Dynamic Optimal Control Models in Advertising: a Survey

Abstract

The last ten years have seen a growing number of optimal control theory applications to the field of advertising. This paper presents an up-to-date survey of dynamic optimal control models in advertising that have appeared in the literature. The basic problem underlying these models is an optimal control problem to determine the optimal rate of advertising expenditures over time in a way that maximizes the present value of a firm’s net profit streams over a finite or infinite horizon. The profit depends on sales (or an appropriate surrogate), the state variable and the rate of advertising expenditures, the control variable. Sales, in turn, is related to advertising expenditures via a differential or difference equation termed a state equation. The models covered in this survey are organized under four headings: advertising capital models, sales-advertising response models, micromodels, and control-theoretic empirical studies. The discussion involves specifications, methods used, results and the economic significance of various models.The survey concludes with suggestions for extensions and future direction of research.

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