短缺部分拖后的变质性物品的联合定价与订货模型

文章研究了允许短缺部分拖后条件下变质性物品的联合定价与订货模型,其中物品的变质速度随时间而变化。当库存水平为正时,需求受物品销售价格的影响,当库存水平为负时,由于一部分顾客没有耐心等待物品的到来而导致销售机会的损失,且缺货量越大损失率越高。在这些假设下,证明了对任意给定的价格,最优订货周期长度和该订货周期内最优存货时间的长度不但存在而且惟一,又证明了在给定订货周期条件下平均利润函数是关于价格的严格凹函数,求出了物品的最优销售价格。最后用案例说明了模型的应用。

Joint pricing and ordering policy for a deteriorating inventory with permissible partial backlogging

In this paper,a joint pricing and ordering model for deteriorating items with partial backlog-ging rate is developed,and the deterioration rate is changed when the time is running on.When the inventory level is positive,the demand rate depends on the selling price; but when the inventory level is negative,some customers are more impatient to wait,therefore the sale opportunity is reduced and a bigger shortage leads to a larger loss.Under these assumptions,for any given selling price the paper develops the criterion for the optimal solution to the replenishment schedule,and proves that the opti-mal replenishment policy not only exists but is also unique.It shows that the total profit per unit time is a concave function of price when the replenishment schedule is given.A simple example is provided for the proposed model at last.