Adaptive control for advertising expenditure

A firm producing a high-frequency purchased product is faced periodically with a large number of decisions involving its advertising policy. A major component of this policy is the advertising expenditure decision which specifies the appropriation of funds for advertising in various regions. In order to make a decision of that nature, the relations between advertising expenditures and sales are required. However, it is commonly acknowledged that these relations change over time as a result of the introduction of new products, changes in consumer tastes, media habits and other market factors. Therefore, an effort to induce learning and to update the parameter values of its sales-advertising model will tend to improve the advertising appropriation decision. Learning can be achieved by experimenting with the advertising expenditures in different regions and in different periods. In this paper, we attempt to construct the advertising expenditure decision model in the framework of dual control where the optimal experimentation and control are simultaneously determined. We exemplify the approach by construction of our model on the basis of actual data on a brand of children´s cereal.