Optimal Institutional Advertising: Minimum-Time Problem

Journal of Optimization Theory and Aplications. Vol. 14, No. 2, pp. 213-231, 1974

Posted: 21 Jun 2009 Last revised: 1 May 2014

Suresh Sethi

University of Texas at Dallas - Naveen Jindal School of Management

Date Written: 1974

Abstract

This paper considers the problem of optimizing the institutional advertising expenditure for a firm which produces two products. The problem is formulated as a minimum-time control problem for the dynamics of an extended Vidale-Wolfe advertising model, the optimal control being the rate of institutional advertising that minimizes the time to attain the specified target market shares for the two products. The attainable set and the optimal control are obtained by applying the recent theory developed by Hermes and Haynes extending the Green's theorem approach to higher dimensions. It is shown that the optimal control is a strict bang-bang control. An interesting side result is that the singular arc obtained by the Green's theorem application turns out to be a maximumtime solution over the set of all feasible controls. The result clarifies the connection between the Green's theorem approach and the maximum principle approach.

Keywords: Management science, time-optimal control, Green's theorem approach, advertising, control theory, bang-bang control

JEL Classification: M37, C61

Suggested Citation

Sethi, Suresh, Optimal Institutional Advertising: Minimum-Time Problem (1974). Journal of Optimization Theory and Aplications. Vol. 14, No. 2, pp. 213-231, 1974. Available at SSRN: https://ssrn.com/abstract=1421481

Suresh Sethi (Contact Author)

University of Texas at Dallas - Naveen Jindal School of Management ( email )

800 W. Campbell Road, SM30
Richardson, TX 75080-3021
United States

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