Operations research was developed under WWII! This is mentioned in other answers, but only as "mathematical programming", while OR is much wider than that. One paper says

" Operations Research is a ‘war baby’. It is because, the first problem attempted to solve in a systematic way was concerned with how to set the time fuse bomb to be dropped from an aircraft on to a submarine. In fact the main origin of Operations Research was during the Second World War. "

googling for "operations research second world war" (or throw into that "submarine") gives a lot of information, one example which looks interesting is

http://www.ibiblio.org/hyperwar/USN/rep/ASW-51/index.html

which is an statistical analysis of anti-submarine warfare.