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Some results on the bomber problem

  • Gordon Simons (a1) and Yi-Ching Yao (a2)

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.

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Corresponding author

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

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References

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Karlin, S. (1968) Total Positivity, Vol. I. Stanford University Press.
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. 173209.
Samuel, E. (1970) On some problems of operations research. J. Appl. Prob. 7, 157164.
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.

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Some results on the bomber problem

  • Gordon Simons (a1) and Yi-Ching Yao (a2)

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