Non-instantaneous Deteriorating Inventory Model for Variable Demand and Holding Cost with Quantity Discount Policy and Partial Backlogging

An essential component of business marketing is advertising. A key factor in both rising and decreasing demand for goods and services is advertising. It’s an effective way of involving customers and motivating them to use the company’s product. An inventory model for non-instantaneous products is developed with linearly increasing holding cost, although the demand for products is influenced by both the selling price and the frequency of advertisement. Vendors frequently provide various policies or discounts in order to promote their businesses and boost sales. In this study, quantity discount is considered as a promotional strategy to attract new customers. Shortages are allowed with partial backlogging and backlogging rate present in the model is assumed to be a waiting time-dependent function. The aim of this chapter is to determine the optimal value of total profit. The optimization problem is solved by using an algorithm that generates the optimal solution for optimal time and selling price, while maximizing the total profit. Concavity is depicted graphically, and the applicability of the proposed model is demonstrated by numerical examples and sensitivity analysis for various parameters.