Li-wen. Optimal Price and Warranty Length in the Static Demand Market Considering Repurchasing Process[J]. Chinese Journal of Management Science, 2015, 23(4): 70-77.

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静态市场下考虑重复购买的价格和质保期联合决策

Optimal Price and Warranty Length in the Static Demand Market Considering Repurchasing Process

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