Optimal advertising policy with the contagion model
- S. P. Sethi
- … show all 1 hide
Rent the article at a discountRent now
* Final gross prices may vary according to local VAT.Get Access
This paper considers an optimal control problem for the dynamics of a contagion model, the optimal control being the rate of advertising expenditure that maximizes the present value of net profit streams over an infinite horizon. By using a Green's theorem approach, it is shown that there are multiple optimal stationary equilibria and that the optimal path from any given initial condition is a nearest feasible path to one of these equilibria.
- Palda, K. S. (1964) The Measurement of Cumulative Advertising Effects. Prentice-Hall, Englewood Cliffs, New Jersey
- Clarke, D. G.,Econometric Measurement of the Duration of the Advertising Effect on Sales, Harvard University, Business School, Division of Research, Working Paper, 1975.
- Tull, D. S. (1965) The Carry-over Effect of Advertising. Journal of Marketing 20: pp. 46-53
- Nerlove, M., Arrow, K. J. (1962) Optimal Advertising Policy under Dynamic Conditions. Economica 39: pp. 129-142
- Ireland, N. J., andJones, H. G.,Optimality in Advertising: A Control Theory Approach, Proceedings of the IFORS/IFAC International Conference, Coventry, England, 1973 (IEE Conference Publication No. 101, pp. 186–199).
- Jacquemin, A. P.,Market Structure and the Firm's Market Power, Journal of Industrial Economics, Vol. 20, No. 2, 1972.
- Gould, J. P. Diffusion Processes and Optimal Advertising Policy. In: Phelps, E. S. eds. (1970) Microeconomic Foundation of Employment and Inflation Theory. W. W. Norton, New York, New York
- Vidale, M. L., Wolfe, H. B. (1957) An Operations Research Study of Sales Response to Advertising. Operations Research 5: pp. 370-381
- Stigler, G. (1961) The Economics of Information. Journal of Political Economy 69: pp. 213-225
- Ozga, S. (1960) Imperfect Markets Through Lack of Knowledge. Quarterly Journal of Economics 74: pp. 29-52
- Sethi, S. P.,Some Explanatory Remarks on the Optimal Control for the Vidale-Wolfe Advertising Model, Operations Research, Vol. 22, No. 4, 1974.
- Bailey, N. T. J. (1957) The Mathematical Theory of Epidemics. Hafner, New York, New York
- Sethi, S. P. (1974) Quantitative Guidelines for Communicable Disease Control Program: A Complete Synthesis. Biometrics 30: pp. 681-691
- Wickwire, K. (1977) Mathematical Models for the Control of Pests and Infectious Diseases: A Survey. Theoretical Population Biology 11: pp. 182-232
- Tapiero, C. S.,On-Line and Adaptive Optimum Advertising Control by a Diffusion Approximation, Operations Research, Vol. 23, No. 5, 1975.
- Zufryden, F. S.,Optimal Multi-Period Advertising Budget Allocation within a Competitive Environment, Operational Research Quarterly, Vol. 26, No. 4, 1975.
- Sethi, S. P.,Optimal Control of the Vidale-Wolfe Advertising Model, Operations Research, Vol. 21, No. 4, 1973.
- Sethi, S. P.,Dynamic Optimal Control Models in Advertising: A Survey, SIAM Review, Vol. 19, No. 4, 1977.
- Sethi, S. P.,Nearest Feasible Paths in Optimal Control Problems: Theory, Examples, and Counterexamples, Journal of Optimization Theory and Applications, Vol. 23, No. 4, 1977.
- Miele, A. In: Leitmann, G. eds. (1962) Extremization of Linear Integrals by Green's Theorem, Optimization Techniques. Academic Press, New York, New York
- Spiegel, M. (1968) Mathematical Handbooks of Formulas and Tables. McGraw-Hill Book Co., New York, New York
- Arrow, K. J., Kurz, M. (1971) Public Investment, the Rate of Return, and Optimal Fiscal Policy. The Johns Hopkins Press, Baltimore, Maryland
- Sethi, S. P.,Optimal Quarantine Programs for Controlling an Epidemic Spread, Journal of Operational Research Society, Vol. 29, No. 3, 1978.
- Optimal advertising policy with the contagion model
Journal of Optimization Theory and Applications
Volume 29, Issue 4 , pp 615-627
- Cover Date
- Print ISSN
- Online ISSN
- Kluwer Academic Publishers-Plenum Publishers
- Additional Links
- Optimal control
- Green's theorem approach
- nearest feasible path
- infinite horizon
- optimal stationary equilibria
- economic application
- Industry Sectors
- S. P. Sethi (1)
- Author Affiliations
- 1. Faculty of Management Studies, University of Toronto, Toronto, Canada