Applications to Marketing

Suresh Sethi

Chapter 7 in Optimal Control Theory, 2021, pp 207-238 from Springer

Abstract: Abstract To describe the specific problems under consideration, let us assume that a firm has some way of knowing or estimating the dynamics of sales and advertising. Such knowledge is expressed in terms of a differential equation with either goodwill or the rate of sales as the state variable and the rate of advertising expenditures as the control variable. We assume that the firm wishes to maximize an objective function (the criterion function) which reflects its profit motives expressed in terms of sales and advertising rates. The optimal control problem is to find an advertising policy that maximizes the firm’s objective function. Section 7.1 covers the Nerlove-Arrow model as well as a nonlinear extension of it, which illustrates the concept of relaxed controls or chattering controls introduced in Sect. 7.1.3. Section 7.2 deals with the Vidale-Wolfe advertising model and its detailed analysis using Green’s theorem in conjunction with the maximum principle. The switching-point analysis for this problem is a good example of the reverse-time construction technique used earlier in Chaps. 4 and 5 . There are many exercises at the end of the chapter.

Date: 2021
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DOI: 10.1007/978-3-030-91745-6_7

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