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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。
Under the condition that the product sale price affects the demand, a dynamic pricing model of perishable products is established by using the optimal control theory. The goal is to maximize the total sales profit during the product sales cycle. Using Pontryagin maximum principle, the optimality conditions of product sales price are obtained. Through the theoretical analysis of the model, if the product sales price is between the unit purchase cost and the product sales price cap, and the product inventory is always positive before the end of the sales cycle, the optimal product sales price at each moment in the sales cycle Must be greater than the lower bound associated with the rate of deterioration and the inventory cost per unit of product. The optimal inventory level for the product at each moment in the sales cycle must be smaller than the upper bound associated with the deterioration rate and inventory cost per unit time.