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Some results on the bomber problem

Published online by Cambridge University Press:  01 July 2016

Gordon Simons  and
Yi-Ching Yao
Gordon Simons*
Affiliation:
University of North Carolina at Chapel Hill
Yi-Ching Yao*
Affiliation:
Colorado State University
*
∗Postal address: Department of Statistics, The University of Carolina, CB#3260 Phillips Hall, Chapel Hill, NC 27599–3260, USA.
∗∗Postal address: Department of Statistics, Colorado State University, Fort Collins, CO80523, USA.
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Abstract

The problem of optimally allocating partially effective, defensive weapons against randomly arriving enemy aircraft so that a bomber maximizes its probability of reaching its designated target is considered in the usual continuous-time context, and in a discrete-time context. The problem becomes that of determining the optimal number of missiles K(n, t) to use against an enemy aircraft encountered at time (distance) t away from the target when n is the number of remaining weapons (missiles) in the bomber's arsenal. Various questions associated with the properties of the function K are explored including the long-standing, unproven conjecture that it is a non-decreasing function of its first variable.

Keywords

POISSON PROCESSOPTIMAL ALLOCATIONTOTAL POSITIVITY
Type
Research Article
Information
Advances in Applied Probability , Volume 22 , Issue 2 , June 1990 , pp. 412 - 432
Copyright
Copyright © Applied Probability Trust 1990 

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Footnotes

This author was supported by the National Science Foundation, Grant No. DMS-8701201.

References

Karlin, S. (1968) Total Positivity, Vol. I. Stanford University Press.Google Scholar
Klinger, A. and Brown, T. A. (1968) Allocating unreliable units to random demands. In Stochastic Optimization and Control, ed. Karreman, H. F., Publ. No. 20, Math. Research Center, U.S. Army and Univ. Wisconsin. Wiley, New York, pp. 173–209.Google Scholar
Samuel, E. (1970) On some problems of operations research. J. Appl. Prob. 7, 157–164.Google Scholar
Weber, R. (1985) A problem of ammunition rationing. Abstract, Conference on Stochastic Dynamic Optimization and Applications in Scheduling and Related Areas, Universität Passau, Fakultät für Mathematik und Informatik, p. 148.Google Scholar