Abstract This paper studies a new lot-size inventory problem for products whose demand pattern is dependent on price, advertising frequency and time. It is considered that the demand rate of an item multiplicatively combines the effects of a power function dependent on the frequency of advertisement and a function dependent on both selling price and time. This last function is additively separable in two power functions, one varies with the selling price and the other depends on the time since the last inventory replenishment. Moreover, it is assumed that the holding cost per unit of item is a non-linear function of time in stock. Shortages are not allowed. The aim consists of determining the frequency of advertisement, the selling price and the length of the stock period to maximize the average profit per unit time. This leads to a mixed integer non-linear inventory problem, which is solved by using an efficient algorithm previously developed. The inventory model considered here extends several inventory models previously proposed in the literature. Some numerical examples are solved to illustrate how the algorithm works to obtain optimal inventory policies. Finally, a sensitivity analysis for the optimal solution with respect to the parameters of the inventory system is presented.

中文翻译：

---

需求依赖于广告的价格、时间和频率的库存系统的最优策略

摘要 本文研究了需求模式依赖于价格、广告频率和时间的产品的新批量库存问题。一个项目的需求率被认为乘法结合了依赖于广告频率的幂函数和依赖于销售价格和时间的函数的影响。最后一个函数可附加地分为两个幂函数，一个随售价变化，另一个取决于自上次补货以来的时间。此外，假设每单位物品的持有成本是库存时间的非线性函数。不允许出现短缺。目标包括确定广告的频率、销售价格和股票期的长度，以使单位时间的平均利润最大化。这导致了混合整数非线性库存问题，该问题可以通过使用先前开发的有效算法来解决。这里考虑的库存模型扩展了先前在文献中提出的几种库存模型。解决了一些数值例子来说明算法如何工作以获得最佳库存策略。最后，针对库存系统参数的最优解进行了敏感性分析。