Abstract Advertisement is one of the most effective ways to spread out the popularity of the product for all categories of customers. Consequently, this has a direct impact to aggrandize product's demand to a great extent. On the other hand, if the maximum lifetime of a product is expired once then it can neither be useable nor be re-useable. Thus the date of maximum life time of the product is an essential issue in inventory management. Advance payment is another important factor among interrelation of suppliers and retailers for a highly demanding seasonal product. Combining these issues, two different inventory models for perishable items are formulated under linearly time-dependent increasing holding cost whereas demand of the product is dependent on the selling price of the product and the frequency of advertisement as well. In the first model, shortages are not considered whereas in the second one, partial backlogged shortages are incorporated. In both cases, the optimality of the proposed inventory models is discussed theoretically along with its solution algorithm. To validate the proposed models, three numerical examples are solved. Finally, the effect of changes of different parameters is studied numerically to perform a sensitivity analysis and a fruitful conclusion is done.

中文翻译：

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具有提前付款、线性时间相关的持有成本和依赖于广告和售价的需求的易腐烂物品的库存模型

摘要 广告是向各类客户传播产品知名度的最有效方式之一。因此，这在很大程度上直接影响了产品的需求量。另一方面，如果产品的最长使用寿命到期一次，则它既不能使用也不能重复使用。因此，产品最长使用寿命的日期是库存管理中的一个重要问题。预付款是高要求季节性产品的供应商和零售商之间相互关系中的另一个重要因素。结合这些问题，在线性时间相关的增加持有成本下制定了两种不同的易腐烂物品库存模型，而产品的需求也取决于产品的售价和广告频率。在第一个模型中，不考虑短缺，而在第二个模型中，包含部分积压的短缺。在这两种情况下，所提出的库存模型的最优性与其求解算法一起在理论上进行了讨论。为了验证所提出的模型，解决了三个数值例子。最后，数值研究了不同参数变化的影响，进行了敏感性分析，得出了富有成效的结论。