价格影响需求的易变质产品动态定价模型

在产品销售价格影响需求的条件下，利用最优控制理论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。利用Pontryagin 最大值原理得到了产品销售价格的最优性条件。通过对模型的理论分析得出如果产品销售价格介于单位产品购买费用和产品销售价格上限之间，且产品库存在销售周期结束之前始终为正时，销售周期内各时刻的产品最优销售价格一定大于与相应时刻变质率和产品单位库存成本有关的一个下界，销售周期内各时刻的产品最优库存水平一定小于与相应时刻变质率和产品单位库存成本有关的一个上界。

Dynamic Pricing Model of Perishable Items with Price-dependent Demand

The dynamic pricing model of the perishable product with the price-dependent demand using the optimal control theory is established． The objective is to maximize the total sales profit within the sale planning horizon． The optimal conditions of the sale price are obtained according to the Pontryagin maximum principle． And if the sale price is between the unit purchasing cost of the product and the upper limit of the sale price，a lower limit of the optimal sale price and a higher limit of the optimal inventory level at every time point of the sale planning horizon are obtained which are both related to the perishable rate and the unit holding cost of the product at every time point of the sale planning horizon．