Optimal advertising duration for profit maximization

The current research elucidates the advertising scheme of automotive innovation by incorporating the various stages of the product life cycle. The study proposes an empirical model for the automotive industry to evaluate a time-point known as a switch-point or a take-off point at which firms should modify the advertising and sales promotion strategies to boost sales volume. The problem applies a time-series innovation diffusion model wherein adoption rate changes when a product enters a growth stage and then again when the company stops the advertising campaign in the maturity stage. The present paper develops a profit maximization problem, which optimizes the overall advertising duration and advertising take-off point. A numerical illustration is provided using the actual sales data of automobile industries, and sensitivity analysis is further performed to validate the effect of critical parameters on the optimization problem.