The Fighter Problem: Optimal Allocation of a Discrete Commodity

Jay Bartroff and Ester Samuel-Cahn

Discussion Paper Series from The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem

Abstract: The Fighter problem with discrete ammunition is studied. An aircraft (fighter) equipped with n anti-aircraft missiles is intercepted by enemy airplanes, the appearance of which follows a homogeneous Poisson process with known intensity. If j of the n missiles are spent at an encounter they destroy an enemy plane with probability a(j), where a(0)=0 and {a(j)} is a known, strictly increasing concave sequence, e.g., a(j)=1 - q j , 0 Pages: 11 pages
Date: 2010-07
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Published in Advances in Applied Probability, (2011), vol. 43, 121-130.

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