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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

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