Inventory models for perishable items with advanced payment, linearly time-dependent holding cost and demand dependent on advertisement and selling price

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.