A linear demand inventory model for deteriorating items with price and time effects: an astute observation through controlled advertisement investment

This study presents an inventory model designed for new technological products, such as laptops and smartphones, which have a very specific obsolescence life. The model is based on a linear demand function that incorporates parameters related to price, time, and advertisement. It permits partial backlogged shortages at specific intervals within a deterministic demand framework for the cycle length T. The objective of the study is to identify the optimal price, replenishment timing, and advertising investment, along with their constraints, as derived from the proposed assumptions for linear demand. The proposed study indicates that retailers may earn a profit of $114.54 per cycle when investing in advertising, whereas they earn only $86.05 per cycle without advertising. Hence, the study demonstrates that advertising enables them to earn an additional $28.49 per cycle. To this end, the theoretical results, optimal conditions, numerical examples, and Hessian matrix analysis are utilized to illustrate how the proposed demand function can maximize profit per unit through the inventory model.