Optimal Dynamics of the Vidale-Wolfe Advertising Model. Part I. Fixed Terminal Market Share.
Abstract
The optimal control problem consist of the Vidale-Wolfe advertising model as its dynamics; the optimal control being the rate of advertising expenditure which must achieve a specified terminal market share in a way which maximizes the present value of net profit streams over a finite horizon. The problem is completely solved with or without an upper limit on advertising rate. The solution in the later case is obtained by using Green's theorem while the former case requires additional use of switching point analysis based on maximum principle. The optimal control is characterized by a combination of bang-bang control, impulse control, and singular control; with the singular are forming a turnpike. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- May 01, 1972
- Accession Number
- AD0748206
Entities
People
- Suresh P. Sethi
Organizations
- Stanford University