In a recent analysis, Martin Grötschel of the Zuse Institute in Berlin found that, using the computers and software that existed in 1982, it would have taken a full eighty-two years to solve a particularly complex production planning problem. As of 2003, the same problem could be solved in about a minute—an improvement by a factor of around 43 million. Computer hardware became about 1,000 times faster over the same period, which means that improvements in the algorithms used accounted for approximately a 43,000-fold increase in performance.
