APPLIED PROBABILITY AND OPERATIONS RESEARCH PDF

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Applied Probability And Operations Research Pdf

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Operations research

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About operational research scientists worked for the British Army.

Early in the war while working for the Royal Aircraft Establishment RAE he set up a team known as the "Circus" which helped to reduce the number of anti-aircraft artillery rounds needed to shoot down an enemy aircraft from an average of over 20, at the start of the Battle of Britain to 4, in Britain introduced the convoy system to reduce shipping losses, but while the principle of using warships to accompany merchant ships was generally accepted, it was unclear whether it was better for convoys to be small or large.

Convoys travel at the speed of the slowest member, so small convoys can travel faster. It was also argued that small convoys would be harder for German U-boats to detect.

On the other hand, large convoys could deploy more warships against an attacker. Blackett's staff showed that the losses suffered by convoys depended largely on the number of escort vessels present, rather than the size of the convoy.

Their conclusion was that a few large convoys are more defensible than many small ones.

As most of them were from Bomber Command they were painted black for night-time operations. At the suggestion of CC-ORS a test was run to see if that was the best colour to camouflage the aircraft for daytime operations in the grey North Atlantic skies.

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Other work by the CC-ORS indicated that on average if the trigger depth of aerial-delivered depth charges DCs were changed from feet to 25 feet, the kill ratios would go up.

The reason was that if a U-boat saw an aircraft only shortly before it arrived over the target then at feet the charges would do no damage because the U-boat wouldn't have had time to descend as far as feet , and if it saw the aircraft a long way from the target it had time to alter course under water so the chances of it being within the foot kill zone of the charges was small.

It was more efficient to attack those submarines close to the surface when the targets' locations were better known than to attempt their destruction at greater depths when their positions could only be guessed. Blackett observed "there can be few cases where such a great operational gain had been obtained by such a small and simple change of tactics". All damage inflicted by German air defences was noted and the recommendation was given that armour be added in the most heavily damaged areas.

This recommendation was not adopted because the fact that the aircraft were able to return with these areas damaged indicated the areas were not vital, and adding armour to non-vital areas where damage is acceptable reduces aircraft performance.

Their suggestion to remove some of the crew so that an aircraft loss would result in fewer personnel losses, was also rejected by RAF command.

Applied probability and operations research pdf

Blackett's team made the logical recommendation that the armour be placed in the areas which were completely untouched by damage in the bombers which returned. They reasoned that the survey was biased, since it only included aircraft that returned to Britain.

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Limit Theorems 8. The Annals of Applied Probability, Vol. Early in the war while working for the Royal Aircraft Establishment RAE he set up a team known as the "Circus" which helped to reduce the number of anti-aircraft artillery rounds needed to shoot down an enemy aircraft from an average of over 20, at the start of the Battle of Britain to 4, in Blackett's team made the logical recommendation that the armour be placed in the areas which were completely untouched by damage in the bombers which returned.