When the americans entered world war ii in 1941, they used the british model to form operations research teams to determine how to deploy troops, submarines, and equipment most effectively. these techniques have evolved into quantitative managemen?

This is true.

Quantitative management employs usage of statistics or, in modern times, using computer simulations in order to predict situations and outcomes. They did this kind of thing, statistical analysis, as they saw that British were successful with it and these kind of ideas eventually developed into quantitative management ideas.