Mathematics – Probability
Scientific paper
2010-07-18
Mathematics
Probability
Scientific paper
A problem of optimally allocating partially effective ammunition $x$ to be used on randomly arriving enemies in order to maximize an aircraft's probability of surviving for time~$t$, known as the Bomber Problem, was first posed by \citet{Klinger68}. They conjectured a set of apparently obvious monotonicity properties of the optimal allocation function $K(x,t)$. Although some of these conjectures, and versions thereof, have been proved or disproved by other authors since then, the remaining central question, that $K(x,t)$ is nondecreasing in~$x$, remains unsettled. After reviewing the problem and summarizing the state of these conjectures, in the setting where $x$ is continuous we prove the existence of a ``spend-it-all'' region in which $K(x,t)=x$ and find its boundary, inside of which the long-standing, unproven conjecture of monotonicity of~$K(\cdot,t)$ holds. A new approach is then taken of directly estimating~$K(x,t)$ for small~$t$, providing a complete small-$t$ asymptotic description of~$K(x,t)$ and the optimal probability of survival.
Bartroff Jay
Goldstein Larry
Samuel-Cahn Ester
No associations
LandOfFree
The Spend-It-All Region and Small Time Results for the Continuous Bomber Problem does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with The Spend-It-All Region and Small Time Results for the Continuous Bomber Problem, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The Spend-It-All Region and Small Time Results for the Continuous Bomber Problem will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-523267