销售价格影响需求的易变质产品动态定价模型

在需求率线性依赖于销售价格的情形下,研究有限销售周期内一次订购模式下单一易变质产品在连续时间上的最优动态定价决策问题.针对给定初始库存水平和初始库存水平待定两种情形,利用最优控制理论分别建立了易变质产品的动态定价模型,目标是最大化产品销售周期内总的销售利润.通过分析,可将问题分别转化为有控制变量约束的拉格郎日问题和波尔扎问题.利用Pontryagin极大值原理求解上述两类问题,均得到系统最优定价决策.对上述第一类问题分别进行了数值仿真,仿真结果表明:不同参数取值情形下,产品最优动态定价决策会在三种情形中变动.

Dynamic Pricing Model of a Deteriorating Item with Price-dependent Demand

Dynamic pricing for a single deteriorating item during a finite sales cycle was studied under the condition that demand rate depended linearly on sales price. Two dynamic pricing models were developed respectively when initial inventory level was known or unknown based on optimal control theory. The objective was to maximize the item’s total profit during the sales cycle. According to analysis, these two models could be respectively formulated as Lagrange problem and Boelza problem with control variable’s constraints. Optimal pricing policies were obtained for each problem above when they were solved by Pontryagin maximum principle. Numerical simulation were done for the first problem and the results showed that the optimal pricing policy changed in three cases under the case of different parameter values.