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This paper demonstrates how a general adaptive control scheme combines experimentation in advertising levels, estimation of sales advertising relationships, and the determination of advertising budgets. Various assumptions of current practices in experimentation and estimation are discussed and it is shown how these can be improved. A set of equations describing the sales-advertising system is proposed, its stochastic nature is analyzed, and an algorithm for calculating the adaptive control policies for this system is developed. To test the performance of the adaptive control scheme, the system is simulated under various conditions which include constant parameters, parameters which are varying over time, different initial estimates, and noise levels. Simulations of actual markets are then run and the amount of learning obtained by the adaptive control scheme is analyzed. Various extensions which can be easily incorporated in the general adaptive control scheme are specified.
Pekelman et al. (Tue,) studied this question.