Operations, Information and Decisions Papers

Document Type

Journal Article

Date of this Version

6-2008

Publication Source

Journal of Optimization Theory and Applications

Volume

137

Issue

3

Start Page

569

Last Page

591

DOI

10.1007/s10957-007-9350-6

Abstract

We propose a novel approach to modeling advertising dynamics for a firm operating over a distributed market domain based on controlled partial differential equations of the diffusion type. Using our model, we consider a general type of finite-horizon profit maximization problem in a monopoly setting. By reformulating this profit maximization problem as an optimal control problem in infinite dimensions, we derive sufficient conditions for the existence of its optimal solutions under general profit functions, as well as state and control constraints, and provide a general characterization of the optimal solutions. Sharper, feedback-form characterizations of the optimal solutions are obtained for two variants of the general problem.

Copyright/Permission Statement

The final publication is available at Springer via http://dx.doi.org/10.1007/s10957-007-9350-6

Keywords

optimal advertising, new product introduction, distributed control, infinite-dimensional analysis, linear-quadratic control

Share

COinS
 

Date Posted: 27 November 2017

This document has been peer reviewed.