Optimizing a three-rates-of-production inventory model under market selling price and advertising cost with deteriorating items

The purpose of this study is to present a three-rates-of-production inventory model with deteriorating items and advertising-cost- and price-dependent demand rate. Shortages are allowed and completely backlogged. The production rate is assumed to be finite and proportional to the demand rate. The main objective is to determine the optimum advertising cost, optimum cycle time, and optimum selling price with the aim of maximizing the total profit. Some useful theorems to characterize the optimal solution so as to determine the values of replenishment schedule, advertising cost, selling price and optimal order quantity are also derived. The article presents special cases which can be obtained from the proposed inventory model. A numerical example and a sensitivity analysis are presented to validate the theoretical results, and managerial insights are provided. The analysis of the model shows that a higher value of the demand rate causes the highest values of order quantity per replenishment cycle and total profit.