Consumer buying behavior and optimal advertising strategy: The quadratic profit function case

Abstract

Nicosia's consumer buyer behavior model for a finite advertising campaign duration and a quadratic profit function, which represents the advertising effectiveness measure, is considered. The optimal dynamic advertising strategy is the solution to a quadratic, two-boundary point, optimal control problem with two control constraints. The closed form solutions of optimal advertising paths are obtained and estimation of the parameters is treated. A numerical example illustrates the methodology and provides a comparison with a constant advertising path. The feasibility of applying constrained dynamic optimization to obtain the optimal advertising path in a more realistic environment is demonstrated.