需求依赖价格的两阶段最优定价问题  

Optimal Two-Period Pricing under Price-Dependent Demand

作　　者：楼振凯 楼旭明 LOU Zhenkai;LOU Xuming(School of Management and Economics,Beijing Institute of Technology,Beijing 100081;School of Economics and Management,Xi'an University of Posts and Telecommunications,Xi'an 710121,China)

机构地区：[1]北京理工大学管理与经济学院,北京100081 [2]西安邮电大学经济与管理学院,西安710121

出　　处：《重庆师范大学学报（自然科学版）》2020年第1期113-118,共6页Journal of Chongqing Normal University:Natural Science

基　　金：国家自然科学基金面上项目(No.71571019)。

摘　　要：【目的】在有限销售周期内、需求率是价格的线性函数并且不允许发生缺货的前提下研究两阶段动态定价问题,为零售商提供定价决策依据。【方法】首先给出合理定价的概念,并证明所得到的最优价格都是合理的。其次证明了无论第二定价点在销售周期内的何处,二次定价所获得的期望收益都比一次定价的多,进而得到了各阶段最优价格的唯一表达式。【结果】零售商要在第二阶段提高售价使自身的期望收益最大化。【结论】通过代入最优价格的表达式求解目标函数的最大值,可得第二定价点是销售周期中点。[Purposes]Under the assumptions that consumers’ demand is linear sensitive to the product’s price and shortage is not allowed,two-stage optimal pricing issue is addressed.The aim is to provide pricing strategies for retailers.[Methods]First,the concept of a reasonable retail price is proposed,and all the optimal prices are proved to be reasonable.It is shown that the expected revenue of pricing for two times is higher than the one of which pricing for only one time,no matter where the second decision point locates.The optimal price for each decision point is acquired and is proved to be unique.[Findings]The retailer ought to enhance the price at the second decision point for obtaining maximum expected revenue.[Conclusions]Further,it is demonstrated that the optimal location of the second decision point is the midpoint of the selling period.

关 键 词：需求依赖价格 二次定价 最优价格 第二定价时点 

分 类 号：O224[理学—运筹学与控制论] F274[理学—数学]