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Expenditure patterns for risky R and D projects

Published online by Cambridge University Press:  14 July 2016

Morton I. Kamien
Affiliation:
Carnegie-Mellon University, Pittsburgh
Nancy L. Schwartz
Affiliation:
Carnegie-Mellon University, Pittsburgh

Summary

In this paper we derive the time pattern of optimal planned expenditures for R and D projects in which the total effort required to complete the research satisfactorily is not known. Theorem 1 summarizes our results under alternative assumptions regarding the behavior of the function governing the supposed probability of completing the R and D satisfactorily with incremental effort. In addition, an easily employed necessary condition for the R and D project to be worthwhile is provided in Theorem 2.

Type
Research Papers
Copyright
Copyright © Applied Probability Trust 1971 

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References

[1] Arrow, K. J. (1968) Applications of control theory to economic growth. Mathematics of the Decision Sciences Part 2, 85119. Edited by Dantzig, G. B. and Veinott, A. F. American Mathematical Society, Providence.Google Scholar
[2] Barlow, R. E. and Proschan, F. (1965) Mathematical Theory of Reliability. Wiley, New York.Google Scholar
[3] Cesari, L. (1966) Existence theorems for optimal solutions in Pontryagin and Lagrange problems. SIAM J. Control A 3, 475498.Google Scholar
[4] Lucas, R. E. Jr. (1968) Optimal management of a research and development project. Management Sci. To appear.Google Scholar
[5] Marschak, T., Glennan, T. K. Jr. and Summers, R. (1968) Strategy for R and D: Studies in the Microeconomics of Development. Springer-Verlag, New York.Google Scholar
[6] Mansfield, E. (1968) The Economics of Technological Change. W. W. Norton and Co., Inc., New York.Google Scholar
[7] Norden, P. (1963) Resource usage and network planning techniques. Operations Research in Research and Development, 149169. Edited by Dean, Burton V. Wiley, New York.Google Scholar
[8] Pontryagin, L. S. et al. (1962) The Mathematical Theory of Optimal Processes. Interscience, New York.Google Scholar