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Further existence theorems for the optimal inventory equation

Published online by Cambridge University Press:  14 July 2016

Edward S. Boylan
Edward S. Boylan*
Affiliation:
Rutgers University, Newark, New Jersey
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For given functions, g(x), h(x), F(x) and a constant, a, f(x) is said to be a solution of the optimal inventory equation if where f(y - z) = f(0) when z > y. (The same convention holds in similar equations below.) A method of deriving a solution to (1) is to define inductively a sequence of approximating functions, fn(x), by:

Type
Short Communications
Information
Journal of Applied Probability , Volume 7 , Issue 2 , August 1970 , pp. 469 - 472
Copyright
Copyright © Applied Probability Trust 1970 

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References

[1] Boylan, E. S. (1967) Multiple (s.S.) policies and the n-period inventory problem. Management Sci. 14, 196–204.CrossRefGoogle Scholar
[2] Boylan, E. S. (1966) Existence and uniqueness theorems for the optimal inventory equation. SIAM J. Appl. Math. 14, 961–969.CrossRefGoogle Scholar
[3] Rudin, W. (1964) Principles of Mathematical Analysis. McGraw Hill, New York.Google Scholar