In operations research, the bomber problem asks the following: Suppose that a bomber must travel a further t discrete time steps before reaching its target to drop its bombs. At each step, there is a probability p that it will encounter an enemy fighter. The bomber carries n air-to-air missiles. If it fires k missiles when it encounters a fighter, then it has a probability of surviving the encounter (each missile has a probability of missing the fighter). If the bomber encounters a fighter at a given state , let be the optimal number of missiles to fire in order to maximise the probability that the bomber will reach its target (where ). [1]

Conjecture

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Richard R. Weber has proved that   is nonincreasing in n and that   is nondecreasing in n. He has also conjectured and attempted to prove that   is also nondecreasing in n. [1]


References

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  1. ^ a b Weber, Richard R. "The Bomber Problem". Retrieved 24 June 2012.